1 Systems Analysis Advisory Committee (SAAC) Friday, November 22, 2002 Michael Schilmoeller John Fazio

1

Systems Analysis Advisory Committee (SAAC)

Friday, November 22, 2002Michael Schilmoeller

John Fazio

Northwest Power Planning Council

2

Original Agenda

• Natural gas prices– Sumas, AECO, Rocky mountains– historical and monthly forwards and volatilities– correlations with other variables– subjective forwards

• Hydro generation– historical and monthly forwards and volatilities– correlations with other variables

Outcomes and Milestones


3

Revised Agenda

• Approval of the Oct 24 meeting minutes• Review and questions from the last meeting

– Representation of dispatchable resources in the portfolio model

– Metrics

• Representations in the portfolio model– Price responsive demand– Renewables and conservation

• Hydro• Loads• Natural gas prices


4

Revised Agenda



– Metrics




5

Revised Agenda



– Metrics



Review


6

October 24 Agenda

• Metrics– Stakeholders– Risk measures– Timing

• Representations in the portfolio model– thermal generation– hydro generation– conservation and renewables– loads– contracts– reliability– ** Plan Issues **

Review


7

Revised October 24 Agenda

• Approval of the Oct 4 meeting minutes• Price Processes• Representations in the portfolio model

– thermal generation

• Metrics– Stakeholders– Risk measures– Timing

• Representations in the portfolio model– ** Plan Issues ** : price responsive demand

Review


8

Plan Issues

• incentives for generation capacity• price responsiveness of demand• sustained investment in efficiency• information for markets• fish operations and power• transmission and reliability• resource diversity• role of BPA• global change

Review


9

Representation of dispatchables

• Main Conclusions– Option calculation of capacity factor and plant value over the

month should be identical with hourly dispatch result when prices are lognormally distributed. Consequently,

– Option model should give a reasonable representation of dispatchable plant performance and value

– Volatility in the option model represents both variation within the month and uncertainty

– Where uncertainty dominates, temporal variation become unimportant

Review


10

Review of Results

• Examine gas and power prices from 1999• How good is the lognormal assumption?• Comparison of option model with hourly dispatch

against lognormally distributed prices• Comparison of option model and hourly dispatch of

actual dispatch for Beaver in 1999• Impact of future uncertainty on capacity factor and

value of Beaver

Review


11

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

Review


12

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

Review


13

Hourly Volatilities from Monthly

• We are dealing with expected variation of electricity and gas price over the specific time period and with uncertainties in these, as well. Using our assumption that the hourly uncertainties are constant and independent of the temporal variations in the respective commodities,

)2(

)2(

implies assumption ceindependenour by which

)()()()()(

,22

)()(,2

)(2

)(2

gegege

gegege hzhzzzhzhz

ggee hhzhhzh

Review


14

Hourly Dispatch

• Try dispatching against a lognormally distributed set of prices, with 1000 observations.

24.07 27.96 123.66 30.62 133.26 43.25 140.18 184.25 131.90 28.19 036.91 54.79 120.06 110.83 1

30.67 67.64 0.885542

0.92182047

=IF(RC[-2]>RC[-3],1,0)

• Maximum discrepancy over prices and volatilities, about 5%

averages

spread option

Review


15


1999 Daily Prices MC and Sumas

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

1 19 37 55 73 91 109

127

145

163

181

199

217

235

253

271

289

307

325

343

361

$ N

om

inal

0.00

0.50

1.00

1.50

2.00

2.50

3.00

On-peak MC

Off-Peak MC

Average MC

Natural Gas

Review


16


0

1

2

3

4

5

1 35 69 103

137

171

205

239

273

307

341

Days

ln(n

om

inal

pri

ce-$

)

Natural Gas

On-Peak MC

Off-PeakMCAverage MC

Review


17


Average (Flat) MC

0

10

20

30

40

50

60

1 3 5 7 9

11 13

15

17

19

ln(p

ric

e)

0

5

10

15

20

Review


18


Sumas Gas

0102030405060

1 3 5 7 9 11 13 15 17 19

0

10

20

30

40

Review


19


De-Trended Sumas Gas Prices

0

10

20

30

40

50

60

1 3 5 7 9

11 13

15

17

19

21

ln(p

ric

e)

00.511.522.533.544.5

Review


20


• Beaver– 9000 BTU/kWh– $4.00/MWh for VOM, variable fuel transportation– Did not incorporate forced outage estimate,

maintenance– Assumed 500MW capacity– “Hourly” dispatch was on daily on- and off-peak

only (would understate volatility)

Review


21


Comparison of techniques

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

1 2 3 4 5 6 7 8 9 10 11 12

Month

Dis

pat

ch f

acto

r

Hourly

Spread

Actual

Review


22


• To show: The main driver of value is not expected variation in price, it is uncertainty

• What is the 1 sigma in daily (hourly?) electricity and gas prices over the next several years?

