The Councils Approach to Modeling

1
The Councils Approach to Modeling

• Michael Schilmoeller
• Northwest Power and Conservation Council
• for the
• California Energy Commission
• June 4, 2007

2
Overview

• The Regional portfolio model
• Council risk metric
• Discussion of uncertainty specific to carbon risk

3
Different Risk Language

• Uncertainty
• Risk
• Stochastic Analysis
• Scenario Analysis

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Different Risk Modeling

• Scenario Analysis on Steroids
• Probabilities associated with all uncertainties
• Imperfect Foresight, Decision Criteria
• Adaptive Plans

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Background on the Efficient Frontier

• Because we face uncertainty, we need to find
  Plans that perform well over wide range of
  possible Futures
• Futures -- possible combinations of hydro
  conditions, loads, fuel prices, market prices,
  CO2 penalties and so on over planning period
• Plans types and amounts of resources and
  earliest be prepared to start construction
  dates (options)

Background
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And a Bit More Abstractly

• Futures circumstances over which the decision
  maker has no control that will affect the outcome
  of decisions
• Plans actions and policies over which the
  decision maker has control that will affect the
  outcome of decisions

Background
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Example Demand Uncertainty
Background
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Sources of Uncertainty

Load requirements Gas price Hydrogeneration Elect
ricity price Forced outage rates Aluminum
price CO2 tax Production tax credits Green tag
value (Renewable Energy Credit)
Background
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Resource Plan
These dates represent the earliest that
construction would begin. All siting, licensing,
and other preparation must be completed by these
dates. The earliest in-service dates are 2 years
later for CCCT, 1 year for SCCT, 3 years six
months for Coal, and 1 year for Wind, due to
construction time requirements. Wind energy
assume a 30 percent availability. Turbines have 5
percent forced outages.
Background
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The Construction Cycle

• After an initial planning period, there typically
  large expenditures, such as for turbines or
  boilers, that mark decision points.

9 months
9 months
18 months
Cash expenditures
Background
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Modeling Cohorts

• Each period can have a cohort of plants, usually
  of different size or capacity
• All cohorts will be affected by changing
  circumstances, but may be at different stages of
  development

Capacity
time
Background
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Distribution of Cost for a Plan
Number of Observations
Background
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Risk and Expected Cost Associated With A Plan
Risk average of costsgt 90 threshold
Likelihood (Probability)
Power Cost (NPV 2004 M)-gt
Background
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Feasibility Space
Increasing Risk
Increasing Cost
Background
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Feasibility Space
Increasing Risk
Increasing Cost
Background
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Efficient Frontier
Background
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Spinner Graphs

• A given plan, across all futures
• Illustrates scenario analysis on steroids
• Link to L28X-f1232 (D)_P.xls

Background
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Modeling Process
Portfolio Model
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Olivia

• Flexible
• The user uses a high-level representation to
  describe their system
• Exploration is easy
• Specific to users system
• Rich in features
• Has a library of physical and financial
  resources, of uncertainty processes and risk
  measures
• Builds on Councils data
• Puts planning flexibility into modeling

Olivia
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Overview

• The Regional portfolio model
• Council risk metric
• Discussion of uncertainty specific to carbon risk

21
Importance of Multiple Perspectives on Risk

• Standard Deviation
• VaR90
• 90th Quintile
• Loss of Load Probability (LOLP)
• Resource - Load Balance
• Incremental Cost Variation
• Average Power Cost Variation (Rate Impact)
• Maximum Incremental Cost Increase
• Exposure to Wholesale Market Prices
• Imports and Exports

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TailVaR90 Risk MeasureFor A Given Plan
Risk average of costsgt 90 threshold
Likelihood (Probability)
Power Cost (NPV 2004 M)-gt
Risk Measures
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The Rationale for TailVaR90

• Measure of likelihood and severity of bad
  outcomes, rather than of predictability
• A measure should not penalize a plan because the
  plan produces less predictable, but strictly
  better outcomes
• We want to pay only for measures that reduce the
  severity and likelihood of bad outcomes
• The measure should capture portfolio
  diversification
• The objective of economic efficiency
• Determined by statute
• Risk measure is denominated in same units as the
  objective, i.e., net present value dollars

Risk Measures
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Coherent Measures of Risk

• In 1999, Philippe Artzner, Universite Louis
  Pasteur, Strasbourg Freddy Delbaen,
  Eidgenossische Technische Hochschule, Zurich
  Jean-Marc Eber, Societe Generale, Paris and
  David Heath, Carnegie Mellon University,
  Pittsburgh, Pennsylvania, published Coherent
  Measures of Risk (Math. Finance 9 (1999), no. 3,
  203-228) or http//www.math.ethz.ch/delbaen/ftp/p
  reprints/CoherentMF.pdf
• Addressing problems with VaR
• Developed a system of desirable properties for
  financial and economic risk measures

