电力系统边际发电成本的概率分布函数估计方法英文版Word下载.docx
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1Introduction
WithChina’spowerindustryrestructuring,aunifiedopenelectricitymarketwillbegradually
established.Peoplepaymoreattentiontotheelectricitypricingissues,whichisnowthecoreelementoftheelectricitymarket.Asatraditionalpricingmethod,marginalcostpricingtheoryhasbeenwidelyusedinthepowersystem,wherepowerismoresuitableforreal-timeoperationofthemarketmechanismwasundoubtedlypricingtheory,namelybasedonthepricingtheoryofthepowersystemshort-termmarginalcost.Short-runmarginalcostofelectricitysystemstatisticalestimationmethodsaremostlybasedonthepowersystemprobabilisticproductionsimulationtechnology,references[2]involvesbivariateprobabilitydistribution,thealgorithmistoocomplex;
themethodofreferences[3]isonlyabouttheestimationofmarginalgenerationaveragecost,butitisnotthecompleteprobabilitydistributiondensityfunction.Existingrandomproductionsimulationtechniquesonlyconsidertheunitforcedoutageandtheuncertaintyofloadforecastwithouttakingintoaccounttheuncertaintyoffuelprices.
Thispaperpresentsamethodofsolvingthesystemshort-runmarginalcostofelectricitydistributionandprobabilitydensityfunction.First,giventheconceptofthemarginalgeneratingunitsandtheirprobabilitycalculationformula,fromwhichwecanobtainthemarginalcostofelectricitydistributionandprobabilitydensityfunction,andthewayofcalculatingtheuncertaintyofthefuelprice,andfinallypresentsthedataanalysisandconclusions.oftheadoptionofIEEE-RTS[4].
2Principles
Assumethatthesystemhasapowergenerationunit,,seekinganapproachtocalculationtheDistributionfunctionQs(x)andthedensityfunctionqs(x)attheconditionofbeinggivenloaddemandLinacertainmomentanditsmarginalcostofelectricityprobability(S).
ThefirstapplicationisstochasticsimulationofpowersystemsZ-transformationmethod[5]ortheeffectivecapacityofthecumulativeamountofthedistributionmethod[6],afterthefirstipowerunitsareloaded,thesystemloadLfacedlossofloadprobabilityLOLPi,whereibelongsto{1,2,...,I}forthemosteconomicalloadsequenceofthepowergenerationunit.Bothmethodsusesystemtimingload.Z-transformmethodsuitableforsmallerscalesystemisanaccuratemethodtocalculatethevolume;
cumulativemethodisaapproximationmethod,whichhasafastercalculationspeedandconsidertheuncertaintyofloaddemandforecasting.Itisalsosuitableforthelarge-scalesystemswithgoodaccuracy.ForZ-transformmethodandtheeffectivecapacityofthedistributioncumulativemethod,andthewaysofaddingtotheuncertaintyofloadforecastingisdetailedinthereference[5,6].
2.1Themarginalgeneratingunitofthesystemanditsprobability
Probabilisticmodelofgeneratinguniticanuseitseffectivecapacityxi(randomvariation)torepresent.
xi
withprobability:
1-FORii,withprobability:
FORi0,
FORiistherandomforcedoutagerateoftheuniti;
Ciiscapacityofuniti(MW).
Definition1AsfortheloadLinamoment,ifthesumoftheeffectivecapacityofthefirsti-1unitsislessthanorequaltoL,whilethesumoftheeffectivecapacityofthefirstiunitsisgreaterthanL,thei-thpowerunitcanbecalledthemarginalgeneratingunitofthesystematthattime.
Theorem1AsfortheloadLinamoment,themarginalprobabilitygeneratingunitofthei-thpowerunitmpiis
mpiLOLPi,1,LOLPi,i1,2,...I
mpI,1LOLIP
(1)WhereinLOLPiisthe
lossofsystemloadprobabilityLOLPafterthei-thpowerunitisloaded,firstI+1powerunitisanimaginarypowersupplythatcansupplypowerforthesystem.
Proof:
FromthedefinitionofLOLP,LOLPirepresentstheprobabilityofwhichthesumoftheeffectivecapacityofthefirstiunitsislessthantheloadL,then
LOLPi,1,LOLPiProp(xjL),Prop(xjL)
j1j1i,1i
Prop(xjL),Prop(xjL),1
j1j1i,1i
(2)
Wherethefirstandsecondoftherightsideformulais,respectively,theprobabilitiesofwhichthesumoftheeffectivecapacityofthefirsti-1unitsislessthanorequaltotheloadLandwhichthesumoftheeffectivecapacityofthefirstiunitsislessthantheloadL.Accordingtothetheoryofprobability,sinceatwoeventsmustoccur,theaboveformularepresentstheprobabilityoftwoeventsoccursimultaneously,namelyLOLPi-1-LOLPirepresentstheprobabilitiesthattheloadLis
greaterthanorequaltothesumoftheeffectivecapacityofthepreviousi-1unit,butlessthanthesumoftheeffectivecapacityofthefirstiunits,thatis,whentheloadisL,itindicatestheprobabilitiesofmarginalpowergenerationunitoftheuniti,then
PPi1,2...,ImpiLOLi,1,LOLi,
WhereLOLP0indicatesLOLP,withoutunitsloading,aslongasL&
gt;
0,LOLP0mustbe1.
