modeling generation capacity investment decisions

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

[email protected] 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Do not cite or distribute without permission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


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


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


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


Screening Curves Show Ranges of Competitiveness for each Technology


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

5% Discount Rate 10% Discount Rate


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


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.


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)


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)


The Energy Flows Are Typically Represented as Network

Primary Energy Production

Secondary Energy Production

Final EnergyDemand

Transmission & Distribution


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


The Results Show Optimal Generation Mix to Meet the Demand

Demand


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.


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.


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


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


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.


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


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


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


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


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


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


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

$)


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


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


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


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


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


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


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


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


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


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.

modeling generation capacity investment decisions

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