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Systems Analysis Advisory Committee (SAAC) Friday, November 22, 2002 Michael Schilmoeller John Fazio 1 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 2 Northwest Power Planning Council Outcomes and Milestones 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 3 Northwest Power Planning Council Revised Agenda • Approval of the Oct 24 meeting minutes • Review and questions from the last meeting – Representation of dispatchable resources in the portfolio model – Metrics • Representations in the portfolio model – Price responsive demand – Renewables and conservation • Hydro • Loads • Natural gas prices 4 Northwest Power Planning Council 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 5 Northwest Power Planning Council Review 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 ** 6 Northwest Power Planning Council Review 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 7 Northwest Power Planning Council Review 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 8 Northwest Power Planning Council Review 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 9 Northwest Power Planning Council Review 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 10 Northwest Power Planning Council Review 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 40 35 30 Market Price $/MWh 25 20 V C max0, pe (h) p g (h) max0, p (h) p ( h) 15 hH e g 10 CN H hH 5 NH or V CN H E[max0, pe (h) p g (h) ] 0 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 where Hour N H is the number of hours in the period (672) 11 E is the expectation operator Northwest Power Planning Council Review Variability viewed as CDF • Turning the MCD curve on its side, we get something that looks like a cumulative probability density function (CDF) Cumulative Frequency Value V is this area 100% 600 90% 80% Count of hours Capacity Factor 500 70% 400 60% 50% Pg 300 40% V NH f ( p ) dp e e 200 100 30% 20% (Fund Thm of Calculus) 0 10% 0% dV N H f ( pe ) 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 dpe $/MWh where f ( pe ) is the value of the CDF or the capacity factor 12 Northwest Power Planning Council Review 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, ( h) z e ( h) e ( h) z g ( h) g ( h) which by our independence assumption implies 2 ( z ( h ) 2 z ( h ) 2 2 z , z z ( h ) z e g e g e g (h) ) ( 2 , ) 2 2 e g e g e g 13 Northwest Power Planning Council Review Hourly Dispatch • Try dispatching against a lognormally distributed set of prices, with 1000 observations. 24.07 27.96 1 =IF(RC[-2]>RC[-3],1,0) 23.66 30.62 1 33.26 43.25 1 40.18 184.25 1 31.90 28.19 0 • Maximum 36.91 54.79 1 20.06 110.83 1 discrepancy over prices and averages 30.67 67.64 0.885542 volatilities, about 0.92182047 spread option 5% 14 Northwest Power Planning Council Review Representation of dispatchables 1999 Daily Prices MC and Sumas 80.00 3.00 70.00 2.50 60.00 2.00 50.00 On-peak MC $ Nominal Off-Peak MC 40.00 1.50 Average MC 30.00 Natural Gas 1.00 20.00 0.50 10.00 0.00 0.00 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 361 1 15 Northwest Power Planning Council Review Representation of dispatchables 5 ln(nominal price-$) 4 Natural Gas 3 On-Peak MC 2 Off-Peak MC Average MC 1 0 1 35 69 103 137 171 205 239 273 307 341 Days 16 Northwest Power Planning Council Review Representation of dispatchables Average (Flat) MC 60 20 50 15 ln(price) 40 30 10 20 5 10 0 0 1 3 5 7 9 11 13 15 17 19 17 Northwest Power Planning Council Review Representation of dispatchables Sumas Gas 60 40 50 30 40 30 20 20 10 10 0 0 11 13 15 17 19 1 3 5 7 9 18 Northwest Power Planning Council Review Representation of dispatchables De-Trended Sumas Gas Prices 60 4.5 4 50 3.5 40 3 ln(price) 2.5 30 2 20 1.5 1 10 0.5 0 0 1 3 5 7 9 11 13 15 17 19 21 19 Northwest Power Planning Council Review Representation of dispatchables • Beaver – 9000 BTU/kWh – $4.00/MWh for VOM, variable fuel transportation – Did not incorporate forced outage estimate, maintenance – Assumed 500MW capacity – “Hourly” dispatch was on daily on- and off-peak only (would understate volatility) 20 Northwest Power Planning Council Review Representation of dispatchables Comparison of techniques 120.0% 100.0% Dispatch factor 80.0% Hourly 60.0% Spread Actual 40.0% 20.0% 0.0% 1 2 3 4 5 6 7 8 9 10 11 12 Month 21 Northwest Power Planning Council Review Representation of dispatchables • To show: The main driver of value is not expected variation in price, it is uncertainty • What is the 1 sigma in daily (hourly?) electricity and gas prices over the next several years? 