Post on 31-Jan-2016
description
Modeling Generation Capacity Investment Decisions
GRIDSCHOOL 2010MARCH 8-12, 2010 RICHMOND, VIRGINIA
INSTITUTE OF PUBLIC UTILITIESARGONNE NATIONAL LABORATORY
Vladimir KoritarovCenter for Energy, Economic, and Environmental Systems Analysis
Decision and Information Sciences DivisionARGONNE NATIONAL LABORATORY
koritarov@anl.gov 630.252.6711
Do not cite or distribute without permission
MICHIGAN STATE UNIVERSITY
Koritarov - 02GridSchool 2010
Resource Planning Methodologies Screening Curves
A comparison of annualized costs of different generating technologies across a range of capacity factors
Deterministic Optimization Models: Optimization models using linear programming (LP) and/or mixed-integer programming (MIP) Representative models: MARKAL, MESSAGE, etc.
Dynamic Programming Optimization Models: Typically include a detailed dispatch model and a dynamic programming (DP) model Provide a rigorous capacity expansion solution by examining thousands of possible future
expansion paths Representative models: WASP, EGEAS, etc.
New Methods for Deregulated electricity markets (e.g., Agent-Based Modeling): Applicable in competitive electricity markets Simulate independent decision-making of market participants May not provide least-cost solution for the system as a whole
Koritarov - 03GridSchool 2010
Characteristics of Main Resource Planning Methodologies
Approach Pros Cons
ScreeningCurves
-Quick and simple analysis-Identifies clear winners and losers
-Does not consider power system characteristics -No dispatch analysis-No reliability analysis
DeterministicOptimizationModels
-Fast solution (single iteration)-Require less input data than DP models
-Computationally intensive for detailed representation of real power systems (large number of variables and equations)-Dispatch model rather simple (usually annual or multi-annual time step)-Inaccurate reliability analysis
Dynamic ProgrammingOptimizationModels
-Rigorous solution-Detailed dispatch analysis-Accurate reliability analysis
-Can be computationally intensive (iterative optimization process)-Require large amount of input data
Koritarov - 04GridSchool 2010
Screening Curves Provide a Simplified Approach for Quick Analysis of Economic Competitiveness
Separate technology costs into “fixed” and “variable” costs
Construct cost curves for each technology
Plot cost ($/kW-yr) vs. capacity factor
Determine least-cost alternatives as a function of utilization
Numerous limitations
Not a substitute for a thorough analysis
Koritarov - 05GridSchool 2010
Total Annualized Cost Includes Fixed and Variable Components
TotalAnnualized
Cost
($/kW-yr)
= ×+ VariableCost
($/kWh)
AnnualizedFixedCost
($/kW-yr)
CapacityFactor
(fraction)
× 8760
(h/yr)
($ /
kW-y
r)
Capacity Factor
Fixed Cost
Annualized Cost
Variable Cost
Koritarov - 06GridSchool 2010
Screening Curves Show Ranges of Competitiveness for each Technology
Koritarov - 07GridSchool 2010
The Competitiveness of Certain Technologies is Sensitive to the Choice of Discount Rate
5% Discount Rate 10% Discount Rate
Koritarov - 08GridSchool 2010
Lowest Cost Options Can be Projected onto a LDC to Obtain an Estimate of Supply Mix
Tot
al A
nnua
lized
F
ixed
and
Var
iabl
e C
ost
($ /
kW-y
r)
Capacity Factor
Coal (600 MW)200
Nuclear (1000 MW)
Gas
(50
MW
).0635 .4866
Time (fraction)
Nor
mal
ized
Loa
d(f
ract
ion)
Nuclear (.6362)
Coal (.2327)
Gas Turbine (.1311)
00
00
.8689
1.0
1.0
.6362
1.0
Koritarov - 09GridSchool 2010
The Screening Curve Approach Does Not Consider Many Important Factors in System Planning
Screening curves do NOT consider:
Unit availability (forced outage and maintenance)
Existing capacity
Unit dispatch factors (minimum load and spinning reserve)
System reliability
Dynamic factors changing over time (load growth and economic trends)
Etc.
