System AnalysisAdvisory Committee

Review

Michael SchilmoellerFriday, January 25, 2013

2

Sources of Uncertainty

Scope of uncertainty

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

• 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 RPM Differs fromOther Planning Models

• 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• Planning to minimize risk rather than

expected cost

7

Uncertainties• Aluminum Prices• Carbon Penalty• Commercial

Availability• Conservation

Performance• Construction Costs• Electricity Price

• Hydrogeneration• Natural Gas Price• Non-DSI Loads• Production Tax Credit

Life• REC Values• Stochastic FOR

8

Excel Spinner Graph Model

• Represents one plan responding under each of 750 futures

• Illustrates “scenario analysis on steroids”

9

Modeling Process

The portfolio model

Like

lihoo

d (P

roba

bilit

y) Avg Cost

10000 12500 15000 17500 20000 22500 25000 27500 30000 32500

Power Cost (NPV 2004 $M)->

Risk = average ofcosts> 90% threshold

Like

lihoo

d (P

roba

bilit

y) Avg Cost

10000 12500 15000 17500 20000 22500 25000 27500 30000 32500

Power Cost (NPV 2004 $M)->

Risk = average ofcosts> 90% threshold

Like

lihoo

d (P

roba

bilit

y) Avg CostAvg Cost

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

Power Cost (NPV 2004 $M)->

Risk = average ofcosts> 90% threshold

10

Space of feasible solutions

Finding Robust Plans

Relian

ce on th

e likeliest ou

tcome

Risk Aversion

Efficient Frontier

11

Impact on NPV Costs and Risk

0

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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

12

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 nkn

kN

N

kn

kn

,

,1

13

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 games mn necessary to obtain a

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

Decision trees & Monte Carlo simulation

n

n

m

m

n

n 11

14

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

15

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

Billions of 2006 Constant Dollars

Tail Risk

Implication to Number of Futures

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

16Implication to Number of Futures

Dependence of Tail Average on Sample Size

0

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11

6

11

6.7

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5

12

0.5

12

1.2

5

12

2

12

2.7

5

12

3.5

12

4.2

5

12

5

12

5.7

5

12

6.5

12

7.2

5

12

8

12

8.7

5

12

9.5

13

0.2

5

13

1

13

1.7

5

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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Freq

uenc

y

Billions of 2006 Constant Dollars

NPV 20-Year Study Costs

17

Accuracy and Sample Size• Estimated accuracy of TailVaR90 statistic is

still only ± $3.3 B (2σ)!*

0

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90

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180

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Freq

uenc

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Billions of 2006 Constant Dollars

NPV 20-Year Study Costs

Implication to Number of Futures

0

10

20

30

40

50

60

70

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!

18

Accuracy Relative to the Efficient Frontier

123200

124200

125200

126200

127200

128200

129200

77000 78000 79000 80000 81000 82000 83000

Ris

k (N

PV

$2

00

6 M

)

Cost (NPV $2006 M)

L813

L813 L813 Frontier

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

Implication to Number of Futures

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

Relian

ce on th

e likeliest ou

tcome

Risk Aversion

Efficient Frontier

Implication to Number of Plans

21

Finding the “Best” Plan

155600

155800

156000

156200

156400

156600

156800

157000

0 500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

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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

Implication to Number of Plans

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– 639 years, 3 months, 7 days

• 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

Implication to Computational Burden

24

How the RPM Satisfies the Requirements of a Risk Model• Statistical distributions of hourly data

– Estimating hourly cost and generation– Application to limited-energy resources– The price duration curve and the revenue curve

• Valuation costing• An open-system models• Unit aggregation• Performance and precision

25

Estimating Energy Generation

Price duration curve (PDC)

Statistical distributions

26

Gross Value of Resources Using Statistical Parameters of

Distributions

e

ee

ge

ee

g

e

ge

dd

ppd

(h))(p

p

p

NN

dNpdNpc

12

1

21

2/)/ln(

ln ofdeviation standard is

price gas theis

pricey electricit average theis

variablerandom )1,0( afor CDF theis

where

(4) )()( Assumes:

1) prices are lognormally distributed

2) 1MW capacity

3) No outages

V

Statistical distributions

27

Estimating Energy Generation

*

*

1)(CDFcf

)(CDF

Calculus) of Thm (Fund

)(CDF

*

*

gg

gg

g

ppgHg

gH

ppg

e

P

eH

p

V

NCp

pNCp

V

dppNCV

Applied to equation (4), this gives us a closed-form evaluation of the capacity factor and energy.

