1 Systems Analysis Advisory Committee (SAAC) Friday March 19, 2004 Michael Schilmoeller John Fazio

1

Systems Analysis Advisory Committee (SAAC)

Friday March 19, 2004Michael Schilmoeller

John Fazio

Northwest Power and Conservation Council

2

Agenda

• Review

• 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

• 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


20

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


21

The Source of the Trade-Off

Increasing Cost

Incre

asin

g R

isk

Alternative PlansAlternative Plans


22

Space of feasible solutions

Efficient Frontier

Incre

asin

g R

isk

Increasing Cost

Alternative Alternative Risk LevelsRisk Levels

Efficient Frontier


23

Finding the Efficient Frontier

We are really only interested in the efficient frontier:

“Risk-Constrained Least-Cost Planning”


24


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


25

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.


26


The solution?

Use a stochastic optimization program


27


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


28

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


29

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!


30

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.


31

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

• Aurora will do an hourly, 20-year study in about an hour. This would take Aurora over 28 years.

• Clearly some approximation/sampling/aggregation is in order!


32

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


33

Using Valuation ToEstimate Cost

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

(1) )()()( pqqpqEpEpqE


34


Resource

qi

load Q

market requirement


35


• 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??


36


• Costs using “valuation” calculation

)(

*

)(

imi

im

iii

iimm

iim

iii

ppqQp

pqqpQp

qQppqc


37


• 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)


38

Our calculation times

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


39


• 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 ....


40


• ... 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


41

Real Feasibility Spaces

• Current spaces


42

Real Feasibility Spaces

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


43

Our Models

• The meta-model: Olivia

• The portfolio model: Olivia’s “daughter”


44

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


45

Olivia


46

Olivia


47

Olivia


48

Olivia


49

Olivia

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


50

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 (L8.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 .....


51

Agenda

• Review

• Models and modeling– Trade-Off: The construction of the efficient frontier

– Estimating the distributions

– Examination of futures

– Construction of futures

– Representation of resources

• Algorithms

• Next meeting


52

Gas Price

0.002.004.006.008.00

10.0012.0014.00

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/M

MB

TU

CO2 Tax

05

10152025303540

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/U

.S.

sh

ort

to

n

Hydrogeneration

0

5000

10000

15000

20000

25000

1 7 13

19

25

31

37

43

49

55

61

67

73

79

quarter

MW

a

On-Peak Off-Peak

Requirement (Imports)

-6000000

-4000000

-2000000

0

2000000

4000000

6000000

8000000

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

MW

h

On-Peak Off-Peak

Regional Loads

0

5000

10000

15000

20000

25000

30000

35000

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

MW

a

Electricity Price

0.0050.00

100.00150.00200.00250.00300.00350.00400.00

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/M

Wh

On-Peak Off-Peak


53

Future 1 Criterion Functions

Criterion Function

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76

quarter

(no

un

its)

CCCT SCCT Coal DR Wind


54

Gas Price

0.002.004.006.008.00

10.0012.0014.00

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/M

MB

TU

CO2 Tax

05

10152025303540

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/U

.S.

sh

ort

to

n

Hydrogeneration

0

5000

10000

15000

20000

25000

1 7 13

19

25

31

37

43

49

55

61

67

73

79

quarter

MW

a

On-Peak Off-Peak


-6000000

-4000000

-2000000

0

2000000

4000000

6000000

8000000

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

MW

h

On-Peak Off-Peak

Regional Loads

0

5000

10000

15000

20000

25000

30000

35000

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

MW

a

Electricity Price

0.0050.00

100.00150.00200.00250.00300.00350.00400.00

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/M

Wh

On-Peak Off-Peak


55

Gas Price

0.002.004.006.008.00

10.0012.0014.00

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/M

MB

TU

CO2 Tax

05

10152025303540

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/U

.S.

