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

Northwest Power Planning Council 2 Original Agenda Natural gas prices –Sumas, AECO, Rocky mountains –historical and monthly forwards and volatilities –correlations with other variables –subjective forwards Hydro generation –historical and monthly forwards and volatilities –correlations with other variables Outcomes and Milestones

Northwest Power Planning Council 3 Revised Agenda Approval of the Oct 24 meeting minutes Review and questions from the last meeting –Representation of dispatchable resources in the portfolio model –Metrics Representations in the portfolio model –Price responsive demand –Renewables and conservation Hydro Loads Natural gas prices

Northwest Power Planning Council 4 Revised Agenda Approval of the Oct 24 meeting minutes Review and questions from the last meeting –Representation of dispatchable resources in the portfolio model –Metrics Representations in the portfolio model –Price responsive demand –Renewables and conservation Hydro Loads Natural gas prices

Northwest Power Planning Council 5 Revised Agenda Approval of the Oct 24 meeting minutes Review and questions from the last meeting –Representation of dispatchable resources in the portfolio model –Metrics Representations in the portfolio model –Price responsive demand –Renewables and conservation Hydro Loads Natural gas prices Review

Northwest Power Planning Council 6 October 24 Agenda Metrics –Stakeholders –Risk measures –Timing Representations in the portfolio model –thermal generation –hydro generation –conservation and renewables –loads –contracts –reliability –** Plan Issues ** Review

Northwest Power Planning Council 7 Revised October 24 Agenda Approval of the Oct 4 meeting minutes Price Processes Representations in the portfolio model –thermal generation Metrics –Stakeholders –Risk measures –Timing Representations in the portfolio model –** Plan Issues ** : price responsive demand Review

Northwest Power Planning Council 8 Plan Issues incentives for generation capacity price responsiveness of demand sustained investment in efficiency information for markets fish operations and power transmission and reliability resource diversity role of BPA global change Review

Northwest Power Planning Council 9 Representation of dispatchables Main Conclusions –Option calculation of capacity factor and plant value over the month should be identical with hourly dispatch result when prices are lognormally distributed. Consequently, –Option model should give a reasonable representation of dispatchable plant performance and value –Volatility in the option model represents both variation within the month and uncertainty –Where uncertainty dominates, temporal variation become unimportant Review

Northwest Power Planning Council 10 Review of Results Examine gas and power prices from 1999 How good is the lognormal assumption? Comparison of option model with hourly dispatch against lognormally distributed prices Comparison of option model and hourly dispatch of actual dispatch for Beaver in 1999 Impact of future uncertainty on capacity factor and value of Beaver Review

Northwest Power Planning Council 11 Price Duration Curve If we assume each hour’s dispatch is independent, we can ignore the chronological structure. Sorting by price yields the market price duration curve (MCD) Value V is this area Review

Northwest Power Planning Council 12 Variability viewed as CDF Turning the MCD curve on its side, we get something that looks like a cumulative probability density function (CDF) Value V is this area Review

Northwest Power Planning Council 13 Hourly Volatilities from Monthly We are dealing with expected variation of electricity and gas price over the specific time period and with uncertainties in these, as well. Using our assumption that the hourly uncertainties are constant and independent of the temporal variations in the respective commodities, Review

Northwest Power Planning Council 14 Hourly Dispatch Try dispatching against a lognormally distributed set of prices, with 1000 observations. =IF(RC[-2]>RC[-3],1,0) Maximum discrepancy over prices and volatilities, about 5% averages spread option Review

Northwest Power Planning Council 15 Representation of dispatchables Review

Northwest Power Planning Council 16 Representation of dispatchables Review

Northwest Power Planning Council 17 Representation of dispatchables Review

Northwest Power Planning Council 18 Representation of dispatchables Review

Northwest Power Planning Council 19 Representation of dispatchables Review

Northwest Power Planning Council 20 Representation of dispatchables Beaver –9000 BTU/kWh –$4.00/MWh for VOM, variable fuel transportation –Did not incorporate forced outage estimate, maintenance –Assumed 500MW capacity –“Hourly” dispatch was on daily on- and off-peak only (would understate volatility) Review

