The Topological Method for Producing the Inverse Form Nodal Equations Electric Power System
The theoretical principles of the topological method for producing the inverse form of nodal voltage equations are described. By transforming the well-known electrical state equations, the exact solution for zero iteration of nodal voltage equations is obtained using the matrix of driving currents distribution coefficients. An analytical investigation was carried out, based on which the topological nature of the nodal current distribution coefficients has been revealed. A topological method for calculating the nodal currents distribution coefficients proceeding from various trees of a complex electric network directed graph is proposed. A program for separating specific trees among the possible graphs of a complex electric network has been developed. A comprehensive program for calculating the current distribution coefficients and setting up the parameters of a steady state operation mode in the MATLAB environment has been elaborated. The proposed procedure makes it possible to significantly reduce the scope of performed activities and allows the nonlinear equations of steady-state operating conditions to be positively solved within a shorter period of time.