sh

ort

to

n

Hydrogeneration

0

5000

10000

15000

20000

25000

1 7 13

19

25

31

37

43

49

55

61

67

73

79

quarter

MW

a

On-Peak Off-Peak


-6000000

-4000000

-2000000

0

2000000

4000000

6000000

8000000

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

MW

h

On-Peak Off-Peak

Regional Loads

0

5000

10000

15000

20000

25000

30000

35000

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

MW

a

Electricity Price

0.0050.00

100.00150.00200.00250.00300.00350.00400.00

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/M

Wh

On-Peak Off-Peak


56

Gas Price

0.002.004.006.008.00

10.0012.0014.00

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/M

MB

TU

CO2 Tax

05

10152025303540

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/U

.S.

sh

ort

to

n

Hydrogeneration

0

5000

10000

15000

20000

25000

1 7 13

19

25

31

37

43

49

55

61

67

73

79

quarter

MW

a

On-Peak Off-Peak


-6000000

-4000000

-2000000

0

2000000

4000000

6000000

8000000

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

MW

h

On-Peak Off-Peak

Regional Loads

0

5000

10000

15000

20000

25000

30000

35000

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

MW

a

Electricity Price

0.0050.00

100.00150.00200.00250.00300.00350.00400.00

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

76

quarter

$/M

Wh

On-Peak Off-Peak


57

Futures

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

• Graph of Futures.xls


58

Agenda

• Review






• Algorithms

• Next meeting


59

Construction of Futures

• Mathematical constructions for–Power requirements

–Natural gas price

–Hydro generation

–Electricity market price

–Aluminum price

–CO2 tax

–Power plant availability


60

Power requirements

• [Expected Load]*exp([factor]+[jump]+[specific deviation])– factor– jump– specific variance


61

Power requirements: Factor

Gas Prices over the next three months

0.000.501.001.502.002.503.003.504.00

1 2 3 4 5 6

Forward month

$/M

MB

TU

Futures Uncertainty


62


2.35 <-price in March2.50 <-price in April2.35 <-price in May2.78 <-price in June3.02 <-price in July2.90 <-price in Aug

0.200.400.600.400.200.50

Futures Uncertainty


63


1.0 0.9 0.8 0.4 0.2 0.00.9 1.0 0.9 0.8 0.4 0.20.8 0.9 1.0 0.9 0.8 0.40.4 0.8 0.9 1.0 0.9 0.80.2 0.4 0.8 0.9 1.0 0.90.0 0.2 0.4 0.8 0.9 1.0

Futures Uncertainty


64

Power requirements: Factor• Prices strongly correlated, one month to the

next.• Size of correlation matrix grows as n2

• As commodities, locations, and periods grow, so does the length n of the vector

• We have 64 variables (commodities and locations), not counting a potential for 61 additional load variables. To represent 60 months (or more) of future behavior results in a large correlation matrix, ({64+60}*60) 2

Futures Uncertainty


65

Zzzzzzzzzzzz

• Trick: Use principle factors

ii

i

i

kkk

1)(kii

k)(k

eee

A

eeeeeeA

of transpose theis 'r eigenvectoth theis

eigenvalueth theis matrix symmetric a is

where''' 222111

• We can typically capture 95%+ of correlation structure with the largest eigenvalues

Futures Uncertainty


66

Zzzzzzzzzzzz

else. everywhere zeros anddiagonal on the entries

associated of deviationsstandard h thematrix wit

theis matrix Thematrices. symmetric are

iprelationsh by the definedmatrix n correlatio theand

))')(((matrix covariance The

S

RSS'

RuXuX

E

Futures Uncertainty


67

Zzzzzzzzzzzz

• We can simulate random vectors with the correct volatilities and correlation structure using

• Efficiencies arise when m<<k

factors" specific"randon of vector 1 a is variablesrandom ofmatrix 1 a is

rseigenvecto m ofmatrix theis means ofmatrix 1 their is

variablesrandom of vector 1 theis where

)(k)(mm)(k

)(k)(k

εFLμX

εLFμX

Futures Uncertainty


68

Zzzzzzzzzzzz

• For a data vector representing a specific parameter at a specific location, the vectors associated with the largest eigenvalues often describe simple, typical changes to the data sequence over time.