Northwest Power Planning Council 21 Representation of dispatchables Review

Northwest Power Planning Council 22 Representation of dispatchables To show: The main driver of value is not expected variation in price, it is uncertainty What is the 1 sigma in daily (hourly?) electricity and gas prices over the next several years? Review

Northwest Power Planning Council 23 Representation of dispatchables Oil price forecast ? ? Review

Northwest Power Planning Council 24 Representation of dispatchables NG price forecast ? ? Review

Northwest Power Planning Council 25 Mid-Columbia price forecast Average annual w/comparisons ? ? Review

Northwest Power Planning Council 26 Uncertainty Dominates Expected variation Uncertainty Addition of uncorrelated volatilities x y=1 z 2 =x 2 +y 2 z Review

Northwest Power Planning Council 27 Uncertainty Dominates Beaver Value, assuming change in volatility due to uncertainty same expected fuel and electricity price, correlation Review

Northwest Power Planning Council 28 Uncertainty Dominates Review

Northwest Power Planning Council 29 Uncertainty Dominates Review

Northwest Power Planning Council 30 Makes sense CF may or may not increase with volatility Review

Northwest Power Planning Council 31 Makes sense Value increases with volatility Review

Northwest Power Planning Council 32 Makes sense Value increases with volatility Review A B

Northwest Power Planning Council 33 Conclusions The monthly spread option model gives a reasonable representation of expected capacity factors (and hence value) of resource options Given that the uncertainty in hourly prices exceeds the expected variation, the detailed information about hourly prices from any one scenario tells us little about the expected capacity factor and value of resource options Review

Northwest Power Planning Council 34 Revised Agenda Approval of the Oct 24 meeting minutes Review and questions from the last meeting –Representation of dispatchable resources in the portfolio model –Metrics Representations in the portfolio model –Price responsive demand –Renewables and conservation Hydro Loads Natural gas prices

Northwest Power Planning Council 35 Price responsive demand Intended to represent short-term (1 day to 1 month) load reduction, on- and off-peak, if the price is right Does not address longer term DSI load curtailment (which is addressed later) Described by a supply curve Energy available represented as special continuous function of price –Zero variable cost, but some fixed cost Supply curve developed by Ken Corum Representations

Northwest Power Planning Council 36 Price responsive demand Baseload 32000MW, Base price $25/MWh, Short-run elasticity is Energy PriceIncrem. (Wholesale) Reduct. $/MWhMW Representations

Northwest Power Planning Council 37 Price responsive demand Side observation: Much of the value of PRD is driven by peak prices. The price of electricity in the portfolio model is subjective, but so are curtailment block prices in our other models. At right, the value of PRD is determined by those prices, the marginal costs in hour segments A and B. Stack Model Representations

Northwest Power Planning Council 38 Conservation & Renewables Represent as non-dispatchable energy Supply curve for conservation developed by Tom Eckman Renewables cost and operating characteristics assembled by Jeff King Representations

Northwest Power Planning Council 39 C&R Weaknesses Lack of short term operating flexibility –If market prices fall below the dispatch cost of a traditional resource, the unavoidable cost of a dispatchable resource is limited to fixed cost (typically 10% to 30% of total cost); Conservation and renewables’ costs are largely capital and unavoidable –Makes C&R less attractive when resource portfolio capacity exceeds loads Some financial risks –Conservation and renewables have higher up-front cost. If resource disappears (failure, technological obsolescence,…), the owner stands to lose more. Representations

Northwest Power Planning Council 40 C&R Strengths “Real option” (modularity) value –C&R can be added incrementally and with a shorter lead time than conventional resources. Fuel Price risk mitigation Emission cost risk mitigation Conservation may have lower availability risk Conservation may have lower credit risk than fixed price forward contracts. Representations

Northwest Power Planning Council 41 NPPC Analysis Credit and availability advantages can be valued by adding these uncertainties to alternatives, such as contracts Modularity benefits require a new approach Example of Sustained Orderly Development (SOD) Representations

