Efficient computation of the periodic steady-state solution of systems containing nonlinear and time-varying components: application to the modeling of TCRs

The application of two Newton techniques to obtain the periodic steady-state solution of electric networks with nonlinear and time-varying components such as TCRs is described in this paper. The entire system is solved in the time domain using a brute force procedure and with two Newton methodologies. These are based on a numerical differentiation (ND) and direct approach (DA) process, respectively, which accelerate the convergence of the time domain computations to the limit cycle. Comparisons are made between both approaches in terms of the required number of full cycles and CPU time to obtain the periodic steady state solution for the entire network containing nonlinear magnetising branches and a TCR.