New Approaches to the Topological Method of Analysis of Electrical Networks

In analyzing the modes of complex electrical networks, they widely use their generalized parameters. The use of generalized parameters greatly facilitates both the formulation and solution of the problem of analyzing complex electrical networks. The complexity of defining generalized parameters led to the use of various mathematical methods for transforming matrices in order to obtain solutions to a problem of large dimensionality. As is known, topological methods have certain advantages in comparison with matrix methods. Therefore, the development of a topological method in the power industry has both theoretical and practical significance. The existing topological methods based on the analysis of the determinants of the node and contour determinants are associated with the difficulties of finding all possible and specific trees of a graph of a complex electrical network. In this paper, we propose an analytical method for determining the topological expressions of the matrix of current distribution coefficients on the basis of a directed graph of a complex electrical network. Algorithms have been developed for determining all possible trees and specific trees, without defining 2 trees, which will significantly increase the efficiency of obtaining the results of the analysis of electric power systems.