Statistical distributions

28

Implementation in the RPM

• Distributions represent hourly prices for electricity and fuel over hydro year quarters, on- and off-peak– Sept-Nov, Dec-Feb, Mar-May, June-Aug– Conventional 6x16 definition– Use of “standard months”

• Easily verified with chronological model• Execution time <30µsecs• 56 plants x 80 periods x 2 subperiods

Statistical distributions

29

Energy-Limited Dispatch

Statistical distributions

30

“Valuation” CostingComplications from correlation of fuel price, energy, market prices

priceLoads (solid) & resources (grayed)

Valuation Costing

)( imi

im ppqQpc --= åOnly correlations are now those with the market

31

Open-System Models

?

Open-System Models

32

Modeling Evolution

• Problems with open-system production cost models– valuing imports and exports– desire to understand the implications of events

outside the “bubble”

• As computers became more powerful and less expensive, closed-system hourly models became more popular– better representation of operational costs and

constraints (start-up, ramps, etc.)– more intuitive

Open-System Models

33

Open Systems Models• The treatment of the Region as an island seems

like a throw-back– We give up insight into how events and

circumstances outside the region affect us– We give up some dynamic feedback

• Open systems models, however, assist us to isolate the costs and risks of participant we call the “regional ratepayer”

• Any risk model must be an open-system model

Open-System Models

34

The Closed- Electricity System Model

fuel price+εi

dispatchprice

energygeneration

energyrequire-ments

market price +εi for electricity

Only one electricity price balances requirements and generation

• If fuel price is the only “independent” variable, the assumed source of uncertainty, electricity price will move in perfect correlation

• That is, outside influences drive the results• We are back to an open system

Open-System Models

35

The RPM Convention

• Respect the first law of thermodynamics: energy generated and used must balance

• The link to the outside world is import and export to areas outside the region

• Import (export) is the “free variable” that permits the system to balance generation and accommodate all sources of uncertainty

• We assure balance by controlling generation through electricity price. The model finds a suitable price by iteration.

Open-System Models

36

Equilibrium search

Open-System Models

37

Unit Aggregation

0.00

2.00

4.00

6.00

8.00

10.00

12.00

4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000

VO

M ($

/MW

h)

Heat Rate (BTU/kWh)

West 1 West 2 West 3

West 4 Beaver East 4

East 5 East 7 East 8

Hermiston Ignore East 1

• Forty-three dispatchable regional gas-fired generation units are aggregated by heat rate and variable operation cost

• The following illustration assumes $4.00/MMBTU gas price for scaling

Source: C:\Backups\Plan 6\Studies\Data Development\Resources\Existing Non-Hydro\100526 Update\Cluster_Chart_100528_183006.xls

Unit Aggregation

38

Cluster Analysis

11

30

12

19

13

05

12

90

11

31

12

46

12

47 1

24

81

02

11

04

10

20

14

67

14

68

16

50

16

51

11

98

11

99

12

01

12

02

10

23

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36

10

28

14

75

14

43

13

68

12

00

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28

10

89 15

71

14

11

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00

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04

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03

10

01

05

41

79

71

29

11

29

21

40

21

40

3

01

23

45

Dendrogram of agnes(x = Both_Units, diss = FALSE, metric = "manhattan", stand = TRUE)

Agglomerative Coefficient = 0.98Both_Units

He

igh

t

Source: C:\Backups\Plan 6\Studies\Data Development\Resources\Existing Non-Hydro\100526 Update\R Agnes cluster analysis\Cluster Analysis on units.doc

Unit Aggregation

39

Performance

• The RPM performs a 20-year simulation of one plan under one future in 0.4 seconds

• A server and nine worker computers provide “embarrassingly parallel” processing on bundles of futures. A master unit summarizes and hosts the optimizer.