22 Northwest Power Planning Council Review Representation of dispatchables • Oil 35 ? price 30 forecast 25 20 History Low 15 Medlo Medium Medhi 10 High ? EIA02-R 5 EIA02-H EIA902-L 8 Others 0 1990 1995 2000 2005 2010 2015 2020 23 Northwest Power Planning Council Review Representation of dispatchables • NG 4.5 ? price 4 forecast 3.5 History 3 Low 2000$/MMBtu Medlo 2.5 Medium Medhi 2 High EIA-Ref 1.5 ? EIA-Low EIA-High 1 DRI-WEFA GRI 0.5 CEC ICF 0 1995 2000 2005 2010 2015 2020 2025 24 Northwest Power Planning Council Review Mid-Columbia price forecast Average annual w/comparisons ? $55 $50 $45 Price (2000$/MWh) $40 $35 $30 $25 Current Trends Hi Shape (092702) $20 ? $15 5th Plan corrected transfer (062402). $10 Adequacy & Reliability Study (Feb 2000) $5 $0 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 25 Northwest Power Planning Council Review Uncertainty Dominates Addition of uncorrelated Error in approx z by max(x,y) volatilities 45.0% 12 z2=x2+y2 40.0% 10 35.0% (z-max(x,y))/z Relative error 30.0% 8 25.0% Z 6 20.0% z Uncertainty 15.0% 4 x 10.0% 2 5.0% 0.0% 0 0 1 2 3 4 5 6 7 8 9 10 y=1 X error Value of z Expected variation 26 Northwest Power Planning Council Review Uncertainty Dominates • Beaver Value, assuming change in volatility due to uncertainty same expected fuel and electricity price, correlation volatility CF Value volatility CF Value Jan 18.3% 13.3% 84569 105.6% 63.3% 2062640 Feb 17.0% 23.2% 146865 108.7% 66.8% 2135302 Mar 18.8% 14.7% 81952 103.4% 62.7% 1819113 Apr 36.8% 49.8% 1065049 105.7% 70.1% 2951938 May 37.3% 55.0% 1390094 117.0% 73.3% 3778254 Jun 69.4% 36.0% 1113231 110.2% 62.4% 2082887 Jul 37.1% 43.1% 929229 113.2% 69.6% 3127952 Aug 39.3% 49.9% 1408176 109.2% 70.7% 3754281 Sep 21.9% 85.6% 2167144 111.7% 77.1% 5141926 Oct 19.2% 100.0% 5536028 119.3% 83.2% 8873424 Nov 43.9% 80.0% 2834708 125.5% 78.9% 5467271 Dec 21.9% 49.3% 758491 112.4% 71.2% 3757433 average 56.9% 72.2% total 17,515,537 44,952,421 27 Northwest Power Planning Council Review Uncertainty Dominates Comparison of dispatch factors 120.0% 100.0% Dispatch factor 80.0% 60.0% 40.0% 20.0% 0.0% 1 2 3 4 5 6 7 8 9 10 11 12 Month Spread with future uncertainty Spread with 1999 prices 28 Northwest Power Planning Council Review Uncertainty Dominates Value of Beaver 10,000,000 9,000,000 8,000,000 Dollars, nominal 7,000,000 6,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Beaver value with uncertainty Beaver value with 1999 prices 29 Northwest Power Planning Council Review Makes sense • CF may or may not increase with volatility European Call Option European Call Option 12 12 10 10 Value of Option ($) Value of Option ($) 8 8 6 6 4 4 2 2 0 0 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Price of underlying Price of underlying 30 Northwest Power Planning Council Review Makes sense • Value increases with volatility European Call Option European Call Option 12 12 10 10 Value of Option ($) Value of Option ($) 8 8 6 6 4 4 2 2 0 0 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Price of underlying Price of underlying 31 Northwest Power Planning Council Review Makes sense • Value increases with volatility n n 1 Cumulative Frequency Single, fixed hour ( x x) P( x i 1 i i X ) ( xi x) i 1 n E ( xi x ) E ( xi ) x 1 A But 1 Prob of price 0.8 n exceeding p 0.6 i 1 ( xi x) A B n 0.4 so E ( xi ) x A B 0.2 B In particular, 0 40.00 38.00 36.00 34.00 32.00 30.00 28.00 26.00 24.00 22.00 20.00 A E (max(0, xi x)) $/MWh 32 Northwest Power Planning Council Review 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 33 Northwest Power Planning Council Review 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 34 Northwest Power Planning Council 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 35 Northwest Power Planning Council Representations