Establishing conditions for the economic viability of fuel cell-based, combined heat and power...

Applied Energy 111 (2013) 904–920

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Applied Energy

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Establishing conditions for the economic viability of fuel cell-based,combined heat and power distributed generation systems

0306-2619/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.apenergy.2013.06.025

⇑ Corresponding author.E-mail address: [email protected] (R.J. Braun).

Kristopher A. Pruitt a, Robert J. Braun b,⇑, Alexandra M. Newman c

a Department of Mathematical Sciences, United States Air Force Academy, Colorado Springs, CO 80840, United Statesb Department of Mechanical Engineering, Colorado School of Mines, Golden, CO 80401, United Statesc Division of Economics and Business, Colorado School of Mines, Golden, CO 80401, United States

h i g h l i g h t s

�We derive conditions for the economic viability of a distributed generation technology.� We demonstrate these conditions for fuel cell-based systems in various commercial building scenarios.� Results indicate that building, market, and configuration significantly impact economic viability.� Impact of fuel cell efficiency and carbon tax on emissions on viability are examined.

a r t i c l e i n f o

Article history:Received 20 December 2012Received in revised form 12 June 2013Accepted 14 June 2013Available online 17 July 2013

Keywords:Mixed integer programmingEconomic viabilityDistributed generationCombined heat and powerFuel cellCarbon tax

a b s t r a c t

Combined heat and power (CHP), distributed generation (DG) technologies have the potential to provideeconomic savings to commercial building owners in certain markets, if the system is appropriately con-figured, sized, and operated. Numerous optimization models exist for determining the design and dis-patch of a DG system, and some require a great deal of time and computing power to determinebuilding-market scenarios for which the optimal solution includes the acquisition of CHP technologies.Thus, it is beneficial to identify which scenarios are likely to be economically viable prior to solving anoptimization model that determines the lowest-cost system design and dispatch. Accordingly, we deriveconditions for the economic viability of a CHP DG technology by comparing the total operational savingsafforded by the technology to its total installed cost. We demonstrate these conditions numerically ineight distinct scenarios that include the installation of a fuel cell-based CHP system for various buildingtypes and energy markets. Using these scenarios, we examine the energy, emissions, operations andmaintenance, and peak demand savings provided by the DG system, and determine which scenariosare likely to result in total savings that exceed the total installed cost. Results indicate that the combina-tion of building type, energy market, and system design and dispatch in a given scenario have a signifi-cant impact on the economic viability of the CHP system.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction more traditional mathematical programming algorithms (see

Combined heat and power (CHP), distributed generation (DG)technologies have the potential to provide economic savings tocommercial building owners in certain markets, if the DG systemis appropriately configured, sized, and operated. We refer to thetask of determining the lowest-cost mix, capacity, and operationalschedule of DG technologies as the design and dispatch problem.Ignoring the mix of DG technologies results in the dispatch prob-lem, see, e.g., [26,29,31], sometimes known as the unit commit-ment problem, depending on the scope. Existing efforts to solvethe design and dispatch problem apply techniques that includesimulation (see [1–8]), evolutionary algorithms (see [9–13]), or

[14–22]). In general, research which applies simulation and evolu-tionary algorithms cannot guarantee global optimality of designand dispatch solutions. By contrast, research which applies moretraditional algorithms, such as Simplex and branch-and-bound,provides a guarantee of global optimality. However, existing Sim-plex and branch-and-bound applications fail to consider many per-formance characteristics that constrain the off-design operation ofDG technologies. Simplifying or neglecting these characteristicspermits the rapid solution of large problem instances. However,insufficiently modeling the system performance could result inthe prescription of a suboptimal or infeasible system design anddispatch.

Pruitt et al. [23,25] demonstrate the advantages of realisticallymodeling the performance characteristics of a DG system with amixed-integer non-linear programming (MINLP) model of the

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Fig. 1. Combined heat and power (CHP), distributed generation (DG) systemconsisting of solid-oxide fuel cells (SOFCs).

K.A. Pruitt et al. / Applied Energy 111 (2013) 904–920 905

design and dispatch problem. This MINLP, referred to as ðPÞ, pre-scribes a minimum cost system design and dispatch, and includesoff-design performance characteristics for the generation and stor-age of power and heat that are simplified or not considered inmixed-integer linear programming (MILP) models. In particular,ðPÞ models the maximum turn-down, start-up fuel consumption,ramping capability, and part-load electric efficiency of power gen-eration technologies, and models the time-varying temperature ofthermal storage technologies. The consideration of these dynamicperformance characteristics can be particularly important whenthe technologies are operated in a load-following (i.e., time-vary-ing), rather than baseload (i.e., fixed), manner.

Given its greater level of detail compared to existing models,ðPÞ provides a novel means of conducting sensitivity analyses toevaluate the economic viability of DG. These sensitivity analysescan be accomplished by varying the parameter values for demand,pricing, and performance to create an array of problem instances,and then solving those instances of ðPÞ to determine which combi-nations of parameter values result in DG acquisition. However,large instances of ðPÞ can be time consuming and computationallyexpensive to solve. Pruitt et al. [23] present a one-year time hori-zon, hourly fidelity instance of ðPÞ which has nearly 200,000 vari-ables and 300,000 constraints, and which requires more than 10 hto reach a solution that is within 8% of global optimality. Addition-ally, for many instances, the combination of energy market, build-ing type, and DG technologies under consideration results in anoptimal design and dispatch solution that does not include theacquisition of DG. Thus, a great deal of time and computing powercan be expended solving various building-market-technology in-stances of ðPÞ in order to discover a combination for which DG iseconomically viable. For this reason, it would be beneficial to iden-tify which combinations are likely to be economically viable priorto solving ðPÞ to determine the optimal design and dispatch.

In addition to addressing programming challenges of large,multi-variable optimization problems, our work is motivated bya desire to understand and elucidate the necessary conditions foreconomic viability of advanced and alternative DG technologiesin the commercial building energy sector. Work of this nature atresidential scales has been ongoing for several years[27,28,33,34]. Numerous advancing energy conversion technolo-gies (e.g., microturbines, solar photovoltaic (PV), and fuel cells) in-tended for commercial DG applications have struggled to attainsignificant market penetration. High capital cost and low utilityenergy pricing are frequently considered as the primary barriersto widespread adoption of new technologies in these stationaryenergy market sectors. The wide variability in utility energy pric-ing, technology-specific capital costs and performance, and pricingof externalities associated with energy supply contribute tocreating a complex picture of market viability and effective policymeasures that provide incentive for new technology adoption.Thus, this effort provides one component of a broader set ofanalysis tools aimed at establishing a more informed viewpointof the conditions required for the economic viability of new andexisting DG technologies.

In this paper, we develop screening criteria for the economicviability of a CHP DG system based on a parametric analysis ofthe objective function of ðPÞ. This comparative static analysis is asimilar approach to that taken in [27], but for a commercial, ratherthan a residential, setting. Additionally, we base our analysis on thestructure of the optimization model (P), which requires the substi-tution of parameters for the variables in the objective function. Be-cause the analysis requires fixed parameter values, only a singledesign and dispatch strategy can be tested at one time. Thus, fora given analysis, we must choose a system configuration, capacity,and operational strategy for which we evaluate economic viability.We then derive necessary conditions on the model parameters for

the selected design and dispatch to result in operational savingsthat exceed the capital and installation costs (i.e., the total installedcost). These conditions provide insight regarding economicallyattractive building, market, and technology characteristics and af-ford screening criteria for the instances of ðPÞ we wish to solve.Armed with a viable system design and dispatch, we can solveðPÞ to determine the optimal design and dispatch. Note, then, thatwhile ðPÞ is an optimization model prescribing the cost-minimiz-ing mix of technologies to procure, and how to operate them, bycontrast, the approach in this paper simply evaluates an existingsystem regarding its economic viability; no optimization occurs.

There are numerous emerging distributed generation technolo-gies that may be suitable for commercial building applications. Inparticular, the unique characteristics of solid oxide fuel cells (SOF-Cs) have encouraged their development for a wide variety of appli-cations that range from portable, mobile and micro-combined heatand power (500 W to 20 kW) to larger-scale stationary power atboth distributed generation (�100 kW to 5 MW) and central utilityscales (>100 MW). Attractive SOFC technology attributes includehigh electric efficiency, high-grade waste heat, fuel flexibility,low emissions, power scalability, and low unit capital cost poten-tial when high production volumes are achieved. The high operat-ing temperature of SOFCs enables production of varying grades ofwaste heat that can then be recovered for process heating, poweraugmentation via gas turbine integration, or for polygenerationof exportable products (e.g., heat, cooling, power, and fuels). Theeffective use of waste heat significantly impacts overall systemefficiency, economics, and environmental emissions. These attri-butes have accelerated SOFC technology development with theaim of replacing traditional combustion-based power generationequipment (such as gas turbines and internal combustion engines)[24].

The specific CHP DG system considered in our comparative sta-tic analysis is depicted in Fig. 1. For this system, if DG is not ac-quired, then the building has its power demand met by theutility and its heating demand met by an existing natural gas-fedboiler. We wish to consider retrofitting the building with a naturalgas-fed, solid-oxide fuel cell (SOFC) system. The system’s primaryproduct is power, which reduces the electric energy that must beimported from the utility, and which provides a source of revenuewhen electricity can be exported from the SOFC system to the util-ity. Additionally, when waste heat capture is included in the sys-tem, high temperature exhaust gas from the SOFCs is supplied tothe building to reduce the thermal energy that must be providedby the boiler. For the sake of simplicity, we do not include othergeneration and storage technologies in this analysis in order to fo-cus on the economic viability of an individual technology (i.e., aSOFC-CHP system). Note that our static analysis allows us tochoose a priori whether we acquire any of a given technology. This

906 K.A. Pruitt et al. / Applied Energy 111 (2013) 904–920

choice, in turn, provides us with an outcome as to the economicviability of that choice. We do not allow the model to turn technol-ogies on and off, because the model is not choosing technologies; itis merely making an evaluation given a choice.

