MANAGING UNCERTAINTY AND FLEXIBILITY IN THE MODERN …hq284pw2370/... · reshaping the industry. In...
Transcript of MANAGING UNCERTAINTY AND FLEXIBILITY IN THE MODERN …hq284pw2370/... · reshaping the industry. In...
MANAGING UNCERTAINTY AND FLEXIBILITY IN THE MODERN
ENERGY SECTOR: QUANTITATIVE MODELING OF TECHNICAL
RISK, ECONOMIC VALUE, AND STRATEGIC COMPETITION
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF
MANAGEMENT SCIENCE AND ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
KARIM FARHAT
JULY 2016
http://creativecommons.org/licenses/by-nc/3.0/us/
This dissertation is online at: http://purl.stanford.edu/hq284pw2370
© 2016 by Karim Farhat. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.
ii
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
John Weyant, Primary Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Kathleen Eisenhardt
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Stefan Reichelstein
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost for Graduate Education
This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.
iii
iv
Abstract
The need to mitigate climate change promises an increasingly different, uncertain, and flexible
energy landscape. In a climate-constrained world, uncertainty and flexibility complicate the
appraisal of new investments in clean energy. They make it more challenging for decision-
makers to quantify the technical risk, economic value, or strategic competitiveness of their
prospective energy initiatives, for orthodox evaluation techniques like worst-case-scenario and
net-present-value become insufficient. Consequently, in order to help investors ride the clean
energy wave, one urgent priority is to clarify and quantify uncertainty and flexibility in
modern energy systems and industries. This dissertation aims to develop assessment models
that achieve this exact goal.
The dissertation takes on three decision-centric research endeavors. The first study sheds light
on the technical uncertainty related to the leakage of anthropogenic carbon dioxide from
geologic storage reservoirs. Specifically, a conceptual methodological framework is developed
to help storage-site managers bridge risk assessment and corrective measures through clear
and collaborative contingency planning. First, a quantitative risk assessment matrix is
presented, highlighting the concept of risk profiles. As the main focus of this study, a
contingency planning matrix is then developed based on the risk assessment matrix, and its
tier structure is discussed. Lastly, the contingency planning matrix is used to guide the design
of a model contingency plan, which covers multiple sections on preparing for leakage risks
and responding to leakage incidents.
The second study switches from technical uncertainty to economic flexibility, investigating
the value of flexible hydrogen-based polygeneration energy systems (PES). PES are multi-
input multi-output industrial facilities. This study models a representative PES that uses coal
as a primary fuel and produces electricity and fertilizers as end-products. A series of economic
v
propositions allows deriving multiple metrics that quantify the levelized cost of hydrogen, the
profitability of PES under both static and flexible operation modes, as well as the real-option
values associated with diversification and flexibility. These metrics are subsequently applied
to evaluate Hydrogen Energy California (HECA), a PES project under development in
California. The results show that the profitability of a static HECA increases in the share of
hydrogen converted to fertilizer rather than electricity. However, when configured as a
flexible PES, HECA almost breaks even. Ultimately, diversification and flexibility prove
valuable for HECA when polygeneration is compared to static monogeneration of electricity,
but these two real options have no value when comparing polygeneration to static
monogeneration of fertilizers.
Finally, aiming to examine uncertainty in strategic competition within an energy industry, the
third study proposes a decision analytic modeling of Porter’s five forces framework, hereby
referred to as DAFF. This work is divided into two parts. The first part addresses the
conceptual foundations of DAFF. After explaining how decision analysis tools can enhance
the operationalization of the five forces theory, this part provides a detailed description of the
various elements in a DAFF model. Subsequently, a series of DAFF models are developed to
fulfill the two main objectives of competitive strategy: positioning in the industry, and
reshaping the industry. In the second part, DAFF is implemented to help inform a major firm’s
competitive strategy in the near-future U.S. residential solar PV industry. A DAFF Bayesian
Network is designed to evaluate competition in the overall industry. The results reveal
moderate competitive powers, with expected earnings before tax (EBT) of 4.05 billion $/year.
Also, due to significant yet asymmetrical competitive interdependence, witnessing a single
competitive force at its strongest or weakest extreme seems sufficient to vary the industry
EBT between 1.86 and 5.77 billion $/year. Analyzing four positioning decisions by the solar
firm expands the Bayesian Network into a Decision Diagram with 32 possible positioning
tracks. Each track yields a unique EBT value ranging between 0.51 and 3.98 billion $/year.
The results show that the highest expected earnings are realized upon: locating in urban areas,
managing customers directly without relying on dealers, and offering loan and lease services
to solar customers.
vi
Acknowledgements
My PhD journey at Stanford University has been one of my best life experiences, thanks to an
amazing group of advisers, instructors, friends, and colleagues.
First and foremost, I would like to express a deep gratitude to my advising team for their
continuous guidance, support, and encouragement over the years. I begin by thanking John
Weyant, my primary adviser, not only for believing in me and being my champion, but also
for nurturing my passion in interdisciplinary energy research. John gave me the freedom to
explore, the intuition to rationalize, and the resources to tackle new and challenging energy
modeling problems. Every time I met with John, I left feeling more confident and enthusiastic
about research, and life. This dissertation would not have been possible without John’s
masterful supervision and advice, and I’m extremely lucky to have had the honor of being one
of his students. I have also had the great fortune of working with Sally Benson, who was my
first research adviser for the Master’s degree in Energy Resources Engineering at Stanford.
Sally taught the engineer in me to appreciate geological sciences, and her deep expertise in
carbon capture and storage was the stimulus for and the facilitator of my continuous education
and interest in this field. Furthermore, Sally introduced me to the extensive web of energy
research and scholars at Stanford; she never hesitated to provide access and opportunities that
expanded my professional horizons far beyond what I could have hoped for on my own.
I want to thank Stefan Reichelstein at the Graduate School of Business, whom I have had the
immense pleasure of learning from and working with. His mentorship and our collaboration
have been essential to my education on energy finance and economic modeling, and his clear
and crisp approach to research has helped me improve the ways I conduct, analyze, and
communicate my scholastic activities. I am also extremely grateful to Kathy Eisenhardt for
introducing me to, teaching me about, and supervising my research on business strategy.
Besides our intellectually stimulating conversations, Kathy always challenged and encouraged
vii
me to give my very best, to walk the extra mile; my research on competitive strategy modeling
would not have been half as good without her guidance.
Outside of my core advising team, I want to thank a number of Stanford faculty members who
equipped me with the knowledge and motivation to undertake this research. I am grateful to
Ronald Howard, Ross Shachter, and Burke Robinson for teaching me everything I know about
decision analysis and for accepting me as a regular guest in their research group meetings.
Terry Root and the late Stephen Schneider have also played an important role in shaping the
energy researcher I am today. I will never forget the 14 hours I spent in a room full of world
leaders negotiating the fate of the Copenhagen Accord in 2009. Terry and Steve were the
reason I was able to gain this life-changing experience, which evolved into a life-long
commitment to advance and promote research on climate change and clean energy.
I would also like to acknowledge my fellow graduate students in the MS&E department.
Specifically, I thank Melanie Craxton, Lauren Culver, Ben Leibowicz, James Merrick, and
Matthew Smith for always being there to brainstorm an idea, help with a complicated
programming code, review a working paper, or grab a beer after a long week. Also, I thank
Mostafa Afkhamizadeh and Marshall Kuypers for the engaging conversations and team
projects we got to share; my research and academic work would not have been as rewarding or
enjoyable without them.
Outside Stanford, I am deeply grateful for meeting and working with Cas Groothuis while he
was the Opportunity Manager Future Energy Technologies at Royal Dutch Shell. Cas
recommended me to join Stanford, and my internship with him in the Netherlands constituted
my first exposure to the world of energy business. Attesting to his superb leadership, he
immediately realized and nurtured my interest in “connecting the dots” and the “big picture,”
and he gave me access to a wide energy network that later helped advance my research. I am
very thankful for having such an amazing first “boss.”
Of course, my family have been very supportive throughout this long process, sending me
their best wishes and prayers, as well as pictures of my cute little nephews, all the way from
Beirut, Lebanon. They are deserving of my gratitude for their love, understanding, and
viii
encouragement. Also, I shall never forget the kindness of my grandmother, who supported me
while in college.
Last, but definitely not least, I want to thank my dear friends Teddy White, Alexander
Greenberg, Bryson Tombridge, David Klein, and Scott McNally, who ensured that my life
beyond graduate school remained enjoyable and fulfilling. These gentlemen were always there
for me when I needed an encouraging word, a refreshing break, or a friendly nudge to help me
stay on task – some of them even endured listening to me defending this very dissertation. For
that, I will always be grateful.
ix
Table of Contents
Abstract .................................................................................................................................. iv
Acknowledgements ................................................................................................................ vi
Table of Contents ................................................................................................................... ix
List of Tables ........................................................................................................................xiii
List of Figures ....................................................................................................................... xv
Chapter 1: Introduction ............................................................................ 1
1 Motivation: A Changing, Uncertain, and Flexible Energy Landscape .............................. 1
2 Scope of Work ................................................................................................................... 6
2.1 Translating Risk Assessment to Contingency Planning for CO2 Geologic
Storage: A Methodological Framework .................................................................. 10
2.2 Economic Value of Flexible Hydrogen-Based Polygeneration Energy
Systems.................................................................................................................... 11
2.3 Decision Analytic Modeling of the Five Forces in Competitive Strategy:
Application in the U.S. Residential Solar PV Industry ........................................... 13
3 Dissertation Organization ................................................................................................ 16
References ............................................................................................................................. 19
Chapter 2: Translating Risk Assessment to Contingency Planning
for CO2 Geologic Storage: A Methodological Framework .................. 29
1 Introduction ..................................................................................................................... 29
2 Risk Management: Assessment, Mitigation, and Contingency Planning ........................ 31
3 Updating the Risk Assessment Matrix ............................................................................ 33
3.1 Functional Subsystems for Risk Identification........................................................ 35
3.2 Bayesian Event Tree for Risk Analysis ................................................................... 36
3.3 Tolerance Levels for Risk Evaluation ..................................................................... 46
x
3.4 Combined Representation of Risk Assessment Elements ....................................... 47
4 Translating the Risk Assessment Matrix to a Contingency Planning Matrix .................. 50
4.1 Transforming Matrix Dimensions ........................................................................... 51
4.2 Transforming Matrix Boundaries ............................................................................ 52
4.3 Classifying Risk into Tiers ...................................................................................... 53
5 A Model Contingency Plan ............................................................................................. 57
5.1 Tiers of Risk-Preparedness and Incident-Response ................................................ 58
6 Conclusions ..................................................................................................................... 69
6.1 Future Work ............................................................................................................ 71
References ............................................................................................................................. 73
Appendix A: Drawbacks of Alternative Three-Tier Systems ............................................... 80
Appendix B: Tier-Based Contingency Planning ................................................................... 82
Chapter 3: Economic Value of Flexible Hydrogen-Based
Polygeneration Energy Systems ............................................................. 84
1 Introduction ..................................................................................................................... 84
2 Research Methodology .................................................................................................... 88
2.1 Levelized Cost of Hydrogen .................................................................................... 89
2.2 Technical Configuration of PES .............................................................................. 91
3 Economic Analysis .......................................................................................................... 93
3.1 Scenario 1: Static PES with Fixed Production Rates .............................................. 94
3.2 Scenario 2: Flexible PES with Variable Production Rates ...................................... 97
4 Profitability and Value of Real-Options ........................................................................ 104
5 Additional Modeling Considerations ............................................................................. 107
5.1 Carbon Capture and Storage.................................................................................. 107
5.2 Time-dependency of prices and variable costs ...................................................... 108
6 Case Study: Hydrogen Energy California ..................................................................... 109
6.1 Technical Configuration ........................................................................................ 109
6.2 Economic Analysis ................................................................................................ 111
xi
7 Conclusions ................................................................................................................... 120
7.1 Future Work .......................................................................................................... 121
References ........................................................................................................................... 123
Appendix A: Derivation of Economic Propositions ............................................................ 127
Appendix B: Cost Estimates for HECA .............................................................................. 144
Chapter 4: Decision Analytic Modeling of the Five Forces in
Competitive Strategy ............................................................................. 147
1 Introduction ................................................................................................................... 147
2 Theoretical Background ................................................................................................ 149
2.1 Decision Analysis .................................................................................................. 149
2.2 The Five Forces that Shape Competition .............................................................. 152
2.3 Decision Analytic Approach to the Five Forces .................................................... 154
3 Methodology: Developing the DAFF Models ............................................................... 159
3.1 Modeling the Competitive Forces, Drivers, and Factors ....................................... 160
3.2 Modeling the Economic Implications of the Five Forces ..................................... 169
3.3 Modeling the Firm’s Actions ................................................................................ 172
4 First Objective of Competitive Strategy: Positioning in the Industry ........................... 176
4.1 First Step: Assess the Profitability of the Overall Industry ................................... 177
4.2 Second Step: Position Competitively and Assess the Profitability of Each
Positioning Segment in the Industry ..................................................................... 181
4.3 Third Step: Assess the Profitability of the Firm in Each Positioning
Segment of the Industry ........................................................................................ 184
4.4 Advantages of the DAFF modeling ....................................................................... 187
5 Second Objective: Reshape the Industry ....................................................................... 194
5.1 First Step: Predict Industry Change ....................................................................... 195
5.2 Second Step: Reshape Industry Change ................................................................ 198
6 Best Practices in DAFF Modeling ................................................................................. 202
7 Broader Alignment between Decision Analysis and Porter’s Competitive Strategy .... 204
xii
8 Conclusions ................................................................................................................... 205
8.1 Future Work .......................................................................................................... 208
References ........................................................................................................................... 212
Chapter 5: DAFF Modeling of Competitive Strategy: Positioning
in the Near-Future U.S. Residential Solar PV Industry .................... 216
1 Introduction ................................................................................................................... 216
1.1 The U.S. Residential Solar PV Industry ................................................................ 218
1.2 The Solar Firm ...................................................................................................... 220
2 Methodology: Developing the DAFF Models ............................................................... 220
2.1 First Step: Assess the Overall Industry ................................................................. 221
2.2 Second Step: Assess Each Positioning Segment in the Industry ........................... 241
3 Results: Outputs from the DAFF Models ...................................................................... 247
3.1 First Step: Assess the Overall Industry ................................................................. 247
3.2 Second Step: Assess Each Positioning Segment in the Industry ........................... 262
4 Conclusions ................................................................................................................... 268
4.1 Future Work .......................................................................................................... 272
References ........................................................................................................................... 274
Appendix A: Degree Characterization for Competitive Uncertainties ................................ 278
Appendix B: Influence of Positioning Tracks on Competitive Forces ................................ 284
xiii
List of Tables
Table 2.1: Examples of Origin FEPs and their corresponding Indicators ................................ 36
Table 2.2: Selection criteria for the three-tier system .............................................................. 53
Table 2.3: Example corrective measures for incident-response ............................................... 63
Table 2.4: Example corrective measures matrix (CMM) for incident-response ...................... 64
Table 2.B1: Tier-based response strategies for contingency planning ..................................... 82
Table 2.B2: Tier-based human and equipment resources for contingency planning ............... 83
Table 3.1: HECA technical parameters .................................................................................. 110
Table 3.2: HECA auxiliary loads ........................................................................................... 111
Table 3.3: Levelized costs of capacity of HECA ................................................................... 112
Table 3.4: Levelized time-averaged fixed operating costs of HECA ..................................... 113
Table 3.5: Levelized time-averaged variable costs of HECA ................................................ 114
Table 3.6: Time-averaged prices of HECA end-products ...................................................... 115
Table 3.7: Economic valuation of HECA .............................................................................. 115
Table 3.B1: System prices of HECA per unit capacity .......................................................... 144
Table 3.B2: System prices of HECA’s subsystems per unit capacity .................................... 144
Table 3.B3: Yearly fixed-operating costs of HECA as fraction of capacity costs ................. 145
Table 3.B4: Yearly fixed-operating costs of HECA Subsystems per unit capacity ............... 145
Table 3.B5: Prices of input commodities and services for HECA ......................................... 146
Table 3.B6: Yearly-averaged variable costs Cost of HECA per unit of production .............. 146
Table 3.B7: Prices of HECA end-products ............................................................................ 146
Table 5.1: DAFF uncertainties influenced by Regional Focus .............................................. 242
Table 5.2: DAFF uncertainties influenced by Downstream Integration ................................ 243
Table 5.3: DAFF uncertainties influenced by Customer Financing ....................................... 244
xiv
Table 5.4: DAFF uncertainties influenced by Panel Manufacturing ...................................... 245
Table 5.A1: Definition of competitive force and driver uncertainties in the U.S.
residential solar industry ..................................................................................... 278
Table 5.A2: Definition of factor uncertainties in the U.S. residential solar PV industry ....... 283
Table 5.B1: Probability of {high} power for each competitive force under each
positioning track ................................................................................................. 284
xv
List of Figures
Figure 2.1: Elements of risk management for CO2 leakage from geologic reservoirs .............. 32
Figure 2.2: Functional subsystems for risk identification ......................................................... 35
Figure 2.3: Example Bayesian event tree (BET) for risk analysis of CO2 leakage ................... 38
Figure 2.4: Sketch of CO2 leakage through caprock high-permeability zone ........................... 40
Figure 2.5: Example probability distributions of CO2 leakage scenarios .................................. 41
Figure 2.6: Example value models of CO2 leakage scenarios ................................................... 45
Figure 2.7: Example risk assessment matrix (RAM) for CO2 leakage. ..................................... 48
Figure 2.8: Translating the risk assessment matrix to a contingency planning matrix ............. 50
Figure 2.9: Tier system tradeoff between resource proximity and resource diversity .............. 55
Figure 2.10: Tier allocation procedure for risk-preparedness and incident-response ............... 60
Figure 2.11: Example decision-making hierarchy of the operating party for
contingency planning ............................................................................................. 66
Figure 2.12: Example notification protocol of the operating party for incident-response ........ 67
Figure 2.13: Example communication scheme for contingency planning ................................ 68
Figure 2.14: Collaborative approach to securing resources for Tiers 2 and 3 ........................... 68
Figure 2.A1: Drawbacks of alternative tier-system approaches for contingency planning ....... 80
Figure 3.1: Simplified process flow sheet of the used PES ....................................................... 92
Figure 3.2: Schematic representation of static and flexible PES ............................................... 94
Figure 3.3: Yearly wholesale prices of electricity in HECA’s region ..................................... 114
Figure 3.4: Profit-margin, value of diversification, and value of flexibility for HECA .......... 117
Figure 3.5: Value of polygeneration for flexible HECA under optimal operations ................ 118
Figure 3.6: Sensitivity analysis on the profitability of flexible HECA ................................... 119
Figure 4.1: Representation of the nodes in a decision diagram ............................................... 152
Figure 4.2: Porter’s five forces framework ............................................................................. 153
xvi
Figure 4.3: Identifying the underlying drivers for the bargaining power of Buyers ............... 161
Figure 4.4: Highlighting the shared underlying drivers for the bargaining power of
Buyers .................................................................................................................. 161
Figure 4.5: Relevance arrows connecting the underlying drivers for the bargaining
power of Buyers ................................................................................................... 162
Figure 4.6: Detailed Network of the five forces, their underlying drivers, and
industry-specific factors ....................................................................................... 165
Figure 4.7: Simple Network of the five forces, their underlying drivers, and
industry-specific factors ....................................................................................... 166
Figure 4.8: Illustrative example of uncertainty assessment in DAFF ..................................... 168
Figure 4.9: DAFF economic sub-model .................................................................................. 172
Figure 4.10: DAFF Bayesian Network for the first objective, first step: assessing the
profitability of the overall industry ...................................................................... 178
Figure 4.11: DAFF Decision Diagram for the first objective, second step: positioning
competitively and assessing the profitability of each positioning segment in
the industry .......................................................................................................... 183
Figure 4.12: DAFF Decision Diagram for the first objective, third step: assessing the
profitability of the firm in each positioning segment of the industry .................. 185
Figure 4.13: Conceptual DAFF Decision Diagram for the first positioning objective ........... 195
Figure 4.14: Dynamic DAFF model for the second objective, first step: predicting
industry change .................................................................................................... 196
Figure 4.15: Guidance on adding temporal relevance arrows between competitive
uncertainties ......................................................................................................... 198
Figure 4.16: Dynamic DAFF model for the second objective, second step: reshaping
industry change .................................................................................................... 199
Figure 4.17: Future opportunities to streamline the DAFF modeling ..................................... 210
Figure 5.1: DAFF modeling of the force of Substitutes and its relevant drivers .................... 222
Figure 5.2: Example probabilistic analysis of a driver: Cost reduction for customer by
industry product ................................................................................................... 224
Figure 5.3: Example probabilistic analysis of a driver: Substitute bill savings ...................... 224
Figure 5.4: Example probabilistic analysis of a driver: Price-performance tradeoff
relative to this industry product ........................................................................... 225
Figure 5.5: Example probabilistic analysis of the power of Substitutes ................................. 225
xvii
Figure 5.6: DAFF modeling of all competitive forces and drivers in the U.S. residential
solar PV industry ................................................................................................. 228
Figure 5.7: DAFF modeling of Technology, Regulation, and Growth factors in the
U.S. residential solar PV industry ........................................................................ 233
Figure 5.8: DAFF modeling of the economic parameters in the U.S. residential solar
PV industry .......................................................................................................... 237
Figure 5.9: A sketch of the complete DAFF Bayesian Network for SunEnergy .................... 241
Figure 5.10: Example of decision influence on conditional probability assignment .............. 245
Figure 5.11: A sketch of the complete DAFF Decision Diagram for SunEnergy ................... 246
Figure 5.12: Competitive landscape in the U.S. residential solar PV industry through
2016 ..................................................................................................................... 248
Figure 5.13: Economic performance of the U.S. residential solar PV industry through
2016 ..................................................................................................................... 252
Figure 5.14: Interdependence between the competitive forces in the U.S. residential
solar PV industry ................................................................................................. 254
Figure 5.15: Effect of the competitive forces on economics of the U.S. residential
solar PV industry ................................................................................................. 261
Figure 5.16: Profitability of the various positioning tracks in the U.S. residential solar
PV industry .......................................................................................................... 264
Figure 5.17: The influence of positioning on the competitive forces in the U.S.
residential solar PV industry ................................................................................ 266
1
Chapter 1
Introduction
1 Motivation: A Changing, Uncertain, and Flexible Energy
Landscape
“We are convinced that changing the way that we produce and use energy is
essential to America's economic future – that it will create millions of new jobs,
power new industry, keep us competitive, and spark new innovation. And we are
convinced that changing the way we use energy is essential to America's national
security, because it will reduce our dependence on foreign oil, and help us deal with
some of the dangers posed by climate change … There is no time to waste. America
has made our choice. We have charted our course, we have made our commitments,
and we will do what we say.”
— Barack Hussein Obama, COP15, 2009
These words were some of President Barack Obama’s remarks at the United Nations
Conference of Parties in Copenhagen, Denmark, in 2009 [1]. As leaders from around the
world gathered to address the global challenge of climate change, their message was clear:
climate change is real, and so are the extensive changes in the energy system needed to
mitigate its impacts [2].
Today, fossil fuels meet 87% of the global energy demand [3] and are used to generate 67% of
the global electricity supply [4]. As elaborated in the fifth assessment report by Working
CHAPTER 1 — Motivation: A Changing, Uncertain, and Flexible Energy Landscape 2
Group III of the Intergovernmental Panel on Climate Change, mitigating the impacts of
climate change requires a substantial reduction in carbon dioxide (CO2) emissions below their
present levels [5], which in turn necessitates drastic changes in current energy generation,
delivery, and consumption [6]. Those changes are already underway, as manifested by the
progressive evolution of energy technologies, markets, and policies over the past few years.
Around the world, research and development (R&D) efforts continue to advance new
technologies that can either clean up or substitute fossil fuels. Carbon dioxide capture and
storage (CCS) is one important technology that can reduce carbon emissions from large power
plants and industrial facilities [7, 8]. Although CO2 capture has been in operation since the
1970s [9], the need for CCS as a climate-change mitigation option has accelerated the
emergence of new and improved capture technologies in recent years [10, 11], covering post-
combustion, pre-combustion, and oxy-combustion processes. In fact, one study documents
that, from a pool of 1000 international patents related to CO2 capture, more than 600 patents
were issued after year 2000, including about 250 patents between 2010 and 2012 [12]. On the
storage side, several countries have initiated or expanded their characterization of feasible CO2
storage capacity, both onshore and offshore, all while testing new techniques and equipment to
monitor, verify, and potentially correct CO2 injection operations [13, 14, 15]. The
advancement in emissions-free renewable energy technologies has been at least as impressive.
Bell Labs produced the first practical solar cell as early as 1954 [16]. However, it was only
this decade that thin-film and crystalline-silicon solar systems have been truly commercialized
[17, 18], which is evident by the tens of solar world-record efficiencies and new technologies
documented since 2005 [19]. Wind energy technologies have enjoyed similar improvements,
both onshore and offshore. Between 2002 and 2011, more sophisticated power electronics,
controls, and gearboxes helped double the capacity factor and more than triple the generation
capacity of individual horizontal-axis wind turbines [20, 21, 22].
The progressive change in energy technologies has been accompanied by a progressive
transformation of energy markets. Between 2005 and 2014, developed OECD economies
shifted their electricity generation to cleaner fuel mix; the share of coal in power generation
decreased from 36% to 31% while that of natural gas increased from 19% to 24% [23]. Also
important to fossil-fuel decarbonization, the deployment of large-scale CCS has doubled over
CHAPTER 1 — Motivation: A Changing, Uncertain, and Flexible Energy Landscape 3
the past five years; 15 projects are operational today, spread across North America, Europe,
and the Middle East [14]. At the same time, both developed and developing countries have
witnessed tremendous market growth for solar and wind energy. Between 2005 and 2013, the
solar installations skyrocketed from about 3 to 140 gigawatts (GW) [24, 25], and wind
installations increased from 58 to 319 GW [24, 26].
Both market and technological changes have been, at least partially, driven and incentivized
by policy changes. Perhaps the most notable example of such changes is the unprecedented
global climate agreement reached in Paris in 2015. After 20 annual summits and numerous
climate meetings under the United Nations’ umbrella, the world nations have committed to a
collaborative effort that caps “the increase in the global average temperature to well below 2
°C above pre-industrial levels” [27]. Building up to that treaty was a set of national policy
initiatives that prepare each country to meet its future emissions’ goals [28]. Focusing
specifically on the U.S., two examples stand out. Earlier in 2015, the U.S. Environmental
Protection Agency (EPA) finalized two regulations that aim to reduce carbon pollution from
the power sector – both new and existing power plants – to 32% below 2005 levels [29, 30].
On the renewables side, the U.S. Congress has enacted a 30% investment tax credit (ITC) for
solar installations since 2006 [31] and a $0.023 per kilowatt-hour (kWh) production tax credit
(PTC) for wind installations since 1993 [32, 33]. Along other forms of governmental subsidies
[34, 35], ITC and PTC have helped accelerate the deployment of wind and solar energy across
the country. Indeed, beyond national measures, state and multi-national policies have also
contributed to shaping, and therefore changing, the energy landscape in the U.S. [36, 37, 38].
Change creates uncertainty, however. Whenever energy technologies, markets, and policies
evolve, the future energy landscape becomes harder to plan or even predict. For instance, as
advanced capture technologies facilitate the large-scale deployment of CCS, it becomes more
urgent to clarify and manage the technical uncertainty of CO2 leakage from storage reservoirs
[39, 40, 41, 42]. Also on the technical side, it is uncertain whether and how the electric grid
can manage the increasing deployment of intermittent renewable energy, especially as wind
and solar technologies become more robust and mainstream [43, 44, 45].
CHAPTER 1 — Motivation: A Changing, Uncertain, and Flexible Energy Landscape 4
Uncertainty also arises in the evolution of energy markets. Starting with fossil fuels, the role
of natural gas as a “bridge fuel” that eases the transition into a cleaner economy is still
uncertain [46, 47]. In the United States, new hydraulic fracturing techniques have unlocked an
abundance of supply, which has in turn contributed to lower prices [48]. Nonetheless, recent
environmental concerns [49, 50, 51] and liquefied-natural-gas export arrangements [52] make
any long-term forecasts of the domestic natural gas market a rather challenging task.
Furthermore, despite continuous progress, the large-scale nature of most CCS projects render
them vulnerable to economic uncertainties associated with upfront and operational costs,
financing mechanisms, and long-term liability [40, 53]. The development of renewable energy
markets is also far from certain. One example to highlight is strategic competition in the solar
industries. As relatively young players, solar firms have been trying to navigate through the
complicated maze of the power sector. They continue to adjust their business models while
gaining further insights into the uncertain, and still underdeveloped, competitive relationship
with their customers and suppliers, their established substitutes and new rivals, as well as their
regulators and financers [54, 55, 56]. Indeed, one can appreciate the extent of uncertainty in
the solar markets by tracking the stock-price fluctuations of top solar firms, which are
indicative of frequent business successes and failures [57, 58].
While changing energy policies contribute to technological and market uncertainty, they
themselves may also be uncertain. Policies aiming to curb greenhouse gas emissions continue
to be a contentious subject among political parties and energy businesses. Attesting to that
fact, the aforementioned U.S. EPA’s plan to regulate emissions from existing power plants
was challenged in court by several states and utilities; literally just days before composing this
Chapter, the U.S. Supreme Court made an unexpected decision to put the EPA’s plan on hold
[59, 60]. Similarly uncertain are the prospects of enforcing some form of carbon pricing.
Many still argue over the potential benefits of a cap-and-trade regime versus a carbon-tax
regime [61, 62, 63]. Meanwhile, legislations around the world have attempted to adopt either
regime; some succeeded [64], some failed [65], and some were repealed [66]. The evolution of
renewables is also shaped by significant policy uncertainties [67]. As wind and solar
technologies mature and become more competitive, it is not clear whether and what
governmental subsidies remain effective [68]; subsidy mandates often have a short lifetime,
CHAPTER 1 — Motivation: A Changing, Uncertain, and Flexible Energy Landscape 5
which creates a recurrent need to renew them [31, 69]. Along the same lines, it is not obvious
whether future grid regulations will respond more or less favorably to the penetration of
renewables [70]; judging by the opposing stands on solar grid-charges by the public utilities
commissions (PUC) in Nevada and California [71, 72], both scenarios seem plausible.
Now someone might ask: what exactly is problematic with change and uncertainty? The fact
is, as the changing climate instigates an uncertain energy landscape, new investments in clean
energy infrastructure become more challenging. Fundamentally, uncertainty makes it difficult
for decision-makers to think and act clearly [73]. In our context, technological, market, and
policy uncertainties obstruct the investors’ propensity to assess their energy investments
deterministically. They complicate the decision-makers’ efforts to quantify the technical risk,
economic value, or strategic competitiveness of their prospective energy projects, because
orthodox evaluation tools like worst-case-scenario and net-present-value become insufficient
[74, 75, 76]. As a result, new energy initiatives may be overpriced or underestimated; new
energy facilities may face cost overruns, delays, or even cancellations; and new energy
businesses may suffer curtailment. Unfortunately, examples of these setbacks are already
making news, be it in CCS [77, 78, 79] or solar energy [80, 81].
One way to manage and hedge against uncertainty is flexibility. In a climate-constrained
world, flexible energy investments might be better posed to deal with technical, market, and
policy uncertainties. Here, it is helpful to distinguish between two types of flexibility:
operational and strategic. Operational flexibility refers to built-in technical capabilities that
allow an energy system to switch between different modes of operation within a specific
timeframe. The interest in developing flexible electricity systems has surged in recent years
[82]. These systems promise to manage not only the uncertain availability and variability of
the increasing renewable energy supply but also the uncertain variation in future energy
demand and prices [83]. One promising technology in that regard is flexible CO2 capture.
Flexible capture allows grid-operators or utilities to synchronize the power output from fossil-
fuel plants with intermittent renewables, and it may contribute to enhancing the economics of
CCS deployment [84, 85, 86, 87]. Battery storage has emerged as another promising example
of flexible energy systems, for it can both reduce the curtailment of excess renewable supply
[88, 89] and improve the grid ancillary services [90]. In fact, recent efforts have also examined
CHAPTER 1 — Scope of Work 6
the prospects of grid flexibility by integrating fossil and renewable energy generation. While
some systems combine the operations of distinct single-input/sing-output facilities [91], other
systems operate a single facility with multiple inputs/outputs. Capable of hedging against
unexpected input-price shocks and exploiting sudden output-price peaks, the latter systems are
uniquely labeled “polygeneration,” and their flexibility benefits respond to uncertainties
beyond power generation to include chemicals and fertilizers synthesis [92, 93, 94].
Equally important, strategic flexibility – also called managerial flexibility – refers to the
ability to modify a managerial course of action over an energy investment within a specific
timeframe [95]. In this case, even if the energy project is operationally inflexible, investment
decisions may preserve the option to expand, retrofit, or otherwise modify the project in
response to future risks or opportunities. One example of strategic flexibility is investing in
capture-ready [96, 97, 98]. Bohm et al. [99] classifies a fossil-fueled plant as capture-ready if
“at some point in the future it can be retrofitted for carbon capture and sequestration and still
be economical to operate.” Another prominent example of strategic flexibility is related to the
emergence of strategic competition in solar markets over the past couple of years. Despite
apparent trends of consolidation and vertical integration – aiming to reduce cost and deter new
entrants [56, 100] – major solar firms have considered expanding and diversifying their
business into energy storage, through acquisition [101], direct investment [102], or partnership
agreements [103]. As the power grid evolves, establishing a strong foothold in energy storage
is a strategic flexibility option that gives solar firms the ability, but not the obligation, to
update their future product offerings whenever needed.
2 Scope of Work
I can probably write a few more pages, and cite a dozen more references, to describe how
climate change is making our energy landscape increasingly different, uncertain, and flexible.
I won’t. Hopefully, by now, I have convinced you that this argument holds some truth.
Consequently, in our progressively modernizing energy sector, it is inevitable that uncertainty
and flexibility impact the value of clean energy investments. Because uncertainty and
flexibility increase the complexity of investment decisions, a proper accounting of both
CHAPTER 1 — Scope of Work 7
attributes becomes both necessary and beneficial. It facilitates clearer and more accurate
analyses of technical, economic, or strategic challenges; it yields more comprehensive results;
and it conveys more insightful and robust recommendations. Therefore, to help investors ride
the clean energy wave, one of the most urgent priorities – for academic scholars and
business experts alike – is to clarify and quantify uncertainty and flexibility in modern
energy systems and industries. This dissertation aims to develop assessment models that
achieve this exact goal.
To fulfill this mission, this dissertation takes on three major research endeavors, which
augment and build on existing efforts in their respective fields. Motivating the selection of
these specific endeavors is their focus on the “decision-maker” in the energy sector.
Fundamentally, the chosen topics and developed models are intended to be significant to and
usable by executives and managers overseeing energy businesses and facilities.
Now, to formally introduce the three research undertakings in this dissertation, let me explain
what topics are discussed and how their quantitative models are developed. The first study
sheds light on the technical uncertainties related to the safe and reliable deployment of CCS.
Interested in connecting the various elements of risk management for CO2 geologic storage, I
propose a methodological framework that translates quantitative risk assessment to
contingency planning for CO2 leakage from geologic storage reservoirs. The second study
switches from technical to economic assessment, investigating the economic value of flexible
hydrogen-based polygeneration energy systems. Beyond specifying the conditions for
breaking even, this study highlights the value of flexibility and diversification enabled by
polygeneration. Finally, the third study examines the competitive uncertainties and their
relation to positioning strategies within an energy industry. Based on Michael Porter’s five
forces framework (FF) [104], I develop decision analytic models that analyze the uncertain
competitive landscape and economic performance of an overall industry, of several
positioning segments within that industry, and of specific firms within those segments. After
explaining their theoretical foundations, the models are used to assess near-future competitive
strategies in the U.S. residential solar photovoltaic (PV) industry.
CHAPTER 1 — Scope of Work 8
Fortunately, these topics have met my aspiration to pursue a consistent yet diversified research
agenda. While all three endeavors attempt to answer the grand question of clarifying and
quantifying uncertainty and flexibility in the energy sector, they differ in their theme,
application, and scope. Thematically, I strive to balance between fossil and renewable
resources, for both will continue to meet our energy needs over the coming few decades. CCS
is a carbon-fuel technology; solar is a non-carbon-fuel technology; and polygeneration is a
hybrid technology that can accommodate both fossil and renewable fuels. The three studies
also differ in their application areas. The CCS study addresses the technical risk associated
with uncertain CO2-leakage events. The polygeneration study addresses the economic value
associated with flexible production operations. As for the solar study, it primarily addresses
strategic positioning, and secondarily alludes to strategic flexibility, in uncertain competitive
landscapes. Lastly, the diversity in scope is rather easy to tell. While the analysis of CCS risk
or polygeneration economics spans an individual energy facility or project, the analysis of
uncertain strategic competition – along with its solar case study – covers a whole energy
industry, multiple segments within that industry, and potentially multiple firms within those
segments.
The diversity and practicality of the aforementioned research topics are mirrored in the
methods and tools used to model and examine them. As my grandmother used to tell me,
there’s more than one way to bake a cake. The same applies to modeling uncertainty and
flexibility in the modern energy sector. To start, my approach to modeling uncertainty – for
both CO2 leakage and solar competitive strategy – is rooted in the field of decision analysis
(DA). DA is a quantitative methodology that analyzes any decision-making situation in terms
of three main components: alternatives, information, and preferences. DA pays special
attention to uncertainty, which accounts for information unknown to the decision-maker, and
it adopts a Bayesian reasoning to express and update the decision-maker’s beliefs about
uncertainty [73].
In the CCS study, I use probabilistic risk assessment (PRA) to characterize potential leakage
features, events, and processes (FEP) in a Bayesian events tree (BET); the PRA technique and
the BET tool are both well-documented and broadly used in the context of decision analysis
[73, 75]. Also, borrowing from the oil and gas industry [105, 106], I design a three-tier system
CHAPTER 1 — Scope of Work 9
that helps prepare for tolerable CO2 leakage events before they happen and helps respond to
those events when they actually happen.
In the competitive strategy study and its solar case in point, I use Bayesian networks and
decision diagrams to model Porter’s five forces in a specific industry and for a specific firm.
Porter identifies five forces that shape competition in relatively stable industries: bargaining
power of buyers, bargaining power of suppliers, threat of substitutes, threat of new entry, and
rivalry. In a Bayesian network, these forces – along with their drivers; technological, political,
and growth factors; and economic implications – are modeled as interdependent uncertainties.
Subsequently, a decision diagram illustrates how strategic positioning influences the powers
of these competitive forces and therefore the economic performance of specific market
segments and firms. Porter’s FF is one of the most famous competitive frameworks in
business strategy [107, 104, 108], and Bayesian networks and decision diagrams are
probabilistic graphical tools that are widely utilized in DA [109, 110].
In the polygeneration study, I shift from the uncertainty face to the flexibility face of my
research coin. Here, I rely on concepts and methods in managerial accounting to derive a
series of propositions that assess the economic value of a polygeneration facility, under both
static and flexible operation modes. Essential to these modeling efforts are two concepts:
levelized cost and value of real-options. Levelized cost is a break-even metric that calculates
the ratio of lifetime-cost to lifetime-production of a facility [111, 112]. As will become
evident, this metric allows deriving the unit profit-margin and the unit value of flexibility
associated with polygeneration. Equally important, real-options analysis is widely applied to
quantify the impacts of climate uncertainty and the related value of flexibility in energy
investments [113, 114, 115]. Numerous real-option models have been developed over the
years [116, 117, 76], and they help value both operational and strategic flexibility in the
changing energy landscape [96, 118, 119, 120]. This work takes a unique – rather simple –
approach to expressing the real-option value of polygeneration flexibility; nonetheless, it
adheres to the fundamental premise of real-options as buying the right, but not the obligation,
to modify the operation or management of a project in the future, in response to unknown risks
or opportunities [121].
CHAPTER 1 — Scope of Work 10
Now comes the time to put all the pieces together. Combining the previously introduced
subject areas and modeling methods, the following sections provide a more formal and
elaborate overview for each of the three research endeavors pursued in this dissertation.
2.1 Translating Risk Assessment to Contingency Planning for CO2 Geologic
Storage: A Methodological Framework
The uncertain occurrences and consequences of CO2 leakage from potential CCS projects
continue to be a major source of public concern [122, 123]. In order to ensure safe and
effective long-term geologic storage of CO2, existing regulations require both assessing
leakage risks and responding to leakage incidents through corrective measures [124].
However, until now, these two pieces of risk management have been usually addressed
separately. This study proposes a conceptual methodological framework that bridges risk
assessment to corrective measures through clear and collaborative contingency planning. We
achieve this goal in three consecutive steps.
First, a probabilistic risk assessment (PRA) approach is adopted to characterize potential
leakage features, events, and processes (FEP) in a Bayesian events tree (BET), resulting in a
risk assessment matrix (RAM). Allowing the visualization of risk identification, analysis, and
evaluation, the proposed RAM depicts a mutually exclusive and collectively exhaustive set of
uncertain leakage scenarios with quantified likelihood, impact, and tolerance levels.
Second, the risk assessment matrix is translated to a contingency planning matrix (CPM).
Notably, the CPM incorporates a tiered contingency system that guides the preparation for
leakage uncertainties and the response to leakage incidents, whenever they actually occur. The
leakage likelihood and impact dimensions of RAM are translated to resource proximity and
variety dimensions in CPM, respectively. To ensure both rapid and thorough contingency
planning, more likely or frequent risks require more proximate resources while more impactful
risks require more various resources. In addition, the minimum and maximum risk tolerance
levels are translated to contingency thresholds, and all foreseeable risk scenarios are
categorized under three contingency tiers: Tier 1, Tier 2, and Tier 3. Here, we highlight how
the upper, lower, and inter-tier contingency boundaries should be collaboratively pre-
CHAPTER 1 — Scope of Work 11
negotiated between the operating party and all relevant stakeholders in order to ensure
effective preparedness and response.
Finally, we present a model contingency plan to demonstrate how all newly introduced
concepts integrate together. Specifically, we focus on explaining how the designed
contingency tiers facilitate important aspects of contingency planning, primarily: evaluating
leakage uncertainties and initiating response procedures; designing a corrective measures
matrix (CMM) that assigns specific control and remediation actions to each potential leakage
scenario; mobilizing, deploying, and sustaining necessary human and equipment resources;
and formulating a decision-making hierarchy, a notification protocol, and a communication
scheme to effectively administer the CO2 storage site.
This study was conducted in collaboration with Professor Sally M. Benson from the
Department of Energy Resources Engineering at Stanford University. While I led the
modeling and the analytical work, Professor Benson provided general guidance and helped co-
author a journal paper, which has been accepted for publication [125].
2.2 Economic Value of Flexible Hydrogen-Based Polygeneration Energy
Systems
Polygeneration energy systems (PES) have the potential to provide a flexible, high-efficiency,
and low-emissions alternative for power generation and chemical synthesis from fossil fuels
[126, 127]. This study aims to develop a set of metrics that calculate the economic value of
fossil-fueled PES, which rely on hydrogen as an intermediate product. To achieve this goal,
we first model a representative PES with carbon capture, which uses coal as a primary energy
input and produces electricity, fertilizer, and pure CO2 as end-products. We then derive a
series of propositions that assess the cost competitiveness of the modeled PES under both
static and flexible operation modes, compare the performance of PES to that of
monogeneration (i.e. single-output) energy systems, and quantify the value of real-options
associated with PES’s diverse and flexible operation.
CHAPTER 1 — Scope of Work 12
Based on the levelized cost of electricity (𝐿𝐶𝑂𝐸) metric, the levelized cost of hydrogen
(𝐿𝐶𝑂𝐻) metric is first introduced. Then, we formulate the levelized incremental cost (𝐿𝐼𝐶) of
converting hydrogen into distinct market commodities such as electricity and fertilizers. By
subtracting the cost from the end-products’ sales, we derive the profit-margins of PES under
multiple operation modes: static monogeneration of electricity (𝑃𝑀0𝑒) or fertilizer (𝑃𝑀0𝑓),
static polygeneration of electricity and fertilizer (𝑃𝑀1), and flexible polygeneration of
electricity and fertilizer (𝑃𝑀2). Subsequently, the real-option values enabled by PES are
encapsulated in two terms: value of diversification (𝑉𝑂𝐷) quantifies the option to produce
multiple outputs, and value of flexibility (𝑉𝑂𝐷) quantifies the option to adjust the production
rates of outputs over time. For consistency, every derived economic metric is expressed as a
monetary value per unit of produced hydrogen ($/𝑘𝑔ℎ); nonetheless, all metrics can be easily
converted to value per unit of any end-product, such as electricity ($/𝑘𝑊ℎ).
To illustrate the practical significance of these metrics, we apply them to evaluate the
economics of Hydrogen Energy California (HECA), a real PES project currently under
development in California [128, 129]. Under our technical and economic assumptions,
HECA’s levelized cost of hydrogen is estimated at 1.373 $/𝑘𝑔ℎ. The profitability of HECA
as a static PES depends on the exact production portfolio, and it increases in the share of
hydrogen converted to fertilizer rather than electricity; 𝑃𝑀1 varies between −0.992 and 1.934
$ 𝑘𝑔ℎ⁄ , corresponding to 𝑃𝑀0𝑒 and 𝑃𝑀0𝑓, respectively. However, when configured as a
flexible PES, HECA almost breaks even on a pre-tax basis, with 𝑃𝑀2 = −0.0439 $ 𝑘𝑔ℎ⁄ .
Consequently, we show that diversification and flexibility are valuable for HECA when
comparing polygeneration to static monogeneration of electricity (positive 𝑉𝑂𝐷 and 𝑉𝑂𝐹),
but these two real options have no value when comparing polygeneration to static
monogeneration of fertilizers (negative 𝑉𝑂𝐷 and 𝑉𝑂𝐹).
Conducting a sensitivity analysis on these findings shows that HECA’s economic value is
mostly sensitive to the price of fertilizer and to discount rate. A flexible HECA breaks even
upon modest increase in fertilizer prices beyond 3.1% or decrease in discount rate beyond
7.5%; conversely, the prices of CO2 and electricity need to increase by at least 14.5% and
34%, respectively, to achieve the same goal.
CHAPTER 1 — Scope of Work 13
This study was completed in collaboration with Professor Stefan Reichelstein from the
Graduate School of Business at Stanford University. While I led most of the theoretical
modeling as well as HECA’s case study, Professor Reichelstein provided general guidance,
oversaw the economic derivations, and helped co-author and publish a journal paper based on
this work [130].
2.3 Decision Analytic Modeling of the Five Forces in Competitive Strategy:
Application in the U.S. Residential Solar PV Industry
Competitive strategy, pioneered by Michael E. Porter since 1979, explains how an
organization facing competition can achieve superior profitability within its industry. Porter
identifies five forces that shape competition in relatively stable industries: Buyers, Suppliers,
Substitutes, New Entrants, and Rivals. He describes what causes each of the forces to be
strong or weak, and he explains that an incumbent firm gains competitive advantage by
positioning where all forces are weakest [104, 108]. Despite its remarkable contributions to
business strategy over the years, Porter’s FF framework has been mostly applied qualitatively
and deterministically [131, 132, 133]. Few systematic methodologies have been developed to
guide the quantification and operationalization of the competitive forces in real life, and no
sufficient attention has been given to the uncertain and interdependent nature of these forces
and their economic implications [134, 135]. To address these issues, we propose a decision
analytic modeling of the five forces, hereby referred to as DAFF. DAFF uses DA techniques
and tools to link a firm’s positioning decisions with uncertain market competition and
economics. The result is a quantitative model that managers can use to evaluate the
profitability of a specific industry, to properly position their business in the industry, and to
predict and shape the future of that industry. To that end, the DAFF approach is not intended
to refute, replace, or modify the theoretical foundations of FF; rather, DAFF aims to maximize
FF’s practical application.
To build the DAFF models, we first extract and document all important terminology related to
the FF strategic framework from literature. Key elements and essential terms are categorized
as decision-related, uncertainty-related, or value-related. The five competitive forces and their
CHAPTER 1 — Scope of Work 14
underlying drivers are modelled as uncertainties. Also counted as uncertainties are industry-
specific regulatory, technological, growth, and complementary factors. Both the generalizable
forces and the industry-specific factors impact the cost, price, and quantity, which are treated
as uncertain economic parameters. Along the way, we describe the probabilistic
interdependence among the uncertainties, and we link them together in a single DAFF
Bayesian Network. We also spend some time explaining how to effectively define
profitability, which is modelled as a value metric.
The final element of the DAFF models is the firm’s actions within the analyzed industry,
which can be categorized into three types of decisions: Value Proposition, Value Chain, and
Economic decisions. Value Proposition decisions dictate what product to make, whereas Value
Chain decisions determine how the product is made. Value Proposition and Value Chain
choices influence the uncertain competitive landscape and therefore yield distinct positioning
alternatives for the firm within its industry. In contrast, Economic decisions do not impact the
competitive landscape; they address three aspects related to the firm’s specific profitability:
Production Scale, Pricing, and Tactical Costing. Adding the firm’s decisions to the DAFF
Bayesian Network results in a DAFF Decision Diagram.
This DAFF Decision Diagram can fulfill the two main objectives of Porter’s competitive
strategy: positioning in the industry and reshaping the industry. Positioning is a short-term
objective, and it requires three consecutive analyses of current and very-near-future
profitability: of the overall industry, of distinct positioning segments in the industry, and of a
specific firm or business within each positioning segment of the industry. Building on the
outcomes from these three steps, reshaping the industry becomes the long-term objective, and
it requires two additional analyses of distant-future profitability, via: predicting the evolution
of the industry structure and modifying the evolution of the industry structure. After detailing
how to model the three steps for industry positioning, we provide a conceptual description of
how to model the remaining two steps for industry reshaping.
Along the way, we explain how the DAFF modeling of these strategic objectives augments
previous efforts to enhance the operationalization of the FF framework. Specifically, we
highlight the following DAFF benefits: generalizing the competitive assessments while
CHAPTER 1 — Scope of Work 15
customizing their features to evaluate different industries and firms; explicitly accounting for
competitive and economic uncertainty; clearly mapping the relation between the industry’s
competitive forces and the firm’s competitive actions; clearly mapping the relation between
competitive forces and economic performance; tracking, comparing, ranking, and prioritizing
the interdependence among the competitive forces, drivers, and industry factors; outlining the
firm’s scope of control; and exposing and reducing cognitive biases. Atop all that, the most
important feature of DAFF – indeed, one that enables all aforementioned benefits – is
quantification.
In order to demonstrate DAFF’s applicability, we use it to assess the competitive strategy of a
major firm within the U.S. residential solar PV industry. Specifically, we undertake the first
two steps of the strategic positioning objective, aiming to answer two questions: Is the
competitive landscape in the U.S. residential solar PV industry favorable in the near future?
And if so, where should the solar firm position its residential business?
In the first part of the case study, we describe how the DAFF models are customized for the
specific industry and firm of interest. Subsequently, upon developing and evaluating a DAFF
Bayesian Network, we find that, among the five competitive forces, only rivalry is expected to
be relatively strong. The chance of residential solar firms suffering from strong rivalry –
hereby expressed as {high Rivals} prospect – over the next two years is 0.6, compared to
about 0.4 for {high Substitutes}, {high Buyers}, {high New Entrants}, and {high Suppliers}.
This predicted competitive landscape yields an expected earnings before tax (EBT) of 4.05
billion $/year for the whole U.S. residential PV market, with a probability-weighted average
cost, price, and installation capacity estimated at 1.19 dollar-per-watt ($/W), 3.35 $/W, and
1.93 GW, respectively.
The Bayesian Network also tracks the interdependence among the five forces and its
corresponding economic implications. We document robust interdependence among four
forces: Substitutes, Buyers, New Entrants, and Rivals. For example, observing strong Buyers
increases the likelihood of witnessing strong Rivals and Substitutes; if the decision-maker
observes a {high Buyers} prospect, the probability of experiencing {high Substitutes}
increases from 0.39 to 0.7, and the probability of {high Rivals} increases from 0.62 to 0.74. A
CHAPTER 1 — Dissertation Organization 16
careful analysis shows that the interactions between the competitive forces need not be
symmetrical. For instance, observing strong Buyers increases the likelihood of witnessing
strong Substitutes significantly, but observing strong Substitutes barely updates the decision-
maker’s knowledge about Buyers. Ultimately, experiencing a single force at its weakest or
strongest extreme may lift the overall industry EBT up to 5.77 billion $/year or drag it down to
1.86 billion $/year, respectively.
Using a DAFF Decision Diagram, we also analyze the competitive uncertainties in multiple
positioning segments that are of interest to the solar firm. We investigate four positioning
decisions. Regional Focus is a Value Proposition decision that addresses what customers to
serve: rural or urban. In contrast, Downstream Integration, Customer Finance, and Panel
Manufacturing are Value Chain decisions that determine how to operate the business: whether
to serve customers directly or through intermediate dealers; whether to sell the solar system
through direct-purchase agreements or offer product financing in the form of loans or leases;
and whether to insource or outsource the manufacturing of the solar panels. Combining the
various decision alternatives results in 32 feasible positioning tracks. Each track yields a
unique competitive landscape and, correspondingly, a unique EBT profit value ranging
between 0.51 and 3.98 billion $/year. The results show that the highest expected profit is
realized in a competitive setting where incumbents choose to: locate in urban areas, manage
customers directly without relying on dealers, and offer loan and lease services to their
customers.
3 Dissertation Organization
This dissertation continues with four chapters that document the aforementioned research
initiatives in detail. Given the diversity of the addressed topics, Chapters 2, 3, and 4 are
formatted such that each may stand alone as a self-contained study, which can be reviewed
and referenced independently. Chapter 5 is an extensive case study based on the methods and
results of Chapter 4. For clarity, we avoid discussing all conclusions in one Chapter. Instead,
an elaborate Conclusions section is presented at the end of each Chapter to summarize the
main findings and suggest relevant areas of future research.
CHAPTER 1 — Dissertation Organization 17
Chapter 2, titled Translating Risk Assessment to Contingency Planning for CO2 Geologic
Storage: A Methodological Framework, is based on a journal paper co-authored with
Professor Sally M. Benson and accepted for peer-reviewed publication [125]. The paper starts
with a brief overview of the terminology used in managing the uncertainties of CO2 storage,
highlighting some existing literature on risk assessment methodologies and corrective
measures. The next section discusses how to model a risk assessment matrix, and it introduces
the concept of “risk profiles.” As the main focus of this paper, a contingency planning matrix
is then developed based on the risk assessment matrix, and its tier structure is discussed.
Lastly, we leverage the contingency planning matrix to design a model contingency plan,
which covers multiple sections on preparing for leakage risks and responding to leakage
incidents.
Chapter 3, titled Economic Value of Flexible Hydrogen-Based Polygeneration Entergy
Systems, is based on a paper co-authored with Professor Stefan Reichelstein and already
published in Applied Energy [130]. The first section introduces the economic concepts and
technical configuration used in assessing polygeneration energy systems. Next, we conduct a
detailed economic analysis for a representative PES in three scenarios: Scenario 1 evaluates
static operation while Scenarios 2a and 2b evaluate two modes of flexible operation. As the
main focus of this paper, the economic definitions and derived propositions in all three
scenarios are then used to calculate PES’s profit-margin and real-option values of
diversification and flexibility. Finally, we demonstrate the applicability of all derived metrics
by examining the economic competitiveness of Hydrogen Energy California, a polygeneration
project currently under development.
Chapter 4 is titled Decision Analytic Modeling of the Five Forces in Competitive Strategy, and
it explains the theoretical foundations of DAFF – the decision analytic modeling of the five
forces. The first section provides a brief overview of decision analysis and Porter’s five forces,
and then it outlines how DA tools can enhance the operationalization of the FF theory. The
next section describes how to develop a DAFF model, including how to use uncertainties and
decisions to model the competitive forces and industry-specific factors, the economics of an
industry or a firm, and the strategic positioning actions of the firm. As the main focus of this
study, we then explain how a firm can use DAFF to execute the two main objectives of
CHAPTER 1 — Dissertation Organization 18
competitive strategy: positioning in and reshaping the industry. The subsequent two sections
offer further guidance on applying DAFF; in addition to discussing some modeling best
practices, we highlight the ability of DAFF to preserve and characterize many of Porter’s
strategic insights that stem from, but extend beyond, the FF framework.
Finally, Chapter 5 is titled DAFF Modeling of Competitive Strategy: Positioning in the Near-
Future U.S. Residential Solar PV Industry. It showcases the application of DAFF to fulfill a
specific strategic objective, by a specific firm, in a specific competitive energy industry. The
objective is positioning in the near future; the firm is a major solar developer; and the
competitive industry is residential solar PV in the United States. In the first section, we build a
DAFF Bayesian Network to analyze competition in the overall industry. By considering a
series of important positioning decisions for the firm, the Bayesian Network is expanded into
a Decision Diagram that analyzes various market segments. The next section displays the
results from both modeling steps. For the overall industry, the DAFF Bayesian Network
outputs: a probability distribution over the power of each competitive force as well as over the
average cost, price, and annual sales; an expected profit value; and quantitative measurements
of the interdependencies among the forces. For each positioning segment within the industry,
the DAFF Decision Diagram yields: a distinct probability distribution over the power of each
force as well as a distinct expected profit value. Ultimately, we explain how the DAFF outputs
can be streamlined into a clear and actionable list of recommendations regarding the firm’s
positioning strategy in the U.S. residential solar market.
CHAPTER 1 — References 19
References
[1] B. Obama, "Remarks by the President at the Morning Plenary Session of the United Nations
Climate Change Conference," The White House, Office of the Press Secretary, 18 December
2009.
[2] UNFCCC, "Statements made at COP 15 / CMP 5. United Nations Framework Convention on
Climate Change," 2009. [Online]. Available:
http://unfccc.int/meetings/copenhagen_dec_2009/items/5087.php. [Accessed 2016].
[3] BP, "BP Energy Outlook downloads," 2015. [Online]. Available:
http://www.bp.com/en/global/corporate/energy-economics/energy-outlook-2035/energy-outlook-
downloads.html. [Accessed 2016].
[4] IEA, "2015 Key World Energy Statistics," 2015. [Online]. Available:
http://www.iea.org/publications/freepublications/publication/KeyWorld_Statistics_2015.pdf.
[5] O. Edenhofer, R.Pichs-Madruga, Y. Sokona, E. Farahani, S. Kadner, K. Seyboth, A. Adler, I.
Baum, S. Brunner, P. Eickemeier, B. Kriemann, J. Savolainen, S. Schlömer, C. v. Stechow, T.
Zwickel and J. M. (eds.), "Summary for Policymakers," in Climate Change 2014: Mitigation of
Climate Change. Contribution of Working Group III to the Fifth Assessment Report of the
Intergovernmental Panel on Climate Change, ambridge University Press, Cambridge, United
Kingdom and New York, NY, USA, 2014.
[6] L. Clarke, K. Jiang, K. Akimoto, M. Babiker, G. Blanford, K. Fisher-Vanden, J.-C. Hourcade, V.
Krey, E. Kriegler, A. Löschel, D. McCollum, S. Paltsev, S. Rose, P. R. Shukla, M. Tavoni, B. C.
C. v. d. Zwaan and D. v. Vuuren, "Assessing Transformational Pathways," in Climate Change
2014: Mitigation of Climate Change. Contribution of Working Group III to the Fifth Assessment
Report of the Intergovernmental Panel on Climate Change, Cambridge University Press,
Cambridge, United Kingdom and New York, NY, USA, 2014.
[7] P. Folger, "Carbon Capture and Sequestration (CCS): A Primer," Congressional Research
Review, Washington, DC, 2013.
[8] B. Metz, O. Davidson, H. d. Coninck, M. Loos and L. Meyer, "IPCC Special Report on Carbon
Dioxide Capture and Storage," Cambridge University Press, Cambridge & New York, 2006.
[9] GCCSI, "Large Scale CCS Projects," 2016. [Online]. Available:
https://www.globalccsinstitute.com/projects/large-scale-ccs-projects. [Accessed 2016].
[10] S. D. Kenarsari, D. Yang, G. Jiang, S. Zhang, J. Wang, A. G. Russell, Q. Weif and M. Fan,
"Review of recent advances in carbon dioxide separation and capture," RSC Adv., vol. 3, p.
22739–22773, 2013.
[11] E. S. Rubin, H. Mantripragada, A. Marks, P. Versteeg and J. Kitchin, "The outlook for improved
carbon capture technology," Progress in Energy and Combustion Science, vol. 38, p. 630–671,
2012.
CHAPTER 1 — References 20
[12] B. Li, Y. Duan, D. Luebke and B. Morreale, "Advances in CO2 capture technology: A patent
review," Applied Energy, vol. 102, p. 1439–1447, 2013.
[13] NETL & DOE, "Carbon Storage Atlas - Fifth Edition," National Energy Technology Laboratory
and The U.S. Department of Energy, Office of Fossil Energy, United States, 2015.
[14] GCCSI, "The Global Status of CCS: 2015, Summary Report," Global CCS Institute, Melbourne,
Australia, 2015.
[15] IEAGHG, "Review of Offshore Monitoring for CCS Projects," IEAGHG, UK, 2015.
[16] A. Chodos, "This Month in Physics History, April 25, 1954: Bell Labs Demonstrates the First
Practical Silicon Solar Cell," APS News, vol. 18, no. 4, April 2009.
[17] V. V. Tyagi, N. A. A. Rahim, N. A. Rahim and J. A. Selvaraj, "Progress insolar PV technology:
Research and achievement," Renewable and Sustainable Energy Reviews, vol. 20, p. 443–461,
2013.
[18] Z. Shahan, "Solar Panel Efficiency Has Come A Long Way (Infographic)," Clean Technica, 6
February 2014.
[19] NREL, "Best Research-Cell Efficiencies," National Renewable Energy Laboratory, United States,
2016.
[20] J. Martino, "Advancements in Wind Turbine Technology: Improving Efficiency and Reducing
Cost," RenewableEnergyWorld.com, 2 April 2014.
[21] F. Blaabjerg and K. Ma, "Future on Power Electronics for Wind Turbine Systems," IEEE Journal
of Emerging and Selected Topics in Power Electronics, vol. 1, no. 3, p. 139–152, 2013.
[22] M. Islam, S.Mekhilef and R.Saidur, "Progress and recent trends of wind energy technology,"
Renewable and Sustainable Energy Reviews, vol. 21, p. 456–468, 2013.
[23] IEA, "Energy Statistics of OECD Countries," International Energy Agency, Paris, France, 2015.
[24] EIA, "International energy data and analysis," 2016. [Online]. Available: http://www.eia.gov/.
[Accessed 2016].
[25] JRC, "PV Status Report," Institute for Energy and Transport, Joint Research Centre, European
Commission, Luxembourg, 2014.
[26] GWEC, "Global Wind Statistics 2014," Global Wind Energy Council, Brussels, 2015.
[27] UNFCCC, "Paris Agreement," United Nations Framework Convention on Climate Change, The
Conference of the Parties on its twenty-first session, FCCC/CP/2015/10/Add.1, 2015.
[28] UNFCCC, "Intended Nationally Determined Contributions (INDCs)," 2016. [Online]. Available:
www4.unfccc.int/submissions/INDC/Submission Pages/Submissions.aspx. [Accessed 2016].
CHAPTER 1 — References 21
[29] EPA, "Carbon Pollution Emission Guidelines for Existing Stationary Sources:Electric Utility
Generating Units," 80 Fed. Reg. 64662, United States, 2015a.
[30] EPA, Standards of Performance for Greenhouse Gas Emissions From New, Modified, and
Reconstructed Stationary Sources: Electric Utility Generating Units, United States: 80 Fed. Reg.
64510, 2015b.
[31] SEIA, "Solar Investment Tax Credit (ITC). Solar Energy Industries Association," 2016a.
[Online]. Available: http://www.seia.org/policy/finance-tax/solar-investment-tax-credit.
[Accessed 2016].
[32] DOE, "Renewable Electricity Production Tax Credit (PTC). U.S. Department of Energy," 2016.
[Online]. Available: http://energy.gov/savings/renewable-electricity-production-tax-credit-ptc.
[Accessed 2016].
[33] E. Lantz, D. Steinberg, M. Mendelsohn, O. Zinaman, T. James, G. Porro, M. Hand, T. Mai, J.
Logan, J. Heeter and L. Bird, "Implications of a PTC Extension on U.S. Wind Deployment,"
National Renewable Energy Laboratory, United States, 2014.
[34] SEIA, "Depreciation of Solar Energy Property in MACRS," 2016b. [Online]. Available:
http://www.seia.org/policy/finance-tax/depreciation-solar-energy-property-macrs. [Accessed
2016].
[35] DOE, "LPO Overview Brochure," U.S. Department of Energy. Loan Programs Office,
Washington, DC, 2015.
[36] CERC, "U.S.-China Clean Energy Research Center," 2016. [Online]. Available: www.us-china-
cerc.org. [Accessed 2016].
[37] NYSDEC, "High-Volume Hydraulic Fracturing in NYS. New York State Department of
Environmental Conservation," 2015. [Online]. Available:
http://www.dec.ny.gov/energy/75370.html. [Accessed 2016].
[38] AB 32, "California Global Warming Solutions Act," Assembly Bill No. 32, California, United
States, 2006.
[39] T. Napp, K. S. Sum, T. Hills and P. S. Fennell, "Attitudes and Barriers to Deployment of CCS
from Industrial Sources in the UK," Grantham Institute for Climate Change. Imperial College
London, London, 2014.
[40] JRC, "2013 Technology Map of the European Strategic Energy Technology Plan," Institute for
Energy and Transport. Joint Research Centre. European Commission, Luxembourg, 2013.
[41] TERI, "India CCS Scoping Study: Final Report," The Global CCS Institute, Project Code
2011BE02, 2013.
CHAPTER 1 — References 22
[42] GAO, "Climate Change: Federal Actions Will Greatly Affect the Viability of Carbon Capture and
Storage As a Key Mitigation Option," U.S. Government Accountability Office, Washington, DC,
2008.
[43] L. Bird, M. Milligan and D. Lew, "Integrating Variable Renewable Energy: Challenges and
Solutions," National Renewable Energy Laboratory, United States, 2013.
[44] K. Stefferud, "California’s Solar PV Forecasting Challenges and Opportunities," EnerNex:
Electric power research, engineering and consulting, 13 September 2013.
[45] A. Ipakchi and F. Albuyeh, "Grid of the Future," IEEE power & energy magazine, no.
March/April, p. 53–62, 2009.
[46] MIT, "The Future of Natural Gas," Energy Initiative - Massachusetts Institute of Technology,
Boston, 2011a.
[47] X. Zhang, N. P. Myhrvold, Z. Hausfather and K. Caldeira, "Climate benefits of natural gas as a
bridge fuel and potential delay of near-zero energy systems," Applied Energy, p. (in press), 2015.
[48] IHS CERA, "Fueling the Future with Natural Gas: Bringing It Home," IHS, 2013.
[49] R. W. Howarth, R. Santoro and A. Ingraffea, "Methane and the greenhouse-gas footprint of
natural gas from shale formations," Climatic Change, vol. 106, p. 679–690, 2011a.
[50] S. G. Osborn, A. Vengosh, N. R. Warner and R. B. Jackson, "Methane contamination of drinking
water accompanying gas-well drilling and hydraulic fracturing," Proceedings of the National
Academy of Sciences of the United States of America , vol. 108, no. 20, p. 8172–8176, 2011.
[51] R. W. Howarth, A. Ingraffea and T. Engelder, "Natural gas: Should fracking stop?," Nature, p.
271–275, 15 September 2011b.
[52] J. Bordoff, "How Exporting U.S. Liquefied Natural Gas Will Transform the Politics of Global
Energy," The Wall Street Journal, 17 November 2015.
[53] N. Kulichenko and E. Ereira, "Carbon Capture and Storage in Developing Countries: a
Perspective on Barriers to Deployment," The World Bank, Washington, DC, 2011.
[54] Seeking Alpha, "Competitive Threats To Residential Solar Standouts Are Exaggerated," Seeking
Alpha, 5 January 2016.
[55] Seeking Alpha, "Increasing Uncertainty In Rooftop Solar's Long-Term Business Model," Seeking
Alpha, 15 November 2015.
[56] N. Litvak, "U.S. Residential Solar Financing 2015-2020," GTM Research, United States, 2015.
[57] N. Alster, "Why Solar Power Stocks Are Still Earthbound," The New York Times, 6 April 2013.
CHAPTER 1 — References 23
[58] A. H. Miller, "Solar stocks fluctuating on market uncertainty," Solar Energy News, 9 March
2011.
[59] J. Pyper, "Breaking: Clean Power Plan Stayed by Supreme Court, Obama Handed a Setback,"
Greentech Media, 9 February 2016.
[60] A. Liptak and C. Davenport, "Supreme Court Deals Blow to Obama’s Efforts to Regulate Coal
Emissions," The New York Times, 9 February 2016.
[61] C. Frank, "Pricing Carbon: A Carbon Tax or Cap-And-Trade?," Brookings, 12 August 2014.
[62] D. M. Uhlmann and R. S. Avi-Yonah, "Combating Global Climate Change: Why a Carbon Tax Is
a Better Response to Global Warming Than Cap and Trade," Stanford Environmental Law
Journal, vol. 28, no. 3, 2009.
[63] L. H. Goulder and A. R. Schein, "Carbon Taxes versus Cap and Trade: A Critical Review,"
Climate Change Economics, vol. 4, no. 3, p. 1350010, 2013.
[64] EC ETS, Directive 2003/87/EC of the European Parliament and of the Council of 13 October
2003 establishing a scheme for greenhouse gas emission allowance trading within the Community
and amending Council Directive 96/61/EC, European Union: European Commission, 2003.
[65] H.R. 2454, American Clean Energy and Security Act of 2009, United States: 111th Congress, 1st
Session, 2009.
[66] R. Taylor and R. Hoyle, "Australia Becomes First Developed Nation to Repeal Carbon Tax," The
Wall Street Journal, 17 July 2014.
[67] J. Hoppmann, J. Huenteler and B. Giroda, "Compulsive policy-making—The evolution of the
German feed-in tariff system for solar photovoltaic power," Research Policy, vol. 43, no. 8, p.
1422–1441, 2014.
[68] M. Yozwiak, "How extending the investment tax credit would affect US solar build," Bloomberg
New Energy Finance, United States, 2015.
[69] UCSUSA, "Production Tax Credit for Renewable Energy," [Online]. Available:
http://www.ucsusa.org/clean_energy/smart-energy-solutions/increase-renewables/production-tax-
credit-for.html. [Accessed 2016].
[70] J. Farrell, "The Future of Solar Economics and Policy," Clean Technica, 20 October 2014.
[71] J. Pyper, "Nevada Regulators Eliminate Retail Rate Net Metering for New and Existing Solar
Customers," Greentech Media, 23 December 2015.
[72] CPUC, Decision Adopting Successor to Net Energy Metering Tariff, California: California Public
Utilities Commission. R.14-07-002, 2015.
CHAPTER 1 — References 24
[73] R. A. Howard and A. E. Abbas, Foundations of Decision Analysis, 1st ed., United States:
Pearson, 2016.
[74] H. Courtney, J. Kirkland and P. Viguerie, "Strategy Under Uncerainty," Harvard Business
Review, 1997.
[75] E. Pate-Cornell, "Uncertainties in risk analysis: Six levels of treatment," Reliability Engineering
and System Safety, vol. 54, pp. 95-111, 1996.
[76] A. K. Dixit and R. S. Pindyck, Investment Under Uncertainty, Princeton: Princeton University
Press, 1994.
[77] T. Macalister, "Spending watchdog to examine scrapping of £1bn carbon capture plan," The
Gaurdian, 31 January 2016.
[78] A. Neslen, "Europe's carbon capture dream beset by delays, fears and doubt," The Guardian, 9
April 2015.
[79] W. Widmer, "Billions over budget. Two years after deadline. What’s gone wrong for the ‘clean
coal’ project that’s supposed to save an industry?," Politico, 26 April 2015.
[80] SolarCity, "Following Nevada PUC's Decision to Punish Rooftop Solar Customers, SolarCity
Forced to Eliminate More than 550 Jobs in Nevada," Press Releases, 6 January 2016.
[81] L. Stoker, "SunEdison to exit ‘uneconomic’ UK market," Solar Power Portal, 7 October 2015.
[82] H. Chandler, "Empowering Variable Renewables: Options for Flexible Electricity Systems,"
International Energy Agency, Paris, 2008.
[83] MIT, "The Future of the Electric Grid (Section 1.2: Challenges and Opportunities),"
Massachusetts Institute of Technology, Boston, 2011b.
[84] M. T. Ho and D. E. Wiley, "Flexible strategies to facilitate carbon capture deployment at
pulverised coal power plants," International Journal of Greenhouse Gas Control, 2016.
[85] S. M. Cohen, A techno-economic plant- and grid-level assessment of flexible CO2 capture,
Austin: University of Texas at Austin, 2012.
[86] H. Chalmers, M. Leach, M. Lucquiaud and J. Gibbins, "Valuing flexible operation of power
plants with CO2 capture," Energy Procedia, vol. 1, no. 1, p. 4289–4296, 2009.
[87] S. Ziaii, S. Cohen, G. T. Rochelle, T. F. Edgar and M. E. Webber, "Dynamic operation of amine
scrubbing in response to electricity demand and pricing," Energy Procedia, vol. 1, p. 4047–4053,
2009.
[88] C. J. Barnhart, M. Dale, A. R. Brandt and S. M. Benson, "The energetic implications of curtailing
versus storing solar- and wind-generated electricity," Energy & Environmental Science, vol. 6, p.
2804–2810, 2013.
CHAPTER 1 — References 25
[89] P. Denholm and M. Hand, "Grid flexibility and storage required to achieve very high penetration
of variable renewable electricity," Energy Policy, vol. 39, p. 1817–1830, 2011.
[90] P. Denholm, J. Jorgenson, M. Hummon, T. Jenkin, a. D. Palchak, B. Kirby, O. Ma and M.
O’Malley, "The Value of Energy Storage for Grid Applications," National Renewable Energy
Laboratory, United States, 2013.
[91] C. A. Kang, A. R. Brandt and L. J. Durlofsky, "Optimal operation of an integrated energy system
including fossil fuel power generation, CO2 capture and wind," Energy, vol. 36, p. 6806–6820,
2011.
[92] J. Meerman, A. Ramirez, W. Turkenburg and A. Faaij, "Performance of simulated flexible
integrated gasification polygeneration facilities, Part B: Economice valuation," Renewable and
Sustainable Energy Reviews, vol. 16, p. 6083–6102, 2012.
[93] C. Rubio-Maya, J. Uche-Marcuello, A. Martínez-Gracia and A. A. Bayod-Rújula, "Design
optimization of a polygeneration plant fuelled by natural gas and renewable energy sources,"
Applied Energy, vol. 88, p. 449–457, 2011.
[94] L. Hu, J. Hongguang, G. Lin and H. Wei, "Techno-economic evaluation of coal-based
polygeneration systems of synthetic," Energy Conversion and Management, vol. 52, p. 274–283,
2011.
[95] L. Trigeorgis, "Foreword (by Scott P. Mason)," in Real Options: Managerial Flexibility and
Strategy in Resource Allocation, Cambridge, Massachusetts and London, England, MIT Press,
1996.
[96] X. Zhang, X. Wang, J. Chen, X. Xie, K. Wang and Y. Wei, "A novel modeling based real option
approach for CCS investment evaluation under multiple uncertainties," Applied Energy, vol. 113,
p. 1059–1067, 2014.
[97] GCCSI, "Definition of CCS Ready," 3 November 2010. [Online]. Available:
http://www.globalccsinstitute.com/insights/authors/christophershort/2010/11/03/definition-ccs-
ready. [Accessed 2016].