Futures Uncertainty


69

Zzzzzzzzzzzz

Futures Uncertainty


70

Zzzzzzzzzzzz

• More elaborate contributions to future values are easy to incorporate

Futures Uncertainty


71


• Linear growth factor: Normal (0, 3) * 0.30 * time value that grows to 0.19

• Quadratic: Normal (0, 3) * 0.05* time value that grows to 0.11


72

Power requirements: Jump

• Wait: 0 to 85 quarters, uniform distribution

• Size: -0.10 to +0.08

• Duration: depends on size, inversely proportional

• Recovery: depends on size


73

Power requirements: Specific

• Minimum: -0.14

• Maximum: +0.14


74

Construction of Futures

• Mathematical constructions for–Power requirements

–Natural gas price

–Hydro generation

–Electricity market price

–Aluminum price

–CO2 tax

–Power plant availability


75

Electricity Market Price

• Regression equation is

IHLpp hLgge lnln

• We can use this to form a sensitivity equation:

)'()'()'ln(ln'lnln HHLLpppp hLgggee


76

Agenda

• Review






• Algorithms

• Next meeting


77

Representation of resources

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

• Stepping through the process of aggregating the resources

• Existing resources and candidate resources


78

Representation of resources

• Smaller gas-fired, oil-fired, waste, and must run units are aggregated

Olivia_Resource TotalBoardman 556Centralia 1,340Colstrip 1&2 614Bridger 704Valmy 261Corrette 160Colstrip 3&4 1,480Encogen 1 73Must Run 762PNW East NG 1 1,069PNW East NG 2 706PNW East NG 3 470PNW East NG 4 95PNW East NG 5 9PNW East NG 6 279PNW East NG 7 42PNW Oil 32PNW So ID NG 1 12PNW So ID NG 2 94PNW West NG 1 490PNW West NG 2 92PNW West NG 3 1,146PNW West NG 4 55PNW West NG 5 513PNW West NG 6 697PNW West NG 7 126Waste Burner 739Grand Total 12,616


79

Must RunUnit Name Olivia_Resource Incr_Cap Fuel Heat Rate VOM Cost

Biomass-One 1 Must Run 21.02 ###7 8000.00 2.15 2.58Columbia Generating Station Must Run 351.00 ###5 10064.00 2.15 0.00Condon Wind Project Phase I Must Run 7.08 ##30 0.00 1.40 1.40Condon Wind Project Phase II Must Run 7.26 ##30 0.00 1.40 1.40D R Johnson Lumber (Riddle, Cogen II) Must Run 6.73 ###7 8000.00 2.15 2.58Everett Cogen 1 Must Run 15.13 ###7 5000.00 2.15 2.42Georgia Pacific (Camas) Must Run 43.72 ###7 5000.00 2.15 2.42Georgia Pacific (Wauna) Must Run 30.27 ###7 5000.00 2.15 2.48Kettle Falls ST Must Run 40.35 ###7 14380.00 2.15 2.99Klondike Must Run 6.91 ##30 0.00 1.40 1.40Libby 1 Champion Must Run 6.31 ###7 12380.00 2.15 2.93Libby 2 Champion Must Run 4.21 ###7 15476.00 2.15 3.07Nine Canyon Must Run 13.85 ##30 0.00 1.40 1.40OR RPS/SBC Wind 03 Must Run 14.40 ##30 0.00 1.40 1.40Pine Products Must Run 4.79 ###7 17000.00 2.15 3.07Potlatch Corp 1-4 Must Run 49.61 ###7 8000.00 2.15 2.69Prairie Wood Products (Cogen 1) Must Run 6.73 ###7 5000.00 2.15 2.58Roosevelt Landfill Must Run 7.72 ###7 10000.00 2.15 2.82SDS Lumber ST Must Run 2.94 ###7 6000.00 2.15 2.58Stateline Must Run 76.32 ##30 0.00 1.40 1.40Steam Plant No 2 2 Must Run 15.97 ###7 14000.00 2.15 2.91Vaagen Bros 1 Must Run 3.36 ###7 8000.00 2.15 2.58Vansycle Ridge Must Run 7.17 ##30 0.00 1.40 2.15Warm Spgs Forest Products 2 Must Run 2.52 ###7 8000.00 2.15 2.58Warm Spgs Forest Products 3 Must Run 2.52 ###7 8000.00 2.15 2.58West Boise Waste 1 Must Run 0.08 ###7 8000.00 2.15 2.58West Point Treatment Plant 3 Must Run 0.92 ###7 8000.00 2.15 2.91Wood Plants 2 Must Run 13.45 ###7 8000.00 2.15 2.58