Review


23

0

5

10

15

20

25

30

35

1990 1995 2000 2005 2010 2015 2020

History

Low

Medlo

Medium

Medhi

High

EIA02-R

EIA02-H

EIA902-L

8 Others


• Oil price forecast

?

?

Review


24


• NG price forecast

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1995 2000 2005 2010 2015 2020 2025

20

00

$/M

MB

tu

History

Low

Medlo

Medium

Medhi

High

EIA-Ref

EIA-Low

EIA-High

DRI-WEFA

GRI

CEC

ICF

?

?

Review


25

Mid-Columbia price forecastAverage annual w/comparisons

$0

$5

$10

$15

$20

$25

$30

$35

$40

$45

$50

$55

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

Pri

ce

(2

00

0$

/MW

h)

Current Trends Hi Shape (092702)

5th Plan corrected transfer (062402).

Adequacy & Reliability Study (Feb 2000)

?

?

Review


26

Uncertainty Dominates

Expected variation

Uncertainty

Addition of uncorrelated

volatilities

x

y=1

z2=x2+y2

z

Error in approx z by max(x,y)

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

0 1 2 3 4 5 6 7 8 9 10

X

Rel

ativ

e er

ror

(z-m

ax(x

,y))

/z

0

2

4

6

8

10

12

Z

error Value of z

Review


27


• Beaver Value, assuming change in volatility due to uncertaintysame expected fuel and electricity price, correlation

volatility CF Value volatility CF ValueJan 18.3% 13.3% 84569 105.6% 63.3% 2062640Feb 17.0% 23.2% 146865 108.7% 66.8% 2135302Mar 18.8% 14.7% 81952 103.4% 62.7% 1819113Apr 36.8% 49.8% 1065049 105.7% 70.1% 2951938May 37.3% 55.0% 1390094 117.0% 73.3% 3778254Jun 69.4% 36.0% 1113231 110.2% 62.4% 2082887Jul 37.1% 43.1% 929229 113.2% 69.6% 3127952Aug 39.3% 49.9% 1408176 109.2% 70.7% 3754281Sep 21.9% 85.6% 2167144 111.7% 77.1% 5141926Oct 19.2% 100.0% 5536028 119.3% 83.2% 8873424Nov 43.9% 80.0% 2834708 125.5% 78.9% 5467271Dec 21.9% 49.3% 758491 112.4% 71.2% 3757433

average 56.9% 72.2%total 17,515,537 44,952,421

Review


28


Comparison of dispatch factors

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

1 2 3 4 5 6 7 8 9 10 11 12

Month

Dis

pat

ch f

acto

r

Spread with future uncertainty Spread with 1999 prices

Review


29


Value of Beaver

01,000,0002,000,0003,000,0004,000,0005,000,0006,000,0007,000,0008,000,0009,000,000

10,000,000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Do

llars

, no

min

al

Beaver value with uncertainty Beaver value with 1999 prices

Review


30

European Call Option

0

2

4

6

8

10

12

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Price of underlying

Val

ue

of

Op

tio

n (

$)

Makes sense

• CF may or may not increase with volatility

Review


0

2

4

6

8

10

12

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Price of underlying

Val

ue

of

Op

tio

n (

$)


31


0

2

4

6

8

10

12

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Price of underlying

Val

ue

of

Op

tio

n (

$)

Makes sense

• Value increases with volatility

Review


0

2

4

6

8

10

12

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Price of underlying

Val

ue

of

Op

tio

n (

$)