• The distributed computation system completes simulations for one plan under the 750 futures in 30 seconds

• Results for 3500 plans (2.6 million 20-year studies) require about 29 hours

Performance and Precision

40

Precision

Source: email from Schilmoeller, Michael, Monday, December 14, 2009 12:01 PM, to Power Planning Division, based on Q:\SixthPlan\AdminRecord\t6 Regional Portfolio Model\L812\Analysis of Optimization Run_L812.xls

Performance and Precision

41

Choice of Excel as a Platform• The importance of transparency and

accessibility, availability of diagnostics• Olivia• The ability of Olivia to write VBA code for

the model• RPM’s layout of data and formulas • High-performance Excel

– XLLs– Carefully controlled calculations

• System requirements• Crystal Ball and CB Turbo

42

What do the Risky Futures Look Like?

• See Appendix J of the Sixth Power Plan– Section Quantitative Risk Analysis identifies

electricity prices, loads, carbon penalty, and natural gas prices to be the principal sources of risk

Risky Futures

43

Regression AnalysisTable J-3: Regression Model Coefficients

on-peak modelCoefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 62.63 1.49 42.15 0.00 59.71 65.54 59.71 65.54 Position_NP 22.02 0.17 126.49 0.00 21.67 22.36 21.67 22.36 ELP_NP (8.23) 0.03 (314.43) 0.00 (8.28) (8.18) (8.28) (8.18) Market_NP 0.80 0.00 309.99 0.00 0.80 0.81 0.80 0.81 CO2_Penalty 7.59 0.02 465.22 0.00 7.56 7.62 7.56 7.62 NGP_East 31.93 0.16 203.77 0.00 31.63 32.24 31.63 32.24

source: C:\Backups\Plan 6\Power Plan Documents\Appendix J Regional Portfolio Model\graphics and illustrations\Regression Analysis of L813 Costs\Regression_on_cost_L813LC_100228_00.xls, wksht "NP_Variables"

off-peak modelCoefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 7.64 0.81 9.48 0.00 6.06 9.22 6.06 9.22 Position_FP 17.40 0.15 115.52 0.00 17.10 17.69 17.10 17.69 ELP_FP (1.62) 0.02 (89.23) 0.00 (1.66) (1.59) (1.66) (1.59) Market_FP 0.59 0.00 189.85 0.00 0.59 0.60 0.59 0.60 CO2_Penalty 3.18 0.01 237.33 0.00 3.16 3.21 3.16 3.21 NGP_East 10.40 0.11 94.40 0.00 10.18 10.61 10.18 10.61

source: C:\Backups\Plan 6\Power Plan Documents\Appendix J Regional Portfolio Model\graphics and illustrations\Regression Analysis of L813 Costs\Regression_on_cost_L813LC_100228_00.xls, wksht "FP_Variables"

What do these have in common? Persistence.

Risky Futures

44

Intuition About Risk

• Worst Futures Spinner.xls• Noticed that high-cost (high-risk) futures

are high-load futures• Began our discussion of unit-energy

costs

Risky Futures

45

Uses and Abuses ofthe Efficient Frontier

123

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129

77 78 79 80 81 82 83

Th

ou

sa

nd

s

Thousands

Side Effects

Inef

fect

ive

source: \EUCI 100323 Presentation\Efficient Frontier\EUCI 100323 01.xls

Efficient Frontier

46

Efficient Frontier

• Provides an alternative to weighting– Easily constructed– General application

• Preserves the trade-off decision

Efficient Frontier

47

What does the Efficient Frontier Tell Us?• The Efficient Frontier does not

tell us what to do• The Efficient Frontier tells us

what not to do• Most useful if there are a large

number of choices

Efficient Frontier

48

Fooled by the Graph• Error 1: The geometry of the

points on the efficient frontier has meaning or otherwise provides guidance, or equivalently …