TherecursiveformulaalsoappliestotheI+1thhypotheticalpower,becauseLOLPI+1equalto0,thenmpI,1equaltoLOLPI.
2.2Theprobabilitydensityanddistributionfunctionofthemarginalcostofgeneratingsystem
Withoutconsideringtheuncertaintyofpowerunitfuelprice,namelyoperatingcostsofeverypowergenerationunitisaconstant.Becausethecostofeverymarginalgeneratingunitisthecostofpowergenerationsystem,soaccordingtotheabovetheorems,whenloadisL,themarginalprobabilitydensityfunctionofthemarginalgenerationcostis,
qs(x)mp1(x,b1),mp2(x,b2),,mpI(x,bI),mpI,1(x,bI,1)(3)Wherebiisthe
operatingcostofuniti,i=1,2,...,I;
bI,1istheoperatingcostofhypotheticalpower,whichequalstothelossescostofthesystem;
(x)isaunitimpulsefunction.Fromtheformula
(1),itiseasyto
verify:
I,1
j1mpj1namely,the
probabilitydensityoffunctionisareasonabledensityfunctioninmathematicsoftheformula(3).Thusprobabilitydistributionfunctionofthemarginalcostofelectricitycanbe:
Qs(x)mp1u(x,b1),mp2u(x,b2),,mpIu(x,bI),mpI,1u(x,bI,1)(4)Whereu(x)istheunit
stepfunction.
TheexpectedmarginalcostofelectricityE[S]andvarianceVar[S]canbeexpressedas
E[S]mpjbj
j1
I,1I,1(5)2,[E[S]]Var[S]mpjb2(6)j
2.3Theinclusionoftheuncertaintyoffuelprice
Asthesamewithgeneratorsrandomlyforcedoutage,theuncertaintyoffuelpriceofthefuturegenerationalsohasanimportantinfluenceontheestimationofthemarginalcostofelectricity.Thestrictlyaccuratemethodistodescribetheunitoperatingcostofeachpowergenerationunitasarandomvariationbi,thatis,usetheprobabilitydensityfunctiontodescribeeachrandomvariablebi.Astheformula(3)showsthat,thedensityfunctionofthemarginalcostofelectricityshoulddescribeastheprobabilityoftakingseveralrandomvariablevalues(ratherthanthedeterminedamount),thedensityfunctionofeachrandomvariablebiis
qbi(x)bp(x,b),i1,2,,I(7)ijij
j1IBi
Wherein,bijisthej-thstatevalueoftheoperationcostbiofuniti;
bpijisthej-thstateprobabilityoftheoperationcostbiofuniti,bpij1;
IBiisthestatevalueofthe
totaloperatingcostsbiofuniti.
Astheuncertaintyoffuelpriceandrandomnessofgeneratingunitforcedoutagearemutuallyindependent,theprobabilitydensityfunctionofthemarginalcostofelectricitygenerationsystemcanbeexpressedas
qs(x)
Impbp(x,b),mpiijiji1J1IBi
iijIIBiI,1(x,bI,1)(8)i1J1
Thatis,thedensityfunctionformula(8)isreasonable,aprobabilitydistributionfunctionofthemarginalcostofelectricityisexpressedas
Qs(x)mpibpiju(x,bij),mpI,1u(x,bI,1)(9)
i1J1IIBimpbp,mpI,11
Thustheexpectedvalueandvarianceofthemarginalcostofelectricitymayalsobeobtained.
3numericalexample
TheabovemethodsweretestedbyIEEE-RTSdata[4].PowerunitdataisshowninTable1,inordertoavoidtheissueofwaterandelectricity,ittakestheplaceofthesamecapacityofthermalpowerunit.thesystemcostofshortagelossesshouldbetakenasthevalueofperkWhelectricity,whichiscloselyrelatedtosociallaborproductivity,andcanbeapproximatedasGDPdividedbythetotalgeneratingcapacity,(itisassumedtobe120%ofthemaximumunitoperatingcostsofpowergeneratingunit).
Table1dataofgeneratingunit
cellnumberofunit(MW)forcedoutageoperatingcostcumulativenumbertheunitcapacityrate,/MWhcapacity(MW)
ThecurveofexpectedvalueofmarginalcostofpowergenerationsystemsisshowninFigure1,representsthemachinewithoutconsideringforcedmethodofcumulation.,whichgivesthecalculativeresultofZ-transformationandaccumulativemethod,forthecalculationofthepresentsystem,theresu