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

Northwest Power and Conservation Council 2 Agenda Review Models and modeling Algorithms Next meeting

Northwest Power and Conservation Council 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

Northwest Power and Conservation Council 4 The Analysis Possible “futures” Likelihood of those circumstances Bad outcomes

Northwest Power and Conservation Council 5 The Trade-off The choice of transportation depends on how we weight the costs or benefits and the risk associated with that choice Cost -> Risk -> A B

Northwest Power and Conservation Council 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

Northwest Power and Conservation Council 7 Decision Making Terms An example of variation is average daily temperature over the course of a year Time (a year) Temperature

Northwest Power and Conservation Council 8 Decision Making Terms For any particular day, the uncertainty in daily temperature can be large. Time (a year) Temperature ?

Northwest Power and Conservation Council 9 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 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

Northwest Power and Conservation Council 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

Northwest Power and Conservation Council 12 Example of a Particular Plan

Northwest Power and Conservation Council 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.)

Northwest Power and Conservation Council 14 Power Cost (¢/kWh)-> Number of Observations Cost for Future 2 Cost for Future 1 Distribution of Cost for a Plan

Northwest Power and Conservation Council 15 Risk and Expected Cost Associated With A Plan Likelihood (Probability) Avg Cost Power Cost (¢/kWh)-> Risk = average of costs> 90% threshold

Northwest Power and Conservation Council 16 A Different Plan: The Trade-off Likelihood (Probability) Risk Avg Cost Power Cost (¢/kWh)->

Northwest Power and Conservation Council 17 Trade-off Basic information about the trade-off between cost and risk Cost (cents/kWh) -> Risk (cents/kWh) -> A B

Northwest Power and Conservation Council 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?

Northwest Power and Conservation Council 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

Northwest Power and Conservation Council 20 Risk and Expected Cost Associated With A Plan Likelihood (Probability) Avg Cost Power Cost (¢/kWh)-> Risk = average of costs> 90% threshold

Northwest Power and Conservation Council 21 The Source of the Trade-Off Increasing Cost Increasing Risk Alternative Plans

Northwest Power and Conservation Council 22 Space of feasible solutions Efficient Frontier Increasing Risk Increasing Cost Alternative Risk Levels Efficient Frontier

Northwest Power and Conservation Council 23 Finding the Efficient Frontier We are really only interested in the efficient frontier: “Risk-Constrained Least-Cost Planning”

Northwest Power and Conservation Council 24 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)

Northwest Power and Conservation Council 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 plans, or so.

Northwest Power and Conservation Council 26 Finding the Efficient Frontier The solution? Use a stochastic optimization program

Northwest Power and Conservation Council 27 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

Northwest Power and Conservation Council 28 Cost Distribution Associated With a Plan Hourly demand Coal Buy in Market Sell in Market Gas Fired Price-driven generation Hydro Contracts Hydro Total Resources Year 1 SummerWinter Year 2 SummerWinter Background

Northwest Power and Conservation Council 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!

Northwest Power and Conservation Council 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 10 th 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 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!

Northwest Power and Conservation Council 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

Northwest Power and Conservation Council 33 Using Valuation To Estimate Cost Average cost, given average price E(p) and average quantity E(q) is given by

Northwest Power and Conservation Council 34 Using Valuation To Estimate Cost Resource q i load Q market requirement

Northwest Power and Conservation Council 35 Using Valuation To Estimate Cost Costs using “rate base” calculation these are usually correlated! But how??

Northwest Power and Conservation Council 36 Using Valuation To Estimate Cost Costs using “valuation” calculation

Northwest Power and Conservation Council 37 Using Valuation To Estimate 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)

Northwest Power and Conservation Council 38 Our calculation times Recall the purpose of all this was to make our calculation times more manageable....

Northwest Power and Conservation Council 39 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 40 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 41 Real Feasibility Spaces Current spaces

Northwest Power and Conservation Council 42 Real Feasibility Spaces Earlier space, more representative of situation with relatively greater risk!

Northwest Power and Conservation Council 43 Our Models The meta-model: Olivia The portfolio model: Olivia’s “daughter”

Northwest Power and Conservation Council 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

Northwest Power and Conservation Council 45 Olivia

Northwest Power and Conservation Council 46 Olivia

Northwest Power and Conservation Council 47 Olivia

Northwest Power and Conservation Council 48 Olivia

Northwest Power and Conservation Council 49 Olivia The relationship among records in the database reflects the structure of calculations in an Excel workbook Structure.pdfStructure.pdf

Northwest Power and Conservation Council 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) hasL8.xls –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 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

Northwest Power and Conservation Council 52

Northwest Power and Conservation Council 53 Future 1 Criterion Functions

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Northwest Power and Conservation Council 57 Futures A workbook has been prepared that illustrates the 750 futures we have used. Graph of Futures.xls

Northwest Power and Conservation Council 58 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 59 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 60 Power requirements [Expected Load]*exp([factor]+[jump]+[specific deviation]) –factor –jump –specific variance

