安防之家讯：cript>基于神经网络的电力系统状态估计①韩富春　王娟娟（太原理工大学电气与动力工程学院　太原　030024）
SQUARESALOGORITHM
Theobservationequationofpowersystemstateestimationisnonlinearandcanbelinearas:
z＝Hx＋v（1）
wherexisandimensionstatevector；zisamdimen－sionmeasurementvector；visameasurementerrorvector，whichisnormalizedas：Hisam×ndimensionobservationmatrix．Rank［H］＝n．Itselementsaredecidedbythestructureofpowersystemandtheconfigurationofmeteringsystem．Ingeneralcase，Hcanactasconstantbe－causeitschangeisminuteineveryiteration．
Theobservationfunctionapplyingweightedleastsquaresalgorithmis：

whereR－1isweight，Δzisthedifferencebetweenthemeasurementandthevalueofthecorrespondingmeasurementfunction．Eq．（2）isexpressedinavec－
torform：

3　THEREALIZATIONOFRLSALGO-RITHMUSINGANEURALNETWORK
Accordingtothereference[3]thataenergyelectroniccircuitcouldrealizeitscircuitmodel．Inreference［1］，thereisanetworkthatcomprisedofamainandasub－sidiarynetwork，showedastheFigure1．Thepaperappliesthenetworktopowersystemstateestima－tionsuccessfully．Themainandthesubsidiaryneu－ronsareconnectedwitheachother．Theleftmainnetworkhasnneurons，everyneuronismodeLEDasanamplifier，andtherelationofitsinputandoutputisnonlinear．IthasinputcapacitanceCiandresis－tanceRi．vi（t）andui（t）arethei－thneuronoutputandinputvoltage．g（u）isadegressivefunction．
Therightsubsidiarynetworkhasmneurons，itsrela－tionbetweenoutputandinputisf（z）．Theoutputvoltageofi－thneuronisqi（t）．Theweightbetweenthei－thneuroninthesubsidiarynetworkandthej－thneuroninthemainnetworkisBij，MatrixB＝（Bij）istheweightedmatrix．R0＝（r1，r2，…，rm）Tisadeviationelectriccurrentvector．Wealsocanconcludeformthetable1thattheoutputinmainnetworkistheinputinsubsidiaryandtheinputinmainnetworkistheoutputinsubsidiary．
AccordingtoKirchhoffvolatileandcurrentlaw，everyneuroninmainnetworkhastheequa－tion:

Inordertoguaranteethestabilityofthenet－workandtheenergyfunctionisusuallycomposedoftheobservationfunctionwhichreflectstheoptimiza－tionquestionandseveralrestrictivefactors．ThenLyapunovfunctionisdefinedas：

whereF(·)isf(z)variableintegral.Selectproperlytheformatf（z）andg（u）andthenetworkisstableandtheminimumoftheenergyfunctioncanbegot－ten．InordertogetthekeyofRLS，weselect

Δxistheoutputofthemainnetwork，Yisdevi－ationelectriccurrent，uistheinputofthemainnet－work．TheseareintroducedintoEq．（8），

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