1 Systems Analysis Advisory Committee (SAAC) Tuesday February 10, 2004 Michael Schilmoeller John Fazio

1

Systems Analysis Advisory Committee (SAAC)

Tuesday February 10, 2004Michael Schilmoeller

John Fazio

Northwest Power and Conservation Council

2

Agenda

• Welcome Back!

• Overview of methods

• Presentation of candidate plan

• Models and modeling

• Algorithms

• Next meeting


3

Similar to Everyday Decision Making under Uncertainty

• Analogy with choosing transportation• Cost and benefits• Risks

– Accidents• Likelihood• Protection afforded

– Likelihood and cost of breakdowns and repairs– Missed meetings or appointments

Overview of Methods


4

The Analysis

• Possible “futures”

• Likelihood of those circumstances

• Bad outcomes


5

The Trade-off

• The choice of transportation depends on how we weight the costs or benefits and the risk associated with that choice

3 4 5 6 7 8 9 10

Cost ->

79

1113

1517

1921

Ris

k ->

AA

BB


6

Decision Making Terms

• Risk– A measure of bad outcomes

• Variation– Normal changes in outcome, which may be

highly predictable

• Uncertainty– The predictability of outcomes


7

Decision Making Terms• An example of variation is average daily temperature

over the course of a year

Time (a year)Time (a year)

Tem

pera

ture

Tem

pera

ture


8


• For any particular day, the uncertainty in daily temperature can be large.

Time (a year)Time (a year)

Tem

pera

ture

Tem

pera

ture

??


9


• Plans– Future actions we can control

• Example: buy a 1978 Toyota corolla

• Futures– Future situations we can not control

• Example: A automobile crash in the local intersection

• Scenarios– Combinations of plans and futures

• Example: how did your Toyota fare in the crash


10

Power Plan Futures

• Behavior for key variables – Power requirements– Natural gas price– Hydro generation– Electricity market price– Aluminum price– CO2 tax– Power plant availability

• Variation and uncertainty, including jumps and complex paths; Relationships among these


11

Power Plans

• Specific recommendations, capacity and timing, for the construction of new additions over the next 20 years– CCCT– SCCT– Conservation– Price responsive demand– Wind– Coal


12

Example of aParticular Plan


13

Power Plans

• We do not make decisions before we need to do so. We want as much information as possible before making a commitment

• Therefore, we want to focus on the “Implementation Plan” that identifies actions over the next three to five years.

• Preparing a 20-year plan enables us to assure our short-term implementation plan create no long-term risk and does not preclude important long-term planning options. (We want to understand the strategic significance of our short-term actions.)


14Power Cost (¢/kWh)->

Nu

mb

er

of

Ob

serv

ati

ons

Cost for Future 2

Cost for Future 1

Distribution of Cost for a Plan

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00


15

Risk and Expected Cost Associated With A Plan

Like

lihood

(Pro

bab

ility

)

Avg Cost

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

Power Cost (¢/kWh)->

Risk = average ofcosts> 90% threshold


16

A Different Plan: The Trade-offLi

kelih

ood

(Pro

bab

ility

)

Risk

Avg Cost

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00



17

Trade-off

• Basic information about the trade-off between cost and risk

3 4 5 6 7 8 9 10

Cost (cents/kWh) ->

79

1113

1517

1921

Ris

k (c

en

ts/k

Wh

) ->

AA

BB


18

Insights

• Insights into– What a plan costs– How we expect it to perform– What the risks are

• How does the plan perform under specific futures?

• What are the chances we may see these futures?


19

Agenda

• Welcome Back!




• Algorithms

• Next meeting


20

• Research the cost and potential for regional demand response (DR)– Preliminary studies suggest DR significantly reduces both

risk and cost

• Continue support of conservation– Conservation additions at levels above those determined

by market price reduces risk at little expected cost– At least a 5 mill/kWh premium

• The region appears to have sufficient conventional resources for the next four to five years, although individual load-serving entities or customers may have vastly different risk-management situations

