Abstract
The paper presents the theoretical foundations of the topological method of generating nodal voltages of electrical networks. By converting the known equations of the electric state, an exact solution of the zero iteration of the nodal voltage equations using the matrix of current distribution coefficients is obtained. Based on an analytical study, the topological nature of the distribution coefficients of the driving currents has been established. A new method has been developed for determining all possible trees of a graph of a complex electrical network. An algorithm has been developed for identifying specific directional trees among possible subgraphs of a complex electrical network. A comprehensive program has been developed for calculating current distribution coefficients and the formation of voltages in the steady state of a complex electrical network. The proposed technique significantly reduces the amount of calculations performed, increases the level of automation and the efficiency of obtaining, within a given accuracy, solutions of non-linear equations of the steady state.