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．IthasinputcapacitanceC_iandresis－tanceR_i．v_i（t）andu_i（t）arethei－thneuronoutputandinputvoltage．g（u）isadegressivefunction．
Therightsubsidiarynetworkhasmneurons，itsrela－tionbetweenoutputandinputisf（z）．Theoutputvoltageofi－thneuronisq_i（t）．Theweightbetweenthei－thneuroninthesubsidiarynetworkandthej－thneuroninthemainnetworkisB_ij，MatrixB＝（B_ij）istheweightedmatrix．R₀＝（r₁，r₂，…，r_m）^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），

w[1][2]下一页