Recommendations


21

Without Demand Response

4.24

Cost (cents/kWh) ->

Ris

k (c

en

ts/k

Wh

) ->

4.26 4.28 4.30 4.32

4.71

4.73

4.75

4.77

• Least cost:– 500MW of

CCCT today

– 500MW of Wind Generation after 2006

– Incent dispatchable conservation at 0.50 ¢/kWh


22

Without Demand Response

4.24

Cost (cents/kWh) ->

Ris

k (c

en

ts/k

Wh

) ->

4.26 4.28 4.30 4.32

4.71

4.73

4.75

4.77

• Least risk:– Incent

dispatchable conservation at 2.50 ¢/kWh


23

With Demand Response

4.24

Cost (cents/kWh) ->

Ris

k (c

en

ts/k

Wh

) ->

4.26 4.28 4.30 4.32

4.71

4.73

4.75

4.77

• Demand Response moves the entire trade-off curve to the left


24

Agenda

• Welcome Back!• Overview of methods• Presentation of candidate plan• Models and modeling

– Trade-Off: The construction of the efficient frontier– Estimating the distributions– Examination of futures– Representation of resources– Load/Resource balance

• Algorithms• Next meeting


25

Risk and Expected Cost Associated With A Plan

Like

lihood

(Pro

bab

ility

)

Avg Cost

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00


Risk = average ofcosts> 90% threshold


26

The Source of the Trade-Off

Increasing Cost

Incre

asin

g R

isk

Alternative PlansAlternative Plans


27

Space of feasible solutions

Efficient Frontier

Incre

asin

g R

isk

Increasing Cost

Alternative Alternative Risk LevelsRisk Levels

Efficient Frontier


28

Finding the Efficient Frontier

We are really only interested in the efficient frontier:

“Risk-Constrained Least-Cost Planning”


29


How many plans are there in our feasibility space? A few ....

In our modeling, we have examined levels of six resources at eight time periods (2004, 2005, 2006, 2007, 2008, 2013, 2018)

Possible States (example) StatesConservation 3CCCT 5SCCT 7Coal 5PRD 4Wind 5


30

The Process

We can reduce the number of states by requiring that no capacity, once added, may be “de-constructed.”

With this constraint, we have merely 2.7 x 1015 plans, or so.


31


The solution?

Use a stochastic optimization program


32


Does distribution meet

risk constraint?

Pick an arbitrary plan and arbitrary

risk constraint

Determine distribution of costs for plan

Look for a plan with lower cost

Look for a plan with lower risk

Does distribution have

lowest cost?

no

no


33

Agenda





34

Cost Distribution AssociatedWith a Plan

Hourly demand

Coal

Buy in Market

Buy in Market

Sell in Market

Gas Fired

Price-driven generation

Hydro

Contracts

Hydro

Total Resources

Year 1Summer Winter

Year 2Summer Winter

Background


35

Modeling Issues

• In principle, we could perform our calculation on an hour-by-hour basis

• Time to make one of those “order-of-magnitude” calculations!


36

Modeling Issues

• Let’s say, we have a very smart optimizer that can find the efficient frontier by examining only 500 plans

• To estimate the 10th percentile tail of a distribution, we need at least 500 futures, each representing 20 years of assumed hydro, fuel cost, loads, etc.


37

Modeling Issues

• We therefore would need to make

8760 hrs/year*20 years/study*500 studies/plan*500 plans/optimization

= 43.8 billion hourly calculations• Clearly some approximation/sampling/aggregation

is in order!


38

Modeling Issues

• A natural thing to do is to aggregate the time scale, and that is exactly what we have done.

• However, in calculating things like cost using aggregate statistics, we need to be careful with things like correlation

• For example, computing cost when quantity and price are related is tricky


39

Using Valuation ToEstimate Cost

• Average cost, given average price E(p) and average quantity E(q) is given by

(1) )()()( pqqpqEpEpqE


40


Resource

qi

load Q

market requirement


41


• Costs using “rate base” calculation

trequiremen totalis

energy alefor wholes ($/MWh) price theis

resource of ($/MWh) price theis

resourceby provided (MWh)quantity is

($)cost totalis

(2) )(

Q

p

ip

iq

c

qQppqc

m

i

i

iim

iii

these are usually correlated!

• But how??


42


• Costs using “valuation” calculation

)(

*

)(

imi

im

iii

iimm

iim

iii

ppqQp

pqqpQp

qQppqc


43


• The valuation formula simplifies the cost calculation, because we only have to consider how each resource’s cost and dispatch relate to the market (rather than to each other)– electric market price to total loads (probably strongly

positively correlated)– electric market price to wind generation (uncorrelated)– electric market price to turbine generation (directly

related to correlation with fuel price)


44

Our calculation times

• Recall the purpose of all this was to make our calculation times more manageable....


