system analysis advisory committee review
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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
10
20
30
40
50
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80
9030
40
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90
100
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120
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180
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210
220
230
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
10
20
30
40
50
60
70
11
6
11
6.7
5
11
7.5
11
8.2
5
11
9
11
9.7
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
10
20
30
40
50
60
70
80
90
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
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
10
20
30
40
50
60
70
80
90
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
Freq
uenc
y
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 $2006 M)
L813
L813 L813 Frontier
C:\Backups\Plan 6\Studies\L813\Analysis of Optimization Run_L813vL811.xls
Implication to Number of Futures
19
Finding the Best Plan
• Each plan is exposed to exactly the same set of futures, except for electricity price
• Look for the plan that minimizes cost and risk
• Challenge: there may be many plans (Sixth Plan possible resource portfolios:1.3 x 1031)
Implication to Number of Plans
20
Space of feasible solutions
The Set of Plans Precedes the Efficient Frontier
Relian
ce on th
e likeliest ou
tcome
Risk Aversion
Efficient Frontier
Implication to Number of Plans
21
Finding the “Best” Plan
155600
155800
156000
156200
156400
156600
156800
157000
0 500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000Ta
ilVar
90 ($
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
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
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
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
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
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
11
36
10
28
14
75
14
43
13
68
12
00
12
28
10
89 15
71
14
11
10
00
12
04
12
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
124
125
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127
128
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
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
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
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
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
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
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
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