While the focus of this paper is centered on fuel cell-based DGsystems, the model ðPÞ developed by Pruitt et al. [23,25] is flexibleenough to allow evaluations of a multitude of distributed energyresources, including solar PV, microturbines, internal combustion(IC) engines, etc., provided cost and performance relations areinputted. Throughout the paper, we use the following notation:

Sets
j 2 J set of all technologies (Consistent with Pruitt et al.
[23], we define the elements of J numerically as4 = CHP SOFC and 6 = Boiler.)

n 2 N
set of all months S� � t 2 T n set of all hours in month n T ¼ nT n
Parameters
d demand time increment (hours)
gPjt ; gQ

j
rated electric and thermal efficiency, respectively,of technology j = 4 in hour t (fraction)
lj
maximum turn-down for technology j = 4(fraction)
mt
net-metering rate paid by utility for exportedpower in hour t (fraction)
rj
start-up time for technology j = 4 to reachoperating temperature (hours)
cj
amortized capital and installation cost oftechnology j = 4 ($/kW)
dPt ; dQ

t
average power and heating demand, respectively,of the building in hour t (kW)
kj
rated power capacity of technology j = 4 (kW) mj average operations and maintenance (O&M) cost of
each technology j = 4,6 ($/kWh)
pt, gt price of electricity and natural gas, respectively,
from the utility in hour t ($/kWh)
pmax
n
peak demand price of power from the utility inmonth n ($/kW/month)
z
tax on carbon emissions ($/kg) zp, zg average carbon emissions rate for utility power and
gas combustion, respectively (kg/kWh)
Variables Aj number of technology j = 4 acquired (integer) Gjt natural gas input to each technology j = 4, 6 in hour
t (kW)
Njt number of technology j = 4 that starts up between
hours t � 1 and t (integer)
Pjt power output from technology j = 4 in hour t (kW) Qjt heat output from each technology j = 4,6 in hour t
(kW)

Uoutt ; Uin

t
power purchased from and exported to,respectively, the utility in hour t (kW)
Umaxn
max power purchased from the utility in month n
(kW)

The remainder of the paper is organized as follows: Section 2presents the analysis of the total cost objective function of ðPÞwhich culminates in a cost-versus-savings economic viabilitycondition for DG. Section 3 then examines the types of operationalsavings provided by a CHP DG system. Section 4 presents eightreal-world scenarios that vary by building type, energy market,and technological characteristics of the DG system. In Section 5,we then examine the sensitivity of the operational savings across

and within the eight scenarios in order to determine the paramet-ric conditions for which DG is most economically viable. Section 6concludes the paper.

2. Cost analysis

In this section, we examine the total cost of supplying thepower and heating demands of the building in Fig. 1, based onthe objective function of ðPÞ. Depending on the system design(i.e., whether or not DG is acquired), the total cost may or maynot include acquisition and operation costs for the SOFC-CHPsystem. By comparing the total costs with and without the SOFCsystem, we are able to derive conditions for the economic viabilityof DG.

The total cost to meet the power and heating demands of thebuilding in Fig. 1 is calculated according to the objective functionof ðPÞ presented in Pruitt et al. [23]. However, because we are onlyexamining the viability of SOFC-CHP systems in this paper, thetotal cost does not include the acquisition and operation costsassociated with other distributed energy resources such as batter-ies, PV cells, power-only SOFCs, microturbines, IC engines, or watertanks (which can be included in [23]). Accordingly, we define thetotal cost over the time horizon of interest as:

Cost ¼ c4k4A4 þXt2T

dm4P4t þ ðgt þ zzgÞ r4l4k4

2gP4t

�N4t þ dG4t

� �� ð1aÞ

þXt2T

d ðpt þ zzpÞUoutt � mtptU

int

h ið1bÞ

þXn2N

pmaxn Umax

n ð1cÞ

þXt2T

d gQ6 m6 þ gt þ zzg

� �G6t ð1dÞ

Total cost component (1a) accounts for the capital and installation,operations and maintenance (O&M), fuel (both start-up and steady-state), and carbon emissions costs for the SOFC system. We calcu-late the steady-state fuel consumption (G4t) for the SOFC systemas the quotient of the power output by the SOFCs and their ratedelectric efficiency. Component (1b) captures the energy and carbonemissions costs for electricity imported from the power utility, aswell as the electricity export revenues from any excess SOFC power.Component (1c) calculates the monthly peak demand charges fromthe power utility. Component (1d) determines the O&M, fuel, andcarbon emissions costs associated with the thermal energy pro-duced by the boiler.

The power demands of the building in Fig. 1 must be met by theSOFC system and/or the power utility. The power supply and de-mand are governed by the following relationships:

P4t þ Uoutt � Uin

t ¼ dPt 8t 2 T ð2aÞ

P4t ¼ gP4tG4t 8t 2 T ð2bÞ

Uoutt ¼max 0;dP

t � P4t

n o8t 2 T ð2cÞ

�Uint ¼min 0;dP

t � P4t

n o8t 2 T ð2dÞ

Umaxn ¼ max

t2T nUout

t

� 8n 2 N ð2eÞ

Eq. (2a) demonstrates that the power produced by the SOFC systemand the net-power from the utility must sum to the building’s de-mand. The power output by the SOFCs equates to the product oftheir fuel input and electric efficiency, according to Eq. (2b). Consis-tent with [23], we model the electric efficiency of the SOFCs asvarying with load. Specifically, the electric efficiency decreases asthe SOFC power output increases. Power cannot be both imported


from and exported to the utility in the same hour. Thus, if the de-mand exceeds the SOFC output in a given hour, power is importedfrom the utility according to Eq. (2c). If the SOFC output exceeds thedemand, then power is exported to the utility according to Eq. (2d).Eq. (2e) determines the peak power imported from the utility ineach month. Note that because of the simple and static nature ofour analysis relative to the prescription an optimization model suchas ðPÞ can provide, we do not model the possibility of choosing toexport part of the SOFC capacity to the building and the remainingpart to the grid in the same hour. However, the SOFC power pro-vided to the building demand and to the grid are variables in ðPÞand, therefore, could assume values that model this behavior afterhaving solved ðPÞ, if it is optimal.

The heating demands of the building in Fig. 1 must be met bythe SOFC system and/or the boiler. The heating supply and demandare governed by the following relationships:

Q 4t þ Q 6t ¼ dQt 8t 2 T ð3aÞ

Q 4t ¼ gQ4 G4t 8t 2 T ð3bÞ

Q 6t ¼ gQ6 G6t 8t 2 T ð3cÞ

Eq. (3a) shows that the heat produced by the SOFC system and theboiler must sum to the building’s heating demand. The heat outputby each generator in a given hour is equivalent to the product of itsfuel input and rated thermal efficiency, according to Eqs. (3b) and(3c). In this case, we assume that the thermal efficiency of the SOFCsystem is fixed over time and includes the efficiency of the heatexchanger.

The power supply and demand relationships established in Eqs.(2a)–(2e), and the heating supply and demand relationshipsestablished in Eqs. (3a)–(3c), permit the substitution of parametersfor variables in total cost function components (1a)–(1d). For in-stance, if no SOFCs are acquired (i.e., A4 ¼ G4t ¼ P4t ¼�N4t ¼ Uin

t ¼ 0 8t), then all of the power demand is met by thepower utility, according to (2a), and all of the heating demand ismet by the boiler, according to (3a). In this case, total cost compo-nent (1a) is zero, component (1b) does not include Uin

t , and wesubstitute Uout

t ¼ dPt ; Umax

n ¼maxt2T n dPt

n o, and G6t ¼ dQ

t =gQ6 in

components (1b)–(1d). The resulting total cost calculation doesnot include DG and is based solely on building and market param-eter values.

CostnoDG ¼Xt2T

dðpt þ zzpÞdPt ð4aÞ

þXn2N

pmaxn maxt2T n dP

t

n oð4bÞ

þXt2T

d m6 þgt þ zzg

gQ6

!dQ

t ð4cÞ

Cost component (4a) calculates the energy and emissions costs asso-ciated with the utility supplying all of the power demand, while com-ponent (4b) determines the monthly demand charges for the peakpower load. Cost component (4c) accounts for the O&M, fuel, andemissions costs associated with the boiler providing all of the heatingdemand. Thus, (4a)–(4c) calculate the total cost to meet the building’sdemands over the time horizon of interest with the existing system,based solely on parametric, as opposed to variable, values.

The parameter substitutions into (1a)–(1d) that result in (4a)–(4c) permit the calculation of the total cost over the time horizonof interest without the acquisition of a DG system. An alternativesubstitution into (1a)–(1d) might force DG acquisition. The totalcost with a DG system (CostDG) is then compared to the total costwithout a DG system (CostnoDG) in order to determine the economicviability of DG.

If SOFCs are acquired (i.e., A4 > 0) and operated in all hours (i.e.,P4t > 0 and N4t = 0"t), then the power and heat provided by theexisting system are reduced. Based on the relationships establishedin (2b)–(2e), we substitute G4t ¼ P4t=gP

4t in total cost component

(1a), substitute Uoutt ¼max 0; dP

t � P4t

n oand �Uin

t ¼min

0; dPt � P4t

n oin component (1b), and substitute Umax

n ¼maxt2T n

max 0; dPt � P4t

n on oin component (1c). These subsitutions permit

us to express the flow of natural gas to the SOFCs and the flow ofelectricity to and from the utility in terms of the power (P4t) gen-erated by the SOFC system. We also substitute

G6t ¼ dQt � gQ

4 P4t=gP4t

� �h i=gQ

6 in component (1d), based on the

relationships established in (2b), (3a), (3b) and (3c). As with theprevious substitutions, this substitution permits us to express theflow of natural gas to the boiler in terms of the power generatedby the SOFC system. The resulting total cost calculation (CostDG) in-cludes DG and is based not only on building and market parame-ters, but also on the selected SOFC design (A4) and dispatch (P4t).

CostDG ¼ c4k4A4 þXt2T

d m4 þgt þ zzg

gP4t

� �P4t ð5aÞ

þXt2T

d ðpt þ zzpÞmax 0;dPt � P4t

n ohþmtpt min 0;dP

t � P4t

n oið5bÞ

þXn2N

pmaxn maxt2T n max 0;dP

t � P4t

n on oð5cÞ

þXt2T

d m6 þgt þ zzg

gQ6

!dQ

t �gQ

4

gP4t

!P4t

!ð5dÞ

Cost component (5a) determines the capital and operational costsassociated with acquiring A4 SOFCs and operating them at an aggre-gate power output of P4t in each hour t. Component (5b) calculatesthe cost of power imported from the utility when the demand ex-ceeds the SOFC power output, and the revenue from power ex-ported to the utility when the demand is less than the SOFCpower output. Component (5c) determines the cost associated withthe peak power load imported from the utility each month, afterconsidering the reduction in peak loads provided by the SOFC sys-tem. Component (5d) calculates the operational costs for the boiler,after considering the thermal energy provided by the SOFC system.

Once we select a specific SOFC system design and dispatch (i.e.,fixed values for A4 and P4t), the total cost with DG ( CostDG) is calcu-lated based solely on fixed parameter values. Different instances ofacquisition and operation strategy can be examined, and lead to dif-ferent parameter substitutions for the design and dispatch variablesin (5a)–(5d). Regardless of instance, fixed values must be substi-tuted for the design (A4) and dispatch (P4t) variables in order to con-duct a comparative static analysis. With a static analysis, the systemdesign and dispatch are selected a priori, rather than optimallydetermined by ðPÞ, as in [23,25]. However, the purpose of the staticanalysis is to determine the economic viability of DG for a particularproblem instance prior to expending the time and computationaleffort associated with solving ðPÞ to determine the optimal designand dispatch. Based on the static representations of total cost with( CostDG) and without (CostnoDG) DG, we derive economic and tech-nological conditions for which the optimal solution to ðPÞ is likelyto include SOFC acquisition and, consequently, for which a buildingowner is likely to invest in a SOFC system.