[98] X. Liang, D. Reiner, J. Gibbins and J. Li, "Assessing the value of CO2 capture ready in new-build
pulverised coal-fired power plants in China," International Journal of Greenhouse Gas Control,
vol. 3, no. 6, p. 787–792, 2009.
[99] M. C. Bohm, H. J. Herzog, J. E. Parsons and R. C. Sekar, "Capture-ready coal plants—Options,
technologies and economics," International Journal of Greenhouse Gas Control, vol. 1, no. 1, p.
113–120, 2007.
[100] R. McIntosh and J. Mandel, "Five Reasons U.S. Solar Installers are Vertically Integrating … For
Now," Rocky Mountain Institute, 10 July 2014.
CHAPTER 1 — References 26
[101] J. S. John, "SunEdison Buys Solar Grid Storage for Battery-Backed PV and Wind Power,"
Greentech Media, 5 March 2015a.
[102] J. S. John, "First Solar Joins $50M Investment in Younicos, Stakes Claim in Energy Storage
Market," Greentech Media, 8 December 2015b.
[103] D. Cardwell, "SolarCity to Use Batteries From Tesla for Energy Storage," The New York Times, 4
December 2013.
[104] M. E. Porter, "The Five Competitive Forces that Shape Strategy," Harvard Business Review,
January 2008.
[105] H. A. Parker, R. T. Teubner and J. C. Sawicki, "Spill Reponse Planning in the Philippines: 3-Tier
Interaction between Government and Industry," 2009. [Online]. Available:
http://www.interspill.org/previous-events/2009/12-May/pdf/1630_parker.pdf.
[106] IPIECA, "Guide to Tiered Preparedness and Response," International Petroleum Industry
Environmental Conservation Association, London, United Kingdom, 2007.
[107] J. Magretta, Understanding Michael Porter: The Essential Guide to Competition and Strategy,
Cambridge: Harvard Business Review Press, 2012.
[108] M. E. Porter, "How Competitive Forces Shape Strategy," Harvard Business Review, March-April
1979.
[109] R. A. Howard and J. E. Matheson, "Influence Diagrams," Decision Analysis, vol. 2, no. 3, p. 127–
143, 2005.
[110] R. D. Shachter, "Evaluating Influence Diagrams," Operations Research, vol. 34, no. 6, p. 871–
882, 1986.
[111] S. Reichelstein and M. Yorston, "The prospects for cost competitive solar PV power," Energy
Policy, vol. 55, p. 117–127, 2012.
[112] T. Ramsden, D. Steward and J. Zuboy, "Analyzing the Levelized Cost of Centralized and
Distributed Hydrogen Production Using the H2A Production Model, Version 2," National
Renewable Energy Laboratory, Golden, Colorado, USA, 2009.
[113] J. Anda, A. Golub and E. Strukova, "Economics of climate change under uncertainty: Benefits of
flexibility," Energy Policy, vol. 37, p. 1345–1355, 2009.
[114] S. Hallegatte, "Strategies to adapt to an uncertain climate change," Global Environmental
Change, vol. 19, no. 2, p. 240–247, 2009.
[115] W. Blyth, R. Bradley, D. Bunn, C. Clarke, T. Wilson and M. Yang, "Investment risks under
uncertain climate change policy," Energy Policy, vol. 35, p. 5766–5773, 2007.
CHAPTER 1 — References 27
[116] D. M. Lander and G. E. Pinches, "Challenges to the practical implementation of modeling and
valuing real options," The Quarterly Review of Economics and Finance, vol. 38, no. 3, p. 537–
567, 1998.
[117] L. E. Brandão, J. S. Dyer and W. J. Hahn, "Using Binomial Decision Trees to Solve Real-
Option," Decision Analysis, vol. 2, no. 2, p. 69–88, 2005.
[118] D. Kroniger and R. Madlener, "Hydrogen storage for wind parks: A real options evaluation for an
optimal investment in more flexibility," Applied Energy, vol. 136, p. 931–946, 2014.
[119] T. K. Boomsma, N. Meade and S.-E. Fleten, "Renewable energy investments under different
support schemes: A real options approach," European Journal of Operational Research, vol. 220,
no. 1, p. 225–237, 2012.
[120] Q. Chen, C. Kang, Q. Xia and J. Zhong, "Real option analysis on carbon capture power plants
under flexible operation mechanism," Minneapolis, 2010.
[121] R. d. Neufville, "Real Options: Dealing With Uncertainty in Systems Planning and Design,"
Integrated Assessment, vol. 4, no. 1, p. 26–34, 2003.
[122] TNS Opinion & Social, "Public Awareness and Acceptance of CO2 capture and storage,"
EuroBarometer, European Commission, Brussels, 2011.
[123] P. Upham and T. Roberts, "Public Perceptions of CCS: the results of NearCO2 European Focus
Groups," NearCO2, 2010.
[124] IEA, "Regulatory Frameworks for CCS," 2015. [Online]. Available:
http://www.iea.org/topics/ccs/subtopics/permittingframeworksforccs/. [Accessed May 2015].
[125] K. Farhat and S. M. Benson, "Translating Risk Assessment to Contingency Planning for CO2
Geologic Storage: A Methodological Framework," International Journal of Greenhouse Gas
Control, (accepted).
[126] J. Meerman, A. Ramírez, W. Turkenburg and A. Faaij, "Performance of simulated flexible
integrated gasification polygeneration facilities. Part A: A technical-energetic assessment,"
Renewable and Sustainable Energy Reviews, vol. 15, p. 2563–2587, 2011.
[127] P. Liu, E. N. Pistikopoulos and Z. Li, "A Multi-Objective Optimization Approach to
Polygeneration Energy Systems Design," AIChE Journal: Process Systems Engineering, vol. 56,
no. 5, p. 1218–1234, 2010.
[128] HECA, "The Project," 2010a. [Online]. Available: http://hydrogenenergycalifornia.com/the-
project. [Accessed 2014].
[129] HECA, "Project Fact Sheet," 2010b. [Online]. Available:
http://hydrogenenergycalifornia.com/factsheets. [Accessed 2013].
CHAPTER 1 — References 28
[130] K. Farhat and S. Reichelstein, "Economic Value of Flexible Hydrogen-Based Polygeneration
Energy Systems," Applied Energy, vol. 164, p. 857–870, 2016.
[131] Accenture Academy, "Explaining Porter’s Five Forces," 2014. [Online]. Available:
https://www.accentureacademy.com/d/course/1000007629. [Accessed 2015].
[132] FME, "Porter's Five Forces - Strategy Skills," 2013. [Online]. Available: http://www.free-
management-ebooks.com/dldebk-pdf/fme-five-forces-framework.pdf. [Accessed 2015].
[133] R. Marks, "Lecture Notes - Industry Analysis," Australian Graduate School of Management,
2003.
[134] M. E. Dobbs, "Guidelines for applying Porter's five forces framework: a set of industry analysis
templates," Competitiveness Review, vol. 24, no. 1, p. 32–45, 2014.
[135] H. Lee, M.-S. Kim and Y. Park, "An analytic network process approach to operationalization of
five forces model," Applied Mathematical Modelling, p. 1783–1795, 2012.
29
Chapter 2
Translating Risk Assessment to
Contingency Planning for CO2 Geologic
Storage: A Methodological Framework
1 Introduction
Fifty five large-scale carbon capture and storage (CCS) projects exist or are planned around
the world today, the majority of which are located in North America, Australia, Europe, and
China [1]. Ensuring reliable long-term storage of carbon dioxide (CO2) in subsurface geologic
formations is important to gain public support and accelerate the deployment of CCS [2, 3, 4].
To that effect, huge research and policy efforts have been devoted to the development of
technologies and regulations that secure safe operations of CO2 storage sites, with a wide
range of requirements and guidelines on risk management [1, 5, 6].
Different regulatory and legislative bodies have adopted different requirements to permit CO2
geologic storage, specifically regarding the need for risk assessment and corrective-measure
plans to address potential CO2 leakage. In the United States, the Federal Environmental
Protection Agency requires a “corrective action plan” and an “emergency and remedial
response plan” with specific timelines, and it provides detailed guidance on how to provide the
requisite information [7, 8]. Nonetheless, the Agency does not request formal documentation
on risk assessment [9]. In Canada, the environmental protection responsibilities are shared
CHAPTER 2 — Introduction 30
between the federal and provincial governments [10]. The federal government adopted the
CSA Z741 standard, which covers “risk assessment” and “risk treatment” [11, 12]. On the
provincial level, Alberta’s legislation does not require “risk assessment” or “corrective action”
plans, but the legislation allows imposing both requirements through regulation [13, 14, 15].
In addition, while British Columbia’s currently proposed regulations mandate a “corrective
measures / contingency plan” and a “description of measures to prevent significant leakage” as
part of the application for a storage permit [16], Saskatchewan’s CO2 storage operations are
managed under existing oil and gas regulations [10]. Similar policy framework exists in
Australia. Through environmental guidelines, the Commonwealth government calls for
“continuous risk assessment as an essential element of the environmental impact assessment”,
but the legislation governing greenhouse gas storage does not require submitting plans for risk
assessment or corrective measures [17, 18]. At the state level, Victoria demands a “risk
management plan” before granting an injection and monitoring license [19] whereas
Queensland does not [20]. In the European Union, the European Commission published a
CCS Directive, which requires both a “risk assessment plan” and a “corrective measures plan”
[21]. In two of the associated four guidance documents, the Commission provides a detailed
description of the requested plans, which includes example templates, proposed areas of
investigation, as well as recommended tools and formats [22, 23]. Finally, China’s legal
framework for managing CO2 storage is still under development, with no existing rules on risk
assessment and corrective measures [24, 25].
With these different approaches to risk management, a clear link between risk assessment and
corrective action for CO2 leakage is often missing. This reality controverts the wide agreement
among industry experts and policy makers on the need to connect the various aspects of risk
management, including the need to design corrective measures based on risk analysis before
permitting operations [8, 23, 26, 27, 28, 29, 30]. The aim of this work is to propose a
methodological framework that bridges risk assessment to corrective measures through clear
and effective contingency planning. This framework achieves two tasks, which summarize the
novelty of this work. First, it expands the formulation of a risk assessment matrix (RAM) to
make it more action- and decision-oriented, which subsequently facilitates its translation to a
contingency planning matrix (CPM). Second, it explains the significance of the various
CHAPTER 2 — Risk Management: Assessment, Mitigation, and Contingency Planning 31
CPM elements, not only for mapping corrective measures to potential leakage scenarios but
also for facilitating critical coordination between the operating party and the regulatory agency
overseeing CO2 storage.
In pursuing both goals, the proposed framework utilizes the extensive body of literature on
risk assessment and corrective measures for CO2 leakage, offering a mean to bridge the
utilization of existing tools instead of proposing new ones. In addition, when demonstrating its
applicability, this framework considers scenarios of CO2 leakage that start and ends in the
subsurface and propagates through geologic pathways only. When applied in real life, and
using similar techniques to the ones presented in this paper, the framework can be expanded to
include scenarios of CO2 leaks that propagate through man-made pathways and reach the
surface.
In the subsequent sections of this paper, we first provide a brief overview of the terminology
used in the risk management of CO2 storage, highlighting some existing literature on risk
assessment methodologies and corrective measures. Next, we discuss how to update the risk
assessment matrix, introducing the concept of risk profiles of CO2 leakage. As the main focus
of this paper, a contingency planning matrix is then developed based on the updated risk
assessment matrix, and its tier structure is discussed. Lastly, we leverage the contingency
planning matrix to design a model contingency plan, covering multiple sections on preparing
for leakage risks and responding to leakage incidents. When discussing specific response
strategies within the plan, we show how different corrective measures can tackle different risk
profiles under different contingency tiers, effectively linking all elements of risk management
for CO2 leakage from geologic storage.
2 Risk Management: Assessment, Mitigation, and Contingency
Planning
Before discussing the details of the proposed framework, it is important to establish a
consistent risk-management terminology that we can refer to throughout this paper. As
depicted in Figure 2.1, managing the risk of CO2 leakage from geologic storage formations
CHAPTER 2 — Risk Management: Assessment, Mitigation, and Contingency Planning 32
includes three essential steps: assessment of risk, mitigation and avoidance of intolerable risk,
and contingency planning for tolerable risk. A robust risk assessment involves the
identification, analysis, and evaluation of potential leakage scenarios. After identifying a
comprehensive set of scenarios, each scenario is analyzed qualitatively or quantitatively to
determine its likelihood of occurrence and its impact on subsurface formations and surface
ecosystems. Leakage risks are then evaluated according to external mandates by the regulatory
agency and internal procedures by the operating party, resulting in a set of risk tolerance
levels. While risks below the minimum tolerance levels can be safely ignored, risks exceeding
the maximum tolerance levels need to be mitigated or avoided altogether through a variety of
preventative measures [22, 26, 27].
Figure 2.1: Elements of risk management for CO2 leakage from geologic reservoirs
On the other hand, leakage scenarios within the tolerance range are managed through
contingency planning, which aims to prepare for leakage risks and respond to leakage
incidents if they occur [28, 31, 32]. Learning from the oil and gas industry, we envision a tier-
Risk Management
Risk Assessment
Mitigation of Intolerable Risk
Contingency Planning for Tolerable Risk
leakage scenario identification
leakage scenario analysis(likelihood, impact)
leakage scenario evaluation(tolerable, intolerable)
Purpose• prepare for leakage risks
• respond to leakage incidents
Elements• thresholds
• response initiation through triggers
• response strategies• corrective measures:
control (stop and contain) & remediate
• human and equipment resources
• administration and coordination schemes
preventative measures
CHAPTER 2 — Updating the Risk Assessment Matrix 33
system approach to contingency planning for CO2 leakage, which integrates five essential
elements: thresholds, response initiation through triggers, response strategies that include
corrective measures, human and equipment resources, and administration and coordination
schemes [23, 33, 34, 35, 36, 37]. While thresholds refer to specific levels of leakage
likelihoods and impacts that bound risk-preparedness, triggers refer to specific irregular
measurements or observations that initiate incident-response. Additionally, corrective
measures cover subsurface and surface activities that aim to both control (stop or contain) the
leakage and remediate its impacts [32, 38]. To that end, thresholds and triggers shape when
corrective measures should be implemented while human and equipment resources and
administration and coordination schemes define what and how corrective measures should be
implemented.
The aforementioned sequential process of risk management shows that the effective design
and deployment of corrective measures for CO2 leakage necessitates a robust contingency
plan, which in turn should be based on the findings of a comprehensive risk assessment. In our
attempt to present a methodological framework that integrates all three elements of risk
management, we focus primarily on contingency planning, which has received comparatively
little attention in literature. Nonetheless, contingency planning is linked to risk assessment and
corrective measures by utilizing the large body of existing literature on both topics [39, 40,
38]. Specifically, we use the features, events, and processes (FEP) methodology for risk
identification [41] and Bayesian event trees (BET) for risk analysis [40, 42, 43]. The
RISQUE method is another valuable resource to assess impacts and elicit informed
probabilities from experts [44, 45]. Subsequently, for corrective measures, we use
representative examples of containment and remediation activities to combat leakage events in
the subsurface [46, 47, 48].
3 Updating the Risk Assessment Matrix
A risk assessment matrix (RAM) is usually represented as a two-dimensional plot of leakage
impact versus leakage likelihood. Our focus on the RAM is motivated by its application in
some existing CCS policies [22, 49] and projects [29, 50] and by its ability to visualize all
CHAPTER 2 — Updating the Risk Assessment Matrix 34
three steps of risk assessment. The leakage scenarios depicted in a RAM result from risk
identification; the likelihood and impact of each scenario are the outcome of risk analysis; and
the determination of insignificant, tolerable, and intolerable scenarios emerge from risk
evaluation. When quantified, a RAM represents a leakage scenario as a single risk point, with
the likelihood and the impact calculated based on expected-average or worst-case estimates
[45, 51]. Other RAMs are qualitative, so a leakage scenario is allocated into a single high,
medium, or low risk zone [29, 52].
While helpful for visualizing and comparing risks, current applications of RAM can still be
improved. For example, a realistic leakage scenario may span more than one risk level
depending on several factors, some of which are uncertain. Such factors include the rate of
leakage, the features of the storage reservoir and surrounding geologic formations, and the
vulnerability of surface ecosystems. In addition, it is hard to distinguish the relative
significance of the various risk drivers in current RAM depictions of leakage. For instance, it
cannot be inferred whether a high likelihood of leakage through a fault into a freshwater
aquifer is due to the high probability that a fault exists or due to the high probability that an
aquifer is nearby the fault given that the latter exists. Adopting a quantifiable probabilistic risk
assessment (PRA) approach that combines FEP and BET offers one way to address those
issues, resulting in a more inclusive RAM and therefore facilitating the transition to a CPM.
PRA relies on systems analysis, decision analysis, and Bayesian reasoning to assess a set of
mutually exclusive and collectively exhaustive scenarios of CO2 leakage in the subsurface
[53]. This approach includes four steps. First, for risk identification, the overall subsurface
system is divided into a series of independent functional subsystems. Potential leakage
scenarios are defined as trajectories that combine multiple subsystems, and FEP guides
specifically the categorization of subsystems where a CO2 leakage may start. Second, the
likelihood of each leakage scenario is assessed as a series of conditional probabilities that
change as a function of a measurable criterion, which is typically a relevant geological feature.
Third, multiple value models are developed to help quantify the impact of leakage on the
subsurface and surface ecosystems. The second and third steps cover risk analysis, and
combining the first three steps results in a BET that systematically describes all foreseeable
conjunctions of leakage events. In the fourth step, specific tolerance levels are determined for
CHAPTER 2 — Updating the Risk Assessment Matrix 35
both the likelihood and the impact of leakage in order to evaluate what risks should be
mitigated and what risks can be safely ignored. Eventually, the overall outcome of this PRA is
a RAM that depicts a comprehensive set of risk profiles of CO2 leakage with quantified
likelihood, impact, and tolerance levels.
3.1 Functional Subsystems for Risk Identification
For CO2 leakage through geologic pathways, the system is defined as the set of geologic
formations in the subsurface, above and including the storage reservoir. As depicted in Figure
2.2, this system can be divided into three functional subsystems: Origin, Endpoint, and
Pathway.
Figure 2.2: Functional subsystems for risk identification
Origin: refers to the functional subsystem which is designated to contain the CO2 under
normal conditions. Physically, it encompasses the storage reservoir and any selected
containment zones. Origin can be further decomposed into a list of subsystems, namely, a
comprehensive count of the geologic irregularities – features, events, or processes (FEP) –
through which CO2 may leak and the rest of the formation where CO2 remains safely stored;
we categorize the former subsystems as FEP and refer to the latter subsystem as Safe.
Although FEPs are site-specific, an example list is presented in Table 2.1.
Endpoint: refers to the functional subsystem where the leaked CO2 finally reaches. Endpoint
can be further decomposed into a list of subsystems, which we limit to three: FrW, O&G, and
Other. FrW refers to all subsurface aquifers containing freshwater. O&G refers to all geologic
formations containing oil or gas resources. For simplicity, freshwater, oil, and gas are assumed
to be the only human-valuable subsurface assets. Accordingly, Other includes all geologic
FEP 1 FEP 2 FEP 3 … FEP 8
FrW
Safe
O&G Other
Direction
of CO2
Leakage
Endpoint
Pathway
Origin
CHAPTER 2 — Updating the Risk Assessment Matrix 36
formations that trap the leaked CO2 yet are not classified as freshwater aquifers or oil and gas
reservoirs.
Table 2.1: Examples of Origin FEPs and their corresponding Indicators
Origin FEP Symbol
{𝑂} Indicator
Symbol
(𝑖)
Caprock high-permeability zone 𝑂1 permeability α
Caprock-absent zone 𝑂2 size of the opening λ
Caprock fracture due to over-pressurization 𝑂3 size of fracture β
Exceeding capillary pressure due to
over-pressurization 𝑂4 capillary pressure δ
Natural fault or fracture 𝑂5 size of fracture β
Induced fault or fracture due to
over-pressurization 𝑂6 size of fracture β
Induced fault or fracture due to CO2
geochemical reactions 𝑂7 size of fracture β
Induced fault or fracture due to seismic activity 𝑂8 Size of fracture β
Pathway: refers to the functional subsystem between the Origin and the Endpoint. Physically,
this area encompasses all subsurface formations through which CO2 migrates after leaving an
Origin formation until reaching an Endpoint formation.
3.2 Bayesian Event Tree for Risk Analysis
The Bayesian Event Tree (BET) is an effective way to track the likelihood and consequences
of the various scenarios of CO2 leakage. A BET models the likelihood of CO2 leakage through
three sequential and uncertain events: Origination, Propagation, and Destination. As we
explain shortly, these events govern the progression of CO2 leakage through the
aforementioned Origin, Pathway, and Endpoint subsystems. Subsequently, for every leakage
prospect, the BET allows modeling the leakage consequences using various value models; we
introduce two: Value of Flow (VF) and Value of Impact (VI). An example BET is shown in
Figure 2.3, followed by a detailed description of its various components and the procedure to
construct it. Important to note, the depicted BET and all related figures are purely
hypothetical; they aim to demonstrate the concepts outlined here and provide a roadmap for
implementing them.
CHAPTER 2 — Updating the Risk Assessment Matrix 37
3.2.1. Probability of CO2 Leakage
For a leakage to occur, three uncertain events must take place sequentially. As explained
below, each event is assigned a probability, and the overall likelihood of a leakage scenario is
the product of those probabilities.
Origination {𝑶}(𝒊): refers to the probability of the existence of a specific Origin, which could
be an FEP or Safe. For an FEP, this likelihood may vary with the subsystem’s exact
characteristics. Therefore, {𝑂} for an FEP is expressed a function of an Indicator 𝑖, which is a
selected attribute of the analyzed FEP. Indicator attributes should be chosen to best-match
their FEP subsystems. Table 2.1 presents a suggested attribute for each of the listed FEP. For
instance, {𝑂1}(𝛼) is the probability of existence of a caprock high-permeability zone 𝑂1 and
is a function of permeability 𝛼. In mathematical terms, Origination {𝑂} can be represented as
a step-wise function of Indicator 𝑖, which is discretized over its total feasible range.
Propagation {𝐏|𝑶}(𝒊): refers to the probability of CO2 entering the Pathway from a specific
Origin, given that this Origin actually exists. Propagation is conditioned on Origination, so
{P|𝑂} can be also represented as a step-wise function over the full discretized range of
Indicator 𝑖. By definition, {P|𝑆𝑎𝑓𝑒} must be always zero. Propagation may be considered a
pinch-point, the point in the analysis at which it doesn’t matter – for subsequent analysis –
how the system reached its current state but how it proceeds from that state [54, 55]. In this
case, if Propagation is positive, CO2 may escape from the Origin to the Pathway. Subsequent
analysis focuses on investigating where the CO2 migrates from the Pathway regardless of how
it reached the Pathway.
Destination {𝑫|𝑶, 𝑷}(𝒊): refers to the probability of CO2 entering a specific Endpoint from
the Pathway, given that it already reached the Pathway through an existing Origin. Here
again, because Destination is conditioned on Origination and Propagation, {𝐷|𝑂, 𝑃} can be
also represented as a step-wise function over the full discretized range of Indicator 𝑖. Also, by
definition, {𝐷|𝑠𝑎𝑓𝑒} is zero because CO2 cannot reach an Endpoint unless it escapes through
an FEP first. Destination is primarily dependent on hydrogeological factors that govern the
transport of CO2 in the Pathway, including the injection locations and rates, local hydrology,
38
Figure 2.3: Example Bayesian event tree (BET) for risk analysis of CO2 leakage
CHPATER 2 — Updating the Risk Assessment Matrix 39
and geologic configuration. However, consistent with the pinch-point definition of
Propagation, CO2 transport in the Pathway is unlikely to be dependent on the specific type of
FEPs in the Origin. Therefore, one simplifying assumption is to treat Destination as
independent of the Propagation {𝑃|𝑂} and Origination {𝑂}(𝑖). In this case, {𝐷|𝑂, 𝑃}(𝑖) =
{𝐷}, which means that Destination is a constant function of Indicator 𝑖.
Leakage Likelihood {𝑳}(𝒊): for CO2 leakage to occur, the CO2 must find an Origin FEP,
move through the Origin FEP into the Pathway, and then enter into an Endpoint. Therefore,
intuitively, the Leakage Likelihood is the product of Origination, Propagation, and
Destination, as illustrated in (1).
{𝐿}(𝑖) = {𝑃}(𝑖) ∙ {P|𝑂}(𝑖) ∙ {𝐷|𝑂, 𝑃}(𝑖) = {𝑃, 𝑂, 𝐷}(𝑖) (1)
The formulation in (1) provides three important insights. First, if Origination, Propagation, or
Destination is zero, the Leakage Likelihood is also zero, and assessing the uncertainty of
subsequent event(s) becomes unnecessary. Second, because {𝐿} is a function of 𝑖, the
likelihood of a specific leakage scenario from a particular FEP is a function of the
characteristics of that FEP. Finally, the analyzed leakage scenarios must be mutually
exclusive and collectively exhaustive. This means that exactly one of the BET scenarios must
occur, and the probability of all scenarios must add up to one. In fact, due to conditional
probability assessment, the branch probabilities at each node of the tree should also sum up to
one. To that end, we note that a leakage scenario need not involve a single Origin and a single
Endpoint. Site-specific data may suggest a leakage incident that occurs through multiple FEPs
and reaches multiple Endpoints, in which case this leakage incident should be presented as a
separate scenario. Such approach ensures that all foreseeable leakage scenarios are accounted
for; specifically, it guards against “perfect storms”, where multiple leakage events of very low
likelihood occur all at once and cause a collective impact greater than the sum of their
individual impacts.
To demonstrate the PRA methodology above, we analyze a subset of three CO2 leakage
scenarios in Figure 2.3, corresponding to three distinct Origin-Pathway-Endpoint trajectories.
Specifically, we assume CO2 storage in a deep saline aquifer (Safe), and we examine the risk
CHPATER 2 — Updating the Risk Assessment Matrix 40
of leakage from a high-permeability zone (𝑂1) in the reservoir’s shale caprock to a freshwater
aquifer (FrW), an oil reservoir (O&G), and another sealed geologic formation (Other). Figure
2.4 depicts the relevant functional subsystems: Origins (Safe, 𝑂1), Pathway, and Endpoints
(FrW, O&G, Other). Subsequently, Figures 2.5a–d show hypothetical probability distributions
of the sequential leakage events: Origination and Propagation through the FEP, Destination
into FrW, O&G, and Other, as well as the overall Leakage Likelihood. The numerical data is
hypothetical and is provided for illustrative purposes only. In practice, the probability inputs
would be obtained based on expert opinions and/or statistical information generated from site
characterization and reservoir modeling; examples of such probabilistic data for the
representation of CO2 leakage risk already exists in literature [45, 56, 57, 58, 59, 60].
Figure 2.4: Sketch of CO2 leakage through caprock high-permeability zone
Because 𝑂1 and Safe are the only two possible Origins, the probability distribution in
Origination is split between {𝑂1} and {𝑆𝑎𝑓𝑒}. Illustrating Origination as function of
Indicator, Figure 2.5a is a log-log plot that shows the probability of existence of a high-
permeability zone in the caprock {𝑂1} with a permeability of 𝛼. The modelled range of 𝛼 is
comparable to that reported by Wang and Small [57], and Griffith [58], for caprock high-
permeability zones and fractures. As shown in Figure 2.5a, {𝑂1} is discretized over seven
intervals of 𝛼. Assuming a typical shale-seal permeability of 10-4
millidarcy (mD) [58, 61], the
CO2FEP = O1
Pathway
FrW
O&G
Other
Origination
Propagation
Destination
CO2
injection well water well oil well
Safe
CHPATER 2 — Updating the Risk Assessment Matrix 41
permeability of a leakage-inducing FEP can only exceed this value, so {𝑂1}(𝛼 < 10−4) is set
at zero. On the other extreme, we assume that it is highly unlikely to find a caprock zone with
permeability greater than 10 mD, so {𝑂1}(𝛼 > 10) is set at 10-5
. For 𝛼 between 10-4
and 10
mD, {𝑂1} decreases almost exponentially from 0.1 to 10-4
. Subsequently, in this specific
example, the probability of having no high-permeability zone in the caprock becomes
{𝑆𝑎𝑓𝑒} = 1 − [∑ {𝑂1}(𝛼)𝛼 ] ≈ 0.839. Though hypothetical, this assumed probability
distribution for Origination is informed by, and is therefore consistent with, the findings of
select literature that addresses uncertainty in reservoir characterization and modeling; for
instance, the results by Wang et al. allow inferring a similar probability distribution from
measurements of moderate pressure buildup in the storage zone [57].
Figure 2.5: Example probability distributions of CO2 leakage scenarios
Because 𝑂1 is the only possible leakage FEP, CO2 will either leak through it or remain in the
designated storage aquifer Safe. As explained already, by definition, the CO2 cannot propagate
1.E-8
1.E-7
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2
{D|O
1,P
} =
{D}
α (mD)
FrW
O&G
Other
1.E-8
1.E-7
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2
{L}
= {O
1,P
,D}
α (mD)
O1, FrW
O1, O&G
O1, Other
1.E-8
1.E-7
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2
{O1
}
α (mD)
1.E-8
1.E-7
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2
{P|O
1}
α (mD)(a) (b)
(c) (d)
CHPATER 2 — Updating the Risk Assessment Matrix 42
from Safe into Pathway, so {P|𝑆𝑎𝑓𝑒} is zero. Figure 2.5b is a log-log plot of Propagation
{𝑃|𝑂1} as a function of Indicator 𝛼, given that the high-permeability zone 𝑂1 actually exists.
For CO2 to leak through 𝑂1, the CO2 plume should first reach 𝑂1 then move through 𝑂1 into
Pathway. In this case, we assume that the likelihood of CO2 transport through the FEP is very
small below a specific permeability threshold of 𝛼 = 0.1 mD. In reality, this threshold could
correspond to capillary entry pressure; as 𝛼 increases, capillary entry pressure decreases until
it finally drops below the capillary pressure at the base of the caprock, at which point CO2 can
escape through the high-permeability zone in the caprock. Therefore, once 𝛼 exceeds 0.1 mD,
Propagation increases rapidly. Still, at the highest permeability range of 𝛼 > 10 mD,
{𝑃|𝑂1} is set at 0.7. Here, we make a realistic assumption that even though CO2 can escape
through 𝑂1, there is still a probability of 1 − {𝑃|𝑂1} = 0.3 that the CO2 plume may not reach
𝑂1 in the first place.
Figure 2.5c plots Destination as function of Indicator. Consistent with the definition of
Propagation as a pinch-point, Destination is assumed to be independent of Origination {𝑂1}
and Propagation {𝑃|𝑂1}. Therefore, {𝐷|𝑂1, 𝑃} is equal to {𝐷}, which is constant across the
whole feasible range of 𝛼. Informed by related findings in existing literature [56, 62], this
example assumes that the leaked CO2 from the saline aquifer is least likely to travel all the
way up to the shallow freshwater aquifer, so {𝐷 = 𝐹𝑟𝑊} is set at 0.05. It is much more likely
that the CO2 gets trapped at a deeper geologic formation along the way, probably in a
subsequent sealed formation (Other) or perhaps in a nearby oil reservoir. Accordingly,
{𝐷 = 𝑂𝑡ℎ𝑒𝑟} and {𝐷 = 𝑂&𝐺} are set at 0.7 and 0.25, respectively. Here, we assume that the
leaking CO2 may reach exactly one of the three aforementioned Endpoints, so the values of
{𝐷} for FrW, O&G, and Other must add up to 1.
Multiplying each probability distribution function in Figure 2.5c by those in Figures 2.5a and
2.5b results in three Leakage Likelihood profiles as a function of 𝛼, corresponding to the three
distinct leakage trajectories. Figure 2.5d shows a log-log plot of the three {𝐿}(𝛼) profiles. As
can be noticed, leakage seems to be less likely at both very high and very low permeability.
This observation can be attributed to two conflicting factors: low Propagation but high
Origination at low permeability and low Origination but high Propagation at high
CHPATER 2 — Updating the Risk Assessment Matrix 43
permeability. In fact, the leakage probabilities at high permeability {𝐿}(𝛼 > 10) are consistent
with some literature findings for similar leakage events through high-permeability zones and
fractures in the caprock [45, 56].
3.2.2. Value of CO2 Leakage
Value models are functions that aim to quantify the consequences of potential CO2 leakage
incidents. As explained in existing literature, these consequences may be characterized in
different metrics and might span a wide spectrum of social, environmental, economic, and
public-safety issues [62, 56]. In this study, we suggest three value models to complement the
aforementioned probabilistic assessment.
Value of Flow – 𝑽𝑭(𝒊): quantifies the amount of the leaked CO2 into each Endpoint
subsystem, which can be expressed as a mass flux, mass flowrate, or total mass during a
specific period of time. While site-specific, VF is usually correlated to Indicator. This
correlation can be derived from characterizing or simulating fluid-flow in the analyzed
subsurface, regardless of the leakage likelihoods. Because the flow of leaked CO2 is
measurable, VF offers a direct way to quantify the consequences of leakage.
At a particular Endpoint, higher VF signifies more severe consequences of leakage. However,
a leakage of a specific VF may lead to different consequences in different Endpoints.
Therefore, while useful for characterizing the consequences of CO2 leakage at individual
Endpoints, VF cannot be used for consistent comparison of the consequences of leakage
across multiple Endpoints. Important for risk assessment and contingency planning,
performing such comparison requires translating VF into monetary terms, whose significance
is the same across all leakage scenarios; proper valuation renders a U.S. dollar spent on
controlling leakage into FrW equivalent to a U.S. dollar spent on controlling leakage into
O&G. Relying on concepts and tools in decision analysis and natural resources economics, it
is possible to express the various social, environmental, economic, and safety consequences of
CO2 leakage in one monetary metric [63, 64, 65, 66]. To that end, we propose two monetary
value models that quantify the consequences of CO2 leakage in the subsurface and on the
surface.
CHPATER 2 — Updating the Risk Assessment Matrix 44
Value of Damage in the Subsurface – 𝑽𝑫𝒔𝒖𝒃(𝒊): corresponds to the cost of any leakage-
induced damages to the subsurface resources. While directly dependent on VF and therefore
on Indicator, separate 𝑉𝐷𝑠𝑢𝑏 models can be designed for FrW, O&G, and Other, influenced
by regulatory requirements. For FrW, 𝑉𝐷𝑠𝑢𝑏 might be a function of several parameters,
including water pH, hardness, and salination, as well as the concentration of any trace metals
or oil and gas contaminants carried by the leaked CO2 stream [38, 56, 67]. For O&G, 𝑉𝐷𝑠𝑢𝑏
may be a function of the quantity and quality of recovery from producing and future
reservoirs, both of which may deteriorate with CO2 leakage. Finally, since Other subsystems
are assumed to have no valuable assets, their corresponding 𝑉𝐷𝑠𝑢𝑏 may be limited to a non-
compliance penalty imposed by the regulatory agency.
Value of Damage on the Surface – 𝑽𝑫𝒔𝒖𝒓(𝒊): corresponds to the cost of any leakage-induced
damages to the surface resources, including environmental and ecological systems and human
structures, activities, and health [62]. In other words, this model accounts for the costs of any
surface damages or harms caused by diminishing the utility of the subsurface resources.
Intuitively, the higher the dependence of ecological and human systems on underground
natural resources, the higher their vulnerability to CO2 leakage, and thus the higher the 𝑉𝐷𝑠𝑢𝑟.
Similar to 𝑉𝐷𝑠𝑢𝑏, distinct 𝑉𝐷𝑠𝑢𝑟 models can be designed for FrW, O&G, and Other, and all
𝑉𝐷𝑠𝑢𝑟 models remain dependent on VF and thus on Indicator. Examples of factors that can be
accounted for in designing 𝑉𝐷𝑠𝑢𝑟 models include the size of human population, per-capita
annual income, size of agricultural activities, and number of natural habitats and ecological
species that depend on the freshwater aquifers where CO2 might leak [62, 56].
Leakage Value of Impact – 𝑽𝑰(𝒊): corresponds to the sum of 𝑉𝐷𝑠𝑢𝑏 and 𝑉𝐷𝑠𝑢𝑟, which allows
expressing all consequences of CO2 leakage in one monetary metric. Consistent with the
formulation of both damage values, VI is a function of VF and thus Indicator 𝑖, as illustrated
in (2). Intuitively, a higher leakage rate (VF) leads to higher contamination of subsurface
resources (𝑉𝐷𝑠𝑢𝑏) and therefore higher disutility of these resources on the surface (𝑉𝐷𝑠𝑢𝑟). In
addition, to facilitate their representation in a BET (Figure 2.3), all value models are
discretized over the same ranges of Indicator 𝑖 used to discretize the conditional probabilities
of leakage.
CHPATER 2 — Updating the Risk Assessment Matrix 45
𝑉𝐼(𝑖) = 𝑉𝐷𝑠𝑢𝑏(𝑖) + 𝑉𝐷𝑠𝑢𝑟(𝑖) = 𝑉𝐷𝑠𝑢𝑏(𝑉𝐹) + 𝑉𝐷𝑠𝑢𝑟(𝑉𝐹) (2)
To complete the risk analysis for the earlier example of CO2 leakage from a high-permeability
caprock zone 𝑂1, we design hypothetical value models for leakage into each of the three
Destination subsystems: FrW, O&G, and Other. In reality, leakage rates are very project-
specific. In this example, we first assume that VF is best represented as a mass flux, and its
values for FrW, O&G, and Other are very similar, as illustrated in Figure 2.6a. In addition, we
assume that the leaking CO2 stream remains relatively concentrated around the high-
permeability FEP. In accordance with relevant literature findings, VF equals about 10-3
kg/m2.s when the permeability of 𝑂1 is high (𝛼 > 10). To put this number in context, Benson
and Hepple report a comparable estimated flux over a 1000 m2 surface area from a storage
site, which leaks 0.1% of its stored CO2 per year after receiving 1 million tonnes of CO2 per
year over a period of 50 years [46]. Furthermore, assuming single-phase flow through the high
permeability zone, VF is set to be proportional to Indicator 𝛼. For very low values of 𝛼, VF is
in the order of 10-7
kg/m2.s, which falls within the lower range of CO2 leakage fluxes reported
from natural analogues [46, 68].
Figure 2.6: Example value models of CO2 leakage scenarios
Subsequently, the VF models are translated to VI models, which are similarly very project-
specific and therefore difficult to generalize. In our example, VI is expressed in (arbitrary)
monetary units and is dependent on Indicator 𝛼 (and therefore on VF), as shown in Figure
2.6b. We assume a high VI for FrW; the leaked CO2 alters the aquifer’s pH and contaminates
it with trace metals (high 𝑉𝐷𝑠𝑢𝑏), and the aquifer is the primary source of freshwater for a
1.E-3
1.E-2
1.E-1
1.E+0
1.E+1
1.E+2
1.E+3
1.E+4
1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2
VI (
mo
net
ary
valu
e)
α (mD)
O1, FrW
O1, O&G
O1, Other
1.E-10
1.E-9
1.E-8
1.E-7
1.E-6
1.E-5
1.E-4
1.E-3
1.E-2
1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2
VF
(kg/
m2.s
)
α (mD)
O1, FrW
O1, O&G
O1, Other
(a) (b)
CHPATER 2 — Updating the Risk Assessment Matrix 46
large county with a predominantly agricultural economy (high 𝑉𝐷𝑠𝑢𝑏). Figure 2.6b shows four
levels of VI for FrW, simulating the costs of four deterioration levels in water quality –
defined in terms of acidity and trace-metal concentration. One real-life (albeit simplified and
perhaps extreme) interpretation of this trend would be as follows: for 10−4 ≤ 𝛼 ≤ 10−3 mD,
water quality worsens but remains suitable for human and natural use; for 10−3 ≤ 𝛼 ≤ 10−2
mD, water becomes unsafe for drinking; for 10−2 ≤ 𝛼 ≤ 1 mD, water becomes unsafe for all
human use; and for 𝛼 ≥ 1 mD, water becomes unsafe for human, cattle, poultry, agriculture,
and wildlife use. On the other hand, we assume a relatively low VI for O&G; the oil reservoir
is depleting, so the leaked CO2 mildly deteriorates the quality and/or quantity of oil recovery
(low 𝑉𝐷𝑠𝑢𝑏), and oil revenues form a small part of the county’s income (low 𝑉𝐷𝑠𝑢𝑟). Figure
2.6b simulates one example trend for the damage costs associated with CO2 leakage into
O&G: for 10−3 ≤ 𝛼 ≤ 0.1 mD, the oil producer handles the increased flux of leaked CO2 by
progressively adjusting its existing oil extraction techniques and schedule; however, for
𝛼 ≥ 0.1 mD, the large flux of leaked CO2 requires a whole new extraction method, resulting
in a significant increase in operating costs. Furthermore, we assume that the regulatory agency
penalizes the operating party for CO2 leakage into the Other zone. The penalty is fixed, so VI
is independent of VF and Indicator 𝛼. Finally, we note that both VF and VI are discretized
over the same seven intervals of 𝛼 used to discretize leakage probabilities.
3.3 Tolerance Levels for Risk Evaluation
After analyzing the likelihood and impact of all foreseeable leakage scenarios, it is important
to evaluate which of the resulting risk scenarios are insignificant, tolerable, or intolerable.
To that end, maximum and minimum tolerance levels can be identified for the Leakage
Likelihood {𝐿} and the Leakage Value of Impact VI, consistent with existing literature on the
ALARP principle [26]. When {𝐿} is lower than its minimum tolerance level, it is evaluated as
insignificant, and the corresponding leakage risks can be safely ignored. However, when {𝐿} is
higher than its maximum tolerance level, it is evaluated as intolerable, and the corresponding
leakage risks must be mitigated. Similar minimum and maximum tolerance levels can be
determined for VI. Because the monetary metric of VI can consistently characterize all
consequences of leakage, the tolerance levels for VI, like those for {𝐿}, are applicable across
CHPATER 2 — Updating the Risk Assessment Matrix 47
all leakage scenarios. When the likelihood and impact of a leakage scenario are between their
maximum and minimum tolerance levels, the leakage risk is deemed tolerable and is managed
through contingency planning.
Defining effective tolerance levels may prove to be challenging, given the relatively limited
experience in operating large-scale CO2 storage projects for long periods of time. Nonetheless,
such boundaries can still be set by relying on existing experience in similar industries,
primarily oil and gas [69]. Following up on the example of CO2 leakage through a caprock
high-permeability zone, we assume that minimum and maximum tolerance levels for {𝐿}
should be set at 10-7
and 0.1, respectively. Similarly, the minimum and maximum tolerance
levels for VI are set at 10-2
and 10+3
, respectively. While re-emphasizing that all numerical
values are purely hypothetical, one example to rationalize these threshold values would be to
set the monetary unit in million U.S. dollars and to assume an international energy firm
managing the CO2 storage project. In such a world, a VI below $0.01 million may be easily
accommodated within the project’s budget. However, learning from past spill incidents in the
oil and gas industry [70, 71, 72], a VI above $1,000 million might compromise not only the
economic feasibility of the project but also the financial stability of the whole firm.
3.4 Combined Representation of Risk Assessment Elements
The three discussed elements of risk assessment can now be jointly represented in a RAM.
Because the likelihood and impact of leakage are discretized over the same ranges of
Indicator, it is possible to plot all leakage scenarios on a two-dimensional RAM, with VI on
one axis and {𝐿} on the other. The result is a set of risk profiles exhibiting two key
characteristics. First, each risk profile identifies a potential leakage trajectory from a specific
Origin, through the Pathway, and into a specific Endpoint. Second, each data point in the risk
profiles corresponds to a leakage scenario in the BET, with a quantifiable Indication 𝑖,
Leakage Likelihood {𝐿} and Leakage Value of Impact VI. Accordingly, the collective risk
profiles summarize the findings of risk identification and risk analysis. Subsequently, for risk
evaluation, the minimum and maximum tolerance levels for VI and {𝐿} can be plotted on the
RAM, marking clear boundaries for insignificant, tolerable, and intolerable risks. All BET
CHPATER 2 — Updating the Risk Assessment Matrix 48
scenarios can and should be plotted on the RAM except those with a zero probability or
impact of leakage. The risks associated with these scenarios are insignificant by design, so
they can be safely excluded.
Carrying on with our hypothetical example of leakage through a caprock high-permeability
zone, the RAM in Figure 2.7 is a log-log plot of VI versus {𝐿}. The three risk profiles,
corresponding to leakage from the high-permeability zone O1 into FrW, O&G, and Other,
span a range of likelihoods and impacts. The exact {𝐿} and 𝑉𝐼 of a leakage trajectory is
dependent on the permeability 𝛼 of O1. In that regard, the plotted risk profiles exclude the
leakage scenarios corresponding to 𝛼 < 10−4 mD, whose probability is assumed zero. In
addition, applying the tolerance levels for {𝐿} and VI shows that the risks associated with CO2
leakage into O&G and Other are tolerable. However, the impact of CO2 leakage into FrW is
intolerable if the permeability of O1 is 𝛼 > 1 mD, so the associated risks must be mitigated
before proceeding with the project. Equivalently, the likelihood of CO2 leakage into FrW is
insignificant if 𝛼 < 0.1 mD, so the associated risks can be safely ignored.
Figure 2.7: Example risk assessment matrix (RAM) for CO2 leakage.
1.E-3
1.E-2
1.E-1
1.E+0
1.E+1
1.E+2
1.E+3
1.E+4
1.E-8 1.E-7 1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0
VI (
mo
ne
tary
un
its)
{L}
O1, FrW
O1, O&G
O1, Other
0.1 - 1 mD
0.01 - 0.1 mD
0.1 - 1 mD
0.01 - 0.1 mD
Insi
gnif
ican
t
Insignificant
Intolerable
Into
lerable
ImpactMaximum
Tolerance Level
Impact Minimum
Tolerance Level
Likelihood Minimum Tolerance Level
Likelihood MaximumTolerance Level
CHPATER 2 — Updating the Risk Assessment Matrix 49
This PRA approach to RAM offers multiple advantages. Broadly, the techniques used to
identify and analyze leakage risks are flexible and generalizable, so they can be expanded and
customized. For example, if multiple freshwater aquifers or oil reservoirs are observed in the
vicinity of the storage zone, each can be assessed as a separate Endpoint, resulting in multiple
FrW and O&G subsystems. Equivalently, the conditional probability analysis in the BET can
be adjusted to achieve clarity [64]; we briefly discuss four examples of such potential
adjustments.
First, depending on available data, the operator may find it clearer to further decompose
Propagation {𝑃|𝑂} into two conditional probabilities: the probability of the CO2 plume
encountering an existing FEP {𝑃𝑒|𝑂}, and the probability of the CO2 plume flowing along the
FEP after encountering it {𝑃𝑓|𝑂, 𝑃𝑒} [60]. In this case, {𝑂, 𝑃𝑒 , 𝑃𝑓} replaces {𝑂, 𝑃} in the BET
to covey the same information: the likelihood that an FEP Origin exists and that the CO2
plume reaches it then escapes through it. Conversely, in the absence of sufficient data, the
operator might find it difficult to assign distinct probabilities to {𝑂} and {𝑂|𝑃}. In this case,
the operator may directly evaluate the joint probability distribution {𝑂, 𝑃}, instead.
Second, because it may be hard to definitively know the long-term-future impacts of leakage,
the VF for each Endpoint can be translated to three mutually exclusive and collectively
exhaustive VI models: high, medium or low. Assuming Destination is a pinch-point, each VI
model occurs with probability {𝐼} referred to as Implication, so the overall Leakage Likelihood
would be updated to {𝐿} = {𝑂, 𝑃, 𝐷, 𝐼}. In this case, RAM would depict each Origin-Pathway-
Endpoint leakage trajectory as a group of three risk profiles, corresponding to the three
possible (high, medium, and low) VI models.
A third BET expansion may account for external events, features, and processes (EFEP),
which occur outside the boundaries of the defined system yet may influence the prospects of
CO2 leakage within the system [73]. In this case, the BET probabilities can be conditioned on
the occurrence of the EFEP, as illustrated in (3–6). Finally, the operator may also choose to
refine the ranges of Indicator 𝑖 over which the probability and impact values are discretized;
eventually, such refinement yields a more detailed representation of risk profiles in RAM.
CHPATER 2 — Translating the Risk Assessment Matrix to a Contingency Planning Matrix 50
{𝑂}(𝑖) = {𝑂|𝐸𝐹𝐸𝑃}(𝑖) ∙ {𝐸𝐹𝐸𝑃} + {𝑂|𝑁𝑜 𝐸𝐹𝐸𝑃}(𝑖) ∙ (1 − {𝐸𝐹𝐸𝑃}) (3)
{𝑃|𝑂}(𝑖) = {𝑃|𝑂, 𝐸𝐹𝐸𝑃}(𝑖) ∙ {𝐸𝐹𝐸𝑃} + {𝑃|𝑂, 𝑁𝑜 𝐸𝐹𝐸𝑃}(𝑖) ∙ (1 − {𝐸𝐹𝐸𝑃}) (4)
{𝐷} = {𝐷|𝐸𝐹𝐸𝑃} ∙ {𝐸𝐹𝐸𝑃} + {𝐷|𝑁𝑜 𝐸𝐹𝐸𝑃} ∙ (1 − {𝐸𝐹𝐸𝑃}) (5)
{𝐼} = {𝐼|𝐸𝐹𝐸𝑃} ∙ {𝐸𝐹𝐸𝑃} + {𝐼|𝑁𝑜 𝐸𝐹𝐸𝑃} ∙ (1 − {𝐸𝐹𝐸𝑃}) (6)
Beyond flexibility and customization, the Bayesian nature of the event tree helps elicit
probabilities from experts and keep the RAM up-to-date; as new information becomes
available, relevant conditional probabilities can be adjusted. Also, the representation of risk in
the form of profiles instead of points allows a leakage trajectory to span multiple risk levels.
As we explain next, all these advantages facilitate translating a RAM to a CPM and thus
designing an effective contingency plan.
4 Translating the Risk Assessment Matrix to a Contingency
Planning Matrix
Figure 2.8: Translating the risk assessment matrix to a contingency planning matrix
The updated risk assessment matrix (RAM) can now be translated into a contingency planning
matrix (CPM), which allows preparing for and responding to tolerable leakage risks. This
translative procedure, shown in Figure 2.8, renders the proposed CPM an effective tool to
design and demonstrate four essential elements of contingency planning: required resources,
VI
{L}
VI
{L}
Likelihood Minimum Tolerance
Level
Likelihood MaximumTolerance
Level
ImpactMaximumTolerance
Level
Impact MinimumTolerance
Level
Max
imu
mC
on
tin
gen
cy T
hre
sho
ld
Risk Assessment Matrix (RAM)
Contingency Planning Matrix (CPM)
Tier 3
Tier 2
Tier 1
risk profileIn
sign
ific
ant
Insignificant
Intolerable
Into
lerable risk
profile
Min
imu
m C
on
tin
gen
cy T
hre
sho
ld
Minimum Contingency Threshold
Maximum Contingency Threshold
CHPATER 2 — Translating the Risk Assessment Matrix to a Contingency Planning Matrix 51
agreed-upon thresholds, preparedness and response tiers, and administration and collaboration
schemes.
4.1 Transforming Matrix Dimensions
The axes of the CPM should address the two main goals of contingency planning: risk-
preparedness and incident-response. To successfully fulfill both goals, suitable resources must
be available. More likely or more frequent risks require more proximate resources, so the
Leakage Likelihood {𝐿} in risk assessment is best translated to Resource Proximity 𝑅𝑝𝑟𝑜𝑥 in
contingency planning, which accounts for the closeness and accessibility of the required
resources. Equivalently, more impactful risks require a wider variety of resources, so the
Leakage Value of Impact VI in risk assessment is best translated to Resource Variety 𝑅𝑣𝑎𝑟𝑖 in
contingency planning, which accounts for the uniqueness, complexity, and/or specialization of
the required resources. Several metrics can be used to quantify these axes of CPM. For
example, while an inverse-distance metric may quantify 𝑅𝑝𝑟𝑜𝑥, the number of dispatched
incident-response teams may quantify 𝑅𝑣𝑎𝑟𝑖. In this regard, the ranges of 𝑅𝑝𝑟𝑜𝑥 and 𝑅𝑣𝑎𝑟𝑖
need not be continuous or linear; the operator may choose to define and discretize the ranges
of both CPM axes based on the specific conditions and characteristics of the storage project.
For example, the continuous range of tolerable Leakage Likelihood {𝐿} = [10−7, 10−1] in
Figure 2.7 may be translated into five discretized values of 𝑃𝑝𝑟𝑜𝑥 = {< 1 2000⁄ ; 1 2000⁄ −
1 1000⁄ ; 1 1000⁄ − 1 500⁄ ; 1 500⁄ − 1 100⁄ ; > 1 100⁄ } km-1
, corresponding to the inverse
radial distance below which contingency-planning resources should be accessible; larger {L}
is translated into larger 𝑅𝑝𝑟𝑜𝑥 and therefore shorter distance between the resources and the
storage site. Finally, the increase in the overall level of risk – defined as the multiplication of
{𝐿} by VI – is translated to an increase in the overall amount of resources that should be
available to combat leakage. As such, constant risk-level contours are translated into constant
resource-amount contours. Intuitively, contingency planning requires fewer resources for
less likely and/or less impactful risks but more resources for more likely and/or more
impactful risks.
CHPATER 2 — Translating the Risk Assessment Matrix to a Contingency Planning Matrix 52
Ultimately, the translation of RAM axes to CPM axes emphasizes that an effective allocation
of resources for contingency planning shall ensure both timely and thorough preparation and
response, irrespective of whether the addressed leakage scenario is high or low in likelihood or
impact. We further clarify this point by considering two opposing risk scenarios. On one hand,
for a high-impact but low-likelihood leakage risk, the proposed guidelines suggest allocating
more various but less proximate resources. In addition to facilitating a thorough response, the
resources’ high variety can compensate for their low proximity and thus facilitate a timely
response. For example, highly various resources may cover unique logistical expenditures that
accelerate the deployment of specific response equipment (e.g. expedited air shipping) or
teams (e.g. high wages) on short-notice [74], or that boost general response operations (e.g.
high rent of temporary accommodation for relocated communities) [75]. Indeed, because of
the low likelihood, it would be inefficient to make these resources available on or close to the
storage site permanently. On the other hand, for a high-likelihood but low-impact leakage risk,
the proposed guidelines suggest allocating more proximate but less various resources. Here,
the resources’ high proximity can preventively compensate for their low variety and thus
facilitate a thorough, as well as timely, response. For example, learning from analogues in the
oil industry [76], very proximate resources may include on-site devices that enable a rapid –
and if necessary, remote – shutdown of operations (e.g. stopping CO2 injection in case of
over-pressurization), which prevents the need for more complex corrective equipment (e.g.
drilling a relief well). However, if intervention is delayed and pressurization escalates, such
complex resources may become necessary.
4.2 Transforming Matrix Boundaries
Both intolerable and insignificant risks are not presented in the contingency planning matrix.
To that end, the tolerance levels in a risk assessment matrix can be considered contingency
thresholds in the contingency planning matrix. The minimum risk tolerance levels for
likelihood {𝐿} and impact (VI) are translated to minimum contingency thresholds, below
which no contingency planning is required. Equivalently, the maximum tolerance levels for
{𝐿} and VI are translated to maximum contingency thresholds, above which contingency
planning is insufficient and risk mitigation is necessary.
CHPATER 2 — Translating the Risk Assessment Matrix to a Contingency Planning Matrix 53
4.3 Classifying Risk into Tiers
Because not all tolerable risks are equal in likelihood or impact, distinct tiers of risk-
preparedness and incident-response must be defined to address different tolerable risks with
different requirements for resources proximity and variety. This study adopts a three-tier
system for preparedness and response.
4.3.1. Scope of the Three-Tier System
The three-tier system is borrowed from the oil and gas industry where it has been extensively
implemented [35, 77, 78, 79]. Table 2.2 lists three main criteria to properly assign a tolerable
leakage risk to one of the three tiers: the geographic location of the leakage scenario and any
resulting response operations; the governance structure among all parties involved in leakage
preparedness and response; and the ownership, proximity, and variety of available resources.
These tiers are discussed in more detail when presenting a model contingency plan later
(Section 5).
Table 2.2: Selection criteria for the three-tier system
Criteria Tier 1 Tier 2 Tier 3
Geographic
location operation site
local vicinity of the
operation site
regional vicinity of the
operation site
Governance
structure
operating party and
its contractors,
regulatory agency
operating party and
its contractors,
regulatory agency,
local stakeholders
operating party and
its contractors,
regulatory agency,
local stakeholders,
regional stakeholders
Resources
ownership,
proximity,
and variety
owned by the operating
party and its direct
contractors
least unique, complex,
and
specialized
trade-off: more proximate
but less various resources
owned by the operating
party, its direct
contractors,
and local stakeholders
moderately unique,
complex, and specialized
owned by the operating
party,
its direct contractors,
local stakeholders,
and regional stakeholders
most unique, complex, and
specialized
trade-off: more various but
less proximate resources
CHPATER 2 — Translating the Risk Assessment Matrix to a Contingency Planning Matrix 54
According to these criteria, Tier 1 is under the direct jurisdiction of the party operating the
storage site and its contractors, and it addresses onsite risks that can be handled through
standard and generic resources of relatively low complexity and specialization. Tier 2 expands
the scope of covered risks to include those that might affect local communities around the
operation site, might require the support and intervention of local governmental authorities
and public-safety departments, or might necessitate the deployment of more complex or
specialized resources. Finally, Tier 3 includes the most risky leakage scenarios whose effects
might expand to the regional level, requiring the support and intervention of regional
authorities, or necessitating the deployment of extensive, highly complex, or highly
specialized resources. In this regard, “regional” in this analysis may refer to district-level,
national-level, or multinational-level geographic zones; the exact definition of “regional”
depends on the scale and conditions of the CO2 storage reservoir and is thus project-specific.
4.3.2. Representation of the Three-Tier System
As can be noticed in Figure 2.8, the three contingency planning tiers cover all tolerable risks.
Tier 1 prepares for risks and responds to incidents that require the smallest 𝑅𝑣𝑎𝑟𝑖 while Tier 3
prepares for risks and responds to incidents that require the largest 𝑅𝑣𝑎𝑟𝑖.
The range of 𝑅𝑣𝑎𝑟𝑖 covered by Tier 1 shrinks as 𝑅𝑝𝑟𝑜𝑥 increases. Tier 1 is primarily
administered by the operating party, which, naturally, tends to concentrate its relevant
resources close to the storage site that it directly manages. Because of space and logistical
constrains, the resources available under this tier tend to be relatively limited in their scope
and variety. Accordingly, as shown in Figure 2.9, Tier 1 covers more proximate but less
various resources relative to constant resource-amount contours. In other words, the closer the
required resources need to be located to effectively address a leakage, the less complex and
specialized they should be to remain covered under Tier 1. However, if the resources need to
be more complex and specialized in addition to being nearby, Tier 1 may not be sufficient, in
which case the leakage should be covered under Tier 2 by bringing onboard further resources
from local stakeholders and communities.
CHPATER 2 — Translating the Risk Assessment Matrix to a Contingency Planning Matrix 55
Figure 2.9: Tier system tradeoff between resource proximity and resource diversity
The opposite argument holds for Tier 3. The range of 𝑅𝑣𝑎𝑟𝑖 covered by Tier 3 shrinks as 𝑅𝑝𝑟𝑜𝑥
decreases. Since Tier 3 requires the engagement of multiple parties within a relatively large
geographical area, the scope of resources available for this tier is relatively large. Accordingly,
Tier 3 covers more various but less proximate resources relative to constant resource-amount
contours. In other words, the farther the required resources can be located to effectively
address a leakage, the more complex and specialized they should be to remain covered under
Tier 3. However, if the required resources can be less complex and specialized in addition to
being distant, Tier 3 may not be necessary, in which case the leakage should be covered under
Tier 2.
Another implication of the proposed tier system and resulting contingency planning matrix
(CPM) is the ability to address one leakage profile at multiple tiers. Knowing the measure of
the geologic Indicator associated with each leakage scenario allows determining its likelihood
and impact-value, which in turn allow determining the proper proximity, variety, and amount
of resources required for effective preparedness and response. Consequently, as illustrated in
Figure 2.9, a risk profile (corresponding to a leakage trajectory) can be covered under Tier 1
for relatively low likelihood and impact or under Tier 3 for relatively high likelihood and
impact.
VI
{L}
Maximum Contingency Threshold
Tier 3
Tier 2
Tier 1
risk profile
lower variety
higher proximity
Min
imu
m C
on
tin
gen
cy T
hre
sho
ld
Minimum Contingency Threshold
Max
imu
mC
on
tin
gen
cy T
hre
sho
ldlower proximity
higher variety
CHPATER 2 — Translating the Risk Assessment Matrix to a Contingency Planning Matrix 56
The boundaries between the three tiers can be thought of as additional contingency thresholds,
which necessitate shifting from one strategy of risk-preparedness and incident-response to the
other. Thus, besides the maximum and minimum thresholds identified earlier, contingency
planning requires defining two tier thresholds: Tier 1-2 threshold determines the boundary
between Tier 1 and Tier 2, and Tier 2-3 threshold determines the boundary between Tier 2 and
Tier 3. Important to note, however, the intra-boundaries between the three tiers are not set at
or dictated by constant resource-amount contours due to the trade-offs highlighted earlier.
Appendix A provides further explanation on how the categorization of risk according to
constant-risk contours may cause nontrivial pitfalls in contingency planning.
4.3.3. Negotiating Contingency Thresholds
When setting contingency thresholds, the operating party is usually guided by several
considerations, including: external regulations and standards, internal safety culture and
resource capabilities, compliance with the terms and conditions of insurance policies, and
accommodation of the interests of communities affected by the CO2 storage project. To that
end, the exact specification of minimum, maximum, and tier thresholds are usually negotiated
through a collaborative effort between the operating party and multiple stakeholders.
To start, although formal minimum and maximum contingency thresholds may be dictated by
regulations or industrial standards, their implementation is usually shaped by the
administrative procedures and protocols of the legally liable party managing the CO2 storage
site. To that end, the actual enforcement of these thresholds requires clear and effective
communication. The operating party has to demonstrate its ability to reduce intolerable risks
below mandated maximum contingency thresholds through insurance, safety measures, and
system reinforcement. If the operating party fails to demonstrate such capability, the
regulatory agency may not permit the project. Alternatively, the operating party may find it
beneficial to adopt stricter thresholds than those dictated by regulations. For example,
insurance rates may be lower if the project deploys more frequent monitoring or more accurate
measurement tools than what is legally required. In this case, the adopted minimum and
maximum thresholds would depend on the operating party’s safety culture and resource
CHPATER 2 — A Model Contingency Plan 57
capabilities: trading more aggressive risk mitigation for less aggressive contingency planning,
or vice versa. The regulatory agency would still need to be consulted on such trade-offs.
Equivalently, local, national, or international laws influence how the operating party sets the
boundaries between the three contingency tiers. For example, the operating party may be
legally required to notify local authorities about small leakage incidents while giving regional
authorities the right to unilaterally and directly intervene in the case of large leakage incidents
[21]. In this case, the regulatory agency would argue for keeping small leakage incidents
within Tier 1 while necessitating Tier 2 (and potentially Tier 3) for large leakage incidents. In
addition, the operating party may be legally required to engage with several stakeholders on
the CO2 storage project, including local communities and their emergency-response
departments. Those relationships shape the operating party’s own preferences on how to
categorize risks into different tiers. For instance, a small company might operate and manage a
CO2 storage site within a county that has a large pool of publically funded resources for
contingency planning. In this case, to minimize costs, the operating party would be inclined to
allocate fewer risks under Tier 1 and more risks under Tier 2 and Tier 3. Alternatively, the
operating company might already have a large inventory of emergency-response equipment,
guided by its established safety procedures and long history of international operations. In this
case, to maximize operational and decision-making autonomy, the operating party would be
inclined to allocate more risks under Tier 1 and fewer risks under Tier 2 and Tier 3.
5 A Model Contingency Plan
The proposed RAM and CPM are essential building-blocks in the construction of an effective
and comprehensive contingency plan. To demonstrate their role, we present an overview of
the basic elements of a model contingency plan for CO2 leakage through geologic pathways,
illustrated in the exhibit “Outline of a Model Contingency Plan.” Although the model plan
includes four major sections, we devote our attention to the design of the contingency tiers in
the third section, where the various elements of RAM and CPM are mostly relevant.
Accordingly, while this paper proceeds with a detailed discussion of the elements of the
CHPATER 2 — A Model Contingency Plan 58
contingency tiers in the proposed model contingency plan, a brief description of the remaining
three major sections of the plan is included in the referenced exhibit.
5.1 Tiers of Risk-Preparedness and Incident-Response
5.1.1. Thresholds
As explained in the derivation of the proposed CPM, a total of six thresholds should be
identified in a contingency plan: two minimum contingency thresholds corresponding to
minimum tolerance levels of risk likelihood and impact; two maximum contingency
thresholds corresponding to maximum tolerance levels of risk likelihood and impact; Tier 1-2
threshold bordering between Tier 1 and Tier 2; and Tier 2-3 threshold bordering between Tier
2 and Tier 3.
5.1.2. Leakage Evaluation
Two types of leakage assessment frameworks are important to establish: one for risk-
preparedness and one for incident-response. Each framework should include a checklist to
characterize the leakage and categorize it under one of the three contingency tiers.
Risk-Preparedness: in order to adequately prepare for risk, each leakage scenario should be
evaluated through a checklist that identifies its: 1) Indicator, Origin, Pathway, and Endpoint;
2) Leakage Likelihood {𝐿}; and 3) consequences quantified through a predicted Leakage Value
of Impact VI. As explained earlier and illustrated in Figure 2.8, {𝐿} and VI in RAM are
translated to 𝑅𝑝𝑟𝑜𝑥 and 𝑅𝑣𝑎𝑟𝑖 in the CPM, respectively. Then, using the CPM, the adequate
tier to prepare for this prospective leakage scenario is specified at the intersection of the
obtained 𝑅𝑝𝑟𝑜𝑥 or 𝑅𝑣𝑎𝑟𝑖 with the corresponding risk profile, as we demonstrate in Figures
2.10a and 2.10b, respectively. Ultimately, the extent of risks covered under each contingency
planning tier influences the amount, type, and location of resources that should be assigned to
that tier.
CHPATER 2 — A Model Contingency Plan 59
Incident-Response: an effective response to a detected CO2 leakage requires a careful yet
prompt evaluation of the leakage consequences. Therefore, the response checklist for a
leakage incident should identify its: 1) Indicator, Origin, Pathway, and Endpoint; and 2)
consequences measured in any feasible form, including Value of Flow 𝑉𝐹, Value of Damage
in Subsurface 𝑉𝐷𝑠𝑢𝑏, Value of Damage on Surface 𝑉𝐷𝑠𝑢𝑟, or Leakage Value of Impact VI. If
VI is not the quickest or most practical way to directly measure the leakage consequences,
5/4/2016 New England Energy System Case Study
7
Directory
Introduction
Tiers of Risk-Preparedness and Incident-Response
Documentation
This section defines the purpose, scope, and relevance of the contingency plan [33]. This section should also introduce the party in-charge of designing and
updating the contingency plan document; such party may be the site-operating firm, a specific team within that firm, or a contracted team by that firm.
• ScopeA comprehensive contingency plan should cover risks associated with surface (e.g. well blowouts) and subsurface releases, through both man-made and
geologic pathways. Accordingly, in this analysis of subsurface leakage through geologic pathways only, this section should list: all possible Origins, Endpoints,
and Pathways, the surface location of Origins; and the location of major human structures (e.g. cities) and ecosystems (e.g. vulnerable habitats) at and in the
vicinity of the storage site. The use of terrestrial maps is important.
• Purpose and ObjectiveThis section defines the roles of the staff members and contractors and the procedures they should follow to prepare for risks and respond to incidents of CO2
leakage from [name] geologic storage reservoir through, in this case, geologic pathways. This section should also outline the objectives of the contingency plan,
which may include: ensuring that preparedness and response are consistent with industrial practices and in compliance with regulatory standards; ensuring a full
and effective integration and utilization of industry and government resources when needed; and prioritizing corrective-actions.
• PrioritiesThis section summarizes the main priorities of the contingency plan, which may include: securing human safety during incident-response; minimizing the
impact of leakage on human health the environment; minimizing the damage to equipment and assets used in incident-response; minimizing the likelihood of
leakage through adequate management of resources; or minimizing disruption to CO2 storage activities.
• Legal and Regulatory ComplianceThis section enlists all relevant governmental requirements, regulations, and laws; industrial standards and protocols; as well as international laws and treaties
with which the contingency plan complies. This section may also include a list of the required reporting to external stakeholders if a leakage incident occurs.
• Plan IntegrationThis section enlists other contingency plans and safety protocols by relevant internal and external stakeholders that complement the contingency plan of
concern, including: health, safety, and environment (HS&E) policies, standards, and guidelines enforced at the storage site by the operating party or its
contractors; governmental plans covering emergency response and relief (e.g. city or county emergency response plans); and industrial plans governing private
service centers for emergency response and relief (e.g. Clean Caribbean and Americas [85], Oil Spill Response and East Asia Response Limited [86]).
A directory is the first section any holder of the contingency plan should have access to in order to reach all decision-making stakeholders. The directory lists
the contact information of people that are directly involved in risk-preparedness and incident-response, including personnel from the operating company,
contractors, regulatory agency, local and regional governmental authorities, and community representatives.
• Thresholds
• Leakage Evaluation
• Response Initiation
• Response Strategies
• General Operations
• Specific Operations: Corrective Measures
• Human and Equipment Resources
• Administration and Coordination
The contingency plan should be a living document, updated as the project progresses from planning operation, and periodically thereafter as more is learned
about the performance of the storage site. To that end, the information included in the contingency plan should be reviewed regularly to incorporate any
changes in risk assessment methods, tier-based preparedness and response procedures, resources inventories and allocation, training and maintenance schedules,
or personnel directory. The operating party should maintain a detailed record of previous leakage incidents, response measures, best practices, and lessons
learned, and it should update the incident-response procedures based on the new information gained from those incidents. In addition, the operating party is
responsible for making the contingency plan available to all relevant internal departments and external stakeholders.
Outline of a Model Contingency Plan
CHPATER 2 — A Model Contingency Plan 60
other value models 𝑉𝐹, 𝑉𝐷𝑠𝑢𝑏, 𝑉𝐷𝑠𝑢𝑟 may be used as proxy. Then, using a customized form
of (2) and the guidelines presented in Section 3.2.2, the measured consequences can be
translated to VI, which in turn can then be translated to 𝑅𝑣𝑎𝑟𝑖. Subsequently, using the CPM,
the adequate tier to respond to this leakage incident is specified at the intersection of the
obtained 𝑅𝑣𝑎𝑟𝑖 with the corresponding risk profile, as shown in Figure 2.10b. In this case, we
note that the 𝑅𝑝𝑟𝑜𝑥 axis – derived from the likelihood {𝐿} – plays no role in choosing the
contingency tier; it is maintained in Figure 2.10b for the sole purpose of properly plotting the
risk profiles.
Figure 2.10: Tier allocation procedure for risk-preparedness and incident-response
The leakage characterization checklist for incident-response is different from that for risk-
preparedness. First, Leakage Likelihood is not considered in incident-response because the
leak has already occurred. Second, because leakage is detectable in incident-response, its
consequences can be measured rather than predicted, which should result in a more accurate
characterization.
5.1.3. Response Initiation
The transition from risk-preparedness to incident-response commences upon the identification
of a measurement that exceeds a trigger value. A trigger is best described as an observation
that renders VI above its preset minimum tolerance level. Unlike in the case of risk-
preparedness where VI is predicted yet is still uncertain, a trigger observation renders VI above
VI
{L}
Tier 3
Tier 2
Tier 1
risk profile
VI
{L}
Tier 3
Tier 2
Tier 1
risk profile
(a) (b)
This leakage scenario is allocated under Tier 2
This leakage scenario is allocated under Tier 2
CHPATER 2 — A Model Contingency Plan 61
its minimum tolerance level with certainty, which in turn means that the minimum
contingency threshold has been exceeded – and a response procedure must be initiated – also
with certainty. To that end, triggers may be manifested as an irregularity in a wide range of
measurable data; examples of triggers include: excessive pressure-buildup in Safe, high level
of pH or trace metals in a FrW, or high concentration of dissolved CO2 in the oil recovered
from an O&G. In addition, the causes of a trigger may be an FEP from within the analyzed
system (e.g. geochemical erosion of the caprock) or an EFEP from outside the analyzed
system (e.g. new hydrocarbons’ drilling activities in the vicinity of the storage site or a large
earthquake in the vicinity of the storage project).
Whether identified through regular or special monitoring or inspection, and regardless of the
instrumentation or methodology used, once a trigger is identified, a response procedure should
be initiated to detect then control or remediate leakage. Because leakage detection through
trigger identification is the first step in incident-response, contingency plans should specify an
extensive list of triggers. To that end, similar to contingency thresholds, response triggers
should be selected by mutual agreement between the operator, regulatory agencies, and other
appropriate stakeholders. The ability to respond quickly and decisively to abnormal events is
one of the primary benefits of pre-negotiating these triggers.
5.1.4. Response Strategies
For each type of leakage event, a pre-planned course of action should be developed,
depending on which tier it falls under. The response strategy should include two types of
actions: general operations and specific operations. A summary Table of both operation types
is presented in Appendix B.
5.1.4.1. General Operations
Because the general operations are applicable to all leakage incidents, they should be designed
and deployed in a way that reflects the priorities identified in the contingency plan. Most
notably, the safety of all personnel responding to leakage incidents should be secured; in this
case, the safety of the responding teams to subsurface leaks through geologic pathways may
CHPATER 2 — A Model Contingency Plan 62
be jeopardized due to either leakage causes (e.g. big earthquakes) or leakage consequences
(e.g. contaminated drinking water). In addition, general response operations should focus on
recovering normal CO2 storage activities as soon as possible.
The responding teams should have a clear action-plan on how to mobilize and deploy
resources. This becomes especially important in Tier 2 and Tier 3 where some required
resources are not owned by the operating party but rather managed and deployed by external
stakeholders (e.g. municipal or state public-safety teams). To that end, Tiers 2 and 3 should
fulfill two additional goals through general operations. First, each local and regional
stakeholder should be assigned a clear responsibility zone to prevent conflicting decisions and
delays in execution. Second, because leakage may impact local and regional populations, the
operating party should be ready to provide supplementary support and services beyond its
typical business. Examples of such services may include: security, evacuation,
accommodation, transportation, and medical supervision for relocated communities; catering
services for both the response teams and the affected communities; and financial
compensation for damages or harms caused to nearby businesses or institutes.