Price responsive demand • Baseload 32000MW, Base price $25/MWh, Short-run elasticity is -0.05 Energy Price Increm. (Wholesale) Reduct. $/MWh MW 100 1433 300 1426 600 937 800 389 1600 927 4000 1192 36 Northwest Power Planning Council Representations Price responsive demand • Side observation: Stack Model Much of the value of PRD is driven by Curtailment block 2 peak prices. The Curtailment block 1 price of electricity in Peaker 3 the portfolio model is Peaker 2 Load Curve Peaker 1 subjective, but so are Price responsive demand A B C D E F curtailment block CCCT 2 prices in our other CCCT 1 models. At right, the value of PRD is Coal 2 determined by those Coal 1 prices, the marginal costs in hour segments A and B. Hydro Hours 37 Northwest Power Planning Council Representations Conservation & Renewables • Represent as non-dispatchable energy • Supply curve for conservation developed by Tom Eckman • Renewables cost and operating characteristics assembled by Jeff King 38 Northwest Power Planning Council Representations 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. 39 Northwest Power Planning Council Representations 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. 40 Northwest Power Planning Council Representations 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) 41 Northwest Power Planning Council Representations Benefits ($) 0 200000 400000 600000 800000 1000000 Sep-03 Sep-04 Sep-05 Sep-06 Sep-07 Sep-08 Sep-09 Northwest Power Planning Council Sep-10 Sep-11 benefit Sep-12 Sep-13 Sep-14 date price Sep-15 Timed case Sep-16 Sep-17 Sep-18 Sep-19 capacity Sep-20 Sep-21 Sep-22 Sep-23 Sep-24 Sep-25 0 100 200 300 400 500 600 Representations Capacity Installed 42 (MWa cum) SOD Analysis SOD Analysis Dispatchable Conservation Supply Curve 1,400 1,200 Resource Potential (aMW) 1,000 800 600 400 200 - $- $10.0 $20.0 $30.0 $40.0 $50.0 $60.0 $70.0 $80.0 $90.0 $100. 0 0 0 0 0 0 0 0 0 00 Levelized Cost (2000$/aMW) 43 Northwest Power Planning Council Representations 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. 44 Northwest Power Planning Council Representations 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). 45 Northwest Power Planning Council Representations 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 46 Northwest Power Planning Council Representations NPPC Analysis construction phase wholesale electricity market optional cancellation period expected price trend price threshold evalulation phase time 47 Northwest Power Planning Council Representations NPPC Analysis • Implement in Portfolio Model – Evaluation period (rolling average prices over the last 18 months?) – Cancellation period – Construction period – Ramp rate constraint 48 Northwest Power Planning Council Representations NPPC Analysis • Real Options – Opportunity to defer, expand, abandon according to changing circumstances – Staging benefits – Switching fuel supplies 49 Northwest Power Planning Council Representations NPPC Analysis • Broad Application of real options to the Electric Power Industry – Renewables • Mark Bolinger, Ryan Wiser and William Golove, “QUANTIFYING THE VALUE THAT WIND POWER PROVIDES AS A HEDGE AGAINST VOLATILE NATURAL GAS PRICES,” Proceedings of WINDPOWER 2002, June 2-5, 2002, Portland, Oregon • http://eetd.lbl.gov/EA/EMP/ – Coal • Y. SMEERS, CORE and L.BOLLE , O. SQUILBIN, “COAL OPTIONS, Evaluation of coal-based power generation in an uncertain context,” Final report, September 2001, OSTC - Global Change and Sustainable Development 1996-2000, Belgium Federal Office for Scientific,Technical and Cultural Affairs • http://www.belspo.be/belspo/ostc/geninfo/publ/pub_ostc/CG2131/rC G23_uk.pdf 50 Northwest Power Planning Council Representations NPPC Analysis • Broad Application of real options to the Electric Power Industry – R&D expenditures • Graham A. Davis, Brandon Owens, “Optimizing the Level of Renewable Electric R&D Expenditures Using Real Options Analysis,” National Renewable Energy Laboratory,Golden, CO 80401 December 18, 2001 – Distribution Systems • Costing Methodology for Electric Distribution System Planning November 9, 2000 Prepared for: The Energy Foundation Prepared by: Energy & Environmental Economics, Inc. Karl E. Knapp, Jennifer Martin, Snuller Price, And Pacific Energy Associates Frederick M. Gordon • http://www.energyfoundation.org/documents/CostMethod.pdf 51 Northwest Power Planning Council Representations 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 52 Northwest Power Planning Council Representations 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 53 Northwest Power Planning Council Representations 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? 