The Matrix Network Topology Analysis With Sparse Matrix Techniques

Network topology analysis is a very important module in the automation of electric power system, and it is the basis for solving some analysis problems of electric power system, to research it has important theoretical and practical value. As the basic software for electric power analysis, it must be more comprehensive, more quickly and more accurate, so that it urgently requires a good network topology analysis algorithm.This thesis expounds the network topology analysis of matrix method. And it makes a deep study and analysis about the matrix method of matrix characteristics, for the purpose of improving the network topology analysis speed. Such a matrix method with sparse matrix techniques for network topology is presented. Don’t need to store and compute the zero elements of adjacency matrix. Thus to save the memory space and improve the speed of calculation. The theoretical basis of this method is:the matrix method of multiplying the adjacency matrix with connectivity matrix repeatedly shows that connectivity matrix as one multiplier of the matrix multiplication is dense matrix and the adjacency matrix is sparse matrix, sparse matrix techniques can apply to adjacency matrix. Because the adjacency matrix is a Boolean matrix, and its elements only have0or1. It just need to store the nonzero elements line number and column number of the matrix, do not need to store the value of elements. This algorithm can greatly save the memory space of the computer.In order to improve the algorithm, on the basis of matrix method with sparse matrix techniques, several measures are applied to increase the speed of the network topology. Firstly, using a array to store the changes of each line of the connectivity matrix, then through the changes to judge whether to save the calculation of the corresponding line to reduce the computational complexity; Secondly, the speed is obviously increased with the method which updates the element of the connectivity matrix immediately after the new one is obtained; Thirdly, halves of the elements of the connectivity matrix are obtained from their symmetrical elements; Finally, optimal numbering is used to farther speed up the network topology.The two algorithms of this thesis still have the advantages of the matrix method, such as clear concept, simple programming and so on. The calculation speed is much faster than the existing matrix method, and can meet the real-time requirements of network topology analysis. Examples proved the feasibility of the two algorithms, the calculation results show that algorithms are greatly raised the analysis speed, and can meet the speed requirement for real-time network topology analysis.