1 systems analysis advisory committee (saac) tuesday, april 29, 2003 michael schilmoeller john fazio

1

Systems Analysis Advisory Committee (SAAC)

Tuesday, April 29, 2003Michael Schilmoeller

John Fazio

Northwest Power Planning Council

2

Agenda

• Approval of the March 31 meeting minutes

• Decomposition of risk associated with a firm contract

• Planning flexibility valuation

• Scenarios in a stochastic framework


3

Agenda






4

Agenda






5

Objectives

• Illustrate how risk attributes depend on the portfolio in which they are placed

• Show how decomposition of these attributes is nevertheless possible


6

Our Example

• One hour• One thousand MW of load• Met with a mix of

– Wholesale market power• Variable market price, lognormal distribution

(mean = $37/MWh, standard deviation = 100%)

– Variable amount of firm energy contract• $15/MW-h ($132/kW-yr)


7

Our Example

1000 MWload

contract

market


8

Our Example

• Our risk measure: CVar @ $6000

That is, the dollar threshold such that losses exceed that threshold have an expected value of $6000


9

Changing Margin

400 surplus

Probability Distribution of Costs

0

200

400

600

800

1000

1200

1400

1600

-5000 5000 15000 25000 35000

Cost ($)

Fre

qu

en

cy

(o

ut

of

20

00

)

300 deficit


0

200

400

600

800

1000

1200

1400

1600

-5000 5000 15000 25000 35000

Cost ($)

Fre

qu

en

cy

(o

ut

of

20

00

)

200 deficit


0

200

400

600

800

1000

1200

1400

1600

-5000 5000 15000 25000 35000

Cost ($)

Fre

qu

en

cy

(o

ut

of

20

00

)

100 deficit


0

200

400

600

800

1000

1200

1400

1600

-5000 5000 15000 25000 35000

Cost ($)

Fre

qu

en

cy

(o

ut

of

20

00

)

100 surplus


0

200

400

600

800

1000

1200

1400

1600

-5000 5000 15000 25000 35000

Cost ($)

Fre

qu

en

cy

(o

ut

of

20

00

)

200 surplus


0

200

400

600

800

1000

1200

1400

1600

-5000 5000 15000 25000 35000

Cost ($)

Fre

qu

en

cy

(o

ut

of

20

00

)

300 surplus


0

200

400

600

800

1000

1200

1400

1600

-5000 5000 15000 25000 35000

Cost ($)

Fre

qu

en

cy

(o

ut

of

20

00

)

400 surplus


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Observation

• This is the situation that many load-serving entities found themselves in after the 2000-2001 energy crisis

• This is the situation that many load-serving entities found themselves in after pursuing individual reserve margin goals in 1979-1982


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Conclusion

• Any specific resource can either increase or decrease risk

• The risk mitigation value of a resource to a portfolio depends on the portfolio


12

Question

• These leaves us with a potentially difficult analysis

• Is there anyway to disaggregate the risk attributes of this contract?


13

Answer

• Value each component of the portfolio in the market and superimpose


14

Example

• Warning: positive numbers are now benefit, not cost.


15

We started out withLoad: Dollars vs Price

-250000

-200000

-150000

-100000

-50000

0

50000

100000

150000

200000

250000

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190

$/MWh

Do

llar

s

1000 MW Load 800 MW Contract 1200 MW Contract


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...obtained the net position...

Net position

-60000

-50000

-40000

-30000

-20000

-10000

0

10000

20000

30000

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

$/MWh

Dol

lars

Surplus 200 Deficit 200


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...applied a probability distribution to the net position...

Net position

-60000

-50000

-40000

-30000

-20000

-10000

0

10000

20000

30000

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190

$/MWh

Do

llar

s

0

200

400

600

800

1000

1200

1400

1600

1800


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... and got the result.

Net position

-60000

-50000

-40000

-30000

-20000

-10000

0

10000

20000

30000

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190

$/MWh

Do

llar

s

0

200

400

600

800

1000

1200

1400

1600

1800


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Decomposition

• The last step here is realizing that we can superimpose the individual distributions

For example, for the 200 MW net deficit position, we had ...


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Total Position

Load: Dollars vs Price

-250000

-200000

-150000

-100000

-50000

0

50000

100000

150000

200000

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

160

170

180

190

$/MWh

Do

llars

1000 MW Load 800 MW Contract


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Total Position

Load: Dollars vs Price

-250000

-200000

-150000

-100000

-50000

0

50000

100000

150000

200000

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

160

170

180

190

$/MWh

Do

llars

0

200

400

600

800

1000

1200

1400

1600

1800

1000 MW Load 800 MW Contract Pow er Prices


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Decomposition

• But we can recover the same distribution as before, because,

($) valueload theis )(($) aluecontract v theis )(

price of pdf theis )(where

)()()()()()()(

pLpCpD

pLpDpCpDpLpCpD


23

Conclusion

• We can value the two elements of the portfolio, load and contract, against the market and then add them

• We can value each element of a portfolio against the market, independent of one another, and have the risk mitigation we need to assess the portfolio.