Koritarov - 010GridSchool 2010
Deterministic Optimization Models Relatively simple, easy to understand approach The solution is obtained fast, in a single model run The input data requirements are lower than for the dynamic programming
optimization models Can be computationally intensive if applied to real power systems (large number of
variables and constraint equations require powerful solvers) Dispatch model is rather simple, usually on an annual basis. Some models use 2 or
even 5-year time step. Numerous limitations in modeling system operation (e.g., no planned maintenance
schedule) Inadequate reliability analysis (typically planning reserve margins and energy-not-
served (ENS) are calculated). The ENS calculation is inaccurate due to simplified dispatch The optimal solution may not be feasible or realistic The LP solution does not consider discrete unit sizes (not all models have MIP
capabilities)
Koritarov - 011GridSchool 2010
Many Deterministic Models Analyze Energy Flows from Primary Resources to Demand
Energy Reserves/ Resources
Example:Oil, natural gas, or coal reserves(billion tons)
Primary Energy Production
Crude oil production (bbls/day)
Secondary Energy Production
Power plant electricity production(MWh)
Final Energy Demand
Electricity delivered to customers(MWh)
Useful EnergyDemand
Lighting, heating, cooling, motive power(MWh)
Koritarov - 012GridSchool 2010
The Energy Flows Are Typically Represented as Network
Primary Energy Production
Secondary Energy Production
Final EnergyDemand
Transmission & Distribution
Koritarov - 013GridSchool 2010
The Level of Detail Depends on the Characteristics of the Power System and Availability of Data
Koritarov - 014GridSchool 2010
The Results Show Optimal Generation Mix to Meet the Demand
Demand
Koritarov - 015GridSchool 2010
Dynamic Programming Optimization Models Most suitable tools for resource planning since long-term capacity expansion
problem is a highly constrained non-linear discrete dynamic optimization problem.
Computationally very intensive since every possible combination of candidate options must be examined to get the optimal plan (Curse of Dimensionality).
A new class of stochastic dynamic programming optimization models introduces uncertainty into the resource planning. These may include uncertainties in demand growth, hydro inflows and generation, fuel prices, wind and solar generation, electricity prices, etc.
For example, WASP model incorporates the uncertainties of hydro generation, however other uncertainties (demand growth, fuel prices, etc.) are modeled through scenario analysis or sensitivity studies.
Some models also try to include risk and calculate net present value (NPV) for different risk levels.
Koritarov - 016GridSchool 2010
Dynamic Programming Optimization Models
Demand forecast
Years
MW
Upper RM
Lower RM
System Capacity
Existing System Capacity
New Capacity Additions
OBJECTIVE: Identify the generating system expansion plan which has the minimum net present value (NPV) of all operating and investment costs for the study period.