5.1.4.2. Specific Operations: Corrective Measures
Specific response operations involve choosing proper corrective measures to control or
remediate leakage. Several corrective measures have been proposed in literature [31, 38, 46,
48, 80], an example list of which is presented in Table 2.3. As shown, we envision four
primary criteria affecting the feasibility and effectiveness of each corrective measure:
objective, target formation, scale of deployment, and cost of deployment. First, it is important
to identify whether the goal of the corrective action is to control (stop or contain) the leakage
or to remediate its impacts. Second, given the specifics of the leakage trajectory and
subsurface configuration, a corrective action may be carried out at the Origin of the leak, on
the transport Pathway, or at the Endpoint (e.g. a freshwater aquifer). Third, some corrective
measures are best applied only in a particular location of the subsurface formation whereas
others could be applied at multiple locations throughout the subsurface. Finally, depending on
the chosen technique, different corrective measures require different monetary investments
63
Table 2.3: Example corrective measures for incident-response [31, 38, 46, 48, 80]
Corrective Actions Objective Target
Formation
Scale of
Deployment Deployment Components Index
Reduce CO2 injection rate to reduce
pressure-buildup control Origin particular location existing wells A
Stop CO2 injection to reduce
pressure-buildup control Origin particular location existing wells B
Partially extract CO2 from the storage
reservoir to reduce pressure-buildup control Origin
particular location;
multiple locations
existing wells; new wells;
pumps C
Extract CO2 at leakage point control Origin particular location new wells; pumps D
Extract water from the storage reservoir to
reduce pressure-buildup control Origin
particular location;
multiple locations
existing wells; new wells;
pumps; water treatment E
Inject water in upper formations of the storage
reservoir as a hydraulic barrier control Pathway multiple locations
existing wells; new wells;
pumps F
Inject water to dissolve the leaking CO2 control Pathway particular location existing wells; new wells;
pumps G
Inject sealing material at leakage point or
pathway (e.g. cement, gels, polymers) control
Origin,
Pathway particular location new wells; pumps; sealants H
Extract CO2 from storage reservoir and re-inject
it into another reservoir remediate Origin
particular location;
multiple locations
existing wells; new wells;
pumps I
Extract contaminated freshwater, treat,
then re-inject remediate
Endpoint
(FrW)
particular location;
multiple locations
existing wells; new wells;
pumps; water treatment J
Treat freshwater in the subsurface
(e.g. inject microbes to restore pH) remediate
Endpoint
(FrW) particular location
existing wells; new wells;
chemicals or
microorganisms
K
Extract oil or gas, treat, then use remediate Endpoint
(O&G)
particular location;
multiple locations
existing wells; new wells;
pumps; separators L
Inject water to enhance recovery remediate Endpoint
(O&G) particular location
existing wells; new wells;
pumps; water treatment M
CHAPTER 2 — A Model Contingency Plan 64
and time commitments to install and operate wells, pumps, separators, or other water-
treatment systems.
After identifying a list of feasible and effective corrective measures, the contingency plan
should include a corrective measures matrix (CMM) that matches each leakage risk profile
(incorporating a group of leakage scenarios of the same Origin-Pathway-Endpoint trajectory)
with the best corrective-action techniques under each contingency tier. Although no extensive
data currently exists on the best corrective measures for each risk profile, a template of the
proposed CMM is presented in Table 2.4; the matrix is filled-in for illustrative purposes only.
As shown, more than one corrective technique can be assigned to each risk profile, and the
methods should be listed in order of priority.
Populating the CMM is dictated not only by the technical effectiveness of the corrective
measures but also by the economic feasibility of deploying them. To that end, the right
portfolio of corrective measures for each risk profile under each tier should balance between
the cost of corrective measures and their benefits, expressed in terms of the “avoided damage”
that would have occurred otherwise due to leakage. In other words, such cost-benefit analysis
compares the VI of a particular leakage scenario to the cost of the corrective measures
controlling or remediating it, and it is a common approach in managing risks that may widely
impact human and natural ecosystems [81, 82]. Ultimately, designing such a CMM before
leakage incidents occur is crucial for ensuring a rapid response to the leakage incidents when
they occur.
Table 2.4: Example corrective measures matrix (CMM) for incident-response
Corrective Measure Tier 1 Tier 2 Tier 3
Risk profile 1 A, E B, E B, E, C
Risk profile 2 A, E, K B, E, K B, E, J
… … … …
Risk profile 9 B B, D B, D, M
CHAPTER 2 — A Model Contingency Plan 65
5.1.5. Human and Equipment Resources
In addition to distinguishing between resources proximity and variety, which is captured in the
CPM, the contingency plan should make a clear distinction between human and equipment
resources. Appendix B presents a summary Table for categorizing resources accordingly.
Consistent with the type of response strategies defined earlier, human resources should be
classified into general- and specialized-response teams. In addition, a detailed inventory
should be developed and maintained by the operating party for all internal and contracted
incident-response personnel. Such inventory should identify the name, job title, team
membership, and contact information for each internal personnel, as well as the formal
affiliation for contracted service-providers. For incident-response activities under Tier 2 and
Tier 3, the inventory should also identify which personnel should act as liaison with external
local or regional response teams (e.g. police, firefighters, industrial response centers) and
communities (e.g. residents, schools).
Similar to human resources, the contingency plan should include a detailed inventory of
equipment resources – both general and specialized – as well as a detailed timeline for their
mobilization. In the case of Tier 1, all equipment is owned by the operating party or its
contractors. However, for Tier 2 and Tier 3, the inventory should specify the source of
equipment deployed by external local or regional stakeholders.
Finally, integral to securing effective response is human training and equipment maintenance.
In addition to initial training, responding personnel should undergo regular refresher sessions
in order to update their knowledge and skills as the project progresses. In fact, beyond Tier 1,
joint drills with external (local and regional) parties become necessary [34]. Equivalently,
equipment stockpiles used for safety as well as for leakage analysis, monitoring, control, and
remediation should undergo periodical inspection and testing to ensure proper functionality.
5.1.6. Administration and Coordination
Effective administration of the tier-based contingency planning is key to secure proper
implementation, communication, and accountability. Establishing an administrative
CHAPTER 2 — A Model Contingency Plan 66
framework for each tier involves identifying a clear hierarchy for decision-making, a
notification protocol to report leakage incidents, and a communication-flow scheme to keep all
relevant parties informed and updated. While the decision hierarchy and communication
scheme are needed for both risk-preparedness and incident-response, the notification protocol
is only relevant if a leakage incident occurs.
Figure 2.11: Example decision-making hierarchy of the operating party for contingency
planning
As shown in Figure 2.11, the decision-making hierarchy within the operating party reflects the
priorities of the contingency plan, expressed earlier in Section 5.1.3. For Tier 1, the primary
decision makers are the onsite operators. The decisions should first secure the safety of
operating personnel during risk-preparedness and incident-response, which is under the broad
supervision of the HS&E team and site management. In addition, securing effective incident-
response requires the presence of skilled and knowledgeable reservoir engineers and modelers
who can refine and update preset corrective-action plans when necessary. Coordinating the
logistics of resources’ mobilization and deployment is also critical. Tiers 2 and 3 require the
deployment of further resources as well as dealing with local and regional stakeholders. To
Tier 3
Tier 2
Tier 1
HeadquartersExecutive Committee
President/CEOVice President for HS&E
Regional Operations CenterRegional Chairman
Vice President for HS&EFinance Member
Legal MemberInformation Coordinator
Local Operations CenterSite Operations Director
Site HS&E Team LeadMaterial/Logistics Coordinator
Finance MemberLegal Member
Information Coordinator
Storage SiteSite Manager on-dutyHS&E Team on-duty
Reservoir Engineering TeamReservoir Modeling Team
Field OperatorsMaterial/Logistics Coordinator
CHAPTER 2 — A Model Contingency Plan 67
that end, additional administrative support and the involvement of more executive decision-
makers become necessary.
Figure 2.12 shows an example notification protocol that may be followed by the operating
party to report leakage to all relevant parties. One aspect to note is that each notification step
should have a clearly defined timeframe. Internal corporate policies might dictate the
timeframe of internal notifications whereas applied regulations and/or agreements might
determine the notification periods for external stakeholders. Developing this notification
procedure and the aforementioned decision-making hierarchy allows all parties to engage in
an organized communication flow, which can be summarized in the example communication
scheme illustrated in Figure 2.13.
Figure 2.12: Example notification protocol of the operating party for incident-response
Equally important is coordination and collaboration among all parties involved in the
contingency plan in order to maximize efficiency and minimize mistakes and costs. We have
already introduced two venues for collaboration in contingency planning: the negotiations
between the operating party and the regulatory agency on setting the contingency thresholds
and response triggers, as well as the joint training exercises among all response teams. An
additional example of collaboration is illustrated in Figure 2.14, showing multiple cooperative
pathways to pool resources for Tier 2 and Tier 3.
Leakage Detection & Evaluation
notify Field
Operator
notify onsite HS&E and Site Manager
exceed minimum contingency threshold?
resolve onsite
No
Yes
larger than Tier 1-2
threshold?
initiate Tier 1 response
No
notify Regulatory
Agency
Yes
initiate Tier 2 response
notify Local Operations
Center
notify local stakeholders
larger than Tier 2-3
threshold?
Initiate Tier 3 response
notify Local Operations
Centers
NoYes
notify Regional Operations
Centers
notify Regulatory
Agency
notify Regulatory
Agency
Notify local stakeholders
notify regional stakeholders
notify Headquarters
CHAPTER 2 — A Model Contingency Plan 68
Figure 2.13: Example communication scheme for contingency planning
Figure 2.14: Collaborative approach to securing resources for Tiers 2 and 3
Under Tier 1, coordination is relatively easy, for most dispatched experts and equipment for
leakage preparedness and response are managed directly by the operating party or its
contractors. However, under Tiers 2 or 3, the operating party’s internal and contracted teams
need to further coordinate with local and regional partners. In this case, different parties might
ContractorsExternal Stakeholders
Regional CenterRegional Chairman
Vice President for HS&EFinance Member
Legal MemberInformation Coordinator
Local Operations CenterSite Operations Director
Site HS&E Team LeadMaterial/Logistics Coordinator
Finance MemberLegal Member
Information Coordinator
Administrative Supportexamples: human resources;
media; legal services
Operational Supportexamples: preparation and
deployment of resources; staff training and equipment
inspection; monitoring and detection of leakage;
implementation of general and specific response strategies
Local Stakeholdersexamples: governmental
authorities, public safety services (e.g. police and firefighting);
sensitive neighboring communities (e.g. schools, hospitals, prisons); other
neighboring communities (e.g. residences and businesses)
Regional Stakeholdersexamples: governmental
authorities; public safety services (e.g. police and firefighting,
military)
Regulatory Agency
Storage SiteSite Manager on-dutyHS&E Team on-duty
Reservoir Engineering TeamReservoir Modeling Team
Field OperatorsMaterial/Logistics Coordinator
HeadquartersExecutive Committee
President/CEOVice President for HS&E
Operating Party
• Joint Tier 1 resources of multiple operators in industry
• Joint Tier 1 resources of multiple local public-safety teams
• Specialized Tier 2 resource hub, funded and administrated by multiple operators in industry
Collaboration to fulfill
Tier 2
• Joint Tier 2 resources of multiple operators in industry
• Joint Tier 2 resources of multiple regional (national) emergency-response institutes
• Specialized Tier 3 resource hub, funded and administrated by multiple operators in industry
Collaboration to fulfill
Tier 3
CHAPTER 2 — Conclusions 69
have different priorities or be accustomed to different managerial styles, in which case
coordination becomes challenging. To that end, major contingency planning decisions will
require negotiation and compromise, and they are better handled when all affected parties
have participated in the development and approval of the contingency plan.
6 Conclusions
Although existing regulations on CO2 geologic storage require both assessing leakage risk and
controlling or remediating leakage incidents through corrective measures, these two pieces of
risk management are usually addressed separately. This study proposes a methodological
framework for contingency planning, which links risk assessment and corrective measures.
We achieve this goal in three consecutive steps: updating the representation of the risk
assessment matrix (RAM); translating the risk assessment matrix to a contingency planning
matrix (CPM) that incorporates a tier contingency system; and then using the emerging tiers as
the basis for developing a model contingency plan for risk-preparedness and incident-
response, which encompasses corrective measures. While this study focuses on the risks of
CO2 leakage in the subsurface and through geologic pathways, the proposed framework can be
expanded to include other types of risks, including leakage at the surface or through man-
made pathways.
The updated RAM allows visualizing the three major steps of risk assessment: risk
identification, risk analysis, and risk evaluation, resulting in a comprehensive set of leakage
risk profiles with quantified likelihood, impact, and tolerance levels. Upon dividing the overall
storage site into functional subsystems, various leakage Origins, Pathways, and Endpoints are
identified; leakage scenarios of the same Origin, Pathway, and Endpoint trajectory form a risk
profile. Subsequently, the likelihood of each leakage scenario is analyzed as a series of
conditional probabilities for leakage Origination, Propagation, and Destination, all of which
change as a function of a measurable Indicator. Equivalently, multiple value models are
developed to quantify the leakage flow and impact, which covers the damages caused both in
the subsurface and on the surface. Finally, through tolerance levels specified for both
CHAPTER 2 — Conclusions 70
likelihood and impact, it becomes possible to evaluate what risks are too high and should be
mitigated, and what risks are too small can be safely ignored.
The updated RAM can then be translated to a CPM. Fundamentally, preparing for leakage
risks and responding to leakage incidents require a wide range of resources. To that end, the
likelihood and impact dimensions of risk assessment are translated to resource proximity and
variety, respectively. To ensure both quick mobilization and thorough deployment of
corrective and remediating resources, more likely or frequent risks require more proximate
resources while more impactful risks require more unique, specialized, or complex resources.
In addition, the minimum and maximum risk tolerance levels are translated to contingency
thresholds, defining the upper and lower boundaries for preparedness and response.
Subsequently, to facilitate the assignment of the right resources to each leakage scenario, all
foreseeable risks are categorized under three contingency tiers: Tier 1, Tier 2, and Tier 3. By
design, Tier 1 trades more impactful, less likely risks for less impactful, more likely risks
while Tier 3 does the opposite.
The CPM tier system becomes the cornerstone in the development of a contingency plan. The
model contingency plan presented in this study demonstrates how the three tiers set the
primary criteria for: implementing response strategies; designing a corrective measures matrix
(CMM) that assigns specific control and remediation measures to each leakage profile;
obtaining, mobilizing, deploying, and sustaining the human and equipment resources needed
for incident-response; and formulating a decision-making hierarchy, a notification protocol,
and a communication scheme that allow the operating party to effectively administer the CO2
storage site. After addressing these main topics, it becomes easy to develop the remaining
sections of a contingency plan, which include a directory of response personnel, background
information on the project scope and priorities, a list of triggers that may initiate response, and
a record of previous leakage incidents, best practices, and lessons learned.
Ultimately, the proposed methodological framework presents a dynamic and collaborative
approach to risk management for CO2 geologic storage. Revised experts’ opinions, best
practices from previous leakage incidents, and new learnings from site operations, all can be
captured in the Bayesian probabilities of leakage likelihoods as well as the value models of
CHAPTER 2 — Conclusions 71
leakage consequences, resulting in an updated set of risk profiles. This redistribution of risk
would be translated into a redistribution of resources under each contingency tier as well as
the renegotiation of boundaries among tiers. Through transparent communications and
proactive collaboration among all stakeholders, these systematic updates ensure that the right
leakage risk scenario is covered under the right contingency tier using the right resources, and
that the right corrective measure is deployed quickly and decisively if a leakage occurs.
Consequently, both technological and administrative innovations improve the preparedness for
and correction of leakage incidents.
6.1 Future Work
Like all models, the proposed methodological framework may still face a unique set of
challenges and limitations when implemented for real CO2 storage projects. For completion,
we list some of these limitations and challenges, which present future opportunities to expand
and enhance this work. First, we note the subjectivity of probability assignment and
interpretation in the proposed RAM; different experts might observe the exact same field data
and still assign different probabilities for a leakage scenario. Indeed, such challenge is not
unique to RAM but rather common across probabilistic assessment models. One way to
address this challenge would be to ensure a clear and consistent understanding of each
analyzed uncertainty by all consulted experts; our approach strives to achieve this goal by
relying on sequential conditional probabilities in the Bayesian event tree to untangle the
various uncertain attributes of a leakage event. Also important is using uniform and unbiased
protocols for probability elicitation from experts. While such initiatives are already underway
[45, 62], it would be valuable to explore how to adapt existing protocols in others fields for
the specific context of CO2 leakage risks [83, 84]. Another related challenge is the potential
need for extensive input data in order to support detailed probabilistic analyses. An important
question that remains to be addressed in this regard is: how to balance between the RAM
accuracy and simplicity? And how to test and verify that the analysis is detailed enough?
With CPM, one potential challenge may be the need for multiple metrics to quantify the 𝑃𝑝𝑟𝑜𝑥
and 𝑃𝑣𝑎𝑟𝑖 axes. For example, the site operator may find it necessary to categorize the
CHAPTER 2 — Conclusions 72
complexity of resources not only by the number of dispatched expert teams but also by the
size of deployed equipment. Accordingly, one may envision translating one RAM into a
collection of CPMs, each with two unique metrics quantifying its two axes. To that end, it
might be useful to explore a proper procedure to design such collection of CPMs while
preserving the overarching three-tier contingency system they share.
Moving forward, however, an immediate next-step should be testing the application of the
proposed framework through a real case-study that uses real data corresponding to a real CO2
storage project. By constructing the RAMs, CPMs, and CMMs for multiple sequential stages
of the project’s operational timeline, such case-study can demonstrate this framework’s ability
not only to analyze leakage risks and develop contingency plans but also to track and update
them over time.
CHAPTER 2 — References 73
References
[1] GCCSI, "The Global Status of CCS," Global CCS Institute, Melbourne, 2014.
[2] TNS Opinion & Social, "Public Awareness and Acceptance of CO2 capture and storage,"
EuroBarometer, European Commission, Brussels, 2011.
[3] P. Upham and T. Roberts, "Public Perceptions of CCS: the results of NearCO2 European Focus
Groups," NearCO2, 2010.
[4] I. Wright, P. Ashworth, S. Xin, L. Di, Z. Yizhong, X. Liang, J. Anderson, S. Shackley, K. Itaoka,
S. Wade, J. Asamoah and D. Reiner, "Public Perception of Carbon Dioxide Capture and Storage:
Prioritised Assessment of Issues and Concerns," CO2 Capture Project.
[5] IEA, "Regulatory Frameworks for CCS," 2015. [Online]. Available:
http://www.iea.org/topics/ccs/subtopics/permittingframeworksforccs/. [Accessed May 2015].
[6] S. Bonham and I. Chrysostomidis, "Regulatory Challenges and Key Lessons Learned From Real
World Development of CCS Projects," CO2 Capture Project, 2012.
[7] EPA, "Federal Requirements Under the Underground Injection Control (UIC) Program for Carbon
Dioxide (CO2) Geologic Sequestration (GS) Wells," Environmental Protection Agency, pp.
Federal Register. Vol. 75, No. 237, 2010.
[8] EPA, "Underground Injection Control (UIC) Program Class VI Well Area of Review Evaluation
and Corrective Action Guidance," Environmental Protection Agency. Office of Water, pp. EPA
816-R-13-005, 2013a.
[9] EPA, "Summary of EPA’s Responses to Public Comments Received on the Draft Class VI Well
Testing and Monitoring Guidance," Environmental Protection Agency. Office of Water, pp. EPA
816-S-13-001, 2013b.
[10] K. Gagnon, "Canada Update: Select CCS Regulatory Developments," Natural Resources Canada,
IEA 6th CCS Regulatory Network Meeting. Paris, 2014.
[11] S. McCoy, "CSA Z741-12 and requirements for geologic storage," 6th International IEA CCS
Regulatory Network Meeting, 2014.
[12] M. Leering, "CSA Z741 – Bi-National Standard for Geological Storage of Carbon Dioxide," CSA
Standards, 2012.
[13] Bill 24, "Carbon Capture and Storage Amendment Act," The Legislative Assembly of Alberta.
Third Session, 27th Legislature, 59 Elizabeth II , 2010.
[14] Alberta Energy, "Carbon Capture and Storage - Summary Report of the Regulatory Framework
Assessment," Alberta Energy, 2012.
CHAPTER 2 — References 74
[15] Alberta, "Alberta Regulation 68/2011. Mines and Minerals Act. Carbon Sequestration Tenure
Regulation," 2011. [Online]. Available: http://www.qp.alberta.ca/. [Accessed May 2015].
[16] British Columbia, "Carbon Capture and Storage Regulatory Policy - Discussion and Comment
Paper," Ministry of Natural Gas Development. Province of British Columbia, 2014.
[17] Office of Parliamentary Counsel, "Offshore Petroleum and Greenhouse Gas Storage Act 2006,"
ComLaw, Canberra, 2006.
[18] Environment Protection and Heritage Council, "Environmental Guidelines for Carbon Dioxide
Capture and Geological Storage," Commonwealth of Australia and each Australian State and
Territory, 2009.
[19] The Parliament of Victoria, "Greenhouse Gas Geological Sequestration Act," The Parliament of
Victoria, 2008.
[20] Queensland Parliamentary Counsel, "Greenhouse Gas Storage Act," Office of the Queensland
Parliamentary Counsel, 2009.
[21] EC, "DIRECTIVE 2009/31/EC OF THE EUROPEAN PARLIAMENT AND OF THE
COUNCILof 23 April 2009on the geological storage of carbon dioxide," European Commission.
Official Journal of the European Union, 2009.
[22] EC, "Guidance Document 1. CO2 Storage Life Cycle Risk Management Framework," European
Communities, 2011a.
[23] EC, "Guidance Document 2. Characterisation of the Storage Complex, CO2 Stream Composition,
Monitoring and Corrective Measures," European Communities, 2011b.
[24] L.-C. Liu, Q. Li, J.-T. Zhang and D. Cao, "Toward a framework of environmental risk
management for CO2 geological storage in china: gaps and suggestions for future regulations,"
Mitigation and Adaptation Strategies for Global Change, pp. 10.1007/s11027-014-9589-9, 2014.
[25] D. Seligsohn, Y. Liu, S. Forbes, Z. Dongjie and L. West, "CCS in China: Toward an
Environmental, Health, and Safety Regulatory Framework," World Resources Institute,
Washington, DC, 2010.
[26] DNV, "Geological Storage of Carbon Dioxide," DNV, DNV-RP-J203, 2012.
[27] ISO, "Risk Management – Principles. ISO 31000:2009," International Organization for
Standardization, 2009.
[28] S. Vajjhala, J. Gode and A. Torvanger, "An International Regulatory Framework for Risk
Governance of Carbon Capture and Storage," Center for International Climate and Environmental
Research, Oslo, Norway, 2007.
CHAPTER 2 — References 75
[29] ScottishPower CCS Consortium, "UK Carbon Capture and Storage Demonstration Competition:
Corrective Measures Plan - UKCCS - KT - S7.20 - Shell - 001," UK Carbon Capture and Storage
Demonstration Competition, 2011.
[30] S. C. Energy, "QUEST Carbon Capture and Storage - Risk-Based Measurement, Monitoring &
Verification," in MVA/MMV Knowledge Sharing Workshop, Mobile Alabama, 2012.
[31] V. Kuurskraa and M. L. Godec, "Remediation of Leakage from CO2 Storage Reservoirs," IEA
Greenhouse Gas R&D Programme, 2007.
[32] J.-C. Manceau, D. G. Hatzignatiou, L. D. Lary, N. B. Jensen, K. Flornes, T. L. Guenan and A.
Reveillere, "Methodologies and Technologies for Mitigation of Undesired CO2 Migration In the
Subsurface," IEAGHG, UK, 2013.
[33] Eni Australia, "Joseph Bonaparte Gulf Oil Spill Contingency Plan," Eni Australia B.V., 2009.
[34] C. K. Berry and J. R. Bogner, "Model Emergency Response Plan," North Carolina Department of
Labor (NCDOL), Raleigh.
[35] IPIECA, "Guide to Tiered Preparedness and Response," International Petroleum Industry
Environmental Conservation Association, London, United Kingdom, 2007.
[36] NIST, "Contingency Plan Template, Appendix I-3," [Online]. [Accessed 2012].
[37] S. K. Singh and R. Ranjan, "Oil Spill Contingency Plan for Upstream Petroleum Operations in
Andhra Pradesh Offshore Area, Rajahmundry Asset," Oil and Natural Gas Corporation Ltd,
Rajahmundry, India, 2007.
[38] J.-C. Manceaua, D. Hatzignatiou, d. N. J. L. de Larya and A. Réveillèrea, "Mitigation and
remediation technologies and practices in case of undesired migration of CO2 from a geological
storage unit - Current status," International Journal of Greenhouse Gas Control, vol. 22, pp. 272-
290, 2014.
[39] A. Nicol and M. Gerstenberger, "Risk Assessment in CCS," Sanya China, 2011.
[40] J. Condora, D. Unatrakarna, M. Wilsona and K. Asgharia, "A Comparative Analysis of Risk
Assessment Methodologies for the Geologic Storage of Carbon Dioxide," Energy Procedia, vol. 4,
p. 4036–4043, 2011.
[41] Quintessa, "CO2 FEP Database," 2010. [Online]. Available:
http://www.quintessa.org/co2fepdb_v1.1.0/PHP/frames.php. [Accessed 2015].
[42] M. Gerstenberger, A. Nicol, M. Stenhouse, K. Berryman, M. Stirling, T. Webb and W. Smith,
"Modularised logic tree risk assessment method for carbon capture and storage projects," Energy
Procedia, vol. 1, pp. 2495-2502, 2009.
CHAPTER 2 — References 76
[43] M. Gerstenberger, A. Christophersena, R. Buxtona and A. Nicola, "Bi-directional risk assessment
in carbon capture and storage with Bayesian Networks," International Journal of Greenhouse Gas
Control, vol. 35, pp. 150-159, 2015.
[44] A. Bowden and A. Rigg, "Assessing Risk in CO2 Storage Projects," APPEA Journal, pp. 677-702,
2004.
[45] A. R. Bowden, D. F. Pershkeb and R. Chalaturnyk, "Geosphere risk assessment conducted for the
IEAGHG Weyburn-Midale CO2 Monitoring and Storage Project," International Journal of
Greenhouse Gas Control, vol. 16S, p. S276–S290, 2013.
[46] S. M. Benson and R. Hepple, "Prospects for Early Detection and Options for Remediation of
Leakage from CO2 Sequestration Projects," in Carbon Dioxide Capture for Storage in Deep
Geologic Formations: Results from the CO2 Capture Project, Vol. 2: Geologic Storage of Carbon
Dioxide with Monitoring and Verification, UK, Elsevier Publishing, 2005, pp. 1189-1203.
[47] V. A. Kuuskraa and M. L. Godec, "Remediation of Leakage from CO2 Storage Reservoirs,"
Advanced Resources International, Inc, Arlington, VA, USA, 2007.
[48] S. M. Benson, "Remediation Technologies," Storage in Saline Formations R&D Workshop,
California, 2011.
[49] NETL, "Risk Analysis and Simulation for Geologic Storage of CO2," National Energy Technology
Laboratory, 2009.
[50] K. Hnottavange-Telleena, E. Chabora, R. J. Finley, S. E. Greenberg and S. Marsteller, "Risk
management in a large-scale CO2 geosequestration pilot project, Illinois, USA," Energy Procedia,
vol. 4, p. 4044–4051, 2011.
[51] K. Edlmann, "Risk Assessment in Geologic Storage of CO2," Oxand.
[52] DNV, "CO2QUALSTORE: Guideline for Selection and Qualification of Sites and Projects for
Geological Storage of CO2," DNV, Hovik, Norway, 2009.
[53] E. Pate-Cornell, "Uncertainties in risk analysis: Six Levels of treatment," Reliability Engineering
and System Safety, pp. 95-111, 1996.
[54] B. J. Garrick, "Recent Case Studies and Advancements in Probabilistic Risk Assessment," Risk
Analysis, vol. 4, no. 4, pp. 267-279, 1984.
[55] E. Pate-Cornell, "Chapter 24 - Nuclear Power Plants: TheOriginalProbabilistic Risk Analysis," in
MS&E250A: Engineering Risk Analysis Class Notes, Stanford, Stanford Bookstore, 2013, p. 177.
[56] FutureGen 2.0, "Final Risk Assessment Report for the FutureGen Project Environmental Impact
Statement," U.S. Department of Energy. Contract No. DE-AT26-06NT42921, 2007.
CHAPTER 2 — References 77
[57] Z. Wang and M. J. Small, "A Bayesian approach to CO2 leakage detection at saline sequestration
sites using pressure measurements," International Journal of Greenhouse Gas Control, vol. 30, pp.
188-196, 2014.
[58] C. A. Griffith, "Physical Characteristics of Caprock Formations used for Geological Storage of
CO2 and the Impact of Uncertainty in Fracture Properties in CO2 Transport through Fractured
Caprocks," Carnegie Mellon University, Pittsburgh, 2012.
[59] S. Jewell and B. Senior, "CO2 Storage Liabilities in the North Sea: An Assessment of Risks and
Financial Consequences," Department of Energy and Climate Change, UK, 2012.
[60] P. D. Jordan, C. M. Oldenburg and J.-P. Nicot, "Estimating the probability of CO2 plumes
encountering faults," Greenhouse Gases Science and Technology, vol. 1, pp. 160-173, 2011.
[61] R. Dunk, "Assessment of Sub Sea Ecosystem Impacts," IEA Greenhouse Gas R&D Programme.
Report No. 2008/8, Gloucestershire, 2008.
[62] A. R. Bowden, D. F. Pershke and R. Chalaturnyk, "Biosphere risk assessment for CO2 storage
projects," International Journal of Greenhouse Gas Control, vol. 16S, pp. S291-S308, 2013.
[63] R. A. Howard, "On Making Life and Death Decisions," Societal Risk Assessment, pp. 89-113,
1980.
[64] R. A. Howard and A. E. Abbas, Foundations of Decision Analysis, Pearson, 2015.
[65] R. S. d. Groot, M. A. Wilson and R. M. Boumans, "A typology for the classification, description
and valuation of ecosystem functions, goods and services," Ecological Economics, vol. 41, pp.
393-408, 2002.
[66] T. Tietenberg and L. Lewis, Environmental & Natural Resource Economics, Pearson, 2015.
[67] IEA, "Potential Impacts on Groundwater Resources of CO2 Geologic Storage," International
Energy Agency Greenhouse Gas R&D Programme, 2011.
[68] K. Damen, A. Faaij and W. Turkenburg, "Health, Safety, and Environmental Risks of
Underground CO2 Storage - Overview of Mechanisms and Current Knowledge," Climatic Change,
vol. 74, p. 289–318, 2006.
[69] R. Melchers, "On the ALARP approach to risk management," Reliability Engineering and System
Safety, vol. 71, pp. 201-208, 2001.
[70] A. Critchlow, "BP faces never ending legal battle for Deepwater disaster," The Telegraph, 17
January 2015.
[71] L. C. S. Jr., M. Smith and P. Ashcroft, "Analysis of Environmental and Economic Damages from
British Petroleum’s Deepwater Horizon Oil Spill," Albany Law Review, vol. 74, no. 1, pp. 563-585,
2011.
CHAPTER 2 — References 78
[72] A. Chamberlin, "BP lost 55% shareholder value after the Deepwater Horizon incident," Market
Realist, 10 September 2014.
[73] D. Savage, P. R. Mual, S. Benbow and R. C. Walke, "A Generic FEP Database for the Assessment
of Long-Term Performance and Safety of Geologic Storage of CO2," Quintessa, QRS-1060A-1
verion 1.0, 2004.
[74] M. R. Blood and A. Chang, "Coast Guard defends cleanup response to Santa Barbara oil spill," Los
Angeles Daily News, 30 May 2015.
[75] G. J. Wilcox, "Court order seeks to hasten relocation of residents near Porter Ranch gas leakq," Los
Angeles Daily News, 22 December 2015.
[76] R. D. Shell, "Preventing and Responding to Oil Spills in the Alaskan Arctic," Royal Dutch Shell
plc, for Shell Exploration and Production International B.V, The Hague, 2011.
[77] ENI, "Joseph Bonaparte Gulf Oil Spill Contingency Plan," ENI Australia, West Perth, 2009.
[78] H. A. Parker, R. T. Teubner and J. C. Sawicki, "Spill Reponse Planning in the Philippines: 3-Tier
Interaction between Government and Industry," 2009. [Online]. Available:
http://www.interspill.org/previous-events/2009/12-May/pdf/1630_parker.pdf.
[79] UK, "The National Contingency Plan: A Strategic Overview for Responses to Marine Pollution
from Shipping and Offshore Installations," 2014. [Online]. Available:
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/408385/140829-
NCP-Final.pdf.
[80] S. M. Benson, R. Hepple, J. Apps, C.-F. Tsang and M. Lippman, "Lessons Learned from Natural
and Industrial Analogues for Storage of Carbon Dioixide in Deep Geological Formations,"
Lawrence Berkeley National Laboratory, Berkeley, California, USA, 2002.
[81] IPCC, "Costs, benefits and avoided climate impacts at global and regional levels. IPCC Fourth
Assessment Report: Climate Change 2007.," 2007. [Online]. Available:
https://www.ipcc.ch/publications_and_data/ar4/syr/en/mains5-7.html. [Accessed 2015].
[82] W. D. Nordhaus, "A Review of the Stern Review on the Economics of Climate Change," Journal
of Economie Literature , vol. 45, no. 3, pp. 686-702, 2007.
[83] M. G. Morgan, M. Henrion and M. Small, Uncertainty: A Guide to Dealing with Uncertainty in
Quantitative Risk and Policy Analysis, New York: Cambridge University Press, 1990.
[84] C. S. Spetzler and C.-A. S. S. V. Holstein, "Probability Encoding in Decision Analysis,"
Management Science, vol. 22, no. 3, pp. 340-358, 1975.
[85] CCA, "Clean Caribbean & Americas," [Online]. Available: http://www.cleancaribbean.org/.
[Accessed 2015].
CHAPTER 2 — References 79
[86] Oil Spill Response , "Services," [Online]. Available: http://www.oilspillresponse.com/services-
landing. [Accessed 2015].
CHAPTER 2 — Appendix A: Drawbacks of Alternative Three-Tier Systems 80
Appendix A: Drawbacks of Alternative Three-Tier Systems
Figure 2.A1: Drawbacks of alternative tier-system approaches for contingency planning
The proposed tier system for contingency planning in Figure 2.9 avoids potential pitfalls in
alternative tier-system designs, as depicted in Figure 2.A1. The resource-variety tier system
in Figure 2.A1a divides the tolerable risk zone into three tiers based only on the impact of
leakage and thus the variety of needed resources; it covers the least impactful leakage
scenarios under Tier 1 and the most impactful scenarios under Tier 3. The problem with this
approach is that it ignores the need for different levels of Resource Proximity to prepare for
and respond to leakage incidents of different likelihoods but of the same impact.
Conversely, the resource-proximity tier system in Figure 2.A1b divides the tolerable risk
zone into three tiers based only on the likelihood of leakage and thus the proximity of needed
VI
{L}
Maximum Contingency Threshold
Tier 3
Tier 2
Tier 1
Min
imu
m C
on
tin
gen
cy T
hre
sho
ld
Minimum Contingency Threshold
Max
imu
mC
on
tin
gen
cy T
hre
sho
ld
VI
{L}
Maximum Contingency Threshold
Tier 1 Tier 2 Tier 3
Min
imu
m C
on
tin
gen
cy T
hre
sho
ld
Minimum Contingency Threshold
Max
imu
mC
on
tin
gen
cy T
hre
sho
ld
VI
{L}
Maximum Contingency Threshold
Tier 3
Tier 2
Tier 1
Min
imu
m C
on
tin
gen
cy T
hre
sho
ld
Minimum Contingency Threshold
Max
imu
mC
on
tin
gen
cy T
hre
sho
ld
VI
{L}
Maximum Contingency Threshold
Min
imu
m C
on
tin
gen
cy T
hre
sho
ld
Minimum Contingency Threshold
Max
imu
mC
on
tin
gen
cy T
hre
sho
ld
Tier 3
Tier 2
Tier 1
A1a A1b
A1c A1d
CHAPTER 2 — Appendix A: Drawbacks of Alternative Three-Tier Systems 81
resources; it covers the least likely and infrequent leakage scenarios under Tier 1 and the most
likely and frequent scenarios under Tier 3. The problem with this approach is that it ignores
the need for different levels of Resource Variety to prepare for and respond to leakage
incidents of different impact levels but of the same likelihood.
Additionally, the resource-amount tier system divides the tolerable risk zone into three tiers
based on the overall level of risk, or equivalently, based on the overall amount of available
resources; leakage scenarios of the lowest risk levels (lowest likelihood and impact) are
covered under Tier 1 whereas those of the highest risk levels (highest likelihood and impact)
are covered under Tier 3. This resource-amount tier system may be designed in two forms
using continuous or discretized resource-amount contours, as illustrated in Figures 2.A1c and
2.A1d, respectively. The problem with this approach is that it equates leakage scenarios
requiring most proximate but least various resources to those requiring least proximate but
most various resources. The adopted tier system in this study avoids this problem due to the
tradeoff illustrated in Figure 2.9 and explained in Section 4.3.2.
CHAPTER 2 — Appendix B: Tier-Based Contingency Planning 82
Appendix B: Tier-Based Contingency Planning
Table 2.B1: Tier-based response strategies for contingency planning
Element Tier 1 Tier 2 Tier 3
Res
po
nse
Str
ate
gie
s
General operational procedures
Secure human health and safety
Mobilize and deploy resources onsite
Recover normal business operations as soon as practically possible
Secure human health and safety
Mobilize and deploy resources onsite and in the local vicinity of storage site
Activate responsibility zones among local stakeholders
Provide external support against local health, economic, or environmental damages
Recover normal business operations as soon as practically possible
Secure human health and safety
Mobilize and deploy resources onsite, and in local and regional vicinity of storage site
Activate responsibility zones among local and regional stakeholders
Provide external support against local and regional health, economic, or environmental damages
Recover normal business operations as soon as practically possible
Specific operational procedures
Apply corrective measures to control (stop or contain) and remediate leakage
Apply corrective measures to control (stop or contain) and remediate leakage
Apply corrective measures to control (stop or contain) and remediate leakage
CHAPTER 2 — Appendix B: Tier-Based Contingency Planning 83
Table 2.B2: Tier-based human and equipment resources for contingency planning Element Tier 1 Tier 2 Tier 3
Hu
ma
n a
nd
Eq
uip
men
t R
eso
urc
es
Human resources
Categorize into general and specific response teams
Inventory internal and contracted response personnel
Conduct regular training programs, focusing on achieving, testing, and validating suitable competence (not only awareness or knowledge) to perform the designated role
Categorize into general and specific response teams
Inventory internal and contracted response personnel
Identify liaison personnel to external local response teams and stakeholders
Conduct regular training programs, focusing on achieving, testing, and validating suitable competence (not only awareness or knowledge) to perform the designated role
Conduct joint training sessions with local stakeholders
Categorize into general and specific response teams
Inventory internal and contracted response personnel
Identify liaison personnel to external local and regional response teams and stakeholders
Conduct regular training programs, focusing on achieving, testing, and validating suitable competence (not only awareness or knowledge) to perform the designated role
Conduct joint training sessions with local and regional stakeholders
Equipment resources
Inventory owned and contracted, general and specialized equipment
Test and maintain equipment regularly to ensure proper operations
Ensure equipment storage is optimal for easy mobilization
Inventory owned and contracted, general and specialized equipment
Inventory the exact location and mobilization time of general and specific equipment owned or operated by local stakeholders
Test and maintain equipment regularly to ensure proper operations
Ensure equipment storage is optimal for easy mobilization
Inventory owned and contracted, general and specialized equipment
Inventory the exact location and mobilization time of general and specific equipment owned or operated by local and regional stakeholders
Test and maintain equipment regularly to ensure proper operations
Ensure equipment storage is optimal for easy mobilization
84
Chapter 3
Economic Value of Flexible Hydrogen-
Based Polygeneration Energy Systems
1 Introduction
Fossil fuels meet 87% of today’s global energy demand [1] and are used to generate 68% of
the global electricity supply [2]. Concerns over climate change, growing energy consumption,
and energy security compel fossil-fuel plants to meet increasing regulatory and market
challenges: lower emissions, higher efficiency, and more flexible operations to complement
intermittent renewables and hedge against fluctuations in energy prices. Polygeneration energy
systems (PES) have the potential to meet all these challenges.
While polygeneration generally describes a wide range of multi-input multi-output industrial
processes [3], this study focuses on polygeneration energy systems that use fossil fuels as
inputs and produce hydrogen as an intermediate product [4]. PES offers multiple advantages
over conventional single-output or monogeneration systems. Technically, polygeneration
allows better process- and heat-integration among various production and ancillary units,
which reduces energy losses and thus results in higher energy-conversion efficiency. This
higher efficiency, combined with the utilization of carbon in chemical synthesis, results in
lower carbon dioxide (CO2) emissions [5, 6]. In addition, the production rates of PES can be
either fixed or adjusted over time. We refer to a system with fixed production rates as static or
CHAPTER 3 — Introduction 85
Acronyms
AGRU acid-gas removal unit
ASU air separation unit
CCS carbon capture and storage
CO2 carbon dioxide
COE cost of energy
HECA Hydrogen Energy California
HSU hydrogen separation unit
MRU mercury removal unit
NPV net present value
PES polygeneration energy system
PRU particulate removal unit
SRU shift-reaction unit
𝑐𝑙 cost of capacity per one unit of output 𝑙 ($/𝑘𝑊ℎ or $/𝑘𝑔𝑙)
𝐶𝐹 capacity factor
𝐶𝑀𝑙𝑘 contribution margin from converting one kilogram of hydrogen to output 𝑙 in
year 𝑘 ($/𝑘𝑔ℎ)
𝐼𝐶𝑀𝐹𝑙𝑘 incremental contribution margin from flexible switching of hydrogen conversion to
output 𝑙 in year 𝑘 ($/𝑘𝑔ℎ)
𝑗𝑙 time-averaged fixed operating cost per one unit of output 𝑙 ($/𝑘𝑊ℎ or $/𝑘𝑔𝑙)
LCOE levelized cost of electricity ($/𝑘𝑊ℎ)
LCOH levelized cost of hydrogen ($/𝑘𝑔ℎ)
LCOP levelized cost of polygeneration ($/𝑘𝑔ℎ)
𝐿𝐼𝐶𝑙 levelized incremental cost of the subsystem producing output 𝑙 ($/𝑘𝑊ℎ or $/𝑘𝑔𝑙)
𝑚 total number of hours in one year (ℎ𝑟)
𝑚𝑙 yearly hours during which production rate of output 𝑙 should be maximized (ℎ𝑟)
𝑁ℎ production capacity of the hydrogen subsystem (𝑘𝑔ℎ/ℎ𝑟)
𝑃𝑙 price of output 𝑙 ($/𝑘𝑊ℎ or $/𝑘𝑔𝑙)
𝑃𝑀 profit-margin of polygeneration system per one kilogram of produced hydrogen ($/𝑘𝑔ℎ)
𝑆𝑎 storage capacity of ammonia (𝑘𝑔𝑎)
𝑆𝐽𝑙𝑘 fixed operating cost per unit-capacity of output 𝑙 in year 𝑘
(($ 𝑦𝑟⁄ )/𝑘𝑊 or ($ 𝑦𝑟⁄ )/(𝑘𝑔𝑙 ℎ𝑟⁄ ))
𝑆𝑃𝑙 system price; cost per unit-capacity of output 𝑙 (in $/𝑘𝑊 or $/(𝑘𝑔𝑙 ℎ𝑟⁄ ))
𝑇 useful lifetime of the facility (𝑦𝑟)
𝑈𝑐 net CO2 production rate per one kilogram of produced hydrogen (𝑘𝑊ℎ/𝑘𝑔ℎ)
𝑉𝑂𝐷 value of diversification ($/𝑘𝑔ℎ)
𝑉𝑂𝐹 value of flexibility ($/𝑘𝑔ℎ)
𝑉𝑂𝑃 value of polygeneration ($/𝑘𝑔ℎ)
𝑤𝑙 time-averaged variable cost per one unit of output 𝑙 ($/𝑘𝑊ℎ or $/𝑘𝑔𝑙)
𝑥𝑘 degradation factor; the percentage of initial capacity that is still functional at year 𝑘
𝑋𝑙 conversion rate of one kilogram of hydrogen to output 𝑙 (in 𝑘𝑊ℎ/𝑘𝑔ℎ or 𝑘𝑔𝑙/𝑘𝑔ℎ)
𝑦𝑙 fraction of hydrogen allocated to the production of fertilizer 𝑙
CHAPTER 3 — Introduction 86
Subscripts
𝑎 ammonia without storage
𝑎𝑠 ammonia with storage
𝑐 carbon dioxide
𝑒 electricity
𝑓 fertilizer
ℎ hydrogen
𝑢𝑟𝑒𝑎 urea
𝑈𝐴𝑁 urea and ammonium nitrate solution
𝑚𝑖𝑛 minimum
𝑚𝑎𝑥 maximum
Greek Symbols
𝜏 discount rate
𝛾𝑘 discount factor in year 𝑘
𝜆 fraction of hydrogen production capacity allocated to electricity generation
1 − 𝜆 fraction of hydrogen production capacity allocated to fertilizer generation
𝐾 constant-equivalent fraction of hydrogen capacity allocated for fertilizer generation
𝛷𝑙 correction factor to account for time-dependent variable costs during 𝑚𝑙
steady-state polygeneration and a system with variable production rates as flexible or
dispatchable polygeneration [7]. Flexible polygeneration can exploit frequent variations in
commodity prices; while fuel switching and mixing capabilities help attenuate the risks of
fuel-price shocks, production diversification and dispatchability help capture the benefits of
product-price peaks [7, 8]. Furthermore, merchant hydrogen markets are currently
underdeveloped [9, 10, 11], which renders hydrogen market prices an imperfect indicator of
cost and value. By converting hydrogen to valuable commodities, polygeneration offers an
incentive to expand investments in hydrogen infrastructure.
The advantages of polygeneration systems merit a rigorous analysis of their economic
competitiveness within the broader energy landscape. In this study, we develop a set of
generalizable metrics that can be used to valuate fossil-fuel polygeneration energy systems.
These economic metrics achieve three goals. First, they calculate the levelized cost and
profitability of both static and flexible polygeneration, irrespective of the type of used fossil-
fuels or generated end-products. Second, they facilitate a consistent comparison of the
economics of polygeneration relative to that of monogeneration, with special emphasis on
electricity monogeneration alternatives (e.g. natural gas or wind). Finally, they quantify the
CHAPTER 3 — Introduction 87
value of two real-options enabled by polygeneration: the value of diversifying end-products
and the value of flexibly varying the production rates of end-products over time.
The main motivation for our analysis stems from the fact that different methodologies have
been used to evaluate polygeneration economics, including net present value [7, 8, 12, 13],
profit index [12], payout time [14], cost of energy [15, 16], and others [17, 18, 19]. While each
methodology has its own merits, the lack of methodological consistency prevents accurate
comparison of polygeneration economics under different technical assumptions and
operational settings. The economic metrics we propose offer one way to overcome this
problem. Specifically, we express all metrics in monetary value per unit of hydrogen
produced, for hydrogen is a common intermediate product across polygeneration energy
systems of various process configurations and end-product portfolios.
While some previous studies have used the cost of energy (COE) ($ 𝑘𝑊ℎ⁄ ) to compare
polygeneration to monogeneration, such an approach faces the following challenges. First,
polygeneration may not necessarily generate electricity as an end-product, in which case the
use of COE becomes impractical. Second, it is problematic to calculate the COE as the cost of
polygeneration less the cost of other non-electricity products from equivalent monogeneration
[15, 16]; this method assigns all cost-savings from polygeneration system-integration to the
power unit and therefore might underestimate the actual cost of electricity. Our approach
addresses this issue by converting the cost per unit of hydrogen to a cost per unit of any end-
product, assuming that all hydrogen is converted to that single end-product. This methodology
facilitates an economic comparison between polygeneration and monogeneration systems,
including traditional power plants.
In addition, an assessment of the economic competitiveness of flexible polygeneration systems
should include a quantification of the economic trade-offs associated with operational
flexibility. Greater flexibility typically implies not only higher revenues but also higher cost of
capacity due to larger equipment size [7, 8]. We address this topic by deriving metrics that
capture the economic impacts of flexible polygeneration, illustrating that production
diversification and flexibility need not always result in economic gains [7].
CHAPTER 3 — Research Methodology 88
On the technical side, there is an extensive literature on optimizing the design and operation of
PES by combining several technologies and processes [6, 13], incorporating investment
planning procedures [20], or investigating the trade-offs associated with operational flexibility
[7]. Other studies also performed detailed techno-economic analyses on specific
polygeneration systems under various input- and output-portfolios [5, 8, 14, 18, 19] and
process configurations [16, 17]. Given the breadth of the available technical analysis, our
work presumes that polygeneration is technically feasible and focuses predominantly on
assessing its economic value. To that end, we use a simple yet generalizable PES
configuration that can operate as both a static and a flexible system. Building specifically on
the work by Chen et al. [7], which optimizes PES operations under uniform levels of
flexibility, we impose different flexibility limits on different production units to explore the
effect of real-life operational constraints on PES economics.
In the following sections, we first introduce the economic concepts and technical
configuration used in assessing PES. Next, we present a detailed economic analysis for the
modeled PES in three scenarios; Scenario 1 evaluates static operations while Scenarios 2a and
2b evaluate two modes of flexible operations. As the main focus of this paper, the economic
definitions and derived propositions in all three scenarios are then used to calculate the profit-
margin and real-options of PES. Lastly, we demonstrate the applicability of the derived
metrics by examining the economic competitiveness of Hydrogen Energy California, a
polygeneration project currently under development.
2 Research Methodology
This section describes the economic concepts and technical specifications used in deriving the
valuation metrics for PES. We first introduce the levelized cost of hydrogen concept, which is
the foundational tool for economic assessment. Then, we explain the process configuration,
fuel-inputs, and product-outputs of the adopted fossil-fuel polygeneration system.
CHAPTER 3 — Research Methodology 89
2.1 Levelized Cost of Hydrogen
Similar to the concept of levelized cost of electricity (𝐿𝐶𝑂𝐸) as cost per unit of energy
generation ($ 𝑘𝑊ℎ⁄ ), the metric of levelized cost of hydrogen (𝐿𝐶𝑂𝐻) refers to the cost per
unit of hydrogen production ($ 𝑘𝑔ℎ⁄ ) [21, 22]. Consistent with MIT’s The Future of Coal
definition of 𝐿𝐶𝑂𝐸 [23], this study defines 𝐿𝐶𝑂𝐻 as: “the constant dollar hydrogen price that
would be required over the life of a hydrogen plant to cover all operating expenses, payment
of debt and accrued interest on initial project expenses, and the payment of an acceptable
return to investors”. In other words, the 𝐿𝐶𝑂𝐻 is a break-even metric that calculates the ratio
of lifetime cost to lifetime hydrogen production of a facility.
The 𝐿𝐶𝑂𝐻 formulation adopted in this study is similar to the 𝐿𝐶𝑂𝐸 model in Reichelstein and
Yorston [24]. As shown in (1), the 𝐿𝐶𝑂𝐻 ($ 𝑘𝑔ℎ⁄ ) is the sum of three terms: cost of capacity
per unit output 𝑐ℎ, time-averaged fixed operating cost per unit output 𝑗ℎ, and time-averaged
variable cost per unit output 𝑤ℎ [24, 25].1
𝐿𝐶𝑂𝐻 = 𝑐ℎ + 𝑗ℎ + 𝑤ℎ (1)
Assuming constant returns-to-scale, the cost of capacity per one kilogram of hydrogen can be
expressed as:
𝑐ℎ ($ 𝑘𝑔ℎ⁄ ) =𝑆𝑃ℎ
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝑥𝑖 ∙ 𝛾𝑖𝑇𝑖=1
(2)
𝑆𝑃 ($ (𝑘𝑔ℎ ℎ𝑟⁄ )⁄ ) in (2) denotes the system price of acquiring one unit of capacity to produce
one kilogram of hydrogen per hour. It includes the cost of engineering procurement and
construction, contingency, and land purchase. The initial investment yields a stream of
hydrogen output over 𝑇 years, with 𝑚 ∙ 𝑥𝑖 ∙ 𝐶𝐹 kilograms delivered in year 𝑖. While 𝑚 =
8,760 refers to the total number of hours in a given year, the system degradation factor, 𝑥𝑖,
accounts for potential losses in generation capacity over time and is technology-specific. In
1 The cost of capacity 𝑐ℎ should be scaled by a factor that accounts for corporate income taxes, as
explained by Reichelstein and Yorston [24]. Our study can be expanded to include the effect of taxes
and subsidies.
CHAPTER 3 — Research Methodology 90
addition, since the facility may not be online at all times, the practical capacity is only a
fraction of the theoretical capacity. This fraction is represented by the capacity factor, 𝐶𝐹.
Furthermore, since the 𝐿𝐶𝑂𝐻 is a break-even formula, it is essential to specify an appropriate
discount rate. We denote this discount rate by 𝜏 and the corresponding discount factor by
𝛾 = (1 1 + 𝜏⁄ ).2
Fixed operating costs can change on a yearly basis. The time-averaged fixed operating cost per
one kilogram of hydrogen 𝑗ℎ ($ 𝑘𝑔ℎ⁄ ) is shown in (3). 𝑆𝐽𝑖 (($ 𝑦𝑟⁄ ) (𝑘𝑔ℎ ℎ𝑟⁄ )⁄ ) denotes the
fixed operating cost incurred by operating one-kilogram-per-hour capacity of the hydrogen
facility in year 𝑖. Expenditures in this category include labor, administration and overhead,
maintenance, and insurance. While fixed operating costs are assumed to scale proportionally
with the capacity of the facility, they are independent of the actual amount of hydrogen
generated by the facility.
𝑗ℎ =∑ 𝑆𝐽ℎ𝑖 ∙ 𝛾𝑖𝑇
𝑖=1
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝑥𝑖 ∙ 𝛾𝑖𝑇𝑖=1
(3)
Finally, variable costs can vary over time. Costs in this category include fuel consumption,
raw-material inputs, auxiliary loads, and cash-conversion expenses. We use 𝑤ℎ𝑖(𝑡) ($ 𝑘𝑔ℎ⁄ )
to denote the time-dependent variable cost per one kilogram of hydrogen in year 𝑖, and we
derive 𝑤ℎ𝑖 ($ 𝑘𝑔ℎ⁄ ) in (4) as the yearly-averaged variable cost.
𝑤ℎ𝑖 =1
𝑚∫ 𝑤ℎ𝑖(𝑡)𝑑𝑡
𝑚
0
(4)
Over the life cycle of the facility, the time-averaged variable cost per one kilogram of
hydrogen 𝑤ℎ ($ 𝑘𝑔ℎ⁄ ) becomes as expressed in (5).
𝑤ℎ =∑ 𝑤ℎ𝑖 ∙ 𝑚 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝛾𝑖𝑇
𝑖=1
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝑥𝑖 ∙ 𝛾𝑖𝑇𝑖=1
=∑ 𝑤ℎ𝑖 ∙ 𝑥𝑖 ∙ 𝛾𝑖𝑇
𝑖=1
∑ 𝑥𝑖 ∙ 𝛾𝑖𝑇𝑖=1
(5)
2 The discount rate we specify should be interpreted as a real, rather than a nominal, interest rate that
accounts for inflation.
CHAPTER 3 — Research Methodology 91
Similar notation is used to characterize the time-dependency of all economic metrics in this
study, including prices. For instance, 𝑃ℎ𝑖(𝑡), 𝑃ℎ𝑖, and 𝑃ℎ refer to the time-dependent price of
hydrogen in year 𝑖, the yearly-averaged price of hydrogen in year 𝑖, and the time-averaged
price of hydrogen, respectively. Referring back to the definition of 𝐿𝐶𝑂𝐻 as a break-even
value, we can obtain the following benchmark result:
A hydrogen production facility is cost-competitive if and only if:
𝑃ℎ > 𝐿𝐶𝑂𝐻 (6)
Cost-competitiveness is defined as the ability of the facility to achieve a positive NPV. Since a
PES produces hydrogen as an intermediate product only, the price of hydrogen 𝑃ℎ must be
substituted with revenue from the hydrogen-enabled end-products, which are commodities
with well-defined market prices. Therefore, the formulation in (6) needs to be expanded to
assess the economic value of polygeneration.
2.2 Technical Configuration of PES
This study analyzes a simple yet generalizable fossil-fuel PES configuration, which can
operate as either a static or a flexible system. Specifically, we consider a PES that uses coal as
fuel, produces hydrogen then ammonia as intermediate products, and produces electricity and
fertilizer (e.g. urea) as final end-products. In the assumed configuration, coal can be also
mixed with biomass or petcoke as fuel inputs.
In a static PES, all units run at steady-state with fixed output flowrates. In a flexible PES,
however, some units can vary their output flowrates over time while other units should run at
steady-state with fixed flowrates in order to maintain acceptable energy- and chemical-
conversation efficiencies [26]. To account for these real-life operational constraints, and to
allow for a generalizable economic assessment, the adopted PES can be conceptually divided
into four subsystems: hydrogen, electricity, ammonia, and fertilizer. While the electricity and
ammonia subsystems can be either flexible or static, the hydrogen and fertilizer subsystems
are always static.
CHAPTER 3 — Research Methodology 92
Figure 3.1 presents a simplified depiction of the process flow sheet for the polygeneration
facility. As shown, coal is first fed into a gasifier where it is mixed with an oxygen (O2)
stream from the air separation unit (ASU) to produce hydrogen-rich syngas. In addition to the
gasifier and the ASU, the hydrogen production subsystem includes: syngas clean-up units
such as particulate removal unit (PRU), mercury removal unit (MRU), and acid-gas removal
unit (AGRU); shift-reaction unit (SRU); and hydrogen separation unit (HSU). All these units
should run at steady-state [26], resulting in a fixed output of hydrogen (H2) and carbon dioxide
(CO2).
Figure 3.1: Simplified process flow sheet of the used PES
Hydrogen is either fed into a combined-cycle turbine unit for electricity generation or mixed
with nitrogen (N2) from the ASU to produce ammonia (NH3), the precursor material for
making fertilizers. Both electricity generation [27, 28] and ammonia synthesis [26] units can
operate flexibly, producing variable power and ammonia flows. Ammonia is then mixed with
a fraction of the CO2 stream to produce fertilizer (e.g. urea). The fertilizer synthesis unit must
run at steady-state [26], resulting in a fixed flow of the end-product. The remaining CO2
gasifier
ASU
syngas
clean-
up
HSU
ammonia
synthesis
fertilizer
synthesis
gas
turbine
steam
turbine
ammonia
storage
air
coal
O2
syngas
(CO +
H2)
steam (H2O)
CO2
H2
CO2
CO2
H2
H2
H2
NH3
electricityhydrogen subsystem
fertilizers
subsystem
electricity
subsystem
vented or
used for CCS
constant flowrate
variable flowrate
N2N2
vented N2
fertilizers
(e.g. urea)
NH3
static units
flexible units
SRU ammonia
subsystem
CHAPTER 3 — Economic Analysis 93
stream is either vented or compressed and transported for geologic sequestration. Finally,
since the steady-state production of fertilizer is dependent on the variable production of
ammonia, intermediate ammonia storage is necessary to buffer the variations in the ammonia
output and secure a fixed ammonia input into the fertilizer subsystem.
Focusing specifically on the ammonia and electricity subsystems, their ranges of flexibility are
constrained by system-integration and efficiency-related standards. For example, part of the
generated electricity is used for auxiliary load within the facility [26], and power turbines must
operate above minimum-capacity limits to avoid severe losses in energy efficiency [28]. In
addition, bounding the range of ammonia production is necessary to cap the size ammonia
storage; the needed intermediate storage becomes increasingly larger as the range of variable
production rates becomes wider. We account for these practical flexibility constraints by
imposing a lower bound on the production rates of both electricity and ammonia. The upper-
bound on production rates is imposed by the name-plate capacity of each production unit.
3 Economic Analysis
Based on the preceding technical configuration, we investigate two scenarios, illustrated in
Figure 3.2. Scenario 1 analyzes a static PES, whereas Scenario 2a and Scenario 2b analyze a
flexible PES. In all scenarios, the PES can still be characterized as a combination of the four
operational subsystems introduced above, with the rate of total hydrogen production fixed at
𝑁ℎ (𝑘𝑔ℎ/ℎ𝑟). For simplicity, we set 𝑁ℎ = 1 in Figure 3.2. For each unit of hydrogen
produced, 𝜆 fraction is allocated to electricity production, and the remaining (1 − 𝜆) is
allocated to ammonia production. While 𝜆 is constant in Scenario 1, 𝜆 may vary with time in
Scenarios 2a and 2b. By definition, one kilogram of hydrogen can be converted to either 𝑋𝑒
kilowatt hours of electricity or 𝑋𝑎 kilograms of ammonia. The subsequent reaction of 𝑋𝑎
kilograms of ammonia with CO2 results in 𝑋𝑓 kilograms of fertilizer; thus, 𝑋𝑎 𝑋𝑓⁄ units of
ammonia are needed to produce one unit of fertilizer.
To account for flexibility constraints, we limit the feasible range of 𝜆, such that 𝜆 ∈
[𝜆𝑚𝑖𝑛 , 𝜆𝑚𝑎𝑥]. 𝜆𝑚𝑖𝑛 is dictated by the minimum allowable rate of electricity generation,
CHAPTER 3 — Economic Analysis 94
which necessitates that 𝜆 > 𝜆𝑚𝑖𝑛 > 0. On the other hand, 𝜆𝑚𝑎𝑥 is dictated by the minimum
allowable rate of fertilizer generation, which necessitates that (1 − 𝜆) > (1 − 𝜆𝑚𝑎𝑥) > 0, or
equivalently, 𝜆 < 𝜆𝑚𝑎𝑥 < 1. Finally, 𝐾 is a constant parameter related to buffering ammonia
production for fertilizer synthesis, to be formally introduced in Scenario 2b.
Figure 3.2: Schematic representation of static and flexible PES
To reflect current market conditions, the analysis in all scenarios assumes that the price of
electricity changes on an hourly basis [29] whereas the price of fertilizer changes on a yearly
basis [30]. The underlying assumption is that electricity is typically sold in competitive
wholesale markets, but fertilizers can be sold through long-term contracts because they can be
stored relatively easily. Also, to simplify the economic modeling, all fixed and variable costs
are assumed to remain constant in a given year, but they may change across years. Section 5.2
discusses the implications of this assumption in more detail.
3.1 Scenario 1: Static PES with Fixed Production Rates
If the polygeneration system is static, all subsystems run at steady-state with constant
production rates. The ammonia stream is directly and completely converted to fertilizer
Hydrogen
Electricity
Ammonia Fertilizers
Ammonia Storage
Hydrogen
Electricity
Scenario 1:
Static PES
Ammonia Fertilizers
Hydrogen
Electricity
Scenario 2a:
Flexible PES
with flexible
fertilizers
subsystemAmmonia Fertilizers
Scenario 2b:
Flexible PES
with static
fertilizers
subsystem
CHAPTER 3 — Economic Analysis 95
without the need for an intermediate storage. For every kilogram of hydrogen, the PES outputs
𝜆 ∙ 𝑋𝑒 kilowatt hours of electricity, (1 − 𝜆) ∙ 𝑋𝑎 kilograms of ammonia, and (1 − 𝜆) ∙ 𝑋𝑓
kilograms of fertilizer. We refer to 𝜆 ∙ 𝑋𝑒, (1 − 𝜆) ∙ 𝑋𝑎, and (1 − 𝜆) ∙ 𝑋𝑓 as production
coefficients.
The economic value of this static PES must account for the generation of electricity and
fertilizer at each point in time. Therefore, the expression in (6) is modified by substituting the
revenue from direct sales of merchant hydrogen with the net revenue from converting
hydrogen to both end-products.
For each unit of produced electricity, the net revenue is the difference between the time-
averaged price 𝑃𝑒 ($ 𝑘𝑊ℎ⁄ ) and the levelized incremental cost of installing and operating the
electricity subsystem, defined as 𝐿𝐼𝐶𝑒 ($ 𝑘𝑊ℎ⁄ ). 𝐿𝐼𝐶𝑒 is distinguished from 𝐿𝐶𝑂𝐸. 𝐿𝐼𝐶𝑒
captures the cost of the electricity subsystem only (e.g. combined-cycle turbine). In contrast,
𝐿𝐶𝑂𝐸 accounts for the full cost of electricity generation, which includes the cost of hydrogen.
Therefore, if 𝜆 = 1, we obtain 𝐿𝐶𝑂𝐸 = 𝐿𝐶𝑂𝐻 𝑋𝑒⁄ + 𝐿𝐼𝐶𝑒.
Similarly, for each unit of produced fertilizer, the net revenue is the difference between the
time-averaged price 𝑃𝑓 ($ 𝑘𝑔ℎ⁄ ) and the levelized incremental cost of both the ammonia and
fertilizer subsystems, defined as 𝐿𝐼𝐶𝑎 ($ 𝑘𝑔𝑎⁄ ) and 𝐿𝐼𝐶𝑓 ($ 𝑘𝑔𝑓⁄ ), respectively. Referring to
Section 2.1, Definition 1 presents each 𝐿𝐼𝐶 metric as the sum of three levelized cost
components: a cost of capacity 𝑐, a time-averaged fixed operating cost 𝑗, and a time-averaged
variable cost 𝑤.
Definition 1:
𝐿𝐼𝐶𝑒 = 𝑐𝑒 + 𝑗𝑒 + 𝑤𝑒 (7)
𝐿𝐼𝐶𝑎 = 𝑐𝑎 + 𝑗𝑎 + 𝑤𝑎 (8)
𝐿𝐼𝐶𝑓 = 𝑐𝑓 + 𝑗𝑓 + 𝑤𝑓 (9)
As a result, it is now possible to assess the economic feasibility of this static PES by
formulating Proposition 1.
CHAPTER 3 — Economic Analysis 96
Proposition 1:
A static polygeneration facility is cost-competitive if and only if:
λ ∙ 𝑋𝑒 ∙ (𝑃𝑒 − 𝐿𝐼𝐶𝑒) + (1 − λ) ∙ (𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎) > 𝐿𝐶𝑂𝐻 (10)
As proven in the derivation of Proposition 1 in Appendix A, the unit revenue for hydrogen in
(6), 𝑃ℎ, is replaced with two net-revenue terms, one for each end-product: (𝑋𝑒 ∙ 𝑃𝑒 −
𝑋𝑒 ∙ 𝐿𝐼𝐶𝑒) corresponding to the net revenue from hydrogen conversion to electricity and
(𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎) corresponding to the net revenue from hydrogen conversion
to ammonia then fertilizer. The net revenue from each end-product is weighted by the fraction
of hydrogen capacity allocated to it: λ for electricity and (1 − λ) for fertilizer.
Proposition 1 provides several insights. For the static PES to break even, the prices of end-
products must be high enough to compensate not only for their incremental cost but also for
the cost of hydrogen. Furthermore, optimizing the economic value of the static PES requires
maximizing hydrogen allocation to the end-product contributing the highest net revenue.
Ultimately, this incentivizes setting λ = 1 when (𝑋𝑒 ∙ 𝑃𝑒 − 𝑋𝑒 ∙ 𝐿𝐼𝐶𝑒) ≥ (𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 −
𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎) and setting λ = 0 otherwise; in both cases, static PES reduces to static
monogeneration of either end-product. Therefore, Proposition 1 shows that the profitability of
a static PES with multiple end-products is bounded by the profitability of the static
monogeneration of its individual end-products.
To elaborate further on the economics of polygeneration, we introduce the levelized cost of
polygeneration, or 𝐿𝐶𝑂𝑃 ($ 𝑘𝑔ℎ⁄ ). Consistent with the earlier definition of 𝐿𝐶𝑂𝐻, we define
𝐿𝐶𝑂𝑃 in (11) as a weighted-average price of polygeneration end-products that would set the
NPV of the PES to exactly zero.
Definition 2:
𝐿𝐶𝑂𝑃 = 𝐿𝐶𝑂𝐻 + λ ∙ 𝑋𝑒 ∙ 𝐿𝐼𝐶𝑒 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 + 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎] (11)
CHAPTER 3 — Economic Analysis 97
Proposition 1 can then be re-arranged to incorporate the mathematical form of 𝐿𝐶𝑂𝑃 in
Definition 2.
Proposition 1’:
A static polygeneration facility is cost-competitive if and only if:
λ ∙ 𝑋𝑒 ∙ 𝑃𝑒 + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑃𝑓 > 𝐿𝐶𝑂𝑃 (12)
The 𝐿𝐶𝑂𝑃 formulation in (11) shows that the levelized cost of a static PES can be expressed
as the sum of the levelized cost of its operational subsystems weighted by their respective
production coefficients. While the levelized costs of individual subsystems can be calculated
using multiple units, (e.g. $/𝑘𝑊ℎ for 𝐿𝐼𝐶𝑒), the conversion rates 𝑋𝑒, 𝑋𝑎, and 𝑋𝑓 ensure that
the overall PES cost is expressed as a monetary value per unit of hydrogen. Clearly, this
approach facilitates comparing the cost of different polygeneration systems with different
configurations, all of which produce hydrogen as an intermediate product.
Furthermore, while (6) shows that the value of monogeneration is dictated by only one price,
Proposition 1’ in (12) shows that the value of polygeneration is determined by a sum of end-
product prices weighted by their respective production coefficients. Consequently, for a fixed
operation mode and thus fixed set of production coefficients, multiple combinations of end-
product prices may achieve break-even. In imperfectly competitive markets, the PES firm can
negotiate multiple portfolios of end-products prices with potential buyers. For instance, the
firm may sell electricity at a competitive market price while having pricing power in selling
fertilizers due to constrained regional supply. Alternatively, in perfectly competitive markets
with preset prices, break-even may be achieved by adjusting production coefficients on both
sides of (12) because 𝜆 is a controllable design parameter. In short, a polygeneration facility
can break even via multiple portfolios of end-product prices and production capacities.
3.2 Scenario 2: Flexible PES with Variable Production Rates
For a PES in flexible mode, both electricity and ammonia generation rates can vary on an
hourly basis; decreasing the power output results in increasing the ammonia output, and vice
CHAPTER 3 — Economic Analysis 98
versa. While a constant hydrogen generation capacity 𝑁ℎ is maintained, the fraction of
hydrogen converted to electricity and ammonia may vary with time. We use the notation 𝜆(𝑡)
in Figure 3.2 to highlight this fact. Still, due to flexibility constraints, the condition that
𝜆𝑚𝑖𝑛 < 𝜆(𝑡) < 𝜆𝑚𝑎𝑥 remains in place. When 𝜆(𝑡) = 𝜆𝑚𝑎𝑥, electricity production is
maximized while fertilizer production is minimized. Conversely, when 𝜆(𝑡) = 𝜆𝑚𝑖𝑛,
electricity production is minimized while fertilizer production is maximized.
The flexible PES is analyzed sequentially in Scenarios 2a and 2b below. Scenario 2a makes
the simplifying assumption that the fertilizer subsystem can run flexibly, so the variable
fertilizer output is perfectly synchronized with the variable ammonia output. In Scenario 2b,
we acknowledge the real-world need for a static fertilizer subsystem. In other words, Scenario
2a presents a hypothetical operational configuration that aims to benchmark the performance
of the more realistic Scenario 2b. Comparing these two scenarios provides insight into the role
of technical constraints in controlling the economic value of flexible polygeneration.
3.2.1. Scenario 2a: Flexible PES with a Flexible Fertilizer Subsystem
As illustrated in Figure 3.2, a variable fertilizer output results from the direct conversion of the
variable ammonia output at each time interval 𝑡, so no intermediate ammonia storage is
needed in this case. Nonetheless, to accommodate the maximum possible flowrates, the
production capacity of the flexible units should be set at 𝜆𝑚𝑎𝑥 ∙ 𝑋𝑒 (𝑘𝑊) for electricity,
(1 − 𝜆𝑚𝑖𝑛) ∙ 𝑋𝑎 (𝑘𝑔𝑎 ℎ𝑟⁄ ) for ammonia, and (1 − 𝜆𝑚𝑖𝑛) ∙ 𝑋𝑓 (𝑘𝑔𝑓 ℎ𝑟⁄ ) for fertilizer.3 Similar
to Scenario 1, the incurred capacity and fixed operating costs are scaled by these constant
production capacities, independent of the variable production rates.
Since both capacity and fixed operating costs are constant in a given year 𝑖, maximizing the
profitability of the flexible PES requires maximizing the contribution margin of hydrogen
3 Our analysis speaks to the cost competitiveness of a flexible PES whose capacity is chosen to
accommodate the maximum possible flowrate of ammonia. In future work, it would be desirable to
explore under what conditions a flexible PES, accommodating a lower flowrate but requiring
correspondingly smaller capacity investments, could be more economical.
CHAPTER 3 — Economic Analysis 99
conversion at every point in time 𝑡 of that year.4 Definition 3 introduces 𝐶𝑀𝑒 ($ 𝑘𝑔ℎ⁄ ) and
𝐶𝑀𝑓 ($ 𝑘𝑔ℎ⁄ ) as the contribution margins associated with converting one kilogram of
hydrogen to 𝑋𝑒 kilowatt hours of electricity and 𝑋𝑓 kilograms of fertilizer, respectively.
Definition 3:
𝐶𝑀𝑒𝑖(𝑡) = [𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖(𝑡)] (13)
𝐶𝑀𝑓𝑖(𝑡) = [𝑋𝑓 ∙ 𝑃𝑓𝑖(𝑡) − 𝑋𝑓 ∙ 𝑤𝑓𝑖(𝑡) − 𝑋𝑎 ∙ 𝑤𝑎𝑖(𝑡)] (14)
When 𝐶𝑀𝑒𝑖(𝑡) > 𝐶𝑀𝑓𝑖(𝑡), electricity production should be maximized and fertilizer
production should be minimized; the opposite must hold when 𝐶𝑀𝑒𝑖(𝑡) < 𝐶𝑀𝑓𝑖(𝑡).
Accordingly, we divide the yearly hours 𝑚 into 𝑚𝑒 and 𝑚𝑓, introduced in Definition 4. 𝑚𝑒𝑖
(ℎ𝑟) corresponds to the hours in year 𝑖 when 𝐶𝑀𝑒𝑖(𝑡) ≥ 𝐶𝑀𝑓𝑖(𝑡) whereas 𝑚𝑓𝑖 (ℎ𝑟)
corresponds to the hours when 𝐶𝑀𝑒𝑖(𝑡) < 𝐶𝑀𝑓𝑖(𝑡).5 Clearly, 𝑚 = 𝑚𝑓𝑖 + 𝑚𝑒𝑖 for every year 𝑖.
Definition 4:
𝑚𝑒𝑖 = 𝜇({𝑡|0 ≤ 𝑡 ≤ 𝑚, 𝐶𝑀𝑒𝑖(𝑡) ≥ 𝐶𝑀𝑓𝑖(𝑡)}) (15)
𝑚𝑓𝑖 = 𝜇({𝑡|0 ≤ 𝑡 ≤ 𝑚, 𝐶𝑀𝑒𝑖(𝑡) < 𝐶𝑀𝑓𝑖(𝑡)}) (16)
Flexibility enables choosing the highest contribution margin in every time period. Thus, we
define the difference between 𝐶𝑀𝑒𝑖(𝑡) and 𝐶𝑀𝑓𝑖(𝑡) as the incremental contribution margin
of flexibility (𝐼𝐶𝑀𝐹). In a given year 𝑖, 𝐼𝐶𝑀𝐹𝑒𝑖 is the yearly-averaged sum of flexibility-
enabled contribution margin over 𝑚𝑒𝑖 hours, attributed to switching hydrogen allocation from
fertilizer to electricity. Equivalently, 𝐼𝐶𝑀𝐹𝑓𝑖 is the yearly-averaged sum of flexibility-enabled
contribution margin over 𝑚𝑓𝑖 hours, attributed to switching hydrogen allocation from
4 Contribution margin refers to the difference between sales and variable costs. The analysis in
Reichelstein and Sahoo [45] explains a related idea on quantifying the temporal co-variation between
prices and generation capacity of an intermittent power source. 5 𝜇 in (15) and (16) is the Lebesgue Measure over the set of real numbers between 0 and 𝑚 [46].
