1. 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 
Do not cite or distribute without permission
MICHIGAN STATE UNIVERSITY

2. 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

3. 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
Rigorous solution
Detailed dispatch analysis
Accurate reliability analysis
Can be computationally intensive (iterative optimization process)
Require large amount of input data

4. 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 2 2

5. Total Annualized Cost Includes Fixed and Variable Components
($/kW-yr) = × +
Variable
($/kWh)
Fixed
Capacity
Factor
(fraction)
8760
(h/yr)
Annualized Cost
Variable Cost
($ / kW-yr)
Fixed Cost
Capacity Factor

6. Screening Curves Show Ranges of Competitiveness for each Technology

7. The Competitiveness of Certain Technologies is Sensitive to the Choice of Discount Rate

8. Fixed and Variable Cost
Lowest Cost Options Can be Projected onto a LDC to Obtain an Estimate of Supply Mix
Fixed and Variable Cost
Total Annualized
($ / kW-yr)
Capacity Factor
Coal (600 MW)
200
Nuclear (1000 MW)
Gas (50 MW)
.0635
.4866
Time (fraction)
Normalized Load
(fraction)
Nuclear (.6362)
Coal (.2327)
Gas Turbine (.1311)
.8689
1.0
.6362

9. 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. 11 11

10. 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)

11. 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
Useful
Energy
Demand
Lighting, heating, cooling, motive power

12. The Energy Flows Are Typically Represented as Network
Final Energy
Demand
Transmission & Distribution
Secondary Energy Production
Primary Energy Production

13. The Level of Detail Depends on the Characteristics of the Power System and Availability of Data

14. The Results Show Optimal Generation Mix to Meet the Demand

15. 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.

16. 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.
Demand forecast
Years MW
Upper RM
Lower RM
System Capacity
Existing System Capacity
New Capacity Additions

17. 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
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
Production Cost
Model
Dynamic Programming
Model

18. DP Expansion Models Typically Have Modular Structure
Module 1
LOADSY
Load
Description
Module 2
FIXSYS
Fixed System
Description
Module 3
VARSYS
Candidates
Description
Module 4
CONGEN
Configuration
Generator
Module 5
MERSIM
Simulation of
System Operation
Module 6
DYNPRO
Optimization of
Investments
Module 7
REPROBAT
Report
Writer
IAEA’s WASP Model

19. 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

20. 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
Original
LDC
LOLP
Convolution process
ENS
Total
capacity
Peak
load 1

21. 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

22. Reliability Constraints Must Be Met for a Configuration to Be Considered for the Expansion Path
Demand forecast (D)
Years MW
(1+A)×D
(1+B)×D
System Capacity
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

23. 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 costs
S = Salvage value
F = Fuel costs
M = O&M costs
U = Unserved energy costs
Note: All costs are discounted net present values

24. 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

25. Simple Dynamic Programming Optimization Problem
Year 1
Year 2
Year 3
VC = 620
FC = 400
TCX= 1420
TC = 2440
State 5
State 2
VC = 580
FC = 360
TCX= 1420
TC = 2360
VC = 420
FC = 300
TCX= 720
TC = 1440
State 6
VC = 560
FC = 400
TCX= 1420
TC = 2380
State 1
State 3
State 7
VC = 320
FC = 400
TCX= 0
TC = 720
VC = 350
FC = 350
TCX= 720
TC = 1420
VC = 600
FC = 350
TCX= 1500
TC = 2450
State 8
State 4
VC = 400
FC = 380
TCX= 720
TC = 1500
VC = 550
FC = 700
TCX= 1420
TC = 2670
State 9
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

26. 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

27. 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

28. 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

29. 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

30. 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

31. EMCAS Profit-Based Expansion Model Integrates Three Key Components
4/15/2017
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?)
Plant Operation
(Operate Given Unit: Generation)
Decision & Risk Analysis
Adding new units will affect the operation and profitability of existing facilities 31
Test 31

32. In EMCAS Uncertainties are Represented as Scenarios
4/15/2017
In EMCAS Uncertainties are Represented as Scenarios
Multiple Possible Futures
Agents compute expected profits under all scenarios to estimate profitability of an investment project
Test

33. 4/15/2017
Agents Choose the Alternative with the Highest Expected Utility Based on their Risk Preference and Multi-Attribute Utility Theory
1.0
Decision Maker’s
Preference
(Utility Function)
Risk
Averse
Risk
Neutral
0.5
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
Risk Prone
0.0
Worst
Value
Best
Value
where ui(xi) utility for single attribute, i = 1,2, ..., m
βi risk parameter, attribute i
upper limit, attribute i
lower limit, attribute i 33
Test 33

34. Capacity Expansion in Deregulated Systems often Follows a Cyclical Pattern

35. The ABMS Expansion Results Can Reproduce such Behavior

36. Example Outputs from EMCAS: Long-Term Expansion Simulations
4/15/2017
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
Test 36

37. 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.