An Algorithm for Finding the Steady State Solution of Electric Networks

An algorithm for finding the steady state solution of systems containing linear, nonlinear elements and/or periodic switching power electronic devices is presented. The method is suitable to be used in connection with programs like the EMTP to determine the network initial conditions. Linear elements are represented as pure conductance matrices: for linear resistances, their corresponding conductance matrices are diagonal with equal elements; for linear inductances and capacitances, their conductance matrices are full real matrices. A nonlinear element is represented by a conductance in parallel with a current source, both obtained iteratively through Newton´s method. The system of nodal equations is solved in the time-domain assuming waveform periodicity. Case studies are presented including a power converter with diodes and silicon controlled rectifiers. The method is shown to be reliable, accurate, easy to implement and has great potential for large system applications