A companion-circuit branch modeling and factorization of sparse matrices for the efficient solution of large-scale power systems

This article presents the application of numerical integration methods, such as forward Euler (FE), backward Euler (BE) and trapezoidal rule (TR), based on discrete Norton equivalent models (DNEM) through companion-circuit branches RL, for a representation of systems of linear equations for the solution of power systems of any scale in the time-domain (TD). This approach allows obtaining a matrix relationship from the companion-circuit analysis (CCA), which is mainly composed of a symmetric in structure and particularly sparse conductance matrix. The solution of this matrix is exploited using two sparse matrix LU and LDU decomposition processes. The resulting unified methods consist of CCA-LU and CCA-LDU, which are applied to the solution and analysis of the 2383-bus modified power system under fault conditions. The performance of the method is compared in terms of CPU time.