A Probabilistic Load Flow Method of Village-level Photovoltaic Power Station Scaled Access to the Distribution Network

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2018ChinaInternationalConferenceonElectricityDistributionTianjin,17-19Sep.2018AProbabilisticLoadFlowMethodofVillage-levelPhotovoltaicloadStationScaledAccesstotheDistributionNetworkWeiChen，ChunhuiXia，XipingPei(LanzhouUniversityofTechnologyLanzhou730050,China)operatingstructurewithmanybranchesandalmostnoAbstract—WiththevigorousimplementationofthePVPovertyconnectionbetweenthefeeders.ThenumberofloadnodesisAlleviationPolicy,alargenumberofPVpowerplantshaveaccesslargeandthereisaseriousthree-phaseasymmetryinthetotheruraldistributionnetwork,inordertoaccuratelyandload[2].Photovoltaicsisanintermittentenergysourceandhascomprehensivelyassesstheinfluenceoftheuncertainandarandomnature.Thetraditionaldeterministicloadflowcannotcorrelativefactorsofdistributedphotovoltaicforruraldistributionnetworks,probabilisticloadflowcalculationsareaccuratelyreflecttheoperatingstatusofthepowersystem.appliedforruraldistributionnetworksthatconsidertheBorkowskafirstproposedtheconceptofprobabilisticloadrelevanceofphotovoltaicoutput.Basedonthecharacteristicsofflow(PLF)inthe1970s[3],itscoreideaistoobtainthePVoutputcorrelation,aprobabilitydistributionmodelwithprobabilsticcharacteristicsoftheoutputrandomvariables,correlatedprobabilisticinputvariableswasconstructedusinginsuchasexpectation,variance,probabilsticdistributionandhybridCopulatheory,andacumulantprobabilisticloadflowotherstatisticalcharacteristics,accordingtotheprobabilsticcalculationmethodbasedonCopulatheorywasproposedtoconsiderthecorrelationofinputvariables.ThroughtheIEEE-33characteristicsoftheinputrandomvariable.thusitrevealsthebussystemandanactualdistributionnetworksimulationinoperatingstatusofthesystem.Atpresent,probabilisticloadGansuProvince,thesimulationresultsshowthatthemodelcanflowanalysismethodsmainlyincludeMonteCarlosimulationdisplaytheprobabilitycharacteristicsofphotovoltaicpowermethod[4-6],analyticalmethod[7-8]andpointestimationgenerationwell,andthehybridCopulafunctionismoreaccuratemethod[9-12].AlthoughthesimulationmethodisofhighthanthesingleCopulafunctionindealingwithcorrelationaccuracy,thelargeamountofcalculationrestrictsthespeedofproblems.TheresultsarecomparedwiththeMonteCarlomethodtoverifytherapidityandaccuracyoftheproposedmethod.thesolution,soitisusuallyusedasacriterionforevaluatingtheIndexTerms—Copulatheory;cumulantmethod;photovoltaic;meritsofvariousalgorithms.Thecumulantmethodintheprobabilsticloadflow;ruraldistributionnetworkanalyticalmethodhasreceivedextensiveattentioninprobabilisticloadflowcalculationduetoitsfastercomputationI.INTRODUCTIONspeed.soneofthestatekeysupportprojects,PVPovertyOwingtotheintermittentandrandomfeatureofphotovoltaicAAlleviationProjectisanimportantwaytosteadilyoutput,itisnecessarytoestablishanaccuratemodelandtakeincreasetheincomeofpoorhouseholds.Itisanimportanteffectivemeasurestoanalysethereliabilityofphotovoltaic.measuretoprotecttheecologicalenvironment,transformruralTherefore,intheanalysisandresearchofmultiplePVpowerenergyusemethods,andimprovefarmers'productionandstationsaccessingtheruraldistributionnetwork,thelivingconditions[1].TheNationalEnergyAdministrationandprobabilisticcharacteristicsoftheoutputofmultiplePVpowerStateCouncilPovertyAlleviationOfficehaveissuedtheplantsmustbeconsidered.Theliterature[4]studiedthe"NoticeontheCompilationofthe13thFive-YearPlanforPVinfluenceofdifferentPVcapacityaccessonthesystem'ssmallPovertyAlleviationPlan",whichproposesthatvillage-leveldisturbance,steadystateandtransientstability,butdidnotphotovoltaicpoverty-reliefpowerstationsshouldbethemainconsiderthecorrelationbetweenPVpowerplants.Intheconstructionmodel.Theruraldistributionnetworkhasaradialliterature[6],itusedtheLatinhypercubesamplingtechniquebasedontheNataftransformtocontrolthecorrelationofstochasticpowerinputvariables,andanalyzetheinfluenceofThisworkwassupportedbyNationalKeyResearchandDevelopmentProgramloadaccessondistributionnetworkvoltageandbranchflow(2016YFB0601600)andNaturalScienceFoundationofChina(51767017,51267012).CICED2018PaperNo.201805280000031�Page1/72179

12018ChinaInternationalConferenceonElectricityDistributionTianjin,17-19Sep.2018probabilitydistributioninthecaseofdifferentloadspatialthecorrelationstructurebetweenthem,wherethechoiceofcorrelation.Theliterature[8,9]usedCopulafunctiontoestablishedgedistributionisnotlimited,Theappropriatedistributionmodelofwindspeedwithcorrelation,respectively,butasinglecanbeselectedaccordingtotheactualsituation,andthemutualCopulafunctionisdifficulttofullydescribethedistributionrelationshipbetweenrandomvariablescanbefullydescribedcharacteristicsamongvariables.Therefore,itisnecessarytobytheCopulafunction;3)TheCopulafunctioncanbeusedtoestablishahybridCopulafunctiontodescribethedistributionconstructamorerealisticmultivariateprobabilitydistribution,characteristics.Intermsofcorrelationmodeling,theliteraturenotlimitedtomulti-dimensionalnormaldistributionandt[13]proposesathird-orderpolynomialtransformationandusesdistribution4)Copulafunctioncandescribelinearcorrelationalinearcorrelationcoefficienttocharacterizethecorrelationofandnonlinearcorrelationbetweenrandomvariables.Therefore,randomvariables.Theliterature[14]usestheSpearmanrankthispaperusesCopulatheorytomodeltheprobabilitycorrelationcoefficienttodescribethecorrelationbetweeninputdistributionofrandomvariableswithcorrelation.randomvariables.However,thecompletecharacterizationofTheCopulafunctioncannotonlydescribethenonlineartherandomvariablecorrelationcharacteristicsisthejointcorrelationbetweenrandomvariables,obtainthenonlinearity,probabilitydistribution,whichhasmanymeasurementindexesasymmetry,andtailcorrelationbetweenrandomvariables;buttoexaminetherelevantcharacteristicsfromdifferentaspects.alsoconnectthejointdistributionfunctionofmultiplerandomThelinearcorrelationcoefficientandtherankcorrelationvariablesandtheirrespectiveedgedistributionfunctions.Itiscoefficientarejustapartofmanymeasurementindicators.aneffectivemethodtoconstructjointprobabilitydistributionofTherefore,theabovemethodcannotfullycharacterizethecorrelationrandomvariables[8].AccordingtoSklar'scorrelationofrandomvariables.theorem[8],ifthecumulativedistributionfunctionoftheInthepaper,tosolvetheproblemofprobabilityloadflowmultidimensionalrandomvariableTX[x,x,,x]is12nwithPVpowercorrelation,acumulantmethodbasedonhybridF(x)，F(x)，，F(x),andthejointdistributionfunction1122nnCopulafunction(HC-CM)tocalculatetheprobabilityloadflowwiththeinputvariablesisproposed.UsinghybridCopulaisF(x1,x2,,xn),thereisaCopulafunctionC,whichmakesfunctiontoestablisharelevantprobabilitymodelofinputthefollowingformula:randomvariables,whichnotonlycandescribethecorrelationF(x,x,,x)C(F(x),F(x),,F(x))12n1122nn(1)structurebetweentheinputrandomvariables,butalsocanF(x),F(x),,F(x)derivethecorrelationdegreeandnotbeaffectedbytheedgeIf1122nnisacontinuousfunction,thedistributiontypeoftheinputrandomvariables.Finally,basingCopulafunctionCisuniquelydetermined.Accordingtoontheproposedprobabilitymodelandthecumulantcalculation,Sklar'stheorem,afterdeterminingtheedgedistributionofcombinedwiththelinearizedmodel.ThefinalruraldistributionmultivariaterandomvariablesandtheappropriateCopula,networkprobabilityloadflowresultsareobtainedbythejointprobabilitydistributionoftheserandomvariablesintegratingtheprobabilitydistributionsundereachsample,canbeobtained,whichisalsotheadvantageofCopulaprovidingacertainreferenceforruralloadnetworkoperationfunctioninpracticalapplications.planning.ThesimulationresultsofloadflowmodeltopresentaprobabilisticloadflowcalculationmethodbasedonahybridB.HybridCopulaFunctionReconstructiontheIEEE33-busdistributionpowersystemandtheactualAsingleCopulafunctionhaslimitationsincharacterizingdistributionnetworkinacertainregionofGansuwereanalyzed.theinter-variablecorrelationstructure.Forexample,theFinally,thesimulationresultsverifytheaccuracy,rapidityandt-Copulafunctionworkswellwhendescribingsymmetricalpracticalityoftheproposedmethod.thick-tailedcorrelationstructures,butithaslimitationswhenitcomestoasymmetricalconditions[15].Therefore,thispaperII.PROBABILITYMODELOFRELATEDRANDOMVARIABLESconstructsahybridCopulafunctiontocharacterizethecorrelationbetweendifferentphotovoltaicintensities.InA.CopulaTheorypracticalapplications,theArchimedeanCopulafunctionhasAsaflexibleandstablecorrelationanalysismethod,theexcellentproperties.Therefore,thehybridCopulafunctionisCopulafunctionhasmanyadvantageswhenitcomestoconstructedusingtheArchimedeanCopulafunction[8].Aanalyzingthecorrelationstructurebetweenmultiplevariables:studyofthejointfrequencyhistogramsoftwoactualPVload1)ThecorrelationmeasurederivedfromtheCopulafunctionplantsinacertainareashowsthattheoutputofthetwoPVloadnotonlydoesnotchangeunderthelineartransformation,butplantshasasymmetrictailcharacteristics[9],andtheuppertailalsoStrictlymonotonoustransformationdoesnotchange,soandlowertailarerelated.Therefore,inordertodescribethetailCopulatheoryhasastrongpracticality;2)Copulatheorycanbecharacteristicsofphotovoltaic,theClaytonfunctionreflectingusedtostudythemarginaldistributionofrandomvariablesandthecharacteristicsofthelowertailandtheGumbelfunctionCICED2018PaperNo.201805280000031�Page2/72180

22018ChinaInternationalConferenceonElectricityDistributionTianjin,17-19Sep.2018reflectingthecharacteristicsoftheuppertailareused;inhaveproposedamethodofpredictingtheregionalloadtoaddition,thenon-linearcorrelationcoefficientofphotovoltaicobtainitsprobabilitydistribution.Asaresultofmediumandisbetweenpositiveandnegative,sotheFrankfunctionisusedlong-termloadforecasting,theprobabilitydistributionofthetodescribetheloadgeneration.SothehybridCopulafunctionloadisbasicallyconsistentwithanormaldistribution.Thehasthefollowingform:probabilitydensityfunctionsoftheactiveandreactiveloadofPVtheloadcanbedescribedasfollows:C(u,v)C(u,v;)C(u,v;)com1Gumbel2Clayton21(P)C(u,v;)P3Frank(2)f(P)exp222PPWhere:1,2,3istheweightcoefficientcorrespondingto21(Q)Qf(Q)exp12Copulafunction,and;123isthephotovoltaic2Q2Q(6)intensityoftwophotovoltaicpowerplants;,,istheWhere:PandQarethemeanvaluesofactiveandreactivecorrelationcoefficientoftwophotovoltaicpowerplants.22PQFortheunknownparameterssuchasweightcoefficientsandpower,respectively;andarethevariancesofactiveandreactivepower,respectively.correlationcoefficientsinthehybridCopulafunction,theB.TheLinearizationModelofPowerFlowEquationexpectationmaximization(EM)methodforsolvingthehybridInthispaper,thelinearpowerflowmodelisadopted.Themodelcanbeusedforestimation[9].FortherandomvariablesbuspowerequationandthebranchpowerflowequationlinearizationintheformofpolarcoordinatescanbeX,Y,thejointdensityfunctioncanbeexpressedas:summarizedasc(u,v,,)c(u,v,)c(u,v,)1Gumbel2ClaytonWf(X)c(u,v,)3Frank(3)Zg(X)(7)III.PROBABILITYLOADFLOWCALCULATIONFORRELATEDWhere:Xisthebusstatevector,includingthevoltageRANDOMINPUTVARIABLESamplitudevectorandphaseanglevectorofthebus;WisA.ProbabilityModelofPVOutputandGeneralLoadinjectedintothebuswiththepowervector,includingthebus'sForphotovoltaicpowergeneration,itcanbeassumedthatactivepowervectorandreactivepowervector;ZisthebranchthereisalinearrelationshipbetweenthephotovoltaicoutputPandthephotovoltaicintensity,ie:powerflowvector,includingbranchTheactivepowervectorPVPrAandreactivepowervectoroftheroad.Equation(7)expandsatPV(4)Where:risthesolarradiationintensity;AisthetotalareaTaylor'sseriesatthereferenceoperatingpoint,andignorestheofthephotovoltaicarray;istheoverallconversionsecondandhigherorderterms.Theexpressionfortheamountefficiency.ofchangeisAlargeamountofmeasuredhistoricaldatashowsthattheXSW0Betadistribution[16]canbeapproximatedandapproximatedinthetimescaleofthehourlevel.TheprobabilitydensityZT0W(8)functioncanbedescribedas:Where:Winjectsthepowerdisturbancevectorforthebus;()PPV1PPV1f(P)()(1)Xisthebusstatevariableperturbationvector;ZisthePV()()PPmaxmax(5)JPrAbranchpowerflowdisturbancevector;0istheiterativelyWhere:maxmaxisthemaximumoutputpoweroftheS、formedJacobianmatrixinthepowerflowcalculation;0andlargestPVarray;isthepositionandshapeparametersofTtheBetadistribution;itsvaluecanbeobtainedbythemeanand0arethesensitivitymatrix,whichisvarianceofthelightintensity;ΓrepresentstheGammaSJ1TGJ1G0(ZX)XX000,000,.function.Theloadhasatime-varyingnature,andmanyliteraturesCICED2018PaperNo.201805280000031�Page3/72181

32018ChinaInternationalConferenceonElectricityDistributionTianjin,17-19Sep.2018C.CumulantCalculationofRelevantInputVariablesthetwoPVpowerplantsfromhistoricalphotovoltaicdata,andThetwoimportantpropertiesofcumulantare:1)theorderperforingaNewton-Raphsonloadflowcalculationatthecumulantsofthesumofindependentrandomvariablesareexpectedvaluetoobtainthesensitivitymatrixandthebranchequaltothesumofallorderandcumulantofeachvariable;2)loadflowmatrix;thenorderandcumulantsoftherandomvariabletimesare2)Accordingtotheabovetheory,thedistributionparameters,equaltoitsn-ordercumulanttimes.Therefore,theprerequisitecorrelationcoefficients,Copulasmodelparameters,weightfortheestablishmentofcumulantpropertiesisthattherandomcoefficientsoftherandomvariablesthemselvesandbetweenvariablesmustbeindependentofeachother.themarecalculated,soastoconstructasuitablehybridCopulaThebasicideaofdealingwiththecorrelationofinputmodel;quantityis:accordingtothehybridCopulatheory,thejoint3)AccordingtothehybridCopulatheorytoestablishajointprobabilitydistributionofrandomvariablesisestablishedandprobabilitydistributionofrandomvariablesanddiscretesampled,thatis,aninputvariableisfirstuniformlysampled,sampling,thatisfirstuniformlysampleavariable,thensampleandthenanotherinputvariableissampledundertheanothervariableintheconditionalprobabilitydistribution,andconditionalprobabilitydistribution,andthecumulantisobtainthecumulant,andthencalculatecumulantsofotherobtained;thecumulantsofotherindependentinputquantitiesirrelevantinputvariables;areobtained;andtheorderinvariantsofthepowersystemstate4)Obtainingtheordercumulantsoftheoutputvariablesbyquantitiesareobtainedaccordingtothelinearizedequationandthelinearizationequationoftheloadsystemandthenatureofthecumulantpropertyofthepowersystem.thecumulant;thenusingtheGram-CharlierseriesexpansionWincludesthechangeamountWofinjectionpowerofmethodtocalculatetheprobabilitydistributionoftheoutput.GthegeneratorbusandthechangeamountWoftheloadLV.CASEANALYSISinjectionpower,accordingtothenatureofthecumulant1)Thispaperuses33-busradialdistributionnetworksystemasavailableanexample.Thesystemconsistsof32lineswithatotalactive(m)(m)(m)WWWGL(9)powerof3715KW,atotalreactivepowerof2300kVar,anda(m)W(m)W(m)voltagereferenceof12.66kV.ThetopologyofthesystemisWhere:W,GandLarethem-ordercumulantsshowninFigure1[17].Atthebus33,twophotovoltaicpowerofthebusinjectionpowervariation,thegeneratorbusinjectionplantswithacapacityof300kWareadded,andtheiroutputpowervariation,andtheloadbusinjectionpowervariation,poweristheactualmeasuredvalueoftheyear.Thepowerrespectively.Theordercumulantsoftheoutputvariablescanfollowsthenormaldistribution.Thepowervalueoftheoriginalbeobtainedbyequation(10).systemistheaveragevalueofthenormaldistribution,andthe(m)(m)(m)XSWstandarddeviationis5%oftheaveragevalue.0(m)(m)(m)ZTW0(10)(m)(m)STWhere:0and0arematricesformedbym-thloadsofSTthesensitivitymatrix0and0elements,respectively.Throughthepowerflowcalculation,itcanobtaintheordercumulantsofthebusstatevariationXandlineflowvariationZ,andthencombinetheGram-CharlierseriesexpansiontoobtainthedistributionoftheprobabilityfunctionofthebusstatevariableXandthebranchloadflowZ.Fig.1Structurediagramof33-bussystemIV.THECALCULATIONPROCESSOFPROBABILISTICLOADFLOWA.TheParameterAnalysisofCopulaFunctionThispaperproposesacumulantprobabilisticloadflowUsingtheestimationmethodtosolvethefunctioncalculationmethodbasedonthehybridCopulafunctiontoparametersandcalculatingthesquaredEuclideandistanceforquicklyandaccuratelycalculatetheprobabilisticloadflowofaeachCopulafunction,theresultsareshowninTable1.Fromthedistributionnetworkcontainingphotovoltaic.Thespecifictable,theKendallrankcorrelationcoefficientofGumbelcalculationprocessisdescribedasfollows:CopulaisclosetotheempiricalCopulafunction,andits1)Readingtherawdataofthepowersystem,calculatingtheEuclideandistanceisthesmallest,whichcanbetterfittherankcorrelationcoefficientandBetadistributionparametersofcorrelationbetweenthetwophotovoltaicpowerplants.CICED2018PaperNo.201805280000031�Page4/72182

42018ChinaInternationalConferenceonElectricityDistributionTianjin,17-19Sep.2018Becausephotovoltaicoutputisaffectedbyfactorssuchasweather,geographicallocation,andphotovoltaicintensityofmorningandevening,evendifferentphotovoltaicpowerplants20atthesamebuswillexhibitdifferentcorrelationcoefficientsat15differenttimeperiods.AsingleCopulafunctioncanhardly),v10describethecorrelation.Figure2showsthehistogramofthePV(ucoutputpowerfrequencyatacertainmoment.Fromthefigure,it5isseenthattheprobabilitydensitywithhigherPVoutputpower0isatalowerpositionandissignificantlyhigherthantheupper110.8positionatalowerprobabilitydensityposition,Whichshows0.50.60.4tailasymmetry.0.2V00UTABLE1PARAMETERESTIMATESFORCOPULAFUNCTIONSFig.3DensityfunctionofphotovalticbasedonhybridCopulaKendallSquared7CopularankArchimedesEuclideanFunctioncorrelationparameterdistance6coefficientnFrequencyhistogramotiNucleardensityestimationExperiencecn5Normaldistributiondensity0.75820uCopulafyit4sClayton0.74995.99526.4879nedGumbel0.75373.76911.3291y3itilFrank0.788517.09324.9611babor2P10-0.200.20.40.60.811.21.4PhotovoltaicoutputFig.4(a)Probabilitydensityfunctionofphotovoltaicoutputafterfitting10.9yit0.8sne0.7EmpiricaldistributionfunctiondyNucleardistributionestimateitilb0.6Betadistributionestimationabor0.5pev0.4tilau0.3muC0.2Fig.2Photovoltaicoutputfrequencyhistogramofadjacentphotovoltaic0.1powerstation0Inthispaper,themixedCopulafunctionmainlyselectsthe-0.200.20.40.60.811.21.4PhotovoltaicintensityArchimedeanfunction,andthedensityfunctionoftheoutputFig.4(b)CumulativedistributioncurveofpoweroutputofphotovoltaicloadofthetwophotovoltaicpowerplantswhenthehybridCopulasfunctionmodelingisobtainedbyusingtheestimatedB.ProbabilisticloadFlowAnalysisvaluesofvariousparametersisshowninFigure3.TheProbabilisticloadflowanalysisbasedonhybridCopulaprobabilitydistributioncurveoftheBetadistributionobtainedtheoryandcumulantmethodisperformedonthebasisofbythemaximumlikelihoodmethodisshowninFigure4(a).Incorrespondingparameters.Thecorrelationbetweeninputthefigure,thehistogramisplottedbasedontheactualPVvariablesisconsidered,ie,theinputvariablesareindependentoutputdata,andtheredcurveisthecurveoftheprobabilityofeachother.Thetraditionalcumulantcalculationmethodisdensityfunctionobtainedafterfitting.Figure4(b)istheusedtoconductprobabilisticloadflowcalculations.ThecumulativedistributioncurveofPVoutput.Itcanbeseenthatprobabilitydistributioncurveofbusvoltageandbranchloadthedistributioncurveofnucleardensityestimationcoincidesflowcanbeobtainedthroughseveraldifferentprobabilisticwiththedistributionoftheempiricalcurve(blackline).loadflowcalculationmethods.Taking33busasanexample,theprobabilitydistributionofitspowerisshowninFigure5.Intheexample,theMonteCarlomethodistakenasthetruevalue.CICED2018PaperNo.201805280000031�Page5/72183

52018ChinaInternationalConferenceonElectricityDistributionTianjin,17-19Sep.2018ItcanbeseenfromthegraphthatthecumulantmethodofthehybridCopulaisclosertothetruevaluethanthetraditionalcumulantmethod,thatis,thetraditionalcumulantmethodisdescribed.Whenthecorrelationbetweenrandomvariablesissignificantlysmallerthanthevariance,itdoesnotmeettheactualoperationconditions;MonteCarlomethodrequiresalargenumberofdeterministicloadflowcalculations,whichtakesalongtimeandrequiresalargeamountofcalculation.ThehybridCopulacumulantmethodgreatlyavoidsalargenumberofrepetitiveloadflowcalculations.Therefore,theMonteCarlomethodisgreatlyimprovedincalculationspeed.Inthispaper,thestatisticalanalysisofthecalculationtimeofFig.6(a)WiringDiagramofaloadGridinHuiningthehybridCopulacumulantmethodandtheMonteCarloCounty,GansuProvincemethodisperformed.TheresultsareshowninTable2.Thisprovestherapidityandeffectivenessofthemethodinthispaper.TABLE2TIMECOMPARISONOFTWOMETHODSMethodTime/tMonteCarlo164.42sCM-HC15.72s2.5MCS2CMnHC-CMoticnufFig.6(b)PDFcurveofbranch61-70activepowery1.5itsnedyitil1VI.CONCLUSIONbabroPWiththerapiddevelopmentofdistributedphotovoltaic,the0.5operationmodeofruraldistributionnetworksandtherandomnessofphotovoltaichaveagreatinfluenceonthe0-0.200.20.40.60.811.21.4branchactivepowerandbusvoltage.ThispaperpresentsaActivepower/MWcumulantprobabilisticloadflowmethodbasedonhybridFig.5ThepoweroftheprobabilitydensitycurvesofthreemethodsCopulatheory.Thealgorithm,usingthehybridCopulaInordertoverifythefeasibilityoftheproposedmethod,thefunction,canmoreaccuratelyrepresenttheprobabilityruraldistributionnetworkinacertainregionofHuiningCounty,distributioncharacteristicsofphotovoltaicoutput,increasetheGansuProvince(Figure6a)wasselected,andthreePVvillagescomputationalefficiency,andcanalsobeappliedtotheat61,67,and70wereplannedtobuildaphotovoltaicloadplantcalculationofprobabilisticloadflowwithcorrelatedinputwithascaleof300kWand1MWand500kW.Figure6(b)randomvariables.Comparedwiththegeneralcumulantmethod,showstheprobabilitydensitycurveoftheactiveloadofthethismethodcanimprovethecalculationaccuracyandreducebranch61-70:Takingintoaccountthecorrelation,thedensitytherunningtimecomparedtothetraditionalMCS.AfterancurveoftheproposedmethodisclosetotheMCS.ThedensityimprovedIEEE-33busdistributionloadsystemandanactualcurveatthelowerpowerhasasignificantlyincreasingtrend,ruraldistributionnetworkinGansuprovince,anumericalwhichissimilartothestandardtestsystem.exampleanalysiswasconductedtoverifytheeffectiveness,speed,andaccuracyoftheproposedmethod.CICED2018PaperNo.201805280000031�Page6/72184

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