外文翻译分析投标商远期合同的投标策略.docx
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外文翻译分析投标商远期合同的投标策略.docx
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外文翻译分析投标商远期合同的投标策略
Analysisofequilibriumaboutbiddingstrategyofsuppliers
withfuturecontracts
ZhiqiangYuan*,DongLiu,ChuanwenJiang
ElectricPowerSchool,ShanghaiJiaoTongUniversity,Shanghai200030,PRChina
Received6May2005;accepted9August2006
Availableonline2October2006
Abstract
Inthispaper,thesupplyfunctionmodelisemployedtosimulatethebiddingstrategyofsuppliersinthepowerpool,andmodelsofthesupplyfunctionwithfuturecontractsarepresented.Itisprovedthatonlyoneoftheparametersbetweenslopeandinterceptofthebiddingcurveisanindependentvariableinordertoachievedefiniteequilibrium.Inthemeantime,theequilibriaofthebiddingstrategyaboutsuppliersarestudiedwhendifferentinterceptsofthebiddingcurvearechosen.SomeexamplesareemployedtostudytheNashequilibriumstrategiesofsupplierswithdifferentfuturecontractsinvariousbiddingstrategymodels.Theresultsshowthattheequilibriaaredifferentindifferentbiddingstrategymodels,butthefuturecontractscaneffectivelymakespotpricesdecreaseinallthemodels.
1.Introduction
Theelectricpowerindustryworldwideisexperiencingunprecedentedrestructuringfromthetraditionalintegratedregulationmonopolytoacompetitivepowermarket.Theobjectofderegulationistointroduceacompetitionmechanismintothepowermarketandprovideincentivesforefficientoperationofthepowerindustry,eventuallyreducingthemarketprice.Theidealmarketisaperfectcompetitivemarketinwhichparticipantsbidtheirmarginalcostintothemarket.Consequently,themarketpriceislowinthiskindofmarket.However,theelectricitymarketisdifferentfromothermerchandisemarkets.Inthepowermarket,onlyafewsupplierscanprovidepowerservicesinsomegeographicregion.Thisisduetotherestrictionofsomefactors,suchaslargeinvestmentscale,smalldemandelasticity,transmissionconstraintsandnolargelystorableelectricity.Consequently,theactualpowermarketismoreclosetoanoligopolisticmarketinwhichthesupplierscanachievemaximumprofitthroughstrategicbidding.Thatmeansthatthegenerationcompaniespossessmarketpower,whichisharmfultotheoperationofthepowersystem
andwillmakeelectricitypricefarhigherthanthemarginalcostofthepowermarket.OnefamousexampleistheelectricitycrisisofCaliforniaofAmericainthesummer2000,whichmadetheelectricitypricefarabovecompetitivelevels.So,itismeaningfultostudythebiddingstrategyofsuppliers.
Generallyspeaking,therearebasicallythreewaysforasuppliertodevelopanoptimalbiddingstrategy[1].Thefirstonereliesonestimationofthemarketclearingprice(MCP)inthenexttradingperiod,thesecondoneisbasedonestimationofthebiddingbehaviorofrivalparticipantsandthethirdoneisgametheorybased.ThemodelsofbiddingstrategyofsuppliersbasedongametheoryusedinthepowermarketaremainlyCournot,Bertrandandthesupplyfunctionmodel[2].Amongthesemodels,boththeCournotandsupplyfunctionmodelsarewidelystudied.
ProbabilitytheoryisemployedtostudythebiddingstrategyofsuppliersbasedonthesupplyfunctionmodelinRefs.[3,4],wherethebiddingcoefficientsofrivalparticipantsareassumedtoobeyajointnormaldistribution.InRef.[5],aconjecturedsupplyfunctionisutilizedtosimulatethebiddingstrategyofsuppliers.InRef.[6],asupplyfunctionmodelwhoseslopeandinterceptofthebiddingcurvevarywiththesamescaleisemployedtoanalyzethebiddingstrategyofsuppliers,wheretheinfluenceofcontractsfordifferenceCFDs[7](CFDsmeansthatifthespotpricerisesabovethestrikeprice,whichisthepricelevelat
whichthecontractcanbecalled,supplierscompensateretailersforthedifference,butifthespotpricefallsbelowthestrikeprice,thentheretailerscompensatesuppliersforthedifference)onmarketequilibriumisconsidered.InRef.[8],theconceptofvirtualrivalandthemethodofparameterestimationareintroducedtostudythebiddingstrategyofsuppliersbasedongametheory,wheretheslopeandinterceptofthebiddingcurveisalsoassumedtovarywiththesamescale.