Coherent Risk Measures
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Desirable Properties For a Risk Metric r

• Subadditivity For all random outcomes (losses)
  X and Y,
• r(XY) ? r(X)r(Y)
• Monotonicity If X ? Y for each future, then
• r(X) ? r(Y)
• Positive Homogeneity For all l ? 0 and random
  outcome X
• r(lX) lr(X)
• Translation Invariance For all random outcomes
  X and constants a
• r(Xa) r(X) a

Metrics
Coherent Risk Measures
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Risk Paradoxes

• The following risk metrics are not coherent
• Standard deviation
• VaR
• Loss of load probability (LOLP)
• Any quantile measure
• Examples of coherent measures
• TailVaR90
• Expected loss (average loss exceeding some
  threshold)
• Risk measure which is sub-additive and monotonic
• Unserved energy (UE)

Issues with Risk Measures
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Risk Paradoxes

• Case 1 We choose standard deviation for
  economic risk measurement.

Issue Plan B produces a more predictable
outcome, as measured by standard deviation, but
all of the outcomes are worse than those
associated with Plan A. This risk metric assigns
more risk to Plan A than to Plan B. Typically,
however, a decision maker is looking at cost,
too, and could discriminate between these cases.
B
A
Issues with Risk Measures
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Risk Paradoxes

• Case 1 We choose standard deviation for
  economic risk measurement.

Issue Two plans produce quite distinct
distributions for cost outcomes. For one of the
plans, the outcomes are much worse under certain
circumstances than for the other plan. However,
the distributions have identical mean and
standard deviation. The risk measure can not
discriminate between the plans.
Issues with Risk Measures
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Risk Paradoxes

• Case 2 We choose LOLP for assessing the
  engineering reliability of two power systems.
• Issue We have two systems, both meeting a load
  of 150MW. The first consists of one 200 MW
  power plant, forced outage rate (FOR) of 8. The
  second system is two 100 MW power plants, FOR
  also 8.
• We know intuitively that portfolio diversity of
  resources should result in a more reliable
  system.

Issues with Risk Measures
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Risk Paradoxes

• Case 2 We choose LOLP for assessing the
  engineering reliability of two power systems.

Issues with Risk Measures
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Risk Paradoxes

• Case 2 We choose LOLP for assessing the
  engineering reliability of two power systems.

The LOLP of the single unit is lower than that
for the diversified system. What is going on
here?
Issues with Risk Measures
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Unserved Energy Gets It Right
Issues with Risk Measures
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Risk Paradoxes

• Case 3 We choose Value at Risk (VaR) to measure
  the economic risks associated with merging two
  power systems.
• We believe that the diversity of the merged
  systems should result in less risk.

Issues with Risk Measures
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Risk Paradoxes

• VaR is an estimate of the level of loss on a
  portfolio which is expected to be equaled or
  exceeded with a given, small probability.

• A quantile associated with the bad tail of a
  distribution (e.g., 85th percentile)
• A time period (e.g., overnight)
• A reference point (e.g., todays value of the
  portfolio)

Issues with Risk Measures
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Risk Paradoxes

• Assume a reference point of zero
• Two values of outcome, a loss of 0.00 and a loss
  of 1.00
• Ten futures

!??
Metrics
Issues with Risk Measures
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Overview

• The Regional portfolio model
• Council risk metric
• Discussion of uncertainty specific to carbon risk

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CO2 Cost

• May 2003 Advisory Committee Meeting
• Characterizing probabilities where no information
  in known
• Ultimately, used thresholding

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CO2 Tax
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CO2 Tax
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Other EffectsRelated to Carbon Risk

• Load requirements
• Hydrogeneration
• Green Tag Value
• Production Tax Credits

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Value of Renewable Energy Credit

• Applies to more than emerging technologies for
  power generation
• Will continue to influence power generation
  economics after technologies mature, after carbon
  risk cost is internalized

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Value of Renewable Energy Credit
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Production Tax Credits

• Changing markets
• As cost of non-fossil fuel technologies improve,
  less support for credits
• Internalizes external costs

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Production Tax Credits
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Production Tax Credits
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Production Tax Credits
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Conclusions

• There are optimal resource choices even when the
  future is uncertain.
• Decision-makers change course based on outcomes
  to minimize adverse outcomes. Planning needs to
  have and cost exit strategies and contingency
  options.
• To value exit strategies and contingency options,
  decision-makers need to assign probabilities to
  futures.