电力负荷特性统计分析方法研究

湖南大学硕士学位论文电力负荷特性统计分析方法研究姓名：贺文武申请学位级别：硕士专业：统计学指导教师：王亚雄20050510I)1,1(GMIIAbstractTheStatisticalAnalysisofPowerLoadCharacteristicsisthesignificantcomponentpartofelectricpowermarketresearch,and,theinvestigationandstudyonLoadCharacteristicsmustbeputintopracticeundertheguideofsystematictheory.Basedonstatisticsmethodswhichcombinedwithotherquantitativeanalysistheories,thearticlestudiesthemainproblemofLoadCharacteristicssystematically,andattemptstoconstructonesuitofstatisticalanalysismethodstosolvethem.Thestudyincludesthreetopics,namelytheLoadCharacteristicsStatisticsMeasurement,theRelevantFactorsAnalysis,andtheLoadCharacteristicsForecast,whichlinkingcloselyandbeingindependentformeachother,areunfoldedsuccessively.Consideringactualityandtheorynecessaries,thearticleposesthemainproblemsabouteachtopic,andthecorrespondingmethodsareputforward.EffectivemeasurementofLoadCharacteristicsisthebasetostudytheLoadCharacteristicsproblems.Therefore,firstofall,thearticleposestheconceptofLoadProbabilityCharacteristics,andtheNon-parameterEstimationmethodsareappliedtomeasureitprecisely.Then,thearticleconstructstheLoadCharacteristicsIndexwhichbasedonGreyTheorytogetherwithothermethodsand,assessesthePowerLoadCharacteristicssyntheticallybymeansofapplicationthetheoryofAttributeMathematics.Becausethecausalityanalysisistheindispensablelinktostudyobjectivethings,thearticle,thendiscussestherelationshipbetweenLoadCharacteristicsandtheFactorrelated,whichismeasuredbyGreyRelatedMatrixandNon-parameterLOWESSRegressionEstimation.AstheLoadCharacteristicsForecastisoneoftheultimateaimofourstudy,thearticlediscussestheproblems,suchastheLoadCharacteristicsTurningChanges,theMulticollinearityroseformmultivariateregressionmodelSuperShort-termLoadForecast,etc.,andtheyarestudiedrespectivelybymeansofGreyForecastModel,PartialLeastSquareRegressionandArtificialNeuralnetworkAlgorithm.Boththetheorystudyandthepositiveanalysisshowedthat,thestudyonmethodsofStatisticalAnalysisofLoadCharacteristicshasconsiderablevalueintheoryandhasfairlygoodapplicability.Surelyenough,theachievementisfarfromthebest.Actually,thestudyinthisfieldinourcountryispreliminary,andthearticleholdthatthestudyonPowerLoadCharacteristicsstillhasawideroomtogetherwithabrightfutureforIIIstudy.KeywordPowerLoadCharacteristicsNon-parameterEstimationGreyTheoryArtificialNeuralNetworkAlgorithmPartialLeastsquareRegression1______2111.120002001200211.4%8.7%10.3%2004200314.9%200420123.852983kw388.33kwh“”[1][2][3]2“”“”——“”[4]1.21989142001[2]31[2][5][6][