CHAPTER 3 — Economic Analysis 100
electricity to fertilizer. 𝐼𝐶𝑀𝐹𝑒𝑖 ($ 𝑘𝑔ℎ⁄ ) and 𝐼𝐶𝑀𝐹𝑓𝑖 ($ 𝑘𝑔ℎ⁄ ) are introduced in Definition 5.
By design, both terms are always positive.
Definition 5:
𝐼𝐶𝑀𝐹𝑒𝑖 =1
𝑚∙ ∫ [𝐶𝑀𝑒𝑖(𝑡) − 𝐶𝑀𝑓𝑖(𝑡)]𝑑𝑡
𝑚𝑒𝑖
(17)
𝐼𝐶𝑀𝐹𝑓𝑖 =1
𝑚∙ ∫[𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑒𝑖(𝑡)]𝑑𝑡
𝑚𝑓𝑖
(18)
The formulation of 𝐼𝐶𝑀𝐹 illustrates the beneficial impacts of price volatility on the economics
of flexible PES. Consistent with the earlier assumption that only electricity price 𝑃𝑒𝑖(𝑡)
changes over time, the effect of higher volatility in 𝑃𝑒𝑖(𝑡) is captured in two ways: higher
𝑃𝑒𝑖(𝑡) leads to higher 𝐶𝑀𝑒𝑖(𝑡) during 𝑚𝑒𝑖 hours and therefore higher 𝐼𝐶𝑀𝐹𝑒𝑖, and lower
𝑃𝑒𝑖(𝑡) leads to lower 𝐶𝑀𝑒𝑖(𝑡) during 𝑚𝑓𝑖 hours and therefore higher 𝐼𝐶𝑀𝐹𝑓𝑖. In short, the
higher the price volatility (around the same price average), the higher the incremental
contribution margin of flexibility.
Similar to the time-averaged variable cost in (6), the time-averaged incremental contribution
margins of flexibility 𝐼𝐶𝑀𝐹𝑒 ($ 𝑘𝑔ℎ⁄ ) and 𝐼𝐶𝑀𝐹𝑓 ($ 𝑘𝑔ℎ⁄ ) are derived from 𝐼𝐶𝑀𝐹𝑒𝑖 and
𝐼𝐶𝑀𝐹𝑓𝑖 in (19) and (20), respectively.
𝐼𝐶𝑀𝐹𝑒 =∑ 𝐼𝐶𝑀𝐹𝑒𝑖 ∙ 𝑥𝑖 ∙ 𝛾𝑖𝑇
𝑖=1
∑ 𝑥𝑖 ∙ 𝛾𝑖𝑇𝑖=1
(19)
𝐼𝐶𝑀𝐹𝑓𝑖 =∑ 𝐼𝐶𝑀𝐹𝑓𝑖 ∙ 𝑥𝑖 ∙ 𝛾𝑖𝑇
𝑖=1
∑ 𝑥𝑖 ∙ 𝛾𝑖𝑇𝑖=1
(20)
As a result, we can now assess the economic feasibility of the flexible PES in this simplified
scenario by formulating two mathematically equivalent statements of Proposition 2a.
CHAPTER 3 — Economic Analysis 101
Proposition 2a:
A flexible PES is cost-competitive if and only if:
[𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎]
+λ𝑚𝑎𝑥 ∙ [𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)]
−λ𝑚𝑖𝑛 ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎 + 𝑗𝑎)] > 𝐿𝐶𝑂𝐻
(21)
Equivalently, the flexible PES is cost-competitive if and only if:
𝑋𝑒 ∙ [𝑃𝑒 − 𝐿𝐼𝐶𝑒]
+(1 − λ𝑚𝑖𝑛) ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎 + 𝑗𝑎)]
−(1 − λ𝑚𝑎𝑥) ∙ [𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)] > 𝐿𝐶𝑂𝐻
(22)
As proven in Appendix A, the left-hand sides in (21) and (22) are identical. The formulation in
(21) benchmarks flexible polygeneration against static fertilizer monogeneration. Specifically,
the net revenue from hydrogen conversion is divided into three terms. As in Scenario 1, the
first term [𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎] corresponds to the net revenue from the static
monogeneration of fertilizer. The second and third terms correspond to the additional net
revenues from flexibility. λ𝑚𝑎𝑥[𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)] represents the net revenue associated
with flexible switching from fertilizer to electricity; the flexibility-enabled incremental
contribution margin is weighed against the flexibility-required capacity and fixed operating
costs of generating electricity. This gained net revenue is scaled by λ𝑚𝑎𝑥, the maximum
fraction of hydrogen capacity allocated to electricity. On the other hand, electricity generation
cannot drop below a lower limit defined by λ𝑚𝑖𝑛, so the corresponding net revenue associated
with flexible switching from electricity to fertilizer is lost. This net revenue is captured in
λ𝑚𝑖𝑛 ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎 + 𝑗𝑎)], which balances the flexibility-enabled
incremental contribution margin against the flexibility-required capacity and fixed operating
costs of generating ammonia then fertilizer.
The formulation in (22) has a similar and symmetric structure to (21), but it benchmarks the
economics of the flexible polygeneration against static electricity monogeneration. In this
case, the gained and lost net-revenue terms associated with flexibility are scaled by (1 −
CHAPTER 3 — Economic Analysis 102
λ𝑚𝑖𝑛) and (1 − λ𝑚𝑎𝑥), corresponding to the maximum and minimum fractions of hydrogen
that can be converted to fertilizer, respectively.
In both (21) and (22), the gained and lost net-revenue terms associated with flexibility are
positive only when the incremental contribution margin surpasses the capacity and fixed
operating costs. Thus, Proposition 2a shows that adding flexibility to a PES may not result in
superior economic value; the latter depends on the specifications of the investigated facility.
We analyze this dependency in more detail in Section 4. Also, (21) and (22) show that
maximizing the revenue of flexible polygeneration requires exploiting the ability to vary λ(𝑡)
between λ𝑚𝑖𝑛 and λ𝑚𝑎𝑥; setting λ𝑚𝑖𝑛 = λ𝑚𝑎𝑥 = λ reduces Proposition 2a to Proposition 1.
3.2.2. Scenario 2b: Flexible PES with a Static Fertilizer Subsystem
We now analyze a flexible PES with a static fertilizer subsystem. Compared to Scenario 2a,
this operational mode induces two technical updates. First, intermediate ammonia storage is
needed to buffer the variable ammonia output (1 − 𝜆(𝑡)) ∙ 𝑋𝑎 (𝑘𝑔𝑎 ℎ𝑟⁄ ) and secure a fixed
ammonia input 𝐾 ∙ 𝑋𝑎 (𝑘𝑔𝑎 ℎ𝑟⁄ ) into the fertilizer processing unit. Intuitively, ammonia is
withdrawn from storage to compensate for shortage when (1 − 𝜆(𝑡)) < 𝐾, and it is added to
storage to save excess when (1 − 𝜆(𝑡)) > 𝐾. The storage capacity is denoted by Sa (𝑘𝑔𝑎),
and we assume optimized storage operations. Specifically, the site can always accommodate
the addition or withdrawal of ammonia at any rate. Also, all ammonia produced in a given
year is converted to fertilizer, resulting in no annual net-storage. These two conditions
maintain the underlying assumption that 𝑚𝑒𝑖 and 𝑚𝑓𝑖 are the same in every year 𝑖 throughout
the facility’s lifetime.
Second, because the fertilizer output is fixed, no excess capacity is needed to accommodate
variable production. Therefore, the capacity of the fertilizer subsystem is reduced from
(1 − 𝜆𝑚𝑖𝑛) ∙ 𝑋𝑓 to 𝐾 ∙ 𝑋𝑓 (𝑘𝑔𝑓 ℎ𝑟⁄ ). A yearly mass balance on ammonia production allows
defining 𝐾 in terms of 𝜆, as depicted in (23). As explained before, ammonia production is
minimized during 𝑚𝑒 hours but maximized during 𝑚𝑓 hours. Equating the yearly variable
CHAPTER 3 — Economic Analysis 103
output from the ammonia subsystem to the yearly fixed input into the fertilizer subsystem
results in 𝐾 = [𝑚𝑒 ∙ (1 − 𝜆𝑚𝑎𝑥) + 𝑚𝑓 ∙ (1 − 𝜆𝑚𝑖𝑛)] 𝑚⁄ .
[𝑚𝑒 ∙ (1 − 𝜆𝑚𝑎𝑥) + 𝑚𝑓 ∙ (1 − 𝜆𝑚𝑖𝑛)] ∙ 𝑋𝑓 = 𝑚 ∙ 𝐾 ∙ 𝑋𝑓 (23)
With these modifications, we can assess the economic feasibility of flexible polygeneration in
this scenario by deriving two equivalent statements of the new Proposition 2b.
Proposition 2b:
A flexible PES is cost-competitive if and only if:
[𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎𝑠]
+λ𝑚𝑎𝑥 ∙ [𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)]
−λ𝑚𝑖𝑛 ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎𝑠 + 𝑗𝑎𝑠)]
+[(1 − λ𝑚𝑖𝑛 − 𝐾) ∙ 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓)] > 𝐿𝐶𝑂𝐻
(24)
Equivalently, the flexible PES is cost-competitive if and only if:
𝑋𝑒 ∙ [𝑃𝑒 − 𝐿𝐼𝐶𝑒]
+(1 − λ𝑚𝑖𝑛) ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎𝑠 + 𝑗𝑎𝑠)]
−(1 − λ𝑚𝑎𝑥) ∙ [𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)]
+[(1 − λ𝑚𝑖𝑛 − 𝐾) ∙ 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓)] > 𝐿𝐶𝑂𝐻
(25)
A detailed derivation of (24) and (25) is presented in Appendix A. The formulations in (24)
and (25) are identical to those in (21) and (22) for Scenario 2a, except for two differences.
First, to account for storage, the levelized-cost terms of ammonia 𝑐𝑎, 𝑗𝑎, and 𝑤𝑎 are updated to
𝑐𝑎𝑠, 𝑗𝑎𝑠, and 𝑤𝑎𝑠, respectively; other metrics incorporating these terms are also updated
accordingly. Second, reducing the fertilizer capacity from (1 − λ𝑚𝑖𝑛) in Scenario 2a to 𝐾 in
Scenario 2b results in a net-revenue gain of [(1 − λ𝑚𝑖𝑛 − 𝐾) ∙ 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓)], which accounts
for savings in capacity and fixed operating costs. All other economic expressions introduced
in Scenario 2a remain valid here. Notably, the flexible PES still captures the full economic
benefits of flexibility even though the fertilizer subsystem is static. Because storage allows all
CHAPTER 3 — Profitability and Value of Real-Options 104
generated ammonia to be eventually converted to fertilizer, flexible ammonia generation is
sufficient to sustain the economic benefits of flexible fertilizer generation.
1 − λ𝑚𝑖𝑛 − 𝐾 = 1 − λ𝑚𝑖𝑛 − 1 +𝑚𝑓 ∙ λ𝑚𝑖𝑛
𝑚+
𝑚𝑒 ∙ λ𝑚𝑎𝑥
𝑚=
𝑚𝑒 ∙ (λ𝑚𝑎𝑥 − λ𝑚𝑖𝑛)
𝑚 (26)
Equally important, (1 − λ𝑚𝑖𝑛 − 𝐾) is directly proportional to 𝑚𝑒, as shown in (26). A larger
𝑚𝑒 means that the flexible PES spends more time maximizing electricity generation on the
expense of fertilizer generation. In this case, a smaller static fertilizer subsystem with
intermediate ammonia storage (Scenario 2b) may achieve better economics than a larger
flexible fertilizer subsystem with no storage (Scenario 2a), even if the latter is technically
feasible.
4 Profitability and Value of Real-Options
Our findings in Scenarios 1 and 2 show that different operation modes result in different
economic values for PES. Compared to a static single-output plant, a polygeneration plant
offers the option of diversifying the static output (Scenario 1) as well as the option of
substituting part of the static output capacity with flexible capacity (Scenario 2). To quantify
the value of these real-options, we first need to characterize the profitability of PES. The
overall net present value (NPV) associated with investing in the capacity to deliver one
kilogram of hydrogen per hour (𝑁ℎ = 1) is given in (27). 𝑃𝑀 is the profit-margin, which
denotes the difference between the net revenue for one kilogram of hydrogen and its levelized
cost. We use 𝑃𝑀 as a profitability metric to assess PES under different operation modes.
𝑁𝑃𝑉 ($) = 𝑃𝑀 ∙ 𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1 (27)
𝑃𝑀0 measures the unit profit-margin of a static single-output plant. 𝑃𝑀0𝑓 ($/𝑘𝑔ℎ) refers to
the profit-margin of a static plant that converts all hydrogen to ammonia and then fertilizer
(𝜆 = 0). Similarly, 𝑃𝑀0𝑒 ($/𝑘𝑔ℎ) refers to the profit-margin of a static power plant that
CHAPTER 3 — Profitability and Value of Real-Options 105
converts all hydrogen to electricity (𝜆 = 1). 𝑃𝑀0𝑓 and 𝑃𝑀0𝑒 are formally defined in (28) and
(29), respectively.
𝑃𝑀0𝑓 = 𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎 − 𝐿𝐶𝑂𝐻 (28)
𝑃𝑀0𝑒 = 𝑋𝑒 ∙ 𝑃𝑒 − 𝑋𝑒 ∙ 𝐿𝐼𝐶𝑒 − 𝐿𝐶𝑂𝐻 (29)
Let 𝑃𝑀1 ($/𝑘𝑔ℎ) denote the unit profit-margin of the static PES in Scenario 1, which can be
directly deduced from Proposition 1. 𝑃𝑀1 is derived in (30) by re-arranging the terms in (10),
𝑃𝑀1 = λ ∙ 𝑋𝑒 ∙ (𝑃𝑒 − 𝐿𝐼𝐶𝑒) + (1 − λ) ∙ (𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎) − 𝐿𝐶𝑂𝐻 (30)
Similarly, 𝑃𝑀2 ($/𝑘𝑔ℎ) refers to the unit profit-margin of the flexible PES in Scenario 2,
which is obtained directly from Proposition 2b. 𝑃𝑀2 can be expressed in two forms, 𝑃𝑀2𝑓
($/𝑘𝑔ℎ) and 𝑃𝑀2𝑒 ($/𝑘𝑔ℎ), presented in (31) and (32), respectively. 𝑃𝑀2𝑓 is derived from
(24) where the economic value of a flexible PES is benchmarked against that of a static
fertilizer plant, and 𝑃𝑀2𝑒 is derived from (25) where the economic value of a flexible PES is
benchmarked against that of a static power plant. Importantly, we note that 𝑃𝑀2𝑒 = 𝑃𝑀2𝑓.
𝑃𝑀2𝑓 = [𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎𝑠]
+λ𝑚𝑎𝑥 ∙ [𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)]
−λ𝑚𝑖𝑛 ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎𝑠 + 𝑗𝑎𝑠)]
+[(1 − λ𝑚𝑖𝑛 − 𝐾) ∙ 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓)] − 𝐿𝐶𝑂𝐻
(31)
𝑃𝑀2𝑒 = 𝑋𝑒 ∙ [𝑃𝑒 − 𝐿𝐼𝐶𝑒]
+(1 − λ𝑚𝑖𝑛) ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎𝑠 + 𝑗𝑎𝑠)]
−(1 − λ𝑚𝑎𝑥) ∙ [𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)]
+[(1 − λ𝑚𝑖𝑛 − 𝐾) ∙ 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓)] − 𝐿𝐶𝑂𝐻
(32)
These profitability metrics can be directly used to quantify the value of real-options enabled
by polygeneration. We first define 𝑉𝑂𝐷 as the value of diversification from a single output to
a portfolio of multiple outputs. 𝑉𝑂𝐷𝑓 ($/𝑘𝑔ℎ) is the difference between the profit-margin of
static polygeneration 𝑃𝑀1 and that of static monogeneration of fertilizer 𝑃𝑀0𝑓; similarly,
CHAPTER 3 — Profitability and Value of Real-Options 106
𝑉𝑂𝐷𝑒 ($/𝑘𝑔ℎ) is the difference between 𝑃𝑀1 and 𝑃𝑀0𝑒. Clearly, both 𝑉𝑂𝐷𝑓 and 𝑉𝑂𝐷𝑒 are
dependent on 𝜆, as shown in (33) and (34), respectively.
𝑉𝑂𝐷𝑓(𝜆) = 𝑃𝑀1(𝜆) − 𝑃𝑀0𝑓 (33)
𝑉𝑂𝐷𝑒(𝜆) = 𝑃𝑀1(𝜆) − 𝑃𝑀0𝑒 (34)
We then define the value of flexibility 𝑉𝑂𝐹 ($/𝑘𝑔ℎ) associated with varying power and
ammonia production rates with time. 𝑉𝑂𝐹 is the difference between the profit-margin of
flexible polygeneration 𝑃𝑀2 and that of static polygeneration 𝑃𝑀1, and it is dependent on 𝜆,
as highlighted in (35). This formulation shows that flexible polygeneration is more profitable
than static polygeneration only if 𝑉𝑂𝐹(𝜆) > 0. There might exist some value of 𝜆 for which a
static PES could outperform a flexible PES, in which case 𝑉𝑂𝐹(𝜆) is negative.
𝑉𝑂𝐹(𝜆) = 𝑃𝑀2𝑓 − 𝑃𝑀1(𝜆) = 𝑃𝑀2𝑒 − 𝑃𝑀1(𝜆) (35)
Overall, we define the value of polygeneration 𝑉𝑂𝑃 ($/𝑘𝑔ℎ) as the sum of the real-option
values associated with both diversification and flexibility. As shown in (36) and (37), one
𝑉𝑂𝑃 metric is needed for each end-product; 𝑉𝑂𝑃𝑓 ($/𝑘𝑔ℎ) compares the profit-margin of a
flexible PES to that of a static fertilizer plant, and 𝑉𝑂𝑃𝑒 ($/𝑘𝑔ℎ) compares the profit-margin
of a flexible PES to that of a static power plant.
𝑉𝑂𝑃𝑓 = 𝑉𝑂𝐹(𝜆) + 𝑉𝑂𝐷𝑓(𝜆) = 𝑃𝑀2𝑓 − 𝑃𝑀0𝑓 (36)
𝑉𝑂𝑃𝑒 = 𝑉𝑂𝐹(𝜆) + 𝑉𝑂𝐷𝑒(𝜆) = 𝑃𝑀2𝑒 − 𝑃𝑀0𝑒 (37)
When 𝑉𝑂𝑃𝑓 > 0, flexible polygeneration is more profitable than static fertilizer
monogeneration. Similarly, when 𝑉𝑂𝑃𝑒 > 0, flexible polygeneration is more profitable than
static power monogeneration. However, we showed in (33) and (34) that static polygeneration
is less profitable than the static monogeneration of at least one end-product. Accordingly,
when both 𝑉𝑂𝑃𝑓 and 𝑉𝑂𝑃𝑒 are positive, flexible polygeneration is more profitable than both
static monogeneration and static polygeneration. In that regard, while 𝑉𝑂𝐹(𝜆) identifies the
condition for a flexible PES to be more profitable than a specific static PES with a specific 𝜆,
CHAPTER 3 — Additional Modeling Considerations 107
𝑉𝑂𝑃 identifies the condition for a flexible PES to be more profitable than any static PES with
any 𝜆.
5 Additional Modeling Considerations
5.1 Carbon Capture and Storage
The proposed economic assessment of PES can be robustly expanded to account for technical
supplements such as carbon capture and storage (CCS). The net CO2 output, defined as the
gross CO2 production less the CO2 used for fertilizer synthesis, may be compressed then
transported in pipelines to be either geologically sequestered or used for enhanced oil recovery
[23]. Since CO2 is produced by a steady-state process (gasification) and partially utilized by
another steady-state process (fertilizer synthesis), its net output is a fixed flow, regardless of
whether the PES is static of flexible.
CCS is treated as a separate subsystem of production capacity 𝑈𝑐 ∙ 𝑁ℎ. (𝑘𝑔𝑐 ℎ𝑟⁄ ), where 𝑈𝑐
(𝑘𝑔𝑐 𝑘𝑔ℎ⁄ ) denotes the net CO2 output rate per one kilogram of produced hydrogen. As
before, 𝐿𝐼𝐶𝑐 refers to the sum of 𝑐𝑐, 𝑗𝑐, and 𝑤𝑐, which correspond to the cost of capacity, time-
averaged fixed operating cost, and time-averaged variable cost of CCS per unit of CO2
($ 𝑘𝑔𝑐⁄ ), respectively. Also, if sold for enhanced oil recovery, the CO2 output generates
revenue proportional to its price 𝑃𝑐 ($ 𝑘𝑔𝑐⁄ ). As such, Propositions 1 and 2b can be revised to
incorporate CCS in a static and a flexible PES, as shown in (38) and (39), respectively. All
other economic metrics and propositions can be updated accordingly.
Proposition 1’’:
A static PES with CCS is cost-competitive if and only if:
λ ∙ 𝑋𝑒 ∙ (𝑃𝑒 − 𝐿𝐼𝐶𝑒) + (1 − λ) ∙ (𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎)
+𝑈𝑐 ∙ (𝑃𝑐 − 𝐿𝐼𝐶𝑐) > 𝐿𝐶𝑂𝐻 (38)
CHAPTER 3 — Additional Modeling Considerations 108
Proposition 2b’:
A flexible PES with CCS is cost-competitive if and only if:
[𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎𝑠]
+λ𝑚𝑎𝑥 ∙ [𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)]
−λ𝑚𝑖𝑛 ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎𝑠 + 𝑗𝑎𝑠)]
+[(1 − λ𝑚𝑖𝑛 − 𝐾) ∙ 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓)] + 𝑈𝑐 ∙ (𝑃𝑐 − 𝐿𝐼𝐶𝑐) > 𝐿𝐶𝑂𝐻
(39)
5.2 Time-dependency of prices and variable costs
So far, we have assumed that, except for the price of electricity, all prices and variable costs
are fixed within a given year. If this assumption is not met, the aforementioned analysis will
still generate the exact same results in Scenario 1 and Scenario 2a, but slightly modified
results in Scenario 2b where fertilizer production is fixed. In this particular case, correction
terms should be added to the formulations of Proposition 2b to account for the different
averaging of the fertilizer contribution margin 𝐶𝑀𝑓𝑖(𝑡) over different time periods.
Specifically, (40) and (41) introduce the two correction terms 𝛷𝑓𝑖 ($/𝑘𝑔ℎ) and 𝛷𝑒𝑖 ($/𝑘𝑔ℎ)
in year 𝑖.
𝛷𝑓𝑖 =1
𝑚[𝑚𝑓𝑖
𝑚∫ [𝐶𝑀𝑓𝑖(𝑡)]𝑑(𝑡)
𝑚
− ∫ [𝐶𝑀𝑓𝑖(𝑡)]𝑑(𝑡)
𝑚𝑓𝑖
] =1
𝑚[𝑚𝑓𝑖𝐶𝑀𝑓𝑖 − ∫ [𝐶𝑀𝑓𝑖(𝑡)]𝑑(𝑡)
𝑚𝑓𝑖
] (40)
𝛷𝑒𝑖 =1
𝑚[𝑚𝑒𝑖
𝑚∫ [𝐶𝑀𝑓𝑖(𝑡)]𝑑(𝑡)
𝑚
− ∫ [𝐶𝑀𝑓𝑖(𝑡)]𝑑(𝑡)
𝑚𝑒𝑖
] =1
𝑚[𝑚𝑒𝑖𝐶𝑀𝑓𝑖 − ∫ [𝐶𝑀𝑓𝑖(𝑡)]𝑑(𝑡)
𝑚𝑒𝑖
] (41)
If all prices and variable costs are allowed to vary with time, Propositions 2b can be easily
revised to incorporate 𝛷𝑓 and 𝛷𝑒, as illustrated in (42).
CHAPTER 3 — Case Study: Hydrogen Energy California 109
Proposition 2b’’:
A flexible PES is cost-competitive if and only if:
[𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝐿𝐼𝐶𝑓 − 𝑋𝑎 ∙ 𝐿𝐼𝐶𝑎𝑠]
+λ𝑚𝑎𝑥 ∙ [𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ (𝑐𝑒 + 𝑗𝑒)]
−λ𝑚𝑖𝑛 ∙ [𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓) − 𝑋𝑎 ∙ (𝑐𝑎𝑠 + 𝑗𝑎𝑠)]
+[(1 − λ𝑚𝑖𝑛 − 𝐾) ∙ 𝑋𝑓 ∙ (𝑐𝑓 + 𝑗𝑓)]
−[𝜆𝑚𝑎𝑥 ∙ 𝛷𝑒 + 𝜆𝑚𝑖𝑛 ∙ 𝛷𝑓] > 𝐿𝐶𝑂𝐻
(42)
6 Case Study: Hydrogen Energy California
To demonstrate the usefulness of our model analysis in the previous sections, we now assess
the economic performance of Hydrogen Energy California (HECA), a polygeneration facility
currently under development in California.
6.1 Technical Configuration
Consistent with the technical configuration presented in Section 2.2, HECA uses a gasification
technology to convert coal and petcoke into clean-burning hydrogen. As an intermediate
product, hydrogen is then converted to electricity and ammonia, which is further processed
into urea and UAN – a solution of urea and ammonium nitrate [31, 32]. The operational
configuration of HECA allows flexible generation of electricity and ammonia, but it requires
static generation of hydrogen, urea, and UAN; the facility also includes a CO2 compression
unit, which can be treated as a separate static CCS subsystem.
The first task is to quantify all technical parameters needed for the economic evaluation. A list
of HECA’s technical parameters and their values is provided in Table 3.1. With a capacity
factor of 𝐶𝐹 = 0.835 and an expected operational lifetime of 25 years, the facility consumes
coal and petcoke at rates equal to roughly 4,209 𝑡𝑜𝑛𝑛𝑒/𝑑𝑎𝑦 and 1,053 𝑡𝑜𝑛𝑛𝑒/𝑑𝑎𝑦,
respectively [33]. The syngas generated from the gasification of coal and petcoke undergoes
shift-reaction to convert most of the carbon monoxide into carbon dioxide, 90% of which is
CHAPTER 3 — Case Study: Hydrogen Energy California 110
captured. A fraction of the captured CO2, corresponding to 𝑈𝑐 = 12.1 𝑘𝑔𝑐 𝑘𝑔ℎ⁄ , is
compressed and sold to nearby oil fields for enhanced oil recovery.
Table 3.1: HECA technical parameters
Parameter Value Unit Reference
𝑇 25 𝑦𝑟 [Assumed]
𝐶𝐹 0.835 [unitless] [34]
𝑚𝑒 5,840 ℎ𝑟 [34]
𝑚𝑓 2,920 ℎ𝑟 [34]
𝐶𝑜𝑎𝑙 𝐼𝑛𝑝𝑢𝑡 4,209 𝑡𝑜𝑛𝑛𝑒/𝑑𝑎𝑦 [33]
𝑃𝑒𝑡𝑐𝑜𝑘𝑒 𝐼𝑛𝑝𝑢𝑡 1,052 𝑡𝑜𝑛𝑛𝑒/𝑑𝑎𝑦 [33]
𝑁ℎ 28,748 𝑘𝑔ℎ/ℎ𝑟 [Calculated]
𝜆𝑚𝑖𝑛 0.521 [unitless] [Calculated]
𝜆𝑚𝑎𝑥 0.717 [unitless] [Calculated]
𝑋𝑒 19.66 𝑘𝑊ℎ 𝑘𝑔ℎ⁄ [Calculated]
𝑋𝑎 5.63 𝑘𝑔𝑎 𝑘𝑔ℎ⁄ [Calculated]
𝑋𝑢𝑟𝑒𝑎 9.93 𝑘𝑔𝑢𝑟𝑒𝑎 𝑘𝑔ℎ⁄ [Calculated]
𝑋𝑈𝐴𝑁 13.72 𝑘𝑔𝑈𝐴𝑁 𝑘𝑔ℎ⁄ [Calculated]
𝑈𝑐 12.10 𝑘𝑔𝑐 𝑘𝑔ℎ⁄ [Calculated]
𝑦𝑢𝑟𝑒𝑎 0.532 [unitless] [Calculated]
𝑦𝑈𝐴𝑁 0.468 [unitless] [Calculated]
𝑆𝑎 9,474,036 𝑘𝑔𝑎 [35]
Produced at a fixed flowrate of 𝑁ℎ = 28,748 𝑘𝑔ℎ/ℎ𝑟, hydrogen is converted to electricity
and ammonia at rates equal to 𝑋𝑒 = 19.66 𝑘𝑊ℎ 𝑘𝑔ℎ⁄ and 𝑋𝑎 = 5.63 𝑘𝑔𝑎 𝑘𝑔ℎ⁄ , respectively.
On a daily basis, the facility operates under two modes: “electricity peak” mode from 7 a.m. to
11 p.m., followed by “electricity off-peak” mode for the rest of the time. During “peak” hours
of electricity demand, the plant runs at maximum power and minimum ammonia generation
capacities, corresponding to 𝜆𝑚𝑎𝑥 = 0.717. Alternatively, during “off-peak” hours, the plant
runs at minimum power and maximum ammonia generation capacities, corresponding to
𝜆𝑚𝑖𝑛 = 0.521 [26]. Summing over one year, this results in 𝑚𝑒 = 5,840 ℎ𝑟 and 𝑚𝑓 = 2,920
ℎ𝑟. Importantly, 𝑚𝑒 and 𝑚𝑓 are exogenously imposed in this case instead of being
endogenously optimized through (15) and (16). This regime will have significant impacts on
the economic value of the facility, as we explain in the next section. Table 3.2 outlines the
CHAPTER 3 — Case Study: Hydrogen Energy California 111
auxiliary load requirements for the system under each operation mode [34]. As shown, both
operation modes consume 247248 𝑀𝑊 of the gross power output, which is less than
𝜆𝑚𝑖𝑛 ∙ 𝑋𝑒 ∙ 𝑁ℎ = 295 𝑀𝑊. In reality, HECA continues to generate a positive net power output
to the grid even under the “off-peak” mode [34].
Table 3.2: HECA auxiliary loads
System/Unit Peak
Mode
Off-Peak
Mode Unit Reference
Hydrogen subsystem 170 164 MW [34]
Electricity subsystem 12 12 MW [34]
Ammonia subsystem 10 17 MW [Estimated]
Urea + UAN subsystem 15 15 MW [Estimated]
CO2 subsystem 40 40 MW [34]
Total 247 248 MW [34]
The produced ammonia reacts with a fraction of the captured CO2 to synthesize urea, part of
which is then further processed with more ammonia to produce UAN. Because hydrogen is
effectively processed into two fertilizer end-products, every unit of hydrogen allocated to
fertilizer synthesis is split into two fractions: 𝑦𝑢𝑟𝑒𝑎 = 0.532 for urea and 𝑦𝑈𝐴𝑁 = 0.468 for
UAN. We then define 𝑋𝑢𝑟𝑒𝑎 = 9.93 𝑘𝑔𝑢𝑟𝑒𝑎 𝑘𝑔ℎ⁄ and 𝑋𝑈𝐴𝑁 = 13.72 𝑘𝑔𝑈𝐴𝑁 𝑘𝑔ℎ⁄ as the
conversion rates of hydrogen to urea and UAN, respectively. Finally, to buffer the variable
ammonia output and secure a constant input for urea and UAN synthesis, ammonia storage is
needed. The storage capacity is 𝑆𝑎 = 9,474,036 𝑘𝑔𝑎, equivalent to 7 days of full loading at a
rate of 𝐾 ∙ 𝑋𝑎 ∙ 𝑁ℎ = 56,393 𝑘𝑔𝑎 ℎ𝑟⁄ [35].
6.2 Economic Analysis
6.2.1. Cost and Revenue
The cost figures for the hydrogen, electricity, and CCS subsystems are based on a study by the
International Energy Agency that analyzes the economics of coal gasification for co-
production of electricity and hydrogen [36]. The cost of CCS in this case covers CO2
compression only, assuming other parties are responsible for CO2 transportation and
CHAPTER 3 — Case Study: Hydrogen Energy California 112
sequestration. In addition, the costs associated with ammonia production, ammonia storage,
urea production, and UAN production, are based on studies by Bartels [37], Leigh [38] and
Morgan [39], Lennon [40], and Damas [41], respectively. Furthermore, because the urea and
UAN units are static, we combine them into one “fertilizer” subsystem. This approach allows
us to directly use the economic metrics derived in Sections 3 and 4. For convenience, the costs
of this joint fertilizer subsystem are expressed per unit of produced urea, so the definition of
𝑋𝑓 and 𝐿𝐼𝐶𝑓 should be updated according to (43) and (44), respectively. All monetary figures
are adjusted to 2012 U.S. dollars, assuming a 1.33 conversion factor from Euro to U.S. dollar
when needed. Finally, as mentioned in Section 2.1, taxes are not accounted for in this analysis.
𝑋𝑓 = 𝑦𝑢𝑟𝑒𝑎 ∙ 𝑋𝑢𝑟𝑒𝑎 (43)
𝐿𝐼𝐶𝑓 ($/𝑘𝑔𝑢𝑟𝑒𝑎) =𝑦𝑢𝑟𝑒𝑎 ∙ 𝑋𝑢𝑟𝑒𝑎 ∙ 𝐿𝐼𝐶𝑢𝑟𝑒𝑎 + 𝑦𝑈𝐴𝑁 ∙ 𝑋𝑈𝐴𝑁 ∙ 𝐿𝐼𝐶𝑈𝐴𝑁
𝑋𝑓 (44)
The levelized capacity, fixed operating, and variable costs are presented in Tables 3.3, 3.4, and
3.5, respectively; a more detailed breakdown of the cost figures is provided in Appendix B.
We assume a constant annual discount rate of τ = 0.07 and no degradation in productivity
over the years (𝑥 = 1) for all cost figures.
Table 3.3: Levelized costs of capacity of HECA
Cost Value Unit
𝑐ℎ 0.5267 $/𝑘𝑔ℎ
𝑐𝑒 0.0123 $/𝑘𝑊ℎ
𝑐𝑎 0.0453 $/𝑘𝑔𝑎
𝑐𝑎𝑠 0.0463 $/𝑘𝑔𝑎
𝑐𝑓 0.0520 $/𝑘𝑔𝑢𝑟𝑒𝑎
𝑐𝑐 0.0016 $/𝑘𝑔𝑐
Table 3.3 lists the levelized costs of capacity for the five major subsystems of HECA. Since
the size of HECA is comparable to that of the facilities analyzed in the referenced literature,
linear scaling factors are used to calculate the capacity cost of each subsystem. Also, we recall
that 𝑐𝑎𝑠 and 𝑐𝑎 correspond to the capacity costs of the ammonia subsystem with and without
intermediate storage, respectively.
CHAPTER 3 — Case Study: Hydrogen Energy California 113
The yearly fixed operating costs are calculated as a constant fraction of the overall capacity
cost (refer to Appendix B), and they remain unchanged every year throughout the lifetime of
the project. Accordingly, the levelized time-averaged fixed operating costs of HECA’s
subsystems are listed in Table 3.4.
Table 3.4: Levelized time-averaged fixed operating costs of HECA
Cost Value Unit
𝑗ℎ 0.2071 $/𝑘𝑔ℎ
𝑗𝑒 0.0086 $/𝑘𝑊ℎ
𝑗𝑎 0.0320 $/𝑘𝑔𝑎
𝑗𝑎𝑠 0.0326 $/𝑘𝑔𝑎
𝑗𝑓 0.0367 $/𝑘𝑔𝑢𝑟𝑒𝑎
𝑗𝑐 0.0006 $/𝑘𝑔𝑐
The variable cost for the hydrogen subsystem incorporates the costs of coal and petcoke as
fuel, Selexol™, flux, catalysts, other chemicals, waste-water treatment, and the unit’s
auxiliary load. On the other hand, the auxiliary loads are assumed to be the only variable costs
for all other subsystems. The prices of all physical commodities are fixed with time, assuming
they are purchased through long-term contracts (refer to Appendix B). However, we assume
that HECA’s net power output is sold in the wholesale market, and the cost of auxiliary power
equals the price of sold power. Hence, the yearly costs of the auxiliary loads in Table 3.2 are
obtained by summing up the hourly costs, which are calculated using variable electricity
prices. To simulate a real-life performance, we use the 2012 wholesale one-day-ahead
electricity prices from the SP26 pricing hub, which covers the Southern California region
where HECA plans to operate [29]. The yearly price data, plotted in Figure 3.3, is assumed to
be replicated every year throughout the facility’s lifetime. Under these assumptions, the time-
averaged variable cost equals the yearly-averaged variable cost for each subsystem, and those
costs are presented in Table 3.5. Finally, important to note, the variable cost of ammonia
storage is assumed to be negligible, resulting in 𝑤𝑎𝑠 = 𝑤𝑎.
CHAPTER 3 — Case Study: Hydrogen Energy California 114
Figure 3.3: Yearly wholesale prices of electricity in HECA’s region [29]
Table 3.5: Levelized time-averaged variable costs of HECA
Cost Value Unit
𝑤ℎ 0.640 $/𝑘𝑔ℎ
𝑤𝑒 0.00119 $/𝑘𝑊ℎ
𝑤𝑎 0.00644 $/𝑘𝑔𝑎
𝑤𝑎𝑠 0.00644 $/𝑘𝑔𝑎
𝑤𝑓 0.00836 $/𝑘𝑔𝑢𝑟𝑒𝑎
𝑤𝑐 0.00339 $/𝑘𝑔𝑐
The last important set of economic data is the prices of end-products, which account for
HECA’s revenues. The revenues from both fertilizers, urea and UAN, are combined in 𝑃𝑓.
This “price of fertilizers” term, expressed per unit of produced urea, is derived in (45) using a
similar formulation to that of 𝐿𝐼𝐶𝑓 in (43). In addition to fertilizers, Table 3.6 shows the time-
averaged prices of electricity and CO2 sales. More detailed price figures are provided in
Appendix B.
𝑃𝑓 ($/𝑘𝑔𝑢𝑟𝑒𝑎) =𝑦𝑢𝑟𝑒𝑎 ∙ 𝑋𝑢𝑟𝑒𝑎 ∙ 𝑃𝑢𝑟𝑒𝑎 + 𝑦𝑈𝐴𝑁 ∙ 𝑋𝑈𝐴𝑁 ∙ 𝑃𝑈𝐴𝑁
𝑋𝑓 (45)
CHAPTER 3 — Case Study: Hydrogen Energy California 115
Table 3.6: Time-averaged prices of HECA end-products
Price Value Unit
𝑃𝑓 0.768 $/𝑘𝑔𝑢𝑟𝑒𝑎
𝑃𝑒 0.0295 $/𝑘𝑊ℎ
𝑃𝑐 0.025 $/𝑘𝑔𝑐
6.2.2. Economic Value
The aforementioned data allows us to calculate the derived metrics in Sections 3 and 4 and
therefore to assess the economic value of HECA under several operation modes. The results
are presented in Table 3.7.
Table 3.7: Economic valuation of HECA
Economic Metric Value Unit
𝐿𝐶𝑂𝐻 1.373 $/𝑘𝑔ℎ
𝐿𝐶𝑂𝐸 0.0953 $/𝑘𝑊ℎ
𝛷𝑒 −0.000354 $/𝑘𝑔ℎ
𝛷𝑓 −0.0105 $/𝑘𝑔ℎ
𝐼𝐶𝑀𝐹𝑓 1.196 $/𝑘𝑔ℎ
𝐼𝐶𝑀𝐹𝑒 −2.223 $/𝑘𝑔ℎ
𝑃𝑀0𝑓 1.934 $/𝑘𝑔ℎ
𝑃𝑀0𝑒 −0.992 $/𝑘𝑔ℎ
𝑃𝑀1 (𝑓𝑜𝑟 𝜆 = 𝜆𝑚𝑎𝑥) −0.163 $/𝑘𝑔ℎ
𝑃𝑀2𝑓 = 𝑃𝑀2𝑒 −0.0439 $/𝑘𝑔ℎ
𝑉𝑂𝐷𝑓 (𝑓𝑜𝑟 𝜆 = 𝜆𝑚𝑎𝑥) −2.097 $/𝑘𝑔ℎ
𝑉𝑂𝐷𝑒 (𝑓𝑜𝑟 𝜆 = 𝜆𝑚𝑎𝑥) 0.829 $/𝑘𝑔ℎ
𝑉𝑂𝐹 (𝑓𝑜𝑟 𝜆 = 𝜆𝑚𝑎𝑥) 0.119 $/𝑘𝑔ℎ
𝑉𝑂𝑃𝑓 −1.978 $/𝑘𝑔ℎ
𝑉𝑂𝑃𝑒 0.948 $/𝑘𝑔ℎ
The levelized cost of hydrogen production is estimated at 𝐿𝐶𝑂𝐻 = 1.373 $/𝑘𝑔ℎ. This cost
can be combined with the cost of the electricity and CCS subsystems to calculate an 𝐿𝐶𝑂𝐸 for
CHAPTER 3 — Case Study: Hydrogen Energy California 116
HECA, as illustrated in (46). Notably, the obtained 𝐿𝐶𝑂𝐸 = 0.0953 $/𝑘𝑊ℎ is comparable to
that of coal power plants with CO2 capture, currently estimated at about 0.089– 0.139 $/𝑘𝑊ℎ
[42, 43, 44].
𝐿𝐶𝑂𝐸 = 𝐿𝐶𝑂𝐻 𝑋𝑒⁄ + 𝐿𝐼𝐶𝑒 + 𝑈𝑐 ∙ 𝐿𝐼𝐶𝑐 𝑋𝑒⁄ (46)
To calculate HECA’s unit profit-margin, we use the profitability metrics from Section 4, with
a few updates. Starting with the static mode of operation, 𝑃𝑀0𝑓, 𝑃𝑀0𝑒, and 𝑃𝑀1 are updated
in accordance with (38) in Section 5.1 to account for the CCS subsystem. With 𝑃𝑀0𝑓 = 1.934
$/𝑘𝑔ℎ, HECA is obviously profitable if run as a static fertilizer-only plant. However, the
facility would not break even if run as a static power-only plant, with 𝑃𝑀0𝑒 = −0.992 $/𝑘𝑔ℎ.
The profit-margin of the static polygeneration mode 𝑃𝑀1 is between 𝑃𝑀0𝑓 and 𝑃𝑀0𝑒; the
exact value of 𝑃𝑀1 changes with the hydrogen allocation fraction 𝜆, as illustrated in Figure
3.4. Under assumed prices and costs, a static HECA breaks-even around 𝜆 = 0.66.
Confirming our argument in Section 4, the value of diversification is not always positive. In
this case, diversifying away from power monogeneration increases profitability, evident by the
positive 𝑉𝑂𝐷𝑒. Conversely, diversifying away from fertilizer monogeneration severely
reduces profitability, evident by the negative 𝑉𝑂𝐷𝑓. Ultimately, increasing electricity
generation reduces both profitability and the associated values of diversification, as illustrated
in Figure 3.4.
Shifting to the flexible polygeneration mode, 𝑃𝑀2𝑒 and 𝑃𝑀2𝑓 are updated per Sections 5.1
and 5.2 to account for the CCS subsystem and the correction factors for the time-dependent
variable costs, respectively. 𝛷𝑒 and 𝛷𝑓 in Table 3.7 correct for the fact that the variable costs
change on an hourly basis due to HECA subsystems’ need for auxiliary power. In addition,
although 𝑚𝑒 and 𝑚𝑓 are exogenously imposed rather than endogenously optimized through
(15) and (16), the incremental flexibility contribution margins 𝐼𝐶𝑀𝐹𝑒 and 𝐼𝐶𝑀𝐹𝑓 are
calculated by following their definitions in (19) and (20). Referring to Table 3.7, 𝐼𝐶𝑀𝐹𝑓 is
clearly positive because the contribution margin from fertilizers exceeds that from electricity
during 𝑚𝑓 hours. However, 𝐼𝐶𝑀𝐹𝑒 is negative, contrary to our assertion in Section 3.2 that it
should also be positive. Caused by the exogeneity of 𝑚𝑒 and 𝑚𝑓, this result essentially means
CHAPTER 3 — Case Study: Hydrogen Energy California 117
that urea and UAN generate higher revenue than electricity even during 𝑚𝑒 hours when
electricity prices are highest. Therefore, flexible power generation may seem like a poor line
of business.
Figure 3.4: Profit-margin, value of diversification, and value of flexibility for HECA
However, flexibility enables a two-way substitution, so a flexible electricity capacity requires
an equivalent flexible fertilizer capacity. For HECA, while a flexible power capacity may not
be beneficial because electricity prices are relatively low, flexible fertilizer capacity is indeed
beneficial for the exact same reason. This is better understood by looking at 𝑃𝑀2 and the
corresponding 𝑉𝑂𝐹. The profit-margin of a flexible HECA is 𝑃𝑀2𝑒 = 𝑃𝑀2𝑓 = −0.0439
$/𝑘𝑔ℎ, so the facility almost breaks-even. As shown in Figure 3.4, a flexible HECA can be
less or more profitable than a static HECA, depending on the exact value of 𝜆 for the latter.
For a small 𝜆, the static HECA is dominated by fertilizer generation, so adding flexibility
leads to switching from high-price fertilizers to low-price electricity during the exogenously
imposed 𝑚𝑒. In this case, flexibility is not useful, and 𝑃𝑀2 is lower than 𝑃𝑀1, evident by the
negative 𝑉𝑂𝐹. Conversely, when 𝜆 is large, the static mode of HECA is dominated by
electricity generation, so adding flexibility leads to switching from low-price electricity to
-3
-2
-1
0
1
2
3
0 0.2 0.4 0.6 0.8 1
Ec
on
om
ic v
alu
e (
$/k
gh
)
λ
PR1 VODe
PR2 VODf
VOF
CHAPTER 3 — Case Study: Hydrogen Energy California 118
high-price fertilizers during 𝑚𝑓. In this case, flexibility is useful, and 𝑃𝑀2 is higher than 𝑃𝑀1,
evident by the positive 𝑉𝑂𝐹.
Ultimately, 𝑉𝑂𝐹 converges to 𝑉𝑂𝑃 at either extreme value of 𝜆. When 𝜆 = 0, 𝑉𝑂𝐹 is at its
minimum value and equal to 𝑉𝑂𝑃𝑓. Conversely, when 𝜆 = 1, 𝑉𝑂𝐹 is at its maximum value
and equal to 𝑉𝑂𝑃𝑒. We conclude that HECA benefits from flexible polygeneration if the
company’s other feasible alternative is investing in a static power-only plant, but it does not
benefit from flexible polygeneration if the other feasible alternative is investing in a static
fertilizer-only plant.
Figure 3.5: Value of polygeneration for flexible HECA under optimal operations
For completeness, we briefly analyze HECA’s performance under a hypothetical optimal
operational schedule, where 𝑚𝑒 and 𝑚𝑓 are obtained endogenously. Under assumed prices and
costs, we find that 𝑚𝑒 = 0 and 𝑚𝑓 = 𝑚, suggesting – as expected – that the facility should
run as a static fertilizer-only plant. Increasing electricity prices, nonetheless, leads to a
different conclusion, as illustrated in Figure 3.5. First, we proportionally increase all prices of
electricity depicted in Figure 3.3, which increases the average price 𝑃𝑒 while preserving the
relative volatility. As electricity prices increase, 𝑚𝑒 increases, signifying the economic
0
500
1000
1500
2000
2500
3000
3500
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
400 450 500 550 600
me
(h
r)
VO
P (
$/k
gh
)
Relative change in Pe (%)
VOPf
VOPe
me
CHAPTER 3 — Case Study: Hydrogen Energy California 119
favorability of installing flexible capacity and switching to electricity generation. When 𝑃𝑒 is
550−574% times its current value, both 𝑉𝑂𝑃𝑒 and 𝑉𝑂𝑃𝑓 are positive; in this case, flexible
polygeneration becomes the most profitable alternative for HECA, better than all static
polygeneration or monogeneration alternatives.
6.2.3. Sensitivity Analysis
Figure 3.6: Sensitivity analysis on the profitability of flexible HECA
Since HECA is a first-of-a-kind facility, it seems particularly important to check the
sensitivity of our results. Specifically, we analyze the sensitivity of HECA’s profitability to
the following variables: price of fertilizers, price of electricity, price of CO2, and discount rate.
Figure 3.6 shows that the profit-margin of a flexible HECA 𝑃𝑀2 is highly sensitive to both the
fertilizers price 𝑃𝑓 and the discount rate 𝜏. In fact, the facility can break even upon modest
increase in 𝑃𝑓 beyond 3.1% or upon modest decrease in 𝜏 beyond 7.5%. Conversely, HECA’s
profit-margin seems to be less sensitive to changes in CO2 price 𝑃𝑐 and least sensitive to
changes in electricity prices, characterized by 𝑃𝑒. To achieve break-even, 𝑃𝑐 would need to
increase by more than 14.5%, whereas 𝑃𝑒 would need to increase by more 34%. The
-2
-1.6
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
-100% -75% -50% -25% 0% 25% 50% 75% 100%
PM
2 (
$/k
gh
)
Relative change in input (%)
Pe
Pf
Pc
τ
CHAPTER 3 — Conclusions 120
aforementioned prices and discount rate affect the unit profit-margin of a static HECA 𝑃𝑀1 in
a very similar manner.
7 Conclusions
The levelized cost of electricity is an important economic concept that can be expanded to
assess the economic value of hydrogen-based polygeneration energy systems (PES). In this
study, we derive a set of metrics that quantify the cost, profitability, and value of real-options
associated with fossil-fuel PES. Because a PES can be divided into a distinct set of operational
subsystems, we first define the levelized cost of hydrogen (𝐿𝐶𝑂𝐻) and the levelized
incremental cost (𝐿𝐼𝐶) of converting hydrogen to market commodities such as electricity and
fertilizers. All cost figures can be combined into one term, the levelized cost of polygeneration
(𝐿𝐶𝑂𝑃), expressed as a monetary value per unit of produced hydrogen ($ 𝑘𝑔ℎ⁄ ). Given that
polygeneration systems share hydrogen as an intermediate product, this approach allows a
systematic comparison of polygeneration costs under multiple technical configurations and
operation modes.
By adding end-products’ sales, we derive the optimal unit profit-margin of PES under two
operation modes: static production of electricity and fertilizer (𝑃𝑀1), and flexible production
of electricity and fertilizer (𝑃𝑀2). We then compare both metrics to the profit-margin of static
monogeneration of electricity or fertilizer (𝑃𝑀0). The difference between 𝑃𝑀1 and 𝑃𝑀0 is
coined as the value of diversification (𝑉𝑂𝐷), and it captures the economic trade-offs
associated with allocating hydrogen to multiple end-product units. Similarly, the difference
between 𝑃𝑀2 and 𝑃𝑀1 is coined as the value of flexibility (𝑉𝑂𝐹), and it captures the
economic trade-offs associated with varying hydrogen allocation to each end-product unit over
time. 𝑉𝑂𝐹 and 𝑉𝑂𝐷 can be combined into one term, referred to as the value of polygeneration
(𝑉𝑂𝑃). Also, we demonstrate how to update these metrics to assess PES with carbon capture
and storage (CCS).
Through a series of derived economic propositions, we show that static polygeneration is more
profitable than static monogeneration if 𝑉𝑂𝐷 is positive. Similarly, flexible polygeneration is
CHAPTER 3 — Conclusions 121
more profitable than static polygeneration if 𝑉𝑂𝐹 is positive, and flexible polygeneration is
more profitable than static monognerration if 𝑉𝑂𝑃 is positive. Notably, however, 𝑉𝑂𝐷, 𝑉𝑂𝐹,
and 𝑉𝑂𝑃 need not always be positive because of the aforementioned economic trade-offs. As
such, no specific operation mode is unconditionally superior; the relative competitiveness of
static monogeneration, static polygeneration, and flexible polygeneration is highly dependent
on the assumed commodity prices and investment costs.
Applying the aforementioned economic metrics to a real polygeneration project, Hydrogen
Energy California, reveals their practical significance. Given a set of technical and financial
assumptions, HECA proves to be profitable as a static fertilizer-only plant with 𝑃𝑀0𝑓 = 1.934
$ 𝑘𝑔ℎ⁄ . However, with 𝑃𝑀0𝑒 = −0.992 $ 𝑘𝑔ℎ⁄ , HECA fails to break even as a static
electricity-only plant although its cost at 𝐿𝐶𝑂𝐸 = 0.0953 $ 𝑘𝑊ℎ⁄ is comparable to coal
power plants with carbon capture. As a static PES, HECA’s profit-margin 𝑃𝑀1 is between
𝑃𝑀0𝑓 and 𝑃𝑀0𝑒, with the exact value dependent on the exact splitting of produced hydrogen
between the two end-products. As a flexible PES, HECA almost succeeds to break even, with
𝑃𝑀2 = −0.0439 $ 𝑘𝑔ℎ⁄ . In this case study, the flexible polygeneration is unequivocally
superior to all other operation modes only if electricity prices increase 5.5-5.74 folds under an
endogenously optimized operational schedule.
7.1 Future Work
Moving forward, several opportunities still exist to expand this work. One potential area of
research involves analyzing the economic value of polygeneration systems powered by
renewable energy. While producing the same end-products (e.g. electricity and fertilizer),
renewable polygeneration might differ from fossil-fuel polygeneration in two major ways,
namely, hydrogen production and the need for CCS. Multiple technologies are available to
produce hydrogen in renewable polygeneration, including biomass gasification and water
electrolysis powered by solar PV and wind turbines. Interestingly, in this case, a separate
source of carbon would be needed to synthesize chemicals, and renewable PES may result in
negative emissions if combined with CCS. In addition, hydrogen can be thought of as a form
of energy-storage if it were used to regenerate electricity.
CHAPTER 3 — Conclusions 122
Furthermore, it would be rather important to examine the effect of taxes, including tax
subsidies, on polygeneration. Such endeavor requires a more careful analysis of investment
tax credits, effective corporate income tax rates, and accelerated depreciation rates that could
be applicable to both fossil-fuel and renewable polygeneration. Finally, this work assumes
deterministic commodity prices of inputs and outputs as well as known energy policies. A
more realistic approach is to consider uncertain market prices then optimize the operational
schedule of PES as prices vary with time. A similar approach can be followed to incorporate
uncertain environmental regulations in the form of future carbon pricing.
CHAPTER 3 — References 123
References
[1] BP, "BP Statistical Review of World Energy," June 2014. [Online]. Available:
http://www.bp.com/en/global/corporate/about-bp/energy-economics/statistical-review-of-world-
energy.html.
[2] IEA, "2014 Key World Energy Statistics," 2014. [Online]. Available:
http://www.iea.org/publications/freepublications/publication/KeyWorld2014.pdf.
[3] L. M. Serra, M.-A. Lozano, J. Ramos, A. V. Ensinas and S. A. Nebra, "Polygeneration and
efficient use of natural resources," Energy, vol. 34, pp. 575-586, 2009.
[4] Nexant, "Polygeneration from Coal: Integrated Power, Chemicals, and Liquid Fuels," Nexant
Chem Systems, White Plains, New York, 2008.
[5] J. Meerman, A. Ramírez, W. Turkenburg and A. Faaij, "Performance of simulated flexible
integrated gasification polygeneration facilities. Part A: A technical-energetic assessment,"
Renewable and Sustainable Energy Reviews, vol. 15, pp. 2563-2587, 2011.
[6] P. Liu, E. N. Pistikopoulos and Z. Li, "A Multi-Objective Optimization Approach to
Polygeneration Energy Systems Design," AIChE Journal: Process Systems Engineering, pp. Vol.
56, No. 5, 2010.
[7] Y. Chen, T. A. Adams II and a. P. I. Barton, "Optimal Design and Operation of Flexible Energy
Polygeneration Systems," Ind. Eng. Chem. Res., vol. 50, pp. 4553-4566, 2011.
[8] J. Meerman, A. Ramirez, W. Turkenburg and A. Faaij, "Performance of simulated flexible
integrated gasification polygeneration facilities, Part B: Economice valuation," Renewable and
Sustainable Energy Reviews, vol. 16, pp. 6083-6102, 2012.
[9] H2Stations, "Hydrogen Filling Stations Worldwide," 2015. [Online]. Available:
http://www.netinform.net/H2/H2Stations/H2Stations.aspx?Continent=AF&StationID=-1.
[10] D. R. Baker, "Hydrogen-fueled cars face uncertain market in California," 2014. [Online].
Available: http://www.sfgate.com/news/article/Hydrogen-fueled-cars-face-uncertain-market-in-
5519890.php. [Accessed 2015].
[11] G. Bromaghim, K. Gibeault, J. Serfass, P. Serfass and E. Wagner, "Hydrogen and Fuel Cells: The
U.S. Market Report," National Hydrogen Association, Washington DC, USA, 2010.
[12] F. Calise, A. Cipollina, M. D. d’Accadia and A. Piacentino, "A novel renewable polygeneration
system for a small Mediterranean volcanic island for the combined production of energy and
water: Dynamic simulation and economic assessment," Applied Energy, vol. 135, pp. 675-693,
2014.
CHAPTER 3 — References 124
[13] C. Rubio-Maya, J. Uche-Marcuello, A. Martínez-Gracia and A. A. Bayod-Rújula, "Design
optimization of a polygeneration plant fuelled by natural gas and renewable energy sources,"
Applied Energy, vol. 88, pp. 449-457, 2011.
[14] L. A. Pellegrini, G. Soave, S. Gamba and S. Langè, "Economic analysis of a combined energy–
methanol production plant," Applied Energy, vol. 88, pp. 4891-4897, 2011.
[15] S. Li, L. Gao, X. Zhang, H. Lin and H. Jin, "Evaluation of cost reduction potential for a coal based
polygeneration system with CO2 capture," Energy, vol. 45, pp. 101-106, 2012.
[16] L. Hu, J. Hongguang, G. Lin and H. Wei, "Techno-economic evaluation of coal-based
polygeneration systems of synthetic," Energy Conversion and Management, vol. 52, pp. 274-283,
2011.
[17] A. Narvaez, D. Chadwick and L. Kershenbaum, "Small-medium scale polygeneration systems:
Methanol and power production," Applied Energy, vol. 113, pp. 1109-1117, 2014.
[18] K. S. Ng, N. Zhang and J. Sadhukhan, "Techno-economic analysis of polygeneration systems with
carbon capture and storage and CO2 reuse," Chemical Engineering Journal, vol. 219, pp. 96-108,
2013.
[19] C.-C. Cormos, "Assessment of flexible energy vectors poly-generation based on coal and
biomass/solid wastes co-gasification with carbon capture," Internationall journal of hydrogen
energy, pp. 7855-7866, 2013.
[20] P. Liu, D. I. Gerogiorgis and E. N. Pistikopoulos, "Modeling and optimization of polygeneration
energy systems," Catalysis Today, vol. 127, p. 347–359, 2007.
[21] T. Ramsden, M. Ruth, V. Diakov, M. Laffen and T. Timbario, "Hydrogen Pathways: Updated
Cost, Well-to-Wheels Energy Use, and Emissions for the Current Technology Status of Ten
Hydrogen Production, Delivery, and Distribution Scenarios," National Renewable Energy
Laboratory, Golden, Colorado, USA, 2013.
[22] T. Ramsden, D. Steward and J. Zuboy, "Analyzing the Levelized Cost of Centralized and
Distributed Hydrogen Production Using the H2A Production Model, Version 2," National
Renewable Energy Laboratory, Golden, Colorado, USA, 2009.
[23] MIT, "The Future of Coal," Massachusetts Institute of Technology, Boston, 2007.
[24] S. Reichelstein and M. Yorston, "The prospects for cost competitive solar PV power," Energy
Policy, vol. 55, pp. 117-127, 2012.
[25] S. Reichelstein and A. Rohlfing-Bastian, "Levelized Product Cost: Concept and Decision
Relevance," The Accounting Review, vol. 90, no. 4, 2015.
[26] M. Lerdal, "Hydrogen Energy California, LowCarbon Solutions for California," Energy Seminar,
Stanford University, Stanford, California, 2012.
CHAPTER 3 — References 125
[27] GE Energy, "Heavy duty gas turbine products," 2009. [Online]. Available: http://www.ge-
energy.com/content/multimedia/_files/downloads/GEH12985H.pdf. [Accessed 2014].
[28] J. Wick, "Advanced Gas Turbine Technology GT26," Alstom, Jornada Tecnológica in Madrid,
Madrid, 2006.
[29] CAISO, "Open Access Same-time Information System (OASIS)," 2012. [Online]. Available:
http://oasis.caiso.com.
[30] IndexMundi, "Urea Monthly Price - US Dollars per Metric Ton," 2015. [Online]. Available:
http://www.indexmundi.com/commodities/?commodity=urea&months=120. [Accessed 2015].
[31] HECA, "The Project," 2010a. [Online]. Available: http://hydrogenenergycalifornia.com/the-
project. [Accessed 2014].
[32] HECA, "Project Fact Sheet," 2010b. [Online]. Available:
http://hydrogenenergycalifornia.com/factsheets. [Accessed 2013].
[33] URS, "Responses to CEC Workshop Requests: Nos. A1 through A32. Amended Application for
Certifi cation HYDROGEN ENERGY CALIFORNIA (08-AFC-8A). Kern County, California,"
California Energy Commission, Sacramento, California, 2012.
[34] CEC, "Hydrogen Energy California Project. Preliminary Staff Assessment, Draft Environmental
Impact Statement," U.S. Department of Energy and California Energy Commission, Sacramento,
California, 2013.
[35] URS, "Responses to Sierra Club Data Requests Set Three: Nos. 132 through 146. Amended
Application for Certifi cation for HYDROGEN ENERGY CALIFORNIA (08-AFC-8A) Kern
County, California," California Energy Commission, 2013.
[36] IEA GHG, "Co-Production of Hydrogen and Electricity by Coal Gasification with CO2 Capture -
Updated Economic Analysis," International Energy Agency Greenhouse Gas R&D Programme,
2008.
[37] J. R. Bartels, "A feasibility study of implementing an Ammonia Economy," Iowa State University,
Ames, Iowa, 2008.
[38] B. Leighty, "Energy Storage with Anhydrous Ammonia: Comparison with other Energy Storage,"
in Ammonia: The Key to US Energy Independence, Minneapolis, 2008.
[39] E. R. Morgan, "Techno-Economic Feasibility Study of Ammonia Plants Powered by Offshore
Wind," University of Massachusetts - Amherst, 2013.
[40] D. Lennon, "Refurbishing Used Plants. Relocating Nitrogenous Fertilizer Plants," Capital Plant
International.
CHAPTER 3 — References 126
[41] C. Damas, "Terra Nitrogen Or CVR Partners: Fertilizer Production Capability," 21 October 2011.
[Online]. Available: http://seekingalpha.com/article/301165-terra-nitrogen-or-cvr-partners-
fertilizer-production-capability.
[42] E. Rubin, G. Booras, J. Davison, C. Ekstrom, M. Matuszewski, S. McCoy and C. Short, "Toward a
Common Method for Cost Estimation for CO2 Capture and Storage at Fossil Fuel Power Plants,"
Global CCS Institute, 2013.
[43] S. Borenstein, "The Private and Public Economics of Renewable Electricity Generation," Journal
of Economic Perspectives, pp. 67-92, 2012.
[44] C. Abellera and C. Short, "The costs of CCS and Other Low-Carbon Technologies," Global CCS
Institute, 2011.
[45] S. Reichelstein and A. Sahoo, "Time of Day Pricing and the Levelized Cost of Intermittent Power
Generation," Energy Economics, vol. 48, pp. 97-108, 2015.
[46] J. E. Marsden, "Elementary Classical Analysis," W. H. Freeman and Co., San Francisco, 1974.
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 127
Appendix A: Derivation of Economic Propositions
Scenario 1: Static PES with fixed production rates
Derivation of Definition 1 and Proposition 1
Below is a step-by-step derivation of Definition 1 and Proposition 1, presented in (7–9) and
(10), respectively. The derivation is based on net present value since the LCOP, as previously
introduced, is a levelized cost figure that equals a weighted-average of end-product prices
such that the NPV of the polygeneration facility is exactly zero.
𝑁𝑃𝑉 ($) = ∑ 𝛾𝑖 ∙ 𝐶𝐹𝐿𝑖
𝑇
𝑖=1
− 𝐶𝑎𝑝𝐸𝑥 (A1)
𝑁𝑃𝑉: net present value ($)
𝛾𝑖: discount factor in year 𝑖
𝐶𝐹𝐿𝑖: cash flow in year 𝑖 ($/𝑦𝑟)
𝐶𝑎𝑝𝐸𝑥: cost of capacity of polygeneration system ($)
𝐶𝑎𝑝𝐸𝑥 = [𝐶𝐴𝑃ℎ + 𝐶𝐴𝑃𝑒 + 𝐶𝐴𝑃𝑎 + 𝐶𝐴𝑃𝑓] (A2)
𝐶𝐴𝑃ℎ: cost of capacity of hydrogen production subsystem ($)
𝐶𝐴𝑃𝑒: cost of capacity of electricity production subsystem ($)
𝐶𝐴𝑃𝑎: cost of capacity of ammonia production subsystem ($)
𝐶𝐴𝑃𝑓: cost of capacity of fertilizers production subsystem ($)
Then, each cost of capacity can be decomposed as follows:
𝐶𝐴𝑃ℎ = 𝑆𝑃ℎ ∙ 𝑁ℎ (A3)
𝐶𝐴𝑃𝑒 = λ ∙ 𝑋𝑒 ∙ 𝑁ℎ ∙ 𝑆𝑃𝑒 (A4)
𝐶𝐴𝑃𝑎 = (1 − λ) ∙ 𝑋𝑎 ∙ 𝑁ℎ ∙ 𝑆𝑃𝑎 (A5)
𝐶𝐴𝑃𝑓 = (1 − λ) ∙ 𝑋𝑓 ∙ 𝑁ℎ ∙ 𝑆𝑃𝑓 (A6)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 128
𝑆𝑃ℎ: system price of hydrogen production per unit capacity ($/(𝑘𝑔ℎ ℎ𝑟⁄ ))
𝑆𝑃𝑒: system price of electricity production per unit capacity ($/𝑘𝑊)
𝑆𝑃𝑓: system price of ammonia production per unit capacity ($/(𝑘𝑔𝑎 ℎ𝑟⁄ ))
𝑆𝑃𝑓: system price of fertilizers production per unit capacity ($/(𝑘𝑔𝑓 ℎ𝑟⁄ ))
And 𝑁ℎ , 𝑋𝑒, 𝑋𝑎, 𝑋𝑓, and λ are as defined before.
Then, by substituting (A3–A6) into (A2):
𝐶𝑎𝑝𝐸𝑥 = 𝑁ℎ ∙ [𝑆𝑃ℎ + λ ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ) ∙ 𝑋𝑎 ∙ 𝑆𝑃𝑎 + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑆𝑃𝑓] (A7)
Now we define the annual cash flow in year 𝑖 as:
𝐶𝐹𝐿𝑖 = −𝐽𝑖
+𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ ∫ [λ ∙ 𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑤ℎ𝑖 − λ ∙ 𝑋𝑒 ∙ 𝑤𝑒𝑖
−(1 − λ) ∙ 𝑋𝑎 ∙ 𝑤𝑎𝑖 − (1 − λ) ∙ 𝑋𝑓 ∙ 𝑤𝑓𝑖] 𝑑𝑡
𝑚
0
(A8)
As before, 𝑚 = 8760 is the total number of hours per year. 𝐶𝐹 and 𝑥𝑖 are the capacity factor
and the system degradation factor, respectively, as defined in the LCOH earlier. Also, as
explained before and illustrated in (A8), the selling price of fertilizers 𝑃𝑓𝑖 is fixed in year 𝑖,
while electricity price 𝑃𝑒𝑖(𝑡) varies on hourly basis. Thus:
∫ [λ ∙ 𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑃𝑓𝑖]𝑑𝑡
𝑚
0
= 𝑚 ∙ [λ ∙ 𝑋𝑒 ∙ 𝑃𝑒𝑖 + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑃𝑓𝑖] (A9)
𝑃𝑒𝑖: yearly-averaged price of electricity in year 𝑖 ($/𝑘𝑊ℎ)
𝑃𝑓𝑖: yearly-averaged price of fertilizers in year 𝑖 ($/𝑘𝑔𝑓)
Beside the revenue generated from selling the end-products, 𝑤ℎ𝑖, 𝑤𝑒𝑖, 𝑤𝑎𝑖, and 𝑤𝑓𝑖 refer to the
variable costs of producing one unit of hydrogen, electricity, ammonia, and fertilizers,
respectively. Since all variable costs are assumed constant in a given year, summing over the
all hours of year 𝑖 results:
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 129
∫ [𝑤ℎ𝑖 + λ ∙ 𝑋𝑒 ∙ 𝑤𝑒𝑖 + (1 − λ) ∙ 𝑋𝑎 ∙ 𝑤𝑎𝑖 + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑤𝑓𝑖]𝑑𝑡
𝑚
0
= 𝑚 ∙ [𝑤ℎ𝑖 + λ ∙ 𝑋𝑒 ∙ 𝑤𝑒𝑖 + (1 − λ) ∙ 𝑋𝑎 ∙ 𝑤𝑎𝑖 + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑤𝑓𝑖]
(A10)
𝑤ℎ𝑖: yearly-averaged variable cost of hydrogen production per unit output in year 𝑖 (in $/𝑘𝑔ℎ)
𝑤𝑒𝑖: yearly-averaged variable cost of electricity production per unit output in year 𝑖 ($/𝑘𝑊ℎ)
𝑤𝑎𝑖: yearly-averaged variable cost of ammonia production per unit output in year 𝑖 (in $/𝑘𝑔𝑎)
𝑤𝑓𝑖: yearly-averaged variable cost of fertilizers production per unit output in year 𝑖 (in $/𝑘𝑔𝑓)
Similarly, we define the fixed-operating cost in year 𝑖 as:
𝐽𝑖 = 𝐽ℎ𝑖 + 𝐽𝑒𝑖 + 𝐽𝑎𝑖 + 𝐽𝑓𝑖
= 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖]
(A11)
𝐽𝑖: total annual fixed-operating cost of polygeneration facility in year 𝑖 ($/𝑦𝑟)
𝐽ℎ𝑖: annual fixed-operating cost of hydrogen production subsystem in year 𝑖 ($/𝑦𝑟)
𝐽𝑒𝑖: annual fixed-operating cost of electricity production subsystem in year 𝑖 ($/𝑦𝑟)
𝐽𝑎𝑖: annual fixed-operating cost of ammonia production subsystem in year 𝑖 ($/𝑦𝑟)
𝐽𝑓𝑖: annual fixed-operating cost of fertilizers production subsystem in year 𝑖 ($/𝑦𝑟)
And such that:
𝑆𝐽ℎ𝑖: annual fixed-operating cost of hydrogen production per unit capacity in year 𝑖
(($ 𝑦𝑟⁄ )/(𝑘𝑔ℎ ℎ𝑟⁄ ))
𝑆𝐽𝑒𝑖: annual fixed-operating cost of electricity production per unit capacity in year 𝑖
(($ 𝑦𝑟⁄ )/𝑘𝑊)
𝑆𝐽𝑎𝑖: annual fixed-operating cost of ammonia production per unit capacity in year 𝑖
(($ 𝑦𝑟⁄ )/(𝑘𝑔𝑎 ℎ𝑟⁄ ))
𝑆𝐽𝑓𝑖: annual fixed-operating cost of fertilizers production per unit capacity in year 𝑖
(($ 𝑦𝑟⁄ )/(𝑘𝑔𝑓 ℎ𝑟⁄ ))
Substituting (A9), (A10), and (A11) into (A8):
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 130
𝐶𝐹𝐿𝑖 = 𝑚 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ [ λ ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖 − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ𝑖
+(1 − λ) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑖)]
−𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + (1 − λ) ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖] (A12)
Then, the NPV becomes:
𝑁𝑃𝑉 ($) = ∑ 𝛾𝑖 ∙ 𝑚 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ [ λ ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖 − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ𝑖
+(1 − λ) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑖)]
𝑇
𝑖=1
− ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ {𝑆𝐽ℎ𝑖 + λ ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖 + 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖]}
𝑇
𝑖=1
−𝑁ℎ ∙ {𝑆𝑃ℎ + λ ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝑆𝑃𝑓 + 𝑋𝑎 ∙ 𝑆𝑃𝑎]}
(A13)
PES is economically competitive if and only if NPV is positive, thus:
∑ 𝛾𝑖 ∙ 𝑚 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ [ λ ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖 − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ𝑖
+(1 − λ) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑖)]
𝑇
𝑖=1
− ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ {𝑆𝐽ℎ𝑖 + λ ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖 + 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖]}
𝑇
𝑖=1
−𝑁ℎ ∙ {𝑆𝑃ℎ + λ ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝑆𝑃𝑓 + 𝑋𝑎 ∙ 𝑆𝑃𝑎]} > 0
(A14)
Upon dividing (A14) by 𝑚 ∙ 𝐶𝐹 ∙ 𝑁ℎ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1 , we get:
∑ 𝛾𝑖 ∙ 𝑥𝑖 ∙ [ λ ∙ 𝑋𝑒 ∙ (𝑃𝑒𝑖 − 𝑤𝑒𝑖) + (1 − λ) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑖) − 𝑤ℎ𝑖]𝑇𝑖=1
∑ 𝛾𝑖 . 𝑥𝑖𝑇𝑖=1
−∑ 𝛾𝑖 ∙ {𝑆𝐽ℎ𝑖 + λ ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖 + 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖]}𝑇
𝑖=1
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
−{𝑆𝑃ℎ + λ ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝑆𝑃𝑓 + 𝑋𝑎 ∙ 𝑆𝑃𝑎]}
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
> 0
(A15)
[ λ ∙ 𝑋𝑒 ∙ (𝑃𝑒 − 𝑤𝑒) + (1 − λ) ∙ (𝑋𝑓 ∙ 𝑃𝑓 − 𝑋𝑓 ∙ 𝑤𝑓 − 𝑋𝑎 ∙ 𝑤𝑎) − 𝑤ℎ]
−{𝑗ℎ + λ ∙ 𝑋𝑒 ∙ 𝑗𝑒 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝑗𝑓 + 𝑋𝑎 ∙ 𝑗𝑎]}
−{𝑐ℎ + λ ∙ 𝑋𝑒 ∙ 𝑐𝑒 + (1 − λ) ∙ [𝑋𝑓 ∙ 𝑐𝑓 + 𝑋𝑎 ∙ 𝑐𝑎]} > 0
(A16)
𝛌 ∙ (𝑿𝒆 ∙ 𝑷𝒆 − 𝑿𝒆 ∙ 𝑳𝑰𝑪𝒆) +(𝟏 − 𝛌) ∙ (𝑿𝒇 ∙ 𝑷𝒇 − 𝑿𝒇 ∙ 𝑳𝑰𝑪𝒇 − 𝑿𝒂 ∙ 𝑳𝑰𝑪𝒂) > 𝑳𝑪𝑶𝑯
(A17)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 131
Scenario 2a: Flexible PES with a flexible fertilizers subsystem
Derivation of Proposition 2a in (21)
Below is a step-by-step derivation of the formulation of Proposition 2a stated in (21). We
recall from (A1) and (A2) that:
𝑁𝑃𝑉 ($) = ∑ 𝛾𝑖 . 𝐶𝐹𝐿𝑖
𝑇
𝑖=1
− 𝐶𝑎𝑝𝐸𝑥 (A1)
𝐶𝑎𝑝𝐸𝑥 = [𝐶𝐴𝑃ℎ + 𝐶𝐴𝑃𝑒 + 𝐶𝐴𝑃𝑎 + 𝐶𝐴𝑃𝑓] (A2)
While 𝐶𝐴𝑃ℎ remains as defined in (A3), the definition of other capacity cost factors are
updated in (A18-A20) to account for the new expanded capacity of all three flexible units:
electricity, ammonia, and fertilizers.