45


• Using 160 periods per 20 year study– 80 hydro-year quarters (Sept-Nov, Dec-Feb, March-May,

June-Aug), on- and off-peak– About 1-2 seconds (5-8 iterations for RRP*)

• Using 750 trials (futures) per plan• About 17 minutes per plan• For 1000 plans, this ordinarily would take 12 days,

but ....


46


• ... Using parallel processing on six machines afforded by Decisioneering’s CB Turbo, we can perform this in two days.

• ... With twelve machines, in one day...• ... You get the picture.• Cost of Crystal Ball Professional: $1600• Cost of CB Turbo: $2500


47

Real Feasibility Spaces

• Current spaces


48

Real Feasibility Spaces

• Earlier space, more representative of situation with relatively greater risk!


49

Measures of Central Tendency

• The median and mean for these plans are closely related

• Using the mean cost is probably fine


50

Risk Measures

• Along the efficient frontier, the risk measures tend to converge


51

Risk Measures



52

Risk Measures



53

Risk Measures



54

Our Models

• The meta-model: Olivia

• The portfolio model: Olivia’s “daughter”


55

Olivia

• Creates Crystal Ball-aware Excel workbooks that run under OptQuest/CB Turbo

• Uses a database for model structure and data reuse– Special editing features and capabilities for duplicating

and extending models, while preserving previous versions

• Permits the user to model their own system


56

Olivia


57

Olivia


58

Olivia


59

Olivia


60

Olivia

• The relationship among records in the database reflects the structure of calculations in an Excel workbook Structure.pdf


61

Olivia’s Daughter

• The Crystal Ball-aware Excel workbook that run under OptQuest/CB Turbo is the “Portfolio model,” or “Olivia’s daughter”

• Current regional model (L4.xls) has– 80 hydro quarters, on- and off-peak– One region– Imports and exports of 4000 MWa– 30 resources, including hydro, commercial hydro response,

conservation supply curves for lost opportunity conservation and “dispatchable” conservation, smelter response to aluminum and power prices, planning flex .....


62

Agenda





63

Futures

• A workbook has been prepared that illustrates the 750 futures we have used.

• Graph of Futures.xls


64

Agenda





65

Representation of resources

• How are the main resource candidates represented in this model?


66

Agenda





67

Load/Resource balance

• What is the representation of the remaining resources?

Coal: 5,115Gas 5,659Other: 1,490

Hydro 12000

sum 24,265


68

Load/Resource balance


69

Agenda

• Welcome Back!• Overview of methods• Presentation of candidate plan• Models and modeling• Algorithms

– Dispatch– Resource-responsive price (RRP)– Planning flexibility– Long-term price response: DSIs and other industrial loads– Supply curves for conservation and for commercial use of hydro– Stochastic hydrogeneration based on 50-year stream flow record

• Next meeting


70

Typical Dispatchable

• Example of 1 MW Single Cycle Combustion Turbine (no dispatch constraints)

• Natural Gas price, $3.33/MBTU

• Heat rate, 9000 BTU/kWh

• Price of electricity generated from gas, $30/MWh

Representations - thermal

0

5

10

15

20

25

30

35

40

1 25 49 73 97 121

145

169

193

217

241

265

289

313

337

361

385

409

433

457

481

505

529

553

577

601

625

649

Hour

Mar

ket

Pri

ce $

/MW

h

Value:note: we assuming the

entire capacity is switched on when the turbine runs

case)our in MW (1 turbine theofcapacity theis

($/MWh) rateheat fixed a assuming

hour, in this gas of price theis )(

($/MWh)hour in thisy electricit of price theis )(

case) in this (672 hours ofset theis

where

)))()((,0max(

C

hp

hp

H

hphpCV

g

e

Hhge


71

Price Duration Curve

• If we assume each hour’s dispatch is independent, we can ignore the chronological structure. Sorting by price yields the market price duration curve (MCD)

0

5

10

15

20

25

30

35

40

1 25 49 73 97 121

145

169

193

217

241

265

289

313

337

361

385

409

433

457

481

505

529

553

577

601

625

649

Hour

Mar

ket

Pri

ce $

/MW

h

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

Count of Hours

$/M

Wh

Value V is this area


operatorn expectatio theis (672) period in the hours ofnumber theis

where])()(,0[max

or

)()(,0max

)()(,0max

EN

hphpECNV

N

hphpCN

hphpCV

H

geH

H

Hhge

H

Hhge


72

Digression to Options

• The value of an option is the expected value of the discounted payoff (See Hull, 3rd ed., p. 295)


price strike theis stock theof price theis

(years) expiration to time theis ratediscount annual theis

operatorn expectatio theis where

)],0max([

XpTrE

XpeEV rT


73

European spread option

• The Margrabe pricing formula for the value of a spread option, assuming no yields