32

Makes sense

• Value increases with volatility

Review

Cumulative FrequencySingle, fixed hour

0

0.2

0.4

0.6

0.8

1

40.00 38.00 36.00 34.00 32.00 30.00 28.00 26.00 24.00 22.00 20.00

$/MWhP

rob

of

pri

ce

e

xc

ee

din

g p

A

B

)),0(max(

,particularIn )(

so

1)(

But)()(

1)()()(

1

11

xxEA

BAxxE

BAn

xx

xxExxEn

xxXxPxx

i

i

n

ii

ii

n

ii

n

iii


33

Conclusions

• The monthly spread option model gives a reasonable representation of expected capacity factors (and hence value) of resource options

• Given that the uncertainty in hourly prices exceeds the expected variation, the detailed information about hourly prices from any one scenario tells us little about the expected capacity factor and value of resource options

Review


34

Revised Agenda



– Metrics




35

Price responsive demand

• Intended to represent short-term (1 day to 1 month) load reduction, on- and off-peak, if the price is right

• Does not address longer term DSI load curtailment (which is addressed later)

• Described by a supply curve• Energy available represented as special continuous

function of price– Zero variable cost, but some fixed cost

• Supply curve developed by Ken Corum

Representations


36


• Baseload 32000MW, Base price $25/MWh, Short-run elasticity is -0.05

Energy Price Increm.(Wholesale) Reduct.$/MWh MW100 1433300 1426600 937800 3891600 9274000 1192

Representations


37


• Side observation: Much of the value of PRD is driven by peak prices. The price of electricity in the portfolio model is subjective, but so are curtailment block prices in our other models. At right, the value of PRD is determined by those prices, the marginal costs in hour segments A and B.

Curtailment block 2

Curtailment block 1Peaker 3

Peaker 2Peaker 1


CCCT 2

CCCT 1

Coal 2

Coal 1

HydroHours

Load Curve

A B C D E F

Stack Model

Representations


38

Conservation & Renewables

• Represent as non-dispatchable energy• Supply curve for conservation developed by

Tom Eckman• Renewables cost and operating

characteristics assembled by Jeff King

Representations


39

C&R Weaknesses

• Lack of short term operating flexibility– If market prices fall below the dispatch cost of a

traditional resource, the unavoidable cost of a dispatchable resource is limited to fixed cost (typically 10% to 30% of total cost); Conservation and renewables’ costs are largely capital and unavoidable

– Makes C&R less attractive when resource portfolio capacity exceeds loads

• Some financial risks– Conservation and renewables have higher up-front cost.

If resource disappears (failure, technological obsolescence,…), the owner stands to lose more.

Representations


40

C&R Strengths

• “Real option” (modularity) value– C&R can be added incrementally and with a

shorter lead time than conventional resources.

• Fuel Price risk mitigation• Emission cost risk mitigation• Conservation may have lower availability

risk• Conservation may have lower credit risk

than fixed price forward contracts.

Representations


41

NPPC Analysis

• Credit and availability advantages can be valued by adding these uncertainties to alternatives, such as contracts

• Modularity benefits require a new approach

• Example of Sustained Orderly Development (SOD)

Representations


42

SOD Analysis

Timed case

0

200000

400000

600000

800000

1000000

Sep

-03

Sep

-04

Sep

-05

Sep

-06

Sep

-07

Sep

-08

Sep

-09

Sep

-10

Sep

-11

Sep

-12

Sep

-13

Sep

-14

Sep

-15

Sep

-16

Sep

-17

Sep

-18

Sep

-19

Sep

-20

Sep

-21

Sep

-22

Sep

-23

Sep

-24

Sep

-25

date

Ben

efit

s ($

)

0

100

200

300

400

500

600

Cap

acit

y In

stal

led

(M

Wa

cum

)

benefit price capacity

Representations


43

SOD Analysis

Dispatchable Conservation Supply Curve

-

200

400

600

800

1,000

1,200

1,400

$- $10.00

$20.00

$30.00

$40.00

$50.00

$60.00

$70.00

$80.00

$90.00

$100.00

Levelized Cost (2000$/aMW)

Re

so

urc

e P

ote

nti

al (

aM

W)

Representations


44

SOD Analysis

• There is only a weak relationship between ramp rates (up or down) and utility conservation acquisition costs.

• Utility conservation acquisition costs ($/aMW) may lower when ramping up than when ramping down, due to:

– Outstanding contracts– “Lags” in personnel changes– Desire to maintain stable infrastructure

• Assumption –– Assume same cost/aMW during ramp down than ramp

up.