As a minimum criterion, a building owner should not invest in aSOFC system unless the total cost (including amortized capital andinstallation costs) to meet the demands of the building over thetime horizon of interest is less with the system than without it.Thus, the economic viability of the SOFC system can be examined


by comparing the total cost (CostnoDG) to meet the building de-mands with the power utility and boiler alone to the total cost(CostDG) to meet the building demands with a system that includesSOFC technology. If the inequality CostDG < CostnoDG is satisfied,then the total cost to meet the building’s demands is lower withthe SOFC system than without it. Based on the definition ofCostnoDG in (4a)–(4c) and the definition of CostDG in (5a)–(5d), analgebraically equivalent inequality to CostDG < CostnoDG is:

c4k4A4 < SavingsEnergy þ SavingsEmissions þ SavingsO&M

þ SavingsPeak ð6Þ

where the right-hand side of (6) represents the energy, carbonemissions, O&M, and peak demand savings, respectively, associatedwith operating the SOFC system. Thus, the system is economicallyviable if the total operational savings it provides (given by theright-hand side of the inequality in (6)) exceed its total installedcost (given by the left-hand side of the inequality in (6)). The repre-sentation of CostDG < CostnoDG in (6) is obtained by subtracting all ofthe terms in CostDG other than c4k4A4 from both sides of theinequality, and then appropriately grouping the resulting termson the right-hand side of the inequality. The full algebraic deriva-tion of economic viability condition (6) is presented in the Appen-dix. In the next section, we examine in more detail the four typesof operational savings that are revealed by our analysis of total costfunction components (1a)–(1d).

3. Savings analysis

In this section, we discuss the different types of savings (relativeto a system without DG) that are obtained from operating the SOFCsystem in Fig. 1. The total operational savings, over the time hori-zon of interest, afforded by the SOFC system are then compared tothe total installed cost to determine the economic viability of thesystem. In performing our analysis, we develop expressions forsavings in terms of: (i) energy, (ii) emissions, (iii) operations andmaintenance, and (iv) peak demand. We derive these expressionsfrom the relevant terms contained in the difference betweenCostnoDG and CostDG, given in expressions (4a) through (4c) and(5a) through (5d), respectively.

3.1. Energy savings

The first type of savings that can result from acquiring andoperating the SOFC system is the reduction of electric and thermalenergy that must be provided by the existing system. The powergenerated by the SOFCs reduces the electric energy that must bepurchased from the power utility, while the exhaust heat producedby the SOFCs reduces the thermal energy (in the form of naturalgas) that must be purchased from the gas utility to fuel the boiler.

The energy savings provided by operating the SOFC system atthe selected power output P4t, over the time horizon of lengthjT j, are calculated according to Eq. (7).

SavingsEnergy

¼ dXt2T

pt min dPt ; P4t

n oþ mtpt max 0; P4t � dP

t

n o|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ðiÞ

� gt

gP4t

� �1� gQ

4

gQ6

!P4t|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ðiiÞ

266664

377775 ð7Þ

When deriving the terms on the right-hand side of economic viabil-ity condition (6), we obtain SavingsEnergy by grouping the terms thatinclude the energy market pricing parameters pt (price of electric-ity), mt (net-metering rate), and gt (price of natural gas), as describedin the Appendix. This grouping provides the SOFC savings associ-ated with the reduction of electricity and natural gas purchasedfrom the utilities. Depending on the market pricing in a given hour

t, the energy savings available from the SOFC system can be positiveor negative. Positive hourly energy savings are achieved if term (i),the decrease in electricity costs, in Eq. (7) is greater than term (ii),the increase in natural gas costs, in a given hour t. By dividing bothsides of the inequality (i) > (ii) by the strictly positive power outputof the SOFCs (P4t), we achieve an equivalent condition for positiveenergy savings in a given hour t.

pt mindP

t

P4t

!;1

( )þ mtpt max 0;1� dP

t

P4t

!( )

>gt

gP4t

� �1� gQ

4

gQ6

!ð8Þ

Condition (8) must be satisfied in order for an individual term t of thesummation in (7) to be positive. The left-hand side of the inequalityin (8) depends on the magnitude of the building’s hourly power de-mand relative to the strictly positive power output of the SOFCs.

If the building demand is greater than or equal to the selectedSOFC power output dP

t =P4t P 1� �

in a given hour t, then (8) reducesto the condition:

pt >gt

gP4t

� �1� gQ

4

gQ6

!ð9Þ

The left-hand side of the inequality in (9) is the hourly price of elec-tricity from the utility, while the right-hand side is the hourly costassociated with natural gas consumption by the SOFC system toproduce electricity. The gas cost for the SOFCs to produce electricitydepends on the price of natural gas, on the electric and thermal effi-ciencies of the system, and includes a ‘‘credit’’ for the exhaust heatwhich reduces the energy (i.e., natural gas) costs of the boiler. Thus,positive energy savings are obtained in a given hour if the price ofelectricity from the utility exceeds the gas cost for the SOFC systemto produce electricity. As an alternative explanation, positive energysavings are achieved if the rate of decrease in power utility costs(expressed by the left-hand side of (9)) is greater than the rate ofincrease in gas utility costs (expressed by the right-hand side of (9)).

The condition for positive hourly energy savings changes whenexcess power is available from the SOFC system. If the building de-mand is less than the selected power output of the SOFCs

0 6 dPt =P4t < 1

� �in a given hour t, then (8) reduces to:

mt þ ð1� mtÞdP

t

P4t

!" #pt >

gt

gP4t

� �1� gQ

4

gQ6

!ð10Þ

In this case, the rate of increase in gas utility costs (expressed by theright-hand side of (10)) is the same as in (9). However, the rate ofdecrease in power utility costs (expressed by the left-hand side of(10)) now depends on the amount of exported power and the net-metering rate paid by the utility. As more power is exported (i.e.,P4t � dP

t ), the rate of decrease in power utility costs approachesthe export price mtpt (since dP

t =P4t ! 0). If, in addition, the exportprice is less than the import price (i.e., mt < 1 and mtpt < pt), positivehourly energy savings are more difficult to obtain compared to thecase in which no power is exported (since the left-hand side of (10)is less than the left-hand side of (9)).

3.2. Emissions savings

The second type of savings that can result from acquiring andoperating the SOFC system is the reduction of taxed carbon dioxideemitted by the existing system. The SOFC system decreases theelectricity that must be purchased from the utility and, conse-quently, reduces the emissions for which the building owner istaxed. Similarly, the SOFCs reduce the boiler’s carbon emissionsby decreasing the natural gas combusted by the boiler.


The carbon emissions savings provided by operating the SOFCsystem at the selected power output P4t, over the time horizon oflength jT j, are calculated according to Eq. (11).

SavingsEmissions ¼ zdXt2T

zp min dPt ; P4t

n o|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}

ðiiiÞ

� zg

gP4t

� �1� gQ

4

gQ6

!P4t|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ðivÞ

266664

377775ð11Þ

When deriving the terms on the right-hand side of economic viabil-ity condition (6), we obtain SavingsEmissions by grouping the termsthat include the carbon emissions parameters z (tax rate), zp (utilityemissions rate), and zg (natural gas emissions rate), as described inthe Appendix. This grouping provides the SOFC savings associatedwith the reduction of taxed carbon emissions from the utility andthe boiler. The emissions savings increase (in absolute value) asthe carbon tax rate z increases. However, depending on the emis-sions rate of the utility relative to that of natural gas combustion,the emissions savings could be positive or negative. Positive hourlyemissions savings are achieved if term (iii), the decrease in utilityemissions costs, in Eq. (11) is greater than term (iv), the increasein natural gas emissions costs, in a given hour t. By dividing bothsides of the inequality (iii) > (iv) by the strictly positive power out-put of the SOFCs (P4t), we achieve an equivalent condition for posi-tive emissions savings in a given hour t:

zp mindP

t

P4t

!;1

( )>

zg

gP4t

� �1� gQ

4

gQ6

!ð12Þ

Condition (12) must be satisfied in order for an individual term t ofthe summation in (11) to be positive. Similar to energy savings, theleft-hand side of the inequality in (12) depends on the magnitude ofthe building’s hourly power demand relative to the strictly positivepower output of the SOFCs.

If the building demand is greater than or equal to the selectedpower output of the SOFC system dP

t =P4t P 1� �

in a given hour t,then (12) reduces to the condition:

zp >zg

gP4t

� �1� gQ

4

gQ6

!ð13Þ

The left-hand side of (13) is the carbon emissions rate associatedwith utility-generated power, while the right-hand side is the car-bon emissions rate for SOFC-generated power. The carbon emissionsrate for the SOFC system is based on the combustion of natural gas,the electric and thermal efficiencies, and includes a ‘‘credit’’ for thereduction in carbon emissions from the boiler. Thus, positive emis-sions savings are obtained in a given hour if the emissions rate ofthe utility exceeds the emissions rate of the SOFC system. As analternative explanation, positive emissions savings are achieved ifthe rate of decrease in off-site emissions costs (expressed by theleft-hand side of (13)) is greater than the rate of increase in on-siteemissions costs (expressed by the right-hand side of (13)).

If excess power is available from the SOFC system, then the con-dition for positive hourly emissions savings changes. When thebuilding demand is less than the selected power output of the SOFCsystem ð0 6 dP

t =P4t < 1Þ in a given hour t, (12) reduces to:

zp dPt

P4t

!>

zg

gP4t

� �1� gQ

4

gQ6

!ð14Þ

In this case, the rate of increase in on-site emissions costs(expressed by the right-hand side of (14)) is the same as in (13).However, the rate of decrease in off-site emissions costs (expressedby the left-hand side of (14)) now depends on the amount ofexported power. As more power is exported (i.e., P4t � dP

t ), the rate

of decrease in off-site emissions costs approaches zero (sincedP

t =P4t ! 0). Hence, when power is exported (i.e., dPt =P4t < 1 and

zp dPt =P4t

� �< zp), positive hourly emissions savings are more diffi-

cult to obtain compared to when no power is exported (since theleft-hand side of (14) is less than the left-hand side of (13)).

3.3. Operations and maintenance savings

The third type of savings that can result from acquiring andoperating the SOFC system is reduced degradation of the existingsystem. When captured, waste heat from the SOFCs decreasesthe thermal energy that must be provided by the boiler and, conse-quently, reduces the operation and maintenance of the boiler.

