Long-term Hydro Scheduling based on Stochastic Mod

Long-termHydroSchedulingbasedonStochasticModelsEPSOM’98,Zurich,September23-25,1998PagePEREIRA-1Long-termHydroSchedulingbasedonStochasticModelsMarioPereiraNoraCampodónicoRafaelKelmanPowerSystemsResearchInc.,PSRIRiodeJaneiro,[e-mail],[e-mail],[e-mail]:Thispaperdescribessomemethodologiesandtoolsbeingdevelopedtoaddressthenewchallenges-andopportunities-posedbypowersectorrestructuringinhydrothermalsystems:(a)optimalstochasticdispatchofmultiplereservoirsystems;(b)jointrepresentationofequipmentoutageandinflowuncertainty;(c)distortionofshort-runmarginalcostssignalswhenappliedtocascadedplantswithdifferentowners;(d)economicefficiencyandmarketpowerissuesinbid-basedhydrothermaldispatch.TheissuesareillustratedwithcasestudiestakenfromtheColombiansystem.Keywords:HydrothermalScheduling,StochasticOptimization,ProbabilisticProductionCosting,MarketPower,DecentralizedDispatch.1IntroductionElectricutilitiesallovertheworldhavebeenundergoingradicalchangesintheirmarketandregulatorystructure.Abasictrendinthisrestructuringprocesshasbeenthereplacementoftraditionalexpansionplanningandoperationprocedures,basedoncentralizedoptimization,bymarket-orientedapproaches:•Generatorsbidpricesfortheirenergyproduction(typicallyonanhourlybasisforthenextday)inaWholesaleEnergyMarket–WEM.Unitsarethenloadedbyincreasingpriceuntildemandismet.Dispatchedgeneratorsareremuneratedonthebasisofthesystemspotprice,whichcorrespondstotheofferofthemostexpensiveloadedunit.•Insteadoffollowinganexpansionscheduleproducedbyacentralplanningagency,privateagentsarefreetodecideontheconstructionofgeneratingunitsandtocompeteforenergysalescontractswithutilitiesandindividualcustomers.OneofthekeycomponentsintheprivateinvestmentdecisionistheforecastofWEMspotrevenuesforeachplant,whicharethencomparedwiththeplantconstructioncost.Accordingtoitsproponents,oneoftheconceptuallyattractiveaspectsofthespotpricingschemeisthat,underperfectcompetition,itprovidesefficienteconomicsignalsforsystemexpansion,i.e.ifthesystemisoptimallydimensioned,thespot-basedremunerationwillmatchinvestmentcostsplusoperatingexpenses[1].Forsimilarreasons,ithasalsobeenarguedthatthebiddingschemeinducesanefficientuseofsystemresourcesinsystemdispatch.However,thetheoreticalandpracticalvalidationoftheaboveclaimswasprimarilybasedonthermalsystems,andcannotbesimplyextrapolatedtohydrothermalsystems.Theobjectiveofthispaperistodescribesomemethodologiesandtoolsbeingdevelopedtoaddressthenewchallenges-andopportunities-posedbypowersectorrestructuringinhydrothermalsystems.Long-termHydroSchedulingbasedonStochasticModelsEPSOM’98,Zurich,September23-25,1998PagePEREIRA-2Thepaperisorganizedasfollows.Insection2wepresentanoverviewofhydrothermalschedulingconceptsanddiscussthecomputationaldifficultyoffindinganoptimalstrategyforamulti-reservoirsystem,theso-called“curseofdimensionality”.Wethendescribeaclassofsolutionprocedures-stochasticdualdynamicprogramming-whichisabletoalleviatethesecomputationalproblems.Insection3,wediscusstheintegrationofprobabilisticproductioncostingmodelstraditionallyusedinthermalsystemanalysisintoahydrothermalschedulingframework.Insection4,weanalyzethedistortionofeconomicsignalsresultingfromWEMspotpriceswhentherearereservoirsincascade,anddescribeanextendedspotmarketwherebothenergyandwateraretraded.Finally,insection5weaddresseconomicefficiencyandmarketpowerissuesinbid-basedhydrothermaldispatch.2OverviewofHydrothermalScheduling2.1PurelyThermalSystemsCharacteristicsInpurelythermalsystems,theoperatingcostofeachplantdependsbasicallyonitsfuelcost.Therefore,theschedulingproblemistodeterminetheplantcombinationthatminimizesthetotalfuelcostrequiredtomeetthesystemload.Initssimplestversion,theschedulingproblemisformulatedas:zt=Min∑j=1Jc(j)gt(j)subjectto(2.1)∑j=1Jgt(j)=dt(2.1a)gt≤g_(2.1b)wherezt,c,dt,gtandg_representrespectivelythesystemoperatingcostinstaget,unitoperationcosts,systemload,powerproductionandgenerationcapacities.Inturn,constraints(2.1a)and(2.1b)representrespectivelyloadsupplyandlimitsongenerationcapacity.Thethermalgenerationdispatchproblem(2.1)canbesolvedbyinspection:loadgeneratorsbyincreasingoperatingcostuntildemandismet.Althoughtheactualschedulingproblemismorecomplexduetofactorssuchaslosses,transmissionlimitations,start-upcosts,rampingratesetc.,thepurelythermalschedulingproblemretainssomebasiccharacteristics:•itisdecoupledintime,thatis,anoperatingdecisioninstaget(e.g.thisweek)doesnotaffectnextweek’soperatingdecisions;•generatingunitshaveadirectoperatingcost,i.e.unitcostc(j)doesnotdependontheoutputoftheothersystemplants;besidesthat,plantoperationdoesnotaffectthegenerationcapacityoravailabilityofotherplants;thisprovidesanaturalcoordinationmechanismforenergypurchaseandsaleLong-termHydroSchedulingbasedonStochasticModelsEPSOM’98,Zurich,September23-25,1998PagePEREIRA-32.2HydrothermalSystemCharacteristics2.2.1TimeDependenceHydroplantscanusethe“free”energystoredintheirreservoirstomeetdemand,thusavoidingfuelexpenseswiththermalunits.However,theavailabilityofthishydroenergyislimitedbyreser