80

Fuels

Fuel###5 Uranium###6 Refuse###7 Other, Bio, ZZ, WC, WH##30 Wind - Cascades & Inland Existing##53 PNW West coal##55 PNW East coal##84 Utility distillate fuel oil#112 PNW West - NG variable cost#114 PNW East - NG variable cost#120 S. ID - NG variable cost


81

East-Side Gas Fired

Unit Name Olivia_Resource Incr_Cap Fuel Heat Rate VOM CostHermiston Power Project PNW East NG 1 604.80 #114 6700.00 3.02 26.85Klamath Cogen Project PNW East NG 1 464.64 #114 6800.00 3.02 27.55Hermiston Generating 1 PNW East NG 2 225.12 #114 7050.00 3.02 27.72Hermiston Generating 2 PNW East NG 2 225.12 #114 7050.00 3.02 27.72Rathdrum Power Project PNW East NG 2 255.36 #114 7000.00 3.02 27.72Coyote Springs 1 PNW East NG 3 235.20 #114 7050.00 3.02 39.11Coyote Springs 2 PNW East NG 3 235.20 #114 6950.00 3.02 39.11Klamath Expansion (GTs) PNW East NG 4 95.00 #114 8700.00 8.62 41.91Kettle Falls GT PNW East NG 5 9.02 #114 9500.00 8.62 44.10Boulder Park PNW East NG 6 22.63 #114 11600.00 44.89Finley PNW East NG 6 23.75 #114 10700.00 46.29Morrow Power PNW East NG 6 10.36 #114 11500.00 48.92Northeast PNW East NG 6 55.10 #114 10750.00 48.92Rathdrum 1 PNW East NG 6 83.60 #114 10350.00 44.89Rathdrum 2 PNW East NG 6 83.60 #114 10350.00 46.11Pasco PNW East NG 7 41.80 #114 11500.00 74.73


82

Oil, Idaho Gas-Fired

Unit Name Olivia_Resource Incr_Cap Fuel Heat Rate VOM CostBoundary GT PNW Oil 0.71 ##84 13000.00 89.95Grays Harbor ICs PNW Oil 7.36 ##84 11600.00 74.73Okanogan Co PUD ICs Ph 2 PNW Oil 23.92 ##84 11600.00 74.73

Unit Name Olivia_Resource Incr_Cap Fuel Heat Rate VOM CostGlenns Ferry Cogeneration PNW So ID NG 1 8.22 #120 8000.00 3.02 32.42Simplot Cogen 1 PNW So ID NG 1 4.07 #120 5000.00 3.45 32.42Danskin PNW So ID NG 2 85.50 #120 12100.00 74.73Rupert Cogeneration PNW So ID NG 2 8.22 #120 8000.00 3.02 32.42