The O&M savings provided by operating the SOFC system at theselected power output P4t, over the time horizon of length jT j, arecalculated according to Eq. (15).

SavingsO&M ¼ dXt2T

gQ4

gP4t

!m6|fflfflfflfflfflffl{zfflfflfflfflfflffl}

ðvÞ

� m4|{z}ðv iÞ

266664

377775P4t ð15Þ

When deriving the terms on the right-hand side of economic viabil-ity condition (6), we obtain SavingsO&M by grouping the terms thatinclude the operations and maintenance parameters m4 (SOFC O&Mcost rate) and m6 (boiler O&M cost rate), as described in the Appen-dix. This grouping provides the SOFC savings associated with reduc-ing the workload on the boiler. Depending on the O&M costs of theboiler relative to those of the SOFC system, the O&M savings couldbe positive or negative. Positive hourly O&M savings are achieved ifterm (v), the decrease in boiler O&M costs, in Eq. (15) is greater thanterm (vi), the increase in SOFC O&M costs, in a given hour t. By mul-tiplying both sides of the inequality (v) > (vi) by the electric-to-ther-mal efficiency ratio gP

4t=gQ4

� �of the SOFCs, we achieve an equivalent

condition for positive O&M savings in a given hour t.

m6 >gP

4t

gQ4

!m4 ð16Þ

Condition (16) must be satisfied in order for an individual term t ofthe summation in (15) to be positive. The left-hand side of (16) isthe O&M cost per unit of thermal energy output from the boiler.However, the O&M costs for the SOFCs are charged per unit of elec-tric energy produced. Thus, the right-hand side of (16) multipliesthe O&M cost of the SOFC system by its electric-to-thermal effi-ciency ratio in order to convert the cost to units of thermal energyoutput. Positive O&M savings are obtained if the O&M cost per unitof thermal energy output is greater for the boiler than for the SOFCsystem.

3.4. Peak demand savings

The final type of savings that can result from acquiring andoperating the SOFC system is the reduced burden on the powerutility during the building’s peak demand periods. The power gen-erated by the SOFCs decreases the maximum power load that mustbe imported from the utility each month and, therefore, decreasesthe monthly peak demand costs.

The peak demand savings provided by operating the SOFC sys-tem at the selected power output P4t, over the course of jN jmonths, are calculated according to Eq. (17).

SavingsPeak ¼Xn2N

pmaxn maxt2T n dP

t

n o|fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}

ðviiÞ

�maxt2T n max 0;dPt � P4t

n on o|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ðviiiÞ

2664

3775 ð17Þ


When deriving the terms on the right-hand side of economic viabil-ity condition (6), we obtain SavingsPeak by grouping the terms thatinclude the peak demand charge parameter pmax

n , as described in theAppendix. This grouping provides the SOFC savings associated withreducing the peak power load imported from the utility. The peakdemand savings increase as the monthly peak demand chargepmax

n increases. Unlike energy, emissions, and O&M savings, the peakdemand savings provided by operating the SOFCs are strictly non-negative. However, positive monthly peak demand savings are onlyachieved if term (vii), the peak demand costs without DG, in Eq.(17) is greater than term (viii), the peak demand costs with DG, ina given month n. The inequality (vii) > (viii) is equivalently ex-pressed as:

maxt2T n

dPt

n o> max

t2T nmax 0;dP

t � P4t

n on oð18Þ

in a given month n. Condition (18) must be satisfied in order for anindividual term n of the summation in (17) to be positive. If theSOFC system produces no power in the peak demand hour t formonth n, then the left-hand and right-hand sides of the inequalityin (18) are equal and the peak demand savings are zero for thatmonth. However, because we assume the hourly power output ofthe SOFCs is strictly positive (P4t > 0"t), the right-hand side of(18) is strictly less than the left-hand side and positive monthlypeak demand savings are achieved.

3.5. Total savings

By summing the four types of savings delineated in Eqs. (7),(11), (15), and (17), we obtain the right-hand side of the inequalityin economic viability condition (6) and, hence, the total operationalsavings provided by the SOFC system. Given that some of the sav-ings-types can be negative, the total operational savings could benegative for certain instances. For these instances, the SOFC systemis not economically viable, since condition (6) would require thetotal installed cost (c4k4A4) to be negative. However, if the totalsavings provided by operating the acquired SOFCs are positiveand exceed the total installed cost, over the time horizon of inter-est, then the SOFC system is economically viable. Stricter condi-tions involving the pay-off period of the capital, target rate ofreturn, or other economic considerations could be imposed bythe building owner (i.e., the investor). However, the bound onc4k4A4 determined by condition (6) represents the maximum totalinstalled cost for which the building owner would obtain any eco-nomic benefit from operating the SOFC system.

4. Building, market, and technology scenarios

In order to numerically demonstrate the general conditions foreconomic viability, we develop eight distinct scenarios based on

Table 1Size and demand statistics for a large hotel and medium office located in southern Californaveraged energy demand.

Statistic CA hotel

Height (floors) 6Area (thousand ft2) 122Average power demand (kW) 201Maximum power demand (kW) 346Minimum power demand (kW) 88Average heating demand (kW) 191Maximum heating demand (kW) 578Minimum heating demand (kW) 60Average thermal-to-electric ratio 0.94Maximum thermal-to-electric ratio 2.04Minimum thermal-to-electric ratio 0.36

varying the building type, energy market, and technological designand dispatch for the system depicted in Fig. 1. Using these scenar-ios, we examine the total operational savings provided by the SOFCsystem and determine which scenarios are likely to result in sav-ings that exceed the total installed cost.

We consider two different building types located in two differ-ent energy markets. The buildings are a large-sized hotel and amedium-sized office building. The energy markets are southernCalifornia and southern Wisconsin. The hourly demand data forthe four building-market combinations are established from simu-lation of both large-hotel and medium-sized office buildings usingEnergyPlus (see [35]) and building envelope characteristics estab-lished from standard building types given in the literature (see[36]). While EnergyPlus allows building load data to be generatedon 15-min intervals, such load data do not actually show peak de-mand energy profiles that exceed the values of the hourly averageddata. Current draws from motor startups, transient loads, etc. arenot resolved in EnergyPlus. Building size and hourly energy de-mand statistics for each building-market combination are providedin Table 1. The hourly power demands on the peak power day ofthe year for each building-market combination are depicted inFig. 2, while the hourly heating demands on the peak heatingday of the year are depicted in Fig. 3.

In general, the power demands for a given building type arehigher when the building is located in southern California versussouthern Wisconsin (see Fig. 2). This is due to the fact that thepower demand includes cooling, via vapor-compression air condi-tioning units, and that the cooling demands are higher in the hottersouthern California climate. Conversely, the heating demands for agiven building type are higher when the building is located insouthern Wisconsin (see Fig. 3), due to the colder climate.

We use actual utility rates in our analysis. Specifically, the elec-tricity and natural gas prices for southern California and southernWisconsin are based on 2010 commercial rate schedules fromSouthern California Edison (see [37]), Southern California Gas Com-pany (see [38]), Wisconsin Electric Power Company (see [39]), andWisconsin Electric-Gas Operations (see [40]), respectively. Fig. 4provides the weekday energy prices for each market.

In addition to the hourly energy prices for electricity, the utili-ties charge for the peak power demand each month, and the mag-nitude of these demand charges is specific to each utility in theUnited States. Southern California Edison charges $6.39 per kWper month and Wisconsin Electric Power Company charges$11.35 per kW per month. The availability of electricity exportfrom the SOFC system to the grid depends on the net-metering pol-icies and interconnection procedures for the market in which thebuilding is located. Based on the 2010 report by the Network forNew Energy Choices (see [43]), California is a favorable marketfor DG net-metering and interconnect, while Wisconsin is not.Thus, for the scenarios demonstrated in this paper, net-metering

ia (CA) and southern Wisconsin (WI). Building demand statistics are based on hourly

WI hotel CA office WI office

6 3 3122 54 54142 54 44264 151 10752 15 15256 4 71,086 105 11050 0 01.84 0.11 0.177.21 4.04 4.740.49 0.00 0.00

0

50

100

150

200

250

300

350

400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Bui

ldin

g Po

wer

Dem

and

(kW

)

Hour of the Day

CA Hotel

WI HotelCA OfficeWI Office

Fig. 2. Building power demands on the peak power day of the year for a large hotel and medium office located in southern California (CA) and southern Wisconsin (WI).

0

150

300

450

600

750

900

1050

1200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Bui

ldin

g H

eatin

g D

eman

d (k

W)

Hour of the Day

WI Hotel

CA Hotel

WI Office

CA Office

Fig. 3. Building heating demands on the peak heating day of the year for a large hotel and medium office located in southern California (CA) and southern Wisconsin (WI).


is available in southern California (at full market price), but is notavailable in southern Wisconsin.

The 2010 reports (see [41,42]) by the Energy InformationAdministration provide the basis for the calculation of the averagecarbon emissions rate for centralized power generation in Califor-nia and Wisconsin. The primary fuel source for centralized powergeneration in California is natural gas. This fuel source, coupledwith the prevalence of renewable power generation, results in arelatively low emissions rate of 0.27 kg of carbon per kWh of elec-tricity. By contrast, centralized power generation in Wisconsin pro-duces a relatively high carbon emissions rate of 0.74 kg/kWh, giventhat the primary fuel source is coal.

The aforementioned building type and energy market scenariosprovide values for the demand, pricing, and emissions parameters.However, in order to perform a static analysis, we must also choosea design and dispatch strategy (i.e., fixed values for A4 and P4t) for

the SOFC system. We derive the operational cost and performancedata for the SOFC system from Stambouli and Traversa [32], Haw-kes et al. [33], Braun [34], and Gerdes et al. [49]. The pricing, emis-sions, and technology parameter values applied in our staticanalyses are listed in Table 2. For the design scenarios tested here,we assume that SOFCs can only be acquired in increments of50 kW (i.e., k4 = 50) of power capacity and that the SOFC systemis sized as closely as possible to the average power demand ofthe building. For example, because the hotel in southern Wisconsinhas an average power demand of 142 kW, we consider a 150 kWSOFC system (i.e., A4 = 3) for acquisition. Additionally, we includescenarios with and without waste heat capture for the SOFCsystem in order to quantify the value of CHP. We assume a 20%increase in total installed cost for CHP integration.

For the dispatch scenarios tested here, we assume that all of theacquired SOFCs are operated at a positive power output in all hours

0

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Util

ity E

nerg

y Pr

ices

($/k

Wh)

Hour of the Day

CA Electricity

WI Electricity

WI Natural Gas

CA Natural Gas

Fig. 4. Weekday electricity and natural gas prices for commercial service in southern California (CA) and southern Wisconsin (WI).