7]3[2][8]SEM[9][10][11][2][12][13][16][12][14][15]1952[2]PJMPJM10[1]200031234541.312352[2]2.1P∈p],(ba)(pF)(pf[7]∫=≤−≤=≤badppfaPPbPPbPaP)()()(}{(2.1)),(~2σµNP)(p)(ps))(())((}{ppspaspbbPaP−Φ−−Φ≈≤(2.2)[17])(pf2.162.1.12.1.1.1),,,(21nPPPPLnnpp,,1Lipp)(ppi−ipp[18])(⋅K∫=1)(dppK[19])1(21)(0≤=uIuK],[hphp+−hhphpv+−=)1(1≤−∑=niihppI(2.3))(0hppKi−hppui−=],[hphp+−0.5)1(21)()1()(11010≤−=−=≤−⋅−∑∑∑===niiniiniiihppIhppKhppIhppK(2.4)p)(ˆpfn2.32.4hnvhhpFhpFpfhphpnnn22/)]()([)(ˆ+−=−−+=∑=+−−⋅=⋅=niihphphppKnhnhv10)(121(2.5)p∑=−⋅=niinhppKnhpf1)(1)(ˆ(2.6))(ˆpfn2.12.67dphppKnhdppfdppfbPaPbanibainba)(1)(ˆ)(}{1∫∑∫∫=−⋅=≈=≤∑∫=−−⋅=nihaphbpiiduuKn1)(1(2.7)5α)(pf21212)](ˆ)([)()(ˆpfKRnhzpfnn⋅⋅⋅±−α(2.8)∫=duuKKR)()(22.1.1.22.6[20]}0)(:{)supp(=xfxfdRfx⊂∈)supp()supp(f+∞→n0→h+∞→nh)()()(2))(ˆ()1(2)2(22hoxfKhxfBiasn+=µ)())(()()()())(ˆ()2(111−−−++=nonhoKRxfnhxfVarn)()(ˆ)3(xfxfpn⎯→⎯))()(,0()(ˆ)(ˆ())(4(21KRxfNxfExfnhpnn⎯→⎯−)5(0)221→hnh))()(,0())()(ˆ()(21KRxfNxfxfnhpn⎯→⎯−hhhdxfVarfBiasAMISE)]ˆ())ˆ([(2∫+=8Rudemo(1982)Bowman(1984)cross-validation∫−=dxxfxfhISE2))()(ˆ()(∫∫∫−+=fdxfdxfdxfˆ2ˆ22(2.9)[20])(ˆ2)()(1111121iinininjjixfnhxxKKhnhISE−=−==−∑∑∑−−⋅=(2.10)if−ˆi∫−=⋅tdttKtuKuKK)()()(2.1.22.1.2.1maxpαmaxP10α90%95%99%2.7∑∫∫=×−∞−∞×⋅=≈njhpppniduuKnpfP1/)(maxmaxmax)(1)(ˆααα(2.11)αminPααpαα−=≤1)(ppP10α0.10.050.010.900.950.992.7αααα−=⋅=≈≤∑∫∫=−1)(1)(ˆ)(1/)(0njhphpppnjjduuKnpfppP(2.12)2.2)/)((1maxmaxpsppP−×−=αφα(2.13)9apzspp×+=α(2.14)2.1.2.2miPI],[IlIuppIP2.7∑∫∫=−−⋅=≈≤=njhpphppppniliuiiujiljiliuduuKnpfpPpPP1/)(/)()(1)(ˆ}{(2.15)mi,,2,1L=}max{{iiPPiI=′=′(2.16)}max{iIPP=(2.17)iP)/)(()/)((piupilisppsppP−−−=φφ(2.18).2.22.2.1TOPSIS[6]10shsjjxxxxd−−=(2.19)jxhxsx10≤≤jdhxsx“”jd0∑=jjjdIϖ(2.20)∑=∏jjjjdIϖϖ)((2.21)jϖAmalkantirary2.2.2[6]11[21][17])1,0(∈γ[6]100)1(×−=γcI(2.22))(tX)(tyt),,2,1{NtL=ttyttxtyx∆∆−∆∆+=)(1)(111)(σσζ),,2,1(NtL=(2.23))()1()(txtxtx−+=∆)()1()(tytyty−+=∆1)1(=−==∆ttt∑=−=NtxtxtxN12)]()([1σ∑==NttxNtx1)(1)(∑=−=NtytytyN12)]()([1σ∑==NttyNty1)(1)(yxtytxtσσζ)()(11)(∆−∆+=),,2,1(NtL=(2.24)0)(≥tφ∑∑−=−==1111)()()(NtNttttφφζγ(2.25)100)1(×−=γcI100)()()(11111×⎟⎠⎞⎜⎝⎛−=∑∑−=−=NtNtctttIφφζ(2.25)[2]“”12)(tφ)(tζ2.3[23][6]2.3.1XXxmmII,,1LXF=FFXkCC,,1LkCKk≤≤1jiCCCFjKiii≠===,,1φIU(2.27)=1C=2C=3C321CCCFxkCµµ=xkx∈kCxj13jtkCxjkµ[24]∑==≥Kkxkxk11,0µµ(2.28)xjkµ∑==≥Kkxjk11,0µ(2.29)1C2CkCKC1I1110aa−1211aa−kkaa111−−KKaa111−−2I2120aa−2221aa−kkaa212−−KKaa212−−jI10jjaa−21jjaa−jkjkaa−−jKjKaa−−1KI10KKaa−21KKaa−akaKk−−1KKKKaa−−12.3.1.1[25]xjt)(txjkµjkajKjjaaaL10jKjjaaaL10Kkaabjkjkjk,,2,1,21L=+=−(2.30)),,min(1jkjkjkjkjkababd−−=+1,,1−=KkL(2.31)=