54 Northwest Power Planning Council Representations 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 55 Northwest Power Planning Council 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 56 Northwest Power Planning Council Hydrogeneration Hydrogeneration NW Sustained Peak - September 25000 Sustained Peak (MW) 22000 19000 16000 13000 2-hr 4-hr 10-hr 10000 8600 8800 9000 9200 9400 9600 9800 10000 Energy (MW-period) 57 Northwest Power Planning Council Hydrogeneration Hydrogeneration • Function vfuncHydroGen(ByVal sYear As Single, ByVal lLoc As Long, ByVal lType As Long, Optional ByVal lPeriods As Long = 1) As Variant • 'Takes: • 'sYear - single [0.00-50.00] representing the years 1929-1978, sorted ascending by annual energy. • ' By passing 50*Rand() as sYear to this function, this permits random draws • ' of hydro condition. Ascending order permits user to correlate annual energy with • ' other variable. To access a particular year, use the sfuncYear() function, below. • ' • 'lLoc - 0, East only • ' 1, West only • ' 2, East+West Generation • ' • 'lType - 0, MWa • ' 1, 10-hour Sustained Peak, MWa • ' 2, off-peak, MWa • ' 3, on-peak, MWa • ' 4, off-peak, MWh, assumes 288 hours (4 weeks) each month, 144 for each half-month period • ' 5, off-peak, MWh, assumes 384 hours (4 weeks) each month, 192 for each half-month period • ' • 'lPeriods - Optional • ' 0, 14 periods of hydro year Sept - August, with two periods of August and two for April • ' 1, (default), 12 months of hydro year Sept - August • '============================================================================================== • 'Returns: • ' A variant containing an array of period Hydrogeneration (MWa) for east-side or • ' west-side generation, or both. Entry 0 is September generation, and if • ' lPeriods = 0, entry 11 is August generation, else entry 13 is Aug 15-31 58 • ' Northwest Power Planning Council Hydrogeneration 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 59 Northwest Power Planning Council Hydrogeneration Hydrogeneration • Function sfuncYear(ByVal lYear As Long, ByVal lType As Long) As Single • 'Takes a calendar year, e.g., 1937, and returns a real single with a value in the • 'middle of the correct "bin" for that year, for use as input to vfuncHydroGen. • 'For example, 1937 is the second lowest year for Eastside Hydro, in terms of • 'annual energy and is therefore the second entry in vfuncHydroGen(*,0). Then • 'sfuncYear(1937,0) = 1.5 (The first bin is [0,1), the second is [1,2), etc. • 'lType - 0, East Generation only • ' 1, West Generation only • ' 2, East+West Generation 60 Northwest Power Planning Council Hydrogenerat Hydrogeneration • Emphasize – 4-week convention for lType options 4 and 5 of vfuncHydroGen • Demonstrate – ..\..\..\Hydro General\HydroGen AddIn\HydroAddIn.xls 61 Northwest Power Planning Council Hydrogeneration 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 62 Northwest Power Planning Council 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 63 Northwest Power Planning Council Loads 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 64 Northwest Power Planning Council Loads HELM’s Load Weather Response Functions 1000000 900000 800000 700000 600000 WRF 1 MWh/Day WRF 2 500000 WRF 3 400000 WRF 4 300000 200000 100000 0 0 10 20 30 40 50 60 70 80 90 100 110 Dry-Bulb Temperature (F) 65 Northwest Power Planning Council Loads HELM’s Load LSL 1 35000 30000 -10 to 38 25000 38 to 45 20000 45 to 52 MW 52 to 57 15000 57 to 61 61 to 64 10000 64 to 110 5000 0 10 11 12 13 15 16 18 19 21 22 23 14 17 20 24 1 2 5 8 9 3 4 6 7 Hours of the day 66 Northwest Power Planning Council Loads HELM’s Load LSL 2 35000 30000 25000 -10 to 