Forwardcontractsareoneoftheefficientmeansforriskmanagement,anditisappliedinthepowermarketofmanycountries.Thepowerpoolwillplantheelectricityofsuppliersaccordingtothemarketrules,thebiddingpriceofsuppliersandforwardcontractswhilethereareforward
contractsbetweensuppliersandbuyers.Thebiddingstrategyofsupplierswillvarywiththeforwardcontractstoachievemaximumprofit.Inthispaper,asupplyfunctionmodelisusedtosimulatethebiddingstrategyofsuppliersinapowerpool.Firstly,asupplyfunctionmodelwithforward
contractsispresented.Accordingly,itisprovedthatonlyoneoftheparametersbetweentheslopeandinterceptofthebiddingcurvecanbestrategyvariableinordertoachievedefiniteequilibrium(theNashequilibriumisastrategyprofileinwhicheachplayer’spartisasgoodaresponsetowhattheothersaremeanttodoasanyotherstrategyavailabletothatplayer[9]).Secondly,theequilibriaofthemarketarestudiedwhendifferentinterceptsofthebiddingcurvearechosen.Finally,theeffectofdifferentfuturecontractsontheequilibriumstrategiesofsuppliersinvariousbiddingstrategymodelsisanalyzed.Besides,thebiddingstrategiesarealsostudiedwhilegenerationconstraintsareactive.
2.Supplyfunctionequilibriummodelwithforwardcontracts
Itissupposedthattheinversedemandfunctionisalinearfunction,thatis
(1)
wherepismarketprice,randsaretheinterceptandslopeoftheinversedemandfunction,respectively,
isthegenerationofthesupplieriandNisthenumberofsuppliers.Eq.
(1)canbetransformedintotheelectricitydemandfunction,
(2)
,
Thebiddingcurveofthesupplierisassumedasalinearfunction,
(3)
where
and
aretheinterceptandslopeofthebiddingcurve,respectively,bothofwhicharelargerthanzero,andi=1,...,N.
Theelectricitypriceisassumedtoclearattheuniformpriceinthepowerpool,andthen,thegenerationsofthesuppliersarecalculatedaccordingtoEqs.
(2)and(3).
Iftheforwardcontractsis
whilethedealingpriceis
theequilibriumstateofthesupplierscanbeobtainedbymaximizinganindividualprofitfunctionofeachsupplier.
(i=1……N)(4)
Withoutlossofgenerality,thecostfunctionofasupplierisassumedtobeaquadraticfunctionofactivepowergeneration.Thatis:
Then,thegenerationofsupplieriis
Correspondingly,thesystemmarginalpriceis
Ifboththeinterceptandslopeofthebiddingcurvearechosentobeindependentstrategyvariablesbythesupplier,themaximumprofitofsuppliericanbeachievedwhenthefollowingdifferentialequationissatisfied
Eqs.(8)and(9)showthattheinterceptandslopeofthebiddingcurvearenotindependent.The2Nvariables,xiandbi,needtobecalculatedbymeansofNequations,sothereexistsaninfinitenumberofequilibriumstates.Thatmeansonlyoneoftheparametersbetweentheinterceptandslopeofthebiddingcurveisindependentinordertoachieveadefiniteequilibrium.
Iftheslopeofthebiddingcurveischosentobethestrategy
variablebysupplieri,Eqs.(6)–(8)yieldthefollowingoptimalreactionfunctionofsupplieri
isthepointthatthebiddingcurvepassesthrough.
Iftheinterceptofthebiddingcurveischosentobethestrategyvariablebysupplieri,Eqs.(6),(7)and(9)yieldthefollowingoptimalreactionfunctionofsupplieri
TheequilibriumbiddingstrategycanbeobtainedbysolvingEqs.(10)or(11).
Whentheslopeofthebiddingcurveischosentobethestrategyvariablebysupplieri,ifthebiddingcurvepassesthroughthepoint
whichmeansthesupplierIisbiddingitsmarginalcostatgenerationofforwardcontracts,thebiddingcurveis
Then,thegenerationofsupplieriis
Correspondingly,thesystemmarginalpriceis
AccordingtodifferentialequationsakintoEq.(8),thefollowingoptimalreactionfunctionofsupplieriexists,
Eq.(15)showsthatthestrategyvariable
isindependentoftheforwardcontractsifthebiddingcurvepassesthroughpoint
.
3Theequilibriumofsupplyfunctionmodelwithgenerationconstraints
Generationconstraintshavenotbeenconsideredintheoptimalreactionfunctionofthemodelsmentionedabove.Whengenerationconstraintsareconsidered,ifthegenerationofsuppliericalculatedfromEqs.(10),(11)or(15)isabovetheupperlimitofgenerationofsupplieri,hisgenerationwillbesettothelimitedvalue.Ifthemarketpricecalculatedfromtheoptimalreactionfunctionofthesuppliersislowandthecalculatedgenerationisbelowtheminimumgenerationofsupplieri,itispossiblethattheprofitofsupplieriisnegative.Asaresult,supplieriwillbuyelectricityfromthespotmarkettomeettheforwardcontractsandmaximizeitsownprofit.Thenecessaryconditionofsuppliertogenerateelectricityis
where
isthemarketpricewithoutsuppliersIfinequality(16)ismet,let
=
otherwise,let
=0.
Ifthereexistsupplierswhosegenerationconstraintsareactive,thensupplierswhosegenerationconstraintsarenotactivewillbefacedwiththefollowingresidualdemandfunction:
whereM–LandN–Marethenumbersofsupplierswhosegenerationisovermaximumandunderminimumgeneration,respectively.
and
arethemaximumandminimumgenerationsofsupplieri,respectively.
ThegenerationsofsupplierswhosegenerationconstraintsarenotactivearecalculatedbyusingEqs.(17),(10),(11)or(15)again.Iftherestillexists
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