Northwest Power Planning Council 42 SOD Analysis Representations

Northwest Power Planning Council 43 SOD Analysis Representations

Northwest Power Planning Council 44 SOD Analysis There is only a weak relationship between ramp rates (up or down) and utility conservation acquisition costs. Utility conservation acquisition costs ($/aMW) may lower when ramping up than when ramping down, due to: –Outstanding contracts –“Lags” in personnel changes –Desire to maintain stable infrastructure Assumption – –Assume same cost/aMW during ramp down than ramp up. Representations

Northwest Power Planning Council 45 SOD Analysis Conservation has been ramped up and down within a range of +/- 10 aMW Assumption – Constrain ramp rate to “monthly availability” of each conservation cost block (e.g. maximum annual change = 12x monthly availability). Representations

Northwest Power Planning Council 46 SOD Analysis Wholesale market prices will fluctuate as a result of: –Over/Under building –Extreme weather events (hot or cold) –Hydro-system availability –Short-run economic/business cycles Assumption:“Randomize” the forecast of future “price spikes” in response to hydro-system availability, ignore “short-run” weather & business cycles Representations

Northwest Power Planning Council 47 NPPC Analysis Representations

Northwest Power Planning Council 48 NPPC Analysis Implement in Portfolio Model –Evaluation period (rolling average prices over the last 18 months?) –Cancellation period –Construction period –Ramp rate constraint Representations

Northwest Power Planning Council 49 NPPC Analysis Real Options –Opportunity to defer, expand, abandon according to changing circumstances –Staging benefits –Switching fuel supplies Representations

Northwest Power Planning Council 50 NPPC Analysis Broad Application of real options to the Electric Power Industry –Renewables Mark Bolinger, Ryan Wiser and William Golove, “QUANTIFYING THE VALUE THAT WIND POWER PROVIDES AS A HEDGE AGAINST VOLATILE NATURAL GAS PRICES,” Proceedings of WINDPOWER 2002, June 2-5, 2002, Portland, Oregon –Coal Y. SMEERS, CORE and L.BOLLE, O. SQUILBIN, “COAL OPTIONS, Evaluation of coal-based power generation in an uncertain context,” Final report, September 2001, OSTC - Global Change and Sustainable Development , Belgium Federal Office for Scientific,Technical and Cultural Affairs k.pdf:// k.pdf Representations

Northwest Power Planning Council 51 NPPC Analysis Broad Application of real options to the Electric Power Industry –R&D expenditures Graham A. Davis, Brandon Owens, “Optimizing the Level of Renewable Electric R&D Expenditures Using Real Options Analysis,” National Renewable Energy Laboratory,Golden, CO December 18, 2001 –Distribution Systems Costing Methodology for Electric Distribution System Planning November 9, 2000 Prepared for: The Energy Foundation Prepared by: Energy & Environmental Economics, Inc. Karl E. Knapp, Jennifer Martin, Snuller Price, And P acific Energy Associates Frederick M. Gordon Representations

Northwest Power Planning Council 52 Working Hypothesis Some participants will find risk attributes of C&R more attractive than others Good portfolio for C&R –Heavy exposure to carbon-based fuel prices (even more benefit if fuel prices are correlated to electricity prices) –Contracts with credit problems –Contracts with duration less than lifetime of C&R measure –Short supply of other resources relative to demand –High but unpredictable load growth potential Representations

Northwest Power Planning Council 53 Working Hypothesis Some participants will find risk attributes of C&R more attractive than others Poor portfolios for C&R –Low exposure to carbon-based fuel prices, e.g., high-quality forward contracts with terms comparable to lifetime of C&R measures –Long supply of resources relative to demand Made worse if portfolio has hydro generation and market prices are negatively correlated with hydro generation –Stagnant or decreasing loads expected Representations

Northwest Power Planning Council 54 NPPC Analysis If C&R are beneficial from the standpoint of cost and risk, what is the best strategy to deploy? What is the value of SOD, and to which measures is SOD beneficially applicable? What are the technology-specific risk attributes for solar, wind, geothermal, biomass, low-head run-of-river hydro? Representations

Northwest Power Planning Council 55 Revised Agenda Approval of the Oct 24 meeting minutes Review and questions from the last meeting –Representation of dispatchable resources in the portfolio model –Metrics Representations in the portfolio model –Price responsive demand –Renewables and conservation Hydro Loads Natural gas prices

