Improving Algorithms for Searching for Trees of Directed Graphs of Electrical Power Systems

The paper outlines ways to improve the topological method based on the theory of directed graphs of a complex power network. The fundamental basis for studying the topological properties of a network is Akhmetbaev’s exact solution of the zero iteration of the nodal voltage equations found using a matrix of distribution coefficients of source currents. An analytical study of the distribution coefficients established their topological content for all possible and specific trees of a directed graph. Improved algorithms for searching and determining all possible and specific trees of the directed graph of a complex electrical network are proposed. The prospects of using the principles of diakoptics to speed up the search and determination of the possible trees of a complex graph are considered. The resulting algorithms significantly speed up the solution of the problems posed.