212,12

22

12

12

212

1

2112

2

2/)/ln(where

)()(

TddT

Tppd

dNpdNpV


74

Variability viewed as CDF

• Turning the MCD curve on its side, we get something that looks like a cumulative probability density function (CDF)

Value V is this area

factorcapacity or the CDF theof value theis )(where

)(

Calculus) of Thm (Fund

)(

e

eHe

e

P

eH

pf

pfNdp

dV

dppfNVg

Cumulative Frequency

0

100

200

300

400

500

600

37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20

$/MWh

Co

un

t o

f h

ou

rs

0%10%20%30%40%50%60%70%80%90%100%

Cap

acit

y F

acto

r



75

Dispatch Model: Conclusion

– Thermal dispatch can be reasonably well using a spread call option on electricity and gas

– The monthly capacity factor of the thermal unit is provided by the “delta” of the option, that is, the change in the option’s price (value) with respect to the underlying spread

– The standard Black-Scholes model for option pricing gives a good estimate of the plant value and capacity factor, with these adjustments:

• The risk free discount rate r is 0• Time to maturity T=1• The hourly price volatility on ln(pt/pt-1) is



76

Example of Spread Option


77

Agenda



• Next meeting


78

Influence Diagram

RescourceOutages

HydroGeneration

DSI Loads

Non-DSILoads

Market Pricesfor Electricity

AluminumPrices

ReserveMargin

Temperature

Fuel Prices

TransmissionCongestion

EmissionPrices

Independent Effects


79

Dependence on Influences

• Wholesales power prices as we currently model them reflect changes in– Natural Gas Prices in the PNW– Loads in the PNW (specifically on-peak loads)– Hydrogeneration

• Modeled as a sensitivity to these


80

Role of Independent Term

• Jumps and excursions unrelated to key fundamental drivers

• Unincorporated fundamental influences– e.g., new technology

• Unanticipated non-fundamentals– Policy changes

• e.g., price caps

– Psychology in the markets


81

Consequence of Independent Term

• Prices are not a well-defined function of natural gas prices, loads, or hydro (“key drivers”)

• Fixing key drivers does not fix the price• A given price can reflect many different

levels of key drivers. In particular,• Price is to a certain extent independent of

any key variable


82

Well-Defined Function

• A machine that always gives you “Y” every time you put in “X.”


83

Problems

• In an open system, such as for a single market participant, who is a price taker, all this works fine. But...

• Intuition tells us that in a closed, or partially closed system, price should be a function of resources available.

• If resource generation is responsive to price, and prices are not driven by supply and demand balance, we will violate the first law of thermodynamics.

• If capacity expansion decisions are made based on revenues in the market, there is no self-limiting due to over building.


84

The Analysis of Olivia RRP• Given a variation in resources, we got the following

behavior. Why is price insensitive to adding resource?

-10,000,000

-8,000,000

-6,000,000

-4,000,000

-2,000,000

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

0 50 100 150 200 250

Price

L/R

Ba

l (m

wh

)

Intertie Capacity

• Positive L/R mean deficit

• Points (L to R) obtained by decreasing size of fixed resource


85

RRP Algorithm

Prices

surplus

deficit


86

Observation 1

• “Price is independent of key drivers”

• Not surprising, therefore that is independent of resources, at least until we would cause imbalance of supply and demand


87

Proposition

• Independence of price from resource generation levels is necessary for the existence of an independent electricity term


88

Proof by Contradiction

• So assume that prices did have to increase under all conditions when we decreased resources


89


-10,000,000

-8,000,000

-6,000,000

-4,000,000

-2,000,000

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

0 50 100 150 200 250

Price

L/R

Ba

l (m

wh

)

Intertie Capacity


90


• If you had some independent term that would add to the price we open up the possibility of decreasing prices

price

resources


91

Another Example

• Eliminating import and export drives us to no independent term!