Koritarov - 017GridSchool 2010
General Structure of Dynamic Programming Optimization Models
DP capacity expansion models typically combine a production cost (dispatch) model and a DP optimization model
The production cost model simulates the operation of the power system for each identified state (system configuration) in each year of the study period
The DP model finds the expansion path with the minimum NPV of all investment and operating costs that meets the demand and satisfies all reliability and other constraints
Production CostModel
Production CostModel
Dynamic Programming
Model
Dynamic Programming
Model
Inputs:• Demand forecast• Load profiles• Existing units• Candidate
technologies• Economic data• Reliability parameters
and constraints• Environmental data
and constraints
Inputs:• Demand forecast• Load profiles• Existing units• Candidate
technologies• Economic data• Reliability parameters
and constraints• Environmental data
and constraints
Results:• NPV of investment and
operating costs• Timing and schedule of
new capacity additions• Operating costs by
period• Investment costs by
year (cash flow)• Reliability results• Environmental
emissions
Results:• NPV of investment and
operating costs• Timing and schedule of
new capacity additions• Operating costs by
period• Investment costs by
year (cash flow)• Reliability results• Environmental
emissions
Koritarov - 018GridSchool 2010
DP Expansion Models Typically Have Modular Structure
Module 1LOADSY
Load Description
Module 3VARSYSCandidates Description
Module 2FIXSYS
Fixed System Description
Module 5MERSIM
Simulation ofSystem Operation
Module 4CONGENConfiguration
Generator
Module 7REPROBAT
Report Writer
Module 6DYNPRO
Optimization of Investments
IAEA’s WASP Model
Koritarov - 019GridSchool 2010
Production Cost Model Simulates the Operation of the System
Simulates all system configurations (states) identified by the model in all years Minimizes variable operating costs for the system (fuel costs + variable O&M) in each
time period Either chronological hourly loads or load duration curves (LDC) are used to represent
system loads in each time period Determines the maintenance schedule of generating units Uses loading order to represent dispatch of generating units:
Economic loading order User-specified loading order Combination (e.g., to accommodate must run units)
(Loading order can be adjusted to satisfy spinning reserve and other requirements) Uses probability mathematics to represent forced outages of generating units:
Monte Carlo approach is typically applied if hourly loads are used in simulation Baleriaux-Booth (equivalent LDC) method is applied if LDCs are used
PURPOSE: To simulate the operation of electric power system so that operating costs and reliability of system operation can be calculated.
Koritarov - 020GridSchool 2010
Baleriaux-Booth Method Considers Forced Outages Probabilities of Generating Units in Combination with System Load
The capacity on forced outage is treated as additional load that must be served by other generating units
Equivalent load duration curve (ELDC) is constructed using a convolution process to take into account forced outages of all generating units
Reliability parameters Loss-of-Load Probability (LOLP) and Energy-not-Served (ENS) are determined based on the remaining area under the ELDC
Time
Capacity
ELDC
OriginalLDC
LOLP
Convolution process
ENS
Total capacity
Peakload
0
1
Koritarov - 021GridSchool 2010
Production Cost Model Provides Inputs for DP Optimization
Calculates the expected energy generation by each generating unit in each time period
Calculates operating costs for each generating unit on the basis of expected energy generation in each time period
Calculates total operating costs for the system in each time period
Calculates system reliability parameters such as LOLP and ENS
Koritarov - 022GridSchool 2010
Reliability Constraints Must Be Met for a Configuration to Be Considered for the Expansion Path
where:
At = Maximum reserve margin
Bt = Minimum reserve margin
Dt = Peak demand (in the critical period)
P(Kt) = Installed capacity in year t
Kt = System configuration in year t
Ct = Critical LOLP (loss-of-load probability)
Reliability constraints:
(1+At) x Dt > P(Kt) > (1+Bt) x Dt
LOLP(Kt) < Ct
Demand forecast (D)
Years
MW
(1+A)×D
(1+B)×D
System Capacity
Koritarov - 023GridSchool 2010
DP Optimization Minimizes the Objective Function
The objective function B typically comprises several cost components:Bj = t(Ijt - Sjt + Fjt + Mjt + Ujt)
where:t = time, t=1,...,T I = Capital costsS = Salvage valueF = Fuel costsM = O&M costsU = Unserved energy costs
Note: All costs are discounted net present values
Koritarov - 024GridSchool 2010
Example of Dynamic Programming Optimization The total cost at each state is based on the following cost components:
TC = VC + FC + TCX