38 38 to 45 20000 45 to 52 MW 52 to 57 15000 57 to 61 61 to 64 10000 64 to 110 5000 0 13 15 19 17 21 23 1 3 7 9 5 11 Hours of Day 67 Northwest Power Planning Council Loads HELM’s Load LSL 3 35000 30000 25000 -10 to 38 38 to 45 20000 MW 45 to 52 52 to 57 15000 57 to 61 61 to 64 10000 64 to 110 5000 0 13 15 17 19 21 23 11 5 9 1 3 7 Hour in Day 68 Northwest Power Planning Council Loads HELM’s Load LSL 4 30000 25000 -10 to 38 20000 38 to 45 45 to 52 MW 15000 52 to 57 57 to 61 10000 61 to 64 64 to 110 5000 0 1 3 9 5 7 23 11 13 15 19 21 17 Hour in Day 69 Northwest Power Planning Council Loads 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 70 Northwest Power Planning Council Loads Non-DSI Loads Total Sales Non-DSI 45000 40000 97.5% 35000 Average Megawatts 30000 25000 20000 97.5% 15000 10000 81 84 87 90 93 96 99 02 05 08 11 14 17 20 23 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 71 Northwest Power Planning Council Loads DSI Loads • Terry Morlan’s model • Inspired by Robin Adams, Resource Strategies, CRU Group 72 Northwest Power Planning Council Loads DSI Loads LME Cash Aluminum Prices: Daily 1989-2002 $3,500 $3,250 Cash 15-Month $3,000 Real Cash $2,750 Linear (Real Cash) US$/Tonne $2,500 $2,250 $2,000 $1,750 $0.80 $0.70 $1,500 $1,250 $1,000 89 90 91 92 93 94 95 96 97 98 99 00 01 02 19 19 19 19 19 19 19 19 19 19 19 20 20 20 73 Northwest Power Planning Council Loads DSI Loads Aluminum Price 1550 • Compute break-even price Premium Rate BPA Rate 0.03 23 for each of nine PNW BPA Allocation 100 aluminum plants Mwh/Tonne 13.199 Plant A • Assume plant will leave the (modern prebake) Potential Demand 457 system if the spread Cost Components between aluminum prices Alumina 403 Carbon 90 and electricity cost Labor/Other 400 Sustaining Capital 80 component gets too small • Examine the impact of 100 Electricity Cost Max 623.5 MW allocation of BPA Electricity Price Max 47.24 power at various prices Electricity Price $30 Demand @ Price 457 74 Northwest Power Planning Council Loads DSI Loads Viable Smelter Loads 3500 3000 $/Mw 2500 20 Aluminum Price 25 2000 28 30 1500 32 35 1000 40 500 0 00 50 00 50 00 50 00 50 00 50 00 50 00 11 11 12 12 13 13 14 14 15 15 16 16 17 Electricity Use 75 Northwest Power Planning Council Loads DSI Loads Viable Smelter Loads (No BPA Allocation) 3500 3000 $/Mw 20 2500 Electricity Use 25 2000 28 30 1500 32 35 1000 40 500 0 50 50 50 50 50 50 50 50 50 50 50 50 50 10 11 12 13 14 15 16 17 18 19 20 21 22 Aluminum Price 76 Northwest Power Planning Council Loads wholesale electricity market DSI Loads minimum restart period minimum shut-down period evalulation phase aluminum-elec price spread expected price trend evalulation phase time 77 Northwest Power Planning Council Loads 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. 78 Northwest Power Planning Council Loads 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 79 Northwest Power Planning Council 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 80 Northwest Power Planning Council Natural Gas Prices 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) 81 Northwest Power Planning Council Natural Gas Prices 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) 82 Northwest Power Planning Council Natural Gas Prices 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 83 Northwest Power Planning Council Almost there... • Then the B-S formula for the value the plant is V pN (d1 ) XN (d 2 ) where N is the CDF for a N (0,1) random variable is standard deviation of ln(p/~) p d1 ln( p / X ) T 2 / 2 d 2 d1 T with the variance of e (h) ze (h) e (h) playing the role of 2 T 84 Northwest Power Planning Council Representations - thermal The payoff • The B.S. formula for the capacity factor the plant is V f N (d1 ) p where d1 ln( p / X ) T 2 / 2 ln( pe / p g ) ( ze e ) / 2 2 2 85 Northwest Power Planning Council Representations - thermal European spread option • The Margrabe pricing formula for the value of a spread option, assuming no yields V p2 N (d1 ) p1 N (d 2 ) where ln( p2 / p1 ) 2T / 2 d1 T d 2 d1 T 2 12 2 2 2 1, 2 1 2 86 Northwest Power Planning Council Representations - thermal

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