Modeling Generation Capacity
Investment Decisions
GRIDSCHOOL 2010
MARCH 8-12, 2010  RICHMOND, VIRGINIA
INSTITUTE OF PUBLIC UTILITIES
ARGONNE NATIONAL LABORATORY
Vladimir Koritarov
Center for Energy, Economic, and Environmental Systems Analysis
Decision and Information Sciences Division
ARGONNE NATIONAL LABORATORY
koritarov@anl.gov  630.252.6711
Do not cite or distribute without permission
MICHIGAN STATE UNIVERSITY
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
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Characteristics of Main Resource Planning
Methodologies
Approach
Pros
Cons
Screening
Curves
-Quick and simple analysis
-Identifies clear winners and losers
-Does not consider power system
characteristics
-No dispatch analysis
-No reliability analysis
Deterministic
Optimization
Models
-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
Programming
Optimization
Models
-Rigorous solution
-Detailed dispatch analysis
-Accurate reliability analysis
-Can be computationally intensive
(iterative optimization process)
-Require large amount of input data
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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 ($/kW-yr) vs. capacity factor
 Determine least-cost alternatives as a function of utilization
 Numerous limitations
 Not a substitute for a thorough analysis
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Total Annualized Cost Includes Fixed and Variable
Components
Total
Annualized =
Cost
($ / kW-yr)
($/kW-yr)
Annualized
Fixed
Cost
($/kW-yr)
+
Variable × Capacity × 8760
Cost
Factor
($/kWh)
(fraction)
(h/yr)
Variable Cost
Fixed Cost
Capacity Factor
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Screening Curves Show Ranges of Competitiveness for
each Technology
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The Competitiveness of Certain Technologies is Sensitive
to the Choice of Discount Rate
5% Discount Rate
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10% Discount Rate
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Total Annualized
Fixed and Variable Cost
($ / kW-yr)
Lowest Cost Options Can be Projected onto a LDC to
Obtain an Estimate of Supply Mix
200
.0635
0
0
Normalized Load
(fraction)
1.0
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.4866
Capacity Factor
Gas Turbine (.1311)
1.0
.8689
Coal (.2327)
.6362
Nuclear (.6362)
0
0
Time (fraction)
1.0
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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.
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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-notserved (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)
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Many Deterministic Models Analyze Energy Flows from
Primary Resources to Demand
Energy
Reserves/
Resources
Example:
Oil, natural
gas, or
coal
reserves
(billion
tons)
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Primary
Energy
Production
Secondary
Energy
Production
Final
Energy
Demand
Useful
Energy
Demand
Crude oil
production
(bbls/day)
Power plant
electricity
production
(MWh)
Electricity
delivered to
customers
(MWh)
Lighting,
heating,
cooling,
motive power
(MWh)
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The Energy Flows Are Typically Represented as Network
Final Energy
Demand
Transmission
& Distribution
Secondary
Energy
Production
Primary
Energy
Production
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The Level of Detail Depends on the Characteristics of the
Power System and Availability of Data
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The Results Show Optimal Generation Mix to Meet the
Demand
Demand
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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.
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Dynamic Programming Optimization Models
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.
MW
System Capacity
Upper RM
Demand forecast
Lower RM
New Capacity Additions
Existing System Capacity
Years
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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
•
•
•
•
•
•
•
Inputs:
Demand forecast
Load profiles
Existing units
Candidate
technologies
Economic data
Reliability parameters
and constraints
Environmental data
and constraints
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•
•
Production Cost
Model
Dynamic
Programming
Model
•
•
•
•
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
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DP Expansion Models Typically Have Modular Structure
Module 1
Module 2
Module 3
LOADSY
FIXSYS
VARSYS
Load
Description
Fixed System
Description
Candidates
Description
Module 4
Module 5
MERSIM
CONGEN
Configuration
Generator
Simulation of
System Operation
Module 6
DYNPRO
Optimization of
Investments
Module 7
REPROBAT
Report
Writer
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IAEA’s WASP Model
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Production Cost Model Simulates the Operation of the
System
PURPOSE: To simulate the operation of electric power system so that operating
costs and reliability of system operation can be calculated.