Table 2Summary of parameter values employed in the static analyses.

Parameter Notation Value Units

Electricity price pt 0.06–0.21 $/kWhNatural gas price gt 0.02–0.03 $/kWhPeak demand charge pmax

n 6.39–11.35 $/kW/monthNet-metering rate mt 0–1 fractionCarbon tax rate z 0.02 $/kgUtility emissions rate zp 0.27–0.74 kg/kWhGas emissions rate zg 0.18 kg/kWhSOFC power capacity k4 50 kWSOFC O&M cost m4 0.02 $/kWhSOFC electric efficiency gP

4t0.41–0.57 HHV

SOFC thermal efficiency gQ4

0.00–0.17 HHV

Boiler O&M cost m6 0.02 $/kWhBoiler thermal efficiency gQ

60.75 HHV


throughout the time horizon (i.e., Njt = 0 and P4t > 0 "t) and arenever forced into standby mode. The validity of this simplificationis easily confirmed by ensuring the power output of the SOFC sys-tem is never forced below the maximum turn-down in a given sce-nario. For the southern California scenarios, we assume the SOFCsystem is baseloaded at rated power capacity in all hours (i.e.,P4t = k4A4 "t). Given the availability of net-metering and the rela-tively high electricity-to-gas price ratio in the California market,the assumption of baseloading is reasonable. For the southern Wis-consin scenarios, we assume the SOFC system load-follows in allhours (i.e., P4t ¼min dP

t ; k4A4

n o8t). The lack of net-metering and

the relatively low electricity-to-gas price ratio make load-follow-ing a reasonable assumption in this market.

When the SOFCs baseload at rated capacity, their electric effi-ciency is fixed at the minimum of 41% (i.e., gP

4t ¼ 0:41 8t), on ahigher heating value (HHV) basis. When the SOFCs load-follow,their electric efficiency varies between 41% and 57%, dependingon their power output. If heat capture is included, via heatexchangers, then we assume a thermal efficiency of 21% for theSOFCs and 80% for the heat exchangers. Thus, the net-thermal effi-ciency of the SOFC system is 17% (i.e., gQ

4 ¼ 0:17) and the overallCHP efficiency ranges from 58% to 74% HHV. If heat capture isnot included, then the thermal efficiency of the SOFC system is zero

(i.e., gQ4 ¼ 0). We assume that the thermal efficiency of the existing

boiler is 75% (i.e., gQ6 ¼ 0:75).

The carbon emissions rate of the SOFC system (i.e., the right-hand side of condition (12)) is calculated based on the emissionsassociated with the combustion of natural gas, the electric andthermal efficiencies of the SOFCs, and the thermal efficiency ofthe boiler. According to NaturalGas.org [44], the carbon emissionsrate from the combustion of natural gas is 0.18 kg per kWh of gasconsumed. Thus, the emissions rate of the SOFC system varies be-tween 0.24 and 0.44 kg of carbon per kWh of electricity produced,depending on the SOFC power output and whether heat capture isincluded in the system design.

Based on varying the building type, energy market, and SOFCsystem design and dispatch, we develop the eight scenarios listedin Table 3. A variety of alternate scenarios can be developed to testthe economic viability of a SOFC system for certain applications.However, these eight scenarios provide a wide range of applica-tions and generally demonstrate the impact on operational savingsof varying the building, market, and DG system parameters.

5. Scenario analysis

In this section, we present two types of sensitivity analyses ofthe annual operational savings (relative to the annual costs in-curred without DG technologies) provided by the SOFC systemsin our scenarios. The first type of analysis examines the sensitivityof the operational savings across scenarios. In other words, we areinterested in how the operational savings of Scenario 1 differ fromthose of Scenario 2, Scenario 3, and so on. This sensitivity analysisprovides insight regarding the general types of buildings, markets,and systems for which DG provides large, positive savings and is,therefore, more likely to be economically viable. The second typeof analysis examines the sensitivity of the operational savingswithin scenarios. In other words, we are interested in how theoperational savings for a particular scenario change as the valuesof certain system and market parameters change. Specifically, weexamine the sensitivity of the operational savings to changes inthe rated electric efficiency of the SOFC system and the carbontax enforced in the market of interest. This sensitivity analysisprovides insight regarding the specific characteristics of DG

Table 3Building, market, and design and dispatch scenarios for which we examine the economic viability of a DG system.

Scenario Building Market System design (Heat capture?) System dispatch (Net-metering?)

1 Hotel CA 200 kW Baseload(No) (Yes)

2 Hotel CA 200 kW Baseload(Yes) (Yes)

3 Office CA 50 kW Baseload(No) (Yes)

4 Office CA 50 kW Baseload(Yes) (Yes)

5 Hotel WI 150 kW Load-follow(No) (No)

6 Hotel WI 150 kW Load-follow(Yes) (No)

7 Office WI 50 kW Load-follow(No) (No)

8 Office WI 50 kW Load-follow(Yes) (No)


systems and energy markets that lead to greater economic viabil-ity. The next two sections present a more detailed discussion ofthe two types of sensitivity analyses.

5.1. Savings sensitivity across scenarios

In this section, we calculate and compare the annual energy,emissions, O&M, and peak demand savings provided by the SOFCsystem in each scenario. Because the system sizes differ acrossscenarios, we present the savings per unit of system capacity(i.e., $ per kW) in order to fairly compare scenarios. The total an-nual savings in each scenario are then compared to the annualizedtotal installed cost of the SOFC system to determine its economicviability.

5.1.1. Energy savingsFor Scenarios 1 through 4, because the SOFC system is baseload-

ed and excess power can be exported to the grid at the market rate(mt = 1) in all hours t, positive energy savings conditions (9) and (10)are equivalent. Thus, for any hour in which the price of electricityfrom the utility exceeds the gas cost for the SOFCs to produce elec-tricity, the energy savings are positive. Because the SOFCs baseloadin Scenarios 1 through 4, the electric efficiency is always the mini-mum of 41%. The thermal efficiency of the SOFC system is 0% in Sce-narios 1 and 3, since heat capture is not included, and 17% inScenarios 2 and 4. Based on the natural gas price of $0.024 perkWh, the electric and thermal efficiencies of the SOFC system, andthe thermal efficiency of the boiler, the maximum cost associatedwith natural gas consumption by the SOFC system to produce elec-tricity is $0.059 per kWh without heat capture and $0.045 per kWhwith heat capture (based on the right-hand sides of (9) and (10)).Since the minimum price of electricity from the utility in Scenarios1 through 4 is $0.081 per kWh, conditions (9) and (10) are satisfiedand positive energy savings are achieved in all hours.

Table 4Annual energy, emissions, O&M, peak, and total savings per kW of SOFC system capacity

Annual Savings ($/kW)Scenario Energy Emissions

1 341.02 �36.362 454.44 �18.933 341.02 �44.864 454.44 �27.425 -39.82 44.976 69.27 57.827 -3.28 37.388 79.24 47.10

The energy savings may not be positive in all hours in Scenarios5 through 8. For these scenarios, the SOFC system load-follows andits power output never exceeds the building demand (i.e.,dP

t =P4t P 1). So, power is never exported to the grid and only con-dition (9), as opposed to (10), applies. Because the SOFCs load-fol-low, the electric efficiency varies between 41% and 57% dependingon the aggregate power output. Given the natural gas price of$0.031 per kWh, the maximum gas cost for the SOFC system to pro-duce electricity varies between $0.054-0.074 per kWh withoutheat capture and between $0.041-0.058 per kWh with heat cap-ture, depending on the electric efficiency (based on the right-handside of (9)). The minimum price of electricity from the utility inScenarios 5 through 8 is $0.056 per kWh. Hence, there could behours for which condition (9) is not satisfied and the energy sav-ings are negative.

Given the hourly power demands of the buildings over the en-tire year, we compute the annual energy savings per kW of SOFCsystem capacity for the eight scenarios. The savings per unit ofpower capacity are calculated as the quotient of the annual energysavings (see Eq. (7)) and the acquired system capacity (k4A4) foreach scenario and are summarized in Table 4.

Large, positive annual energy savings are achieved in all of thesouthern California scenarios given the high electricity-to-gas priceratio. On the other hand, positive annual energy savings are onlyobtained in the southern Wisconsin scenarios that include heatcapture. Even with heat capture, the energy savings are relativelysmall given the low electricity-to-gas price ratio.

5.1.2. Emissions savingsFor Scenarios 1 through 4, because the SOFC system is baseload-

ed and the power output could be less than or greater than thebuilding demand, positive emissions savings conditions (13) or(14), respectively, could apply. Regardless of which condition ap-plies, the hourly emissions savings are positive when the rate of

provided in each scenario.

O&M Peak Total

�175.20 76.68 206.14�102.56 76.68 409.63�175.20 76.68 197.64�102.56 76.68 401.14�137.39 136.25 4.01�83.84 136.25 179.50�108.46 136.24 61.88�67.96 136.24 194.62

-200-150-100-50

050

100150200250300350400450500

Energy Emissions O&M Peak Total

Ann

ual S

avin

gs ($

/kW

)

-39.82+44.97

-137.39

+136.25

+4.01

Fig. 5. Total annual savings for the hotel located in southern Wisconsin withoutheat capture (Scenario 5).


decrease in off-site (i.e., utility) emissions is greater than the rate ofincrease in on-site (i.e., SOFCs and boiler) emissions. Based on the0.18 kg per kWh carbon emissions rate associated with the com-bustion of natural gas, and the fixed efficiencies of the SOFCs andboiler, the on-site emissions increase at a rate (based on theright-hand sides of inequalities (13) and (14)) of 0.44 kg per kWhfor Scenarios 1 and 3 (without heat capture) and a rate of 0.34 kgper kWh for Scenarios 2 and 4 (with heat capture). Since the max-imum rate of decrease in off-site emissions (based on the left-handside of inequalities (13) and (14)) for Scenarios 1 through 4 is0.27 kg per kWh, conditions (13) and (14) are not satisfied andthe emissions savings are negative in all hours.

For Scenarios 5 through 8, only condition (13), as opposed to(14), applies, since the SOFC system load-follows and the poweroutput never exceeds the building demand. As the SOFC poweroutput changes and the electric efficiency varies between 57%and 41%, the on-site emissions increase at a rate (based on theright-hand side of (13)) of 0.32 and 0.44 kg per kWh for Scenarios5 and 7 (without heat capture) and a rate of 0.24 and 0.34 kg perkWh for Scenarios 6 and 8 (with heat capture). Since the off-siteemissions decrease at a rate (based on the left-hand side of(13)) of 0.74 kg per kWh for Scenarios 5 through 8, condition(13) is satisfied and positive emissions savings are achieved inall hours.

