COMPUTER METHODS OF SHORT CIRCUIT STUDIES FOR PROTECTION OF LARGE POWER SYSTEMS

Abstract

The recent past has witnessed a rapid increase in the complexity and size of modern power systems. This complexity in system interconnections and the increased concern for system security has brought about an increased size of system studies. Solution techniques requiring less computational effort and storage are therefore required to tackle the problems of large dimensions. For these reasons, the application of sparsity and diakoptics approach has aroused considerable interest during the recent years, to develop computer aided techniques for the analysis of large system problems. This thesis is concerned primarily with the application of these techniques to the various aspects of fault analysis problem of large networks. In parti cular, exploiting the sparsity in the network admittance matrices g^d application of diakoptics methods are sought, with a view to evolve improved computational procedures for the digital short circuit studies of large power systems. A protection engineer is often confronted with the precalculation of short circuit currents and voltages resulting from various types of faults including multiple faults throughout the large interconnected power system.

This analysis is of utmost importance to provide an acceptable degree of reliable service to the.consumers. This also necessitates selection of a highly reliable protection system so as to minimize or contain the hazards to electric power system to prevent any cascading failures and capital loss to the utility. The state of art of digital short circuit studies and methods of analysis of large systems, using sparsity and diakoptics techniques are reviewed first in this thesis for completeness. It provides an extensive litera ture survey in this area- The classical approach for the solution of digital short circuit studies using the Z-BUS by the building algorithm is quite well known. However, the formation of Z-BUS by building algorithm for large system encounters a serious computational limitation both in terms of storage and computer time. Consequently the methods of fault analysis based on buildins; algorithm have reached a limit. It is, therefore, worthwhile to evolve improved computational algorithms, requiring less computational effort and storage. The thesis embodies the basic computational tools for the analysis, mathematical modelling and computer implementation for the analysis of large faulted power systems. The various techniques have been applied viz ordered triangular factorization, bi-factorization method -IVetc. for obtaining the solution of large sets of simul taneous linear equations. Significant test results from the studies about sparsity characteristics, ordering of variables, ordering times and computational efforts, performed on power networks on varying sizes upto 118 bus system are presented. Sparse matrices require highly complex and effi cient programming. These matrices also require the storage and processing of non-zero elements in single dimensional arrays along with the indexing information. Data structures and methods of storage of sparse matrices are discussed. A general purpose data structure called the Linknet structure based on the linked lists concept for representing a large network in a computer is present ed and illustrated by a sample example. A program based on nodal elimination of Y-BUi> using linknet structure is presented along with a flow chart. An efficient algorithm based on the triangularized Y-BUS for generating a column or group of columns of Z-BUS is given. The algorithm has been programmed and illustrated by the test results of the 118 bus system. Experimental results on networks of varying sizes indicate significant savings both in storage and computer time for sparse matrix methods as compared to the explicit inversion methods. -VThe versatile numerical technique of sparse Z-BUS is also a relatively new development for fault analy sis. This method has been critically examined and has been extended for a number of applications in the area of fault analysis in this thesis. The algorithm has been programmed and extensively tested upto 118 node power systems. With out doubt, the use of sparse Z-BUS calculation technique constitutes a significant advance in the area of fault analysis. It provides an efficient method of calculating the diagonal and off-diagonal elements of Z-BUS from the triangularized Y-BUS by aback substitution process. A formulation based on sparse Z-BUS has been proposed to generate the appropriate Thevenin equivalents of large power systems associated with the faulted nodes. Experimental results upto 118 bus systems indicate the efficiency of the method. The method can be used to obtain the reduced electrical network equivalents of large power systems. A procedure has also been proposed to generate the complete symmetric Z-BUS from sparse Z method. It has also been shown how the sparse Z-BUS can be effectively employed for digital simulation of single faults using the generali§- ed fault equations. The extensive test results show that the sparse Z-BUS algorithm and its extensions as proposed in this thesis offer a great reduction in the execution time and core memory requirements as compared to factored Y-BUS and conventional building algorithm.

This thesis present^ a new fast approach for general fault analysis (for both series and shunt faults), using the piecewise approach of Podmore Q.29 ] and sparse Z-BUS technique of Takahashi et. ,al C^3 : A fundamental difference between the two methods is that the Thevenin equivalents are calculated quite efficiently by the sparse Z-BUS in the proposed method as compared to triangularization of Y-BUS in Ql29 3. Further, in the proposed technique all the thevenin equivalents can be generated in one run whereas a retriangularization of Y-BUS is needed in Ql29 2, for different fault cases. Two new algorithms have been proposed for general fault analysis which allow determina tion of sequenoe currents and voltages at the faulted nodes or in the entire network. The proposed algorithms have been programmed and extensively tested on several net works including IEEE, 118 bus system for a combination of faults and implemented on the IBM 360/44 digital computer. A sample system illustrates the procedure for general fault analysis. Lastly the application of diakoptics technique for symmetric as well as asymmetric faults is presented. Finally, a generalized technique using diakoptics procedure is discussed. It is shown that the previously presented sparse matrix procedures can be effectively employed to increase the computational efficiency of various diakoptic formulations for fault analysis. -Vll- The procedure to be adopted for the selection of a suitable fault analysis method depends on the accuracy of results desired and cost of obtaining them. The system analyst has to investigate the various solu tion alternatives and select the most suitable from the point of view speed and desired aocuracy as required from an engineering point of view. It is hoped that the general fault analysis programs and algorithms presented in this thesis would serve as useful analysis tools for, protection engineers and system analysts.