 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
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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
1
Convolution process
Original
LDC
ELDC
ENS
LOLP
0
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Capacity
Peak
load
Total
capacity
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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
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Reliability Constraints Must Be Met for a Configuration to
Be Considered for the Expansion Path
MW
System Capacity
(1+A)×D
(1+B)×D
Demand forecast (D)
Years
Reliability constraints:
(1+At) x Dt > P(Kt) > (1+Bt) x Dt
LOLP(Kt) < Ct
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where:
At =
Bt =
Dt =
P(Kt) =
Kt =
Ct =
Maximum reserve margin
Minimum reserve margin
Peak demand (in the critical period)
Installed capacity in year t
System configuration in year t
Critical LOLP (loss-of-load probability)
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DP Optimization Minimizes the Objective Function
 The objective function B typically comprises several cost components:
Bj = t(Ijt - Sjt + Fjt + Mjt + Ujt)
where:
t =
I =
S =
F =
M =
U =
time, t=1,...,T
Capital costs
Salvage value
Fuel costs
O&M costs
Unserved energy costs
Note: All costs are discounted net present values
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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 year
VC = Variable operating cost for the current year
FC = Fixed cost for new units constructed in the current year
TCX = 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
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Simple Dynamic Programming Optimization Problem
Year 1
Year 2
Year 3
State 5
VC = 620
FC = 400
TCX= 1420
TC = 2440
State 6
VC = 580
FC = 360
TCX= 1420
TC = 2360
State 7
VC = 560
FC = 400
TCX= 1420
TC = 2380
State 8
VC = 600
FC = 350
TCX= 1500
TC = 2450
State 2
VC = 420
FC = 300
TCX= 720
TC = 1440
State 1
VC = 320
FC = 400
TCX= 0
TC = 720
State 3
VC = 350
FC = 350
TCX= 720
TC = 1420
State 4
VC = 400
FC = 380
TCX= 720
TC = 1500
State 9
VC = 550
FC = 700
TCX= 1420
TC = 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
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Dynamic Programming Optimization is Usually
Conducted as An Iterative Optimization Process
Cost (1000$)
 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
106,800
106,600
106,400
106,200
106,000
105,800
105,600
105,400
105,200
105,000
1
2
3
4
5
Iteration
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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
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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 decisionmaking process
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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
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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
3,000
h
plh
plm
m
pll
l
Load
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pw
pa
pd
pw
pa
pd
pw
pa
pd
Hydro
h
pch
pcm
m
pcl
l
All Technologies/All Draws
Mix
pb
pi
pp
pb
pi
pp
pb
pi
pp
Other Competitors
2,000
b
i
p
b
i
p
b
i
p
Profit (Millions $)
Capacity
Company C: Profitability Exceedance Curves
0.20 @ 2,228
1,000
0.20 @ 1,098
259
0
214
0.65 @ 425
0.85 @ -180
0.95 @ -476
0.65 @ 338
0.85 @ -828
-1,000
1.00 @ -586
Tech 2
Tech 2 Weighted Average
-2,000
0.95 @ -1,590
1.00 @ -1,956
Tech 3
Tech 3 Weighted Average
-3,000
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Profit Exceedance Probability (fraction)
0.9
1.0
Koritarov - 030 30
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?
The operation of existing facilities will affect
market prices and when and where it becomes
profitable to add new units
Capacity
Expansion
(Build New Unit:
What? When?)
Decision
& Risk
Analysis
Plant Operation
(Operate Given Unit: Generation)
Adding new units will affect
the operation and profitability of existing facilities
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In EMCAS Uncertainties are Represented as Scenarios
Capacity
h
plh
plm
m
pll
l
Load
pw
pa
pd
pw
pa
pd
pw
pa
pd
Hydro
h
pb
pi
pp
m
pb
pi
pp
l
pb
pi
pp
pch
pcm
Mix
pcl
b
i
p
b
i
p
Multiple Possible Futures
b
i
p
Other Competitors
Agents compute expected profits under all scenarios to estimate profitability of an
investment project
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Agents Choose the Alternative with the Highest Expected Utility
Based on their Risk Preference and Multi-Attribute Utility Theory
Decision Maker’s
Preference
(Utility Function)
m
u( x )   ki  ui ( xi )
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

ui ( xi )  1/(1  e i )  1  e
where
i ( xi  xi ) /( xi  xi )
ui(xi)
utility for single attribute, i = 1,2, ..., m
βi
risk parameter, attribute i
xi
upper limit, attribute i
xi
lower limit, attribute i
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Risk
Averse
Risk
Neutral
0.5
i 1
where
1.0
Risk Prone
0.0
Worst
Value
Best
Value

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Capacity Expansion in Deregulated Systems often
Follows a Cyclical Pattern
70
U.S. Annual Capacity Additions (GW)
Generating Capacity (GW)
60
50
40
Natural Gas
Other
30
20
10
Source: EIA, 2006
0
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
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The ABMS Expansion Results Can Reproduce such
Behavior
300
New Additions
Peak Load
Peak Load / Capacity [GW]
250
Total Capacity
200
150
100
50
0
2006
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2010
2014
2018
2022
2026
2030
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Example Outputs from EMCAS: Long-Term Expansion
Simulations
40
Coal
NGCC
35
Capacity Additions [GW]
25
20
15
10
5
0
2006
2010
2014
2018
2022
2026
2030
40
35
Capacity Additions [GW]
 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
GT
30
30
GenCo_AT
GenCo_CZ1
GenCo_CZ2
GenCo_DE1
GenCo_DE2
GenCo_DE3
GenCo_DE4
GenCo_DE5
GenCo_PL1
GenCo_PL2
GenCo_PL3
GenCo_NEW
25
20
15
10
5
0
2006
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2010
2014
2018
2022
2026
2030
Koritarov - 036 36
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.
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