SAAC Review

SAAC Review

Michael SchilmoellerTuesday February 2, 2011

SAAC

2

Sources of Uncertainty

Scope of uncertainty

• Fifth Power Plan– Load requirements– Gas price– Hydrogeneration– Electricity price– Forced outage rates– Aluminum price– Carbon allowance cost– Production tax credits– Renewable Energy Credit

(Green tag value)

• Sixth Power Plan– aluminum price and

aluminum smelter loads were removed

– Power plant construction costs

– Technology availability– Conservation costs and

performance

3

CharacteristicsResource Planning?

Reduce size and likelihood of bad outcomes

✔ ✔

Cost – risk tradeoff: reducing risk is a money-losing proposition

✔ ✔

Imperfect Information ✔ ✔

Buying an automobile?

No "do-overs", irreversibility

✔ ✔

4

CharacteristicsResource Planning?

Use of scenarios ✔ ✔

Resource allocations reflect likelihood of scenarios

✔ ✔

Resource allocations reflect severity of scenarios

✔ ✔

… even if "we cannot assign probabilities"

✔ ✔

Buying an automobile?

Some resources in reserve, used only if necessary

✔ ✔

5

Identifying Long-Term Ratepayer Needs

• Why and for whom is a plant built?– For the market or the ratepayer?– Built for independent power producers (IPPs) for sales into the

market, with economic benefits to shareholders?

• How much of the plant is attributable to the ratepayer?– This is usually a capacity requirement consideration– To what extent does risk bear on the size of the plant’s share ?

6

How the NWPCCApproach Differs

• No perfect foresight, use of decision criteria for capacity additions

• Likelihood analysis of large sources of risk (“scenario analysis”)

• Adaptive plans that respond to futures

7

Excel Spinner Graph Model

• Represents one plan responding under each of 750 futures

• Illustrates “scenario analysis on steroids”

8

Modeling Process

The portfolio model

Likeli

hood

(Pro

babil

ity) Avg Cost

10000 12500 15000 17500 20000 22500 25000 27500 30000 32500

Power Cost (NPV 2004 $M)->

Risk = average ofcosts> 90% threshold

Likeli

hood

(Pro

babil

ity) Avg Cost

10000 12500 15000 17500 20000 22500 25000 27500 30000 32500



Likeli

hood

(Pro

babil

ity) Avg CostAvg Cost

10000 12500 15000 17500 20000 22500 25000 27500 30000 3250010000 12500 15000 17500 20000 22500 25000 27500 30000 32500



9

Space of feasible solutions

Finding Robust Plans

Reliance on the likeliest outcom

e

Risk Aversion

Efficient Frontier

10

Impact on NPV Costs and Risk

0

10

20

30

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80

9030

40

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Freq

uenc

y

Billions of 2006 Constant Dollars

NPV 20-Year Study Costs

Scope of uncertainty

C:\Documents and Settings\Michael Schilmoeller\Desktop\NWPCC - Council\SAAC\Presentation materials\L813 NPV Costs.xlsm

11

Decision Trees• Estimating the number of branches

– Assume possible 3 values (high, medium, low) for each of 9 variables, 80 periods, with two subperiods each; plus 70 possible hydro years, one for each of 20 years, on- and off-peak energy determined by hydro year

– Number of estimates cases, assuming independence: 6,048,000

• Studies, given equal number k of possible values for n uncertainties:

• Impact of adding an uncertainty:

Decision trees & Monte Carlo simulation

iesuncertaint values, , nkkN n

kN

N

1

12

Monte Carlo Simulation• MC represents the more likely values• The number of samples is determined by the

accuracy requirement for the statistics of interest• The number of samples mk necessary to obtain

a given level of precision in estimates of averages grows much more slowly than the number of variables k:

Decision trees & Monte Carlo simulation

kk

mm

k

k 11

13

Monte Carlo Samples

• How many samples are necessary to achieve reasonable cost and risk estimates?

