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Systems Analysis Advisory Committee (SAAC)
Friday March 19, 2004Michael Schilmoeller
John Fazio
Northwest Power and Conservation Council
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Agenda
• Review
• Models and modeling
• Algorithms
• Next meeting
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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The Analysis
• Possible “futures”
• Likelihood of those circumstances
• Bad outcomes
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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Decision Making Terms
• Risk– A measure of bad outcomes
• Variation– Normal changes in outcome, which may be
highly predictable
• Uncertainty– The predictability of outcomes
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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Decision Making Terms
• For any particular day, the uncertainty in daily temperature can be large.
Time (a year)Time (a year)
Tem
pera
ture
Tem
pera
ture
??
Northwest Power and Conservation Council
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Decision Making Terms
• 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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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Example of aParticular Plan
Northwest Power and Conservation Council
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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.)
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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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
Power Cost (¢/kWh)->
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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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?
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• 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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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The Source of the Trade-Off
Increasing Cost
Incre
asin
g R
isk
Alternative PlansAlternative Plans
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Space of feasible solutions
Efficient Frontier
Incre
asin
g R
isk
Increasing Cost
Alternative Alternative Risk LevelsRisk Levels
Efficient Frontier
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Finding the Efficient Frontier
We are really only interested in the efficient frontier:
“Risk-Constrained Least-Cost Planning”
Northwest Power and Conservation Council
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Finding the Efficient Frontier
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
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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.
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Finding the Efficient Frontier
The solution?
Use a stochastic optimization program
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Finding the Efficient Frontier
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
Northwest Power and Conservation Council
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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
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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!
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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.
Northwest Power and Conservation Council
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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!
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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
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Using Valuation ToEstimate Cost
• Average cost, given average price E(p) and average quantity E(q) is given by
(1) )()()( pqqpqEpEpqE
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Using Valuation ToEstimate Cost
Resource
qi
load Q
market requirement
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Using Valuation ToEstimate Cost
• 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??
Northwest Power and Conservation Council
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Using Valuation ToEstimate Cost
• Costs using “valuation” calculation
)(
*
)(
imi
im
iii
iimm
iim
iii
ppqQp
pqqpQp
qQppqc
Northwest Power and Conservation Council
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Using Valuation ToEstimate Cost
• 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)
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Our calculation times
• Recall the purpose of all this was to make our calculation times more manageable....
Northwest Power and Conservation Council
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Our calculation times
• 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 ....
Northwest Power and Conservation Council
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Our calculation times
• ... 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
Northwest Power and Conservation Council
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Real Feasibility Spaces
• Current spaces
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Real Feasibility Spaces
• Earlier space, more representative of situation with relatively greater risk!
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Our Models
• The meta-model: Olivia
• The portfolio model: Olivia’s “daughter”
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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
Northwest Power and Conservation Council
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Olivia
Northwest Power and Conservation Council
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Olivia
Northwest Power and Conservation Council
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Olivia
Northwest Power and Conservation Council
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Olivia
Northwest Power and Conservation Council
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Olivia
• The relationship among records in the database reflects the structure of calculations in an Excel workbook Structure.pdf
Northwest Power and Conservation Council
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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 .....
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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Gas Price
0.002.004.006.008.00
10.0012.0014.00
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CO2 Tax
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Requirement (Imports)
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Electricity Price
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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
Northwest Power and Conservation Council
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Gas Price
0.002.004.006.008.00
10.0012.0014.00
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$/M
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CO2 Tax
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10152025303540
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Hydrogeneration
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Requirement (Imports)
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Northwest Power and Conservation Council
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Gas Price
0.002.004.006.008.00
10.0012.0014.00
1 6 11
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21
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31
36
41
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quarter
$/M
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CO2 Tax
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10152025303540
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$/U
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Hydrogeneration
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Requirement (Imports)
-6000000
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Northwest Power and Conservation Council
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Gas Price
0.002.004.006.008.00
10.0012.0014.00
1 6 11
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21
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31
36
41
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51
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76
quarter
$/M
MB
TU
CO2 Tax
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10152025303540
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$/U
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Hydrogeneration
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Requirement (Imports)
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Futures
• A workbook has been prepared that illustrates the 750 futures we have used.