Representations


45

SOD Analysis

• Conservation has been ramped up and down within a range of +/- 10 aMW

• Assumption – Constrain ramp rate to “monthly availability” of each conservation cost block (e.g. maximum annual change = 12x monthly availability).

Representations


46

SOD Analysis

• Wholesale market prices will fluctuate as a result of:–Over/Under building–Extreme weather events (hot or cold)–Hydro-system availability–Short-run economic/business cycles

Assumption:“Randomize” the forecast of future “price spikes” in response to hydro-system availability, ignore “short-run” weather & business cycles

Representations


47

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


48

NPPC Analysis

• Implement in Portfolio Model– Evaluation period (rolling average prices

over the last 18 months?)– Cancellation period– Construction period– Ramp rate constraint

Representations


49

NPPC Analysis

• Real Options– Opportunity to defer, expand, abandon according to

changing circumstances– Staging benefits– Switching fuel supplies

Representations


50

NPPC Analysis

• Broad Application of real options to the Electric Power Industry– Renewables

• Mark Bolinger, Ryan Wiser and William Golove, “QUANTIFYING THE VALUE THAT WIND POWER PROVIDES AS A HEDGE AGAINST VOLATILE NATURAL GAS PRICES,” Proceedings of WINDPOWER 2002, June 2-5, 2002, Portland, Oregon

• http://eetd.lbl.gov/EA/EMP/

– Coal• Y. SMEERS, CORE and L.BOLLE , O. SQUILBIN, “COAL OPTIONS,

Evaluation of coal-based power generation in an uncertain context,” Final report, September 2001, OSTC - Global Change and Sustainable Development 1996-2000, Belgium Federal Office for Scientific,Technical and Cultural Affairs

• http://www.belspo.be/belspo/ostc/geninfo/publ/pub_ostc/CG2131/rCG23_uk.pdf

Representations


51

NPPC Analysis

• Broad Application of real options to the Electric Power Industry– R&D expenditures

• Graham A. Davis, Brandon Owens, “Optimizing the Level of Renewable Electric R&D Expenditures Using Real Options Analysis,” National Renewable Energy Laboratory,Golden, CO 80401 December 18, 2001

– Distribution Systems• Costing Methodology for Electric Distribution System Planning November 9, 2000

Prepared for: The Energy Foundation Prepared by: Energy & Environmental Economics, Inc. Karl E. Knapp, Jennifer Martin, Snuller Price, And Pacific Energy Associates Frederick M. Gordon

• http://www.energyfoundation.org/documents/CostMethod.pdf

Representations


52

Working Hypothesis

• Some participants will find risk attributes of C&R more attractive than others

• Good portfolio for C&R– Heavy exposure to carbon-based fuel prices (even

more benefit if fuel prices are correlated to electricity prices)

– Contracts with credit problems– Contracts with duration less than lifetime of C&R

measure– Short supply of other resources relative to demand– High but unpredictable load growth potential

Representations


53

Working Hypothesis

• Some participants will find risk attributes of C&R more attractive than others

• Poor portfolios for C&R– Low exposure to carbon-based fuel prices, e.g., high-

quality forward contracts with terms comparable to lifetime of C&R measures

– Long supply of resources relative to demand• Made worse if portfolio has hydro generation and

market prices are negatively correlated with hydro generation

– Stagnant or decreasing loads expectedRepresentations


54

NPPC Analysis

• If C&R are beneficial from the standpoint of cost and risk, what is the best strategy to deploy?

• What is the value of SOD, and to which measures is SOD beneficially applicable?

• What are the technology-specific risk attributes for solar, wind, geothermal, biomass, low-head run-of-river hydro?

Representations


55

Revised Agenda



– Metrics




56

Hydrogeneration

• Excel Add-in has 50-year record

Demonstrate:– Parameters to pull out different data– Use as random draw & correlation with other

assumptions– Use of function to pull out specific year

• Reflects 10-hour sustained peaking capability from the trapazoidal approximation studies

Hydrogeneration


57

Hydrogeneration

Hydrogeneration

NW Sustained Peak - September

10000

13000

16000

19000

22000

25000

8600 8800 9000 9200 9400 9600 9800 10000

Energy (MW-period)

Su

sta

ine

d P

ea

k (

MW

)

2-hr 4-hr 10-hr


58

Hydrogeneration• Function vfuncHydroGen(ByVal sYear As Single, ByVal lLoc As Long, ByVal lType As Long, Optional ByVal lPeriods As Long = 1) As Variant

• 'Takes:• 'sYear - single [0.00-50.00] representing the years 1929-1978, sorted ascending by annual energy.• ' By passing 50*Rand() as sYear to this function, this permits random draws• ' of hydro condition. Ascending order permits user to correlate annual energy with• ' other variable. To access a particular year, use the sfuncYear() function, below.• '• 'lLoc - 0, East only• ' 1, West only• ' 2, East+West Generation• '• 'lType - 0, MWa• ' 1, 10-hour Sustained Peak, MWa• ' 2, off-peak, MWa• ' 3, on-peak, MWa• ' 4, off-peak, MWh, assumes 288 hours (4 weeks) each month, 144 for each half-month period• ' 5, off-peak, MWh, assumes 384 hours (4 weeks) each month, 192 for each half-month period• '• 'lPeriods - Optional• ' 0, 14 periods of hydro year Sept - August, with two periods of August and two for April• ' 1, (default), 12 months of hydro year Sept - August• '==============================================================================================• 'Returns:• ' A variant containing an array of period Hydrogeneration (MWa) for east-side or• ' west-side generation, or both. Entry 0 is September generation, and if• ' lPeriods = 0, entry 11 is August generation, else entry 13 is Aug 15-31• '

Hydrogeneration


59

Hydrogeneration

• To call as random hydro condition generator:

=vfuncHydroGen(Rand(), 2, 0)

• This would produce an array of 12 months of data, MWa, for total system generation

Hydrogeneration


60

Hydrogeneration

Hydrogeneration

• Function sfuncYear(ByVal lYear As Long, ByVal lType As Long) As Single

• 'Takes a calendar year, e.g., 1937, and returns a real single with a value in the

• 'middle of the correct "bin" for that year, for use as input to vfuncHydroGen.

• 'For example, 1937 is the second lowest year for Eastside Hydro, in terms of

• 'annual energy and is therefore the second entry in vfuncHydroGen(*,0). Then

• 'sfuncYear(1937,0) = 1.5 (The first bin is [0,1), the second is [1,2), etc.

• 'lType - 0, East Generation only

• ' 1, West Generation only

• ' 2, East+West Generation


61

Hydrogeneration

• Emphasize– 4-week convention for lType options

4 and 5 of vfuncHydroGen

• Demonstrate– ..\..\..\Hydro General\HydroGen AddIn\HydroAddIn

.xls

Hydrogeneration


62

Revised Agenda



– Metrics




63

Loads

• Non-DSI Loads– Calibrate with data from NWPP– Short-term uncertainty driven by random

temperatures (HELM)– Long term uncertainty from Terry Morlan’s

work

• DSI Loads– Terry Morlan’s aluminum industry model

Loads


64

Loads

• Non-DSI Loads– Develop monthly on- and off-peak energy

values from an hourly model– Calibrated to most recent NPPC forecasts– Access to function to permit coordination

with hydro condition

Loads


65

HELM’s Load

Weather Response Functions

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1000000

0 10 20 30 40 50 60 70 80 90 100 110

Dry-Bulb Temperature (F)

MW

h/D

ay

WRF 1

WRF 2

WRF 3

WRF 4

Loads


66

HELM’s Load

LSL 1

0

5000

10000

15000

20000

25000

30000

35000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hours of the day

MW

-10 to 38

38 to 45

45 to 52

52 to 57

57 to 61

61 to 64

64 to 110

Loads


67

HELM’s Load

LSL 2

0

5000

10000

15000

20000

25000

30000

35000

1 3 5 7 9 11

13

15

17

19

21

23

Hours of Day

MW

-10 to 38

38 to 45

45 to 52

52 to 57

57 to 61

61 to 64

64 to 110

Loads


68

HELM’s Load

LSL 3

0

5000

10000

15000

20000

25000

30000

35000

1 3 5 7 9 11

13

15

17

19

21

23

Hour in Day

MW

-10 to 38

38 to 45

45 to 52

52 to 57

57 to 61

61 to 64

64 to 110

Loads


69

HELM’s Load

LSL 4

0

5000

10000

15000

20000

25000

30000

1 3 5 7 9

11 13 15 17 19 21 23

Hour in Day

MW

-10 to 38

38 to 45

45 to 52

52 to 57

57 to 61

61 to 64

64 to 110

Loads


70

Non-DSI Loads

• Short-term uncertainty:

Use 50-year record of daily temperatures to create estimates of on- and off-peak loads by month. Draw randomly.