Northwest Power Planning Council 56 Hydrogeneration Excel Add-in has 50-year record Demonstrate: –Parameters to pull out different data –Use as random draw & correlation with other assumptions –Use of function to pull out specific year Reflects 10-hour sustained peaking capability from the trapazoidal approximation studies Hydrogeneration

Northwest Power Planning Council 57 Hydrogeneration

Northwest Power Planning Council 58 Hydrogeneration Function vfuncHydroGen(ByVal sYear As Single, ByVal lLoc As Long, ByVal lType As Long, Optional ByVal lPeriods As Long = 1) As Variant 'Takes: 'sYear - single [ ] representing the years , sorted ascending by annual energy. ' By passing 50*Rand() as sYear to this function, this permits random draws ' of hydro condition. Ascending order permits user to correlate annual energy with ' other variable. To access a particular year, use the sfuncYear() function, below. ' 'lLoc - 0, East only ' 1, West only ' 2, East+West Generation ' 'lType - 0, MWa ' 1, 10-hour Sustained Peak, MWa ' 2, off-peak, MWa ' 3, on-peak, MWa ' 4, off-peak, MWh, assumes 288 hours (4 weeks) each month, 144 for each half-month period ' 5, off-peak, MWh, assumes 384 hours (4 weeks) each month, 192 for each half-month period ' 'lPeriods - Optional ' 0, 14 periods of hydro year Sept - August, with two periods of August and two for April ' 1, (default), 12 months of hydro year Sept - August '============================================================================================== 'Returns: ' A variant containing an array of period Hydrogeneration (MWa) for east-side or ' west-side generation, or both. Entry 0 is September generation, and if ' lPeriods = 0, entry 11 is August generation, else entry 13 is Aug ' Hydrogeneration

Northwest Power Planning Council 59 Hydrogeneration To call as random hydro condition generator: = vfuncHydroGen(Rand(), 2, 0) This would produce an array of 12 months of data, MWa, for total system generation Hydrogeneration

Northwest Power Planning Council 60 Hydrogeneration Function sfuncYear(ByVal lYear As Long, ByVal lType As Long) As Single 'Takes a calendar year, e.g., 1937, and returns a real single with a value in the 'middle of the correct "bin" for that year, for use as input to vfuncHydroGen. 'For example, 1937 is the second lowest year for Eastside Hydro, in terms of 'annual energy and is therefore the second entry in vfuncHydroGen(*,0). Then 'sfuncYear(1937,0) = 1.5 (The first bin is [0,1), the second is [1,2), etc. 'lType - 0, East Generation only ' 1, West Generation only ' 2, East+West Generation

Northwest Power Planning Council 61 Hydrogeneration Emphasize –4-week convention for lType options 4 and 5 of vfuncHydroGen Demonstrate –..\..\..\Hydro General\HydroGen AddIn\HydroAddIn.xls..\..\..\Hydro General\HydroGen AddIn\HydroAddIn.xls Hydrogeneration

Northwest Power Planning Council 62 Revised Agenda Approval of the Oct 24 meeting minutes Review and questions from the last meeting –Representation of dispatchable resources in the portfolio model –Metrics Representations in the portfolio model –Price responsive demand –Renewables and conservation Hydro Loads Natural gas prices

Northwest Power Planning Council 63 Loads Non-DSI Loads –Calibrate with data from NWPP –Short-term uncertainty driven by random temperatures (HELM) –Long term uncertainty from Terry Morlan’s work DSI Loads –Terry Morlan’s aluminum industry model Loads

Northwest Power Planning Council 64 Loads Non-DSI Loads –Develop monthly on- and off-peak energy values from an hourly model –Calibrated to most recent NPPC forecasts –Access to function to permit coordination with hydro condition Loads

Northwest Power Planning Council 65 HELM’s Load Loads

Northwest Power Planning Council 66 HELM’s Load LSL Hours of the day MW -10 to to to to to to to 110 Loads