Given the hourly power demands of the buildings over theentire year, and a $0.02 per kg carbon tax, the annual emissions

savings per kW of SOFC system capacity are calculated as the quo-tient of the annual emissions savings (see Eq. (11)) and the ac-quired system capacity (k4A4) for each scenario. As Table 4shows, the annual emissions savings are negative in all of thesouthern California scenarios given the relatively low carbon emis-sions rate of the utility in that market. Conversely, positive annualemissions savings are obtained in all of the southern Wisconsinscenarios given the relatively high emissions rate in that market.

5.1.3. O&M savingsPositive O&M savings condition (16) cannot be satisfied unless

heat capture is included to offset a portion of the thermal energyprovided by the boiler. In other words, if the heat provided bythe boiler is not reduced, then there are no savings associated withdecreasing the operation and maintenance on the boiler. Thus, thehourly O&M savings are negative for Scenarios 1, 3, 5, and 7, sincethose scenarios do not include heat capture. With heat capture, thehourly O&M savings are positive when the O&M costs per unit ofthermal energy produced are higher for the boiler than for theSOFC system. For all scenarios, we assume that the SOFC O&M costsare $0.02 per kWh of electric energy produced and that the boilerO&M costs are $0.02 per kWh of thermal energy produced. Hence,the SOFC O&M costs must be converted to units of thermal energyproduced, based on the electric and thermal efficiencies of theSOFC system.

For Scenarios 2 and 4, in which the SOFCs baseload, the electricand thermal efficiencies are fixed. Thus, the SOFC O&M costs arefixed at $0.05 per kWh of thermal energy produced. For Scenarios6 and 8, in which the SOFCs load-follow, the electric efficiency var-ies based on the power output. Accordingly, the SOFC O&M costsvary between $0.05 and 0.07 per kWh of thermal energy produced(see right-hand side of (16)). Since the boiler O&M costs are $0.02per kWh for all scenarios, condition (16) is not satisfied and theO&M savings are negative in all hours.

Given the hourly power demands of the buildings over the en-tire year, the annual O&M savings per kW of SOFC system capacityare calculated as the quotient of the annual O&M savings (see Eq.(15)) and the acquired system capacity (k4A4) for each scenario.The annual O&M savings are negative for all scenarios as summa-rized in Table 4. The savings are greater (i.e., less negative) for the

scenarios that include heat capture; however, the thermal effi-ciency of the SOFCs must increase significantly in order to achievepositive O&M savings.

5.1.4. Peak demand savingsBecause, by assumption, the SOFCs produce power in all hours,

whether baseloading or load-following, condition (18) is satisfiedand positive peak demand savings are achieved in all scenarios.Additionally, because the SOFC system is sized based on the build-ings’ average power load, which is between the minimum and peakpower loads, the SOFCs operate at rated capacity during peak de-mand hours in all scenarios. As a result, the monthly peak demandsavings are calculated as the product of the peak demand chargeand the acquired system capacity.

Given the monthly peak power demands of the buildings overthe entire year, the annual peak demand savings per kW of SOFCsystem capacity are calculated as the quotient of the annual peakdemand savings (see Eq. (17)) and the acquired system capacity(k4A4) for each scenario. The fifth column of Table 4 illustrates thatthe annual peak demand savings are positive in all scenarios. Addi-tionally, the savings are the same for all of the southern Californiascenarios (1–4) and nearly the same for all of the southern Wiscon-sin scenarios (5–8). This is due to the fact that the rated powercapacity of the SOFC system is sized to the average power demandof the building in each scenario and the fact that the system alwaysoperates at rated capacity during peak demand hours. However,the savings are larger in the southern Wisconsin market wherethe peak demand charges are nearly double those of the southernCalifornia market.

5.1.5. Total savingsBased on summing the four types of annual operational savings,

the total annual savings per kW of SOFC system capacity arepositive in all scenarios. However, there is a 100-fold increase insavings from the worst-case scenario (5) to the best-case scenario(2). Thus, the combination of building type, energy market, andsystem design and dispatch in a given scenario clearly has a signif-icant impact on the economic viability of the SOFC system. Itshould be noted here that the savings are relevant for systemcapacities within the range explored in this analysis(50–200 kW). These savings per kW of capacity do not necessarilyscale for larger (e.g., MW-scale) system sizes. Additionally, whencomparing these savings to the total installed cost, this analysisdoes not take into account capital costing based on economies-of-scale. That is, we do not address the fact that the unit capital

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Ann

ual S

avin

gs ($

/kW

)

+341.02

-36.36

-175.20

+76.68

+206.14

Fig. 6. Total annual savings for the hotel located in southern California without heatcapture (Scenario 1).

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0100200300400500600700800

Electricity Import

Electricity Export

Gas Import Gas Credit Energy

Annu

al S

avin

gs ($

/kW

)

+733.84

+107.55

-500.37

+113.42

+454.44

Fig. 8. Contributions of electricity and natural gas import and export to the annualenergy savings for the hotel located in southern California with heat capture(Scenario 2).


cost ($/kW) of a given SOFC-CHP system varies depending on thecapacity rating of the system.

The worst-case scenario presented in this chapter is the hotel,located in southern Wisconsin, without heat capture for the SOFCsystem (Scenario 5). Fig. 5 depicts the total annual savings for Sce-nario 5 based on the accumulation of annual energy, emissions,O&M, and peak demand savings. For this scenario, the negative en-ergy savings are barely offset by the positive emissions savings,and the negative O&M savings are nearly offset by the positivepeak demand savings. Summing the four savings types results invery small total operational savings ($4.01 per kW). With nearlyno operational savings, the SOFC system is not economically viable.In order to increase the viability of the system, we might consider amore favorable energy market for the hotel.

By locating the hotel, with the power-only SOFC system, in thesouthern California market (Scenario 1), we increase the opera-tional savings 50-fold. Fig. 6 demonstrates that Scenario 1 resultsin total operational savings of $206.14 per kW. Although the emis-sions savings in the southern California market are negative, theyare more than offset by the large, positive energy savings. In fact,when comparing Scenarios 1 and 5, the emissions, O&M, and peakdemand savings are all less in Scenario 1. However, the energy sav-ings are large enough to result in greater total savings in Scenario 1.In order to increase the economic viability of the system even fur-ther, we might consider upgrading the SOFCs with heat capture.

Adding heat capture to the SOFC system for the hotel in south-ern California (Scenario 2) nearly doubles the total operational sav-

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avin

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+454.44

-18.93-102.56

+76.68

+409.63

Fig. 7. Total annual savings for the hotel located in southern California with heatcapture (Scenario 2).

ings compared to the system without heat capture (Scenario 1).Fig. 7 depicts the energy, emissions, O&M, and peak demand sav-ings for Scenario 2, which result in total operational savings of$409.63 per kW.

By adding heat capture to the SOFC system in Scenario 2, the en-ergy savings increase by over 30%, the emissions savings increaseby nearly 50%, and the O&M savings increase by over 40% com-pared to Scenario 1. Energy savings provide the largest contribu-tion to the total annual savings in Scenario 2. Fig. 8 delineatesthe individual contributions to energy savings provided by the de-crease in electricity import from the utility, the increase in electric-ity export to the utility, the increase in natural gas import to theSOFC system, and the decrease (i.e., ‘‘credit’’) in natural gas importto the boiler. While the additional natural gas import to fuel theSOFC system increases the annual cost by over $500 per kW, thereduction in electricity import from the utility decreases the an-nual cost by enough (over $733 per kW) to produce positive annualenergy savings. Of the eight scenarios tested here, Scenario 2 pro-vides the greatest total annual operational savings and, conse-quently, represents the scenario for which the SOFC system ismost economically viable.

The 200 kW SOFC system in Scenario 2 of our analysis results intotal annual operational savings of $81,926, which representsroughly 27% of the annual operating costs without a DG system.The total annual operational savings correspond to the right-handside of economic viability condition (6). By dividing both sides ofthe inequality in (6) by the system capacity (k4A4 = 200), we obtainan equivalent economic viability condition c4 < 409.63. The param-eter c4 is the annual capital and installation cost (i.e., annual totalinstalled cost) per unit of capacity of the SOFC-CHP system, while409.63 is the annual operational savings per unit of capacity pro-vided by that system. Thus, the amortized capital and installationcosts of the SOFC system cannot exceed $409.63 per kW annuallyif the system operation is to provide any economic benefit. Forthe other scenarios tested here, the annual total installed cost re-quired to achieve economic viability is even less than $409.63per kW.

Various methods of amortization, interest rates, and systemlifetimes can be employed to obtain the annualized total installedcost. As one example, an initial total installed cost of $1,850 per kWcompounded continuously at 8% interest over a 15-year systemlifetime results in an annual cost of $409.48 per kW. At this cost,the SOFC-CHP system barely achieves economic viability (i.e., thecost nearly equals the savings). However, if the same initial totalinstalled cost of $1,850 per kW is amortized over the same lifetimeof 15 years employing discrete compounding at 8% interest (i.e., a


capital recovery factor of 0.117), then the resulting annual cost isonly $216.45 per kW. Thus, with the discrete method of amortiza-tion, the SOFC-CHP system achieves greater economic viability.Lower initial investment costs, a lower interest rate, and/or a long-er system lifetime also produce greater economic viability.

Presently, the uninstalled unit cost of stationary SOFC systemsintended for commercial building applications ranges from$4,000 to $47,500 per kW depending on the system size, annualproduction level, and specific type of SOFC technology (see [45–47]). Additionally, the costs associated with the installation ofSOFC systems can be as much as the unit capital cost. However,as the technology matures and production volumes increase, SOFCcapital costs are expected to reach the $800 per kW range (roughly$1200–1600 per kW total installed cost) for large-scale systems(see [48]). At a total installed cost of $1200 per kW, a simplesystem payback of under three years is feasible (for scenariosresulting in annual operational savings greater than $400 perkW). Regardless of the method and parameters used to annualizethe total installed cost, the resulting value must be less than theannual operational savings for the SOFCs to achieve economicviability.

5.2. Savings sensitivity within scenarios

The previous subsection examined the sensitivity of the annualoperational savings across the scenarios presented in Table 3. Thisanalysis allows us to identify building types, locations, and systemconfiguration scenarios for which DG might achieve economic via-bility. However, within each of these scenarios, the building, mar-ket, and system parameters are fixed. The analysis presented inthis subsection examines the sensitivity of the annual operationalsavings to changes in the parameters within a scenario. Specifi-cally, we investigate the impact on the operational savings ofvarying the SOFC system’s rated electric efficiency and the energymarket’s carbon tax because these parameters can have a signifi-cant impact on the economic viability and offer insight into estab-lishing requirements for the eventual success of such DG systems.We perform this sensitivity analysis for each of the hotel scenarios(i.e., 1, 2, 5, and 6) in order to demonstrate the results over a rangefrom the worst-case (5) to best-case (2) scenario.