• How precise is the sample mean of the tail, that is, TailVaR90?

Implication to Number of Futures

14

Assumed Distribution

0123456789

10111213141516

109

115

121

127

133

139

145

151

157

163

169

175

181

187

193

199

205

211

217

223

Freq

uenc

y


Tail Risk


C:\Documents and Settings\Michael Schilmoeller\Desktop\NWPCC - Council\SAAC\Presentation materials\L813 NPV Costs 02.xlsm

15Implication to Number of Futures

Dependence of Tail Average on Sample Size

0

10

20

30

40

50

60

70

116

116.

7511

7.5

118.

2511

911

9.75

120.

512

1.25

122

122.

7512

3.5

124.

2512

512

5.75

126.

512

7.25

128

128.

7512

9.5

130.

2513

113

1.75

75 samples per average

C:\Documents and Settings\Michael Schilmoeller\Desktop\NWPCC - Council\SAAC\Presentation materials\L813 NPV Costs 02.xlsm, worksheet “Samples_75”

σ=1.677

0

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90

30

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Freq

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y



16

Accuracy and Sample Size• Estimated accuracy of TailVaR90 statistic is

still only ± $3.3 B (2σ)!*

0

10

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90

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0

10

20

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40

50

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116

116.

7511

7.5

118.

25 119

119.

7512

0.5

121.

25 122

122.

7512

3.5

124.

25 125

125.

7512

6.5

127.

25 128

128.

7512

9.5

130.

25 131

131.

75

75 samples per average

*Stay tuned to see why the precision is actually 1000x better than this!

17

Accuracy Relative to the Efficient Frontier

123200

124200

125200

126200

127200

128200

129200

77000 78000 79000 80000 81000 82000 83000

Ris

k (N

PV $

2006

M)

Cost (NPV $2006 M)

L813

L813 L813 Frontier

C:\Backups\Plan 6\Studies\L813\Analysis of Optimization Run_L813vL811.xls


18

Conclusion

• At least 75 samples are needed for determining the value of our risk metric– Known distribution of statistic– The precision of the sample

• Our risk metric is 1/10 of the total number of futures

• We need to test our plan under 750 futures to obtain defensible results


19

Finding the Best Plan

• Each plan is exposed to exactly the same set of futures, except for electricity price

• Look for the plan that minimizes cost and risk

• Challenge: there may be many plans (Sixth Plan possible resource portfolios:1.3 x 1031)

Implication to Number of Plans

20

Space of feasible solutions

The Set of Plans Precedes the Efficient Frontier

Reliance on the likeliest outcom

e

Risk Aversion

Efficient Frontier


21

Finding the “Best” Plan

155600

155800

156000

156200

156400

156600

156800

157000

0 500

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2500

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3500

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4500

5000

5500

6000

6500

7000

7500

8000Ta

ilVar

90 ($

M N

PV)

simulation number

Reduction in TailVar90with increasing

simulations (plans)

C:\Documents and Settings\Michael Schilmoeller\Desktop\NWPCC - Council\SAAC\Presentation materials\Asymptotic reduction in risk with increasing plans.xlsm


22

How Many 20-Year Studies?

• How long would this take on the Council’s Aurora2 server?

studiesyear -20 10 2.625

750 3500 futures plans

6

n

Implication to Computational Burden

23

• Assume a benchmark machine can process 20-year studies as fast:– Xeon 5365, 3.0 MHz, L2 Cache 2x4, 4 cores/4

threads per core– 38 GFLOPS on the LinPack standard– To the extent this machine underperforms the Council

server, the time estimate would be longer• Total time requirement for one study on the

Tianhe-1A: 3.54 days (3 days, 12 hours, 51 minutes) and estimated cost $37,318

On the World’s Fastest Machine


24

How Do We AchieveOur Objectives?

• If it takes more that a workday to perform the simulation, the risk of making errors begins to dampen exploration

• In the next presentation, we consider alternatives and the RPM solution


25

End

SAAC Review

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