24

Agenda



• Planning flexibility valuation• Scenarios in a stochastic framework• (Done)


25

Objectives

• Illustrate how valuation of planning flexibility can be performed


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Overview

• Review of the Excel function for capturing planning flexibility

• Describe some experiments performed with one of Olivia’s spreadsheets

• Summarize an insight• Abstract to a quantification principle


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NPPC Analysis

construction phase

optional cancellation period

evalulation phase

time

wh

ole

sale

ele

ctri

city

ma

rke

t

price threshold

expected price trend

Representations


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Captured with aUser-Defined Excel function


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Experiment

• Set up the worksheet for a plant with a construction phase of three periods and no optioning period; and a plant with the same construction phase, but an option period comprising 2 periods.

• Use the difference in the net revenues over the study period for these plants


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Experiment

• Perform simulations, arranging for every possible pattern of criteria appear over the study.

For example, if 1 denotes a positive criterion and 0 a negative criterion, and we consider five periods enumerate all the binary numbers between 00000 and 11111.


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Results

• The pattern that gives rise the greatest value of planning flexibility is

111000000111000000111000000....

• What is going on here?


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Prices


33

Construction withoutFlexibility


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Construction withFlexibility


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• Valuation is straight-forward, using a geometric series

r

aS

rnr

raS

ararararaS

nSnra

n

n

n

nn

n

1

small becomes or infinity approaches as and1

1then

termson sum theis polynomial in the termsofnumber theis

polynomial theofant indetermin theis tcoefficienconstant a is

132


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• Valuation is

))1(1/())1/(1)1/(23()/1(

isy flexibilit of valuethen the

yearsin jump theofduration theis pricein jumpsbetween years ofnumber theis

ratediscount real theis unit theofcapacity theis

($/MWyr)capacity of valueannual theis costovernight of (1/3)on constructi ofcost annual is

1 mnnn dddPCV

mndCVP


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Shorter Lead Time


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Shorter Lead Time

• Another geometric series


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Principles ofValuing Modularity

• As in the first presentation, the value of modularity can be assessed for each resource independent of others

• Valuation depends on an assumed market price behavior


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Perfect Foresight

• The perfect foresight assumption is what we typically use in planning

• It assumes that plants can be brought on line at the point in time that optimizes their value


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Value of Capacity withPerfect Foresight


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Perfect Foresight

• With perfect foresight, assumed by many of our models, the value of capacity is overstated. It needs to be discounted for decision making under uncertainty.

• Resources with planning flexibility would see a smaller discount than those without this flexibility.


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Conclusions

• Value of modularity can be estimated from a particular pattern of price behavior, using time-value of money calculations and geometric series

• Resource optionality can be assessed independent of loads and other resources, by assessing in the market


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Conclusions

• Plants with planning flexibility should have a smaller value discount relative to plants without such flexibility

• We expect to be able to verify these values with Olivia

• Olivia may provide additional insights and working hypotheses for estimating this long-term real option value


46

Agenda





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Objectives

• Explore the value of using subjective probabilities to address future scenarios


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Types of uncertainty

• Variability– Predictable– The descriptive statistics, such as mean,

dominate the valuation calculation (e.g., hydrogeneration).

– Weak temporal correlation (little year to year)

• Futures– Unpredictable– Only one future will manifest– Stronger temporal correlation


49

Refinements

• PacifiCorp further distinguishes futures into– “scenario risk,” the consequences of which

PacifiCorp feels more comfortable quantifying, although “probabilities can not be assigned,” and

– “paradigm risk,” which PacifiCorp feels uncomfortable characterizing quantitatively. These are changes in the underlying structure of the business model


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Objective of Futures Analysis

• Illuminate and evaluate the future consequence of today’s decisions

• Identify “robust” solutions• Identify contingency options


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Example

We will• Examine three plans in three futures for

risk and cost• Look at the outcome in terms of risk/cost

trade-off and make a decision• Look at the outcomes using stochastic

analysis and make a decision• Compare the outcomes


52

Example

• CO2 tax cost mitigation

• We consider a single year, 2005

• We buy a quantity of outsets that matches our production of CO2


53

Assumptions

• Tax offsets have price that closely approximates the emission tax rate.

