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）
摘 要 本文以Tank和Hopfield神经网络为基础，建立了一种由主从网络构成的电力系统状态估计神经网络模型。理论分析和实例模拟结果表明：该网络是稳定的，该方法是可行有效的。
关键词 状态估计 电力系统 神经网络
1 INTRODUCTION
Among the current state estimators，due togood estimation qualities and astringency，weightedleast estimator is a classical algorithm and an aca－demic basis．Butit also has some shortcomingssuchas the calculation of matrices．The paper applies aneural network modelto solve the real－time leastsquares（RLS）problem．Theoretical analysis andsimulations prove that this network is very suitableto solve this kind of problem and has greatly im－proved on the traditionalpower state estimation al－gorithm．
2 A MODEL OF WEIGHTED LEAST SQUARESALOGORITHM
The observation equation ofpower systemstate estimation is nonlinear and can be linear as:
z＝Hx＋v （1）
where x isan dimension state vector；z isa mdimen－sion measurement vector；v is a measurement errorvector，which is normalized as：
H is a m×n dimension observation matrix．Rank［H］＝n．Its elements are decided by the structureof power system and the configuration of meteringsystem．In general case，H can act as constant be－cause its change is minute in every iteration．
The observation function applying weightedleastsquares algorithmis：
where R－1 is weight，Δz is the difference betweenthe measurementand the value ofthe correspondingmeasurementfunction．Eq．（2）is expressed in a vec－
tor form：
3 THEREALIZATION OFRLSALGO-RITHM USINGANEURALNETWORK
According to the reference[3]that a energy function was used to research the stability of a feed－back neuralnetwork and simulation electroniccircuitcould realize its circuitmodel．In reference［1］，thereis a network that comprised of a main and a sub－sidiary network，showed as the Figure 1．The paperapplies the network to power system state estima－tion successfully．The main and the subsidiary neu－rons are connected with each other．The left mainnetwork has n neurons，every neuron is modeled asan amplifier，and the relation ofitsinput and outputis nonlinear．It has input capacitance Ci and resis－tance Ri．vi（t）and ui（t）are the i－th neuron output and input voltage．g（u）is a degressive function．
The rightsubsidiary network hasmneurons，itsrela－tion between output and input is f（z）．The outputvoltage ofi－th neuron isqi（t）．The weightbetweenthe i－th neuron in the subsidiary network and thej－th neuron in the main network isBij，Matrix B＝（Bij）is the weighted matrix．R0＝（r1，r2，…，rm）Tis a deviation electric current vector．We also canconclude form the table 1 that the output in mainnetwork is the input in subsidiary and the input inmain network is the outputin subsidiary．
According to Kirchhoff volatile and current law，every neuron in main network has the equa－tion:
In order to guarantee the stability of the net－work and the energy function is usually composed ofthe observation function which reflects theoptimiza－tion question and several restrictive factors．ThenLyapunov function is defined as：
where F(·)is f(z)variable integral.Select properly the formatf（z）and g（u）and the network is stableand the minimumofthe energy function can be got－ten．In order to get the key of RLS，we select
Δx is the outputofthe main network，Yis devi－ation electric current，u is the inputof the main net－work．These are introduced into Eq．（8），
where u=(u1，…，un，)，△x=(△xi…,△xn)are the input and outputvoltages of g（u）．q is the output of f(z),and I is an identity matrix.
is stable.The energy function E has only mini-mum，thatis to say the network isstable．Eq．（12）is equal to zero,then
Compared with WLS,this key is the same as
4 SIMULATIONRESULTS
Selectk1＝1，k2＝1，R＝10 kΩ，and apply anetwork composed of a main network with 7 neu－rons and a subsidiary with 16 neurons to calculatethe test system which is illustrated in the reference［2］and showed in table2．Weights and originalvolatiles are showed in the reference［2］．Configura－tion of the testsystemis showed as Figure 2The estimations are listed as follows．
5 CONCLUSION
The paper realizes this algorithm in C lan－guage，and the course issimulated in a conventionalcomputer．Form the results in the table 1 and 2，itis concluded that the network model introduced inthe paper is very suitable to solve the real－time leastsquares problem．And the estimation values ob－tained by the proposed method are very similar tothe values obtained by normal method．As regardsthe computing time，itis difficult to compare．Butitis thought that it will become much shorter if theproposed method is simulated with the neuralcom－puter［5］．
本文关键字：网络 电工文摘，电工技术 - 电工文摘