𝐶𝐴𝑃𝑒 = λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑁ℎ ∙ 𝑆𝑃𝑒 (A18)
𝐶𝐴𝑃𝑎 = (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑁ℎ ∙ 𝑆𝑃𝑎 (A19)
𝐶𝐴𝑃𝑓 = (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑓 ∙ 𝑁ℎ ∙ 𝑆𝑃𝑓 (A20)
Then, by substituting (A3) and (A18-A20) into (A2):
𝐶𝑎𝑝𝐸𝑥 = 𝑁ℎ ∙ {𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛) ∙ [𝑋𝑎 ∙ 𝑆𝑃𝑎 + 𝑋𝑓 ∙ 𝑆𝑃𝑓]} (A21)
The annual cash flow in year 𝑖 is defined as:
𝐶𝐹𝐿𝑖 = −𝐽𝑖
+𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ ∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ
+(1 − 𝜆(𝑡)) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑖)] 𝑑𝑡
(A22)
Similar to the costs of capacity, the fixed-operating costs in year 𝑖 are updated, such that:
𝐽𝑖 = 𝐽ℎ𝑖 + 𝐽𝑒𝑖 + 𝐽𝑎𝑖 + 𝐽𝑓𝑖
= 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖)] (A23)
The maximization problem in (A22) means that at every time period 𝑡, the flexible PES
operator should allocate hydrogen to electricity and fertilizers production in a way that
maximizes the overall contribution margin.
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 132
Substituting of 𝐶𝑀𝑒𝑖 and 𝐶𝑀𝑓𝑖 in (13) and (14), respectively, the integral can be rewritten as:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖)
+(1 − 𝜆(𝑡)) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑖) − 𝑤ℎ
] 𝑑𝑡
= ∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓𝑖]𝑑𝑡 − 𝑚 ∙ 𝑤ℎ
(A24)
The integral aims to maximize the contribution margin over the whole year. Intuitively, this
integral can be decomposed to two parts, over 𝑚�̃� and 𝑚�̃�:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓𝑖]
= ∫ 𝑚𝑎𝑥⏟𝜆(𝑡)𝑚𝑒𝑖̃
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓𝑖]𝑑𝑡
+ ∫ 𝑚𝑎𝑥⏟𝜆(𝑡)𝑚𝑓𝑖̃
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓𝑖]𝑑𝑡
(A25)
Now resolving the maximization problem in each integral is straightforward. During 𝑚�̃�
hours, the contribution margin from electricity generation is higher than that from fertilizers
generation, by definition. Thus, the solution to the first maximization problem over 𝑚�̃� is to
maximize electricity production by setting 𝜆(𝑡) = 𝜆𝑚𝑎𝑥. Similarly, the solution to the second
maximization problem over 𝑚�̃� is to maximize fertilizers production by setting 𝜆(𝑡) = 𝜆𝑚𝑖𝑛.
Thus:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓𝑖]𝑑𝑡
= ∫ [𝜆𝑚𝑎𝑥 ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐶𝑀𝑓𝑖]
𝑚𝑒𝑖̃
𝑑𝑡
+ ∫ [𝜆𝑚𝑖𝑛 ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆𝑚𝑖𝑛) ∙ 𝐶𝑀𝑓𝑖]
𝑚𝑓𝑖̃
𝑑𝑡
(A26)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 133
Upon re-arranging (A26):
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓𝑖]𝑑𝑡
= ∫ [𝜆𝑚𝑎𝑥 ∙ (𝐶𝑀𝑒𝑖(𝑡) − 𝐶𝑀𝑓𝑖)]
𝑚𝑒𝑖̃
𝑑𝑡 + ∫ 𝐶𝑀𝑓𝑖
𝑚𝑒𝑖̃
𝑑𝑡
− ∫ [𝜆𝑚𝑖𝑛 ∙ (𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑒𝑖)]
𝑚𝑓𝑖̃
𝑑𝑡 + ∫ 𝐶𝑀𝑓𝑖
𝑚𝑓𝑖̃
𝑑𝑡
= 𝜆𝑚𝑎𝑥 ∙ ∫(𝐶𝑀𝑒𝑖(𝑡) − 𝐶𝑀𝑓𝑖)
𝑚𝑒𝑖̃
𝑑𝑡 − 𝜆𝑚𝑖𝑛 ∙ ∫(𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑒𝑖)
𝑚𝑓𝑖̃
𝑑𝑡 + ∫ 𝐶𝑀𝑓𝑖
𝑚
0
𝑑𝑡
(A27)
Then, using the definitions of 𝐼𝐶𝑀𝐹𝑒𝑖 and 𝐼𝐶𝑀𝐹𝑓𝑖 in (17) and (18), respectively:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓]𝑑𝑡
= 𝑚 ∙ 𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝑚 ∙ 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+𝑚 ∙ [𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑖]
(A28)
Substituting the result of (A23). (A24), and (A28) into (A22), we get:
𝐶𝐹𝐿𝑖 = −𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖)]
+𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+[𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑖] − 𝑤ℎ𝑖}
(A29)
Then the NPV becomes:
𝑁𝑃𝑉 ($) = − ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖
+(1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖)]
𝑇
𝑖=1
+ ∑ 𝛾𝑖 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+[𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑖] − 𝑤ℎ𝑖}
𝑇
𝑖=1
−𝑁ℎ ∙ {𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛)[𝑋𝑎 ∙ 𝑆𝑃𝑎 + 𝑋𝑓 ∙ 𝑆𝑃𝑓]}
(A30)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 134
PES is economically competitive if and only if NPV is positive, thus:
− ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖
+(1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖)]
𝑇
𝑖=1
+ ∑ 𝛾𝑖 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+[𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑖] − 𝑤ℎ𝑖}
𝑇
𝑖=1
−𝑁ℎ ∙ {𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛)[𝑋𝑎 ∙ 𝑆𝑃𝑎 + 𝑋𝑓 ∙ 𝑆𝑃𝑓]} > 0
(A31)
Upon dividing (A31) by 𝑚 ∙ 𝐶𝐹 ∙ 𝑁ℎ ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1 , we get:
−∑ 𝛾𝑖 ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖)]𝑇
𝑖=1
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
+
∑ 𝛾𝑖 ∙ 𝑥𝑖 ∙ {𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+[𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑖] − 𝑤ℎ𝑖}𝑇
𝑖=1
∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
−{𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛)[𝑋𝑎 ∙ 𝑆𝑃𝑎 + 𝑋𝑓 ∙ 𝑆𝑃𝑓]}
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
> 0
(A32)
−𝑗ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑗𝑒 − (1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑗𝑎 + 𝑋𝑓 ∙ 𝑗𝑓)
+𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓 + [𝑋𝑓 . 𝑃𝑓 − 𝑋𝑓 . 𝑤𝑓 − 𝑋𝑎 . 𝑤𝑎] − 𝑤ℎ
−𝑐ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑐𝑒 − (1 − λ𝑚𝑖𝑛)(𝑋𝑎 ∙ 𝑐𝑎 + 𝑋𝑓 ∙ 𝑐𝑓) > 0
(A33)
𝜆𝑚𝑎𝑥 ∙ (𝐼𝐶𝑀𝐹𝑒 − 𝑋𝑒 ∙ 𝑐𝑒 − 𝑋𝑒 ∙ 𝑗𝑒)
−𝜆𝑚𝑖𝑛 ∙ (𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑎 ∙ 𝑗𝑎 − 𝑋𝑓 ∙ 𝑗𝑓 − 𝑋𝑎 ∙ 𝑐𝑎 − 𝑋𝑓 ∙ 𝑐𝑓)
+[𝑋𝑓 . 𝑃𝑓 − 𝑋𝑓 . 𝑤𝑓 − 𝑋𝑎 . 𝑤𝑎 − 𝑋𝑎 ∙ 𝑗𝑎 − 𝑋𝑓 ∙ 𝑗𝑓 − 𝑋𝑎 ∙ 𝑐𝑎 − 𝑋𝑓 ∙ 𝑐𝑓] > 𝑐ℎ + 𝑗ℎ + 𝑤ℎ
(A34)
(𝑿𝒇. 𝑷𝒇 − 𝑿𝒇. 𝑳𝑰𝑪𝒇 − 𝑿𝒂. 𝑳𝑰𝑪𝒂)
+𝝀𝒎𝒂𝒙 ∙ (𝑰𝑪𝑴𝑭𝒆 − 𝑿𝒆 ∙ (𝒄𝒆 + 𝒋𝒆))
−𝝀𝒎𝒊𝒏 ∙ (𝑰𝑪𝑴𝑭𝒇 − 𝑿𝒇 ∙ (𝒄𝒇 + 𝒋𝒇) − 𝑿𝒂 ∙ (𝒄𝒂 + 𝒋𝒂)) > 𝑳𝑪𝑶𝑯
(A35)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 135
Derivation of Proposition 2a in (22)
The derivation of the formulation of Proposition 2a in (22) follows a very similar path to that
in (21). Following the same steps from (A18) through (A26), we re-arrange (A27) as follows:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒𝑖(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓𝑖]𝑑𝑡
= ∫ [(1 − 𝜆𝑚𝑎𝑥) ∙ (𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑒𝑖)]
𝑚𝑒𝑖̃
𝑑𝑡 + ∫ 𝐶𝑀𝑒𝑖
𝑚𝑒𝑖̃
𝑑𝑡
+ ∫ [(1 − 𝜆𝑚𝑖𝑛) ∙ (𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑒𝑖)]
𝑚𝑓𝑖̃
𝑑𝑡 + ∫ 𝐶𝑀𝑒𝑖
𝑚𝑓𝑖̃
𝑑𝑡
= (1 − 𝜆𝑚𝑎𝑥) ∙ ∫(𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑒𝑖)
𝑚𝑒𝑖̃
𝑑𝑡
+(1 − 𝜆𝑚𝑖𝑛) ∙ ∫ (𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑒𝑖)
𝑚𝑓𝑖̃
𝑑𝑡 + ∫ 𝐶𝑀𝑒𝑖
𝑚
0
𝑑𝑡
(A36)
Then, using the definitions of 𝐼𝐶𝑀𝐹𝑒𝑖 and 𝐼𝐶𝑀𝐹𝑓𝑖 in (17) and (18), respectively:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ 𝐶𝑀𝑒(𝑡) + (1 − 𝜆(𝑡)) ∙ 𝐶𝑀𝑓]𝑑𝑡
= −𝑚 ∙ (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 + 𝑚 ∙ (1 − 𝜆𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 + 𝑚 ∙ [𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖]
(A37)
Substituting the result of (A23) and (A37) in (A22), we get:
𝐶𝐹𝐿𝑖 = −𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖) ]
+𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {(1 − 𝜆𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖
+[𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖] − 𝑤ℎ𝑖}
(A38)
Then the NPV becomes:
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 136
𝑁𝑃𝑉 ($) = − ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖
+(1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖) ]
𝑇
𝑖=1
+ ∑ 𝛾𝑖 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {(1 − 𝜆𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖
+[𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖] − 𝑤ℎ𝑖}
𝑇
𝑖=1
−𝑁ℎ ∙ [𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛)(𝑋𝑎 ∙ 𝑆𝑃𝑎 + 𝑋𝑓 ∙ 𝑆𝑃𝑓)]
(A39)
PES is economically competitive if and only if NPV is positive, thus:
− ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖) ]
𝑇
𝑖=1
+ ∑ 𝛾𝑖 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {(1 − 𝜆𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖
+[𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖] − 𝑤ℎ𝑖}
𝑇
𝑖=1
−𝑁ℎ ∙ [𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛)(𝑋𝑎 ∙ 𝑆𝑃𝑎 + 𝑋𝑓 ∙ 𝑆𝑃𝑓)] > 0
(A40)
Upon dividing (A40) by 𝑚 ∙ 𝐶𝐹 ∙ 𝑁ℎ ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1 , we get:
−∑ 𝛾𝑖 ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑆𝐽𝑎𝑖 + 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖)]𝑇
𝑖=1
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
+
∑ 𝛾𝑖 ∙ 𝑥𝑖 ∙ {(1 − 𝜆𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖
+[𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖] − 𝑤ℎ𝑖}𝑇
𝑖=1
∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
−[𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛)(𝑋𝑎 ∙ 𝑆𝑃𝑎 + 𝑋𝑓 ∙ 𝑆𝑃𝑓)]
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
> 0
(A41)
−𝑗ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑗𝑒 − (1 − λ𝑚𝑖𝑛) ∙ (𝑋𝑎 ∙ 𝑗𝑎 + 𝑋𝑓 ∙ 𝑗𝑓)
+(1 − 𝜆𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓 − (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒 + [𝑋𝑒 . 𝑃𝑒 − 𝑋𝑒 . 𝑤𝑒] − 𝑤ℎ
−𝑐ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑐𝑒 − (1 − λ𝑚𝑖𝑛)(𝑋𝑎 ∙ 𝑐𝑎 + 𝑋𝑓 ∙ 𝑐𝑓) > 0
(A42)
(1 − 𝜆𝑚𝑖𝑛) ∙ (𝐼𝐶𝑀𝐹𝑓 − 𝑋𝑎 ∙ 𝑗𝑎 − 𝑋𝑓 ∙ 𝑗𝑓 − 𝑋𝑎 ∙ 𝑐𝑎 − 𝑋𝑓 ∙ 𝑐𝑓)
−(1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒 − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑗𝑒 − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑐𝑒 + 𝑋𝑒 ∙ 𝑗𝑒 + 𝑋𝑒 ∙ 𝑐𝑒
+[𝑋𝑒 . 𝑃𝑒 − 𝑋𝑒 . 𝑤𝑒] − 𝑋𝑒 ∙ 𝑗𝑒 − 𝑋𝑒 ∙ 𝑐𝑒 > 𝑐ℎ + 𝑤ℎ + 𝑗ℎ
(A43)
[𝑿𝒆. 𝑷𝒆 − 𝑿𝒆. 𝑳𝑰𝑪𝒆]
+(𝟏 − 𝝀𝒎𝒊𝒏) ∙ [𝑰𝑪𝑴𝑭𝒇 − 𝑿𝒂 ∙ (𝒄𝒂 + 𝒋𝒂) − 𝑿𝒇 ∙ (𝒄𝒇 + 𝒋𝒇)]
−(𝟏 − 𝝀𝒎𝒂𝒙) ∙ [𝑰𝑪𝑴𝑭𝒆 − 𝑿𝒆 ∙ 𝒋𝒆 − 𝑿𝒆 ∙ 𝒄𝒆] > 𝑳𝑪𝑶𝑯
(A44)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 137
Scenario 2b: Flexible PES with a static fertilizers subsystem
Derivation of Proposition 2b in (24)
Below is a step-by-step derivation of the formulation of Proposition 2b stated in (24). We
recall from (A1) that:
𝑁𝑃𝑉 ($) = ∑ 𝛾𝑖 . 𝐶𝐹𝐿𝑖
𝑇
𝑖=1
− 𝐶𝑎𝑝𝐸𝑥 (A1)
The cost of capacity in this case should account for the updated capacity of the fertilizers
subsystems as well as the intermediate storage of ammonia.
𝐶𝑎𝑝𝐸𝑥 = [𝐶𝐴𝑃ℎ + 𝐶𝐴𝑃𝑒 + 𝐶𝐴𝑃𝑎𝑠 + 𝐶𝐴𝑃𝑓] (A45)
𝐶𝐴𝑃𝑎𝑠: cost of capacity of ammonia generation and intermediate storage ($)
While 𝐶𝐴𝑃ℎ and 𝐶𝐴𝑃𝑒 are as defined in (A3) and (A18), respectively, the definition of 𝐶𝐴𝑃𝑓 is
updated in (A46), and 𝐶𝐴𝑃𝑎𝑠 is introduced in (A47) to represent the new capacity cost of
ammonia generation and storage.
𝐶𝐴𝑃𝑓 = 𝐾 ∙ 𝑋𝑓 ∙ 𝑁ℎ ∙ 𝑆𝑃𝑓 (A46)
𝐶𝐴𝑃𝑎𝑠 = (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑁ℎ ∙ 𝑆𝑃𝑎𝑠 (A47)
𝑆𝑃𝑎𝑠: system price of ammonia generation and intermediate storage per unit of generation
capacity ($/(𝑘𝑔𝑎 ℎ𝑟⁄ ))
Then, by substituting (A3), (A18), (A46) and (A47) into (A45):
𝐶𝑎𝑝𝐸𝑥 = 𝑁ℎ ∙ [𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝑃𝑎𝑠 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝑃𝑓] (A48)
Similar to the costs of capacity, the fixed-operating costs in year 𝑖 are updated, such that:
𝐽𝑖 = 𝐽ℎ𝑖 + 𝐽𝑒𝑖 + 𝐽𝑎𝑠𝑖 + 𝐽𝑓𝑖
= 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖 ] (A49)
The annual cash flow in year 𝑖 is defined as:
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 138
𝐶𝐹𝐿𝑖 = −𝐽𝑖 + 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ ∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖)] 𝑑𝑡 (A50)
Maximizing the cash flow from the flexible PES requires following the same operational
policy described in the simplified Scenario 2a. Thus, using the definitions of 𝐶𝑀𝑒𝑖 and 𝐶𝑀𝑓𝑖
in (13) and (14), the maximization problem be expressed as:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖)] 𝑑𝑡
= ∫ λ𝑚𝑎𝑥 ∙ (𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑒𝑖̃
+ ∫ λ𝑚𝑖𝑛 ∙ (𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ [𝐾 ∙ (𝐶𝑀𝑓𝑖(𝑡)) − 𝑤ℎ] 𝑑𝑡
𝑚
0
(A51)
Upon re-arranging (A51):
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖)] 𝑑𝑡
= ∫ λ𝑚𝑎𝑥 ∙ (𝐶𝑀𝑒𝑖(𝑡) − 𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑒𝑖̃
+ ∫ λ𝑚𝑎𝑥 ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑒𝑖̃
− ∫ λ𝑚𝑖𝑛 ∙ (𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑒𝑖(𝑡)) 𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ λ𝑚𝑖𝑛 ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ [𝐾 ∙ (𝐶𝑀𝑓𝑖(𝑡)) − 𝑤ℎ] 𝑑𝑡
𝑚
0
(A52)
Then, using the definitions of 𝐼𝐶𝑀𝐹𝑒𝑖 and 𝐼𝐶𝑀𝐹𝑓𝑖 in (17) and (18), respectively, and
expanding 𝐾:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖)] 𝑑𝑡
= 𝑚 ∙ (λ𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − λ𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖) + ∫ λ𝑚𝑎𝑥 ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑒𝑖̃
+ ∫ λ𝑚𝑖𝑛 ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑓𝑖̃
+ (𝑚 − 𝑚𝑒𝑖 ∙ 𝜆𝑚𝑎𝑥 − 𝑚𝑓𝑖 ∙ 𝜆𝑚𝑖𝑛) ∙ 𝐶𝑀𝑓𝑖 − 𝑚 ∙ 𝑤ℎ
(A53)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 139
But we know that 𝐶𝑀𝑓𝑖(𝑡) = 𝐶𝑀𝑓𝑖 because we assumed constant fertilizers price and variable
costs in a given year 𝑖. Under these conditions, (A53) can be re-written as:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖)] 𝑑𝑡
= 𝑚 ∙ (λ𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − λ𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖) + (𝑚𝑒𝑖 ∙ 𝜆𝑚𝑎𝑥 + 𝑚𝑓𝑖 ∙ 𝜆𝑚𝑖𝑛) ∙ 𝐶𝑀𝑓𝑖
+(𝑚 − 𝑚𝑒𝑖 ∙ 𝜆𝑚𝑎𝑥 − 𝑚𝑓𝑖 ∙ 𝜆𝑚𝑖𝑛) ∙ 𝐶𝑀𝑓𝑖 − 𝑚 ∙ 𝑤ℎ
(A54)
Which then simplifies to:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
𝑚
0
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖)] 𝑑𝑡
= 𝑚 ∙ (λ𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − λ𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖) + 𝑚 ∙ (𝑋𝑓𝑃𝑓𝑖 − 𝑋𝑓𝑤𝑓𝑖 − 𝑋𝑎𝑤𝑎𝑠𝑖) − 𝑚 ∙ 𝑤ℎ
(A55)
Substituting the result of (A55) and (A49) into (A50), we get:
𝐶𝐹𝐿𝑖 = −𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖 ]
+𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+[𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑠𝑖] − 𝑤ℎ𝑖}
(A56)
Then, substituting (A56) and (A48) into (A1), the NPV becomes:
𝑁𝑃𝑉 ($) =
− ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖]
𝑇
𝑖=1
+ ∑ 𝛾𝑖 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+[𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑠𝑖] − 𝑤ℎ𝑖}
𝑇
𝑖=1
−𝑁ℎ ∙ [𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝑃𝑎𝑠 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝑃𝑓]
(A57)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 140
PES is economically competitive if and only if NPV is positive, thus:
− ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖 ]
𝑇
𝑖=1
+ ∑ 𝛾𝑖 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+[𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑠𝑖] − 𝑤ℎ𝑖}
𝑇
𝑖=1
−𝑁ℎ ∙ [𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝑃𝑎𝑠 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝑃𝑓] > 0
(A58)
Upon dividing (A55) by 𝑚 ∙ 𝐶𝐹 ∙ 𝑁ℎ ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1 , we get:
−∑ 𝛾𝑖 ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖]𝑇
𝑖=1
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
+
∑ 𝛾𝑖 ∙ 𝑥𝑖 ∙ {𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓𝑖
+[𝑋𝑓 . 𝑃𝑓𝑖 − 𝑋𝑓 . 𝑤𝑓𝑖 − 𝑋𝑎 . 𝑤𝑎𝑠𝑖] − 𝑤ℎ𝑖}𝑇
𝑖=1
∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
−[𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝑃𝑎𝑠 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝑃𝑓]
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
> 0
(A59)
−𝑗ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑗𝑒 − (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑗𝑎𝑠 − 𝐾 ∙ 𝑋𝑓 ∙ 𝑗𝑓
+𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓 + [𝑋𝑓 . 𝑃𝑓 − 𝑋𝑓 . 𝑤𝑓 − 𝑋𝑎 . 𝑤𝑎𝑠] − 𝑤ℎ
−𝑐ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑐𝑒 − (1 − λ𝑚𝑖𝑛)𝑋𝑎 ∙ 𝑐𝑎𝑠 − 𝐾 ∙ 𝑋𝑓 ∙ 𝑐𝑓 > 0
(A60)
−𝑗ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑗𝑒 − (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑗𝑎𝑠 − (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑓 ∙ 𝑗𝑓
+𝜆𝑚𝑎𝑥 ∙ 𝐼𝐶𝑀𝐹𝑒 − 𝜆𝑚𝑖𝑛 ∙ 𝐼𝐶𝑀𝐹𝑓 + [𝑋𝑓 . 𝑃𝑓 − 𝑋𝑓 . 𝑤𝑓 − 𝑋𝑎 . 𝑤𝑎𝑠] − 𝑤ℎ
−𝑐ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑐𝑒 − (1 − λ𝑚𝑖𝑛)𝑋𝑎 ∙ 𝑐𝑎𝑠 − (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑓 ∙ 𝑐𝑓
+(1 − λ𝑚𝑖𝑛 − 𝐾) ∙ 𝑋𝑓 ∙ (𝑐𝑓 + 𝑋𝑓) > 0
(A61)
[𝑿𝒇. 𝑷𝒇 − 𝑿𝒇. 𝑳𝑰𝑪𝒇 − 𝑿𝒂. 𝑳𝑰𝑪𝒂𝒔]
+𝝀𝒎𝒂𝒙 ∙ [𝑰𝑪𝑴𝑭𝒆 − 𝑿𝒆 ∙ (𝒄𝒆 + 𝒋𝒆)]
−𝝀𝒎𝒊𝒏 ∙ [𝑰𝑪𝑴𝑭𝒇 − 𝑿𝒇 ∙ (𝒄𝒇 + 𝒋𝒇) − 𝑿𝒂 ∙ (𝒄𝒂𝒔 + 𝒋𝒂𝒔)]
+(𝟏 − 𝛌𝒎𝒊𝒏 − 𝑲) ∙ [𝑿𝒇 ∙ (𝒄𝒇 + 𝒋𝒇)] > 𝑳𝑪𝑶𝑯
(A62)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 141
Derivation of Proposition 2b in (25)
The derivation of the formulation of Proposition 2b in (25) follows a very similar path to that
in (24). Following the same steps from (A45) through (A51), we re-arrange (A52) as follows:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖)
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖) − 𝑤ℎ
] 𝑑𝑡
𝑚
0
= ∫ (𝜆𝑚𝑎𝑥 − 1) ∙ (𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑒𝑖̃
+ ∫(𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑒𝑖̃
+ ∫ (𝜆𝑚𝑎𝑥 − 1) ∙ (𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑒𝑖̃
+ ∫ (λ𝑚𝑖𝑛 − 1) ∙ (𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ (𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ (𝜆𝑚𝑖𝑛 − 1) ∙ (𝐶𝑀𝑓𝑖(𝑡) − 𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ [𝐾 ∙ (𝐶𝑀𝑓𝑖(𝑡)) − 𝑤ℎ] 𝑑𝑡
𝑚
0
(A63)
The expression in (A63) can be re-arranged, such that:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖)
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖) − 𝑤ℎ
] 𝑑𝑡
𝑚
0
= ∫ (𝜆𝑚𝑎𝑥 − 1) ∙ (𝐶𝑀𝑒𝑖(𝑡) − 𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑒𝑖̃
+ ∫ (𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑒𝑖̃
+ ∫ (λ𝑚𝑖𝑛 − 1) ∙ (𝐶𝑀𝑒𝑖(𝑡) − 𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑓𝑖̃
+ ∫(𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ (𝜆𝑚𝑎𝑥 − 1) ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑒𝑖̃
+ ∫ (𝜆𝑚𝑖𝑛 − 1) ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ [𝐾 ∙ (𝐶𝑀𝑓𝑖(𝑡)) − 𝑤ℎ] 𝑑𝑡
𝑚
0
(A64)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 142
Then, using the definitions of 𝐼𝐶𝑀𝐹𝑒𝑖 and 𝐼𝐶𝑀𝐹𝑓𝑖 in (17) and (18), respectively, and
expanding 𝐾:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖)
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖) − 𝑤ℎ
] 𝑑𝑡
𝑚
0
= −𝑚 ∙ (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 + ∫ (𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑒𝑖̃
− ∫(1 − 𝜆𝑚𝑎𝑥) ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑒𝑖̃
+𝑚 ∙ (1 − λ𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 + ∫(𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚𝑓𝑖̃
− ∫(1 − 𝜆𝑚𝑖𝑛) ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑓𝑖̃
+(𝑚 − 𝑚𝑒𝑖 ∙ 𝜆𝑚𝑎𝑥 − 𝑚𝑓𝑖 ∙ 𝜆𝑚𝑖𝑛) ∙ 𝐶𝑀𝑓𝑖 − 𝑚 ∙ 𝑤ℎ
(A65)
Re-arranging (A65), we get:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖)
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖) − 𝑤ℎ
] 𝑑𝑡
𝑚
0
= 𝑚 ∙ (1 − λ𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − 𝑚 ∙ (1 − 𝜆𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 + ∫ (𝐶𝑀𝑒𝑖(𝑡))𝑑𝑡
𝑚
0
− ∫ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚
0
+ ∫ 𝜆𝑚𝑖𝑛 ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑓𝑖̃
+ ∫ 𝜆𝑚𝑎𝑥 ∙ (𝐶𝑀𝑓𝑖(𝑡)) 𝑑𝑡
𝑚𝑒𝑖̃
+(𝑚 − 𝑚𝑒𝑖 ∙ 𝜆𝑚𝑎𝑥 − 𝑚𝑓𝑖 ∙ 𝜆𝑚𝑖𝑛) ∙ 𝐶𝑀𝑓𝑖 − 𝑚 ∙ 𝑤ℎ
(A66)
But we know that 𝐶𝑀𝑓𝑖(𝑡) = 𝐶𝑀𝑓𝑖 because we assumed constant fertilizers price and variable
costs in a given year 𝑖. Under these conditions, (A66) reduces to:
∫ 𝑚𝑎𝑥⏟𝜆(𝑡)
[(𝜆(𝑡)) ∙ (𝑋𝑒 ∙ 𝑃𝑒𝑖(𝑡) − 𝑋𝑒 ∙ 𝑤𝑒𝑖) − 𝑤ℎ
+(𝐾) ∙ (𝑋𝑓 ∙ 𝑃𝑓𝑖 − 𝑋𝑓 ∙ 𝑤𝑓𝑖 − 𝑋𝑎 ∙ 𝑤𝑎𝑠𝑖)] 𝑑𝑡
𝑚
0
= 𝑚 ∙ (1 − λ𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − 𝑚 ∙ (1 − λ𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖 + 𝑚 ∙ 𝐶𝑀𝑒𝑖 − 𝑚 ∙ 𝑤ℎ
(A67)
Substituting the results of (A66) and (A49) into (A50), we get:
𝐶𝐹𝐿𝑖 = −𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖 ]
+𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {(1 − λ𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − (1 − λ𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖
+[𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖] − 𝑤ℎ𝑖}
(A68)
CHAPTER 3 — Appendix A: Derivation of Economic Propositions 143
Then, substituting (A68) and (A48) into (A1), the NPV becomes:
𝑁𝑃𝑉 ($) =
− ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖]
𝑇
𝑖=1
+ ∑ 𝛾𝑖 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {(1 − λ𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − (1 − λ𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖
+[𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖] − 𝑤ℎ𝑖}
𝑇
𝑖=1
−𝑁ℎ ∙ [𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝑃𝑎𝑠 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝑃𝑓]
(A69)
PES is economically competitive if and only if NPV is positive, thus:
− ∑ 𝛾𝑖 ∙ 𝑁ℎ ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖]
𝑇
𝑖=1
+ ∑ 𝛾𝑖 ∙ 𝐶𝐹 ∙ 𝑥𝑖 ∙ 𝑁ℎ ∙ 𝑚 ∙ {(1 − λ𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − (1 − λ𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖
+[𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖] − 𝑤ℎ𝑖}
𝑇
𝑖=1
−𝑁ℎ ∙ [𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝑃𝑎𝑠 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝑃𝑓] > 0
(A70)
Upon dividing (A70) by 𝑚 ∙ 𝐶𝐹 ∙ 𝑁ℎ ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1 , we get:
−∑ 𝛾𝑖 ∙ [𝑆𝐽ℎ𝑖 + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝐽𝑒𝑖 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝐽𝑎𝑠𝑖 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝐽𝑓𝑖]𝑇
𝑖=1
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
+
∑ 𝛾𝑖 ∙ 𝑥𝑖 ∙ {(1 − λ𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓𝑖 − (1 − λ𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒𝑖
+[𝑋𝑒 . 𝑃𝑒𝑖 − 𝑋𝑒 . 𝑤𝑒𝑖] − 𝑤ℎ𝑖}𝑇
𝑖=1
∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
−[𝑆𝑃ℎ + λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑆𝑃𝑒 + (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑆𝑃𝑎𝑠 + 𝐾 ∙ 𝑋𝑓 ∙ 𝑆𝑃𝑓]
𝑚 ∙ 𝐶𝐹 ∙ ∑ 𝛾𝑖 ∙ 𝑥𝑖𝑇𝑖=1
> 0
(A71)
−𝑗ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑗𝑒 − (1 − λ𝑚𝑖𝑛) ∙ 𝑋𝑎 ∙ 𝑗𝑎𝑠 − 𝐾 ∙ 𝑋𝑓 ∙ 𝑗𝑓
+(1 − λ𝑚𝑖𝑛) ∙ 𝐼𝐶𝑀𝐹𝑓 − (1 − λ𝑚𝑎𝑥) ∙ 𝐼𝐶𝑀𝐹𝑒 + [𝑋𝑒 . 𝑃𝑒 − 𝑋𝑒 . 𝑤𝑒] − 𝑤ℎ
−𝑐ℎ − λ𝑚𝑎𝑥 ∙ 𝑋𝑒 ∙ 𝑐𝑒 − (1 − λ𝑚𝑖𝑛)𝑋𝑎 ∙ 𝑐𝑎𝑠 − 𝐾 ∙ 𝑋𝑓 ∙ 𝑐𝑓 > 0
(A72)
[𝑿𝒆. 𝑷𝒆 − 𝑿𝒆. 𝑳𝑰𝑪𝒆]
+(𝟏 − 𝝀𝒎𝒊𝒏) ∙ [𝑰𝑪𝑴𝑭𝒇 − 𝑿𝒇 ∙ (𝒄𝒇 + 𝒋𝒇) − 𝑿𝒂 ∙ (𝒄𝒂𝒔 + 𝒋𝒂𝒔)]
−(𝟏 − 𝝀𝒎𝒂𝒙) ∙ [𝑰𝑪𝑴𝑭𝒆 − 𝑿𝒆 ∙ (𝒄𝒆 + 𝒋𝒆)]
+(𝟏 − 𝛌𝒎𝒊𝒏 − 𝑲) ∙ [𝑿𝒇 ∙ (𝒄𝒇 + 𝒋𝒇)] > 𝑳𝑪𝑶𝑯
(A73)
CHAPTER 3 — Appendix B: Cost Estimates for HECA 144
Appendix B: Cost Estimates for HECA
Table 3.B1: System prices of HECA per unit capacity
Subsystem Process Cost Unit Reference
Hydrogen
Subsystem
Coal & petcoke handling and
storage 22,083 $/(𝑡𝑜𝑛𝑛𝑒/𝑑𝑎𝑦) [36]
Gasification 11,528 $/(𝑘𝑔ℎ/ℎ) [36]
Air separation 6,663 $/(𝑘𝑔ℎ/ℎ) [36]
Syngas treatment 3,027 $/(𝑘𝑔ℎ/ℎ) [36]
Acid gas removal 5,732 $/(𝑘𝑔ℎ/ℎ) [36]
Sulfur recovery and trail gas
treatment 1,859 $/(𝑘𝑔ℎ/ℎ) [36]
Hydrogen separation 927 $/(𝑘𝑔ℎ/ℎ) [36]
Utilities and offsites 11,116 $/(𝑘𝑔ℎ/ℎ) [36]
Electricity
Subsystem Power production 1,045 $/(𝑘𝑊 𝑔𝑟𝑜𝑠𝑠) [36]
Ammonia
Subsystem
Ammonia production 3,863 $/(𝑘𝑔𝑎/ℎ) [37]
Ammonia storage 0.686 $/(𝑘𝑔𝑎) [38, 39]
Fertilizers
Subsystem
Urea production 1,643 $/(𝑘𝑔𝑢𝑟𝑒𝑎/ℎ) [40, 41]
UAN Production 1,802 $/(𝑘𝑔𝑈𝐴𝑁/ℎ) [40, 41]
CO2
Subsystem CO2 compression and drying 135 $/(𝑘𝑔𝑐/ℎ) [36]
Aggregating these figures for each subsystem, we then get:
Table 3.B2: System prices of HECA’s subsystems per unit capacity
Subsystem Cost Value Unit Reference
Hydrogen Subsystem 𝑆𝑃ℎ 44,894 $/(𝑘𝑔ℎ/ℎ) [36]
Electricity Subsystem 𝑆𝑃𝑒 1,045 $/(𝑘𝑊) [36]
Ammonia Subsystem
(without storage) 𝑆𝑃𝑎 3,863 $/(𝑘𝑔𝑎/ℎ) [37]
Ammonia Subsystem
(with storage) 𝑆𝑃𝑎𝑠 3,947 $/(𝑘𝑔𝑎/ℎ) [37-39]
Fertilizers Subsystem 𝑆𝑃𝑓 4,435 $/(𝑘𝑔𝑢𝑟𝑒𝑎/ℎ) [40, 41]
CO2 Subsystem 𝑆𝑃𝑐 135 $/(𝑘𝑔𝑐/ℎ) [40, 41]
CHAPTER 3 — Appendix B: Cost Estimates for HECA 145
Table 3.B3: Yearly fixed-operating costs of HECA as fraction of capacity costs
Subsystem Process Cost
(% of capacity cost) Reference
Hydrogen
Subsystem
Coal & petcoke handling and
storage 3% [36]
Gasification 4.8% [36]
Air separation 3% [36]
Syngas treatment 4.8% [36]
Acid gas removal 3% [36]
Sulfur recovery and trail gas
treatment 3% [36]
Hydrogen separation 3% [36]
Utilities and offsites 2.1% [36]
Power
Subsystem Power production 6.1% [36]
Ammonia
Subsystem
Ammonia production 6.1% [estimated]
Ammonia storage 6.1% [estimated]
Fertilizers
Subsystem
Urea production 6.1% [estimated]
UAN Production 6.1% [estimated]
CO2
Subsystem CO2 compression and drying 3% [36]
Again, by aggregating these figures for each subsystem, we get:
Table 3.B4: Yearly fixed-operating costs of HECA Subsystems per unit capacity
Subsystem Cost Value Unit Reference
Hydrogen Subsystem 𝑆𝐽ℎ 1,514 ($ 𝑦𝑟⁄ ) (𝑘𝑔ℎ/ℎ)⁄ [36]
Electricity Subsystem 𝑆𝐽𝑒 63 ($ 𝑦𝑟⁄ )/(𝑘𝑊) [36]
Ammonia Subsystem
(without storage) 𝑆𝐽𝑎 234 ($ 𝑦𝑟⁄ )/(𝑘𝑔𝑎/ℎ) [estimated]
Ammonia Subsystem
(with storage) 𝑆𝐽𝑎𝑠 239 ($ 𝑦𝑟⁄ )/(𝑘𝑔𝑎/ℎ) [estimated]
Fertilizers Subsystem 𝑆𝐽𝑓 268 ($ 𝑦𝑟⁄ )/(𝑘𝑔𝑢𝑟𝑒𝑎/ℎ) [estimated]
CO2 Subsystem 𝑆𝐽𝑐 4 ($ 𝑦𝑟⁄ )/(𝑘𝑔𝑐/ℎ) [36]
CHAPTER 3 — Appendix B: Cost Estimates for HECA 146
Table 3.B5: Prices of input commodities and services for HECA
Input Cost Unit Reference
Coal (sub-bituminous) 60 $/𝑡𝑜𝑛𝑛𝑒 (personal communication)
Petcoke 50 $/𝑡𝑜𝑛𝑛𝑒 (personal communication)
Electricity (average) 29.5 $/MWh [29]
Selexol™ 0.00376 $/𝑘𝑔ℎ [36]
Flux 0.00432 $/𝑘𝑔ℎ [36]
Catalysts 0.00769 $/𝑘𝑔ℎ [36]
Chemicals 0.00601 $/𝑘𝑔ℎ [36]
Waste-water treatment 0.00928 $/𝑘𝑔ℎ [36]
Using this data, as well as the auxiliary loads in Table 3.2 of this study, we can find the
variable costs of HECA:
Table 3.B6: Yearly-averaged variable costs Cost of HECA per unit of production
Subsystem Input Cost Unit
Hydrogen Subsystem
Coal & petcoke 0.443 $/𝑘𝑔ℎ
Flux 0.00338 $/𝑘𝑔ℎ
SelexolTM
0.00294 $/𝑘𝑔ℎ
Catalyst 0.00602 $/𝑘𝑔ℎ
Other chemicals 0.00471 $/𝑘𝑔ℎ
Waste-water treatment 0.00727 $/𝑘𝑔ℎ
Auxiliary power 0.173 $/𝑘𝑔ℎ
Power Subsystem Auxiliary power 0.00119 $/𝑘𝑊ℎ
Ammonia Subsystem Auxiliary power 0.00644 $/𝑘𝑔𝑎
Fertilizers Subsystem Auxiliary power 0.00836 $/𝑘𝑔𝑢𝑟𝑒𝑎
CO2 Subsystem Auxiliary power 0.00331 $/𝑘𝑔𝑐
Table 3.B7: Prices of HECA end-products
End-Product Price Unit Reference
Urea 385 $/𝑡𝑜𝑛𝑛𝑒 (personal communication)
UAN 315 $/𝑡𝑜𝑛𝑛𝑒 (personal communication)
Electricity
(yearly-averaged) 29.5 $/𝑀𝑊ℎ [29]
CO2 25 $/𝑡𝑜𝑛𝑛𝑒 (personal communication)
147
Chapter 4
Decision Analytic Modeling of the Five
Forces in Competitive Strategy
1 Introduction
Despite apparent differences among industries, all firms compete for profit. Competitive
strategy, pioneered by Michael E. Porter since 1979, explains how an organization facing
competition can achieve superior profitability within its industry. Porter identifies five forces
that shape competition in relatively stable industries. Relying on Industrial Organization
theory and using examples from representative industries, he describes what causes each of
the five competitive forces to be strong or weak, and he explains that an incumbent business
gains competitive advantage by positioning where all five forces are weakest [1, 2]. Over the
years, Porter’s five forces framework (FF) has generated valuable strategic insights, has
inspired strategic victories for firms and businesses, and has occupied a permanent position in
strategic management classes and business schools’ curricula. However, despite its remarkable
contribution to competitive strategy, the framework has been mostly applied qualitatively and
deterministically [3, 4, 5]. Few systematic methodologies have been developed to guide the
quantification and operationalization of the competitive forces in real life, and no sufficient
attention has been given to the uncertain and interdependent nature of these forces and their
economic implications [6, 7].
CHAPTER 4 — Introduction 148
To address these issues, this work proposes decision analysis (DA) as a method to model and
apply the five forces strategic framework in a specific industry and by a specific firm. As a
normative application of decision theory, DA describes how decision-makers, facing many
alternatives and uncertainties, should make an irrevocable allocation of resources to maximize
their utility. In the world of competitive strategy, we propose a decision analytic modeling of
the five forces, hereby referred to as DAFF. This modeling approach describes how an
executive or a manager, facing multiple positioning alternatives and uncertain competitive
powers, should commit to an irrevocable allocation of resources in order to maximize
profitability. Put differently, DAFF uses DA techniques and tools to link the firms’
positioning alternatives with uncertain market competition and economics, in accordance with
the pillars of Industrial Organization. The result is a thorough and quantitative model that
managers can use to evaluate the profitability of a specific industry, to properly position their
business in the industry, and to predict and shape the future of that industry.
Both FF and DA have been used to help firms improve their strategic performance in their
respective industries [8, 9]. By applying the FF theory using the DA method, this work adds
value to both fields of competitive strategy and decision analysis. On one hand, DAFF allows
strategists to quantify the five competitive forces, assess the significance of uncertainty in the
forces and their underlying drivers, capture and exploit interdependencies and interactions
among the forces, link the forces to measurable economic indicators, and specify the decisions
that firms or business units can actually make to influence competition or deter its threat. On
the other hand, the same model allows decision analysts to account for all competitive forces
and their drivers, understand the causal relationships in a competitive industry, and ensure that
the modeling of a firm’s decision problem is consistent with the mature literature on
competitive strategy and competitive advantage.
To explain DAFF and develop its models, the rest of this Chapter is organized as follows.
Section 2 starts by offering a brief formal introduction to both decision analysis and the five
forces strategic framework. Then, as the main motivation behind this work, we highlight key
considerations which have sometimes been neglected or oversighted when implementing the
five forces framework, and we provide a brief overview of previous endeavors aiming to
enhance the application of FF. Center to this study, we describe how DA can augment
CHAPTER 4 — Theoretical Background 149
previous work, accounting for all essential attributes of FF and further improving its
operationalization and implementation in real life. Section 3 provides a detailed description of
how to develop a DAFF model, including how to use DA’s building blocks of uncertainty,
decision, and value to model the five competitive forces and industry-specific factors, the
economics of an industry or a firm, and the firm’s competitive actions. Then, we explain how
a firm can use DAFF to operationalize the two main objectives of competitive strategy:
positioning in and reshaping the industry. Section 4 provides a three-step procedure on how
to model the industry-positioning objective, highlighting the benefits of the decision analytic
approach in each step. Subsequently, Section 5 lays out a conceptual roadmap to modeling the
industry-reshaping objective by augmenting the DAFF model from Section 4. Sections 6 and 7
provide additional guidance on DAFF. While Section 6 discusses additional modeling best
practices, Section 7 highlights the ability of DA to uphold and characterize many of Porter’s
strategic insights that stem from, yet extend beyond, the FF framework. Finally, Section 8
concludes this Chapter by summarizing the main modeling aspects and advantages of DAFF
and then offering some ideas for future work.
2 Theoretical Background
2.1 Decision Analysis
Decision analysis (DA) is a logical procedure that balances the various attributes of a decision
problem. Sometimes, decisions are difficult because they require making trade-offs among
several considerations, some of which are hard to observe, measure, or quantify. Other reasons
that contribute to the complexity of decisions include uncertainty, the lack of clear
information, the lack of sufficient alternatives, and conflicting preferences. Focusing on
strategic decisions, DA comprises of techniques and tools that allow a decision-maker to
achieve clarity of action in her decision, and even more fundamentally, to achieve clarity of
thought. In that regard, a key distinction in DA is the difference between the quality of a
decision and the quality of its outcome; DA emphasizes that the quality of a decision is
determined when making a decision, hence before the outcome is revealed. Put differently, the
CHAPTER 4 — Theoretical Background 150
decision should never be judged retrospectively based on its outcome, for a good decision may
still result in a bad outcome due to unknown information at the time of making the decision.
DA enables making good strategic decisions [10].
An essential DA foundation is the decision basis, which decomposes every decision situation
into three fundamental elements: alternatives, information, and preferences [10]. The
alternatives describe the options and choices available to the decision-maker at the time of
making a specific decision; this element addresses what the decision-maker can do. For
example, in the automobile industry, an auto manufacturer who wants to launch a new
environmentally friendly car may need to decide between two feasible alternatives: an
[electric car] or a [hybrid car].
Information describes the knowledge that the decision-maker has about the various aspects of
the decision situation. This element addresses what the decision-maker knows, and it
includes both certain information that the decision-maker knows for sure as well as uncertain
information that the decision-maker lacks completely or is unsure about. DA pays special
attention to uncertainty, which is explicitly accounted for in the decision problem. To help
the decision-maker think about uncertainty, DA models uncertainty via two means. First, the
decision-maker is invited to identify all possible realizations of each uncertainty, referred to as
degrees. Then, the decision-maker assigns a probability to each degree, depending on her
beliefs about the likelihood of it actually happening. The degrees should be mutually
exclusive and collectively exhaustive, so only one degree could be realized, and the
probability on all degrees should add up to one. To continue the car example, suppose that the
automaker is unsure about its consumers’ driving habits, which is an important consideration
in deciding what type of car to produce. The consumer’s driving habits become an uncertainty
in this case, and the automaker characterizes this uncertainty using only two degrees: {≤ 100
miles short trips; > 100 miles long trips}. Then, based on market research and other available
yet imperfect information, the automaker assigns a 0.7 probability that consumers will use the
car for short trips and a probability of 0.3 that consumers will drive the car on long trips.
The final element in the decision basis is preferences, which address what the decision-
maker wants. Preferences describe what the decision-maker mostly cares about and thus is
CHAPTER 4 — Theoretical Background 151
trying to optimize. They are usually presented as monetary values that the decision-maker
assigns to each potential combination of alternatives and uncertainties, called prospects. In
our example, the automaker is mostly concerned about the net present value (NPV) for the
new line of cars it intends to launch, so it assigns an NPV figure for each of the following
prospects: {electric car, short trips}, {hybrid car, long trips}, {hybrid car, short trips},
{electric car, long trips}. The decision-maker then chooses the alternative that achieves the
highest probability-weighted-average value.
On top of the three elements of the decision basis, three additional elements should be
available in every decision problem to ensure good decision quality. The first is a proper
framework, which refers to the context within which the decision problem should be
evaluated. Choosing the framework too broadly or too narrowly results in getting the right
answer to the wrong problem, which is rarely useful. In our car example, the automaker is not
deciding on whether or not to produce a new car (this framework is too broad) or what type of
battery the car should have (this framework is too narrow). The proper framework in this case
already assumes that an environmentally friendly car will be produced, and it postpones the
decision on the battery type till later. The second additional element for good decision quality
is proper logic, which dictates the relationship between the decisions, uncertainties, and
values. Much of the analytical calculations and algorithms needed to solve a decision problem
are governed by Bayesian probability logic. Finally, a good decision requires a clear
commitment to action; there is no point in spending time and resources analyzing a decision
unless the decision-maker is committed to implementing the outcome solution to the decision
problem [10].
Among the various tools that DA uses to model a decision problem, we focus on two tools
called Bayesian networks and decision diagrams [11]. Both tools can model multiple
decisions, multiple uncertainties, and a single value, connected as a network of nodes. While
the decision is generally presented in rectangle-like node, the uncertainty is presented in an
oval-like node, and the value function is presented as a diamond-like node. Sometimes, certain
information is also explicitly modeled to ease the analysis. Certain information is described as
“deterministic” and is presented in oval-like nodes with double-lined borders to distinguish it
from regular single-line ovals presenting uncertainties. A schematic of the various shapes
CHAPTER 4 — Theoretical Background 152
representing decisions, uncertainties, deterministic information, and values is presented in
Figure 4.1. To reiterate, each decision node incorporates multiple alternatives; each
uncertainty node incorporates multiple degrees; and the value node assigns a value to each
prospect. The process of solving a decision diagram to find the optimal alternative under
uncertainty is mature and well-documented in literature [10, 11, 12, 13], and several
commercial software packages are available for that purpose [14, 15].
Figure 4.1: Representation of the nodes in a decision diagram
2.2 The Five Forces that Shape Competition
The Five Competitive Forces that Shape Strategy by Michael Porter is one of the most well-
known papers in business strategy. In this updated version of his work on competitive
strategy, Porter explains that competition for profits in stable industries extends beyond direct
rivals to include four other players in the marketplace: buyers, suppliers, potential new
entrants, and substitutes. Therefore, despite apparent differences in industries’ structures and
functions, the competition within each industry is shaped by five competitive forces, depicted
in Figure 4.2: the bargaining power of buyers, the bargaining power of suppliers, the threat of
new entrants, the threat of substitutes, and rivalry among incumbents. For brevity, we refer to
these forces throughout the rest of this study as Buyers, Suppliers, New Entrants, Substitutes,
and Rivals, respectively. The strength of each of the five forces is shaped by a set of
generalizable market drivers and another set of industry-specific factors, both of which have
been continuously discussed, refined, and updated by Porter over the years [1, 2, 8, 16]. In that
regard, Porter’s recent work clearly identifies four factors: industry growth rate, technology
and innovation, government regulations and policies, and complementary products and
services. Again, for brevity, we refer to these factors as Growth, Technology, Regulation, and
Complements, respectively. While the five forces shape the underlying structure of any
industry, the four factors are visible attributes of a specific industry.
Uncertainty ValueDecisionDeterministic Information
CHAPTER 4 — Theoretical Background 153
Figure 4.2: Porter’s five forces framework
Porter’s five forces framework (FF) advises the current incumbents to reduce the power of all
forces in order to increase their profitability. This means that firms should try to limit the
bargaining power of buyers and suppliers, decrease the threat of new entrants and substitutes,
and reduce the intensity of destructive rivalry with direct competitors. However, unlike the
forces, stronger factors may increase or decrease profitability. Depending on the unique
aspects of each industry, each factor influence the five forces in a way that can either increase
or decrease their strength and thus profitability [2]. The role of the internet in the automobile
industry is a good example [17]. As one of the most prominent technological innovations in
the past decade, the internet has impacted automakers in two opposing ways. On one hand,
direct online purchases have lowered the Buyers power by weakening the role of dealers as
intermediate channels [18]. On the other hand, car valuation sites such as Kelly Blue Book
have increased the Buyers power by allowing end-customers to effortlessly compare and shop
for cars at multiple venues [19]. Another important thing to note is that a factor may affect
each force either directly or indirectly through one of the force’s drivers. For example, in the
solar industry, regulation may directly decrease the threat of Substitutes by mandating the
deployment of a specific solar production capacity within a specific region and timeline [20].
Alternatively, regulation may indirectly decrease the bargaining power of Buyers by allowing
BuyersHow much bargaining power
do buyers have?
SuppliersHow much bargaining power
do supplier bear?
New EntrantsWhat is the threat of new entrants into the market?
SubstitutesWhat is the threat of substitute
products or services?
RivalsWhat rivalry exists among
present incumbents?
CHAPTER 4 — Theoretical Background 154
solar firms to impose a high early-termination penalty on their solar-panel leases, which
effectively increases the switching costs for customers [21].
By analyzing the power of the competitive five forces, their underlying drivers, and the
industry-specific factors, a firm can assess the level and distribution of profitability in the
industry. In turn, such assessment can guide and inform the design of effective strategies that
improve the firm’s performance relative to the industry average. In that regard, the FF
framework facilitates the fulfillment of three strategic objectives by the firm: positioning
where competition is weakest, uncovering new favorable positions by predicting and
exploiting future changes in the industry structure, and becoming an industry leader by
reshaping future changes in the industry structure. Successful firms usually strive to fulfill one
or more of these objectives [2].
2.3 Decision Analytic Approach to the Five Forces
Despite their importance, multiple key considerations have sometimes been downplayed,
oversighted, or neglected in the daily conduct of FF competitive analyses within businesses,
corporations, and consulting practices. Primarily, they include: standardization of the analysis;
role of uncertainty; relation between the competitive forces and economic performance;
relation between the industry’s competitive forces and the firm’s strategic actions;
interdependence among the forces, drivers, and factors; and quantification. DAFF offers one
way to effectively account for and uphold all these considerations in the FF applications,
building on and augmenting a diverse set of previous research endeavors that have aimed to
enhance FF’s operationalization.
Standardization of the analysis: attempting to enhance the clarity and standardization of the
competitive forces’ analyses, Dobbs proposed the design of generalizable templates for FF
practitioners [6]. As will become evident, the proposed DAFF approach expands this effort by
developing generalizable models that represent and incorporate not only the five competitive
forces but also the other building blocks of the FF framework, including: the industry-specific
factors, the economic parameters that characterize the performance of an overall industry or of
a specific firm, and the set of competitive actions and activities taken by the firm.
CHAPTER 4 — Theoretical Background 155
Role of uncertainty: the vast majority of FF applications discuss the power of the competitive
forces as certain happening facts, assuming that industry players have perfect clairvoyance on
competition. Such an approach is problematic for two main reasons. First, it does not account
for the reality that, due to asymmetric market information, different players may have different
and uncertain beliefs about the strength of the competitive drivers or factors in their present
industry. More importantly, it does not allow predicting the evolution of the competitive
forces and factors in the future. As Magretta nicely explains in her book [8]: “Porter examines
… companies, after the fact, and asks, what explains their success?” This is a clear recognition
that the FF framework has been mostly used to retrospectively assess a company’s
performance in the past. The main question then becomes: how can we use this framework to
proactively assess a company’s performance in the future?
DA resolves this issue by modeling the competitive forces, drivers, and factors – both current
and future – as uncertainties. Accounting for uncertainty is not a new endeavor in the field of
business strategy. For example, cautioning against the dangers of ignoring or misrepresenting
uncertainty, Courtney et al. identifies multiple levels of uncertainty in strategy and proposes
multiple ways to address them [22]. Even earlier work by Ghemawat recognizes the need for
modeling uncertainty in strategic decisions, primarily because these decisions may involve
irrevocable investments and therefore may require an irreversible allocation of nontrivial
resources [23]. In their work on “co-opetition”, Brandenburger and Nalebuff also characterize
uncertainty as “fog”, which, depending on the specific business setting, may be either
beneficial or harmful [24]. In fact, Porter himself notes the significance of uncertainty
assessment in strategy [25]; in the updated publication The Five Competitive Forces that
Shape Strategy, Porter uses the words “likely” and “less likely” multiple times throughout the
manuscript, which validates the inability to perfectly characterize current or future competitive
landscapes [2]. By modeling unknown competitive information as uncertainties, DA helps
decision-makers avoid the false logic that Magretta warns against: “I can’t predict the future.
Strategy requires a prediction of the future. Therefore, I cannot commit to strategy” [8].
Strategy does not require predicting the future. Strategy requires taking an insightful action
about the future after considering all available information, which is exactly what DA allows
CHAPTER 4 — Theoretical Background 156
doing. To that end, DA and Porter’s FF framework strongly support a common conclusion:
not knowing the future is not a good excuse to dodge strategy.
Relation between the competitive forces and economic performance: we address two
considerations here. First, as clearly explained by Porter himself [2, 25] and further reflected
upon in competitive strategy literature [26, 27], the five forces framework depicts the
economic performance of the firm as a function of competition in the industry. FF literature
explains that weaker competitive forces result in lower costs and/or higher prices, which in
turn result in higher profitability. However, it is unclear what exactly defines a force as
“strong” or “weak”, and to what extent each force can (and does) affect economic parameters
such as price or cost. To resolve this ambiguity, DA models the parameters characterizing the
economic performance (e.g. price and cost) as uncertainties, similar to the five forces.
Consistent with FF theory, the competitive forces’ uncertainties interact directly with the
economic parameters’ uncertainties, capturing all available – albeit imperfect – market
information based on the decision-maker’s personal or corporate intelligence. In addition, DA
modeling allows distinguishing between the effect of the forces on the economics of the
overall industry and the effect of the forces on the economics of a specific firm.
The second consideration to address is FF’s emphasis on maximizing profitability [2].
Because DA models use one value metric to articulate preferences and rank prospects,
profitability should be clearly defined as a single quantitative and measurable metric. In that
regard, profitability may be expressed as “unit-profit-margin” (PM) or “return on invested
capital” (ROIC) as advised by Porter [8], net present value, earnings before tax, or otherwise.
Relation between the industry’s competitive forces and the firm’s strategic actions: when it
comes to strategic decisions, we first highlight that FF and DA are normative not descriptive;
both approaches advise what a firm’s optimal strategy should be rather than describing or
justifying what its strategy actually is. With that in mind, FF identifies three competitive
objectives that each firm should strive to fulfil: positioning in the industry, predicting and
exploiting future industry change, and reshaping the industry [2]. However, pursuing each of
these broad objectives requires a series of specific firm actions – and thus decisions – that are
hard to capture in generalizable – and intentionally simple – strategic frameworks. To that
CHAPTER 4 — Theoretical Background 157
end, DA augments FF by helping the firm develop a clear recipe of the specific choices it can
make and the specific conditions it can control in order to achieve superior performance. DA
models allow processing as many decisions as necessary, with a specific set of alternatives for
each decision. The DA models then link all these decisions to one another and to the
competitive forces, thus establishing a clear roadmap for the firm to fulfill one or more of the
aforementioned competitive objectives. Indeed, as the experimental work by Song et al.
shows, analyzing this link between the firm’s competitive decisions and the industry’s
competitive forces is essential to understand and predict what, why, and how specific
strategies can prevail in specific industries [28].
Interdependence among the forces, drivers, and factors: while the FF literature provides a
careful explanation of each competitive force and its possible drivers, the interaction among
forces is rarely emphasized [2, 8, 29]. The illustration of the FF framework in Figure 4.2
shows two-way connections between rivalry and the other four forces. However, it is not clear
why these four forces do not directly interact, and how the different forces’ drivers relate to
one other. Most significantly, a careful analysis of FF literature shows that some drivers are in
fact shared among multiple forces, yet those drivers are sometimes introduced separately for
each force, and the implications of their interdependence are not fully explored. Recently,
some research efforts have relied on Analytical Hierarchy Process (AHP) and Analytical
Network Process (ANP) models to investigate this competitive interaction. However, such
endeavors remain limited in scope, focusing either on a narrow list of competitive drivers or
on specific industries [7, 30, 31]. As a result, the majority of FF applications today fail to
capture the interactions not only between the five forces and the firm’s actions but also among
the five forces, their underlying drivers, and the industry-specific factors.
Augmenting the AHP/ANP research endeavors, DA modeling allows capturing multiple forms
of competitive interaction. By modeling the forces, drivers, and factors as a network of
uncertainties, DA naturally asserts some relevance – or lack thereof – between the various
elements of the competitive landscape. Relevance is an important concept in DA that stems
from ascribing Bayesian conditional probability to the degrees of the various uncertainties.
Similarly, DA allows decisions to directly influence uncertainties by modifying the
probability distribution over their degrees [10]. Relevance and influence allow not only
CHAPTER 4 — Theoretical Background 158
tracking but also quantifying the interactions among the uncertain competitive forces, drivers,
factors, and economic parameters, as well as between them and the firm’s strategic decisions.
We explain both concepts in more detail in the following sections.
Quantification: although Porter emphasizes the importance of quantifying the FF analyses, the
framework is usually applied qualitatively. With the aforementioned AHP/ANP studies being
a notable exception [7, 30, 31], most FF applications today tend to use fuzzy and simplistic
heuristics for assessing the strength of the forces [3, 4, 5]. Quantifying the FF framework
requires non-trivial effort to gather, analyze, and interpret market data. The first challenge lies
in quantifying uncertain or imperfect information related to the competitive forces, their
underlying drivers, and industry factors. The task becomes trickier when such quantification
has to capture the competitive interdependencies. Another challenge relates to quantifying the
impact of the forces on the profitability of the industry or that of a specific firm. Along those
lines, quantification should also cover how a firm’s action may change the state of an
uncertain force, driver, factor, or economic parameter. DA facilitates quantification in many
distinct ways. Primarily, DA assigns a numerical probability value to each uncertainty degree,
defines a quantitative metric – profitability in this case (e.g. ROIC) – to rank prospects, and
assigns a numerical value to each prospect. Also, to achieve clarity, DA encourages
quantifying the very definitions of the uncertainty degrees and decision alternatives. Referring
to the car example earlier, we see that the “consumer’s driving habits” uncertainty has two
layers of quantification: the degrees’ definitions {≤ 100 miles short trips; > 100 miles long
trips} and their probabilities (0.7 and 0.3) are both expressed numerically.
Broadly, DAFF helps map clear, quantitative, and economically sound connections between
the three main pieces of the competitive strategy puzzle: the firm’s strategic decisions, the
uncertain competitive forces and factors, and the overall as well as firm-specific profitability
in a given industry. The genius of Porter’s work stems from its bridging between economics
and business. Porter aimed to connect the firm’s competitive strategy to its financial
performance. Our work aims to preserve this connection, quantify it, and provide a clear
procedure on how to implement it. Put differently, Porter explained what this connection is;
we aim to augment his work by describing how this connection can be practically drawn.
Porter advised on where a business should be relative to its industry; we aim to explain how
CHAPTER 4 — Methodology: Developing the DAFF Models 159
the business can get there. Ultimately, our goal is to help managers achieve competitive
advantage by providing them with practical tools to model and analyze their decision-making
process for positioning in the industry, for predicting future industry change, or for reshaping
the industry to their advantage.
Here, we realize that the FF theory itself has faced some criticisms since its conception,
including its relatively “abstract”, “static”, and “highly analytical” nature; its “overstress of
macro-analysis at the industry level”; its “oversimplification of the industry value chains”; its
“failure to link directly to possible management actions”; its “overreliance on microeconomic
theory and economic jargon”; and its inability to capture the effects of the “digitalization,
globalization, and deregulation” in today’s economy [29, 32]. This work aims to show how
FF, when modeled using DA tools, can become easily analyzable and operational; can
generate useful insights at the level of both the industry and the individual firms; can capture
the complexities of the industry value chain; and can provide a clear recipe of managerial
strategic actions. In addition, our work illustrates how FF’s deep foundation in Industrial
Organization and microeconomic theory is, in fact, an advantage and a necessity for its
success. Put differently, the DAFF approach is not intended to refute, replace, or modify of the
FF theory. The DAFF models proposed in this study aim to enhance the practical
implementation of the FF framework rather than challenging the theory behind it.
With that in mind, we devote the next section to model the FF competitive framework using
decision analytic tools and techniques.
3 Methodology: Developing the DAFF Models
To build the DAFF models, we first need to extract and document all important terminology
related to the five forces strategic framework from literature. This task is accomplished by
relying primarily on two recent references: Michael Porter’s The Five Competitive Forces
That Shape Strategy [2] and Joan Magretta’s Understanding Michael Porter: Guide to
Competition and Strategy [8]. To the best of our ability, the FF scripts in both references were
carefully reviewed, translated into DA terms, and subsequently transformed into DAFF
CHAPTER 4 — Methodology: Developing the DAFF Models 160
models. Accordingly, this section shows how all key elements and essential terms of the FF
framework are categorized as decision-related, uncertainty-related, or value-related. The
five competitive forces, their underlying drivers, the industry-specific factors, and the
economic parameters are all modeled as uncertainty nodes; the firm’s competitive decisions
(or actions) are modeled as decision nodes; and the profitability of the overall industry or of a
specific firm is modeled as a value node.
3.1 Modeling the Competitive Forces, Drivers, and Factors
We start with the most prominent component of the DAFF model: the five forces. An
uncertainty node is used to model the power (strength) of each competitive force: Buyers,
Suppliers, Substitutes, New Entrants, and Rivals. Subsequently, we identify the drivers that
shape the power of each force. Similar to the forces, each driver is represented as an
uncertainty node. Our interpretation of the FF literature reveals asymmetrical sets of drivers
shaping each competitive force. Specifically, we identify 22 drivers for Buyers, 12 drivers for
Suppliers, 3 drivers for Substitutes, 45 drivers for New Entrants, and 21 drivers for Rivals. For
illustration, the 22 driver uncertainties that are relevant to the power of Buyers are shown in
Figure 4.3. Next, we realize that many of these drivers are shared among the forces. In fact,
we identify a total of 13 common drivers, each relevant to two or three of the competitive
forces. For example, as shown in Figure 4.4, Buyers share 10 drivers with other forces: one
with Substitutes, one with Rivals, six with New Entrants, and two with both Rivals and New
Entrants.
After modeling the forces and their underlying drivers as uncertainty nodes, these nodes are
connected using directed arrows to form a Bayesian network [33]. In DA, an arrow
connecting two uncertainties is called a relevance arrow, and it implies a probabilistic
dependency (relationship) between the uncertainties. The existence of an arrow shows that two
uncertainties may or may not be relevant, while the lack of an arrow indicates that the two
uncertainties are definitely irrelevant [10]. Based on our interpretation of any discussed
relevance in the FF literature, we model a set of relevance arrows among the forces and their
drivers. For example, Figure 4.5 shows the relevance arrows for the force of Buyers. We
CHAPTER 4 — Methodology: Developing the DAFF Models 161
Figure 4.3: Identifying the underlying drivers for the bargaining power of Buyers
Figure 4.4: Highlighting the shared underlying drivers for the bargaining power of Buyers
Relative dependence of the buyer on industry
product
Buyer’s switching cost between this
industry’s products
Product differentiation
among incumbents
Bargaining Power of Buyers
price sensitivity of
the buyer
Product cost as
fraction of the
buyer’s budget
concentration of buyers relative to
incumbents
Buyer’s threat to integrate backward
Ability to influence
buyers downstream
High fixed costs
Buyer’s need to trim
purchase cost of the
product
Profits earned by the buyer
Amount of cash available to the
buyer
Industry product pays for
itself
product leads to performance
improvement for buyer
product reduces costs for buyer
Number of
buyers
Volume of
purchase per buyer
Buyer’s switching cost
from this industry’s
products to substitutes
Willingness of price
discounting by
incumbents
Buyer’s ability to
alter product
Buyer’s ability to
retain trained
employees
Buyer’s ability to
alter production
system
Relative dependence of the buyer on industry
product
Buyer’s switching cost between this
industry’s products
Product differentiation
among incumbents
Bargaining Power of Buyers
price sensitivity of
the buyer
Product cost as
fraction of the
buyer’s budget
concentration of buyers relative to
incumbents
Buyer’s threat to integrate backward
Ability to influence
buyers downstream
High fixed costs
Buyer’s need to trim
purchase cost of the
product
Profits earned by the buyer
Amount of cash available to the
buyer
Industry product pays for
itself
product leads to performance
improvement for buyer
product reduces costs for buyer
Number of
buyers
Volume of
purchase per buyer
Buyer’s switching cost
from this industry’s
products to substitutes
Willingness of price
discounting by
incumbents
Buyer’s ability to
alter product
Buyer’s ability to
retain trained
employees
Buyer’s ability to
alter production
system
Substitutes
Buyers
New Entrants
Rivals
CHAPTER 4 — Methodology: Developing the DAFF Models 162
Figure 4.5: Relevance arrows connecting the underlying drivers for the bargaining power
of Buyers
make a simplifying assumption – as DA analysts usually do – that undiscussed relevance
implies no relevance. To that end, the relevance arrows we show in this work represent a
foundational, yet not necessarily final, set of relevance relations among the forces and their
drivers. When using the proposed DAFF models in practice to assess a specific industry, some
relevance arrows may be added or subtracted; those adjusted arrows would indicate potential
relevance relations that may or may not be important in the considered industry.
Relevance arrows are usually assigned in the direction that makes it easiest for the decision-
maker to assess the uncertainties. As a matter of terminology, the uncertainty where the arrow
originates is a parent while the one where the arrow ends is a child. Exploiting this “family
tree” analogy, commonly used in DA [34], we refer to the parent of a parent uncertainty as a
grandparent uncertainty, to the parent of a grandparent uncertainty as a great-grandparent
uncertainty, and so on. Accordingly, a child node may have many ancestral nodes.
The probability distribution in the child uncertainty node is conditioned on that in the parent
uncertainty node. Probability computations are most intuitive when the parent node is a
Relative dependence of the buyer on industry
product
Buyer’s switching cost between this
industry’s products
Product differentiation
among incumbents
Bargaining Power of Buyers
price sensitivity of
the buyer
Product cost as
fraction of the
buyer’s budget
concentration of buyers relative to
incumbents
Buyer’s threat to integrate backward
Ability to influence
buyers downstream
High fixed costs
Buyer’s need to trim
purchase cost of the
product
Profits earned by the buyer
Amount of cash available to the
buyer
Industry product pays for
itself
product leads to performance
improvement for buyer
product reduces costs for buyer
Number of
buyers
Volume of
purchase per buyer
Buyer’s switching cost
from this industry’s
products to substitutes
Willingness of price
discounting by
incumbents
Buyer’s ability to
alter product
Buyer’s ability to
retain trained
employees
Buyer’s ability to
alter production
system
Substitutes
Buyers
New Entrants
Rivals
CHAPTER 4 — Methodology: Developing the DAFF Models 163
contributing cause to, or an underlying driver of, the child node. Adhering to this logic, we
model the five force uncertainties as children, and their underlying driver – mostly causal –
uncertainties as ancestors. The relevance arrows usually point from the drivers towards the
forces, as we demonstrate in Figure 4.5. A careful interpretation of the FF literature suggests
that not all drivers affect the forces equally, for some drivers are causal parents of other
drivers. Therefore, driver uncertainties are generally grouped in levels: driver uncertainty
nodes at the parent level have arrows pointing directly into the five forces; grandparent driver
nodes have arrows pointing into parent driver nodes; great-grandparent driver nodes have
arrows pointing into grandparent driver nodes; and so on.
As a side note, we briefly discuss what happens if the direction of a relevance arrow is flipped.
The causal reasoning is lost, so the probability assessment becomes harder. Nonetheless, by
DA rules, such assessment is still possible and should be equally robust. Referring to Figure
4.5, it might be hard – rather odd – for a manager to analyze the Product differentiation among
incumbents driver based on her knowledge (i.e. by conditioning it) on the Price sensitivity of
the buyer driver. That said, the manager may still infer something about the uniqueness of a
product by learning about the sensitivity of the buyer to its price; luxury-sports cars is a good
example: learning that a buyer is extremely price insensitive may increase the decision-
maker’s belief that the product is highly unique. Inference and arrow-flipping are mature
notions in DA [10], and they both stem from the Bayesian nature of relevance. Accordingly,
relevance is broader than and superior to causality because it allows two-way information flow
between uncertainties. Causality is nice to have to facilitate probability elicitation, but it is not
necessary for DAFF modeling.
In addition to the five forces and the 88 relevant drivers, the proposed DAFF adds one
uncertainty node for each of the four industry-specific factors: Growth, Regulations,
Technology, and Complements. A decision analytic interpretation of the FF literature reveals
that the factor uncertainties may share relevance arrows either with the forces directly or with
their underlying drivers. For example, Growth may be directly relevant to Suppliers power, as
well as to three drivers: Commitment of incumbents to retain and fight over market share,
Basis of competition, and Expected retaliation.
CHAPTER 4 — Methodology: Developing the DAFF Models 164
As a result of identifying and connecting the uncertainty nodes of the forces, drivers, and
factors, we generate two Bayesian networks, presented in Figures 4.6 and 4.7. We label the
diagram in Figure 4.6 Detailed Network because it maps the complete set of competitive
forces, drivers, and factors that appear in the two examined references of FF literature [2, 8].
On the other hand, the DAFF model in Figure 4.7 is labelled Simple Network because it
depicts only two ancestral levels of drivers for each force (parents and grandparents), thus
limiting the number of uncertainties that need to be assessed.
Here, we make two key modeling notes. First, the common drivers (shared among two or
more forces) in both the Detailed and Simple networks are distinguished in a separate level
above all other uncertainty nodes. This representation aims to highlight the role these common
nodes play in shaping the interactions among the forces. Second, because the goal of DAFF is
to achieve clarity, and due to the discrepancy in the number of and relevance among the
drivers and factors shaping each force, the decision-maker may indeed choose to expand or
reduce the number of analyzed competitive uncertainties. If the decision-maker is not able to
assess a specific driver or factor because it is too complex or vague, new parent or children
nodes can be added to facilitate the assessment of that uncertainty through relevance (and
conditional probability elicitation). Magretta emphasizes that “a good five forces analysis
allows [the decision-maker] to see through the complexity of competition” [8]; this is exactly
what these Bayesian networks aim to accomplish. In contrast, if the decision-maker deems
some drivers or factors unimportant or unnecessary for properly analyzing the competitive
landscape, those uncertainties can be removed from the Bayesian network. The latter option
should be exercised with great care, however, for all uncertainties and their relevance
relationships in Figures 4.6 and 4.7 are directly derived from the FF literature, whose findings
– according to Porter – are generalizable across industries.