where:TC = Committed cost for current yearVC = Variable operating cost for the current yearFC = Fixed cost for new units constructed in the current yearTCX = Committed cost for previous year (state)
Variable operating cost (VC) for the current year includes: Fuel costs for existing and new generating units Variable O&M costs for existing and new units ENS costs
Fixed cost (FC) includes capital cost, salvage value, and fixed O&M costs for all units constructed in the current year
Previous year cost (TCX) includes production costs for earlier years and fixed costs for all generating units installed before the current year
Koritarov - 025GridSchool 2010
Simple Dynamic Programming Optimization Problem
State 1
State 9
State 8
State 7
State 6
State 5
State 4
State 3
State 2
Year 1 Year 3Year 2
VC = 320FC = 400TCX= 0TC = 720
VC = 420FC = 300TCX= 720TC = 1440
VC = 350FC = 350TCX= 720TC = 1420
VC = 400FC = 380TCX= 720TC = 1500
VC = 620FC = 400TCX= 1420TC = 2440
VC = 580FC = 360TCX= 1420TC = 2360
VC = 560FC = 400TCX= 1420TC = 2380
VC = 600FC = 350TCX= 1500TC = 2450
VC = 550FC = 700TCX= 1420TC = 2670
State 6 is the least-cost state in Year 3 Following the backward pointers, it is easily found that the least-cost path is: 1-3-6
Koritarov - 026GridSchool 2010
Dynamic Programming Optimization is Usually Conducted as An Iterative Optimization Process
Each solution represents the best path found among all possible paths containing system configurations (states) in the current model run
Thousands of system configurations are examined in each model run The solution that cannot be further improved by modifying “tunnel
widths” to include additional paths is the optimal solution
105,000
105,200
105,400
105,600
105,800
106,000
106,200
106,400
106,600
106,800
1 2 3 4 5
Iteration
Co
st
(10
00
$)
Koritarov - 027GridSchool 2010
Key Outputs from DP Optimization Models Include Optimal expansion schedule over the study period Expected generation from all units for all periods Reliability performance
LOLP Unserved energy (ENS) Reserve margins
Foreign and domestic expenditures Cash flow over time Pollutant emissions Sensitivity to key parameters
Koritarov - 028GridSchool 2010
A New Class of Models Is Being Developed for Modeling Capacity Expansion in Competitive Electricity Markets
Multiple competing market participants instead of single decision maker
Each market participant (e.g., generation company) makes its own independent decisions
Market participants have only limited information about the competition
Markets are also open to new entrants
Ideally an individual player cannot control the market
Market participants face multiple uncertainties (demand forecast, fuel prices, electricity market prices, actions of competitors, new market entrants, etc.)
Projection of future market prices of electricity is a major input for decision-making process
Koritarov - 029GridSchool 2010
Objectives for Constructing New Capacity in Restructured Markets Differ from those under Vertically Integrated Systems
Expansion investments are based on financial considerations, not lowest societal cost or energy security concerns
Profits are often the main driving force behind the decision making process
Financial decision criteria are typically based on measures such as rate of return on investment, payback period, and risk indicators
Other factors such as market share may influence the decision making process
Capacity expansion by competitors and new market entrants are uncertain
Emphasis is on the risk and risk management for corporate survival versus guaranteed rate of return under the traditional regulatory structure
Koritarov - 030GridSchool 2010
Agent-Based Modeling of Investment Decision Making in Competitive Electricity Markets
Generation companies are represented as individual agents performing profit-based company-level investment planning
Generation companies develop expectations and make independent investment decisions each year under multiple uncertainties
Uncertainties are often modeled as scenarios with associated probabilities of occurrence
Argonne’s EMCAS model uses a scenario tree and calculates profitability curves for various investment options
30
Company C: Profitability Exceedance CurvesAll Technologies/All Draws
1.00 @ -586
0.95 @ -4760.85 @ -1800.65 @ 338
0.20 @ 1,098
259
1.00 @ -1,956
0.95 @ -1,590
0.65 @ 425
0.85 @ -828
0.20 @ 2,228
214
-3,000
-2,000
-1,000
0
1,000
2,000
3,000
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Profit Exceedance Probability (fraction)
Pro
fit
(Mil
lio
ns
$)
Tech 2
Tech 2 Weighted Average
Tech 3
Tech 3 Weighted Average
Other CompetitorsOther CompetitorsHydroHydroLoadLoad
h
m
l
plh
plm
pll
pa
pw
pd
pa
pw
pd
pa
pw
pd
h
m
l
pch
pcm
pcl
pi
pb
pp
pi
pb
pp
pi
pb
pp
b
i
p
b
i
p
b
i
p
b
i
p
b
i
p
b
i
p
Capacity Mix
Koritarov - 031GridSchool 2010 31
EMCAS Profit-Based Expansion Model Integrates Three Key Components
Generation capacity investment (expansion) decisions When, what, how much (and where) should I invest?