• Graph of Futures.xls
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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Construction of Futures
• Mathematical constructions for–Power requirements
–Natural gas price
–Hydro generation
–Electricity market price
–Aluminum price
–CO2 tax
–Power plant availability
Northwest Power and Conservation Council
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Power requirements
• [Expected Load]*exp([factor]+[jump]+[specific deviation])– factor– jump– specific variance
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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
Northwest Power and Conservation Council
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Power requirements: Factor
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
Northwest Power and Conservation Council
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Power requirements: Factor
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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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Zzzzzzzzzzzz
Futures Uncertainty
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Zzzzzzzzzzzz
• More elaborate contributions to future values are easy to incorporate
Futures Uncertainty
Northwest Power and Conservation Council
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Power requirements: Factor
• 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
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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
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Power requirements: Specific
• Minimum: -0.14
• Maximum: +0.14
Northwest Power and Conservation Council
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Construction of Futures
• Mathematical constructions for–Power requirements
–Natural gas price
–Hydro generation
–Electricity market price
–Aluminum price
–CO2 tax
–Power plant availability
Northwest Power and Conservation Council
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Electricity Market Price
• Regression equation is
IHLpp hLgge lnln
• We can use this to form a sensitivity equation:
)'()'()'ln(ln'lnln HHLLpppp hLgggee
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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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
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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
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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
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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
Northwest Power and Conservation Council
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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
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“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
Northwest Power and Conservation Council
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Load/Resource balance
• What is the representation of the remaining resources?
Coal: 5,115Gas 5,968Other: 1,533
Hydro 12000
sum 24,616
Northwest Power and Conservation Council
86
Load/Resource balance
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Declining Resources
PNW So ID NG 2 94PNW West NG 6 697PNW West NG 7 126
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Agenda
• Review
• 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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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
Representations - thermal
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
Northwest Power and Conservation Council
91
Digression to Options
• The value of an option is the expected value of the discounted payoff (See Hull, 3rd ed., p. 295)
Representations - thermal
price strike theis stock theof price theis
(years) expiration to time theis ratediscount annual theis
operatorn expectatio theis where
)],0max([
XpTrE
XpeEV rT
Northwest Power and Conservation Council
92
European spread option
• The Margrabe pricing formula for the value of a spread option, assuming no yields
Representations - thermal
212,12
22
12
12
212
1
2112
2
2/)/ln(where
)()(
TddT
Tppd
dNpdNpV
Northwest Power and Conservation Council
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
Representations - thermal
Northwest Power and Conservation Council
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
Representations - thermal
Northwest Power and Conservation Council
95
Example of Spread Option
•( Testbed_new.xls )
Northwest Power and Conservation Council
96
Agenda
• Review
• 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
Northwest Power and Conservation Council
97
Influence Diagram
RescourceOutages
HydroGeneration
DSI Loads
Non-DSILoads
Market Pricesfor Electricity
AluminumPrices
ReserveMargin
Temperature
Fuel Prices
TransmissionCongestion
EmissionPrices
Independent Effects
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
101
Well-Defined Function
• A machine that always gives you “Y” every time you put in “X.”
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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.
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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
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RRP Algorithm
Prices
surplus
deficit
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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
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Proposition
• Independence of price from resource generation levels is necessary for the existence of an independent electricity term
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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
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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
Northwest Power and Conservation Council
109
Resource-responsive price
• We can examine the function of RRP by considering a small toy application
• ( Testbed_new.xls )
Northwest Power and Conservation Council
110
Agenda
• Review
• 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
Northwest Power and Conservation Council
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
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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.
Northwest Power and Conservation Council
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Candidate Plan Under Future 1000
Choosing a Plan
CO2 taxCO2 taxhigh gas priceshigh gas prices
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114
Candidate Plan Responds
Choosing a Plan
CO2 taxCO2 taxhigh gas priceshigh gas prices
lower power priceslower power prices
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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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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!
Northwest Power and Conservation Council
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
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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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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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?
Northwest Power and Conservation Council
122
Planning flexibility
Example of decision criteria ( L8.xls )
Northwest Power and Conservation Council
123
Planning flexibility
The function that performs planning flexibility can be examined as a standalone routine in ( PlanningFlex.xls )
Northwest Power and Conservation Council
124
Agenda
• Review
• 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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
130
Long-term price response
Example of the function of the DSI LTPRD function
( Testbed_new.xls )
Northwest Power and Conservation Council
131
Agenda
• Review
• 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
Northwest Power and Conservation Council
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
Northwest Power and Conservation Council
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 )
Northwest Power and Conservation Council
134
Agenda
• Review
• 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
Northwest Power and Conservation Council
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.
Northwest Power and Conservation Council
136
Stochastic hydrogeneration
• 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
Northwest Power and Conservation Council
137
Stochastic hydrogeneration
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
Northwest Power and Conservation Council
138
Stochastic hydrogeneration
• We can look at simplified model:– Hydro Add-In
Northwest Power and Conservation Council
139
Agenda
• Review
• Models and modeling
• Algorithms
• Next meeting
Northwest Power and Conservation Council
140
End
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