83

West-Side Gas-Fired

Unit Name Olivia_Resource Incr_Cap Fuel Heat Rate VOM CostFrederickson Power 1 PNW West NG 1 239.04 #112 7000.00 3.02 27.67River Road 1 PNW West NG 1 238.08 #112 7000.00 3.02 27.67Wah Chang PNW West NG 1 12.88 #112 5800.00 3.45 27.67SP Newsprint (Newberg) PNW West NG 2 46.08 #112 5500.00 8.62 27.98Willamette Industries (Albany) GT Upgrade PNW West NG 2 46.08 #112 5500.00 8.62 28.37Big Hanaford PNW West NG 3 238.08 #112 7200.00 3.02 30.13Chehalis Generation Facility PNW West NG 3 499.20 #112 7000.00 3.02 27.98March Point 1 PNW West NG 3 73.04 #112 8000.00 3.02 31.19Sumas Energy 1 PNW West NG 3 100.43 #112 8000.00 3.02 31.19Tenaska 1 PNW West NG 3 235.20 #112 7700.00 3.02 31.19March Point 2 PNW West NG 4 54.78 #112 8000.00 3.02 35.41Beaver 1-7 PNW West NG 5 512.64 #112 9200.00 3.02 44.29Beaver 8 PNW West NG 6 23.28 #112 11500.00 49.11Frederickson 1 PNW West NG 6 80.37 #112 10600.00 45.94Frederickson 2 PNW West NG 6 80.37 #112 10600.00 45.94Fredonia 1 PNW West NG 6 117.45 #112 10711.00 49.11Fredonia 2 PNW West NG 6 117.45 #112 10711.00 46.33Fredonia 3 PNW West NG 6 50.35 #112 10300.00 44.89Fredonia 4 PNW West NG 6 50.35 #112 10300.00 45.94Point Whitehorn 2 PNW West NG 6 84.44 #112 10600.00 46.29Point Whitehorn 3 PNW West NG 6 84.44 #112 10600.00 45.94Springfield ICs Phase II PNW West NG 6 8.74 #112 11600.00 44.29Bailey (Clatskanie GT) PNW West NG 7 10.17 #112 11500.00 54.39BP (Cherry Point) GTs PNW West NG 7 69.16 #112 13000.00 54.39Equilon GTs PNW West NG 7 36.58 #112 13000.00 58.62Georgia-Pacific (Bellingham) GTs PNW West NG 7 10.17 #112 13000.00 54.39


84

“Waste Burner”

Unit Name Olivia_Resource Incr_Cap Fuel Heat Rate VOM CostCoffin Butte 1 Waste Burner 1.85 ###6 8000.00 2.15 10.77Columbia Generating Station Waste Burner 655.20 ###5 10064.00 2.15 10.77Frontier Energy Waste Burner 8.41 ###7 17000.00 2.15 9.74Marion Solid Waste 1 Waste Burner 12.61 ###6 8000.00 2.15 12.40Pocatello Waste 1 Waste Burner 0.13 ###7 8000.00 2.15 21.82Short Mountain 1 Waste Burner 0.67 ###6 9517.00 2.15 12.40Short Mountain 2 Waste Burner 0.67 ###6 9517.00 2.15 12.40Short Mountain 3 Waste Burner 0.67 ###6 9517.00 2.15 15.61Short Mountain 4 Waste Burner 0.67 ###6 9517.00 2.15 12.40Skagit Co Waste 1 Waste Burner 1.68 ###6 8000.00 2.15 10.77Spokane MSW 1 Waste Burner 19.33 ###6 8000.00 2.15 12.68Steam Plant No 2 1 Waste Burner 15.97 ###7 14000.00 2.15 10.77Weyco Energy CTR 1 Waste Burner 21.02 ###6 12500.00 2.15 17.38


85

Load/Resource balance

• What is the representation of the remaining resources?

Coal: 5,115Gas 5,968Other: 1,533

Hydro 12000

sum 24,616


86

Load/Resource balance


87

Declining Resources

PNW So ID NG 2 94PNW West NG 6 697PNW West NG 7 126


88

Agenda

• Review


• 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


89

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


90

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


91

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


92

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


93

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



94

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



95

Example of Spread Option

•( Testbed_new.xls )


96

Agenda

• Review








• Next meeting


97

Influence Diagram

RescourceOutages

HydroGeneration

DSI Loads

Non-DSILoads

Market Pricesfor Electricity

AluminumPrices

ReserveMargin

Temperature

Fuel Prices

TransmissionCongestion

EmissionPrices

Independent Effects


98

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


99

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


100

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


101

Well-Defined Function

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


102

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.