• There exists a formula or other objective means for determining an optimal point on the efficient frontier

Abusing the EF

49

49

Unclear About Control

• Error 2: The “expected cost” on the efficient frontier is controllable, equivalently …

• We can “buy” risk reduction with the increase in expected costs

Abusing the EF

50

50

Unclear About Control

• Controllable costs are typically much smaller

Abusing the EF

123200

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77000 78000 79000 80000 81000 82000 83000

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$2

00

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)

Cost (NPV $2006 M)

L813

L813 L813 Frontier

51

51

Option Costs and Risk Benefits

ClaimAnnual

RiskAnnual

PremiumAnnual

Rate1 in 10 over 20 years $ 3 B 2006 1 in 190 $ 15 M 2006 0.50%

injury in auto 13,262.00$ 1 in 128 207.22$ 1.56%major wind damage 6,518.00$ 1 in 258 50.53$ 0.78%

major water damage 5,033.00$ 1 in 387 26.01$ 0.52%

1 in 100 over 20 years $ 10 B 2006 1 in 2000 $ 15 M 2006 0.15%fire in home 21,979.00$ 1 in 1057 41.59$ 0.19%

source: C:\Backups\EUCI 100323 Presentation\Efficient Frontier\EUCI 100323 01.xlsand http://insuranceriskcalculator.com

52

Mislead by Averages

• Error 3: “We know what ‘expected cost’ means.”

• In fact, there are many different ways to compute an average, and they all have different meanings.

• More important, the average of a distribution may be very meaningful in one situation and meaningless in another.

• Example of “average” SCCT dispatch across futures of a low-risk portfolio

Abusing the EF

53

Conservation Representation

• The construction of conservation supply curves

• Discretionary and lost opportunity

• Fifth Power Plan findings• Conservation risk premium

• Sources of premium value …• Sixth Power Plan findings …

Conservation

54

Sources of Premium Value

• Capacity deferral• Protection from fuel and electricity price

excursions, in particular due to carbon risk• Short-term price reduction• Purchases at below-average prices

(“dollar-cost averaging”)• Opportunity to develop and resell

conservation energyC:\Backup\Plan 5\Portfolio Work\Olivia\SAAC 2010\110519 SAAC Meeting\Conservation Premium\The sources of premium value 101206 1600.lnk

Conservation

55

Effect of Premium on 6th Plan Conservation Energy and Cost

Conservation

56

Crystal Ball Decision Cells and the Resource Portfolio (“Plan”)

57

…And From the Last Meeting,September 27, 2012 …

58

Random Variables in the RPM– Aluminum Prices– Carbon Penalty– Commercial Availability– Conservation Performance– Construction Costs– Electricity Price– Hydrogeneration– Natural Gas Price– Non-DSI Loads– Production Tax Credit Life– REC Values– Stochastic FOR

59

Electricity Prices

6th Plan, Chap 9, page 9-11 ff

60

Causal Regimes

5th Plan, Appn P, page P-65 ff

• Short-term (hourly to monthly)– Positive correlation of electricity price with loads– Hourly correlations to hydro, natural gas price– Quarterly averages correlations to all three

• Long-term (quarterly to yearly)– Negative correlation of electricity price with loads– Supply and demand excursions– Changing technology, regulation

61

Electricity Prices Before Adjustments

5th Plan, Appn P, page P-65 ff

Adjustments for longer-term response include• Hydro year selection• Quarterly loads• Gas price effects• Energy balance (supply vs. demand) effects

The model generates an “independent” electricity price future devoid of these effects; adjustments for these effects are made deterministically during the chronological simulation

62

“Independent” Electricity Price

8 random variables, determining the underlying scenario path of electricity price and the nature of up to two excursions

63

Jumps in Electricity Price

5th Plan, Appn P, page P-65 ff

64

Underlying “Path” of Electricity Price

5th Plan, Appn P, pages P-25 ff and P-65 ff

The underlying path consists of the original benchmark forecast and the combined effects of a random offset and a random change in slope