• Long-term uncertainty:

Make the long-term uncertainty consistent with Terry Morlan’s estimates

Loads


71

Non-DSI Loads

Total Sales

10000

15000

20000

25000

30000

35000

40000

45000

1981

1984

1987

1990

1993

1996

1999

2002

2005

2008

2011

2014

2017

2020

2023

Av

era

ge

Me

ga

wa

tts

Non-DSI

Loads

97.5%

97.5%


72

DSI Loads

• Terry Morlan’s model

• Inspired by Robin Adams, Resource Strategies, CRU Group

Loads


73

DSI Loads

LME Cash Aluminum Prices:Daily 1989-2002

$1,000$1,250$1,500$1,750$2,000$2,250$2,500$2,750$3,000$3,250$3,500

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

US

$/To

nn

e

Cash

15-Month

Real Cash

Linear (Real Cash)

$0.70 $0.80

Loads


74

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


75

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


76

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


77

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


78

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


79

Revised Agenda



– Metrics




80

Natural Gas Prices

• Data from Gas Daily• Statistics?

– Historical Dailies– Price processes– Distributions within the month, year– Future uncertainties (Terry)– Reasons for variation over time– Correlation with electricity, load, temperature,

aluminum prices, hydro

Natural Gas Prices


81

Natural Gas Prices

• 1. Mean Reversion - Vasicek Model• P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*sqrt(dt)*N(0,1)• 2. Mean reversion - CIR Model• P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*Sqrt(P(t))*sqrt(dt)*N(0,1)• 3. Geometric Brownian Motion - GBM• P(t+dt) - P(t) = Drift*P(t)*dt + Sigma*P(t)*sqrt(dt)*N(0,1)• 4. Mean reversion - unrestricted • P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*P(t)^Gamma*sqrt(dt)*N(0,1)• 5. Jump-diffusion (Use the same time step for estimation and simulation - h doesn't

scale!!)• P(t+dt) = P(t)exp( Drift*dt + Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j))• Y=1 with probability h and Y=0 with probability (1-h)• 6. Brennan and Schwartz Model• P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*P(t)*sqrt(dt)*N(0,1)• 7. Mean reversion with jump-diffusion, Vasicek type diffusion• P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j)• Y=1 with probability h and Y=0 with probability (1-h)

Natural Gas Prices


82

Natural Gas Prices

• 8. Mean reversion with jump-diffusion, CIR type diffusion• P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt +

P(t)^0.5*(Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j))• Y=1 with probability h and Y=0 with probability (1-h)• 9. Mean reversion with jump-diffusion, Brennan-Shcwartz type diffusion• P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt +

P(t)*(Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j))• Y=1 with probability h and Y=0 with probability (1-h)• 10. Mean reversion with jump-diffusion, "Unrestricted" type diffusion• P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt +

P(t)^gamma*(Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j))• Y=1 with probability h and Y=0 with probability (1-h)

Natural Gas Prices


83

Next Meeting

• Natural Gas Prices• Electricity• Statistics

– Historical Dailies– Price processes– Distributions within the month, year– Reasons for variation over time– Correlation among electricity, load, temperature,

aluminum prices, hydro, natural gas prices


84

Almost there...

• Then the B-S formula for the value the plant is

Representations - thermal

TddTXpd

NN

dXNdpNV

12

21

21

2/)/ln()p~ln(p/ ofdeviation standard is variablerandom )1,0( afor CDF theis

where

)()(

with the variance of playing the role of)()()( hhzh eee

2T


85

The payoff

• The B.S. formula for the capacity factor the plant is


2/)()/ln(2/)/ln(

where

)(

22

21

1

ezge epp

TXpd

dNp

Vf


86

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

Documents

1 Systems Analysis Advisory Committee (SAAC) Friday, November 22, 2002 Michael Schilmoeller John Fazio