After identifying and connecting the competitive uncertainties in a Bayesian network, we
transition to describe how to characterize the degrees of each uncertainty. To start, each driver
or factor uncertainty node may incorporate multiple degrees, so long as they are mutually
exclusive and collectively exhaustive (i.e. their probabilities add up to one). We make a
decision to customize the characterization of the degrees for both the drivers and the factors,
165
Figure 4.6: Detailed Network of the five forces, their underlying drivers, and industry-specific factors
Threat of new entrants
Barriers to entry
Expected retaliation
Size-independent advantages
for incumbents
Capital needed by new entrant
Network effects
Supply-side economies of scale for incumbent
Unequal access to
distribution channels for new entrant
Government regulations and
policies
Previous responses
by incumbents
Extent of Resources
available for incumbent
Capital availability
for new entrant
Relative Dependence of the buyer on industry
product
Buyer’s switching cost between this
industry’s products
Bargaining Power of Suppliers
Concentration of suppliers relative to
incumbents
Fragmentation of industry
Relative dependence of suppliers
on this industry profits
Incumbent switching
costs between suppliers
Supplier switching
costs between
incumbents
Product differentiation
among suppliers
Availability of
substitutes for what
the suppliers provideSuppliers
threat to integrate foreword
Threat of substitutes
Price-performance trade-off to this industry
product
Commitment of
incumbents to retain and
fight over market share
Industry growth
rate
Product differentiation
among incumbents
Efficiency of expansion of Incumbents production
capacity
Bargaining Power of Buyers
price sensitivity of
the buyer
Product cost as
fraction of the
buyer’s budget
concentration of buyers relative to
incumbents
Buyer’s threat to integrate backward
Ability to influence
buyers downstream
Rivalry
Intensity of competition
Basis of competition
Ability to enforce
practices desirable for the industry
Extent of exit
barriers
High commitment to business
Technology and
innovation
Complementary products and
services
High fixed costs
High fixed costs and
low variable
costs
Perishable product
Buyer’s need to trim
purchase cost of the
product
Willingness of price
discounting by
incumbents
Extent of market
segments
Ability to meet the needs of multiple customer segments
Inability to read
incumbents’ signals
Lack of familiarity
with incumbents
Profits earned by the buyer
Amount of cash
available for the buyer
Industry product pays for
itself
Product leads to
performance improvement
for buyer
Product reduces costs for
buyer
Number of buyers
Buyer’s trust in
incumbents
Well-established
brand
Proprietary technology
Prime location
Preferential access to resources
Cumulative in-house industry
experienceLimitation
to wholesale or retail channels
Reserved space on shelves
Control over
wholesale or retail channels
Efficiency of capital markets Fixed
facilities
Need to build
inventory
R&D spending
Marketing spending
Ability to command
better terms with
suppliers
Spread of fixed
costs over large
volumes
Excess cash
Borrowing power
Available production
capacity
Price advantage
for incumbents
Cost or quality
advantage for
incumbents
Need to bypass
incumbent existing
advantages by new entrant
Need to invest large
financial resources
by new entrant
Need for large-scale production
by new entrant
Consumer adoption
rate of product by
new entrant
Importance of non-
profit goals
Presence of an
industry leader
Importance of prestige in industry
Importance of job-
creation in industry
Buyer’s ability to retrain
trained employees
Buyer’s ability to alter product
specifications
Buyer’s ability to alter
production system
Incumbent’s investment in services by current suppliers
Incumbent’s production
location near current
suppliers
Number of
industries the
suppliers serve
Profits extracted
by suppliers
from other industries
Availability of
Substitutes for this
industry’s product
Volume of
purchase per
buyer
Buyer’s switching cost from this
industry’s products to substitutes
Substitutes
Buyers
New Entrants
Rivals
Suppliers Factors
166
Figure 4.7: Simple Network of the five forces, their underlying drivers, and industry-specific factors
Threat of new entrants
Barriers to entry
Expected retaliation
Size-independent advantages
for incumbents Capital
needed by new entrant
Network effects
Supply-side economies of scale for incumbent
Unequal access to
distribution channels for new entrant
Government regulations and
policies
Previous responses
by incumbents
Extent of Resources available
for incumbent
Capital availability
for new entrant
Relative Dependence of the buyer on industry
product
Buyer’s switching cost between this
industry’s products
Bargaining Power of Suppliers
Concentration of suppliers relative to
incumbents
Fragmentation of industry
Relative dependence of suppliers
on this industry profits
Incumbent switching
costs between suppliers
Supplier switching
costs between
incumbents
Product differentiation
among suppliers
Availability of
substitutes for what
the suppliers provideSuppliers
threat to integrate foreword
Threat of substitutes
Price-performance trade-off to this industry
product
Commitment of
incumbents to retain and
fight over market share
Industry growth
rate
Product differentiation
among incumbents
Efficiency of expansion of Incumbents production
capacity
Bargaining Power of Buyers
price sensitivity of
the buyer
Product cost as
fraction of the
buyer’s budget
concentration of buyers relative to
incumbents
Buyer’s threat to integrate backward
Ability to influence
buyers downstream
Rivalry
Intensity of competition
Basis of competition
Ability to enforce
practices desirable for the industry
Extent of exit
barriers
High commitment to business
Technology and
innovation
Complementary products and
services
High fixed costs
Perishable product
Buyer’s need to trim
purchase cost of the
product
Willingness of price
discounting by
incumbents
Extent of market
segments
Ability to meet the needs of multiple
customer segments
Inability to read
incumbents’ signals
Lack of familiarity
with incumbents
Number of buyers
Importance of non-
profit goalsIncumbent’s investment in services by current suppliers
Incumbent’s production
location near current
suppliers
Number of
industries the
suppliers serve
Profits extracted
by suppliers
from other industries
Availability of
Substitutes for this
industry’s product
Volume of
purchase per
buyer
Buyer’s switching cost from this
industry’s products to substitutes
Substitutes
Buyers
New Entrants
Rivals
Suppliers Factors
CHAPTER 4 — Methodology: Developing the DAFF Models 167
per the specific context of the competitive analysis. Because we encourage the degrees’
quantification, it is hard to uniformly define the degrees for all drivers and factors in all
industries, especially that drivers and factors are heavily shaped by the specific industry of
interest. For example, let us attempt to characterize the degrees of the driver Product cost as
function of buyer’s budget in two industries: the auto industry and the cellphone industry.
Clearly, the cost of a car is very different than that of a cellphone. Thus, assuming a simple
pay-upfront purchase, we may want to express “budget” as “monthly income” and define two
degrees {< 5% monthly income; ≥ 5% monthly income} for this driver in the cellphone
industry while expressing “budget” as “yearly income” and defining two degrees {< 10%
yearly income; ≥ 10% yearly income} for this driver in the auto industry. Similar rationale
applies when customizing the characterization of the degrees for the factor uncertainties;
Regulation overseeing grid-connectivity in the residential solar industry, for instance, is very
different that Regulation overseeing direct sales in the auto industry.
Finally, we explain how to characterize the degrees of the five forces. Each force uncertainty
is modeled with two degrees: {high; low}. The direct reason behind this characterization is
that Porter’s scripts (as well as Industrial Organization) provide no better option. Both FF
literature and mainstream FF applications always assess the forces’ power as “high” or “low”,
“strong” or “weak”. Such an approach is understandable, for it is hard to come up with a more
specific or quantitative way to characterize all forces in all industries; practically, managers
can intuitively comprehend what a “high” or “low” power of the force means. Ultimately,
because the purpose of our work is to operationalize the FF theory rather than adjust or expand
it, we choose to standardize the definition of the degrees for all five force uncertainties. This
modeling approach preserves DA’s ability to quantify the competitive analysis and to track the
competitive interdependencies. By linking each of the forces’ uncertainties to the economic
parameters’ uncertainties, the decision-maker can still quantify the implication of each force
on the profitability of the overall industry or of the firm. In addition, standardizing the forces’
degrees does not impact our ability to model their relevance and thus to track their
interdependence. We address these points in more detail in the next sections.
To demonstrate all newly introduced concepts in this section, we refer back to our earlier
example of launching a new environmentally friendly car. For simplicity, let us focus on only
CHAPTER 4 — Methodology: Developing the DAFF Models 168
three competitive uncertainties, illustrated in Figure 4.8: the bargaining power of Buyers and
its two parental drivers Price sensitivity of the buyer and Buyer’s switching cost between this
industry’s products. The analysis proceeds as follows. First, the automobile manager defines
two quantifiable, mutually exclusive and collectively exhaustive degrees for the Price
sensitivity of the buyer: {price elasticity of demand = [-3, -2]; price elasticity of demand = [-2,
-1]}. Similarly, she defines two degrees for the Buyer’s switching cost between this industry’s
products: {resale depreciation ≤ $2000; resale depreciation > $2000}. She also assigns two
degrees to the power of Buyers: {high; low}.
Figure 4.8: Illustrative example of uncertainty assessment in DAFF
Following the direction of the relevance arrows, the manager then starts her uncertainty
assessment from the most ancient ancestral level. Therefore, the manager first assesses the
probability of the car buyer’s price sensitivity. Based on her market intelligence, she assigns a
probability of 0.6 to the degree {price elasticity of demand = [-3,-2]} and a probability of 0.4
to {price elasticity of demand = [-2,-1]}. Similarly, the manager assesses the probability of the
buyer’s switching cost, and she assigs a 0.8 and 0.2 probabilities to the {resale depreciation ≤
$2000} and {resale depreciation > $2000} degrees, respectively. Finally, the manager assesses
the probability of the power of Buyers, conditioned on the two parent drivers. For example,
the manager asks: given that the Price sensitivity of the buyer is {price elasticity of demand =
Force
Drivers
Buyer’s switching cost between this
industry’s products
Bargaining Power of Buyers
Price sensitivity of
the buyer
Price elasticity of demand = [-3, -2]
Price elasticity of demand = [-2, -1]
0.6 0.4
Resale depreciation
≤ $2000
Resale depreciation
> $2000
0.8 0.2
Price elasticity of demand = [-3, -2] Price elasticity of demand = [-2, -1]
Resale depreciation
≤ $2000
Resale depreciation
> $2000
Resale depreciation
≤ $2000
Resale depreciation
> $2000
high low high low high low high low
0.9 0.1 0.6 0.4 0.5 0.5 0.2 0.8
high = 0.68low = 0.32
CHAPTER 4 — Methodology: Developing the DAFF Models 169
[-3, -2]} and that the Buyer’s switching cost between this industry’s products is {resale
depreciation ≤ $2000}, what is the probability that the power of Buyers is {high}? Based on
her market intelligence, the manager assigns a 0.9 probability to that prospect. After assigning
similar conditional probabilities to all eight prospects, the DAFF model computes the overall
probability of {high} or {low} bargaining power of Buyers. In this case, Figure 4.8 shows that
the probability of {high} is 0.68 and that of {low} is 0.32.
3.2 Modeling the Economic Implications of the Five Forces
FF emphasizes that maximizing profitability is the main goal of competitive strategy. The first
point that we should therefore clarify is: what defines profitability? Porter’s literature cites two
metrics to evaluate profitability: return on invested capital (ROIC) [2, 8] and unit profit
margin (UPM) [8]. ROIC is defined in (1) – as Porter recommends – as the ratio of annual
earnings before tax (EBT) over invested capital (CAPEX) [35]. As we know from managerial
accounting, EBT can be further decomposed into revenue (REV) less variable and fixed
operating expenses, denoted by VOPEX and FOPEX, respectively. Porter asserts that ROIC is
an effective metric to assess the industry’s profitability because it accounts for invested
capital. If ROIC is higher than the weighted-average cost of capital (WACC), the industry is
generating value. On the other hand, UPM is originally defined by Magretta as price less unit
cost [8]. To add clarity, we adopt a more elaborate definition in (2), where UPM is expressed
as a ratio of annual earnings before tax over annual revenue [36].
The use of either metric comes with its own set of challenges. To start, Porter cautions about
the use of UPM in assessing the profitability of the overall industry because it does not
account for CAPEX. Equally important, within a single firm, CAPEX may be shared among
multiple business units that operate in distinct industries; in this case, the use of ROIC to
assess a business unit’s relative profitability becomes challenging. In fact, multiple business
units might even share VOPEX or FOPEX, which further complicates the computation of both
UPM and ROIC in their respective industries. For instance, because of different product
specifications, geographic locations, customers, and substitutes, residential-scale and utility-
scale solar energy systems are distinct enough to be classified as separate industries. Yet, a
solar firm may operate in both industries [37]. Such a firm may own a solar-panel
CHAPTER 4 — Methodology: Developing the DAFF Models 170
manufacturing facility that caters to both its utility and residential businesses (shared
CAPEX), and its advertising endeavors may be designed to raise brand awareness, which
would also benefit both businesses (shared FOPEX). As a result, selecting a proper
profitability metric is dependent on the decision-maker’s specific objectives for the
competitive analysis. We discuss this topic in detail in the coming sections.
𝑅𝑂𝐼𝐶 =𝐸𝐵𝑇
𝐶𝐴𝑃𝐸𝑋=𝑅𝐸𝑉 − 𝑉𝑂𝑃𝐸𝑋 − 𝐹𝑂𝑃𝐸𝑋
𝐶𝐴𝑃𝐸𝑋=𝑄 ∙ (𝑃 − 𝐶𝑣 − 𝐶𝑓)
𝐶𝐴𝑃𝐸𝑋 (1)
𝑈𝑃𝑀 =𝐸𝐵𝑇
𝑅𝐸𝑉=𝑅𝐸𝑉 − 𝑉𝑂𝑃𝐸𝑋 − 𝐹𝑂𝑃𝐸𝑋
𝑅𝐸𝑉=𝑄 ∙ (𝑃 − 𝐶𝑣 − 𝐶𝑓)
𝑄 ∙ 𝑃 (2)
The formulations in (1) and (2) highlight two considerations related to linking the
aforementioned profitability metrics to the five competitive forces. First, the cited profitability
metrics incorporate three types of costs: CAPEX, VOPEX, and FOPEX. We know from the
FF literature that the five forces affect cost, but there is no clear reference as to how each force
affects each type of cost. Second, it is important to realize that ROIC and UPM share the same
basic economic parameters of: price, cost, and quantity. In fact, we demonstrate in (1) and (2)
how both profitability metrics can be reformulated in terms of price P, quantity Q, and two
per-unit costs Cv, and Cf, associated with VOPEX and FOPEX, respectively. VOPEX and
FOPEX can be (and usually are) reported per unit of goods or services because they are highly
dependent on sales, so together they reflect the ongoing cost of running the business.
The second consideration focuses on the need to evaluate quantity. While the FF literature
explicitly explains how stronger forces reduce price and increase cost, it provides little, if
any, guidance on the relationship between the forces and quantity. We address this issue now
by modeling a clear mapping between the competitive forces and all three broad categories of
economic parameters: Price, Cost, and Quantity. The impact of the forces on specific types of
economic parameters (e.g. sales quantity versus production quantity, or CAPEX versus
OPEX) is addressed in detail in the next section, when modeling the specific objectives of
competitive strategy.
CHAPTER 4 — Methodology: Developing the DAFF Models 171
Price, Cost, and Quantity are modeled in DAFF as uncertainty nodes. As explained by Porter
[2] and further clarified by Magretta [8], all five forces affect Cost while only four forces
affect Price: Buyers, Substitutes, New Entrants, and Rivals. Accordingly, nine relevance
arrows are added, five extending from the forces nodes into the Cost node and four extending
from the forces nodes into the Price node. Now, because FF provides no exact guidance on the
relevance between the competitive forces and Quantity, we undertake this modeling task by
referring back to the foundational pillars of FF that govern competition: microeconomic
theory and Industrial Organization. The economic models in both fields highlight four
relationships that are important to our task. In any given industry, demand-curves describe a
clear relationship between Price and Quantity, and cost-curves describe a clear relationship
between Cost and Quantity. Both relationships can be modeled as decision analytic relevance.
In addition, industry growth changes the shape of the demand-curve and thus the optimal
quantity output at market-equilibrium. As such, it is reasonable to model potential relevance
between the Growth factor and Quantity. Moreover, because substitutes lie outside the
industry’s formal boundaries, their desirability does not only affect the price or cost of the
product or service but also the quantity purchased by consumers; multiple mature economic
notions such as “elasticity of substitution” and “indifference curves” clearly capture this
relevance between Substitutes and Quantity [38]. As a result, we propose four relevance
arrows extending into Quantity from: Price, Cost, Growth, and Substitutes.
Subsequently, the profitability metric is modeled as a value node, and it is connected to the
Price, Cost, and Quantity nodes using a new type of arrows that we call functional arrows.
While relevance arrows convey potential probabilistic dependence, functional arrows convey
discrete mathematical relationships between the DA nodes; they always extend into the value
node. Figure 4.9 combines all the economic modeling steps discussed thus far and presents an
economic sub-model that can be integrated into a complete DAFF model.
After modeling Price, Cost, and Quantity and linking them to both the profitability value as
well as the force and factor uncertainties, we clarify how to characterize the degrees of each of
these economic uncertainties. Similar to drivers and factors, economic uncertainty nodes can
incorporate multiple degrees, which are industry-specific. Here again, Industrial Organization
provides necessary guidance on two tasks: defining the degrees of the Price, Cost, and
CHAPTER 4 — Methodology: Developing the DAFF Models 172
Quantity and assigning probabilities to those degrees. The widely documented Industrial
Organization models are simple yet effective means to estimate the range of Price, Cost, or
Quantity values in the industry. The difference between a purely monopolistic and a perfectly
competitive optimal price (or quantity) output is one good example of such range [38]. Along
the same lines, these models allow computing the exact optimal economic outputs under
specific competitive scenarios (equivalent to specific prospects of the five forces), which then
helps the decision-maker determine the likelihoods of the preset degrees of specific economic
uncertainties under these scenarios. For example, entry-deterrence models allow computing
the “limit-output”, defined as the quantity that a monopolist needs to produce in order to deter
entry [38]. Upon knowing the limit-output, a decision-maker can assign a more accurate
probability distribution over the Quantity degrees, given that both Rivals and New Entrants are
weak; in this case, the Quantity degree that is closest to the limit-output should be assigned the
highest conditional probability.
Figure 4.9: DAFF economic sub-model
3.3 Modeling the Firm’s Actions
The final element that needs to be modeled in DAFF is the firm’s list of competitive actions
within the analyzed industry. These actions can be categorized into three types of decisions:
Value Proposition decisions, Value Chain decisions, and Economic decisions.
Substitutes BuyersNew
EntrantsRivals Suppliers
Price CostQuantity
Profitability
Substitutes
Buyers
New EntrantsRivals
Suppliers Factors
Economic parameters
Industry growth rate
CHAPTER 4 — Methodology: Developing the DAFF Models 173
Value Proposition and Value Chain decisions are the two ingredients in Porter’s recipe for
strategic positioning [8]. Value Proposition decisions relate to the manager’s choice of what
product to make: what needs to meet in the industry, and what customers to serve. Then, Value
Chain decisions involve a series of managerial choices on how the product should be made:
how to design, produce, test, distribute, sell, and service. In other words, Value Proposition
decisions require the decision-making manager to look externally, focusing on the overall
industry; in contrast, Value Chain decisions require the manager to look internally, focusing
on the firm’s own activities and operations. In this regard, DAFF is a useful tool to bridge
between analyzing the five forces and making proper positioning decisions. The powers of the
five forces are different in different segments within the same industry. Upon choosing a
series of distinct Value Proposition and Value Chain alternatives, the decision-maker positions
her firm in a specific segment within the industry, hoping that the selected position yields
weak competitive forces and thus superior profitability for the firm.
Unlike Value Proposition and Value Chain decisions, Economic decisions are not strategic.
Economic decisions focus on three important choices: Production Scale, Pricing, and Tactical
Costing. Clearly, these decisions relate specifically to the firm’s profitability, and they shape
the firm-specific price, quantity, and cost. No matter what Value Proposition or Value Chain
decisions a firm makes to position in the industry, it should always optimize three aspects of
its business in order to maximize performance: how many units to produce, how to price these
units, and how to cost these units. The firm may choose to set the price at, above, or below the
optimal market-equilibrium price; similarly, it may underproduce or overproduce relative to
its expected demand. On the cost front, we make an important note. Big part of the firm’s
costs is already dictated by Value Chain decisions because, as Porter explains, value-chain
“activities [are] the elemental units of cost behavior” [25]. However, full costs are determined
not only by Value Chain strategic decisions that reflect positioning within the industry but
also by more detailed and mundane tactical decisions that reflect operative efficiency within
the firm. It is those latter decisions that we account for in Tactical Costing.
All three types of the firm’s actions are modeled in DAFF as decision nodes, and the
decision-maker may consider any number of alternatives for each decision. Decision nodes are
linked to the competitive and economic uncertainty nodes using a specific type of arrows
CHAPTER 4 — Methodology: Developing the DAFF Models 174
called influence arrows. By design, an influence arrow always extends from the decision
node to the uncertainty node [10]. Combining the firm’s decision nodes with the economic
sub-model in Figure 4.9 and the Bayesian network in Figure 4.6 (or 4.7) results in a complete
DAFF model, referred to as a decision diagram.
Value Proposition and Value Chain decision nodes can directly influence the five forces, their
underlying drivers, the four industry factors, as well as the economic parameters. Referring
back to our earlier car example, the auto manufacturer has to make a Value Proposition
decision regarding the type of car to produce: [electric] or [hybrid]. This decision may
influence the Buyer’s switching cost from this industry’s products to substitutes driver because
it may be easier to resell a hybrid car than an electric car [39, 40]. Notably, the influence of
this decision propagates all the way to the Substitutes and Buyers, for the aforementioned
driver is shared between these two forces. Additionally, this decision may directly influence
Cost because of the inherent technical differences between the two types of vehicles,
regardless of market competition [41, 42, 43].
While the competitive and economic uncertainties in DAFF are generalizable across
industries, Value Proposition and Value Chain decisions are industry- and firm-specific.
Accordingly, influence arrows are customized for each DAFF decision diagram corresponding
to a specific competitive analysis in a specific industry. Focusing on the competitive
uncertainties, one useful modeling practice to simplify the decision diagram is to add
influence arrows from Value Proposition and Value Chain decisions to the most ancient
ancestral level of drivers. In this case, the decisions update the probabilistic information in
these driver nodes only, but the Bayesian structure of the uncertainty network guarantees that
their influence propagates through the subsequent descendant nodes until reaching the five
competitive forces.
Finally, because Economic decisions relate to the firm’s specific profitability, they may only
influence the economic parameters. Specifically, Tactical Costing influences Cost while
Production Scale and Pricing influence Quantity, where they contribute to determining the
firm’s sales; the specifics of this modeling will become clearer when we discuss the objectives
of competitive strategy in the next section. For now, we note that, unlike Value Proposition
CHAPTER 4 — Methodology: Developing the DAFF Models 175
and Value Chain decisions, Economic decisions are modeled uniformly in all DAFF decision
diagrams across all industries.
This brings us to the end of this section. So far, we have introduced the various DA elements
and tools and used them to characterize and connect the different components of the FF
framework. The result is a complete DAFF model. In the next section, we move to explain
how DAFF models can fulfill each of the objectives of the FF competitive strategy. Along the
way, we highlight how modeling these strategic objectives resolves multiple deficiencies in
the operationalization and practical application of the – otherwise insightful – FF framework.
Here, we recall that the FF literature discusses three competitive-strategy objectives for every
firm: properly position in the industry, predict and exploit future industry change, and reshape
future industry change [2]. Based on our DA methodology, however, we propose
consolidating the goals of FF into two strategic objectives only, each of which would be
realized through sequential steps of analyzing the industry structure and the firm’s actions.
Specifically, the two DA-oriented competitive-strategy objectives are: position in the
industry and reshape the industry.
Positioning in the industry is a short-term objective, and it requires three consecutive
analyses of current and very-near-future profitability: of the overall industry, of distinct
positioning segments in the industry, and of a specific firm or business upon positioning in
each segment of the industry. Building on the outcomes from these steps, reshaping the
industry becomes the long-term objective, and it requires two additional analyses of distant-
future profitability: via predicting the evolution of the industry structure and via modifying the
evolution of the industry structure. These two strategic objectives and the steps required to
fulfill them are the focus of the following two sections. Because positioning in the industry is
the central concern of this study, we provide a detailed account on how to model its three steps
using the DAFF components introduced so far. Then, we describe, conceptually, how to
expand the DAFF approach to model the remaining two steps of reshaping the industry.
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 176
4 First Objective of Competitive Strategy: Positioning in the
Industry
Michael Porter argues that “strategy explains how an organization, faced with competition,
achieves superior performance” [8]. Translating this into decision analytic terms, strategy
explains how a decision-maker, faced with uncertain competition, can make choices that
achieve superior profitability, consistent with his unique set of preferences.
To achieve superior profitability, the business must first properly position in its industry.
Effective positioning requires rigorous analysis of the competitive landscape, which can be
achieved in three steps: assessing the profitability of the overall industry; identifying a series
of strategic Value Proposition and Value Chain alternatives that define unique positioning
segments in the industry then assessing the profitability of each of those segments; and finally
assessing the profitability of the business in all potential positioning segments. When thinking
through all three steps, the manager has to decide on one important aspect before delving into
the modeling details: the timeframe of the competitive analysis.
We leave it to the decision-maker to specify the exact timeframe for the positioning objective,
based on his specific goals from the competitive analysis and the specific industry of his
business. Nonetheless, we emphasize that any chosen timeframe must meet two criteria:
consistent across all three steps, and short-term in the context of the analyzed industry. The
consistency of the timeframe across the three positioning steps is necessary because their
analyses are sequential, one building on the top of the next. Equally important, the short-term
criteria is based on the premise that the decision-maker aims to locate his business in the most
preferred industry segment, very soon, before any structural changes affect the profitability of
that segment. Here, the decision-maker does not aim to change the behavior of other
industry players just yet; he only aims to understand their behavior and locate where it
is least threatening.
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 177
4.1 First Step: Assess the Profitability of the Overall Industry
Before making any decisions, including what to produce, how to produce, and how much to
produce and charge, the firm must have a clear understanding of the industry’s overall
structure and its average profitability. To that end, we first need to develop a DAFF model
that assesses the industry’s competitive landscape and its economic implications. The
complete DAFF model, including a detailed economic sub-model, for this first step of the first
competitive objective is presented in Figure 4.10. We call it the DAFF Bayesian Network.
To start, either the Simple or Detailed network, presented respectively in Figures 4.6 and 4.7,
can be used to represent the uncertain powers of the five forces and their underlying drivers.
We use the Simple Network here purely for convenience. Also, because the effects of the
factors on the powers of the forces are very industry-specific, all but one factor uncertainties
are removed from the displayed Bayesian Network; the Growth factor is maintained because it
has generalizable economic impacts, as will become evident. Furthermore, per Porter’s
recommendation, we adopt ROIC as the value metric to express the industry’s average
profitability.
The remaining task is to design a more elaborate DAFF economic sub-model that links the
competitive uncertainties to the ROIC value metric through a well-defined set of economic
parameters. These overall-industry parameters are labeled with an asterisk (*), and they
account for the fact that ROIC incorporates an average price P and three measures of cost:
CAPEX, Cv, and Cf. As explained earlier, Cv and Cf refer, respectively, to VOPEX and
FOPEX per unit of produced goods or services. Consistent with our approach in Section 3, the
price and the three cost parameters are modeled as uncertainties and are connected to the force
uncertainties using relevance arrows. As a reminder, the stronger the forces are, the more
likely the price is low and the costs are high [8]. Focusing on costs, because the FF literature
does not detail how the different forces affect the different types of cost, we model potential
relevance between all the forces and all the cost parameters. For example, in the automobile
industry, technological advances or strong customer preferences may necessitate additional
safety features in passenger cars. Higher safety measures may entail not only more expensive
parts in the car (higher Cv) but also more labor hours (higher Cf) or more complicated
178
Figure 4.10: DAFF Bayesian Network for the first objective, first step: assessing the profitability of the overall industry
Threat of new entrants
Barriers to entry
Expected retaliation
Size-independent advantages
for incumbents Capital
needed by new entrant
Network effects
Supply-side economies of scale for incumbent
Unequal access to
distribution channels for new entrant
Previous responses
by incumbents
Extent of Resources available
for incumbent
Capital availability
for new entrant
Relative Dependence of the buyer on industry
product
Buyer’s switching cost between this
industry’s products
Bargaining Power of Suppliers
Concentration of suppliers relative to
incumbents
Fragmentation of industry
Relative dependence of suppliers
on this industry profits
Incumbent switching
costs between suppliers
Supplier switching
costs between
incumbents
Product differentiation
among suppliers
Availability of
substitutes for what
the suppliers provideSuppliers
threat to integrate foreword
Threat of substitutes
Price-performance trade-off to this industry
product
Commitment of
incumbents to retain and
fight over market share
Industry growth
rate
Product differentiation
among incumbents
Efficiency of expansion of Incumbents production
capacity
Bargaining Power of Buyers
price sensitivity of
the buyer
Product cost as
fraction of the
buyer’s budget
concentration of buyers relative to
incumbents
Buyer’s threat to integrate backward
Ability to influence
buyers downstream
Rivalry
Intensity of competition
Basis of competition
Ability to enforce
practices desirable for the industry
Extent of exit
barriers
High commitment to business
High fixed costs
Perishable product
Buyer’s need to trim
purchase cost of the
product
Willingness of price
discounting by
incumbents
Extent of market
segments
Ability to meet the needs of multiple
customer segments
Inability to read
incumbents’ signals
Lack of familiarity
with incumbents
Number of buyers
Importance of non-
profit goalsIncumbent’s investment in services by current suppliers
Incumbent’s production
location near current
suppliers
Number of
industries the
suppliers serve
Profits extracted
by suppliers
from other industries
Availability of
Substitutes for this
industry’s product
Volume of
purchase per
buyer
Buyer’s switching cost from this
industry’s products to substitutes
Substitutes
Buyers
New Entrants
Rivals
Suppliers Factors
Economic parameters
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 179
machinery (higher CAPEX) to assemble and install these parts. For every possible grouping of
a Cv degree and a Cf degree, we can calculate their exact sum as per-unit average operating
cost (CAO). CAO is modeled as a deterministic node because it is known with certainty for
every realized combination of Cv and Cf.
Subsequently, we transition to model quantity in the specific context of the overall industry.
Quantity here is defined as total annual sales volume (Q), and it is relevant to four
uncertainties: price P, average operating cost CAO, Growth factor, and Substitutes force.
Because the total sales volume is reached through some sort of market-equilibrium between
supply and demand, we assert that only P and CAO are relevant to Q, implying no relevance
between the CAPEX and the sales volume. To support this assertion, we first clarify that our
managerial-accounting definition of average operating cost CAO is equivalent to the
microeconomic-theory definition of average variable cost (CAV) 1
; effectively, both measures
refer to expenses that can change with the scale of business operations in the short-term
(which is the timeframe of this positioning objective). We know that market-equilibrium is set
where marginal revenue equals marginal cost. CAV, and thus CAO, is considered a good
approximation of marginal cost in the short-term. In addition, P equals marginal revenue under
the simplifying assumption of a linear demand-curve [38]. Accordingly, the equilibrium
between marginal revenue and marginal cost can be approximated as an equilibrium between
P and CAO, both of which then dictate Q.
The relevance between P and Q is shaped by the industry’s demand-curve, so higher P
increases the likelihood of smaller Q (assuming the product is not Giffen goods).
Subsequently, for a specific pair of P and CAO degrees, the closer CAO is to P, the more likely
the industry is competitive, and therefore the more likely Q is large; of course, we assume here
that the industry rivals always price above cost (P > CAO). One straightforward illustration of
this relevance is monopoly behavior: assuming all else equal, the sales volume in a monopoly
setting is always less than that in a perfectly competitive market, resulting in a deadweight
1 Our choice to use a managerial-accounting metric stems from our interest in making the analysis as simple and
accessible to business managers as possible. While relying on Industrial Organization to model the economic
implications of FF, we shall not forget that, eventually, managers are the primary decision-makers and the target
audience in this crusade to operationalize the FF framework. To that end, we strive to bridge between strategy,
managerial accounting, and Industrial Organization to achieve robust yet intuitive economic modeling.
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 180
loss. Finally, consistent with the explanation in Section 3, we emphasize that the relevance of
Growth and Substitutes to Q is highly industry-specific and can be further informed and
shaped by testing a few Industrial Organization models. However, as a broad generalization, Q
is more likely to be large when Growth is fast and Substitutes are weak [38].
We continue this discussion of the industry’s economic sub-model by focusing on the time
horizons. As already established, assessing the overall industry profitability for positioning is
a short-term analysis; this means that the probability distribution over the degrees of each
uncertain economic parameter should reflect the decision-maker’s beliefs about the expected
value of that parameter in the very near future. But if probability assignments over the
economic degrees are guided by the analysis’s (short-term) timeframe, what guides the
definition of the degrees themselves? In other words, how do we characterize the range of
feasible degrees for each economic parameter in the first place? To answer this question, we
refer to the FF literature. Porter suggests that the ROIC, and therefore its economic attributes,
should be characterized over a full business cycle. In other words, when modeling each
economic uncertainty, the numerical-value range of its degrees should be comparable to the
numerical-value range observed in the industry during a full business cycle. An example here
might be helpful. Let us assume that the full business cycle in a mining industry is one decade
[2], and that a current incumbent wants to use the DAFF model to analyze the profitability of
the whole mining industry next year. When modeling the CAPEX uncertainty, the incumbent
first defines three CAPEX degrees whose numerical values cover the full range of observed
CAPEX over the last decade (full-business-cycle time horizon). Then, he assigns a probability
to each CAPEX degree, under all possible scenarios of the forces’ powers, based on his beliefs
about the value of CAPEX next year (near-future time horizon).
Ultimately, the resulting DAFF Bayesian Network in Figure 4.10 generates two primary
outcomes. First, it computes a probability distribution for the power of each of the five
competitive forces, thus providing a snapshot of the industry’s overarching competitive
landscape. Second, it yields a probabilistic-weighted-average value of ROIC, referred to as
expected ROIC. This expected value indicates the average profitability of the whole industry
within the short-term timeframe set by the decision-maker. One can then quickly gain insight
about the extent of the industry profitability by comparing the resulting expected ROIC to its
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 181
historical values. Intuitively, stronger competitive forces will result in lower ROIC; the DAFF
model quantifies this trend after accounting for all the interactions among the competitive
forces and factors. Building on these results, the DAFF Bayesian Network can also test the
sensitivity of the expected ROIC to the power of one or more of the five forces. The outcome
would be an ROIC range corresponding to the power range of the investigated force(s).
Additionally, the resulting DAFF model can compute how observing one force at either
extreme (strong or weak) may update the probability distribution of other forces, thus
quantifying the extent of interdependency and interaction among these forces.
4.2 Second Step: Position Competitively and Assess the Profitability of Each
Positioning Segment in the Industry
After assessing the competitive forces and their economic implications for the whole industry,
a manager should make a series of strategic choices that position her business in the most
profitable segment of the industry. As noted by Song et al. [28], the prospects of any
positioning decision are highly dependent on the uncertain competitive landscape, so a clear
mapping between the management’s feasible positioning alternatives and the industry’s forces
is essential for guiding the firm’s competitive strategy. In our DAFF approach, strategic
positioning is characterized by two of the three types of actions undertaken by firms: Value
Proposition and Value Chain decisions.
As explained earlier, Value Proposition and Value Chain decisions allow the firm to focus and
tailor its activities and to target a specific segment in the industry, thus narrowing down the
group of competitive players that the firm interacts with. In other words, positioning decisions
influence the power of the competitive forces not by changing the behavior of other industry
players but by changing the identity of those players. Every combination of Value Proposition
and Value Chain alternatives results in a unique positioning track, which in turn defines a
unique segment of the industry where the firm can locate and operate. For example, a
decision-maker in the auto industry may want to analyze the influence of three Value
Proposition and/or Value Chain decisions on the competitive landscape, and two alternatives
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 182
are available for each decision. In this case, the automaker has a set of eight (i.e. 23) possible
positioning tracks to choose from, each of which defines a unique industry segment.
Because positioning decisions are very circumstance-, industry-, and firm-specific, Figure
4.11 shows how to add generic Value Proposition and Value Chain decisions to the DAFF
Bayesian Network introduced in Figure 4.10, resulting in a DAFF Decision Diagram.
Needless to say, the non-generalizable nature of positioning means that the influence relation
between a specific Value Proposition or Value Chain decision and a competitive uncertainty
may change from one industry to the other. Let us consider the influence relation between
Product design decision and Preferential access to resources uncertainty as an example. In
China, where silicon is abundant, the decision by a solar-panel-manufacturing firm to produce
[photovoltaic solar systems] instead of [concentrated solar systems] might influence (increase)
the likelihood of it gaining easy access to raw materials. On the other hand, the decision by a
US automaker to produce an [electric car] instead of a [hybrid car] will not influence the
likelihood of it gaining wide access to skilled labor.
In addition, the DAFF Decision Diagram in Figure 4.11 highlights two important modeling
aspects. First, the economic parameters are still industry-based not firm-based; more
specifically, the degrees in Cost, Price, and Quantity uncertainties, as well as the profitability
measures in the ROIC value node, still represent average industry values. Second, we recall
from Section 3.3 that a positioning decision node can influence any uncertainty node,
including the forces, drivers, industry-specific factors, and economic parameters. In fact, one
positioning decision might influence more than one uncertainty, and one uncertainty might be
influenced by more than one positioning decision. Regardless of what and how many
uncertainties the decision-maker draws influence arrows into, the Bayesian nature of the
decision diagram ensures that the influence of each positioning decision will propagate all the
way to the value node. As a result, the DAFF Decision Diagram in Figure 4.11 computes a
unique expected ROIC value for each unique positioning track (combination of positioning
alternatives) and therefore for each unique industry segment. Following up on the earlier
example, analyzing three Value Chain decisions, each with two alternatives, outputs eight
positioning tracks and therefore eight expected ROIC values. Intuitively, the firm should
choose to position in the industry segment with the highest ROIC.
183
Figure 4.11: DAFF Decision Diagram for the first objective, second step: positioning competitively and assessing the profitability of each
positioning segment in the industry
Threat of new entrants
Barriers to entry
Expected retaliation
Size-independent advantages
for incumbents Capital
needed by new entrant
Network effects
Supply-side economies of scale for incumbent
Unequal access to
distribution channels for new entrant
Previous responses
by incumbents
Extent of Resources available
for incumbent
Capital availability
for new entrant
Relative Dependence of the buyer on industry
product
Buyer’s switching cost between this
industry’s products
Bargaining Power of Suppliers
Concentration of suppliers relative to
incumbents
Industry concentration
Relative dependence of suppliers
on this industry profits
Incumbent switching
costs between suppliers
Supplier switching
costs between
incumbents
Product differentiation
among suppliers
Availability of
substitutes for what
the suppliers provideSuppliers
threat to integrate foreword
Threat of substitutes
Price-performance trade-off to this industry
product
Commitment of
incumbents to retain and
fight over market share
Industry growth
rate
Product differentiation
among incumbents
Efficiency of expansion of Incumbents production
capacity
Bargaining Power of Buyers
price sensitivity of
the buyer
Product cost as
fraction of the
buyer’s budget
concentration of buyers relative to
incumbents
Buyer’s threat to integrate backward
Ability to influence
buyers downstream
Rivalry
Intensity of competition
Basis of competition
Ability to enforce
practices desirable for the industry
Extent of exit
barriers
High commitment to business
High fixed costs
Perishable product
Buyer’s need to trim
purchase cost of the
product
Willingness of price
discounting by
incumbents
Extent of market
segments
Ability to meet the needs of multiple
customer segments
Inability to read
incumbents’ signals
Lack of familiarity
with incumbents
Number of buyers
Importance of non-
profit goalsIncumbent’s investment in services by current suppliers
Incumbent’s production
location near current
suppliers
Number of
industries the
suppliers serve
Profits extracted
by suppliers
from other industries
Availability of
Substitutes for this
industry’s product
Volume of
purchase per
buyer
Buyer’s switching cost from this
industry’s products to substitutes
Substitutes
Buyers
New Entrants
Rivals
Suppliers Factors
𝑃 𝐶𝑣
𝑅𝑂𝐼𝐶
𝐶𝑓
𝐶𝐴𝑃𝐸𝑋 𝐶
𝑄
Economic parameters
Value Chain 1 Value Chain 2Value
Proposition 1
Firm’s strategic decisions
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 184
4.3 Third Step: Assess the Profitability of the Firm in Each Positioning
Segment of the Industry
The last step in modeling the positioning objective requires calculating the firm-specific
profitability in the industry segment where it chooses to position. To achieve this goal, we
only need to update the economic sub-model of the DAFF Decision Diagram in order to
account for the firm’s economic performance, as shown in Figure 4.12. Here, we add the three
Economic decisions we introduced earlier: Tactical Costing, Pricing, and Production Scale.
Based on the available resources and/or implemented management system, a firm may
implement a series of tactical measures that affect its cost structure without affecting (and
regardless of) its strategic positioning in the industry. Those tactical measures are captured in
a set of Tactical Costing alternatives that increase or decrease the cost for the firm by a
specific percentage points relative to its industry-segment average. For example, an electric
vehicle manufacturer who has decided to produce a luxury sports car (strategic positioning
decision) still needs to make a decision on how to schedule the car assembly (tactical
decision). If the company deploys state-of-the-art labor-scheduling protocols and procedures,
it may endure below-average utility expenses; the opposite is true if the company deploys
outdated labor-scheduling protocols. Either way, the company’s labor-scheduling practices
affect its cost without affecting its strategic positioning, so it is accounted for in Tactical
Costing. To that end, the cost structure for the firm is dictated by both the average cost in the
positioning industry segment and the tactical operational practices in the firm, which shift the
cost above or below the industry’s average.
To properly model the firm’s costs in our DAFF Decision Diagram, we add firm-specific
economic parameters Cv0, Cf
0, and CAPEX0 corresponding, as before, to capital expenditure,
unit-based fixed operating cost, and unit-based variable operating cost, respectively. CAPEX0
for a specific firm is determined by the Tactical Costing of that firm as well as by CAPEX of
the industry segment where the firm positions. Accordingly, CAPEX0 is modeled as a
deterministic node that is known with certainty for a given pair of CAPEX degree and
185
Figure 4.12: DAFF Decision Diagram for the first objective, third step: assessing the profitability of the firm in each positioning segment of
the industry
Threat of new entrants
Barriers to entry
Expected retaliation
Size-independent advantages
for incumbents Capital
needed by new entrant
Network effects
Supply-side economies of scale for incumbent
Unequal access to
distribution channels for new entrant
Previous responses
by incumbents
Extent of Resources available
for incumbent
Capital availability
for new entrant
Relative Dependence of the buyer on industry
product
Buyer’s switching cost between this
industry’s products
Bargaining Power of Suppliers
Concentration of suppliers relative to
incumbents
Industry concentration
Relative dependence of suppliers
on this industry profits
Incumbent switching
costs between suppliers
Supplier switching
costs between
incumbents
Product differentiation
among suppliers
Availability of
substitutes for what
the suppliers provideSuppliers
threat to integrate foreword
Threat of substitutes
Price-performance trade-off to this industry
product
Commitment of
incumbents to retain and
fight over market share
Industry growth
rate
Product differentiation
among incumbents
Efficiency of expansion of Incumbents production
capacity
Bargaining Power of Buyers
price sensitivity of
the buyer
Product cost as
fraction of the
buyer’s budget
concentration of buyers relative to
incumbents
Buyer’s threat to integrate backward
Ability to influence
buyers downstream
Rivalry
Intensity of competition
Basis of competition
Ability to enforce
practices desirable for the industry
Extent of exit
barriers
High commitment to business
High fixed costs
Perishable product
Buyer’s need to trim
purchase cost of the
product
Willingness of price
discounting by
incumbents
Extent of market
segments
Ability to meet the needs of multiple
customer segments
Inability to read
incumbents’ signals
Lack of familiarity
with incumbents
Number of buyers
Importance of non-
profit goalsIncumbent’s investment in services by current suppliers
Incumbent’s production
location near current
suppliers
Number of
industries the
suppliers serve
Profits extracted
by suppliers
from other industries
Availability of
Substitutes for this
industry’s product
Volume of
purchase per
buyer
Buyer’s switching cost from this
industry’s products to substitutes
Substitutes
Buyers
New Entrants
Rivals
Suppliers Factors
𝑃 𝐶𝑣 𝐶𝑓
𝐶𝐴𝑃𝐸𝑋 𝐶
𝑄
Economic parameters
Value Chain 1 Value Chain 2Value
Proposition 1
Firm’s decisions
𝐶𝐴𝑃𝐸𝑋0
Tactical Costing
Pricing
Production Scale
𝑀 0 0
𝑄0
𝑅𝑂𝐼𝐶
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 186
Tactical Costing alternative. A relevance arrow and an influence arrow extend into CAPEX0
from CAPEX and Tactical Costing, respectively. We follow a similar procedure to model Cv0
and Cf0.
Subsequently, the firm has the ability to choose how to price its product, regardless of what
the optimal market-equilibrium is. Here, we introduce a new economic parameter, the firm’s
Market Share (MS0), defined as a fraction of the overall annual sales volume in the firm’s
industry segment (Q ). Relying on Industrial Organization theory, we model four economic
attributes affecting MS0: the firm’s Pricing, industry average Price P
*, Industry concentration
driver, and the power of New Entrants force. Industry concentration refers to the number and
relative size of current incumbents in the industry. Reasonably, learning about current
incumbents and future new-entrants informs the decision-maker’s beliefs about her firm’s
likelihood to gain, sustain, or lose market share in the near-future [38]. Also, for any given
setting of incumbents and new entrants, one can argue that as Pricing increases beyond P*,
customers will increasingly refrain from purchasing the firm’s product, leading to a smaller
MS0. To account for all these effects, the DAFF Decision Diagram in Figure 4.12 presents the
firm’s MS0
as an uncertainty node with four arrows directed into it: one influence arrow from
the Pricing decision node and three relevance arrows from the New Entrants, Industry
concentration, and P* uncertainty nodes.
The rest of the economic modeling is just math. The product of MS0 and Q
* results in D
0,
defined as the expected demand for the firm’s product (or service). Then, the firm’s annual
sales volume (Q0) become the minimum of {D
0, Production Scale}. If the firm overproduces
beyond its expected demand (Production Scale > D0), its sales will be constrained by demand
(Q0 = D
0); equivalently, if the firm underproduces below its expected demand (Production
Scale < D0), its sales will be constrained by supply (Q
0 = Production Scale). As shown in
Figure 4.12, both D0 and Q
0 are modeled as deterministic nodes because they are fully
specified upon knowing their parents. Finally, recalling the two definitions in (1) and (2), we
can compute the expected profitability for the firm in each positioning industry segment either
in the form or ROIC0 or PM
0. Figure 4.12 models ROIC
0 as the value node with functional
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 187
arrows extending into it from the firm’s Pricing, expected annual sales volume Q0, and all
three types of costs Cv0, Cf
0, and CAPEX0.
Before ending this section, we underscore that this proposed modeling of the firm’s
profitability is an extension to – not a formal part of – the FF framework or theory. While
necessary for operationalizing the positioning objective in competitive strategy, the discussed
economic sub-model for the firm’s profitability represents our own assessment – and
assumptions – on a how a manager values a specific line of business. Unlike all previous
modeling endeavors so far, this economic sub-model is not a direct translation of the FF
literature. To that end, we shall leave it to the decision-maker to use, modify, or even replace
this sub-model in order to evaluate her business’s specific profitability.
4.4 Advantages of the DAFF modeling
We now bring all newly introduced concepts together in order to highlight the benefits of
using the DAFF approach to model this first objective of competitive strategy.
Comprehensive representation of competitive strategy: Broadly, Porter’s literature tends to
discuss FF and value-chain as two distinct strategic frameworks, aiming, respectively, to
evaluate the whole industry then to develop a competitive advantage for the firm within the
industry [8]. Evidently, DAFF combines the modeling of both frameworks, which further
enhances their operationalization. The presented DAFF Decision Diagram in Figure 4.11
illustrates that FF and value-chain are highly interconnected, and when modeled together, they
offer a clear procedure for firms to properly position in their respective industries. For
example, value-chain choices on product design and distribution channels can easily affect
whether a firm “enters, stays in, or exits” a specific industry, which Porter emphasizes as
important positioning decisions. Also, the pool of possible Value Proposition and Value Chain
alternatives allows the firm to be both creative and flexible in choosing its positioning
strategies, which in turn widens the scope of the “cost-leadership”, “differentiation”, and
“focus” strategies highlighted by Porter [28].
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 188
Balance between generality and customization: An important advantage of the DAFF
Bayesian Network in Figure 4.10 is balancing between the need to generalize and the ability
to customize the probabilistic assessment of the competitive uncertainties. By adding or
eliminating drivers at the various ancestral levels, the model allows the decision-maker to
emphasize (or deemphasize) specific attributes in her industry. Yet, despite what drivers the
decision-maker chooses to analyze, she will always end up with a clear probability distribution
for each of the five force uncertainties. For example, a manger in the residential solar industry
may not be able to properly assess the power of Substitutes because the Price-performance
tradeoff to this industry product driver seems too vague. In this case, the manager can add a
few parents to that driver in order to better inform her assessment. Such parent nodes may
include Bill savings from substitutes, Installation and maintenance time for substitute, or
Climate impact of substitute. Then, the manager investigates: what is the probability that the
Price-performance tradeoff to this industry product is favorable, given that Bill savings from
substitutes is {25% reduction in the monthly utility bill}, Installation and maintenance time
for substitute is {15 minutes per month}, and Climate impact of substitute is {50% reduction
in the household carbon emissions}?
The Decision Diagrams in Figures 4.11 and 4.12 further emphasize DAFF’s ability to balance
between generality and customization. To properly position, every firm in any industry should
examine a series of Value Proposition and Value Chain decisions and should link those
decisions to the competitive and economic uncertainties. Equivalently, to compute its
profitability, every firm in any industry should factor in its Tactical Costing, Production
Scale, and Pricing decisions. While DAFF explains how to model each of these decision
categories, it leaves it to the manager to define every particular decision and its alternatives,
based on the specifics of the analyzed business and industry. Because of that, the DAFF
Decision Diagrams can model clear competitive actions for a wide range of decision problems
that are material to a wide range of decision-makers.
In addition, through customization, the DAFF modeling endorses Porter’s recommendation to
the firm to be “unique” instead of “best” in its industry [8]. This is achieved in two ways.
First, DAFF forces the firm to choose only one of many feasible positioning tracks, which
encourages specialization. Second, the DAFF inputs are subjective in nature; even if we
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 189
assume a single DAFF model with fixed configuration, different decision-makers may have
different market information and business intuition, which results in different design of
uncertainty degrees or different probability assignments over those degrees. Inevitably, the
subjective input will generate subjective outputs and recommendations, unique to the
decision-maker’s outlook on the industry. Here, we note that as DAFF facilitates the modeling
of “being unique”, it also obstructs the modeling of “being best.” Choosing the “best”
positioning alternative cannot be properly modeled by DAFF, for “best” is too vague to pass
the DA clarity-test and to define a proper value metric for ranking the decision-maker’s
preferences.
Quantification: In her book, Magretta quotes Porter that “strategy requires clear, analytic
thinking” [8]. As evident by now, the DAFF models allow quantifying all the necessary
components for a competitive analysis, including: the description of feasible alternatives for
every competitive decision; the description of possible realizations (i.e. degrees) for every
competitive driver, factor, force, or economic uncertainty; the likelihood (i.e. probability) of
each degree; and the value of profitability. In turn, this multi-layered quantification enables
other DAFF benefits, which we subsequently discuss.
Comparison, ranking, and prioritization: Customization and quantification facilitate consistent
comparison of the forces, their drivers, and industry-specific factors by examining their impact
on profitability. More powerful forces lead to lower prices, higher costs, and therefore lower
ROIC. To that end, the range of power for every force can be translated to a range of ROIC,
and the forces can be compared and ranked based on their respective ranges of expected
profitability. Extremely strong (probability of {high} = 1) Buyers may not lead to the same
ROIC as extremely strong Substitutes, for instance. In general, a wider ROIC range signifies a
more impactful force.
Because drivers and factors are probabilistically relevant to the forces, changing any of them
can also result in a distinct ROIC range. However, depending on the exact conditional
probability distributions, drivers or factors at the same ancestral level – even those sharing the
same child nodes – may have different impacts on profitability. To that end, the relative
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 190
significance of drivers and factors may vary from one industry to the other even though their
structural configuration – in the DAFF models – remains consistent across industries.
In general, this form of sensitivity analysis that investigates the effect of the various
uncertainties on the value is common in DA and is widely applied in the form of tornado
diagrams [10]. Indeed, this ranking and comparison exercise also resolves one of the perceived
deficiencies in applying the FF framework, raised by Grundy [29]. As a practical implication
of this sensitivity analysis, the manager may choose to prioritize the most impactful drivers or
factors and focus all subsequent analyses on them. Such prioritization may entail eliminating
the least-impactful drivers or factors, seeking more information on or control over the most
impactful drivers or factors, or both.
Similar logic applies to assessing the impact of the firm’s positioning decisions on
profitability. Because every positioning track is associated with a distinct ROIC, positioning
tracks can be ranked from most to least profitable. The manager may then decide to spend
additional resources further analyzing the most profitable tracks while discarding the least
profitable ones.
Mapping interdependence and interaction: The FF literature stresses that a good industry
analysis should investigate “how shifts in one competitive force [might] trigger reactions in
others” [2]. DAFF offers one method to conduct such an investigation both rigorously and
quantitatively. The presented DAFF Bayesian Network in Figure 4.10 tracks the interactions
among the forces via two means: shared drivers and relevance paths – the latter referring to
a sequence of relevance arrows. In both cases, the uncertainty nodes communicate because of
their Bayesian probability distributions. When new information becomes available regarding a
specific uncertainty, the decision-maker may adjust the probability distribution over the
degrees of that uncertainty, which may simultaneously update the probability distributions of
that uncertainty’s parents and/or children.
As mentioned before, one example of a shared driver node is the Buyer’s switching cost from
this industry’s products to substitutes, which is a common ancestor to both Buyers and
Substitutes. Similarly, one example of a relevance path is the sequence of relevance arrows
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 191
from Basis of competition to Barriers to entry. To simulate this relevance, we start by
assuming that the decision-maker receives new information that reveals price-based
competition between the incumbents. Given this information, the decision-maker may infer
that {low} Production differentiation among incumbents is more likely (causing incumbents
to compete on price). This in turn triggers the following sequential probability updating:
{low} Buyer’s switching cost between this industry’s products is more likely; {high}
Consumer adoption rate of product by new entrant is more likely; and therefore {low}
Barriers to entry are more likely. Of course, we simplistically use {high} and {low} degrees
for all uncertainties in this example for illustrative purposes only. Practically, the exact
relevance path(s) from one uncertainty to another in a Bayesian network can be tracked via
established DA techniques such as Bayes-Ball [44].
Furthermore, the DAFF models are beneficial not only for highlighting relevance but also for
capturing irrelevance. As explained earlier, the lack of a relevance arrow between two
uncertainties signifies that – in the absence of additional information – the two uncertainties
are not relevant. When such an assumption does not hold in a specific industry, more
relevance arrows can be added. For example, the Detailed Network in Figure 4.6 shows no
relevance between Buyers trust in incumbents and Well-established brands because we didn’t
detect any assertion regarding such relevance in the reviewed FF scripts. Nonetheless, it is
easy to imagine multiple industries (e.g. automobiles, electronics, and sports merchandise)
where such relevance is possible and thus should be captured.
Finally, the DAFF modeling enables – rather imposes – a consistency check on the
interdependencies among the force, driver, and factor uncertainties by exposing, then ruling
out, illogical or conflicting evaluations of those uncertainties. For example, the DAFF model
allows checking whether it is possible for the probability of {high} Buyers power to be less
than 0.6, given that the probabilities of {high} Substitutes and {high} New Entrants are both
greater than 0.8.
Outlining the firm’s scope of control: Though substantial, the effect of positioning on the five
forces’ powers is still limited because decisions can influence some, but not all, of the forces’
ancestral drivers and factors. This DAFF feature is consistent with Porter’s caution against
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 192
“competitive convergence” where competing firms eventually run out of ways to
differentiate themselves [2]. To that end, DAFF modeling captures both the firm’s ability to
control being unique and its inability to control competitive convergence, and how both
phenomena may co-exist in the industry. On one hand, “best vs. unique” can be controlled by
the firm through positioning: being unique, as opposed to being best, is driven by the firm’s
need to choose one positioning track, which determines the identity and type of players it
interacts with. On the other hand, “competitive convergence” cannot be controlled by the
firm’s positioning decisions: competitive convergence stems from the firm’s inability to
change the short-term activities and decisions of the players it interacts with. Tesla Motors is a
good example here [45, 46]. By positioning in luxury-sports electric vehicles, Tesla was able
to limit its competitors to high-end car manufacturers like Porsche and Cadillac while
avoiding direct interaction with mass-market manufacturers such as Ford and Toyota.
Nonetheless, Tesla was not able to change its competitors’ decisions on whether to produce
electric vehicles. As such, Tesla succeeded in being unique at the beginning with Roadster and
then Model S. However, eventually, competitive convergence emerged, with Porsche rolling
out Panamera S E-Hybrid and Cadillac rolling out the ELR plug-in hybrid, both with similar
features and price-range to Tesla’s Model S [47].
Along the same lines, we recall that the FF framework asserts a disproportional relation
between the powers of the five forces and average profitability; firms should position in
industry segments that maximize the latter by minimizing the former. Nonetheless, while
specific positioning can push the forces to a relatively weaker level, it does not guarantee that
all forces will reach their absolute weakest level because it cannot simultaneously influence
all their underlying drivers and factors. Here, DAFF modeling can manifest how optimal
positioning may not reduce the power of all forces simultaneously; instead, it might be
achieved at some level of trade-off or balance among the forces’ powers. Let us consider
SolarCity for instance [48]. As the largest player in the residential solar industry, SolarCity
adopts a direct-to-customer retail model whereby it internalizes all system-installation services
for its customers [49]. This positioning strategy may decrease Buyers power by canceling the
need for intermediary channels, but it may also increase Rivals power by limiting the majority
of business to urban areas where the number of competitors, and thus the intensity of
CHAPTER 4 — First Objective of Competitive Strategy: Positioning in the Industry 193
competition, is high [50, 51]. A positioning track is judged by its expected profitability, so
direct-to-customer retailing and the resulting five-force balance may indeed be optimal, but
only if it maximizes the ROIC.
Valuating broader control or additional information: By robustly quantifying and mapping all
the competitive forces, drivers, and factors, their interactions, as well as their influence by the
firm’s positioning decisions, the proposed DAFF models in Figures 4.10 and 4.11 allow
measuring two key metrics: value of control (VOC) and value of information (VOI). VOC is
a DA concept that quantifies the cost of controlling an uncertainty; effectively, it assumes that
the decision-maker can somehow purchase the ability to adjust the outcome of that uncertainty
to her benefit. For example, to compute the value of fully controlling Buyers power, the
decision-maker sets the power of this force to its absolute maximum (probability of {high} =
1) or minimum (probability of {low} = 1) then calculates VOC as the difference between the
ROIC values with and without control. The resulting VOC plays an important role in
benchmarking how much a manager should spend on controlling a competitive force; a
decision-maker should never pay more than the VOC of a specific uncertainty to control the
outcome of that uncertainty. Equivalently, VOI is a similar DA metric that quantifies the cost
of resolving an uncertainty; in this case, the decision-maker gets to learn what the outcome of
the uncertainty is rather than dictating what it should be [10].
Exposing and reducing cognitive biases: A decision-maker usually thinks of few drivers,
factors, or forces when assessing competition. Naturally, this go-to set of competitive
attributes is highly dependent on the decision-maker’s prior experiences and knowledge, and it
may not be sufficient to understand and analyze the industry of her current business. To that
end, designing degrees and assigning probabilities for every uncertainty node in the DAFF
Bayesian Network urges the decision-maker to think critically about a wide range of
competitive attributes, which helps expose and reduce any cognitive biases that may magnify
the role of some attributes while attenuating (even ignoring) the role of others.
Moreover, at the end of the assessment, the decision-maker may dislike or reject the output
probability distribution for a particular force or the output ROIC value for a particular industry
segment. Because the outputs are calculated based on all the inputs into the model, the
CHAPTER 4 — Second Objective: Reshape the Industry 194
apparent discrepancy between the expected and actual results must be due to either a cognitive
bias by the decision-maker (that needs to be exposed) or an erroneous belief-input into one or
more uncertainty nodes (that needs to be fixed). It is easy to track back the information in the
DAFF models until reaching the real cause of this discrepancy. At that point, either the
decision-maker will realize her cognitive bias and become convinced with the present output,
or he will adjust her input. Ultimately, this iterative process of rationalizing the output with
the input achieves consistency and clarity of thought when assessing the competitive
landscape in the industry, no matter how complex or detailed the DAFF model might be.
5 Second Objective: Reshape the Industry
Fundamentally, this second objective of competitive strategy requires tracking the changes in
the five forces’ powers and their economic implications in the long run. The managerial
decision-maker may be interested either in passively predicting or in actively modifying the
competitive structure in the various positioning segments of her industry. In the next two
sections, we provide a conceptual overview on how to model these two tasks explicitly using
the DAFF approach, and we highlight the intuitive transition from one task to the other. As
will become evident, predicting the competitive evolution of the industry is a necessary first
step to reshaping it, and the decision-maker can achieve both goals by continuously
understanding, anticipating, and influencing the behavior of its buyers, suppliers, rivals, new
entrants, and substitutes.
Because reshaping the industry requires tracking competition over time, the DAFF modeling
of this second objective can be perceived as a dynamic extension of the DAFF modeling of
the first objective. We recall that one main distinction between the two competitive strategy
objectives is timeframe. As the decision-maker aims to properly position in the industry in the
short-term, she aspires to reshape the industry in the long-term. In essence, then, the long-term
timeframe is nothing more than a sequence of short-term periods, and the decision-maker can
dynamically assess the distant future of competition by modeling how the competitive forces
transition from one short-term period to the next.
CHAPTER 4 — Second Objective: Reshape the Industry 195
To facilitate the development of the dynamic DAFF models, we condense the representation
of the original positioning DAFF models in Section 4. The DAFF Decision Diagram in Figure
4.11 can be reduced to a three-node conceptual model, presented in Figure 4.13. The decision
node D in the conceptual model encapsulates all Value Proposition and Value Chain
decisions, and the uncertainty node F incorporates all force, driver, factor, and economic
uncertainties. The value node V remains as defined previously, reflecting the metric used to
assess profitability in the various positioning segments of the industry. Here, we clarify our
explicit intention to base the conceptual model on the decision diagram in the second step
(Figure 4.11), rather than the third step (Figure 4.12), of the first objective. Because the
manager’s strategic goal is to track the evolution of the competitive forces in every positioning
segment of the industry, she ought to focus on industry-level profitability; once that
profitability is properly evaluated, it becomes relatively easy to deduce the firm’s profitability
by applying the economic sub-model and following the procedure we outlined in Section 4.3.
Figure 4.13: Conceptual DAFF Decision Diagram for the first positioning objective
5.1 First Step: Predict Industry Change
The dynamic DAFF model for predicting industry change is presented in Figure 4.14. The
model assumes that the decision-maker wants to assess the change in the competitive
landscape over three sequential periods of time: (t), (t + 1), and (t + 2). Period (t), on its
own, represents the short-term timeframe for effective positioning. Positioning decisions D(t)
influence the competitive landscape F(t) exactly as we explained in Section 4. However, the
new dynamic nature of the DAFF model is manifested in the relevance arrows that extend
F
D
V
Forces, drivers,
factors, economic
parameters
Value Proposition
Value Chain
Profitability
CHAPTER 4 — Second Objective: Reshape the Industry 196
from F(t) to F(t + 1) and then from F(t + 1) to F(t + 2). Those arrows signify that each of
the five force uncertainties at (t + 2) is relevant to its earlier state at (t + 1), which in turn is
relevant to its state at (t). The same is true for each factor, driver, and economic uncertainty.
Effectively, this means that learning about the competitive and economic uncertainties in the
near future helps inform their assessment in the distant future. Finally, the competitive
landscape at (t + 2) dictates the expected profitability of each positioning segment in the
industry at (t + 2), per our earlier explanation in Section 4.
Figure 4.14: Dynamic DAFF model for the second objective, first step: predicting industry
change
The evolution of the competitive uncertainties over time is the main distinctive feature of this
dynamic DAFF model. In that regard, we make three important modeling notes. First, we
leave it to the decision-maker to determine the scale of each time period and the number of
time periods over which she wishes to assess industry change in the long-term, for both
features are very industry-specific. For example, the mining manager in our earlier example
may wish to set (t) equal to one year while (t + 1) and (t + 2) equal to three years each; such
timeframe would allow the manager to predict industry change over the coming seven years.
Second, to keep the dynamic DAFF model simple, relevance arrows from (t) to (t + 1) and
from (t + 1) to (t + 2) should be added very selectively; we call both types of arrows
Short-term
Long-term
Long-term
CHAPTER 4 — Second Objective: Reshape the Industry 197
temporal. In details, if an uncertainty node has parents, it shall not originate or receive a
temporal relevance arrow. Conversely, if an uncertainty node has no parents, it shall originate
or receive only one temporal relevance arrow. Figure 4.15 shows an example from the force of
Buyers. The Price sensitivity of the buyer driver has six ancestral nodes with no parents.
Assessing the probabilities of these nodes based on prior knowledge may become harder the
further the decision-maker looks into the future. However, the near-future state of these
uncertainties at (t) may inform the decision-maker’s assessment of their distant-future state at
(t+1). Accordingly, a temporal relevance arrow is added for each of the six ancestral nodes,
extending from its state at (t) to its state at (t + 1). Subsequently, the probabilistic assessment
of each of the remaining four drivers – including the Price sensitivity of the buyer itself – at
(t + 1) is informed by its parents at the same time period. Because the Price sensitivity of the
buyer driver has four parent nodes that facilitate its analysis by the decision-maker, we advise
that no temporal relevance arrow is needed between its states at (t) and (t + 1). However, an
analyst may still find it useful to add that arrow to achieve clarity. In fact, the analyst may
even decide to add a temporal relevance arrow from a parent at (t) to a child at (t + 1). We
distinguish both types of arrows as dotted lines in Figure 4.15. While adding either arrow is
not technically wrong, it might increase the complexity of the competitive analysis. If we
assume two degrees per uncertainty in Figure 4.15, then adding two additional temporal
relevance arrows to the Price sensitivity of the buyer at (t + 1) increases the number of
required probability assignments for that node from 16 (24) to 64 (2
6), which is a difficult task
for managers to handle.
The final note is related to positioning. Similar to Figure 4.11, Figure 4.14 shows that the
firm’s positioning decisions influence the competitive landscape in the short-term. However,
in this first step of the second objective, the decision-maker aims not only to understand the
short-term behavior but also to anticipate the long-term behavior of the industry players in
each positioning segment. Subsequently, the expected profitability for each segment is
evaluated at the end of the last period of the selected timeframe; for example, in Figure 4.14,
the expected profitability value corresponds to the end of period (t + 2). In short, while the
DAFF model in Figure 4.11 provides managers with a tool to identify the most profitable
positioning segment in their industry in the short-term, the DAFF model in Figure 4.14 allows
CHAPTER 4 — Second Objective: Reshape the Industry 198
managers to predict the most profitable positioning segment in their industry in the long-term.
Both DAFF models highlight where the competitive behavior is least threatening, but they
provide no guidance on how to modify that behavior. Modeling the manager’s efforts to
modify her competitors’ behavior, and consequently to reshape her industry, is what we
discuss in the next section.
Figure 4.15: Guidance on adding temporal relevance arrows between competitive
uncertainties
5.2 Second Step: Reshape Industry Change
Reshaping the industry requires influencing the competitive behavior. We now explain how
DAFF can model the firm’s attempts to change the behavior of its industry players over time
in order to gain competitive advantage. The dynamic DAFF model for reshaping industry
change is presented in Figure 4.16. Compared to the earlier model in Figure 4.14 for
predicting industry change, the DAFF model in Figure 4.16 adds three major elements, each of
which enables and informs the firm’s strategic interactions with the other competitive players.
First, a decision node D is added at (t + 1) and (t + 2), which allows the decision-maker to
re-assess positioning over time. Second, a new influence arrow is added from D(t) to F(t + 1)
and similarly from D(t + 1) to F(t + 2). While the arrow from D(t) to F(t) influences the
Relative dependence of the buyer on industry
product
Product differentiatio
n among incumbents
price sensitivity of
the buyer
Product cost as fraction of the buyer’s
budget
Buyer’s need to trim
purchase cost of the
product
product leads to
performance improvement for buyer
Profits earned by the buyer
Amount of cash
available to the buyer
Industry product pays
for itself
product reduces costs for
buyer
?
?
(t) (t+1)
temporal
relevance
arrows
Relative dependence of the buyer on industry
product
Product differentiatio
n among incumbents
price sensitivity of
the buyer
Product cost as fraction of the buyer’s
budget
Buyer’s need to trim
purchase cost of the
product
product leads to
performance improvement for buyer
Profits earned by the buyer
Amount of cash
available to the buyer
Industry product pays
for itself
product reduces costs for
buyer
CHAPTER 4 — Second Objective: Reshape the Industry 199
identity of the firm’s competitors, the arrow from D(t) to F(t + 1) influences the behavior of
those competitors. The same argument applies to the influence arrows from D(t + 1) to
F(t + 1) and F(t + 2), respectively. Third, a new type of arrows is added from the
competitive uncertainties F at one time period into the positioning decisions D at the next time
period. This is illustrated in two arrows from F(t) to D(t + 1) and then from F(t + 1) to
D(t + 2) in Figure 4.16. In decision analysis, an arrow extending from an uncertainty into a
decision is called an information arrow; it means that the decision-maker will know exactly
how that uncertainty will be resolved before making the decision.
Figure 4.16: Dynamic DAFF model for the second objective, second step: reshaping
industry change
The firm’s original positioning inevitably triggers a series of reactions from other industry
players. Those reactions induce the firm to respond, which in turn induces other players to
respond back. This continuous strategic interaction between the firm and other industry
players is captured effectively in the sequence of influence and information arrows illustrated
in Figure 4.16. When a firm selects a positioning track at (t), it not only chooses a set of
players to interact with at (t) (short-term) but also induces a reaction from those players and
causes a change in their behavior at time (t + 1) (long-term). When (t + 1) begins, the firm
Short-term
Long-term
Long-term
CHAPTER 4 — Second Objective: Reshape the Industry 200
learns how the competitive landscape turned out in the previous time period (t), and it uses
this new information to re-assess its positioning. Based on the change in the competitive
behavior, the new positioning allows the firm to update the set of players it chooses to interact
with at (t + 1) (which is the short-term now), and it induces a reaction from those players and
causes a change in their behavior at time (t + 2) (which is the long-term now). This cycle
goes on as long as the decision-maker desires, repeating with every new time period in the
decision-maker’s timeframe. Eventually, the DAFF model produces an expected profitability
for every positioning policy, defined as the sequence of positioning tracks that the firm adopts
over all time periods. A positioning policy may reveal that a firm position in one industry
segment throughout all time periods, or it may reveal positioning in different segments during
different periods. As before, the firm should adopt the positioning policy that results in the
highest expected value of profitability.
Let us consider one of our earlier examples from the automobile industry to clarify this
modeling procedure. Going back to 2006, suppose that an auto manufacturer, we call Electra,
is launching a new car line and is thinking of three positioning decisions: car technology
[hybrid, electric], car model [luxury, economy], and customer sales [direct, dealer]. Electra is
interested in assessing its ability to reshape the competitive landscape over the coming nine
years, assuming that three years is a reasonable estimation of a short-term period.
Accordingly, we model three time periods (t), (t + 1), (t + 2), each spanning three years. If
Electra positions in [electric, luxury, direct] in 2007, it will compete with a unique set of
players and thus be exposed to a unique competitive landscape up until 2009. For example,
less direct rivals may exist in the [electric, luxury, direct] segment in comparison with the
[hybrid, economy, dealer] segment. Then, Electra has to analyze how its positioning in 2007
will change the behavior of the players it chooses to compete with up until 2012. For instance,
six years may be sufficient for a big manufacturer like General Motors to enter the [electric,
luxury, direct] segment and start competing directly with Electra. As 2010 commences,
Electra gains more information about the competitive landscape in each positioning segment
up until 2009. This new information helps Electra decide whether to adopt a new positioning
track, such as switching to the economy car model in order to enter the mass market and
increase sales. If Electra updates its positioning to [electric, economy, direct] in 2010, it needs
CHAPTER 4 — Second Objective: Reshape the Industry 201
to consider how this new positioning may change the identity of the players it competes with
up until 2012, and how those players may react to its new positioning up until 2015.
Eventually, the DAFF model outputs the expected profitability for every possible positioning
policy in 2015, which advises Electra on the exact sequence of positioning tracks it should
pursue every three years till the end of 2015. A positioning policy example is presented in (3)
for illustrative purposes only. Also, for full disclosure, we confess that our hypothetical story
on Electra is undeniably inspired by that of Tesla Motors [52].
[electric, luxury, direct]𝑡 where (𝑡) = 2007 − 2009
[electric, economy, direct]𝑡+1 where (𝑡) = 2010 − 2012
[electric, economy, direct]𝑡+2 where (𝑡) = 2013 − 2015
(3)
After explaining the details of the dynamic DAFF model, it is important that we take a step
back to discuss how this approach upholds FF’s theories in competitive strategy. To start, the
notion that positioning influences the five forces by changing the behavior of other industry
players is consistent with Industrial Organization theory and supported by Porter. Porter
recognizes early in his work that “there are feedback effects of firm conduct (strategy) on
market structure” [53]. Equally important, the DAFF dynamic model can demonstrate how
and why a business succeeds or fails over time, which is a central question to tackle when
designing a dynamic theory of strategy [25]. For a business to continue to succeed, its
positioning at every period should not only influence future market conditions but also be
informed by and consistent with historic market conditions. The dynamic DAFF models
clearly capture both requirements through the influence and information arrows, respectively.
Here, we emphasize the role of information arrows in accommodating sudden or rapid
industry changes. When an industry faces new or quickly evolving challenges, information
arrows preserve and transfer that intellegence from one period of the competitive analysis to
the next. A firm’s positioning strategy that does not account for the most recent competitive
information may be outdated, resulting in long-term failure despite short-term superior
performance. Ultimately, the dynamic DAFF modeling succeeds in fulfilling a key issue that a
dynamic theory of strategy must address: tracking the sequential interdependence between the
performance of the firm and that of the industry it operates in over time [25]. In the DAFF
CHAPTER 4 — Best Practices in DAFF Modeling 202
model of Figure 4.16, we see how the industry’s current structure informs the firm’s future
decisions, and how the firm’s current decisions influence the industry’s future structure.
6 Best Practices in DAFF Modeling
So far, we have discussed the various aspects and advantages of applying the DA method to
model and operationalize the FF framework and to fulfill its corresponding objectives in
competitive strategy. Reasonably, however, the introduced DAFF models may become too
complex or confusing in the absence of clear guidance on their development and use. This
section aims to highlight five major best-practices that business analysts and managers should
keep in mind when building and assessing the proposed DAFF Bayesian networks and
decision diagrams.
First, any DAFF model should start with and include all five competitive forces. The decision-
making manager can then proceed to add the driver and factor uncertainties that would help
her assess the five force uncertainties. As mentioned before, the decision-maker need not
analyze every driver mapped in the Detailed Network of Figure 4.6. Sometimes, the decision-
maker may have deep and perfect knowledge of specific market drivers, or she may deem
some drivers immaterial to competition in her industry; in both cases, these driver
uncertainties can be excluded from the DAFF model. On the other hand, if the decision-maker
is not able to assess specific drivers or factors due to their complexity or vagueness, new
parent uncertainties can be added to facilitate their assessment.
Second, the number of arrows extending into an uncertainty – either from a decision or from a
parent uncertainty – should be limited. Mathematically, when a decision node with N
alternatives extends an influence arrow into an uncertainty, the number of probability
assignments required at that uncertainty increases N folds; the same is true for a relevance
arrow extending from a parent uncertainty with N degrees. Therefore, it is preferable to cap
the number of arrows pointing into an uncertainty at four, but surely no more than five. For an
uncertainty node with five parents, each with two degrees, the number of probability
assignments required is 32 (25), which is already a challenging task for managers to handle.
CHAPTER 4 — Best Practices in DAFF Modeling 203
Third, also related to uncertainty modeling, probability elicitation from experts and decision-
makers should be handled efficiently. While an iterative analysis of the uncertainties in the
DAFF model may help expose cognitive biases, we caution that this iterative process should
not be abused. As obvious as it may sound, we stress that every probabilistic input should be a
true and honest representation of the decision-maker’s information, which in turn should be
shaped, informed, and validated by objective and factual data. If the probabilistic input into
the model is manipulated to yield a desirable output by the decision-maker, the model will
almost certainly fail to offer any new insights, defeating the purpose of the DAFF modeling
exercise in the first place. To ensure effective modeling of uncertainty, several protocols for
performing probability assessment have been proposed in literature [54]; among others, the
Stanford/SRI protocol [55] is widely used by DA practitioners.
The fourth modeling note is related to choosing a proper measure of profitability. We reiterate
that Porter recommends the use of ROIC because it comprehensively accounts for revenue and
cost figures, including CAPEX. The additional benefit of ROIC is that it can be computed
from the firms’ balance sheets and income statements – documents that are readily available
and that managers are familiar with. From a different perspective, NPV is a preferred and
widely used metric for assessing value in DA. Unlike the ROIC ratio, NPV is an absolute
measure, which facilitates clear ranking of decision prospects. If two prospects have equal
NPV, we can reasonably conclude that they have equivalent scale and profitability. The same
argument does not apply to ROIC, for two prospects of different scales and/or different
combination of EBT and CAPEX may still have the same ROIC ratio. Of course, the use of
NPV has its own challenges, especially in the dynamic assessment of competitive landscapes.