5.2.1. Electric efficiencyFor the analysis presented in Section 5.1, the rated electric effi-

ciency (i.e., the efficiency at maximum power output) of the SOFCsystem is fixed at 41%, on a HHV basis, and the maximum

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SOFC Rated Electric Efficiency

CA Hotel w/ heat (S2)CA Hotel w/o heat (S1)WI Hotel w/ heat (S6)WI Hotel w/o heat (S5)

Fig. 9. Sensitivity of the annual energy savings to changes in the rated electricefficiency of the SOFC system, with and without heat capture, integrated with alarge hotel located in southern California (CA) and southern Wisconsin (WI).

turn-down electric efficiency (i.e., the efficiency at minimumpower output) is fixed at 57%. In this section, we vary the ratedelectric efficiency of the SOFC system between 40% and 60% todetermine the associated impact on the operational savings.Regardless of the rated electric efficiency, we assume the maxi-mum turn-down electric efficiency is 16 percentage-points greaterthan the rated electric efficiency. For example, if the rated electricefficiency is 60%, then the electric efficiency at the maximum turn-down is 76%. The rated thermal efficiency remains fixed at 17% forthose scenarios that include heat capture.

The electric efficiency of the SOFC system contributes to the an-nual energy, emissions, and O&M savings, according to Eqs. (7),(11) and (15), respectively. Fig. 9 demonstrates the impact on theannual energy savings of increasing the rated electric efficiencyfrom 40% to 60%. The annual energy savings increase as the ratedelectric efficiency increases. Regardless of the electric efficiencyand whether heat capture is included, the southern California sce-narios (1 and 2) provide greater energy savings than the southernWisconsin scenarios (5 and 6). This is due primarily to the highprice of utility-purchased electricity in southern California andthe favorable net-metering policies that encourage the SOFCs tobaseload. The relatively low price of electricity and unfavorablenet-metering policies in southern Wisconsin lead to lower energysavings. In fact, for the southern Wisconsin scenario (5) withoutheat capture, the annual energy savings are not positive unlessthe rated electric efficiency increases beyond 45%.

Increasing the rated electric efficiency also increases the annualemissions savings, as depicted in Fig. 10. In contrast to the energysavings, the southern Wisconsin scenarios provide greater emis-sions savings than the southern California scenarios, regardless ofthe electric efficiency. The average rate of centralized carbon emis-sions in the southern California market is so low that positive an-nual emissions savings are only achievable at a rated electricefficiency greater than 60%. On the other hand, the centralized car-bon emissions in the southern Wisconsin market are high enoughthat positive emissions savings are achievable across the entirerange of electric efficiencies tested. For both energy markets, how-ever, the scenarios (2 and 6) that include heat capture providegreater savings than those that do not include heat capture dueto the decrease in emissions from the boiler.

The final type of savings that is affected by changes in the ratedelectric efficiency of the SOFC system is the O&M savings that re-sult from reducing the workload on the boiler. According toFig. 11, the O&M savings decrease, or remain the same, as the ratedelectric efficiency increases. Furthermore, due to the relatively low

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WI Hotel w/ heat (S6)WI Hotel w/o heat (S5)CA Hotel w/ heat (S2)CA Hotel w/o heat (S1)

Fig. 10. Sensitivity of the annual emissions savings to changes in the rated electricefficiency of the SOFC system, with and without heat capture, integrated with alarge hotel located in southern California (CA) and southern Wisconsin (WI).

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WI Hotel w/ heat (S6)CA Hotel w/ heat (S2)WI Hotel w/o heat (S5)CA Hotel w/o heat (S1)

Fig. 11. Sensitivity of the annual O&M savings to changes in the rated electricefficiency of the SOFC system, with and without heat capture, integrated with alarge hotel located in southern California (CA) and southern Wisconsin (WI).


O&M costs for the boiler, the annual O&M savings are negativeregardless of the electric efficiency of the SOFCs. For scenarios (1and 5) that do not include heat capture, positive O&M savingscan never be achieved because there is no reduction in the thermalenergy provided by the boiler. However, for scenarios (2 and 6)that include heat capture, the O&M savings decrease as the ratedelectric efficiency increases. This is due to the fact that increasingthe electric efficiency of the SOFCs decreases the amount of ex-haust gas output. With less exhaust gas available to offset the ther-mal energy provided by the boiler, the O&M savings decrease.

Increasing the rated electric efficiency of the SOFC system in-creases the annual energy and emissions savings, but decreases(or does not impact) the annual O&M savings. The net effect ofthese changes in annual energy, emissions, and O&M savings isthat the total annual savings increase with the rated electric effi-ciency. According to condition (6), the SOFC system becomes eco-nomically viable when the total annual savings it provides exceedthe annual total installed cost. Thus, as the total annual savings in-crease, the economic viability of the SOFC system increases. Giventhe total annual savings for a specific scenario, we refer to the totalinstalled cost that precisely equals the annual savings as the an-nual ‘‘break-even’’ cost. At total installed costs below the break-even cost, positive net savings are achievable and the SOFC systemis economically viable.

0500

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Initi

al B

reak

-eve

n C

ost (

$/kW

)


CA Hotel w/ heat (S2)

CA Hotel w/o heat (S1)

WI Hotel w/ heat (S6)

WI Hotel w/o heat (S5)

Fig. 12. Sensitivity of the initial break-even cost to changes in the rated electricefficiency of the SOFC system, with and without heat capture, integrated with alarge hotel located in southern California (CA) and southern Wisconsin (WI). Thebreak-even cost is the total installed cost that equates exactly to the operationalsavings provided by the SOFC system.

Based on the annual break-even cost, we calculate an initial (i.e.,upfront) break-even cost for the SOFC system by reversing theamortization process (i.e., estimating the upfront cost that resultsin a given total installed cost after discrete compounding at 8%interest over a 15-year lifetime). Fig. 12 illustrates the effect ofincreasing the rated electric efficiency of the SOFC system on themaximum total installed cost (break-even cost) for the system. Interms of economic viability, the southern California scenarios (1and 2) dominate the southern Wisconsin scenarios (5 and 6) acrossthe range of electric efficiencies. At the lowest rated electric effi-ciency (i.e., 40%) for the southern Wisconsin scenario (5) withoutheat capture, the SOFCs are not economically viable because thebreak-even cost is negative. At the highest rated electric efficiency(i.e., 60%) for the southern Wisconsin scenario (6) with heat cap-ture, the SOFCs are only economically viable for initial total in-stalled costs at or below $2500 per kW. By contrast, the southernCalifornia scenario (2) with heat capture demonstrates economicviability for the SOFCs at a cost of $4500 per kW, when the ratedelectric efficiency is 60%.

Another point of interest is understanding the impact ofincreasing the electric efficiency of the SOFC system on the effec-tive cost of electricity (COE). In Section 3, we present a formulafor the hourly gas cost for the SOFC system to produce electricity(see the right-hand sides of inequalities (9) and (10)). That formula,gt=gP

4t

� �1� gQ

4 =gQ6

� �, includes the hourly price of natural gas (gt),

the rated electric gP4t

� �and thermal gQ

4

� �efficiencies of the SOFC

system, and the rated thermal efficiency gQ6

� �of the boiler. How-

ever, a widely accepted method for calculating the total COE ofan SOFC system (see [34]) includes not only fuel costs, but also cap-ital and O&M costs. The capital cost component of COE is calculatedby dividing the annual total installed cost by the product of theSOFC capacity factor and the total annual hours the system is avail-able. The O&M component of COE is simply the O&M cost per unitof electric energy from the SOFC system. Fig. 13 depicts the totalCOE from the SOFC system, calculated as the sum of capital,O&M, and gas costs, over a range of electric efficiencies. In thisgraph, we apply an initial total installed cost of $4000 per kW, acapital recovery factor of 0.117, and SOFC capacity factors of 1and 0.78 for the California and Wisconsin scenarios, respectively.

In all scenarios, we apply a SOFC O&M cost of $0.02 per kWh.We calculate the fuel costs based on the maximum price of naturalgas in the market of interest. As the rated electric efficiency of theSOFC system increases, the COE from the system decreases. SOFCelectricity costs as low as $0.105 per kWh are achieveable for thesouthern California scenario (2) with heat capture, when the rated

0.1000.1050.1100.1150.1200.1250.1300.1350.1400.1450.1500.1550.1600.1650.170

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SOFC

Cos

t of E

lect

ricity

($/k

Wh)


WI Hotel w/o heat (S5)WI Hotel w/ heat (S6)CA Hotel w/o heat (S1)CA Hotel w/ heat (S2)

Fig. 13. Sensitivity of the cost of electricity (COE) from the SOFC system to changesin the rated electric efficiency of the system, with and without heat capture,integrated with a large hotel located in southern California (CA) and southernWisconsin (WI).

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s ($

/kW

)

Carbon Tax Rate ($/kg)

WI Hotel w/ heat (S6)WI Hotel w/o heat (S5)CA Hotel w/ heat (S2)CA Hotel w/o heat (S1)

Fig. 14. Sensitivity of the annual emissions savings to changes in the carbon taxrate for the SOFC system, with and without heat capture, integrated with a largehotel located in southern California (CA) and southern Wisconsin (WI).


electric efficiency is 60%. Overall, it is also observed from Fig. 13that the value of the SOFC waste heat amounts to between $0.01and $0.018 per kWh.

5.2.2. Carbon taxIn addition to the rated electric efficiency of the SOFCs, the car-

bon tax rate in the market of interest also affects the economic via-bility of the SOFC system. For all of the analysis presented up tothis point, the carbon tax rate is assumed to be $0.02 per kg(roughly $20 per metric ton). For the analysis presented next, wevary the carbon tax rate between $0.02 per kg and $0.10 per kg(roughly $100 per metric ton). In order to isolate the impact ofchanges in the carbon tax, we return the rated electric efficiencyof the SOFC system to the fixed 41%.

Unlike the electric efficiency, the carbon tax rate contributesonly to the annual emissions savings, according to Eq. (11).Fig. 14 demonstrates the impact on the annual emissions savingsof varying the carbon tax rate between $0.02–0.10 per kg. As thecarbon tax increases, the annual emissions savings in the southernWisconsin scenarios (5 and 6) increase. On the other hand, the an-nual emissions savings in the southern California scenarios (1 and2) decrease as the carbon tax increases. As previously

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Carbon Tax Rate ($/kg)

CA Hotel w/ heat (S2)CA Hotel w/o heat (S1)WI Hotel w/ heat (S6)WI Hotel w/o heat (S5)

Fig. 15. Sensitivity of the initial break-even cost to changes in the carbon tax ratefor the SOFC system, with and without heat capture, integrated with a large hotellocated in southern California (CA) and southern Wisconsin (WI). The break-evencost is the total installed cost that equates exactly to the operational savingsprovided by the SOFC system.

demonstrated in Fig. 10, the emissions savings are positive in Sce-narios 5 and 6, and negative in Scenarios 1 and 2. Thus, increasingthe carbon tax causes the annual emissions savings to be more po-sitive in Scenarios 5 and 6, and more negative in Scenarios 1 and 2.The increase or decrease in the annual emissions savings has impli-cations for the total annual savings.

