On-line fault section estimation in power systems with radial basis function neural network Tianshu Bi a , Zheng Yan a , Fushuan Wen a , Yixin Ni a, * , C.M. Shen a ,FelixF.Wu a , Qixun Yang b a Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, People's Republic of China b Department of Electrical Engineering, North China Electric Power University, Beijing, People's Republic of China Received 9 January 2001; received in revised form 26 March 2001; accepted 11 April 2001 Abstract Faultsectionestimationisofgreatimportancetotherestorationofpowersystems.Manytechniqueshavebeenusedtosolvethisproblem. Inthispaper,theapplicationofradialbasisfunctionneuralnetworkRBFNN)tofaultsectionestimationisaddressed.Theorthogonalleast square OLS) algorithm has been extended to optimize the number of neurons in hidden layer and the connection weights of RBF NN. A classical back-propagation neural network BP NN) has been developed to solve the same problem for comparison. Computer test is conducted on a four-bus test system and the test results show that the RBF NN is quite effective and superior to BP NN in fault section estimation. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fault section estimation; Radial basis function neural network; Orthogonal least square algorithm; Power systems 1. Introduction Toenhanceservicereliabilityandtoreducepowersupply interruption, rapid restoration of power system is essential. As the ®rst step to system restoration, fault section estima- tionshouldbeimplementedquicklyandaccuratelyinorder toisolatethefaultyelementsfromtherestofthesystemand to take proper countermeasures to recover normal power supply. However, fault section estimation is dif®cult, especially for the cases with malfunctions of relays and circuit breakers, or multiple faults at the same time. There- fore,on-lineautomaticfaultsectionestimationissigni®cant to the restorative operations. Fault section estimation aims at identifying the faulty elements in power systems by using the information of the current status of protective relays and circuit breakers available from SCADA systems. Several approaches have been investigated such as expert-system-based [1±4], optimization-based [5±10] and arti®cial-neural-network- based [11±15] approaches. The expert-system-based methodhasbeenwidelystudiedanddeveloped.Themethod provides powerful inference and explanation capabilities. However, completed knowledge acquisition, organization, validation and maintenance of the expert system are quite dif®cult and become the bottleneck of the applications. Besides, the expert system might take time to search through the huge knowledge base to get the ®nal diagnosis conclusion and sometimes unable to meet on-line application requirement. When there are malfunctions of relays or circuit breakers, expert system might make wrong conclusion for the lack of capability in identifying the false information. Another potential solution to fault section estimation is theengineeringoptimization-basedmethod.Theprincipleis toformulatefaultsectionestimationasanintegeroptimiza- tion problem and then use a global optimization method such as Boltzmann machine [5], genetic algorithm [6±8], antsystem[9]ortabusearch[10]tosolveit.Someproblems still remain unsolved in practical applications, such as how to determine suitable parameters of these optimization methods for fast and correct fault section estimation, how to make the method suitable to work under malfunctions of relays or circuit breakers. Inrecentyears,researchendeavorshavebeendirectedto thearti®cialneuralnetworkANN)[11±15],becauseithas the capabilities of learning, generalization and fault tolerance. In addition, the neuron computations are parallel which make it suitable for on-line environment. Among all the applications, the most widely used model is back- propagationneuralnetworkBPNN)[11±15].Thestandard BP NN uses gradient descent algorithm to determine the connection weights. The BP NN structure has to be priori known and the algorithm might converge very slowly and Electrical Power and Energy Systems 24 2002) 321±328 0142-0615/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII:S0142-061501)00037-0 www.elsevier.com/locate/ijepes * Corresponding author. Tel.: 1852-2857-8491; fax: 1852-2559-8738. E-mail address: yxni@eee.hku.hk Y. Ni).