The NPV calculation assumes that the future discounted cash flows are known throughout the
business’s lifetime. However, as demonstrated in the DAFF dynamic model, the future
economics of the business might change with the uncertain competitive landscape. Ultimately,
we understand that different managers may be inclined to use different profitability metrics
based on their firms’ established ways of doing and evaluating business. Whatever
profitability metric the firm chooses to use in its DAFF modeling, it must always meet three
criteria: account for the effect of the competitive forces on the basic economic parameters; be
quantitative and computable; and be intuitive to the decision-maker.
CHAPTER 4 — Broader Alignment between Decision Analysis and Porter’s Competitive
Strategy 204
Finally, we briefly discuss how managers should think about their positioning alternatives. To
be unique, different firms within the same industry may – and perhaps should – choose to
model different positioning decisions, or different alternatives for the same positioning
decisions. Working towards that goal, we assert that, consistent with strategy literature, the
manager in a specific firm should select the set of feasible positioning alternatives based on
her firm’s own competences and available resources [26], and in accordance with her firm’s
cultural and behavioral norms [56]. Indeed, because different decision-makers may have
different information and beliefs (guiding their probability assessment) about the industry and
how their actions change the competitive landscape, firms with the same set of feasible
positioning alternatives may end up pursuing different positioning strategies.
7 Broader Alignment between Decision Analysis and Porter’s
Competitive Strategy
As we progressed in modeling the five forces framework using decision analytic tools, we
uncovered additional areas of alignment between decision analysis and Porter’s competitive
strategy, which we briefly overview in this section.
To start, a notable similarity exist between Porter’s display and description of tailored value
chains [8] and DA’s display and description of strategy tables [10, 57]. Both concepts
suggest that the set of strategic activities defining the firm’s competitive behavior cannot be
chosen randomly; those activities must be guided by an overarching theme or trend. In
Porter’s world, the firm’s activities along its value chain must serve the firm’s value
proposition and therefore be different than those of its rivals. In the DA world, the firm’s
activities must make sense together, which excludes a nontrivial pool of positioning
combinations that are technically correct yet practically unintuitive for the decision-maker.
Along the same lines, both DA and Porter highlight the importance of fit. Porter notes that fit
among the value-chain activities deters imitation, which allows the firm to sustain its
competitive advantage. Magretta explains: “as fit lowers the probability of successful
imitation, it raises the penalty of failure precisely because the activities are interconnected. A
CHAPTER 4 — Conclusions 205
small shortfall in one can produce ripple effects elsewhere.” DA can effectively capture this
“fit” and its corresponding “ripple effects” in its Bayesian networks and decision diagrams.
One way to demonstrate such capability is to examine how two positioning decisions
influence the same uncertainty. Our story on Electra provides a good example. Let us suppose
that switching from [dealer-sales] to [direct-sales] of an electric economy car reduces the
probability of strong Rivals from 0.6 to 0.4. Equivalently, switching from an [economy] to a
[luxury] model of an electric dealer-sold car yields the same outcome. However, if both the
[luxury] and [direct-sales] alternatives are combined in one positioning track, the probability
of strong Rivals drops from 0.6 to 0.1. In this case, the fit between the [luxury] and [direct-
sales] alternatives reinforces their collective effect, resulting in a less competitive landscape.
The probabilistic interdependence between the multiple elements of a DA decision diagram
can also manifest the “ripple effect”. Changing a positioning decision may change the
probability distributions of the influenced driver uncertainties, which in turn may change the
probabilities of their relevant uncertainties. As a result, the stronger the dependencies between
the nodes of a DA model, the harder it is to copy the firm’s network of positioning activities.
By facilitating the design of tailored positioning alternatives, enforcing trade-offs when
choosing positioning alternatives, and ensuring fit among the chosen positioning alternatives,
DAFF allows the firm to fulfill Porter’s ultimate recipe for establishing and sustaining
competitive advantage. While tailoring and trading-off positioning decisions “prevent existing
rivals from copying [the firm’s] good strategy, either by straddling or repositioning”, fit helps
sustain competitive advantage “against new entrants, even the most determined of them” [8].
8 Conclusions
This study explains the foundations of DAFF, a decision analytic modeling approach to
Michael Porter’s five forces framework in competitive strategy. We start by briefly
introducing the concepts of decision analysis (DA) and the five forces framework (FF), and
we identify key areas where DA can augment previous endeavors to further the
operationalization and implementation of FF by real firms and in real industries. As the main
focus of this research, we then provide a detailed description of the various DAFF
CHAPTER 4 — Conclusions 206
components, and we develop a series of DAFF models to fulfill the two main objectives of
competitive strategy: positioning in the industry, and reshaping the industry.
The various elements of the FF strategic framework are first translated into DA terms and
categorized as uncertainty-related, value-related, or decision-related. The five competitive
forces – Substitutes, Buyers, Suppliers, New Entrants, and Rivals – and their underlying
drivers are modelled as uncertainties. Also counted as uncertainties are industry-specific
factors related to governmental regulations (Regulation), technological advances
(Technology), market growth rate (Growth), and complementary products and services
(Complements). Both the generalizable forces and drivers as well as the industry-specific
factors impact Cost, Price, and Quantity, which are treated as uncertain economic parameters.
After modeling all these uncertainties, we explain how to effectively define profitability and
model it as a value metric. The final element of DAFF is the firm’s set of competitive actions
within the analyzed industry, which can be categorized into three types of decisions: Value
Proposition, Value Chain, and Economic decisions. Putting these elements together results in
two types of DAFF models: the DAFF Bayesian Network evaluates the competitive
performance of the whole industry whereas the DAFF Decision Diagram evaluates the
performance of specific industry segments and/or firms.
Subsequently, we show how the proposed DAFF models allow fulfilling the two main
objectives of Porter’s competitive strategy: positioning in and reshaping the industry.
Positioning is a short-term objective, and it entails three consecutive analyses focusing on
current and very-near-future profitability: of the overall industry, of distinct positioning
segments in the industry, and of a specific firm or business within each positioning segment.
Building on the outcomes from these three steps, reshaping the industry becomes the long-
term objective, and it requires two additional analyses focusing on distant-future profitability:
predicting the evolution of the industry structure then modifying the evolution of the industry
structure. After detailing how to model the three steps for industry positioning, we provide a
conceptual description of how to model the remaining two steps for industry reshaping.
Practically, the DAFF modeling of industry reshaping proves to be a dynamic extension of the
DAFF modeling for industry positioning.
CHAPTER 4 — Conclusions 207
Along the way, we highlight several benefits for using DAFF to conduct FF-based competitive
analyses, primarily the ability to: generalize the assessment model while customizing its
features to evaluate different industries and firms; explicitly account for competitive and
economic uncertainty; clearly map the relation between the industry’s competitive forces and
the firm’s competitive actions; clearly map the relation between competitive forces and
economic performance; compare, rank, prioritize, and track the interdependence among the
competitive forces, drivers, and industry factors; outline the firm’s scope of control; and
expose and reduce cognitive biases. Atop all that, perhaps the most important feature of DAFF
– indeed, one that enables all aforementioned benefits – is quantification. DAFF allow
quantifying multiple aspects of the competitive analyses, including: the definition of all
possible realizations for each force, driver, factor, or economic uncertainty; the likelihood of
each realization; the firm- or industry-specific profitability value; as well as the maximum
value that the firm should pay to reduce uncertainty through additional information or broader
control.
Eventually, this work shows that DAFF upholds and incorporates Porter’s “four principle
issues [that] emerge … as one contemplates a theory of strategy”: approach to theory building,
chain of causality, time horizon, and testing [25]. First, DAFF balances between what Porter
refers to as the “framework” and the “model” approaches to building a strategy. On one hand,
the generalizable structure of the decision diagrams allows them to both “capture much of the
complexity of actual competition” and “help the analyst to better think through the problem by
understanding the firm and its environment and defining and selecting among the strategic
alternatives available, no matter what the industry and starting position [are]” [25]. On the
other hand, DAFF relies on “mathematical models of limited complexity” to quantify the
economic impact of the competitive forces, realizing the need to make some simplifying and
manager-friendly assumptions and adjustments along the way. The second principle issue, the
chain of causality, is captured in the “flexible ancestral” structure of the Bayesian networks.
As already established, DAFF allows the decision-maker to analyze competitive drivers at
multiple ancestral levels in order to achieve clarity of thought, and those driver uncertainties
are usually connected in a causal direction to facilitate probability assessment. Third, the time
horizon aspect of the strategy theory is clearly accounted for in modeling the short-term and
CHAPTER 4 — Conclusions 208
long-term competitive objectives, where we demonstrated how a firm can comprehend,
anticipate, and respond to the behavior of other industry players over multiple periods of time.
Finally, on the issue of testing, Porter states that “empirical testing is vital for both
frameworks and models.” The DAFF approach is hard to test empirically, for DAFF models
aim to assess the competitive landscape in the near or distant future, not in the past. However,
both DA and Porter converge on recognizing the important role of case-studies as a testing
tool. Evident in both competitive strategy literature [2, 8] and DA consulting practices [58,
59], “in-depth case studies [can] identify significant variables, explore the relationships among
them, and cope with industry and firm specificity in strategy choices” [25].
8.1 Future Work
The ultimate objective of this research is to present and promote DAFF models as generic
robust tools that managers and executives can easily and intuitively use to evaluate
competitive strategies for their line of business. However, like any modeling approach, DAFF
has its own challenges and shortcomings. Perhaps the most apparent challenge is related to the
potential need for extensive data input. If the number of uncertainties in the DAFF model is
too big, the decision-maker might find their probabilistic analysis too time-consuming.
Similarly, a congested network of relevance arrows linking these uncertainties might force the
decision-maker to consider very hard trade-offs when assigning conditional probabilities, thus
compounding the difficulty of the competitive analysis. Fundamentally, this potential
computational burden exposes DAFF’s most significant vulnerability: seeing the “trees” while
losing the “forest.” Originally, we asserted that the detailed nature of the DAFF models help
the decision-maker gain clarity regarding the competitive landscape in her industry. Ironically,
however, this same need to dig deep into each DAFF element (tree) might also obstruct the
decision-maker’s ability to see the big picture (forest), which is essential in strategy.
Consequently, even if managers understand the DAFF approach and appreciate its benefits,
they might find the DAFF models too complex to apply on daily basis in real life.
To resolve this dilemma, and to encourage DAFF’s wide adoption and utilization by
businesses and firms, future work should focus on exploring ways to streamline the DAFF
Bayesian networks and decision diagrams. We offer a glimpse of how to propel and expand
CHAPTER 4 — Conclusions 209
the DAFF research in that direction. The premise is rather straightforward: the large number of
driver uncertainties might render a DAFF model too big or complex; yet, these drivers are
necessary to properly assess the competitive five forces; so, how about we eliminate all the
drivers after assessing the forces, and while preserving the competitive intelligence derived
from them? In theory, this proposition is feasible and can be achieved by reversing the
direction of the relevance arrows between the competitive forces and drivers; if applied
correctly, it can simplify the DAFF analyses drastically.
As sketched in Figure 4.17, the proposed endeavor expands the scope of the formal execution
process of DAFF modeling, asserting it is best conducted in three sequential stages and as a
collaboration between the decision-making manager and an expert analyst. In Stage 1, the
manager identifies the positioning concerns that should be addressed in the competitive
analysis, and the analyst translates those concerns into a clear set of positioning alternatives.
The outcome of Stage 1 is a simple yet comprehensive DAFF representation that lists the to-
be-analyzed firm’s positioning decisions and industry’s five force uncertainties. In Stage 2, the
analyst works with the decision-maker to add and examine the driver uncertainties needed to
help assess the five force uncertainties. The analyst then develops a complete DAFF Bayesian
Network or Decision Diagram, connecting the positioning decisions to the drivers and
connecting the drivers to the forces. Stage 2 is all what we have expounded in this work.
Instead of stopping at Stage 2, we envision a Stage 3 where the analyst works on condensing
and simplifying the complete DAFF model from Stage 2 while preserving all its competitive
intelligence. To do this, the analyst reverses the direction of the relevance arrows between the
force and driver uncertainties, a technique commonly referred to as “tree flipping” in DA
[10]. Upon applying this technique, the five forces become the most ancestral uncertainties,
and their probabilistic distributions become unconditioned on the drives. At this point, the
drivers are no longer needed for assessing the competitive forces or the economic performance
in the industry, and they can be removed from the DAFF model altogether. Although
reversing relevance arrows is an established practice in DA [10, 13, 44], future work should
focus on developing robust tree-flipping algorithms that specifically simplify the DAFF
models; ideally, such algorithms would automate the transformation of the complete DAFF
model in Stage 2 to the simplified DAFF model in Stage 3.
CHAPTER 4 — Conclusions 210
Figure 4.17: Future opportunities to streamline the DAFF modeling
While eliminating the drivers, tree flipping preserves all the probabilistic intelligence in the
complete DAFF model. Eventually, as shown in Figure 4.17, Stage 3 simplifies the DAFF
model representation drastically; the firm’s positioning decisions become directly linked to the
industry’s force uncertainties, and the force uncertainties become directly linked to one
another. Equally important, Stage 3 helps preserve the “forest”; the decision-making manager
remains focused on the big-picture related to competition and positioning, while the expert
analyst leads the work on fully examining then eliminating the detailed drivers in the analysis.
Positioning Decision A
Positioning Decision B
Force 1
Positioning Decision C
Force 2
Force 3
Force 4
Force 5
Stage 1
Add drivers to connect the positioning decisions to the
competitive forces
Flip the tree to remove all drivers
Positioning Decision A
Positioning Decision B
Force 1
Positioning Decision C
Force 2
Force 3
Force 4
Force 5
Factor I Factor IIStage 2
Positioning Decision A
Positioning Decision B
Force 1
Positioning Decision C
Force 2
Force 3
Force 4
Force 5
Stage 3
Forest
Trees
Forest
Co
mp
leted research
Futu
re research
CHAPTER 4 — Conclusions 211
Overall, the streamlined representation in Stage 3 helps managers better comprehend the
DAFF model and grasp its findings, which in turn incentivizes DAFF’s adoption as a generic
assessment tool in competitive strategy.
CHAPTER 4 — References 212
References
[1] M. E. Porter, "How Competitive Forces Shape Strategy," Harvard Business Review, March-April
1979.
[2] M. E. Porter, "The Five Competitive Forces that Shape Strategy," Harvard Business Review,
January 2008.
[3] Accenture Academy, "Explaining Porter’s Five Forces," 2014. [Online]. Available:
https://www.accentureacademy.com/d/course/1000007629/?tabId=1&moduleId=507. [Accessed
2015].
[4] FME, "Porter's Five Forces - Strategy Skills," 2013. [Online]. Available: http://www.free-
management-ebooks.com/dldebk-pdf/fme-five-forces-framework.pdf. [Accessed 2015].
[5] R. Marks, "Lecture Notes - Industry Analysis," Australian Graduate School of Management, 2003.
[6] M. E. Dobbs, "Guidelines for applying Porter's five forces framework: a set of industry analysis
templates," Competitiveness Review, vol. 24, no. 1, p. 32–45, 2014.
[7] H. Lee, M.-S. Kim and Y. Park, "An analytic network process approach to operationalization of
five forces model," Applied Mathematical Modelling, pp. 1783-1795, 2012.
[8] J. Magretta, Understanding Michael Porter: The Essential Guide to Competition and Strategy,
Cambridge: Harvard Business Review Press, 2012.
[9] SDG, "Strategic Decision Group International LLC," 2015. [Online]. Available:
http://www.sdg.com/about-sdg/. [Accessed 2015].
[10] R. A. Howard and A. E. Abbas, Foundations of Decision Analysis, 1st ed., United States: Pearson,
2016.
[11] R. A. Howard and J. E. Matheson, "Influence Diagrams, INFORMS," Decision Analysis, pp. Vol.
2, No. 3, pp. 127–143, 2005.
[12] R. D. Shachter, "Evaluating Influence Diagrams," Operations Research, pp. Vol. 34, No. 6, pp.
871-882, 1986.
[13] R. D. Shachter and D. Bhattacharjya, "Solving influence diagrams: Exact algorithm," Wiley
Encyclopedia of Operations Research and Management Science, 2010.
[14] Decisions Systems Laboratory, "GeNIe and SMILE," 2013. [Online]. Available:
https://dslpitt.org/genie/. [Accessed 2013].
[15] Lumina, "Influence Diagrams," 2015. [Online]. Available:
http://www.lumina.com/technology/influence-diagrams/. [Accessed 2015].
CHAPTER 4 — References 213
[16] M. E. Porter, Competitive Strategy Techniques for Analyzing Industries and Competitors, Free
Press, 1998.
[17] M. E. Porter, "Strategy and the Internet," Harvard Business Review, 2001.
[18] The Boston Globe, "Automaker Tesla looks to bypass car dealers," 2013. [Online]. Available:
https://www.bostonglobe.com/business/2013/11/20/tesla-battles-auto-dealers-direct-sales-
consumers/3f1xBFN21xH8QqQc3jijTP/story.html. [Accessed 2015].
[19] KBB, "Kelly Blue Book," 2015. [Online]. Available: http://www.kbb.com/. [Accessed 2015].
[20] CPUC, "California Renewables Portfolio Standard (RPS)," 2015. [Online]. Available:
http://www.cpuc.ca.gov/PUC/energy/Renewables/. [Accessed 2015].
[21] E. Halper, "Rules prevent solar panels in many states with abundant sunlight," Los Angeles Times,
2010.
[22] H. Courtney, J. Kirkland and P. Viguerie, "Strategy Under Uncerainty," Harvard Business Review,
1997.
[23] P. Ghemawat, Commitment: The Dynamic of Strategy, New York: Free Press, 1991.
[24] A. M. Brandenburger and B. J. Nalebuff, Co-opetition, New York: Doubleday, 2011.
[25] M. E. Porter, "Towards a Dynamic Theory of Strategy," Strategic Management Journal, pp. 95-
117, 1991.
[26] Y. E. Spanos and S. Lioukas, "An Examination into the Causal Logic of Rent Generation:
Constrasting Porter's Competitive Strategy Framework and the Resource-Based Perspective,"
Strategic Management Journal, vol. 22, pp. 907-934, 2001.
[27] N. J. Foss, "Research in Strategy, Economics, and Porter," Journal of Management Studies, vol.
33, pp. 1-24, 1996.
[28] M. Song, R. J. Calanton and C. A. D. Benedetto, "Competitive Forces and Strategic Choice
Decisions: An Experimental Investigation in the United States and Japan," Strategic Management
Journal, vol. 23, pp. 969-978, 2002.
[29] T. Grundy, "Rethinking and reinventing Michael Porter's five forces model," Strategic Change, pp.
213-229, 2006.
[30] K.-J. Wu, M.-L. Tseng and A. S. Chiu, "Using the Analytical Network Process in Porter’s Five
Forces Analysis – Case Study in Philippines," Procedia - Social and Behavioral Sciences, pp. 1-9,
2012.
[31] J. Franek and A. Kresta, "Competitive strategy decision making based on the five forces analysis
with AHP/ANP approach," VŠB-Technical University of Ostrava, Ostrava, 2013.
CHAPTER 4 — References 214
[32] L. Downes, "Beyond Porter," Context Magazine, 1997.
[33] R. D. Shachter, "Model Building with Belief Networks and Influence Diagrams," 2007. [Online].
Available: http://www.usc.edu/dept/create/assets/001/50850.pdf. [Accessed 2015].
[34] R. D. Shachter, "An ordered examination of influence diagrams," Networks, vol. 20, no. 5, pp. 535-
563, 1990.
[35] Investopedia, "Return On Invested Capital - ROIC," 2015. [Online]. Available:
http://www.investopedia.com/terms/r/returnoninvestmentcapital.asp. [Accessed 2015].
[36] Investopedia, "Profit Margin," 2015. [Online]. Available:
http://www.investopedia.com/terms/p/profitmargin.asp. [Accessed 2015].
[37] SunPower, 2015. [Online]. Available: http://us.sunpower.com/.
[38] J. Church and R. Ware, Industrial Organization: A Strategic Approach, United States: The
McGraw-Hill Companies, 2000.
[39] B. Halvorson, "Will Low Resale Values Spoil The Cost Benefits Of Electric-Car Ownership?,"
2013. [Online]. Available: http://www.thecarconnection.com/news/1089368_will-low-resale-
values-spoil-the-cost-benefits-of-electric-car-ownership. [Accessed 2015].
[40] C. Rogers, "Resale Prices Tumble on Electric Cars," 2015. [Online]. Available:
http://www.wsj.com/articles/resale-prices-tumble-on-electric-cars-1424977378. [Accessed 2013].
[41] RAND, "Vehicle Production and Lifecycle Cost," [Online]. Available:
https://www.rand.org/content/dam/rand/pubs/monograph_reports/MR1578/MR1578.ch4.pdf.
[Accessed 2015].
[42] K. Aguirre, L. Eisenhardt, C. Lim, B. Nelson, A. Norring, P. Slowik and N. Tu, "Lifecycle
Analysis Comparison of a Battery Electric Vehicle and a Conventional Gasoline Vehicle," 2012.
[Online]. Available:
http://www.environment.ucla.edu/media/files/BatteryElectricVehicleLCA2012-rh-ptd.pdf.
[Accessed 2015].
[43] E. Dodge, "The Case for Electric Vehicles, Part 2: EV Costs," 2014. [Online]. Available:
http://breakingenergy.com/2014/10/02/the-case-for-electric-vehicles-part-2-ev-costs/. [Accessed
2015].
[44] R. D. Shachter, "Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite
Information in Belief Networks and Influence Diagrams)," Morgan Kaufmann Publishers Inc. San
Francisco, 1998.
[45] Tesla Motors, "About Tesla," 2016. [Online]. Available: https://www.teslamotors.com/about.
[46] The Dialogue, "Tesla Cars Evolution," 2016. [Online]. Available: http://www.the-
dialogue.com/en/en21-tesla-cars-evolution/.
CHAPTER 4 — References 215
[47] UCSUSA, "Electric Vehicle Timeline," 2015. [Online]. Available:
http://www.ucsusa.org/clean_vehicles/smart-transportation-solutions/advanced-vehicle-
technologies/electric-cars/electric-vehicle-timeline.html#.Vi6kuLerQdU. [Accessed 2015].
[48] SolarCity, "SolarCity delivers Better Energy," 2016. [Online]. Available:
http://www.solarcity.com/company/about.
[49] GTM, "Here Are the Top 5 Residential Solar Installers of 2014," Greentech Media, 2015. [Online].
Available: http://www.greentechmedia.com/articles/read/Here-Are-the-Top-Five-Residential-
Solar-Installers-of-2014. [Accessed 2015].
[50] SEIA, "Solar Industry Data," 2015. [Online]. Available: http://www.seia.org/research-
resources/solar-industry-data. [Accessed 2015].
[51] J. Burr, T. Dutzik, J. Schneider and R. Sargent, "Shining Cities - At the Forefront of America’s
Solar Energy Revolution," Environment America Research & Policy Center , 2014.
[52] E. Musk, "The Secret Tesla Motors Master Plan (just between you and me)," Tesla Motors, United
States, 2006.
[53] M. E. Porter, "The Contributions of Industrial Organization to Strategic Management," The
Academy of Management Review, pp. 609-620, 1981.
[54] M. G. Morgan, M. Henrion and M. Small, "Performing Probability Assessment," in Uncertainty: A
Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, New York,
Cambridge University Press, 1990.
[55] C. S. Spetzler and C.-A. S. S. V. Holstein, "Probability Encoding in Decision Analysis,"
Management Science, vol. 22, no. 3, pp. 340-358, 1975.
[56] M. A. Hitt, M. T. Dacin, B. B. Tyler and D. Park, "Understanding the Differences in Korean and
U.S. Executives' Strategic Orientations," Strategic Management Journal, vol. 18, no. 2, pp. 159-
167, 1997.
[57] R. A. Howard, "Decision Analysis: Practice and Promise," Management Science, vol. 34, no. 6, pp.
679-695, 1988.
[58] L. Neal and C. Spetzler, "An Organization-Wide Approach to Good Decision Making," Harvard
Business Review, Cambridge, 2015.
[59] C. S. Spetzler, "Chevron Overcomes the Biggest Bias of All," Strategic Decision Group, Palo Alto,
2011.
216
Chapter 5
DAFF Modeling of Competitive Strategy:
Positioning in the Near-Future U.S.
Residential Solar PV Industry
1 Introduction
Decision analytic modeling of the five forces strategic framework (DAFF) offers a robust and
quantitative approach to competitive analysis. After introducing the foundations of DAFF in
Chapter 4, this Chapter aims to demonstrate the applicability of DAFF by using it to evaluate
the competitive strategy of a major solar firm in the United States. Specifically, we undertake
a case study that aims to answer two questions: Is the competitive landscape in the U.S.
residential solar photovoltaic (PV) industry favorable between 2014 and 2016? And if so,
where should the solar firm position its residential business?
To answer these two questions, the authors of this study joined the solar firm’s strategic
planning team in the summer of 2014 and worked on developing two models: a DAFF
Bayesian Network and a DAFF Decision Diagram. Consistent with our explanation in Chapter
4, both DAFF models help the firm fulfill the first objective of competitive strategy, namely,
choose an appropriate positioning track within the target industry. In collaboration with the
company’s residential and strategic planning teams, this study completes the first two steps of
the positioning objective. First, we assess the competitive landscape and profitability of the
overall U.S. residential solar PV industry. Then, we identify a series of unique positioning
CHAPTER 5 — Introduction 217
segments in the industry, and we analyze the profitability of each of those segments. Although
the work does not proceed to the third step of assessing the firm’s specific profitability in
every positioning segment, the first two steps prove sufficient to deliver valuable insights into,
and therefore to make clear recommendations on, the optimal positioning strategies. Here, we
note that in order to freely discuss and publically share the DAFF models’ inputs and outputs,
it was necessary that we refrain from disclosing the real identity of the solar firm in this case
study. Therefore, we shall conveniently refer to the firm as “SunEnergy” throughout this
Chapter.
The subsequent sections of this case-study competitive analysis proceeds as follows. First, we
provide a brief overview of the residential solar PV industry in the United States and some
background information on the examined solar firm. In Section 2, we explain how to develop
the DAFF models for SunEnergy’s positioning. In the first step aiming to analyze competition
in the overall industry, we build a DAFF Bayesian Network and describe its various
components, including: the five forces, their underlying drivers, the industry-specific factors,
and the economic parameters. Then, in the second step aiming to analyze various positioning
segments within the industry, we describe a series of Value Proposition and Value Chain
decisions that are important to SunEnergy. Adding those decisions to the DAFF Bayesian
Network yields a DAFF Decision Diagram. In Section 3, we explain the results from both
modeling steps. The first step allows assessing not only the uncertain power of each of the five
competitive forces but also the probabilistic interdependence among these forces. The DAFF
Bayesian Network also outputs probability distributions for the average cost, price, and annual
sales, as well as an expected average profit value for all industry incumbents. In the second
step, the DAFF Decision Diagram yields an expected profit value for each possible
positioning track, and we demonstrate the influence of the various positioning alternatives on
the power of each competitive force. We end this section by distilling the outputs from the
DAFF models into a clear and actionable list of recommendations regarding SunEnergy’s
positioning strategy in the U.S. residential solar PV market. Finally, Section 4 concludes this
case study by offering a summary of the main findings, reflecting on the advantages and
limitations of the DAFF modeling endeavors, and discussing how this analysis can be further
expanded in the future.
CHAPTER 5 — Introduction 218
1.1 The U.S. Residential Solar PV Industry
The United States has witnessed a tremendous growth in the deployment of solar photovoltaic
(PV) energy systems over the past few years [1]. Between 2010 and 2014, the yearly solar
installations increased from 850 to about 6000 megawatts (MW) [2], and the total solar
workforce expanded from 93000 to roughly 174000 employees [3]. To put these figures in
context, we note that the capacity of an average nuclear power plant is on the order 1000 MW,
and its operation requires 400–700 full-time employees [4]. In addition, as reported by
Greentech Media, solar energy was the second-largest source of new electricity generation
capacity in 2013, exceeded only by natural gas [5]. Thus, beyond its vital role as a renewable
energy resource that can mitigate climate change [6], solar PV is progressively earning a
competitive and permanent place in the U.S. energy mix.
As the market for solar energy continues to develop and mature, the evolution of business
practices has carved out three distinct and relatively stable industries for solar PV:
residential, commercial and institutional (C&I), and utility. In accordance with Michael
Porter’s guidance on how to define industry boundaries [7], we recognize distinct product
offerings and competitive structures in the three solar industries, despite their shared
geographical scope. The major difference in product offerings is related to scale. Dictated by
the habits and needs of the electricity consumer, the size of the solar system varies by orders
of magnitude from one industry to the other: residential systems are usually 0.001–0.01 MW;
C&I systems are on the order of 0.01–1 MW; and utility systems are typically 1–100 MW [8].
Also related to system size is system maintenance. While utility solar systems are usually
equipped with sophisticated monitoring and remote-control capabilities to accurately predict
and adjust their real-time power output, C&I and residential systems may have simpler
capabilities, or even lack them altogether [9].
In terms of competitive structure, the most notable differences between the three industries are
those involving buyers and substitutes. The industries’ very labeling highlights their distinct
buyers: while the residential solar industry caters to households and homeowners, the C&I
solar industry targets for-profit and not-for-profit organizations, and the utility solar industry
focuses on serving electric utilities. Obviously, these solar customers differ drastically in their
CHAPTER 5 — Introduction 219
organizational hierarchies, decision-making processes, financial capabilities, and needs.
Specifically, the different needs are illustrated not only in the aforementioned scale and
specifications of the solar system but also in what can feasibly substitute it. A homeowner
aiming to reduce his electricity bill may substitute the rooftop solar panels with a direct-load-
control or demand-response subscription [10, 11]. On the other hand, a commercial customer
aiming to offset its carbon emissions or to enhance its “green” branding may choose to build
or invest in a wind farm, an option that is not feasible for households [12]. Finally, in order to
reduce the carbon intensity of its power generation fleet, a utility may choose to retrofit some
of its existing fossil-fuel plants with carbon capture and storage systems instead of developing
new solar farms [13]; such alternative is available to neither residential nor C&I customers.
Although different solar regulations may be imposed in different states, these regulations share
the same underlying objectives such as managing access to the grid, providing financial
subsidies, or designing roadmaps to accelerate large-scale deployment [14]. This common
regulatory foundation, in addition to interstate free trade, makes it reasonable to assume that
the whole U.S. is the proper geographical scope for all three solar industries.
For this case study, we focus solely on the residential solar PV industry in the United States.
In 2014, about 20% of the 6000 MW installed solar capacity was residential in nature,
corresponding to a market size of roughly $5.6 billion [15]. With an average annual growth
rate around 50% between 2011 and 2014, industry analysts predict that “the outlook for the
U.S. residential solar market is extremely bright” [15, 16]. Different firms adopt different
business models in the industry, with activities that include the production, sales, installation,
financing, and servicing of solar panels. In 2014, despite the relatively large number of solar
installers, only 10 firms were responsible for installing 60% of the added capacity, two of
which installed more than 45% of that capacity. In addition, about two-thirds of the residential
systems today are categorized as “third-party ownership” (TPO), which means that they are
owned (e.g. leased) by the solar firm instead of the actual end-customer. In fact, 90% of the
TPO systems are owned by seven solar firms only, many of which are major installers. This
business reality, enforced by a series of recent mergers and acquisitions, seems to be
consolidating the residential solar industry around a few incumbents [15], one of which is the
focus of this case study: SunEnergy.
CHAPTER 5 — Methodology: Developing the DAFF Models 220
1.2 The Solar Firm
Through 2014 – the time of conducting this analysis – SunEnergy was an established solar
company with diverse business operations that include the design, production, installation,
operation, monitoring, maintenance, and financing of solar energy projects. The company
housed a large number of employees and installed numerous solar systems in multiple
locations across the U.S.
SunEnergy succeeded in becoming an established player in the utility and C&I solar
industries, but its residential business was still in relatively early stages. At the same time, the
company was aware of the wide consensus among experts’ predictions regarding the steady
growth of residential solar this decade [16, 17, 18]. Given its history in the solar business, and
motivated by the prospects of furthering its growth, SunEnergy became increasingly interested
in expanding its activities in the U.S. residential solar industry.
2 Methodology: Developing the DAFF Models
Before delving into any modeling details, we first need to define a proper timeframe for the
competitive analysis and therefore for the DAFF models. In consultation with SunEnergy’s
strategic planning and residential solar business teams, the timeframe was set to cover the
upcoming two years, extending from the fall of 2014 through the end of 2016. Consistent with
our notes in Chapter 4, this near-future timeframe allows SunEnergy to position where its
competitors are least threating, but it is not sufficient, nor intended, to exploit or modify the
strategic behavior of those competitors.
Also important to DAFF modeling is designating a specific decision-maker. Multiple parties
may contribute to information gathering and data analysis, but one decision-maker shall have
the final say on the inputs into the DAFF models. In this study, multiple members of
SunEnergy’s strategic planning and residential business teams collaborated to supply and
analyze market information, but the Director of Strategic Planning was the designated
decision-maker.
CHAPTER 5 — Methodology: Developing the DAFF Models 221
With that in mind, we rely on GeNIe to perform all the DAFF modeling in this case study.
Developed by the Decision Systems Laboratory at the University of Pittsburgh, GeNIe is an
open-access software package that is widely used to design and analyze decision-theoretic
models [19].
2.1 First Step: Assess the Overall Industry
In this step, we develop a DAFF Bayesian Network to analyze competition and its impact on
the economic performance of the overall residential solar PV industry in the U.S. As discussed
in Chapter 4, this endeavor requires a detailed characterization of: the five competitive forces
and their underlying drives; the regulatory, technological, and growth-rate factors; and the
economic parameters that determine the industry’s profitability.
2.1.1. Competitive Forces and Drivers
For every competitive force, the DAFF modeling requires: identifying a set of driver
uncertainties that are relevant to the force uncertainty, defining the possible realizations (i.e.
degrees) of the force and each driver uncertainty, assigning probabilities over these degrees,
and then computing the output probability distribution over the power of the force.
We offer a detailed account of these requirements for the force of Substitutes, whose network
of driver uncertainties is illustrated in Figure 5.1. To start, we define substitutes as “any
product or service that residential customers can use to reduce their electricity bill.” In that
regard, potential substitutes may include smart meters, smart thermostats, more efficient home
appliances, or direct-load-control and demand-response subscriptions. As shows in Figure 5.1,
the power of Substitutes is conditioned on three parent drivers: Price-performance tradeoff
relative to this industry product, Regulatory and technical feasibility, and consumer switching
cost from this industry product to substitutes. The power of Substitutes is more likely to be
high when potential solar substitutes offer better price-performance tradeoff, are backed by
more favorable regulations, are more technically feasible, or can be easily adopted by a
disgruntled solar customer.
CHAPTER 5 — Methodology: Developing the DAFF Models 222
Figure 5.1: DAFF modeling of the force of Substitutes and its relevant drivers
To achieve clarity, we condition the probabilistic analysis of the Price-performance tradeoff
relative to this industry product uncertainty on three criteria that are deemed important by
SunEnergy: Substitute performance, Substitute upfront cost, and Substitute bill savings; each
of these criteria is modeled as a parent driver node to the Price-performance tradeoff relative
to this industry product node. Subsequently, to further inform the analysis of the Substitute
performance driver, we condition it on three additional drivers: Substitute installation and
maintenance, Substitute control and operation, and Substitute climate impact; reasonably, a
substitute is more likely to outperform a solar system if it is faster to install and maintain,
easier to automate, or more capable of reducing greenhouse gas emissions. Similarly, already
illustrating one form of interaction between two competitive forces, we assert that the solar
Product perceived cost as fraction of the customer budget (Buyers driver) may help inform the
Threat of substitutes
Price-performance tradeoff relative to
this industry product
Product perceived
cost as fraction of
the customer
budget
Regulatory and technical
feasibility
Customer switching cost from this
industry product to substitutes
Substitute upfront
cost
Substitute bill savings
Substitute performance
Substitute climate impact
Substitute control & operation
Substitute installation & maintenance
Cost reduction
for customer
by industry product
Substitutes
Buyers
CHAPTER 5 — Methodology: Developing the DAFF Models 223
analysis of the Substitute upfront cost, and the Cost reduction for customer by industry
product (another Buyers driver) may help inform the analysis of the Substitute bill savings.
Finally, because home energy technologies and regulations continue to evolve, the analysis of
the Regulatory and technical feasibility driver is conditioned on uncertain regulatory and
technological factors, as we discuss in the next Section.
After introducing and connecting the force and driver uncertainties, we proceed to define and
characterize their degrees. As explained in Chapter 4, each uncertainty is characterized by two
or more mutually exclusive and collectively exhaustive (MECE) degrees, representing the
possible resolutions of that uncertainty in the future. In our work with SunEnergy’s teams, we
also make an effort to quantify the definitions of the driver degrees, to the extent possible.
Each degree is then assigned a probability, indicative of the decision-maker’s beliefs about its
future realization. In this case, SunEnergy’s probability assignments reflect the company’s
collective intelligence on the competitive landscape over the next two years.
Referring back to the uncertainty network for Substitutes in Figure 5.1, we demonstrate the
degree definitions and probability assignments for all uncertainty nodes with red borders.
Figures 5.2–5.5 are snapshots of the assessment tables for these uncertainties, obtained
directly from the GeNIe DAFF model. We start with the most ancestral driver in Figure 5.2:
Cost reduction for customer by industry product. Here, the two quantifiable MECE degrees
benchmark cost reductions from the solar system against the homeowner’s electricity bill; they
are defined as: {<15% reduction in power bill} and {>15% reduction in power bill}. Because
this uncertainty has no parents, each of its degrees is assigned an unconditional probability
value, and the two probability values sum up to one.
Similarly, two MECE degrees are defined for the Substitute bill savings driver in Figure 5.3:
{less bill savings} and {more bill savings} (compared to a solar system). However, this
uncertainty is conditioned on one parent – the aforementioned Cost reduction for customer by
industry product driver – and so is the probability distribution over its two degrees.
Accordingly, for every prospect of the parent uncertainty, the two degrees are assigned distinct
probability values that add up to one. For instance, given that a solar system achieves
224
Figure 5.2: Example probabilistic analysis of a driver: Cost reduction for customer by industry product
Figure 5.3: Example probabilistic analysis of a driver: Substitute bill savings
225
Figure 5.4: Example probabilistic analysis of a driver: Price-performance tradeoff relative to this industry product
Figure 5.5: Example probabilistic analysis of the power of Substitutes
CHAPTER 5 — Methodology: Developing the DAFF Models 226
{<15% reduction in power bill}, the probability of customers enjoying {less bill savings}
from substitutes is 0.25 whereas the probability of {more bill savings} is 0.75; conversely,
given that a solar system achieves {>15% reduction in power bill}, these probabilities change
to 0.8 and 0.2, respectively. Accounting for all these potential scenarios, the DAFF model then
computes an overall probability distribution for Substitute bill savings, outputting a 0.61
probability for {less bill savings} and a 0.38 probability for {more bill savings}.
Three degrees are also modelled for the Price-performance tradeoff relative to this industry
product driver in Figure 5.4: {substitute superior to solar}, {substitute equivalent to solar},
and {substitute inferior to solar}. In this case, each degree is assigned eight distinct
conditional probability values, corresponding to eight distinct parental prospects; for each
prospect, the probability values of the three degrees sum up to one. For example, given that
the substitutes yield {less bill savings}, {high upfront costs}, and {inferior performance}
compared to the solar system, the probability of {substitute superior to solar} is 0.01 whereas
the probability of {substitute inferior to solar} is 0.98. By balancing the evaluations of all
prospects, the DAFF model outputs an overall probability distribution for the three degrees of
the Price-performance tradeoff relative to this industry product driver: 0.29 for {substitute
superior to solar}, 0.25 for {substitute equivalent to solar}, and 0.46 for {substitute inferior to
solar}. This means that, per SunEnergy’s intelligence, solar panels are likely to offer better
price-performance tradeoff to customers than other home energy equipment or services.
Analyzing the two degrees {high} and {low} of the power of Substitutes in Figure 5.5 follows
the same logic. Each degree is assigned 12 distinct conditional probabilities corresponding to
12 distinct combinations of parental prospects; for each parental prospect, the probability
values of the two degrees add up to one.
Before ending this discussion on modeling the force of Substitutes and its drivers, we make an
important note. Compared to the original DAFF modeling of Substitutes in Chapter 4, Figure
5.1 introduces three changes. First, we expand the analysis of Price-performance tradeoff
relative to this industry product driver by conditioning it on six new ancestral drivers. Second,
we add the parent driver Regulatory and technical feasibility. Third, we eliminate the original
driver Availability of substitutes for this industry’s products. Based on available market data,
CHAPTER 5 — Methodology: Developing the DAFF Models 227
we know, with certainty, that substitutes do exist for residential solar panels, including gadgets
such as smart thermostats [20] and services such as demand-response programs [21, 22].
SunEnergy’s belief about the persistence of the substitutes’ availability and variety in the near
future cancels the need for analyzing this driver uncertainty. As will become evident, all these
DAFF customizations are necessary not only to fit the specific context of the investigated
residential solar industry in the U.S. but also to help SunEnergy’s decision-makers understand,
analyze, and communicate relevant information and findings.
The DAFF modeling of the other four competitive forces and their underlying drivers
proceeds in a very similar fashion. The resulting Bayesian network connecting the various
competitive force and driver uncertainties is presented in Figure 5.6, and a full list of their
degrees is presented in Appendix A. At this point, we provide a brief overview of the DAFF
modeling for the remaining four forces: Buyers, New Entrants, Rivals, and Suppliers.
When analyzing the power of Buyers, the nature of the residential solar business necessitates
that we distinguish between two types of buyers: end-customers and dealers. Similar to their
role in the auto industry, dealers act as intermediaries that help deliver the solar system to the
final end-customer – the household in this case. However, unlike auto manufacturers in most
states, residential solar developers are allowed to directly sell and service end-customers
without the need to engage dealers in the transaction.
To capture this competitive configuration, we condition the uncertain power of Buyers on two
uncertain parent drivers: Power of end-customers and Power of dealers. Subsequently, the
analysis of these two drivers is further informed by conditioning them on three levels of
additional ancestral drivers. The Power of end-customers is conditioned on the Customer price
sensitivity and the Customer switching cost away from this industry product, which in turn are
further shaped by investigating the customers’ need for the solar system and their ability to
afford it. Equivalently, the Power of dealers is conditioned on the Dealer ability to influence
customers downstream, Dealer volume of sales per incumbent, and Dealer threat to integrate
backward, which in turn are further shaped by examining the dealers’ brands, business
models, and geographical scope of reach. Intuitively, dealers with strong brands, preferential
access to populated residential areas, or national footprint are more likely to have
228
Figure 5.6: DAFF modeling of all competitive forces and drivers in the U.S. residential solar PV industry
Threat of new
entrants
Barriers to entry
Expected retaliation
Previous responses
by incumbents
Relative reliance of customer on
industry product
Bargaining Power of Suppliers
Customer switching cost
among industry products
Concentration of suppliers relative to
incumbents
Fragmentation of the industry
Relative dependence of suppliers
on this industry profits
Incumbent switching
costs between suppliers
Supplier switching
cost between
incumbents
Product differentiation
among suppliers
Availability of substitutes for
what the supplier provides
Supplier threat to integrate foreword
Threat of substitutes
Price-performance tradeoff relative to
this industry product
Commitment of incumbent to
retain and fight over market
share
Product differentiation
among incumbents
Bargaining Power of
Buyers
Costumer price
sensitivity
Product perceived
cost as fraction of
the customer
budget
Dealer ability to influence
customers downstream
Dealer threat to integrate backward
Customer switching cost away from the
incumbent product
Rivalry
Intensity of competitionBasis of
competition
Ability to enforce
practices desirable for whole industry
Extent of exit
barriers
High commitment to business
Customer need to trim immediate
cost of industry product
Willingness of price
discounting by incumbents
Inability to read other
incumbents’ signals
Importance of non-profit
goals
Incumbent joint
investments with current
supplier
Number of industries supplier
serve
Profits extracted by
suppliers from other
industries
Regulatory and technical
feasibility
Dealer partnership
with incumbent
Customer switching cost from this
industry product to substitutes
Substitutes
Buyers
New Entrants
Rivals
Suppliers
Substitute upfront
cost
Substitute bill savings
Substitute performance
Substitute climate impact
Substitute control & operation
Substitute installation & maintenance
Power of end-customers
Power of dealers
Dealer volume of sales per
incumbent
Dealer reach
Dealer brand
Performance improvement for customer by industry
product
Amount of cash
available for
customer
Cost reduction
for customer
by industry product
Size dependent
disadvantages for new entrant
Size independent
disadvantages for new entrant
Unequal access to
distribution channel by
new entrant
Customer adoption
rate of product by new entrant
Extent of resources available
for incumbents
Incumbent economies
of scaleIncumbent
prime location
Incumbent cumulative
in-house experience
Incumbent established
brand
Incumbent IP
Control over
distribution channel by incumbent
Limitation of distribution
channels
Size and availability of capital
needed by new
entrant
Incumbent assets
Incumbent R&D
spending
Incumbent customer acquisition cost
Efficiency of capital markets
Incumbent network effects
Customer trust in
incumbent
Excess cash
Borrowing power
Available production
capacity
Market segmentation
Ability to meet the needs of multiple
customer segments
High fixed costs
and low variable
costs
Presence of an
industry leader
Incumbent inventory
CHAPTER 5 — Methodology: Developing the DAFF Models 229
higher bargaining power. Ultimately, the power of Buyers is more likely to be high when the
power of either the end-customers or the dealers is high.
The ancestral drivers for the Power of end-customers are consistent with the original DAFF
modeling of the Buyers force in Chapter 4. In contrast, the Power of dealers ancestral drivers
emerged during our discussions with SunEnergy’s teams; business experts believe that these
uncertainties play an important role in shaping competition within the residential solar
industry and therefore must be accounted for.
Moving on, Figure 5.6 shows that the analysis of the power of New Entrants is informed by
several drivers. These drivers are structured over three ancestral levels, starting with two
parents: Barriers to entry and Expected retaliation. Reasonably, the power of New Entrants is
more likely to be low when new firms in the industry either struggle to overcome steep
barriers to entry or expect fierce retaliation by incumbents upon entry. To facilitate its
probabilistic assessment by the decision-maker, Barriers to Entry is conditioned on five
drivers. The Size dependent disadvantages for new entrant driver accounts for the economies
of scale achieved by current solar incumbents whereas the Size independent disadvantages for
new entrant driver accounts for the incumbents’ brands, intellectual property (IP), human
capital, and geographical spread. Indeed, current residential solar firms seem to be proactive in
building strong brands and IP, with examples ranging from SolarCity’s famous “green trucks”
to SunPower’s, SolarCity’s, and Panasonic’s continuous fight to claim the “most efficient
rooftop solar panel” title [23, 24]. Equivalently, the Unequal access to distribution channel by
new entrant driver examines the extent to which current incumbents have access and control
over the distribution channels of solar systems. Then, the fourth driver, Customer adoption
rate of product by new entrant is shaped by the networking effects in the industry as well as
by the reliance of the customer on the solar system; new entrants are more likely to enjoy high
adoption rates of their product when the networking effects among existing incumbents are
weak, when the solar savings are high, and when the switching costs for the customer are low.
Finally, the Size and availability of capital needed by new entrant driver is informed by key
financial attributes such as the efficiency of the available capital markets, as well as the
customer acquisition cost, R&D spending, assets, and inventories of the incumbents.
CHAPTER 5 — Methodology: Developing the DAFF Models 230
Similarly, Expected retaliation is conditioned on four drivers: Extent of resources available for
incumbents, Previous responses by incumbents, Willingness of price discounting by
incumbents, and Commitment of incumbent to retain and fight over market share. The Extent
of resources available for incumbents is further clarified by accounting for the incumbent’s
excess cash, production capacity, and borrowing power. With that in mind, a new entrant is
more likely to experience fierce retaliation if the solar incumbents have deep pockets and/or
are capable and willing to engage in price wars, fight over market share, pursue hostile
acquisitions, or match their competitors’ offers.
While this DAFF modeling of the New Entrants preserves the overarching Bayesian structure
presented in Chapter 4, it eliminates and rearranges multiple driver uncertainties – and the
relevance arrows linking them – in order to ease the probabilistic analysis. For example, the
decision-maker felt more comfortable evaluating how the Unequal access to distribution
channels directly affects the strength of Barriers to Entry, without considering the Need to
bypass incumbent existing advantages by new entrant; as a result, the latter driver does not
appear in Figure 5.6.
As for the power of Rivals, Figure 5.6 shows that Rivalry is conditioned on three direct parent
drivers: Basis of competition, Intensity of competition, and Inability to read other incumbents’
signals. Those drivers are, in turn, conditioned on two ancestral levels of causal drivers. For
example, the assessment of the Basis of competition driver is better informed by conditioning
it on four additional drivers that convey the following story: rivals are more likely to lead
price-based competition if the solar market is homogenous and segmentation is limited (e.g.
all solar customers are homeowners with bad credit score); if the differentiation in solar
offerings is short-term or nonexistent (e.g. all solar systems come with free installation or in
one color); if the customers’ switching costs are low (e.g. customers face little legal
complications or penalties); and if the competitors’ willingness to discount price is high (e.g.
companies make frequent special offers around the year). Equivalently, the Intensity of
competition driver is shaped by another four drivers that examine the rivals’ inclination to:
collaborate, exit the industry, defend current revenue from the industry, and maintain current
market-share in the industry. Ultimately, the power of Rivals is more likely to be high if
competition among the current incumbents is price-based, intense, and not transparent.
CHAPTER 5 — Methodology: Developing the DAFF Models 231
In comparison to the original DAFF modeling presented in Chapter 4, we, here again, either
eliminate or rearrange relevance among some of the Rivals drivers in order to simplify their
probabilistic evaluation. For instance, the decision-maker was able to evaluate the Inability to
read other incumbents’ signals driver directly, without needing to condition it on the Lack of
familiarity with incumbents; the latter driver uncertainty is therefore excluded from Figure 5.6.
Finally, to evaluate the power of Suppliers, we first limit our definition of solar suppliers to
“component providers” (e.g. solar modules, microinverters, etc.) and “customer-lead
generators.” With that in mind, we condition the force of Suppliers on five direct parent
drivers. Supplier switching cost between incumbents and Incumbent switching cost between
suppliers drivers gauge the relative ability of either an incumbent or a supplier to credibly
threaten the other party with ending their dealings; for instance, if solar firms can easily
replace their microinverter suppliers, the latter are more likely to have low bargaining power.
In that regard, analyzing the Incumbent switching cost between suppliers can be further
informed by examining three additional ancestral drivers: Product differentiation among
suppliers, Availability of substitutes for what the supplier provides, and Incumbent joint
investments with current supplier. The third driver of Suppliers’ power is the Relative
dependence of suppliers on this industry profits, which in turn can be better evaluated by
looking into the Profits extracted by suppliers from other industries as well as the Number of
industries the supplier serve. The last two drivers that help assess Suppliers power are:
Supplier threat to integrate forward and Concentration of suppliers relative to incumbents.
Eventually, Suppliers are more likely to have high bargaining power in the residential solar
industry if they: can easily replace their customer incumbents, are diversified enough and only
generate a minor portion of their revenue or profit from this industry, have enough resources
to credibly threaten entering into this industry, or are highly concentrated.
Compared to the original DAFF modeling of Suppliers in chapter 4, only one driver -
Incumbent’s production location near current suppliers – is excluded from the Bayesian
network in Figure 5.6. This driver is eliminated because it is known with certainty: current
market data confirms the existence of a multitude of solar suppliers all around the globe, many
of which can be easily accessed by the residential solar firms in the U.S. [25, 26].
CHAPTER 5 — Methodology: Developing the DAFF Models 232
Broadly, while clarifying and simplifying the competitive analysis, all aforementioned
adjustments in the DAFF modeling of the competitive uncertainties remain consistent with,
and representative of, FF theory. We recall that the original goal of analyzing the competitive
drivers is to better inform the analysis of the competitive forces. Unavoidably, different
drivers may be more or less important in different industries. The competitive drivers in
Figure 5.6 are the ones that SunEnergy deem significant in the residential solar PV industry.
2.1.2. Technological, Regulatory, and Growth Factors
The DAFF modeling of the factor uncertainties is very industry-specific. Residential solar,
like all major energy businesses in the U.S., is heavily shaped by technological advances,
governmental regulations, and growth opportunities. In this case study, we model an extensive
list of Technology, Regulation, and Growth factors that, according to SunEnergy, are likely to
influence the industry’s competitive landscape in the near future. The DAFF modeling of
these factor uncertainties in a Bayesian network is presented in Figure 5.7, and the definitions
of their degrees are listed in Appendix A. As with the competitive force and driver
uncertainties, we aim to quantify the degrees of the factor uncertainties, to the extent possible.
Starting with the Technology factors, we do not envision substantial breakthroughs in solar
technologies within the timeframe of this competitive analysis. However, we recognize the
potential proliferation of two important technologies that may be relevant to residential solar:
electric vehicles [27] and storage batteries [28, 29]. Because electric vehicles are mostly
charged at home [30, 31], their adoption may change the profile of grid-electricity usage in the
household, which we describe in terms of “total demand” and “peak demand”. The rise of
electric vehicles is also relevant to the spread of battery storage systems since, fundamentally,
both consumer products rely on the advancement in battery technologies [32]. While battery
storage systems do not change the household’s total demand for electricity from the grid, they
can help shift this demand from one time period to the other, therefore reducing the home’s
peak demand. Ultimately, the change in the home’s total and peak demand due to electric
vehicles and battery storage might change the size of the home solar system, which is
otherwise heavily dictated by enacted regulations. In that regard, electric vehicles and storage
233
Figure 5.7: DAFF modeling of Technology, Regulation, and Growth factors in the U.S. residential solar PV industry
Substitutes
Buyers
New Entrants
R1: Power market structure
R2: magnitude of utility rates
R3: hourly variation in utility rates
R5: Solar system control
R4: Solar system
connectivity charges
R8: Solar rate
R7: Solar system cap
R9: Solar net-negative
compensation structure
R6: Solar territorial
cap
T1: Proliferation of electric vehicles
T2: Proliferation of storage batteries
T3: Change in home total
demand
R10: Application
of ITC & Depreciation
T4: Change in home peak
demand
T5: Change in size of home solar system
T6: Optimal size of home solar
system
R11: Exploitation
of FMV
G1: Industry growth rate
Substitute bill savings
Substitute control & operation
Regulatory and technical
feasibility
Substitute climate impact
Cost reduction for customer by industry
product
Performance improvement for customer by industry
product
Product perceived cost as fraction of the customer
budget
Relative reliance of
customer on industry product
Customer need to trim immediate cost of industry
product
Commitment of incumbent to retain and
fight over market share
Excess cash
Rivals
Suppliers
Factors
CHAPTER 5 — Methodology: Developing the DAFF Models 234
batteries can be viewed not only as relevant technologies but also as major complements to
residential solar, and by analyzing their prospects, we account for two of Porter’s four factors.
We model the impact of both complementary technologies in a series of six Technology
uncertainty nodes, labelled T1 through T6 in Figure 5.7.
In addition, we investigate 11 Regulation uncertainties that cover both the mechanical and the
financial aspects of the residential solar business; those factors are labelled R1 through R11 in
Figure 5.7. First, we consider the overall structure of electricity markets in the U.S. (R1),
focusing on the extent of deregulation that may occur in the next two years [33, 34, 35]. Given
our knowledge about deregulation, we then assess the magnitude (R2) and hourly variations
(R3) of electricity rates that homeowners pay their utilities. By triggering certain behavioral
changes in the way people consume power, those rates might impact the home’s total and/or
peak demand. Other Regulation factors assess whether a utility would charge specific fees to
connect the residential solar systems to the grid (R4), would demand direct and full control of
the residential solar systems under its jurisdiction (R5), or would impose an upper cap either
on the total capacity of solar installations in a specific area (R6) or on the capacity of a single
solar system (R7). We also evaluate the uncertainty around the rate (R8) and payment
schedule (R9) for any excess solar energy that the household produces and sends back to the
grid. As shown in Figure 5.7, the regulated solar rates and capacity caps influence not only the
optimal size of the residential solar system but also how it is likely change in the presence (or
absence) of the aforementioned complementary technologies.
The last two Regulation factors – R10 and R11 – focus on the financing of the residential solar
systems. Currently, solar installations across the country are eligible for a 30% “investment
tax credit” (ITC), granted to the legal owner of the solar system [36]. If the project developer
(e.g. SunEnergy) owns and operates the system for the homeowner, it can realize additional
savings by applying an accelerated depreciation schedule to the system’s net present value
(NPV) [37]. While both forms of subsidies remain active and available till the end of 2016,
R10 captures the uncertainty around how and to what extent they will be utilized. In R11, we
investigate whether the “fair market value” (FMV) rules are exploited by industry incumbents.
A solar company that owns and operates a residential solar system has to report that system’s
FMV in its tax forms [38], which in turn determines the amount of tax subsidies it receives.
CHAPTER 5 — Methodology: Developing the DAFF Models 235
Recently, the Treasury Department has detected a controversial practice whereby some solar
firms may be inflating the FMV in order to increase their tax subsidies [39]. The last factor
uncertainty we model is the industry growth rate (G1), which, as depicted in Figure 5.7, might
be relevant to the proliferation of complementary technologies.
Now, after identifying and connecting the various factor uncertainties, it is crucial that we
analyze the relevance relations between these factors and the competitive forces and drivers.
In Figure 5.7, we connect the factors to multiple competitive drivers using relevance arrows.
Those arrows reflect SunEnergy’s beliefs on how the aforementioned Technology, Regulation,
and Growth factors shape competition in the residential solar industry. Obviously, SunEnergy
seems to be more concerned with industry factors that affect the downstream side of business.
By influencing the attractiveness of the solar system relative to its substitutes, the modeled
Regulation and Technology uncertainties may be relevant to two competitive forces:
Substitutes and Buyers. In turn, the industry Growth may be relevant to three forces: Buyers,
New Entrants, and Rivals. While Growth may be dependent on the end-customers’ needs and
budgets for the solar panels, it may change the urgency of market-share fights by, as well as
the availability of investment cash for, both current rivals and future new entrants.
Notably, Figure 5.7 shows no relevance arrows from or into the FMV factor. The reasoning is
that FMV does not impact the competitive landscape, but it directly affects the economics of
residential solar projects and therefore the profitability of the overall industry. In fact, multiple
other factors also have a direct impact on the industry economics. These attributes of the
competitive analysis are expounded in the next section, where we model both the economic
parameters for the residential solar industry as well as the relevance relations that these
parameters exhibit with the competitive forces, drivers, and factors.
2.1.3. Economic Parameters
The economic parameters are the last necessary component for developing a complete DAFF
Bayesian Network and therefore for assessing competition in the overall industry. As
explained in Chapter 4, these economic parameters account for the industry’s average cost,
CHAPTER 5 — Methodology: Developing the DAFF Models 236
price, quantity, and ultimately, profitability. The DAFF modeling of the economic parameters
is presented in Figure 5.8.
To start, SunEnergy chooses the “cost of goods sold” (COGS) as the metric to measure the
average cost in the U.S. residential solar PV industry. By SunEnergy’s accounting, COGS
cover both the fixed operating expenses (FOPEX) and variable operating expenses (VOPEX)
of the business, spanning the following major categories: cost of the solar kit (e.g. solar
modules and balance of system); installation fees (e.g. labor and permitting); sales and
marketing (e.g. customer acquisition cost); and general, admin and R&D. Nonetheless,
because many of the U.S. solar firms operate either internationally [40, 41] or in multiple solar
industries (residential, C&I, and utility) [9], it is hard to distinguish the capital investments
associated with their residential solar business in the U.S. only; for instance, investments in
panel manufacturing facilities or administrative offices are shared across multiple corporate
business units. Consequently, to simplify the analysis, the capital costs are not accounted for
in this case study.
Based on public market information [42] and private corporate data, the COGS of residential
solar in the U.S. is modeled in Figure 5.8 as a Real Cost uncertainty with three possible
degrees: {2 $/W}, {3.5 $/W}, and {5 $/W}. Here, we make four important notes. Firstly, this
economic parameter captures the real cost of installing and operating one unit capacity of the
solar system, before accounting for any governmental subsidies. Secondly, we assert that the
selected numerical range – between 2 and 5 $/W – is informed by, and therefore is comparable
to, the cost figures observed in the industry over the past 3–5 years. From Chapter 4, we recall
that the industry economics should be evaluated over a full business cycle; in this case, we
estimate that a full business cycle in the U.S. residential solar PV industry is around 3–5 years.
Thirdly, the three numerical degrees denote an approximate discretized probability distribution
over a linear cost range between 2 and 5 $/W. For instance, if the decision-maker thinks that
the competitive circumstances render the cost around 4 $/W, he may assign a 0, 0.65, and 0.35
probability to the {2 $/W}, {3.5 $/W} and {5 $/W} degrees, respectively. This discretization
of an otherwise continuous random variable is robustly applied in decision analysis to
facilitate uncertainty assessment [43], and it proves beneficial here for computing the industry
237
Figure 5.8: DAFF modeling of the economic parameters in the U.S. residential solar PV industry
Substitutes
Buyers
New Entrants
Rivals
Suppliers
Factors
Real CostEffective
CostEffective
Price
Threat of new
entrants
Bargaining Power of Suppliers
Threat of substitutes
Bargaining Power of
BuyersRivalry
System UnitsTotal
Quantity
G1: Industry growth rate
T5: Change in size of
home solar system
T6: Optimal size of home solar system
R10: Application
of ITC & Depreciation
R11: Exploitation
of FMV
R4: Solar system
connectivity charges
EBT Economic Parameters
CHAPTER 5 — Methodology: Developing the DAFF Models 238
economics. Lastly, consistent with our DAFF modeling of Porter’s work, cost is influenced by
all five competitive forces, so a relevance arrow is added from each force uncertainty into the
Real Cost uncertainty.
Subsequently, for a given realization of Real Cost, we can model the effective cost that a solar
developer like SunEnergy actually incurs by factoring in any governmental subsidies (ITC and
depreciation), exploitations of FMV, and/or utility-imposed connectivity charges to the grid.
To that end, an Effective Cost uncertainty is modelled in Figure 5.8 with four parents: Real
Cost, R4: Solar system connectivity charges, R10: Application of ITC and Depreciation, and
R11: Exploitation of FMV. In addition, we model four numerical degrees for Effective Cost:
{0 $/W}, {2 $/W}, {4 $/W}, and {$6/W}. As before, those degrees denote a discretized
probability distribution over an effective-cost range between 0 and 6 $/W, which is
comparable with market data over the past 3–5 years.
In modeling the Effective Cost, we make a simplifying yet important assumption that
applicable governmental subsidies are always captured by the industry incumbent, even if the
end-customer is the legal owner of the solar system. One way to vindicate this assumption is
to think of a situation where the end-customer transacts subsidies freely and instantaneously
with the solar firm in exchange for a lower price. For example, if the homeowner buys a solar
system for $X and receives a subsidy of $Y, his effective price will be $(X–Y). Alternatively,
he can agree to transfer that $Y subsidy to the firm, and the firm will in return agree to reduce
the system price to $(X–Y). Once again, the homeowner’s effective price becomes $(X–Y).
Evidently, this modeling approach raises the notion of Effective Price, which we model as an
uncertainty in Figure 5.8. Formally, we define Effective Price as “the end-customer’s net
payment, and the industry incumbent’s net revenue, over the entire lifetime of the solar system
and after clearing all transactions of applicable governmental subsidies.”
Consistent with our DAFF discussions in Chapter 4, the Effective Price is conditioned on four
of the five competitive forces: Substitutes, Buyers, New Entrants, and Rivals. Furthermore,
since both costs and prices are ultimately decided by the firm, the Effective Price is also
conditioned on the Effective Cost. Three primary arguments justify this relevance. First, it is
reasonable to assume that the solar developer shall never want to set the Effective Price below
CHAPTER 5 — Methodology: Developing the DAFF Models 239
the Effective Cost, in which case it would suffer negative returns. Second, firms with
drastically different costs are unlikely to set the same price for their product; intuitively, a
low-cost competitor may be inclined to adopt a low-price strategy in order to attract more
customers. Third, this relevance relation captures the aforementioned effect of governmental
policies and subsidies on price through cost; as shown in Figure 5.8, R4, R10, and R11 are
grandparent nodes to Effective Price. Eventually, public [25, 42, 44, 45] and private data over
one business cycle suggests that the Effective Price may range from 1 to 7 $/W, which we
model as an approximate discretized probability distribution with four degrees: {1 $/W}, {3
$/W}, {5 $/W}, and {7 $/W}.
Beyond cost and price, we investigate potential changes in the sales volume of residential
solar systems over the next two years. Consistent with our explanation in Chapter 4, the
number of sold systems is more likely to be high when the threat of substitutes is low, the
industry growth is fast, the system price is low, and the margins are tight (price is set close to
the cost). As such, the unit sales are modeled as a System Units uncertainty in Figure 5.8,
conditioned on four parents: Effective Cost, Effective Price, Substitutes, and G1: Industry
growth rate. Public [46] and corporate projections estimate the annual installations to range
between 90000 and 540000 units. To capture this range, we define four System Units degrees:
{0}, {90000}, {300000}, and {540000}. Notably, the {0} degree accounts exclusively for all
prospects where the realized cost exceeds the realized price; in this case, we know with
certainty that solar developers will not sell their rooftop solar panels for negative returns.
The economic modeling of the average annual unit sales, along with the previous
technological modeling of the average unit size, informs our analysis of the average annual
capacity sales throughout the timeframe of this competitive analysis. As a result, Figure 5.8
shows a Total Quantity uncertainty with three parents: System Units, T5: Change in size of
home solar system, and T6: Optimal size of home solar system. Upon estimating the average
peak demand of various types of households in various geographic locations, SunEnergy
believes that the added annual capacity of residential solar in the U.S. over the next two years
might be anywhere between 0.1 and 5 gigawatts (GW). Therefore, we model the Total
Quantity uncertainty with six degrees: {0 GW}, {0.1 GW}, {1 GW}, {2 GW}, {3 GW}, {4
GW}, an {5 GW}. Here, again, the {0 GW} degree is needed to properly handle the lack of
CHAPTER 5 — Methodology: Developing the DAFF Models 240
solar installations due to unfavorable economics; whenever System Units is {0}, the Total
Quantity must be {0 GW}.
To conclude the DAFF modeling of the economic parameters, we use “earnings before tax”
(EBT) as the proper value metric to measure the overall industry profitability. Figure 5.8
shows the EBT value metric with three functional arrows extending into it from the Effective
Cost, Effective Price, and Total Quantity uncertainties. As formulated in (1), EBT calculates
the average annual net income of all incumbents in the industry, after accounting for the
governmental subsidies but before accounting for federal and state income taxes [47]. In other
words, the output EBT represents the expected average of annual profits from the residential
solar PV industry in the next two years. The emphasis on using an absolute-profit metric
instead of a relative-profitability ratio stems from SunEnergy’s interest in assessing not only
the relative favorability but also the absolute scale of the industry’s economics; a small
market is less likely to be a priority business opportunity for SunEnergy, even if the
profitability ratio is high.
𝐸𝐵𝑇 ($ 𝑦𝑒𝑎𝑟⁄ ) = 𝑇𝑜𝑡𝑎𝑙 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 ∙ (𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑃𝑟𝑖𝑐𝑒 − 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝐶𝑜𝑠𝑡) (1)
Similar to those of forces, drivers, and factors, the assigned probabilities over the degrees of
all economic uncertainties are reflective of the SunEnergy’s beliefs regarding the industry’s
near future. Ultimately, combining the DAFF elements in Figures 5.6, 5.7, and 5.8 results in a
complete DAFF Bayesian Network that assesses the profitability of the overall residential
solar PV industry in the U.S. A simplified sketch of the complete DAFF Bayesian Network is
shown in Figure 5.9. Here, for clarity, the representation of competitive drivers and factors is
condensed in the form of uncertainty “clouds”, each displaying the total number of uncertainty
nodes it incorporates and accounts for.
Now, after modeling the competitive forces and their economic implications for the whole
industry, SunEnergy shall make a series of strategic choices that position the company in the
most profitable segment of the industry. To achieve this goal, we transition to the second step
of this competitive analysis where we model several positioning decisions.
CHAPTER 5 — Methodology: Developing the DAFF Models 241
Figure 5.9: A sketch of the complete DAFF Bayesian Network for SunEnergy
2.2 Second Step: Assess Each Positioning Segment in the Industry
An effective strategy for SunEnergy requires a clear mapping between its feasible positioning
alternatives and the industry’s competitive forces. As explained in Chapter 4, strategic
positioning encompasses two types of decisions that can be undertaken by firms: Value
Proposition and Value Chain. While Value Proposition decisions define what product to
make, Value Chain decisions define how the product is made. In this case study, we model
four positioning decisions that SunEnergy deems important for clear market segmentation: one
Value Proposition decision and three Value Chain decisions. By modeling these decisions and
their influence on the aforementioned competitive forces, drivers, factors, and economic
parameters, we complete the construction of a DAFF Decision Diagram for the residential
solar PV industry in the U.S.
To start, the Value Proposition decision addresses the firm’s ability – rather need – to choose
the regions where it sells and services solar systems. One key distinction to make here is
between rural and urban regions. Compared to rural areas, urban centers are characterized by
Regulation (11)
Drivers ofSubstitutes (9)
Drivers of Buyers (20)
Drivers of New Entrants (30)
Drivers of Rivals (16)
Drivers of Suppliers (11)
Substitutes
Growth (1) Technology (6)
BuyersNew
EntrantsRivals Suppliers
Real Cost
Effective Cost
Effective Price
System Units
Total Quantity
CHAPTER 5 — Methodology: Developing the DAFF Models 242
higher population but smaller houses [48, 49], which translates into more but smaller solar
systems. The solar preferences of urban and rural customers may also differ for a variety of
reasons, including: weather, accessibility to the electric grid, and the nature of daily activities
within the household. Consequently, our DAFF modeling incorporates Regional Focus as a
Value Proposition decision with two alternatives: [Urban, Rural]. This decision influences the
probability distribution over multiple driver, factor, and economic-parameter uncertainties,
which we list in Table 5.1.
Table 5.1: DAFF uncertainties influenced by Regional Focus
Classification Uncertainty
Substitutes Customer switching cost from this industry product to substitutes
Regulatory and technical feasibility
Buyers
Customer switching cost among industry products
Dealer brand
Dealer reach
Product differentiation among incumbents
Relative reliance of customer on industry product
New Entrants
Incumbent customer acquisition cost
Incumbent established brands
Incumbent network effects
Limitation of distribution channels
Previous responses by incumbents
Rivals Ability to meet the needs of multiple customer segments
Suppliers
Availability of substitutes for what suppliers provide
Concentration of suppliers relative to incumbents
Supplier switching cost among incumbents
Factors G1: Industry growth rate
Economic
parameters Total Quantity
After choosing what region to serve, SunEnergy cares to examine where to operate along the
industry’s value chain. To address this point, we assess the feasible extent of vertical
integration, especially downstream. The solar firm may choose to manage its sales either
directly with the end-customer or through an intermediary dealer. In that regard, the dealer’s
responsibility may span a wide range of marketing, engineering, and financial services,
CHAPTER 5 — Methodology: Developing the DAFF Models 243
including (but not limited to): lead generation or closing, system installation or maintenance,
and financial securitization [47]. In the absence of such intermediary, the solar firm maintains
a direct and exclusive relationship with its residential solar customers on all fronts.
Consequently, we add Downstream Integration as a Value Chain decision in our DAFF
model, with two alternatives: [Dealer, No Dealer]. Inevitably, this decision influences multiple
competitive drivers that shape not only the bargaining power of Buyers but also the power of
both incumbent Rivals and future New Entrants. The probabilistic influence of Downstream
Integration on the competitive landscape is documented in Table 5.2. In general, while the
reliance on dealers may crowd the industry with an additional group of influential players and
therefore escalate competition, it may also allow more flexibility in the solar firm’s business
model; such flexibility results in a wider reach to underserved customers and therefore yields a
higher industry growth rate.
Table 5.2: DAFF uncertainties influenced by Downstream Integration
Classification Uncertainty
Buyers
Dealer partnership with incumbent
Dealer threat to integrate backward
Dealer volume of sales per incumbent
New Entrants
Incumbent assets
Incumbent customer acquisition cost
Incumbent economies of scale
Incumbent established brands
Incumbent inventory
Size-dependent disadvantages for new entrants
Rivals
Ability to meet the needs of multiple customer segments
Extent of exit barriers
Fragmentation of the industry
High fixed costs and low variable costs
Factors G1: Industry growth rate
R11: Exploitation of FMV
Another significant aspect of the solar firm’s business model is the type of financing services
available to its customers. If the homeowner wants to own his rooftop solar panels, he may
purchase the system either directly (i.e. full-upfront payment) or through a loan.
Alternatively, the homeowner may lease the solar system for either a full-upfront payment or
CHAPTER 5 — Methodology: Developing the DAFF Models 244
monthly payments (with no upfront fee). Leasing maintains the firm as the legal owner of the
solar system while providing the end-customer with the solar service only. Depending on its
financial structure and capabilities, a solar firm may choose to provide any of these financing
services, either directly or through a financing partner (i.e. a dealer). To capture the
competitive tradeoffs associated with these various options, we model Customer Financing as
a Value Chain decision with four alternatives: [Direct Purchase, Loan, Full-upfront Lease, No-
upfront Lease]. The DAFF uncertainties influenced by this decision are presented in Table 5.3.
Table 5.3: DAFF uncertainties influenced by Customer Financing
Classification Uncertainty
Substitutes Customer switching cost from this industry product to substitutes
Buyers
Amount of cash available for customer
Customer switching cost among industry products
Cost reduction for customer by industry product
Dealer ability to influence customers downstream
Dealer partnership with incumbent
Dealer threat to integrate backwards
Product differentiation among incumbents
Product perceived cost as fraction of the customer budget
New Entrants
Buyer trust in incumbent
Efficiency of capital markets
Incumbent established brands
Rivals Ability to meet the needs of multiple customer segments
Factors R10: ITC and depreciation
R11: Exploitation of FMV
Importantly, the combination of both Customer Financing and Downstream Integration
heavily influences the exploitation of fair market value. If the solar firm sells its systems either
through direct purchase or a loan, exploiting the FMV is infeasible, regardless of the firm’s
extent of vertical integration; in these two cases, the system price on the company’s income
statement has to match the one on the customer’s receipt. However, under a lease agreement,
exploiting the FMV becomes a feasible (albeit controversial) possibility if the solar firm is
vertically integrated. In this case, the firm acts as a solar developer, installer, and financer, and
it can buy/sell the system from/to itself; in other words, it can transact the system internally.
CHAPTER 5 — Methodology: Developing the DAFF Models 245
Lastly, focusing on the opposite side of the Value Chain, industry incumbents have the ability
to choose how to source the components of their solar system. One decision of particular
interest to SunEnergy is whether to manufacture the solar-panel components (e.g. cells,
modules, or inverters) in-house or purchase them from a third-party supplier. Solar modules
still contribute a significant portion of the overall system cost [42], so carefully managing their
supply is necessary for an effective competitive strategy. Consequently, we add Panel
Manufacturing as a Value Chain decision in our DAFF model, and we define its two
alternatives as: [Insource, Outsource]. Table 5.4 lists the Supplier and other competitive
uncertainties that are probabilistically influenced by Panel Manufacturing.