A more complete description will be provided with the description of natural gas prices

65

Random Variables

• The values for the 288 random variables are drawn at the beginning of each game, or “future”

• All aspects of the future are calculated in the model before the chronological simulation of the resource portfolio’s performance

• Where decisions are necessary during the chronological simulation, the model references only “past” values of the given future

• You can use the Navigator feature in the RPM to explore these on your own

66

A Unit-Service Cost

• The Council has emphasized the least-risk plans on the efficient frontier

• The choice of least-risk plans is strongly (exclusively?) influenced by a handful of futures. About 70 of the 75 “worst” (highest-cost) futures are common among all the plans on the efficient frontier

• The costs in these futures is largely determined by the higher loads in these futures

• Is it appropriate that least-risk plans are strongly influenced by high-load futures?

67

What’s the Difference?

• If there is only a single, fixed load forecast, there isn’t any difference: a plan that provides for minimum cost for the Region provides minimum unit energy cost.

• However, if loads vary from future to future, however, there may be a significant difference

68

A Few Key Points

• Loads are “frozen efficiency” loads– Loads changes therefore do not reflect any

energy efficiency measures• A unit-service cost (¢/kWh) is NOT a utility

rate (¢/kWh)

69

21,000

22,000

23,000

24,000

25,000

26,000

27,000

28,000

29,000

30,000

31,000

10.0

12.0

14.0

16.0

18.0

20.0

22.0

24.0

26.0

28.0

30.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

MW

a

Period

Costs and Loads

… And Costs Are Distributed Over Fewer Units of Energy

Higher load future: 29,571 MWa Lower load future: 25,428 MWaDifference: 4,143 MWa (-14 %)

Higher load future cost: $23.5 BLower load future cost: $21.5 BDifference: $2.0 B (-8.5 %)

While cost in the last year goes down 8.5 percent, unit-service cost per kWh increases by 6.4 percent !

064.01254285.23

295715.21

29571/5.23

29571/5.2325428/5.21

70

What do Plans Selected Using the Modified Metric Look Like?

71

Differences between theLeast-Risk Plans

• Because high-load futures play a less prominent role in the selection of resources, we would expect to see less resource capacity optioned

Cns

rvn_

Lost

Opp

ortu

nity

Cns

rvn_

Dis

patc

habl

e

CC

CT

_CY

_Dec

19

CC

CT

_CY

_Dec

21

CC

CT

_CY

_Dec

23

SC

CT

_CY

_Dec

17

SC

CT

_CY

_Dec

19

SC

CT

_CY

_Dec

21

SC

CT

_CY

_Dec

23

New metric 50 60 1512 1512 1512 324 810 810 810Existing metric 60 100 1890 1890 1890 648 1458 1620 1620

72

Differences between theLeast-Risk Plans

Cns

v_M

Wa

CO

2Avg

2025

woT

CO

2Avg

2030

woT

Cns

v_LO

_en

Cns

v_LO

cst

Cns

v_N

LOen

Cns

v_N

LOcs

t

Cnv

t_cs

t

CO

2Avg

2030

wT

CO

2Avg

2025

wT

Rat

eStD

evIn

cr

Rat

eMax

Incr

New metric 5890.4 34.1 35.3 3087.0 33.6 2803.4 35.3 34.4 26.2 25.3 0.1 0.3Existing metric 6074.0 33.9 34.7 3157.0 35.2 2917.1 40.0 37.5 25.3 25.0 0.1 0.3

• The effect on conservation targets, CO2 produced, and rate variation is minimal, however (e.g., conservation drops 184MWa)

• With fewer new, cleaner turbines, CO2 production increases slightly

73

Conclusions• This cost measure provides an alternative

concept of “bad” – or risky – and “good” futures.• The calculation of average and risk would

remain the same• Will result in different least-risk plans, probably

with less capacity and conservation optioned• The new cost and risk metrics would be added

to the existing metrics, not replace them

74

End