Northwest Power and Conservation Council 61 Power requirements: Factor Futures Uncertainty

Northwest Power and Conservation Council 62 Power requirements: Factor Futures Uncertainty

Northwest Power and Conservation Council 63 Power requirements: Factor Futures Uncertainty

Northwest Power and Conservation Council 64 Power requirements: Factor Prices strongly correlated, one month to the next. Size of correlation matrix grows as n 2 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 65 Zzzzzzzzzzzz Trick: Use principle factors We can typically capture 95%+ of correlation structure with the largest eigenvalues Futures Uncertainty

Northwest Power and Conservation Council 66 Zzzzzzzzzzzz Futures Uncertainty

Northwest Power and Conservation Council 67 Zzzzzzzzzzzz We can simulate random vectors with the correct volatilities and correlation structure using Efficiencies arise when m<<k Futures Uncertainty

Northwest Power and Conservation Council 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

Northwest Power and Conservation Council 69 Zzzzzzzzzzzz Futures Uncertainty

Northwest Power and Conservation Council 70 Zzzzzzzzzzzz More elaborate contributions to future values are easy to incorporate Futures Uncertainty

Northwest Power and Conservation Council 71 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

Northwest Power and Conservation Council 72 Power requirements: Jump Wait: 0 to 85 quarters, uniform distribution Size: to Duration: depends on size, inversely proportional Recovery: depends on size

Northwest Power and Conservation Council 73 Power requirements: Specific Minimum: Maximum: +0.14

Northwest Power and Conservation Council 74 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 75 Electricity Market Price Regression equation is We can use this to form a sensitivity equation:

Northwest Power and Conservation Council 76 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 78 Representation of resources Smaller gas- fired, oil- fired, waste, and must run units are aggregated

Northwest Power and Conservation Council 79 Must Run

Northwest Power and Conservation Council 80 Fuels

Northwest Power and Conservation Council 81 East-Side Gas Fired

Northwest Power and Conservation Council 82 Oil, Idaho Gas-Fired

Northwest Power and Conservation Council 83 West-Side Gas-Fired

Northwest Power and Conservation Council 84 “Waste Burner”

Northwest Power and Conservation Council 85 Load/Resource balance What is the representation of the remaining resources? Coal:5,115 Gas 5,968 Other: 1,533 Hydro12000 sum24,616

Northwest Power and Conservation Council 86 Load/Resource balance

Northwest Power and Conservation Council 87 Declining Resources

Northwest Power and Conservation Council 88 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 Value: note: we assuming the entire capacity is switched on when the turbine runs

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) Value V is this area Representations - thermal

Northwest Power and Conservation Council 91 Digression to Options The value of an option is the expected value of the discounted payoff (See Hull, 3 rd ed., p. 295) Representations - thermal

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

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 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(p t /p t-1 ) is  Representations - thermal

Northwest Power and Conservation Council 95 Example of Spread Option ( Testbed_new.xls )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 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.”

Northwest Power and Conservation Council 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.

Northwest Power and Conservation Council 103 The Analysis of Olivia RRP Given a variation in resources, we got the following behavior. Why is price insensitive to adding resource? Positive L/R mean deficit Points (L to R) obtained by decreasing size of fixed resource

Northwest Power and Conservation Council 104 RRP Algorithm Prices surplus deficit

Northwest Power and Conservation Council 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

Northwest Power and Conservation Council 106 Proposition Independence of price from resource generation levels is necessary for the existence of an independent electricity term

Northwest Power and Conservation Council 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, ,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000, Price L/R Bal (mwh) Intertie Capacity

Northwest Power and Conservation Council 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

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 )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 Resource Planning 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

Northwest Power and Conservation Council 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 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 113 Candidate Plan Under Future 1000 Choosing a Plan CO2 tax high gas prices

Northwest Power and Conservation Council 114 Candidate Plan Responds Choosing a Plan CO2 tax high gas prices lower power prices

Northwest Power and Conservation Council 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 Cash expenditures 18 months 9 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. Cash expenditures 18 months 9 months

Northwest Power and Conservation Council 117 Valuing Flexibility construction phase optional cancellation period evaluation phase time criterion To capture the value of flexibility, we need to model decision making 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

Northwest Power and Conservation Council 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 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?

Northwest Power and Conservation Council 122 Planning flexibility Example of decision criteria ( L8.xls )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 )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 Loads 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 126 DSI Loads Loads

Northwest Power and Conservation Council 127 DSI Loads Loads

Northwest Power and Conservation Council 128 DSI Loads minimum shut-down period evalulation phase time wholesale electricity market aluminum-elec price 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 )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 )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

Northwest Power and Conservation Council 138 Stochastic hydrogeneration We can look at simplified model: –Hydro Add-InHydro Add-In

Northwest Power and Conservation Council 139 Agenda Review Models and modeling Algorithms Next meeting

Northwest Power and Conservation Council 140 End