For the southern Wisconsin scenarios, the total annual savingsincrease as the carbon tax rate increases. By contrast, the total an-nual savings decrease as the carbon tax rate increases for thesouthern California scenarios. Applying the same approach as withthe electric efficiency sensitivity analysis, we calculate the initialbreak-even cost for the SOFC system based on the total annual sav-ings. Fig. 15 depicts the initial break-even cost for the SOFCs as thecarbon tax rate varies between $0.02–0.10 per kg.

At a carbon tax rate of $0.02 per kg, the southern California sce-narios dominate the southern Wisconsin scenarios in terms of eco-nomic viability. In the best-case scenario (2) at this tax rate, theSOFCs are economically viable at total installed costs approaching$3500 per kW. In the worst-case scenario (5) at this tax rate, theSOFCs are not viable at any positive cost. However, as the carbontax increases, the SOFCs become more viable in southern Wiscon-sin and less viable in southern California. In fact, at carbon tax ratesgreater than $0.07 and $0.08 per kg for scenarios without (1 and 5)and with (2 and 6) heat capture, respectively, the SOFCs achievegreater economic viability in southern Wisconsin than in southernCalifornia. For a carbon tax rate of $0.10 per kg, the best-case sce-nario (6) achieves approximately the same break-even cost ($3500per kW) as the best-case scenario (2) for a carbon tax rate of $0.02per kg. However, at the higher tax rate, the best-case scenario is lo-cated in southern Wisconsin, rather than in southern California.Thus, relatively large carbon taxes have the potential to renderDG economically viable in markets in which such technologieswould not otherwise be economically attractive.

6. Conclusions

The cost versus savings analysis presented in this paper revealsbuilding, market, and technology characteristics for which DGmight achieve greater market penetration. The cost analysis dem-onstrates that lower total installed costs are likely to encouragegreater investment in DG technologies. Future projections of SOFCcapital costs as low as one-fifth of current costs could result ingreater investment in markets where DG is not currently viable.In addition to the cost analysis, the analysis of the operational sav-ings provided by acquired DG technologies identifies economicallyattractive building-market-technology combinations. For the com-binations tested here, the O&M savings are always negative andthe peak demand savings are always positive. However, the energyand emissions savings depend heavily on the market in which DGis considered.

The energy savings analysis indicates that a market with a highprice of electricity relative to the price of natural gas, and with net-metering at full market price, is more likely to result in positiveoperational savings from DG. For example, the best-case (in termsof energy savings) southern California scenario, with a high elec-tricity-to-gas price ratio and market-price net-metering, resultsin annual energy savings almost six times greater than the corre-sponding southern Wisconsin scenario, which has a low electric-ity-to-gas price ratio and no net-metering. Additionally, even inthe most favorable markets, greater energy savings are achievedby acquiring technologies with greater electric and thermalefficiencies. For southern California, a SOFC CHP system with arated electric efficiency of 60% provides nearly double the annualenergy savings compared to a power-only SOFC system with arated electric efficiency of only 40%.


The emissions savings analysis demonstrates that a marketwith a higher rate of carbon emissions, relative to that resultingfrom the combustion of natural gas, is more likely to result in po-sitive operational savings. For example, the best-case (in terms ofemissions savings) southern Wisconsin scenario, with a relativelyhigh carbon emissions rate, results in annual emissions savingsfour times greater than the corresponding southern California sce-nario, which has a relatively low emissions rate. In favorable mar-kets, in terms of carbon emissions, the annual emissions savingsare further increased by implementing greater emissions tax rates.For southern Wisconsin, increasing the carbon tax fivefold in-creases the annual emissions savings up to sixfold.

Unfortunately, for most markets, it is difficult to achieve both po-sitive energy savings and positive emissions savings. The annualstate electricity and natural gas profiles (see [41,42]) prepared bythe Energy Information Administration demonstrate that marketswith the highest electricity prices often have the lowest carbonemissions rates. We demonstrate such a market with the southernCalifornia scenarios. However, Connecticut, Maine, New Hampshire,New Jersey, New York, and Vermont have electricity pricing and car-bon emissions rates very similar to those in California. Conversely,markets with the lowest electricity prices often have the highestemissions rates. The southern Wisconsin scenarios exemplify amarket such as this. However, Indiana, Iowa, Kentucky, Missouri,New Mexico, North Dakota, Utah, West Virgina, and Wyoming alsohave relatively low electricity prices coupled with relatively highcarbon emissions rates. In general, this phenomenon of opposingelectricity prices and carbon emissions rates is due to the highercost of low-emitting fuel sources, like gas and nuclear, and the lowercost of high-emitting fuel sources, like coal. The analysis provided inthis paper can help identify markets that balance the trade-off be-tween energy and emissions savings in order to obtain positive totalsavings. The markets which provide the greatest total savings to DGowners are most likely to witness DG investment.

By examining the conditions for which building owners aremost likely to invest in DG technologies, this paper providesscreening criteria for the instances of complex optimization mod-els (e.g., ðPÞ) we wish to solve. For a given scenario (i.e., a probleminstance), if the savings provided by acquiring and operating a DGtechnology exceed its total installed cost, then the technology iseconomically viable. If the technology is economically viable, thenthe optimal system design and dispatch determined by solving theinstance of ðPÞ is likely to include that technology. However, theðPÞ-solution could identify a more favorable (i.e., lower-cost)capacity and operational strategy for the technology than that usedto initially assess its economic viability. This is particularly truewhen the assessed technology can be integrated with other tech-nologies (e.g., electric and thermal storage) in the more robust sys-tem originally modeled by Pruitt et al. [23]. For this reason, oureconomic viability analysis is a useful complement to, but not areplacement for, an optimization model such as ðPÞ.

Acknowledgments

The authors thank the National Science Foundation for partialsupport of this research effort under award #CNS-0931748.

Appendix

Here we provide the full derivation of the terms on the right-handside of economic viability condition (6) that results in the equationsfor energy savings (7), emissions savings (11), O&M savings (15), andpeak demand savings (17). Condition (6) is based on comparing thetotal cost (CostDG) to meet the building demands with a system thatincludes SOFC technology to the total cost (CostnoDG) to meet thebuilding demands with the power utility and boiler alone.

CostDG < CostnoDG

Substitute the expression for CostDG shown in (5a)–(5d) and theexpression for CostnoDG shown in (4a)–(4c).

c4k4A4 þXt2T

d m4 þgt þ zzg

gP4t

� �P4t

þXt2T

d ðpt þ zzpÞmax 0; dPt � P4t

n oþ mtpt min 0; dP

t � P4t

n oh iþXn2N

pmaxn maxt2T n max 0; dP

t � P4t

n on o

þXt2T

d m6 þgt þ zzg

gQ6

!dQ

t �gQ

4

gP4t

!P4t

!

<Xt2T

dðpt þ zzpÞdPt

þXn2N

pmaxn maxt2T n dP

t

n o

þXt2T

d m6 þgt þ zzg

gQ6

!dQ

t

Subtract all of the terms found on the left-hand side of the inequal-ity, other than c4k4A4, from both sides of the inequality. This sub-traction eliminates all terms that include the parameter dQ

t .

c4k4A4 < �Xt2T

d m4 þgt þ zzg

gP4t

� �P4t þ

Xt2T

dðpt þ zzpÞdPt

�Xt2T

d ðpt þ zzpÞmax 0; dPt � P4t

n oþ mtpt min 0; dP

t � P4t

n oh iþXn2N

pmaxn maxt2T n dP

t

n o�Xn2N

pmaxn maxt2T n max 0; dP

t � P4t

n on o

þXt2T

d m6 þgt þ zzg

gQ6

!gQ

4

gP4t

!P4t

Distribute multiplication across parentheses and group terms thatinclude common parameters (e.g., group all terms that include theprice of electricity, pt).

c4k4A4 <Xt2T

dptdPt �

Xt2T

dpt max 0; dPt � P4t

n o�Xt2T

dmtpt min 0;dPt � P4t

n o

�Xt2T

dgt

gP4t

� �P4t þ

Xt2T

dgt

gQ6

!gQ

4

gP4t

!P4t

þXt2T

dzzpdPt �

Xt2T

dzzp max 0;dPt � P4t

n o

�Xt2T

dzzg

gP4t

� �P4t þ

Xt2T

dzzg

gQ6

!gQ

4

gP4t

!P4t þ

Xt2T

dm6gQ

4

gP4t

!P4t �

Xt2T

dm4P4t

þXn2N

pmaxn maxt2T n dP

t

n o�Xn2N

pmaxn maxt2T n max 0;dP

t � P4t

n on o

Extract common terms and combine summations.

c4k4A4 < dXt2T

pt dPt �max 0;dP

t � P4t

n o� �� mtpt min 0; dP

t � P4t

n oh i

� dXt2T

gt

gP4t

� �1� gQ

4

gQ6

!" #P4t

þ zdXt2T

zp dPt �max 0;dP

t � P4t

n o� �

� zdXt2T

zg

gP4t

� �1� gQ

4

gQ6

!" #P4t þ d

Xt2T

m6gQ

4

gP4t

!�m4

" #P4t

þXn2N

pmaxn maxt2T n dP

t

n o�maxt2T n max 0; dP

t � P4t

n on oh i

Substitute the following identities into the first and third lines ofthe inequality: For any numbers x and y, (i) x �max{0,


x � y} = min{x, y} and (ii) �min{0, x � y} = max{0, y � x}. Combinesummations.

c4k4A4 < dXt2T

pt min dPt ; P4t

n oþ mtpt max 0; P4t � dP

t

n oh

� gt

gP4t

� �1� gQ

4

gQ6

!P4t

#

þ zdXt2T

zp min dPt ; P4t

n o� zg

gP4t

� �1� gQ

4

gQ6

!P4t

" #

þ dXt2T

m6gQ

4

gP4t

!�m4

" #P4t

þXn2N

pmaxn maxt2T n dP

t

n o�maxt2T n max 0;dP

t � P4t

n on oh iThe four lines on the right-hand side of the inequality identify theexpressions for energy (7), emissions (11), O&M (15), and peak de-mand (17) savings, respectively. The derivation of economic viabil-ity condition (6), shown below, is complete.

c4k4A4 < SavingsEnergy þ SavingsEmissions þ SavingsO&M þ SavingsPeak

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