-10,000,000

-8,000,000

-6,000,000

-4,000,000

-2,000,000

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

0 50 100 150 200 250

Price

L/R

Ba

l (m

wh

)

Intertie Capacity


92

Finally, Some Computational Considerations

• Computation time is dramatically increased when we try to fine-tune RRP

• Computation time is increased when we reduce imports and exports


93

Resource-responsive price

• We can examine the function of RRP by considering a small toy application

• ( Testbed_new.xls )


94

Agenda



• Next meeting


95

Sources of ResourcePlanning Flexibility

• Modularity (small size)– Reduces fixed-cost risk

– Can more exactly match requirements

• Short Lead-Time– Can respond rapidly to opportunities or requirements

• Cost-effective Deferral– Usually available for only a limited time

• Cost-effective Cancellation– e.g., high salvage value or small capital commitment

Choosing a Plan


96

Candidate Plan Under Future 1000

Choosing a Plan

CO2 taxCO2 taxhigh gas priceshigh gas prices


97

Candidate Plan Responds

Choosing a Plan

CO2 taxCO2 taxhigh gas priceshigh gas prices

lower power priceslower power prices


98

The Construction Cycle• Planning flexibility is related to the construction

cycle of power plants• The construction cycles may be viewed in terms of

cash flows and decision points

Cas

h ex

pend

itur

esC

ash

expe

ndit

ures

18 months18 months 9 months9 months 9 months9 months


99

The Construction Cycle• After an initial planning period, there

typically large expenditures, such as for turbines or boilers, that mark decision points.

Cas

h ex

pend

itur

esC

ash

expe

ndit

ures

18 months18 months 9 months9 months 9 months9 months


100

Valuing Flexibility

construction phase

optional cancellation period

evaluation phase

time

crite

rion

• To capture the value of flexibility, we need to model decision making

On-Line!On-Line!


101

Planning flexibility

The function that performs planning flexibility can be examined as a standalone routine in ( PlanningFlex.xls )


102

Agenda



• Next meeting


103

DSI LoadsAluminum Price 1550Premium Rate 0.03BPA Rate 23BPA Allocation 100

Mwh/Tonne 13.199Plant A

(modern prebake)Potential Demand 457Cost Components Alumina 403 Carbon 90 Labor/Other 400 Sustaining Capital 80

Electricity Cost Max 623.5

Electricity Price Max 47.24

Electricity Price$30

Demand @ Price 457

• Compute break-even price for each of nine PNW aluminum plants

• Assume plant will leave the system if the spread between aluminum prices and electricity cost component gets too small

• Examine the impact of 100 MW allocation of BPA power at various prices

Loads


104

DSI Loads

Viable Smelter Loads

0

500

1000

1500

2000

2500

3000

3500

1100

1150

1200

1250

1300

1350

1400

1450

1500

1550

1600

1650

1700

Electricity Use

Alu

min

um

Pri

ce

20

25

28

30

32

35

40

$/Mw

Loads


105

DSI Loads

Viable Smelter Loads(No BPA Allocation)

0

500

1000

1500

2000

2500

3000

3500

1050

1150

1250

1350

1450

1550

1650

1750

1850

1950

2050

2150

2250

Aluminum Price

Ele

ctr

icit

y U

se

20

25

28

30

32

35

40

$/Mw

Loads


106

DSI Loads

minimum shut-down period

evalulation phase

time

who

lesa

le e

lect

ricity

mar

ket

aluminum-elecprice spread

expected price trend

minimum restart period

evalulation phase

Loads


107

DSI Loads

• Model DSI load as a function of electricity prices and aluminum prices.

• Represents monthly response. Would stay down for several months and take several months to bring back on-line.

• Has value as a exchange option or spread option.

Loads


108

Long-term price response

See the RRP model for an example of the function of the DSI LTPRD function


109

Agenda



• Next meeting


110

Supply curves

• Provides for reversible supply curves– Used for modeling commercial hydro

generation

• Provides for lost opportunity supply curves– Used for modeling conservation measures,

such as energy efficiency measures introduced in new construction, that disappears after an fixed “window of opportunity”

– Lost opportunity supply can be proportional to a factor such as load growth


111

Supply curves

• Can represent either incremental energy and costs, or cumulative energy and real levelized costs

• A workbook illustrating the supply curve logic appears in ( Supply Curve.xls )


112

Agenda



• Next meeting


113

Stochastic hydrogeneration

• Function has been removed from the Excel Add-in and placed in a regular worksheet for use with CB Turbo

• Estimated on- and off-peak energy for each of the fifty stream flow records

• Does not respond to price, but may be used with the reversible, incremental supply curve logic to capture that aspect.


114

Agenda

• Welcome Back!




• Algorithms

• Next meeting


115

End

Documents

1 Systems Analysis Advisory Committee (SAAC) Tuesday February 10, 2004 Michael Schilmoeller John Fazio