Table 5.4: DAFF uncertainties influenced by Panel Manufacturing
Classification Uncertainty
Buyers Product differentiation among incumbents
New Entrants
Incumbent assets
Incumbent IP
Incumbent R&D spending
Incumbent established brands
Rivals Extent of exit barriers
High fixed costs and low variable costs
Suppliers
Availability of substitutes for what suppliers provide
Concentration of suppliers relative to incumbents
Incumbent joint investments with current suppliers
Supplier threat to integrate forward
Figure 5.10: Example of decision influence on conditional probability assignment
In terms of probability assignment, we note that conditioning the probability distribution on a
decision alternative is similar to conditioning it on an uncertainty degree. To illustrate this
CHAPTER 5 — Methodology: Developing the DAFF Models 246
concept, Figure 5.10 shows the two degrees for the Incumbent economies of scale driver,
conditioned on the two alternatives of Downstream Integration. For every alternative, the two
degrees are assigned distinct probability values. Here again, the numerical values of
probability modifications by positioning decisions are reflective of SunEnergy’s beliefs and
market intelligence.
Figure 5.11: A sketch of the complete DAFF Decision Diagram for SunEnergy
Adding the aforementioned four decisions to our Bayesian Network yields a complete
Decision Diagram, a simplified version of which is depicted in Figure 5.11. For clarity, only
influence arrows extending from the decisions to the uncertainties are displayed in Figure 5.11
– relevance and information arrows are not. Every combination of the Value Proposition and
Value Chain alternatives results in a unique positioning track, which in turn defines a unique
segment of residential solar where SunEnergy can locate and operate. In that regard, we recall
from Chapter 4 that, by design, the alternatives of a particular decision are mutually exclusive;
Regulation (11)
Drivers ofSubstitutes (9)
Drivers of Buyers (20)
Drivers of New Entrants (30)
Drivers of Rivals (16)
Drivers of Suppliers (11)
Substitutes
Growth (1) Technology (6)
BuyersNew
EntrantsRivals Suppliers
Real Cost
Effective Cost
Effective Price
System Units
Total Quantity
Regional FocusDownstream Integration
Customer Financing
Panel Manufacturing
Value Proposition Value Chain Value Chain Value Chain
CHAPTER 5 — Results: Outputs from the DAFF Models 247
in other words, a solar firm chooses one and only one alternative for each decision. Because
the positioning alternatives are mutually exclusive, so are their combinations in the form of
positioning tracks. Furthermore, although positioning decisions affect the probability
distribution of only specific uncertainty nodes, their influence propagates through the decision
diagram until ultimately impacting the industry’s profitability. As a result, the DAFF Decision
Diagram model yields a unique competitive landscape, and therefore a unique expected EBT
value, for every positioning track.
3 Results: Outputs from the DAFF Models
After completing the DAFF modeling of the five forces, their economic implications, and the
multiple positioning alternatives available for SunEnergy in the residential solar PV industry,
we now transition to presenting the results of this competitive analysis. We follow the same
order in the previous section, first reflecting on the performance of the overall industry, and
then evaluating the attractiveness of the various positioning segments. The outputs from the
DAFF models highlight several insights that help inform SunEnergy’s competitive strategy.
3.1 First Step: Assess the Overall Industry
3.1.1. Competitive Landscape
The DAFF Bayesian Network allows quantifying, visualizing, and reflecting on the powers of
the five competitive forces, which account for both the intelligence in and interaction among
the extensive set of analyzed drivers and factors. As direct outputs of this DAFF model, the
probability distributions for the power of each competitive force and its parent drivers are
plotted in Figure 5.12. The results show that, according to SunEnergy’s beliefs and
knowledge, the residential solar PV industry is likely to witness limited bargaining powers for
both buyers and suppliers, as well as limited competitive threats by both substitutes and new
entrants, through the end of 2016. Nonetheless, the industry is likely to experience stronger
rivalry among current incumbents, especially as they try to expand their business with the
growing market.
CHAPTER 5 — Results: Outputs from the DAFF Models 248
Figure 5.12: Competitive landscape in the U.S. residential solar PV industry through 2016
As manifested in Figure 5.12, SunEnergy believes that the threat of Substitutes through 2016
will be {high} with probability of 0.39 and {low} with probability of 0.61. This limited threat
emerges from balancing the effects of three market drivers. Although it is not clear whether
solar substitutes will enjoy distinctively more favorable regulatory or technological
ecosystems (probability of {more favorable} is 0.52), it is very unlikely that they will offer a
superior price-performance tradeoff to solar panels (probability of {superior} is 0.28).
Additionally, it is unlikely that customers will have the luxury to feely give up or replace their
panels with another home-energy-saving gadget or service, due to strict contract agreements
and/or high penalties imposed by the solar firms (probability of {no legal complications or
high penalty} is 0.35).
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Supplier threat to integrate forward
Concentration of suppliers relative to incumbents
Relative dependence of suppliers on this industry profits
Incumbent switching costs between suppliers
Supplier switching cost between incumbents
Bargaining Power of Suppliers
Inability to read other incumbents’ signals
Intensity of competition
Basis of competition
Rivalry
Expected retaliation
Barriers to entry
Threat of New Entrants
Power of dealers
Power of end-customers
Bargaining Power of Buyers
Customer switching cost from this industry product to substitutes
Regulatory and technical feasibility
Price-performance tradeoff relative to this industry product
Threat of Substitutes
Probability
high
high
high
high
high
low
low
low
low
low
high low
high low
superior equivalent inferior
more favorable
legal complications or high penalty(opposite)
less favorable
highlow
highlow
price non-price
high low
able to read other incumbents' signals(opposite)
<10% increase in production cost >10% ...
<10% increase in production cost>10% ...
solar is top profit source(opposite)
>10 suppliers per incumbent<10 ...
<1 supplier forward-integration per year>1 ...
CHAPTER 5 — Results: Outputs from the DAFF Models 249
Similarly, SunEnergy believes that the power of Buyers through 2016 will be {high} with
probability of 0.38 and {low} with probability of 0.62. Two drivers contribute to this result.
First, end-customers will likely maintain limited bargaining powers (probability of {low}
Power of end-customers is 0.56) due to a host of reasons, including: the customers’ original
perception of achieving attractive utility-bill savings (>15%) and of affording the solar
purchase through loans and leases, and the customers’ subsequent constraints to switch away
from the solar system due to the aforementioned strict contracts or high penalties. Second,
dealers will likely have even weaker bargaining powers (probability of {low} Power of
dealers is 0.68), for two main reasons. The majority of dealers tend to be small and local
vendors – unable to influence a wide range of customers or credibly threat to take over the
incumbents’ business. At the same time, solar incumbents seem to be increasingly interested
in either securing exclusive partnerships with dealers or acquiring the dealers’ business and
doing it themselves.
The threat of New Entrants is projected to be {high} with probability of 0.41 and {low} with
probability of 0.59. This relatively limited threat is a result of slightly challenging barriers to
entry (probability of {high} Barriers to entry is 0.54) but relatively fierce retaliation expected
from incumbents (probability of {high} Expected retaliation is 0.63). The analysis shows that,
because the solar energy market is still relatively recent and growing, it is less likely that the
incumbent’ economies of scale or size of capital will play a significant role in deterring entry.
However, the proactive attempts by the incumbents to control distribution channels (e.g. build
partnerships with dealers) and exploit networking effects (e.g. win the customers’ trust and
advocacy) will likely compel new entrants to find novel ways for promoting and delivering
their products. Equivalently, SunEnergy believes that the retaliatory behavior of incumbents
will likely be driven by the inclination to either acquire new entrants or engage them in
discount wars.
Unlike the other four competitive forces, Rivalry over the next two years is expected to be
{high} with probability of 0.62 and {low} with probability of 0.38. This result accounts for
three main considerations. To start, the industry’s visibility will likely help incumbents read
their rivals’ signals and guess their moves (probability of {able to read other incumbents’
signals} is 0.75). Although this visibility may incentivize collaboration, its benefits are
CHAPTER 5 — Results: Outputs from the DAFF Models 250
drastically diminished by the other two considerations. First, competition will mostly likely be
price-based, due to both the absence of significantly differentiated products by solar firms
(e.g. efficiency ranges, colors, and dimensions of solar panels) and – congruently – the
absence of significantly differentiated needs by solar customers (e.g. purpose and time of use,
maintenance and control services, and physical appearance of the solar system); in other
words, the homogeneity of both the solar products and the solar needs leave incumbents with
price as the main dimension to compete on (probability of {price} Basis of competition is
0.65). In addition, as incumbents focus on growing and gaining market-share, without secure
and diversified revenue streams from other non-solar industries, the intensity of their
competition will likely escalate (probability of {high} Intensity of competition is 0.63).
Finally, the competitive analysis reveals that the bargaining power of Suppliers will be {high}
with probability of 0.39 and {low} with probability of 0.61. This outcome balances the effect
of five market drivers. On one hand, because the residential solar systems and services are
pretty standardized, the incremental costs that suppliers may face upon switching between
incumbents are likely to be minor (probability of {<10% increase in production cost} is 0.7);
this increases the suppliers’ leverage. On the other hand, four drivers seem to disfavor
suppliers. To start, because of standardization, the incumbents’ switching costs between
suppliers are equally likely to be minor (probability of {<10% increase in production cost} is
0.61). This reality is further amplified by the low concentration of suppliers relative to
incumbents (probability of {>10 suppliers per incumbent} is 0.71). Add to that, the majority
of suppliers will probably continue to rely on the solar industry as their major source of profit
(probability of {solar is top profit source} is 0.8), and they are unlikely to integrate forward
and start competing directly with incumbents (probability of {<1 supplier forward-integration
per year} is 0.75).
Given this overview of the competitive landscape in the U.S. residential solar PV industry
over the next two years, we pause to make an important statement. After going through this
modeling exercise, we assert that the aforementioned insights and conclusions about
competition could have been obtained by conducting a detailed qualitative analysis of the
five forces instead of building a DAFF model. However, if such an assertion is true, then one
must wonder: what are the additional benefits from using the newly proposed DAFF approach
CHAPTER 5 — Results: Outputs from the DAFF Models 251
instead of the conventional qualitative-analysis approach? Simply put, while a qualitative
analysis of the five forces can generate robust insights regarding the overarching competitive
trends in the industry, its benefits end there. Conversely, the benefits of DAFF extend beyond
highlighting the competitive trends, to include: establishing a quantitative relation between
competition and the economic performance in the industry; identifying and quantifying
competitive interdependence and its economic implications; and quantifying, comparing, and
ranking various positioning strategies for the firm in the industry. We proceed to demonstrate
each of these DAFF advantages in the following sections.
3.1.2. Economic Performance
Before delving into the economics, one consideration to keep in mind is the subjective
significance of the results in Figure 5.12. As we note in Chapter 4, DAFF standardizes the
characterization of the five force uncertainties, via the two degrees {high} and {low}, in order
to simplify and generalize their assessment across industries and decision-makers. The
tradeoff associated with this modeling approach is that the significance of the forces’ powers
becomes subjective; the probability distribution over {high} and {low} is interpreted
differently by different decision-makers. To give a hypothetical example in the context of this
case study, SunEnergy’s Director of Strategic Planning may interpret a 0.6 probability for
{high} Buyers power as a “mildly challenging” competitive prospect, but the Director of
Business Development of a rival solar firm may interpret the same information as a “severely
challenging” competitive prospect. To resolve this ambiguity, we need to translate the
subjectively interpretable competitive forces into objectively explicable and quantifiable
metrics, whose numerical values are perceived consistently by all players. Surely enough, this
goal is fulfilled in the DAFF model through the economic parameters and their precise
relations with the competitive forces.
We summarize the expected economic performance of the U.S. residential solar industry over
the next two years in Figures 5.13a–c. These figures plot discretized probability distributions
for the Effective Cost, Effective Price, and Total Quantity of installed solar systems, after
accounting for all relevant driver and factor uncertainties. In Figure 5.13a, SunEnergy’s
intelligence about competition and governmental regulations allows deducing that the
CHAPTER 5 — Results: Outputs from the DAFF Models 252
Effective Cost will very likely be lower than 4 $/W, with an expected (i.e. probability-
weighted average) value of 1.19 $/W through 2016. Equivalently, Figure 5.13b shows that the
Effective Price of the solar system will likely be in the 3–5 $/W range, with an expected value
of 3.35 $/W. These cost and price prospects, as well as SunEnergy’s intelligence on the power
of Substitutes, the industry Growth rate, and the average size of the solar system, yield
attractive projections for annual sales. In Figure 5.13c, the DAFF output shows a high level of
confidence that the Total Quantity – representing the yearly installation capacity – will be
between 1 and 3 GW, with an expected value of 1.93 GW. With this information, we can now
complete the first objective of this competitive analysis by calculating the expected profit for
the whole industry: given the probabilistic outcomes for all three economic parameters, the
DAFF model computes the expected EBT of the U.S. residential solar PV industry
through 2016 at 4.05 billion $/year.
Figure 5.13: Economic performance of the U.S. residential solar PV industry through 2016
3.1.3. Competitive Interdependence
Beyond quantifying the impact of competition on the industry economics, the DAFF Bayesian
Network provides crucial insights regarding the strategic interdependence and interaction
among the competitive forces. On way to comprehend this DAFF characteristic is to think of
the Bayesian network as a living model that can, and should, be continuously updated; the
decision-maker can always modify the probability assignments for uncertainties in order to
capture newly attained market information. Because of probabilistic relevance, observing new
information about a specific uncertainty may allow inferring new information about relevant
0
0.1
0.2
0.3
0.4
0.5
0.6
0 2 4 6
Pro
bab
ility
Effective Cost ($/W)
0
0.1
0.2
0.3
0.4
0.5
0 0.1 1 2 3 4 5
Pro
bab
ility
Total Quantity (GW/year)
0
0.1
0.2
0.3
0.4
0.5
0.6
1 3 5 7
Pro
bab
ility
Effective Price ($/W)
(a) (b) (c)
CHAPTER 5 — Results: Outputs from the DAFF Models 253
uncertainties [43]. Both observations and inferences result in updated probability distributions
over relevant competitive uncertainties.
To demonstrate both notions of information-update in and interdependence among the
competitive forces, we describe a thought experiment whereby we examine the sensitivity of
the obtained results to extreme competitive scenarios. In a nutshell, the experiment goes as
follows: if the decision-maker observes, with certainty, that the power of a force is at its
highest or lowest extreme, how does this new information about the power of one force update
his beliefs about the power of other forces? Put differently, if the decision-maker gets perfect
clairvoyance on one force, what would he infer about the other forces?
To conduct this experiment, we test two scenarios for each force: all the driver uncertainties of
a given force are resolved to render that force’s power either strongest (probability of {high} =
1) or weakest (probability of {low} = 1). Then, for each scenario, we examine how
maximizing (or minimizing) the power of the observed force updates the power of the other
four forces. The results are summarized in Figures 5.14a–e.
In the tornado plot of Figure 5.14a, we analyze how our beliefs about the power of Substitutes
changes upon observing each of the other four forces (and their drivers) at their extreme
values. The vertical axis shows the competitive forces we observe: Buyers, New Entrants,
Rivals, or Suppliers. The power of each force is observed as either {high} or {low}. The
horizontal axis then indicates how the probability of {high power of Substitutes} changes
upon observing each of the other four forces. Given the decision-maker’s base-case
information about competition, the probability of {high power of Substitutes} is 0.39, as
documented in Figure 5.12. Now, observing {high power of Buyers} updates our beliefs about
Substitutes, such that the likelihood of {high power of Substitutes} increases from 0.39 to 0.7.
Conversely, if the decision-maker observes {low power of Buyers}, the probability of {high
power of Substitutes} decreases from 0.39 to 0.25. In plain English, observing strong Buyers
increases the likelihood of witnessing strong Substitutes, and observing weak Buyers
decreases the likelihood of witnessing strong Substitutes. Overall, these results signify a
strong dependence of the threat of Substitutes on the bargaining power of Buyers.
CHAPTER 5 — Results: Outputs from the DAFF Models 254
Figure 5.14: Interdependence between the competitive forces in the U.S. residential solar
PV industry
0.2 0.3 0.4 0.5 0.6 0.7 0.8Probability of {high power of Substitutes}
Substitutes
Observed as "Low" Observed as "High"
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Probability of {high power of Buyers}
Buyers
Observed as "Low" Observed as "High"
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Probability of {high power of New Entrants}
New Entrants
Observed as "Low" Observed as "High"
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Probability of {high power of Rivals}
Rivals
Observed as "Low" Observed as "High"
Buyers
New Entrants
Rivals
Suppliers
Substitutes
New Entrants
Rivals
Suppliers
Substitutes
Buyers
Rivals
Suppliers
Substitutes
Buyers
New Entrants
Suppliers
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Probability of {high power of Suppliers}
Suppliers
Observed as "Low" Observed as "High"
Substitutes
Buyers
New Entrants
Rivals
(a) (b)
(c)
(e)
(d)
Observed as {low} Observed as {high} Observed as {low} Observed as {high}
Observed as {low} Observed as {high} Observed as {low} Observed as {high}
Observed as {low} Observed as {high}
CHAPTER 5 — Results: Outputs from the DAFF Models 255
To understand the reasons behind this interdependence, we refer back to the Bayesian network
in Figures 5.6 and 5.7. Evidently, multiple Substitutes drivers have three Buyers drivers as
direct parents: Cost reduction for customer by industry product, Product perceived cost as
fraction of the customer budget, and Customer switching cost from this industry product to
substitutes. Observing the Buyers drivers changes the probability of their degrees to either 0 or
1. Subsequently, the updated probability distributions for the parent Buyers drivers yield
updated probability distributions for the children Substitutes drivers. A second form of
probabilistic relevance also contributes to the interaction between the two forces: several
Buyers and Substitutes drivers have common ancestors, especially the Regulation
uncertainties. Observing the children Buyers drivers allows the decision-maker to infer new
probability distributions for the parent Regulation factors, which then yields new probability
distributions for the children Substitutes drivers. For example, if the Director of Strategic
Planning at SunEnergy gets to know, undoubtedly, that the residential solar system will
achieve {< 15% reduction in power bill} and will {not improve power purchase and
utilization} in the next two years, he may infer that the optimal size of the home solar system
will more likely be {less than 50% of home peak demand}, which in turn allows deducing
that substitutes will more likely achieve {higher emissions reduction}. As discussed in
Chapter 4, Bayes-ball is a good technique to track these interdependence relations [50].
Continuing with Figure 5.14a, we notice that the power of Substitutes is also dependent on the
threat of New Entrants; the probability of {high power of Substitutes} increases to 0.49 upon
observing {low power of New Entrants} and decreases to 0.33 upon observing {high power of
New Entrants}. Interestingly, in this case, the forces move in opposite directions: observing
weak New Entrants increases the likelihood of witnessing strong Substitutes; the opposite
is also true. This relation is rather intuitive: if an industry has a large number of substitutes,
those substitutes may credibly discourage new players from entering the market. In our case
study, this interaction can be tracked in the DAFF network of Figure 5.6. Observing the power
of New Entrants entails observing the Relative reliance of customer on industry product
driver, which in turn allows inferring new information about its parent Cost reduction for
customer by industry product driver. Changing the probability distribution of the latter driver
leads to updating the probability distribution of its child Substitute bill savings, which is a
CHAPTER 5 — Results: Outputs from the DAFF Models 256
Substitutes driver. In simpler words, the story goes as follows. Firms prefer to enter markets
where customers rapidly adopt the product because it is of real value to them. Accordingly,
one indication of low threat of entry is the observation that residential customers are not
heavily reliant on the solar system. Such observation allows inferring that solar panels enable
no significant reductions in the customers’ utility bills. In turn, the poor bill savings from solar
systems raise the relative value of savings from solar substitutes, which eventually contributes
to increasing the overall threat of substitutes.
Another important insight from Figure 5.14a is that, for a particular force, the
interdependence relations with other forces need not be in the same direction or of the
same magnitude. In terms of direction, we just explained that the likelihood of witnessing
strong Substitutes in the industry increases upon observing strong Buyers but decreases upon
observing strong New Entrants. Equally noteworthy, the magnitude of change in the
probability of {high power of Substitutes} is larger upon observing {high power of Buyers}
than it is upon observing {low power of Buyers}. This result is primarily a modeling feature
rather than a strategic intuition. Observing {high power of Buyers} changes the probability of
{high power of Substitutes} by 0.62 (from 0.38 to 1), whereas observing {low power of
Buyers} changes the probability by 0.38 (from 0.38 to 0). As new information updates the
probabilities throughout the Bayesian network, larger changes in the probability of the
observed force (Buyers in our example) cause larger changes in the probability of the tested
force (Substitutes in our example). In fact, because the Bayesian network has to always
balance the numerous probabilistic relations among various uncertainties, observing one force
at either extreme is unlikely to cause another force to reach either extreme. In other words, if
the probability of a {high} force at base-case is less than 0.5, it becomes progressively harder
for new competitive observations to further weaken that force; similarly, if the probability of a
{high} force at base-case is greater than 0.5, it becomes progressively harder for new
competitive observations to further strengthen that force.
The same logic applies to all the remaining interdependence relations depicted in Figure
5.14b–e; we proceed to discuss the most prominent of these relations. Moving on to Figure
5.14b, the tornado diagram shows the sensitivity of the power of Buyers to observing the four
other forces: Substitutes, New Entrants, Rivals, and Suppliers. Starting with the dependence of
CHAPTER 5 — Results: Outputs from the DAFF Models 257
Buyers on Substitutes, we see that, observing strong Substitutes increases the likelihood of
witnessing strong Buyers; the opposite is also true. Compared to the results in Figure 5.14a,
we see that the forces still move in the same direction, but the dependence of Buyers on
Substitutes is less significant than the dependence of Substitutes on Buyers. This outcome
highlights an important takeaway: the interdependence between two competitive forces
need not be symmetrical.
As explained before, the interdependence between the forces is governed by the probabilistic
relevance between the uncertainties, which in turn is dictated by the assignment of conditional
probabilities. The conditional probabilities between two uncertainties need not be the same in
both the forward and reverse directions of assessment. A simple example to clarify this point
is the relevance between “lung disease” and “smoking”; here, we can make two assessments:
the probability that a person {has a lung disease given that he smokes}, and the probability
that a person {smokes given that he has a lung disease}. Obviously, these two conditional
probabilities having different meanings and may have different values. The asymmetry in the
interdependence between Buyers and Substitutes can be explained similarly. In our DAFF
logic, the customer advantages (e.g. cost reductions) from the solar system are modelled as
drivers for Buyers. Observing Buyers means observing the exact customer advantages from
the solar system, which then may update the decision-maker’s information about the relative
appeal of potential substitutes. Equivalently, observing Substitutes means observing the exact
customer advantages from solar substitutes, which then may update the decision-maker’s
information about the relative appeal of the solar system. Nonetheless, in this case study,
SunEnergy believes that the performance of substitutes does not help infer much about the
performance of residential solar. Also, the force of Buyers is shaped by other drivers beyond
the customer savings from the solar system, including the customer switching cost and the
power of dealers. Both attributes dilute the sensitivity of Buyers to Substitutes, resulting in the
weak dependence we observe in Figure 5.14b.
Another noticeable result in Figure 5.14b is the interdependence between Buyers and Rivals:
observing strong Rivals increases the likelihood of witnessing strong Buyers; the opposite
is also true. This interdependence is primarily attributed to three shared ancestral drivers,
illustrated in Figure 5.6: Product differentiation among incumbents, Customer switching cost
CHAPTER 5 — Results: Outputs from the DAFF Models 258
among industry products, and Willingness of price discounting by incumbents. Included in the
observation of {high power of Rivals} are the observations that {no product differentiation}
exists among the solar offerings in the residential industry, that customers suffer {no legal
complications and low financial penalty} upon switching between solar providers, and that
solar firms are {willing to share > 15% of profits with customers}. The lack of product
differentiation leaves the end-customer with price as the only dimension to bargain over.
Accordingly, the lack of product differentiation effectively increases the customer’s price
sensitivity, which, along with the customer’s ability to freely switch between solar vendors,
increases the bargaining power of Buyers. Equivalently, the observation that the solar
incumbents are willing to share a substantial portion of the system value with the Buyers (e.g.
high dealer commission) allows inferring that the power of Buyers will more likely be {high}.
Interestingly, the same shared drivers are responsible for the comparable dependence of Rivals
on Buyers, depicted in Figure 5.14d: observing strong Buyers increases the likelihood of
witnessing strong Rivals; the opposite is also true. After explaining how these drivers affect
the bargaining power of Buyers, let us now do the reverse analysis and explain how they affect
Rivalry among incumbents. Simply put, all three shared drivers are related to the economic
performance of the solar system. Upon observing {high power of Buyers}, both {no product
differentiation} and {no legal complications and low financial penalty} induce the
homeowners to prioritize “economics” as the most important consideration when shopping for
solar panels. Likewise, observing the willingness of solar firms to {share > 15% of profits
with customers} reflects a business culture that is strongly biased towards managing
economics instead of, for example, delivering a fast service or gaining customer loyalty. When
both the customers and the firms focus on the solar system’s economics, price-based
competition becomes inevitable, and therefore {high} Rivalry becomes more likely.
Rivals also exhibits symmetrical interdependence with New Entrants, evident in the tornado
plots of both Figures 5.14d and 5.14c. The probabilistic dependence between the two forces is
similar in magnitude, but the two forces move in opposite directions. In Figure 5.14d,
observing strong New Entrants decreases the likelihood of witnessing strong Rivals.
Equivalently, in Figure 5.14c, observing strong Rivals decreases the likelihood of
witnessing strong New Entrants. The opposites hold true in both cases. Here again, the
CHAPTER 5 — Results: Outputs from the DAFF Models 259
strategic interaction between the two forces balances the effects of their common ancestral
drivers: Commitment of incumbent to retain and fight over market share, Willingness of price
discounting by incumbent, and Customer switching cost among industry products. In a
competitive landscape where rivalry is high, we observe that solar firms {focus on relative
growth} and express clear willingness to {share > 15% of profits with customers}. Both
behaviors indicate a high likelihood that industry incumbents will seek to retaliate from new
entrants, therefore deterring the threat of new entry. However, the ramifications of both
behaviors are counteracted by the third driver, which shifts the forces of Rivals and New
Entrants in the same direction. High rivalry may imply {no legal complications and low
financial penalty} when customers switch among solar providers, which then may accelerate
the adoption rate of the solar offerings by new entrants and therefore increase the overall
threat of entry.
Figure 5.14c depicts two additional results concerning New Entrants that are worth discussing.
Specifically, observing strong Buyers or Suppliers increases the likelihood of witnessing
strong New Entrants. This result stems from the ability of either Buyers or Suppliers to
extend their activities into the solar industry; observing {high power of Buyers} signifies a
real threat of backward integration by dealers, and observing {high power of Suppliers}
signifies a real threat of forward integration by suppliers. In both cases, the danger of new
entry becomes more imminent.
The last strategic insight in Figure 5.14 concerns the limited interaction between Suppliers
and the other competitive forces. As evident in Figures 5.14a, 5.14b, and 5.14d, observing
the power of Suppliers (and its drivers) does not update the decision-maker’s beliefs about the
power of Substitutes, Buyers, or Rivals, respectively, in this case study. Equivalently, Figure
5.14e shows that the power of Suppliers is not sensitive to the change in the power of
Substitutes, Buyers, or New Entrants. The minor dependence of Suppliers on Rivals can be
attributed to the single common ancestral driver between both forces: Fragmentation of
industry. Observing {high Rivalry} accounts for the existence of oligopolistic competition
among established solar firms. The presence of multiple, similarly sized firms signifies
relatively low population (i.e. high concentration) of suppliers relative to incumbents, which in
turn implies higher bargaining power for Suppliers.
CHAPTER 5 — Results: Outputs from the DAFF Models 260
3.1.4. Economic Interdependence
Equally important to examining the interactions among the competitive forces is testing the
sensitivity of the industry’s economic performance to their change. To that end, Figures
5.15a–d plot the range of the Effective Cost, Effective Price, Total Quantity, and EBT
associated with observing each force between its two extremes. Consistent with Porter’s
teachings, and consequently with DAFF’s underlying logic, Figures 5.15a and 5.15b show that
stronger forces yield higher costs and lower prices. In fact, observing a force at its highest
extreme may yield a COGS as high as 1.83 $/W and a price as low as 3.09 $/W. On the other
hand, observing a force at its lowest extreme may yield a cost as low as 1.00 $/W and a price
as high as 3.66 $/W.
Notably, the power of Buyers has the highest impact on Effective Cost, which we attribute to
two main reasons. First, referencing our discussions on Figure 5.14, we know that observing
strong Buyers increases the likelihood of witnessing strong Substitutes (Figure 5.14a), strong
New Entrants (Figure 5.14c), and strong Rivals (Figure 5.14d); in other words, observing
powerful Buyers implies a competitive reality in which three other forces are likely to be
powerful (Substitutes, New Entrants, and Rivals). Inevitably, such combination of four strong
competitive forces increases the likelihood of witnessing high production, installation, and
servicing costs. The second reason has to do with the direct probabilistic relevance between
the Buyers’ driver uncertainties and the Regulation uncertainties, especially those affecting
solar financing. Observing strong Buyers entails knowing, with certainty, that the solar
Product perceived cost as fraction of the customer budget is {> 20% of household annual
income}. Given this information, the decision-maker may reasonably infer that the R10: ITC
and Depreciation subsidies are not fully utilized, which raises the expected Effective Cost of
the solar system.
Beyond price and cost, the total sales of the solar system are also sensitive to the force of
Buyers, as illustrated in Figure 5.15c. That said, Total Quantity is even more sensitive to the
resolution of two other forces: Substitutes and New Entrants. Per our DAFF modeling,
observing {high power of Substitutes} increases the likelihood of witnessing limited solar
sales. However, observing {high power of New Entrants} induces a probabilistic inference in
CHAPTER 5 — Results: Outputs from the DAFF Models 261
the opposite direction; it allows inferring a more likely {rapid Growth rate} and a less likely
{high power of Substitutes}, both of which then imply higher chances of witnessing vast solar
sales.
Figure 5.15: Effect of the competitive forces on economics of the U.S. residential solar PV
industry
Subsequently, upon balancing the relevance relations among the numerous uncertainties, the
DAFF Bayesian Network allows us to evaluate how sensitive the solar industry’s EBT is to
observing the extremes of each competitive force. Remarkably, Figure 5.15d shows that in a
competitive setting where the power of Buyers is {high}, profits can be as low as 1.82 billion
$/year; conversely, in a competitive setting where the power of Buyers is {low}, profits can be
1 1.25 1.5 1.75 2
Effective Cost ($/W)
3 3.25 3.5 3.75 4
Effective Price ($/W)
1 1.25 1.5 1.75 2 2.25 2.5
Total Quantity (GW)
1.5 2.5 3.5 4.5 5.5 6.5
EBT (billion $/year)
Suppliers
Rivals
New Entrants
Buyers
Substitutes
(a) (b)
(c) (d)
observed as {high}
observed as {Low}
CHAPTER 5 — Results: Outputs from the DAFF Models 262
as high as 5.77 $/year. Beside this wide range of expected EBT, the DAFF model offers a key
insight that may seem counterintuitive: unlike the other four competitive forces, observing
{high power of New Entrants} yields a higher expected EBT and therefore signifies a more
favorable competitive landscape. To comprehend this result, we first reemphasize the need to
distinguish between “relevance” and “causality” in probabilistic assessment. We assert that
higher threat of entry does not cause more favorable competitive landscape in the residential
solar industry. Rather, observing a high threat of entry implies that the competitive landscape
is likely attractive; naturally, the more profitable the industry, the more firms are interested in
joining it.
Overall, Figure 5.15 shows that Substitutes and Buyers are the top two competitive influencers
of economic performance in the U.S. residential solar PV industry, followed by Rivals and
New Entrants. While observing the competitive forces is a beneficial thought-experiment to
understand their impacts on the overall industry, reaching perfect clairvoyance on competition
is almost impossible. Therefore, when designing its competitive strategy, SunEnergy has to
not only gather information about the competitive powers in its environment but also control
these powers through proper positioning. The effect of positioning decisions on SunEnergy’s
success is what we discuss in the next section.
3.2 Second Step: Assess Each Positioning Segment in the Industry
This case study examines a set of 32 feasible positioning tracks for SunEnergy in the U.S.
residential solar PV industry. Each positioning track yields a unique competitive landscape
and, accordingly, a unique profit (EBT) value. Figure 5.16 ranks the expected EBT for all
positioning tracks. For convenience, we abbreviate the labeling of the Customer Financing
alternatives such that “purchase”, “loan”, “leaseF” and “leaseN” correspond to [Direct
Purchase], [Loan], [Full-upfront Lease], and [No-upfront Lease], respectively.
We start with a series of modeling notes in order to guarantee the precise and proper
interpretation of the numerical findings in Figure 5.16. First, we remind that the EBT value of
a positioning segment corresponds not to an individual solar firm (e.g. SunEnergy) but to all
solar firms positioning in that segment. Second, because positioning tracks are mutually
CHAPTER 5 — Results: Outputs from the DAFF Models 263
exclusive, their EBT values are not additive; rather, each positioning track characterizes a
prospective reality about the residential solar industry and therefore should be assessed
independently. Third, while our DAFF value node accounts for the operational costs and
revenues in a specific positioning segment, it does not account for any capital investment that
might be needed upfront to start a business in that segment. To that end, the EBT values
presume that firms are already operational in the positioning segment. To demonstrate these
points, let us interpret one positioning track as an example: the EBT value for the [Urban,
Dealer, Loan, Insource] positioning track represents the “expected earnings before tax for the
whole residential solar market in the U.S., where all solar firms locate in urban areas, rely on
dealers to acquire and manage customers, sell their solar systems through loans, and
manufacture their own solar components.”
Given our specific market assumptions, information, and beliefs, Figure 5.16 shows that
different positioning tracks may render the expected EBT of the residential solar industry as
high as 3.98 billion or as low as 0.51 billion $/year. The highest profits are realized in a
competitive setting where incumbents choose to: locate in urban areas, cut dealers out,
and offer leasing services to their customers. On the other hand, the lowest profits result
when firms decide to: run the solar business in rural areas, use dealers, and sell through direct-
purchase agreements. Notably, both the top-two and the bottom-two positioning tracks score
very comparable EBT values despite their different Panel Manufacturing alternatives.
Replicated multiple times throughout the numerical outputs of Figure 5.16, this observation
signifies that, relative to Regional Focus, Downstream Integration, and Customer Financing,
Panel Manufacturing is the least influential positioning decision in shaping the competitive
landscape and the industry’s profitability.
Another important insight is related to the collective influence of positioning decisions. While
the [Urban, No-upfront Lease, No Dealer, Insource] positioning track is likely to yield the
highest profit, this result is not sufficient to conclude that [Urban], [No-upfront Lease], [No
Dealer], and [Insource] are, independently, the best positioning alternatives for their respective
decisions. It is only the combination these alternatives that collectively influences the
competitive forces and factors in the most favorable way to solar firms. For instance, when
CHAPTER 5 — Results: Outputs from the DAFF Models 264
combined with [Rural, Loan, and Outsource], [Dealer] results in slightly higher expected EBT
than [No Dealer].
Figure 5.16: Profitability of the various positioning tracks in the U.S. residential solar PV
industry
This characteristic of positioning alternatives is a good manifestation of “strategic fit”, an
important notion introduced by Porter and discussed earlier in Chapter 4. When positioning
activities fit together, not only they become harder to imitate by competitors, but also their
combined benefit becomes larger than the sum of their individual benefits. A representative
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Rural, Purchase, Dealer, Outsource
Rural, Purchase, Dealer, Insource
Rural, Purchase, NoDealer, Outsource
Rural, Purchase, NoDealer, Insource
Rural, Loan, NoDealer, Outsource
Rural, Loan, Dealer, Outsource
Rural, Loan, NoDealer, Insource
Rural, Loan, Dealer, Insource
Rural, LeaseF, Dealer, Outsource
Rural, LeaseF, Dealer, Insource
Rural, LeaseF, NoDealer, Outsource
Rural, LeaseF, NoDealer, Insource
Rural, LeaseN, Dealer, Outsource
Rural, LeaseN, Dealer, Insource
Rural, LeaseN, NoDealer, Outsource
Rural, LeaseN, NoDealer, Insource
Urban, Purchase, Dealer, Outsource
Urban, Purchase, Dealer, Insource
Urban, Purchase, NoDealer, Outsource
Urban, Loan, Dealer, Outsource
Urban, Purchase, NoDealer, Insource
Urban, Loan, Dealer, Insource
Urban, LeaseF, Dealer, Outsource
Urban, LeaseF, Dealer, Insource
Urban, Loan, NoDealer, Outsource
Urban, Loan, NoDealer, Insource
Urban, LeaseN, Dealer, Outsource
Urban, LeaseN, Dealer, Insource
Urban, LeaseF, NoDealer, Outsource
Urban, LeaseF, NoDealer, Insource
Urban, LeaseN, NoDealer, Outsource
Urban, LeaseN, NoDealer, Insource
EBT (billion $/year)
base-case
individual benefit
combined benefit
example of "strategic fit"
CHAPTER 5 — Results: Outputs from the DAFF Models 265
example of fit in this case study is highlighted in Figure 5.16. We start with a base-case
positioning track of [Urban, Direct Purchase, Dealer, Insource], which achieves an expected
EBT of $1.81 billion $/year. If the solar firms cut the dealers out and choose to position in
[Urban, Direct Purchase, No Dealer, Insource] instead, the expected EBT increases to 2.29
billion $/year (gains of 0.48 billion). Otherwise, if solar firms shift from a direct-purchase
sales model to full-upfront lease contracts and position in [Urban, Full-upfront Lease, Dealer,
Insource], the expected EBT increases to 2.81 billion $/year (gains of 1 billion). Now, if solar
firms choose to both cut dealers out and offer full-upfront leases, thus positioning in [Urban,
Full-upfront Lease, No Dealer, Insource], the expected EBT increases all the way to 3.62
billion $/year; the combined gains of 1.81 billion here are larger than the sum of the two
individual gains of 0.48 and 1 billion, which can be attributed to the strategic fit between the
[Dealer] and [Full-upfront Lease] positioning alternatives.
Subsequently, to better understand how positioning influences the competitive forces, Figure
5.17 plots the range of change in the power of each competitive force under the various
feasible positioning tracks in the industry. The principal message from Figure 5.17 is
consistent with that conveyed in Figure 5.16: positioning can significantly influence the
competitive landscape faced by the solar firm. For example, we see that some positioning
tracks reduce the likelihood of {high threat of Substitutes} all the way to 0.28 while other
positioning tracks raise the likelihood of this prospect to 0.54. Buyers seem to be the most
prone to control by the four considered decisions; different positioning strategies may set the
probability of {high bargaining power of Buyers} anywhere between 0.18 and 0.71.
Conversely, Suppliers seem to be the least sensitive to positioning; the 32 positioning tracks
result in a slim change in the probability of {high bargaining power of Suppliers}, ranging
between 0.39 and 0.41. Appendix B tabulates the power of each competitive force for each
positioning track, in more detail.
Interestingly, comparing the results in Figures 5.14 and 5.17 shows that the four competitive
forces mostly sensitive to observing new information are also the ones mostly sensitive to
positioning: Substitutes, Buyers, New Entrants, and Rivals. The opposite is true for Suppliers.
While this outcome is not necessarily generalizable, it does reflect our intentional attempt in
this case study to focus on controlling the forces that are strongly interdependent. These forces
CHAPTER 5 — Results: Outputs from the DAFF Models 266
play a major role in shaping the economics of the residential solar industry, so influencing
them further SunEnergy’s ability to position where the industry performance is superior.
Figure 5.17: The influence of positioning on the competitive forces in the U.S. residential
solar PV industry
Also in Figure 5.17, we highlight the positioning alternatives that cause four of the
competitive forces to be strongest or weakest: Substitutes, Buyers, New Entrants, and Rivals.
This mapping provides additional insight into the role of individual positioning decisions, and
the results reaffirm our earlier conclusions in Figure 5.16. To start, managing customers
directly and cutting dealers out seem to be the optimal Downstream Integration alternative;
[No Dealer] both reduces competition (Figure 5.17) and increases profitability (Figure 5.16).
Equivalently, allowing customers to finance their solar system through loans or no-upfront
leases seem to be the optimal Customer Financing alternatives; [Loan] and [No-upfront
Lease] minimize competitive threats and enhance profitability. On the other hand, the
influence of the Regional Focus positioning decision is rather unique. Here, positioning in
[Urban] areas seem to expose solar firms to higher competitive forces (Figure 5.17) even
though it eventually results in higher expected EBT (Figure 5.16); the opposite is true for
positioning in [Rural]. One explanation for this trend is that urban regions offer a bigger solar
market with more potential customers. In this case, although stronger competitive forces may
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Substitutes
Buyers
New Entrants
Rivals
Suppliers
Probability of {High} power of force
Urban
Dealer
Purchase
Rural
NoDealer
LeaseNLoan
CHAPTER 5 — Results: Outputs from the DAFF Models 267
erode some of the firms’ profit margins, the total sales are high enough to overcompensate for
this effect and still uphold [Urban] as an attractive positioning alternative.
Building on the preceding results, we now attempt to answer the central question of this case
study: where should SunEnergy position in the U.S. residential solar PV industry over the next
two years? In line with Porter’s teachings and our DAFF modeling, SunEnergy should
position where it achieves the highest expected EBT. If SunEnergy anticipates gaining the
same market-share and enduring comparable (or no) upfront capital costs in all market
segments, then it should position in the highest-EBT track of Figure 5.16: [Urban, No-upfront
Lease, No Dealer, Insource]. If, for whatever reason, implementing this positioning strategy is
not possible, SunEnergy should pick the second-highest-EBT track [Urban, No-upfront Lease,
No Dealer, Outsource], then the third [Urban, Full-upfront Lease, No Dealer, Insource], and so
forth. Following the same rationale, SunEnergy should avoid positioning in the lowest-EBT
track [Rural, Direct Purchase, Dealer, Outsource]. Nonetheless, if SunEnergy believes that its
prospective market-share or upfront capital investments in the residential business are likely to
differ with its positioning, then the best positioning strategy cannot be directly deduced from
our results, and further analysis is needed; as explained in Chapter 4, it is precisely here that
the third step of the first objective in competitive strategy becomes essential. Still, even
without the third-step analysis, our results from the first and second steps provide SunEnergy
with clearer intuition on the optimal competitive strategy in the U.S. residential solar PV
industry over the next two years. By now, SunEnergy knows how to better prioritize its
positioning plans: focus on the top tracks and avoid the bottom tracks in Figure 5.16. Along
the same lines, SunEnergy also knows that it is beneficial to: locate in urban areas with higher
sales despite stronger competition; manage customers directly without relying on dealers –
except in some rural setting; offer leases and loans to finance its customers’ solar systems
while avoiding direct-purchase agreements; and combine lease-offerings with direct-customer-
management in one business model to generate a strategic fit that is hard to imitate. These
concrete positioning recommendations would have been hard to materialize without DAFF.
CHAPTER 5 — Conclusions 268
4 Conclusions
Is the competitive landscape in the U.S. residential solar PV industry favorable in the near
future? And if so, where should SunEnergy position? The purpose of this case study is to
answer these two key questions, and our attempt to do so centers on developing and evaluating
decision analytic five forces (DAFF) models. After presenting a brief overview of the solar
photovoltaic industries in the United States as well as of SunEnergy’s business, we delve into
constructing the various elements of the DAFF models. First, we describe how to design the
five competitive forces and their underlying drivers as uncertainties. Also accounted for as
uncertainties are several important regulatory, technological, and growth factors that shape the
residential solar business. Both the generalizable forces and the industry-specific factors
impact the cost, price, and sales of solar systems, all of which are treated as uncertain
economic parameters. Here, we spend some time explaining how to account for governmental
subsidies and tax regulations in our economic modeling, and we justify the use of earnings
before tax (EBT) as the value metric. Along the way, we describe the probabilistic relevance
among the competitive, regulatory, technological, growth, and economic uncertainties, so that
we can eventually connect them in a single DAFF Bayesian Network. This Network captures a
lot of SunEnergy’s knowledge and beliefs about the overall residential solar industry in the
U.S. and its potential advancement in the next two years.
On its own, the DAFF Bayesian Network provides important results on the competitive
performance of the overall industry. Among the five competitive forces, only rivalry is
expected to be relatively strong; the chance of residential solar firms suffering {high power of
Rivals} over the next two years is 0.62, compared to about 0.4 for {high} powers of
Substitutes, Buyers, New Entrants, and Suppliers. This predicted competitive landscape yields
an expected EBT of 4.05 billion $/year for the whole U.S. residential solar market, with a
probability-weighted average cost, price, and installation capacity estimated at 1.19 $/W, 3.35
$/W, and 1.93 GW, respectively.
The DAFF Bayesian Network also highlights the interdependence among the five forces. Most
notably, we document robust interdependence among Substitutes, Buyers, New Entrants, and
Rivals. A careful tracking of the competitive DAFF logic shows that the interdependence
CHAPTER 5 — Conclusions 269
relations associated with a given force need not have the same magnitude or direction, and the
interdependence between two competitive forces need not be symmetrical. In this case study,
observing strong Buyers increases the likelihood of witnessing strong Substitutes significantly,
but observing strong Substitutes increases the likelihood of witnessing strong Buyers only
mildly. Conversely, the interdependence between Buyers and Rivals is more symmetrical,
where observing strong Buyers signifies strong Rivals, and vice versa. In addition, both
Substitutes and Rivals show inversely proportional dependence on New Entrants; observing
strong New Entrants decreases the likelihood of witnessing strong Rivals or strong Substitutes.
One important DAFF element that plays a major role in shaping these interactions among the
forces is the shared parent drivers. When the decision-maker gains new market intelligence,
these shared drivers facilitate the probabilistic updating of his beliefs about one or multiple
competitive forces through conditional reasoning and inference.
Along the same lines, Substitutes and Buyers prove to be the top two competitive influencers
of economic performance in the U.S. residential solar PV industry. The industry’s profitability
seem to be mostly sensitive to the power of Buyers, for changing the latter updates the
decision-maker’s beliefs about three other forces: Substitutes, New Entrants, and Rivals.
Accordingly, EBT can be as small as 1.82 billion $/year in a competitive setting where the
power of Buyers is {high} and as large as 5.77 billion $/year in a competitive setting where
the power of Buyers is {low}. Solar incumbents can capitalize on this insight to reduce
competition in their industry, regardless of how they choose to position. Effectively,
incumbents can work collaboratively to deter the threat of Substitutes (e.g. lobby collectively
for more favorable regulations), or they can work individually to secure advantageous
relations with their Buyers (e.g. negotiate exclusive partnerships with dealers).
After assessing the competitive performance of the overall industry, we analyze the
competitive performance in multiple positioning segments that are of interest to SunEnergy.
Four positioning decisions are investigated, each influencing multiple force and factor
uncertainties. Regional Focus is a Value Proposition decision that addresses what customers
to serve: [Rural] or [Urban]. Then, Downstream Integration, Customer Finance, and Panel
Manufacturing are Value Chain decisions that determine how to operate the business: whether
to serve customers directly [No Dealer] or through intermediate dealers [Dealer]; whether to
CHAPTER 5 — Conclusions 270
sell the solar system through [Direct Purchase] or offer product financing in the form of
[Loan], [Full-upfront lease], or [No-upfront lease]; and whether to [Insource] or [Outsource]
the manufacturing of the solar panels. Adding the four decisions to the Bayesian Network
results in a complete DAFF Decision Diagram, and combining the various decision
alternatives results in 32 possible positioning tracks.
Each positioning track is characterized by a unique competitive landscape and,
correspondingly, a unique EBT profit value. The highest EBT of 3.98 billion $/year is realized
by positioning in [Urban, No Dealer, No-upfront Lease, Insource] while the lowest EBT of
0.51 billion $/year is obtained upon positioning in [Rural, Dealer, Direct Purchase, Insource].
Overall, the outputs from the Decision Diagram show that Customer Financing and
Downstream Integration are influential in shaping the residential solar industry. While loans
and leases consistently achieve lower competitive forces and higher EBT, direct-purchase
agreements prove to be robustly inferior. Similarly, cutting dealers out and managing
customers directly prove to be a favorable positioning strategy in most cases, especially in
urban areas. In contrast, the influence of Panel Manufacturing seems to be diluted by other
positioning decisions, resulting in no clear impact on the five forces or EBT. Regional Focus
plays a unique role in market segmentation; locating in urban areas exposes the solar firm to
higher competitive forces but also larger customer pool. Consequently, while urban
positioning is likely to yield lower prices and higher costs per solar system, its relatively high
sales are likely to compensate for its relatively low margins and ultimately produce superior
EBT compared to rural positioning.
As should be clear by now, the DAFF models track and quantify strategic interactions not only
among the industry’s competitive forces but also among the firm’s positioning decisions and
between the forces and the decisions. These interactions are neither universal across industries
nor generalizable in a given industry, however; rather, they are primarily shaped by the firm’s
subjective information and beliefs. Even if we assume a standardized DAFF model for the
U.S. residential solar PV industry within the next two years, different decision-makers from
different solar firms may have different market intelligence and business intuition, which
results in different design of uncertainty degrees or different probability assignments over
those degrees. In fact, beyond the subjective assessment of uncertainty, different corporate
CHAPTER 5 — Conclusions 271
cultures and managerial experiences may incentivize decision-makers to model different
positioning decisions or alternatives. For instance, a decision-maker with an economics
background may want to focus on financing decisions whereas a decision-maker with an
engineering background may want to focus on product-design decisions. Inevitably, the
subjective input into the DAFF models results in subjective outputs and recommendations,
unique to the decision-maker’s outlook on the industry. In a way, we assert this DAFF
characteristic as an advantage, for it preserves and promotes Michael Porter’s teachings that
firms should compete to be “unique” not “best.” In this case study, the DAFF models ensures
that SunEnergy adopts a unique competitive strategy that matches its unique information,
preferences, and resources in the residential solar industry.
Although DAFF may provide different results and recommendations to different decision-
makers, it always provides the same clarity to all decision-makers. Regardless of whether the
competitive forces turn out to be strong or weak, and irrespective of what positioning tracks
yield the highest EBT, DAFF ensures that the decision-maker achieves “clarity of thought”
when assessing competition in his business. In fact, when we asked SunEnergy’s Director of
Strategic Planning about the benefits he gained from this modeling exercise, clarity was on the
top of his list. As he insightfully explained, DAFF incorporates and enforces clarity in every
step of modeling the five forces and the positioning decisions. From a structural standpoint,
the model requires the decision-maker to think about an extensive list of drivers and factors
that shape the competitive landscape. As emphasized in Chapter 4, examining this list of
uncertainties reduces cognitive biases that may magnify the role of some competitive
attributes while attenuating (or even ignoring) the role of others. One level deeper, clarity is
also ensured via the need to design mutually exclusive and collectively exhaustive degrees, as
well as the need to analyze prospects that involve multiple tradeoffs among those degrees. On
multiple occasions, our probability elicitations from SunEnergy’s decision-maker have led to
“aha!” moments with regards to the industry’s activities and the competitive players’ behavior.
A similar level of clarity is achieved when thinking about positioning. Rather than cramming
all positioning decisions in one vague or seemingly indivisible plan, DAFF allows the
decision-maker to model a distinct decision for virtually every step along the business’s value
CHAPTER 5 — Conclusions 272
chain. Additionally, examining the various combinations of positioning alternatives helps
widen the decision-maker’s perspective about the range of strategic choices at his disposal.
4.1 Future Work
Despite its many advantages, the proposed DAFF model in this case study can still be
improved on multiple fronts. To start, the current profit-value metric covers all solar firms in
every positioning segment. Only if we assume that SunEnergy’s market-share and upfront
capital costs are comparable across all positioning segments will the current model allow an
accurate ranking of the company’s own profit in those segments. Because such assumptions
may be impractical, future work may extend the DAFF modeling in two ways. First, it would
be rather useful to undertake the third step of this competitive analysis, which allows adding
SunEnergy’s market-share as an uncertainty and updating the decision diagram’s value node
into SunEnergy-specific EBT. Second, for every positioning track, SunEnergy’s residential
solar team can provide refined estimates of any upfront capital investments that the company
may need in order to initiate or expand its residential business.
Beyond these economic updates, SunEnergy may gain deeper insight into competitive
positioning either by adding new positioning decisions or alternatives or by further
disintegrating current positioning decisions along the value chain. In that regard, for some
positioning decisions, it may be more realistic to introduce new alternatives as the
combination of multiple existing alternatives. For example, in addition to positioning in either
[Urban] or [Rural] areas, Regional Focus would examine positioning in [Urban and Rural]
combined. Moreover, it would be beneficial to add another alternative to Customer Financing
in order to account for Power Purchase Agreements (PPA) in the industry. PPA is similar to
leasing, for both options maintain the system ownership under the solar firm. However, while
the lease requires the customer to pay a fixed monthly fee for the solar energy, PPA requires
the customer to pay per unit of solar energy consumed. Lastly, it might be helpful to
decompose Downstream Integration into multiple decision nodes that distinguish between
different types of dealers: financial dealers (e.g. asset securitization), operation dealers (e.g.
maintenance) and customer-relations dealers (e.g. sales generation). True to the premise of
CHAPTER 5 — Conclusions 273
DAFF, all these modeling extensions would further clarify positioning and therefore would
further inform SunEnergy’s competitive strategy.
CHAPTER 5 — References 274
References
[1] S. Kann, M. Shiao, C. Honeyman, N. Litvak, J. Jones, L. Cooper, T. Kimbis, J. Baca, S. Rumery
and A. Holm, "U.S. Solar Market Insight: Q1 2015 Executive Summary," Greentech Media and
Solar Energy Industries Association, United States, 2015.
[2] SEIA-a, "Solar Industry Data," 2015. [Online]. Available: http://www.seia.org/research-
resources/solar-industry-data. [Accessed 2015].
[3] The Solar Foundation, "National Solar Jobs Census," 2015. [Online]. Available:
http://www.thesolarfoundation.org/solar-jobs-census/national/. [Accessed 2015].
[4] NEI, "Fact Sheets: Nuclear Power Plants Benefit State and Local Economies," 2015. [Online].
Available: http://www.nei.org/Master-Document-Folder/Backgrounders/Fact-Sheets/Nuclear-
Power-Plants-Contribute-Significantly-to-S. [Accessed 2015].
[5] M. Munsell, "US Solar Market Grew 41%, Had Record Year in 2013," Greentech Media, 07
March 2014.
[6] O. Edenhofer, R. Pichs-Madruga, Y. Sokona, K. Seyboth, P. Matschoss, S. Kadner, T. Zwickel, P.
Eickemeier and G. Hansen, "Summary for Policymakers," in IPCC Special Report on Renewable
Energy Sources and Climate Change Mitigation, Cambridge, United Kingdom and New York,
NY, USA, Cambridge University Press, 2011.
[7] M. E. Porter, "The Five Competitive Forces that Shape Strategy," Harvard Business Review,
January 2008.
[8] A. Goodrich, T. James and M. Woodhouse, "Residential, Commercial, and Utility-Scale
Photovoltaic (PV) System Prices in the United States: Current Drivers and Cost-Reduction
Opportunities," National Renewable Energy Laboratory. Contract No. DE-AC36-08GO28308,
Golden, Colorado, 2012.
[9] C. Brehaut, "Global PV Monitoring 2014-2018: Technologies, Markets and Leading Players,"
GTM Research, Greentech Media, United States, 2014.
[10] V. Bugnion, "Clearly Energy: Residential Demand-Response Programs," 2014. [Online].
Available: https://www.clearlyenergy.com/residential-demand-response-programs. [Accessed
2015].
[11] Navigant Research, "Residential Demand Response. Direct Load Control and Dynamic Pricing
Programs, DR Markets, and DR Management Systems for Residential Customers: Global Market
Analysis and Forecasts," 2014. [Online]. Available:
https://www.navigantresearch.com/research/residential-demand-response. [Accessed 2015].
[12] J. Niccolai, "Google invests in another wind farm for its data centers," Computerworld, 21 April
2011.
CHAPTER 5 — References 275
[13] S. Specker, J. Phillips and D. Dillon, "The Potential Growing Role of Post-Combustion CO2
Capture Retrofits in Early Commercial Applications of CCS to Coal-Fired Power Plants," MIT
Coal Retrofit Symposium, 2009.
[14] K. Farhat, S. Comello, S. Reichelstein, F. Mormann and D. Reicher, "Appendix D: State-Level
Incentives," in The Federal Investment Tax Credit for Solar Energy: Assessing and Addressing the
Impact of the 2017 Step-Down, Stanford, Stanford University, 2015.
[15] N. Litvak, "U.S. Residential Solar Financing 2015-2020," GTM Research, United States, 2015.
[16] M. Yozwiak, "How extending the investment tax credit would affect US solar build," Bloomberg
New Energy Finance, 2015.
[17] S. Kann, M. Shiao, C. Honeyman, N. Litvak, J. Jones, C. Smith, L. Cooper, T. Kimbis, J. Baca, S.
Rumery and A. Holm, "Solar Market Insight Report 2015 Q2: Market Outlook," 2015. [Online].
Available: http://www.seia.org/research-resources/solar-market-insight-report-2015-q2. [Accessed
2015].
[18] K. Aanesen, S. Heck and D. Pinner, "Solar power: Darkest before dawn," McKinsey & Company,
2012.
[19] Decision Systems Laboratory, "GeNIe & SMILE," 2013. [Online]. Available:
https://dslpitt.org/genie/. [Accessed 2015].
[20] Nest, "Saving energy starts with your thermostat," 2015. [Online]. Available:
https://nest.com/thermostat/real-savings/. [Accessed 2016].
[21] EcoFactor, "Optimized Demand Response," 2015. [Online]. Available:
http://www.ecofactor.com/services/#drcloud. [Accessed 2016].
[22] Navigant, "Residential Demand Response Revenue is Expected to Reach $2.3 Billion Annually by
2023," Navigant Research, 24 November 2014.
[23] Ranking the Brands, "SolarCity," 2015. [Online]. Available:
http://www.rankingthebrands.com/Brand-detail.aspx?brandID=3097.
[24] E. Wesoff, "‘World’s Most Efficient Rooftop Solar Panel’ Revisited," Greentech Media, 13
October 2015.
[25] D. Feldman, R. Margolis and D. Boff, "Q1/Q2 ‘14 Solar Industry Update," SunShot - U.S.
Department of Energy, 2014.
[26] ENF, "Solar Panel Manufacturers," 2014. [Online]. Available:
http://www.enfsolar.com/directory/panel. [Accessed 2014].
[27] E. Atkin, "We Are On The Verge Of An Electric Car Battery Breakthrough," ClimateProgress, 31
August 2014.
CHAPTER 5 — References 276
[28] S. Lacey, "Storage Is the New Solar: Will Batteries and PV Create an Unstoppable Hybrid
Force?," Greentech Media, 15 June 2014.
[29] D. Savenije and E. Howland, "10 predictions for the electric sector in 2014," Utility Dive, 6
January 2014.
[30] J. Smart and S. Schey, "Battery Electric Vehicle Driving and Charging Behavior Observed Early in
The EV Project," Advanced Vehicle Testing Activity - Idaho National Laboratory, 2012.
[31] D. R. Baker, "Most electric vehicle drivers charge them at home," SFGate, 21 November 2013.
[32] D. Howell, "Tesla Battery Factory Might Power Up SolarCity, Apple," Investors.com, 21 02 2014.
[33] W. Warwick, "A Primer on Electric Utilities, Deregulation, and Restructuring of U.S. Electricity
Markets," Pacific Northwest National Laboratory, Richland, Washington, 2002.
[34] EIA, "Status of Electricity Restructuring by State," U.S. Energy Information Administration, 2010.
[Online]. Available: http://www.eia.gov/electricity/policies/restructuring/restructure_elect.html.
[Accessed 2016].
[35] W. Pentland, "After Decades Of Doubt, Deregulation Delivers Lower Electricity Prices," Forbes,
13 October 2013.
[36] SEIA-b, "Solar Investment Tax Credit (ITC)," 2015. [Online]. Available:
http://www.seia.org/policy/finance-tax/solar-investment-tax-credit. [Accessed 2015].
[37] SEIA-c, "Depreciation of Solar Energy Property in MACRS," 2015. [Online]. Available:
http://www.seia.org/policy/finance-tax/depreciation-solar-energy-property-macrs. [Accessed
2015].
[38] Investopedia-a, "Fair Market Value," 2016. [Online]. Available:
http://www.investopedia.com/terms/f/fairmarketvalue.asp. [Accessed 2016].
[39] H. K. Trabish, "Why Treasury Is Investigating SolarCity and Solar Third-Party Funds," Greentech
Media, 19 December 2013.
[40] A. H. Miller, "SunPower expanding internationally," CleanEnergyAuthority.com, 21 December
2012.
[41] RePower, "Solar Universe Enters International Market and Debuts First Franchise in Puerto Rico,"
2013. [Online]. Available: https://repower.solaruniverse.com/press-releases/solar-universe-
announces-local-franchise-offices-in-puerto-rico. [Accessed 2015].
[42] S. Kann, M. Shiao, S. Mehta, C. Honeyman, N. Litvak, J. Jones, J. Baca, S. Rumery and A. Holm,
"U.S. Solar Market Insight Report - Q1, 2014," Greentech Media and Solar Energy Industries
Association, United States, 2014.
CHAPTER 5 — References 277
[43] R. A. Howard and A. E. Abbas, Foundations of Decision Analysis, 1st ed., United States: Pearson,
2016.
[44] Z. Shahan, "What Is The Current Cost Of Solar Panels?," CleanTechnica, 4 February 2014.
[45] M. Munsell, "Solar PV Pricing Continues to Fall During a Record-Breaking 2014," Greentech
Media, 13 March 2015.
[46] N. Litvak, "U.S. Residential Solar Financing: 2014-2018," GTM Research, California, 2014.
[47] Investopedia-b, "Earnings Before Tax - EBT," 2016. [Online]. Available:
http://www.investopedia.com/terms/e/ebt.asp. [Accessed 2016].
[48] R. Dietz, "The Geography of Home Size and Occupancy," National Association of Home Builders,
2 December 2011.
[49] United States Census Bureau, "Census Urban and Rural Classification and Urban Area Criteria,"
2010. [Online]. Available: https://www.census.gov/geo/reference/ua/urban-rural-2010.html.
[Accessed 2015].
[50] R. D. Shachter, "Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite
Information in Belief Networks and Influence Diagrams)," Morgan Kaufmann Publishers Inc. San
Francisco, 1998.
CHAPTER 5 — Appendix A: Degree Characterization for Competitive Uncertainties 278
Appendix A: Degree Characterization for Competitive Uncertainties
Table 5.A1: Definition of competitive force and driver uncertainties in the U.S. residential
solar industry
Uncertainty Degrees
Substitutes
Power of Substitutes high low
Price-performance tradeoff
relative to this industry’s
product
substitute superior to
solar
substitute equivalent
to solar
substitute inferior to
solar
Regulatory and technical
feasibility
substitute more favorable than
solar
substitute less favorable than
solar
Substitute performance superior inferior
Substitute upfront cost higher upfront cost lower upfront cost
Substitute bill savings less bill savings more bill savings
Substitute installation &
maintenance faster or easier slower and harder
Substitute control &
operation
more
automated
with higher
consumer
control
less automated
with higher
consumer
control
more
automated
with lower
consumer
control
less automated
with lower
consumer
control
Substitute climate impact more emissions’ reduction less emissions’ reduction
Buyers
Bargaining Power of Buyers high low
Power of end-customers high low
Power of dealers high low
Costumer price sensitivity elasticity of demand =
[−3.5 , −2.5] elasticity of demand =
[−2.5, −1.5]
Customer switching cost
away from the incumbent
product
legal complications or high
financial penalty
no legal complications and low
financial penalty
Dealer ability to influence
customers downstream
heavily influence
customer choice
mildly influence
customer choice
not influence
customer choice
CHAPTER 5 — Appendix A: Degree Characterization for Competitive Uncertainties 279
Dealer volume of sales per
incumbent
dealer involved in < 10% of
incumbent sales
dealer involved in > 10% of
incumbent sales
Dealer threat to integrate
backward
backward integration of less
than one dealer per year (on
average)
backward integration of more
than one dealer per year (on
average)
Customer need to trim
immediate cost of industry
product
customer can afford upfront cost customer cannot afford upfront
cost
Dealer partnership with
incumbent exclusive partnership non-exclusive partnership
Dealer reach local national
Dealer brand impactful not impactful
Product perceived cost as
fraction of the customer
budget
< 20% of annual household
income
> 20% of annual household
income
Cost reduction for customer
by industry product < 15% reduction in power bill > 15% reduction in power bill
Amount of cash available for
customer
less than ten-times the system
price
more than 10-times the system
price
Performance improvement
for customer by industry
product
improves power purchase or
utilization
Does not improve power
purchase and utilization
New Entrants
Threat of new entrants high low
Barriers to entry high low
Expected retaliation high low
Size independent
disadvantages for new
entrant
cost disadvantage or need large
scale
no cost disadvantage and no
need for large scale
Size dependent
disadvantages for new
entrant
sustainable size independent
disadvantage
no sustainable size independent
disadvantage
Unequal access to
distribution channel by new
entrant
use existing retail channels need to invest in new retail
channels
Customer adoption rate of
product by new entrant < 70% market-share annual
growth
> 70% market-share annual
growth
Size and availability of
capital needed by new
entrant
need working capital is < $100
million
need working capital is > $100
million
CHAPTER 5 — Appendix A: Degree Characterization for Competitive Uncertainties 280
Previous responses by
incumbents acquisition or match offering
no acquisition and no match
offering
Extent of resources available
for incumbents
time before cash runs out is < 1
year
time before cash runs out is > 1
year
Incumbent economies of
scale
economies of scale are fully
realized
economies of scale are in-
progress
Incumbent established brand one or more well-established
brands no well-established brands
Incumbent IP new technology retention rate is
< 3 years
new technology retention rate is
> 3 years
Incumbent cumulative in-
house experience
employee retention rate per year
is < 90% employee retention rate per year
is > 90%
Incumbent prime location proximity to innovation
resources
no proximity to innovation
resources
Limitation of distribution
channels saturated dealer channels unsaturated dealer channels
Control over distribution
channel by incumbent
exclusive dealer-incumbent
agreements
non-exclusive dealer-incumbent
agreements
Customer trust in incumbent positive reputation for
incumbent in specific segments
no positive reputation for
incumbent in any segment
Incumbent network effects weak network effects strong network effects
Efficiency of capital markets weighted average cost of capital
(WACC) is < 13%
weighted average cost of capital
(WACC) is > 13%
Incumbent customer
acquisition cost > 0.5 $/𝑊 < 0.5 $/𝑊
Incumbent R&D spending > 3% of annual revenue, and
less than annual profits
< 3% annual revenue, or greater
than annual profits
Incumbent assets available funds are > $1 billion
per year
available funds are < $1 billion
per year
Incumbent inventory < 100 MW in total capacity > 100 MW in total capacity
Available production
capacity
production capacity meets
market demand
production capacity does not
meet market demand
Borrowing power high asset growth and
performance
low asset growth and
performance
Excess cash cash-in-hand is > 10% of total
assets
cash-in-hand is < 10% of total
assets
Rivals
Rivalry high low
Basis of competition price non-price
CHAPTER 5 — Appendix A: Degree Characterization for Competitive Uncertainties 281
Intensity of competition high low
Inability to read other
incumbents’ signals
incumbent able to read other
incumbents’ market signals
incumbent not able to read other
incumbents’ market signals
Market segmentation less than 2 segments and
dimensions
more than 2 segments and
dimensions
Extent of exit barriers
exist cost prevent incumbent’s
investment in the top 30% of
the business
exist cost does not prevent
incumbent’s investment in the
top 30% of the business
High commitment to
business < 50% of the incumbent
revenue is from this industry
> 50% of the incumbent
revenue is from this industry
Ability to enforce practices
desirable for whole industry
industry leaders engage in
collaborations
industry leaders do not engage
in collaborations
High fixed costs and low
variable costs
ratio of fixed cost to variable
cost is < 1
ratio of fixed cost to variable
cost is > 1
Ability to meet the needs of
multiple customer segments
less than 2 segments or
dimensions
more than 2 segments or
dimensions
Importance of non-profit
goals
care for branding or social
impact
does not care for branding or
social impact
Presence of an industry
leader
at least one incumbent with
≥ 30% market share
no incumbent with ≥ 30%
market share
Suppliers
Bargaining Power of
Suppliers high low
Supplier threat to integrate
foreword
backward integration of less
than one supplier per year (on
average)
backward integration of more
than one supplier per year (on
average)
Supplier switching cost
between incumbents
< 10% increase in production
cost for supplier
> 10% increase in production
cost for supplier
Incumbent switching costs
between suppliers
< 10% increase in production
cost for incumbent
> 10% increase in production
cost for incumbent
Relative dependence of
suppliers on this industry
profits
this industry is the top source of
profit for supplier
this industry is not the top
source of profit for supplier
Concentration of suppliers
relative to incumbents < 10 suppliers per incumbent > 10 suppliers per incumbent
Availability of substitutes for
what the supplier provides
< 2 current and < 1 future
substitute per year
< 2 current or > 1 future
substitute per year
Incumbent joint investments
with current supplier
incumbent partner with or invest
in the supplier’s business
incumbent does not partner with
and does not invest in the
supplier’s business
Product differentiation
among suppliers
< 50% (by monetary value) of
the system is standardized
> 50% (by monetary value) of
the system is standardized
CHAPTER 5 — Appendix A: Degree Characterization for Competitive Uncertainties 282
Profits extracted by
suppliers from other
industries < 50% of supplier profits > 50% of supplier profits
Number of industries
supplier serve < 3 industries ≥ 3 industries
Substitutes & Buyers (shared driver)
Customer switching cost
from this industry product to
substitutes
legal complications or high
financial penalty
no legal complications and low
financial penalty
Buyers & New Entrants (shared driver)
Relative reliance of customer
on industry product
ratio of solar value
to lifetime utility
cost for customer is
< 15%
ratio of solar value
to lifetime utility
cost for customer is
between 15% and
25%
ratio of solar value
to lifetime utility
cost for customer is
> 15%
Buyers, New Entrants, & Rivals (shared driver)
Customer switching cost
among industry products
legal complications or high
financial penalty
no legal complications and low
financial penalty
Willingness of price
discounting by incumbents willing to share < 15% of
profits with customers
willing to share > 15% of
profits with customers
Buyers & Rivals (shared driver)
Product differentiation
among incumbents
no product
differentiation
short-term product
differentiation
long-term product
differentiation
New Entrants & Rivals (shared driver)
Commitment of incumbent to
retain and fight over market
share
focus on absolute growth focus on relative growth
Rivals & Suppliers (shared driver)
Fragmentation of the
industry monopoly leaders & followers oligopoly
CHAPTER 5 — Appendix A: Degree Characterization for Competitive Uncertainties 283
Table 5.A2: Definition of factor uncertainties in the U.S. residential solar PV industry
Uncertainty Degrees
Technology (and Complements)
T1: Proliferation of electric
vehicles
electric vehicle in the
household
no electric vehicle in the
household
T2: Proliferation of storage
batteries
battery storage system in the
household
no battery storage system in the
household
T3: Change in home total
demand
smaller total
demand same total demand larger total demand
T4: Change in home peak
demand
smaller peak
demand same peak demand larger peak demand
T5: change in size of home
solar system 35% smaller same 35% bigger
T6: Optimal size of home
solar system
< 50% of
home peak
demand
Between 50%
and 90% of
home peak
demand
Between 90%
and 110% of
home peak
demand
> 110% of
home peak
demand
Regulation
R1: Power market structure regulated market deregulated market
R2: magnitude of utility rates high rates low rates
R3: hourly variation in
utility rates high variations low variations
R4: Solar system
connectivity charges connectivity charges no connectivity charges
R5: Solar system control controlled by utility not controlled by utility
R6: Solar territorial cap territorial supply cap no territorial supply cap
R7: Solar system cap below home peak
demand
at home peak
demand
above home peak
demand
R8: Solar rate equal to retail rate below retail rate but
above LCOE equal to LCOE
R9: Solar net-negative
compensation structure carry-over credit monthly payments
R10: Application of ITC &
Depreciation
30% ITC and
accelerated
depreciation
30% ITC only none
R11: Exploitation of FMV applicable not applicable
Growth
G1: Industry growth rate fast slow
CHAPTER 5 — Appendix B: Influence of Positioning Tracks on Competitive Forces 284
Appendix B: Influence of Positioning Tracks on Competitive Forces
Table 5.B1: Probability of {high} power for each competitive force under each positioning
track
Probability of {high} power of…
Positioning Track Substitutes Buyers New
Entrants Rivals Suppliers
Rural, Purchase, Dealer, Outsource 0.388 0.623 0.548 0.644 0.417
Rural, Purchase, Dealer, Insource 0.388 0.621 0.501 0.661 0.409
Rural, Purchase, NoDealer, Outsource 0.388 0.230 0.359 0.682 0.398
Rural, Purchase, NoDealer, Insource 0.388 0.227 0.314 0.696 0.396
Rural, Loan, NoDealer, Outsource 0.277 0.188 0.349 0.607 0.398
Rural, Loan, Dealer, Outsource 0.277 0.518 0.516 0.566 0.417
Rural, Loan, NoDealer, Insource 0.277 0.185 0.304 0.615 0.396
Rural, Loan, Dealer, Insource 0.277 0.515 0.468 0.578 0.409
Rural, LeaseF, Dealer, Outsource 0.344 0.537 0.514 0.600 0.417
Rural, LeaseF, Dealer, Insource 0.344 0.534 0.466 0.611 0.409
Rural, LeaseF, NoDealer, Outsource 0.344 0.213 0.349 0.637 0.398
Rural, LeaseF, NoDealer, Insource 0.344 0.209 0.305 0.644 0.396
Rural, LeaseN, Dealer, Outsource 0.287 0.412 0.502 0.532 0.417
Rural, LeaseN, Dealer, Insource 0.287 0.409 0.454 0.552 0.409
Rural, LeaseN, NoDealer, Outsource 0.287 0.185 0.344 0.576 0.398
Rural, LeaseN, NoDealer, Insource 0.287 0.183 0.300 0.592 0.396
Urban, Purchase, Dealer, Outsource 0.539 0.705 0.536 0.696 0.404
Urban, Purchase, Dealer, Insource 0.539 0.704 0.487 0.720 0.398
Urban, Purchase, NoDealer, Outsource 0.539 0.249 0.331 0.715 0.385
Urban, Loan, Dealer, Outsource 0.396 0.590 0.499 0.627 0.404
Urban, Purchase, NoDealer, Insource 0.539 0.247 0.290 0.737 0.385
Urban, Loan, Dealer, Insource 0.396 0.588 0.450 0.645 0.398
Urban, LeaseF, Dealer, Outsource 0.488 0.615 0.498 0.661 0.404
Urban, LeaseF, Dealer, Insource 0.488 0.612 0.449 0.678 0.398
Urban, Loan, NoDealer, Outsource 0.396 0.201 0.329 0.641 0.385
Urban, Loan, NoDealer, Insource 0.396 0.198 0.284 0.656 0.385
Urban, LeaseN, Dealer, Outsource 0.400 0.482 0.482 0.586 0.404
Urban, LeaseN, Dealer, Insource 0.400 0.481 0.433 0.616 0.398
Urban, LeaseF, NoDealer, Outsource 0.488 0.233 0.325 0.677 0.385
Urban, LeaseF, NoDealer, Insource 0.488 0.230 0.282 0.692 0.385
Urban, LeaseN, NoDealer, Outsource 0.400 0.194 0.323 0.604 0.385
Urban, LeaseN, NoDealer, Insource 0.400 0.193 0.281 0.631 0.385