• Experts expect a $6/ton CO2 tax around 2005


54

Plans

• Approaches– Plan to start buying tax offsets at $6/ton in

2005

– Buy tax offsets forward (2005) at $6/ton

– Buy options (strike of $10/ton) on tax offsets in 2005 for $1/ton premium.


55

Example

• Future 1: Insignificant tax• Future 2: $15/ton tax in 2005• Future 3: $3/ton tax in 2005


56

Outcomes

Future 1: Insignificant tax

• Wait and buy: we never see anything that concerns us, so we pay nothing

• Buy forwards: Costs $6/ton• Buy options: Costs $1/ton


57

Outcomes

Future 2: $15/ton tax in 2005

• Wait and buy: Costs $15/ton• Buy forwards: Costs $6/ton• Buy options: Costs $11/ton ($1/ton

premium plus purchase at $10/ton)


58

Outcomes

Future 3: $3/ton tax in 2005

• Wait and buy: Costs $3/ton• Buy forwards: Costs $6/ton• Buy options: Costs $4/ton


59

Outcomes


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Outcomes

If we average the costs and use the worst case outcome as a measure of risk, we have the following …


61

Outcomes


62

Results

• Buying forward “dominates” waiting

• Buying forwards and buying options are on the “efficient frontier”

• The forward contract, with no cost uncertainty, is attractive


63

Issues

• We get new information– A political outcome makes it very unlikely

that there will be any CO2 tax in 2005

• This has no impact on the preceding two diagrams, but it has significant impact on our valuation (or, more important, the valuation of the person writing the check)


64

What is going on?

• The selection of futures we examine has an impact on the construction of the diagrams. Our eye tells us that the points all have equal likelihood, whereas this generally will not be the view of the decision maker.


65

What is going on?

• If we weight the values by their likelihood, we get an outcome that makes more sense to the decision maker

For example, is we believe there is 2/3 probability there will be no tax ...


66

What is going on?


67

What is going on?


68

Results

• Now the wait strategy is practically dominated by the buy option strategy, but there is a much more clear trade-off between the option strategy and the forward strategy

• If it is truly unlikely there will be a CO2 tax in 2005, forward contracts look like a waste of money.


69

Results

• If we use something like CVar for our risk measurement and have more points, the risk could also change ranks among the plans


70

Conclusions

• When we use frequency-based probabilities in “stochastic” analysis, we typically concerned with the descriptive statistics for the distribution, such as mean.


71

Conclusions

• When we use subjective probabilities for analysis of futures, we are using them to identify plans that are “robust,” i.e., plans that perform well in most of the likely futures and do not perform terribly poorly in the worst cases.


72

Conclusions

• Subjective probabilities permit us to more realistic attribute value to contingency options

• As a practical matter, we experts and analysts will advise the decision makers regarding the likelihood of various futures, although the ultimate assessment always must reside with them.


73

Agenda





74

Next Meeting

• Next meeting June 5, 2003– More discussion of statistics– Results with Olivia


75

Risk Mitigation

• Options.• Right, but not the obligation to take a particular action or engage in a

particular transaction.• Has two sides, and must be traded between participants.• Usually asymmetric with respect to a given risk: limits outcome in a

single direction.

• Hedging.• Commitment to action or transaction that reduces the variability or

uncertainty of outcome. Does not provide optionality.• Usually symmetric with respect to a given risk: limits outcome in

both directions.

• Neither in itself decreases expected costs.


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Risk Mitigation: Optionality

• Long-term flexibility• Start-up and shut-down speed and flexibility

• Demand reduction• Mothball and delay flexibility• Operational and administrative control, independence• Sizing flexibility (capital cost flexibility)

• Short-term flexibility• Dispatchability, if fixed cost component is small• Demand curtailment


77

Risk Mitigation: Hedging

• Long-term hedges• Independence from fuel price• Resource diversity• High availability and proven technology• Reliable technology• Cash flow: how and when capital is committed (complex)• R&D

• Short-term hedges• Diversity of fuels• Reliability of resource and reduced maintenance


78

Which Risks Does the Prototype Address?

• We may need greater richness in the description of variables, such as separate uncertainty forecasts for each fuel

• We may need less richness in other areas, such as the subperiods (on- and off-peak) we chose

• New risk mitigation issues that have arise since its inception

• Multiple regions and transmission congestion• Planning flexibility• DSI load response• Credit risk/long-term availability• Availability of new technologies• More detailed price behavior (jumps, etc.)

Background

1 systems analysis advisory committee (saac) tuesday, april 29, 2003 michael schilmoeller john fazio

Documents

risk attributes

riskthe risk mitigation

net position

firm energy contract

mw net deficit position

expected value

mw of loadmet

construction phase