Northwest Power Planning Council 67 HELM’s Load Loads

Northwest Power Planning Council 68 HELM’s Load Loads

Northwest Power Planning Council 69 HELM’s Load LSL Hour in Day MW -10 to to to to to to to 110 Loads

Northwest Power Planning Council 70 Non-DSI Loads Short-term uncertainty: Use 50-year record of daily temperatures to create estimates of on- and off-peak loads by month. Draw randomly. Long-term uncertainty: Make the long-term uncertainty consistent with Terry Morlan’s estimates Loads

Northwest Power Planning Council 71 Non-DSI Loads Non-DSI Loads 97.5%

Northwest Power Planning Council 72 DSI Loads Terry Morlan’s model Inspired by Robin Adams, Resource Strategies, CRU Group Loads

Northwest Power Planning Council 73 DSI Loads Loads

Northwest Power Planning Council 74 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 Planning Council 75 DSI Loads Loads

Northwest Power Planning Council 76 DSI Loads Loads

Northwest Power Planning Council 77 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 Planning Council 78 DSI Loads Model DSI load as a function of electricity prices and aluminum prices. Represents monthly response. Would stay down for several months and take several months to bring back on-line. Has value as a exchange option or spread option. Loads

Northwest Power Planning Council 79 Revised Agenda Approval of the Oct 24 meeting minutes Review and questions from the last meeting –Representation of dispatchable resources in the portfolio model –Metrics Representations in the portfolio model –Price responsive demand –Renewables and conservation Hydro Loads Natural gas prices

Northwest Power Planning Council 80 Natural Gas Prices Data from Gas Daily Statistics? –Historical Dailies –Price processes –Distributions within the month, year –Future uncertainties (Terry) –Reasons for variation over time –Correlation with electricity, load, temperature, aluminum prices, hydro Natural Gas Prices

Northwest Power Planning Council 81 Natural Gas Prices 1. Mean Reversion - Vasicek Model P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*sqrt(dt)*N(0,1) 2. Mean reversion - CIR Model P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*Sqrt(P(t))*sqrt(dt)*N(0,1) 3. Geometric Brownian Motion - GBM P(t+dt) - P(t) = Drift*P(t)*dt + Sigma*P(t)*sqrt(dt)*N(0,1) 4. Mean reversion - unrestricted P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*P(t)^Gamma*sqrt(dt)*N(0,1) 5. Jump-diffusion (Use the same time step for estimation and simulation - h doesn't scale!!) P(t+dt) = P(t)exp( Drift*dt + Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j)) Y=1 with probability h and Y=0 with probability (1-h) 6. Brennan and Schwartz Model P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*P(t)*sqrt(dt)*N(0,1) 7. Mean reversion with jump-diffusion, Vasicek type diffusion P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j) Y=1 with probability h and Y=0 with probability (1-h) Natural Gas Prices

Northwest Power Planning Council 82 Natural Gas Prices 8. Mean reversion with jump-diffusion, CIR type diffusion P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + P(t)^0.5*(Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j)) Y=1 with probability h and Y=0 with probability (1-h) 9. Mean reversion with jump-diffusion, Brennan-Shcwartz type diffusion P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + P(t)*(Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j)) Y=1 with probability h and Y=0 with probability (1-h) 10. Mean reversion with jump-diffusion, "Unrestricted" type diffusion P(t+dt) - P(t) = Beta*(Alpha - P(t))*dt + P(t)^gamma*(Sigma*sqrt(dt)*N(0,1)+Y*N(Drift_j,Sigma_j)) Y=1 with probability h and Y=0 with probability (1-h) Natural Gas Prices

Northwest Power Planning Council 83 Next Meeting Natural Gas Prices Electricity Statistics –Historical Dailies –Price processes –Distributions within the month, year –Reasons for variation over time –Correlation among electricity, load, temperature, aluminum prices, hydro, natural gas prices

Northwest Power Planning Council 84 Almost there... Then the B-S formula for the value the plant is Representations - thermal with the variance of playing the role of

Northwest Power Planning Council 85 The payoff The B.S. formula for the capacity factor the plant is Representations - thermal

Northwest Power Planning Council 86 European spread option The Margrabe pricing formula for the value of a spread option, assuming no yields Representations - thermal