103

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


104

RRP Algorithm

Prices

surplus

deficit


105

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


106

Proposition

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


107

Eliminating Import/Export

• 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


108

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


109

Resource-responsive price

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

• ( Testbed_new.xls )


110

Agenda

• Review








• Next meeting


111

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


112

Flexibility Has Value

• Flexibility was explicitly valued in the 1991 Plan with the ISAAC model

• The value of flexibility played a key role in the 2000-2001 as we saw load management and conservation respond to circumstances much faster and more effectively than conventional thermal supply-side resources. Generally, load exchange programs make this capacity a “reversible” resource.


113

Candidate Plan Under Future 1000

Choosing a Plan

CO2 taxCO2 taxhigh gas priceshigh gas prices


114

Candidate Plan Responds

Choosing a Plan

CO2 taxCO2 taxhigh gas priceshigh gas prices

lower power priceslower power prices


115

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


116

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


117

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!


118

Alternative Decision Rules• Loads and resources (reserve margin)

– Does not provide guidance on what kinds of resources to build

– Less sensitive to current conditions

– Traditional

• Diversified portfolio standard– Assumes the conclusion

– The portfolio should be selected to manage risk

• Forecast value over study time period– Assumes perfect foresight

– Defeats the purpose of planning flexibility


119

Forward Prices• Forward prices are prices that will be paid for power

delivered in the future

• Does not assume a formal market

• Regulators and regulated utilities are interested in forward prices because they serve as a good measure of

– the prudence of acquiring new resources, and therefore

– the likelihood of rate base treatment

• Deregulated utilities or IPPs use forward price contracts to

– reduce risks

– secure construction financing


120

Recent Spot Prices

• When commodities can not be stored, futures and forward contract prices are a poor predictor of future spot prices, in fact...

• Persistence forecasts with current spot prices perform at least as well

• Most of the variation in forward prices can be explained with current spot prices


121

Forward Price Decision Rules

• Gas turbines and coal plants– Would a plant dispatch enough and at market prices sufficient to have

covered its costs over the last 18 months?

• Conservation– How much conservation would be developed based on market price? How

much should we pay to induce more, if doing so reduces cost or risk?

• Price Responsive Demand– If wholesale power prices exceeded 15¢/kWh, could the project support a

couple of FTEs and tracking software?

• Wind– Would the value of energy generated have covered costs over the last 18

months?


122

Planning flexibility

Example of decision criteria ( L8.xls )


123

Planning flexibility

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


124

Agenda

• Review








• Next meeting


125

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


126

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


127

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


128

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


129

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


130

Long-term price response

Example of the function of the DSI LTPRD function

( Testbed_new.xls )


131

Agenda

• Review








• Next meeting


132

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


133

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 )


134

Agenda

• Review








• Next meeting


135

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.


136


• Flat generation based on regulator output (BPAREGU.OUT)

• 10-hour, weekday on-peak generation relationship to flat from earlier work by Dr. Mike McCoy, Pete Swartz, John Fazio

• Conversion to 6 x 16 hour on-peak generation performed algebraically


137


power.peak sustained hour,-10 andpower average of in termspower peak -on us giveswhich )6510516(

)6516(ˆ105

so )105247(

ˆ105247us gives for solving So

)6510516(

65ˆ10516hourspeak total

peak) sus-non(weekday peak) sus(weekday peak)(saturday 247

)105247(ˆ105then

peak sustainedhour -10 tocontributenot do that hoursover (MW)power average thedenote X(MW) week entire over thepower averageor flat thedenote

(MW)power weekdays)(5peak -onhour -10 sustained thedenote ˆ(MW)power 16hours) x (6dayspeak -on thedenote

Let

XEE

EEX

X

XEX

E

XEE

EEE

pp

p

p

p

p

p

p


138


• We can look at simplified model:– Hydro Add-In


139

Agenda

• Review


• Algorithms

• Next meeting


140

End

Documents

1 Systems Analysis Advisory Committee (SAAC) Friday March 19, 2004 Michael Schilmoeller John Fazio