Infrastructure operational decisions How much will my unit be dispatched under various futures? How much profit will it make under all reasonable outlooks?
Decision and risk analysis How much risk do I want to take? How do I trade off potentially conflicting objectives?
Capacity Expansion(Build New Unit:What? When?)
Plant Operation(Operate Given Unit: Generation)
Decision& Risk
Analysis
Adding new units will affect
the operation and profitability of existing facilities
The operation of existing facilities will affect
market prices and when and where it becomes
profitable to add new units
Koritarov - 032GridSchool 2010
In EMCAS Uncertainties are Represented as Scenarios
Other CompetitorsOther CompetitorsHydroHydroLoadLoad
h
m
l
plh
plm
pll
pa
pw
pd
pa
pw
pd
pa
pw
pd
h
m
l
pch
pcm
pcl
pi
pb
pp
pi
pb
pp
pi
pb
pp
b
i
p
b
i
p
b
i
p
b
i
p
b
i
p
b
i
p
Capacity Mix
Multiple Possible Futures
Agents compute expected profits under all scenarios to estimate profitability of an investment project
Koritarov - 033GridSchool 2010 33
Agents Choose the Alternative with the Highest Expected Utility Based on their Risk Preference and Multi-Attribute Utility Theory
1
( x ) ( )m
i i ii
u k u x
where u(x) total utility for attribute set x = x1, x2, ..., xm
ui(xi) utility for single attribute, i = 1,2, ..., m
ki trade-off weight, attribute i
)/()(1)1/(1)( iiiiii xxxxii eexu
where ui(xi) utility for single attribute, i = 1,2, ..., m
βi risk parameter, attribute i
upper limit, attribute i
lower limit, attribute i
ix
ix
Risk Prone
RiskAverse
RiskNeutral
Decision Maker’sPreference(Utility Function)
0.0
0.5
1.0
WorstValue
BestValue
Koritarov - 034GridSchool 2010 34
Capacity Expansion in Deregulated Systems often Follows a Cyclical Pattern
0
10
20
30
40
50
60
70
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Ge
ne
rati
ng
Ca
pa
cit
y (
GW
)
Natural Gas
Other
U.S. Annual Capacity Additions (GW)
Source: EIA, 2006
Koritarov - 035GridSchool 2010 35
The ABMS Expansion Results Can Reproduce such Behavior
0
50
100
150
200
250
300
2006 2010 2014 2018 2022 2026 2030
Pea
k L
oad
/ C
ap
aci
ty [
GW
]
New Additions
Peak Load
Total Capacity
Koritarov - 036GridSchool 2010
Example Outputs from EMCAS: Long-Term Expansion Simulations
Capital investment plans By technology By company
Generation by unit Price forecasts
Monthly price distributions Chronological price bands
Monthly reliability indices Consumer costs Company revenues, costs, profits
36
0
5
10
15
20
25
30
35
40
2006 2010 2014 2018 2022 2026 2030
Ca
pa
cit
y A
dd
itio
ns
[G
W]
Coal NGCC
GT
0
5
10
15
20
25
30
35
40
2006 2010 2014 2018 2022 2026 2030
Ca
pa
cit
y A
dd
itio
ns
[G
W]
GenCo_AT GenCo_CZ1 GenCo_CZ2 GenCo_DE1
GenCo_DE2 GenCo_DE3 GenCo_DE4 GenCo_DE5
GenCo_PL1 GenCo_PL2 GenCo_PL3 GenCo_NEW
Koritarov - 037GridSchool 2010
Results From any Expansion Model Require Additional Analysis
Fuel supply requirements and availability
Financial analysis and cash flow requirements
Manpower requirements Infrastructure requirements Plant siting analysis Transmission expansion analysis Environmental analysis Etc.