Fast time domain computation of the periodic steady-state of systems with nonlinear and time-varying components

Abstract

This paper describes and applies a Newton method for the acceleration of the time domain computations to obtain the periodic steady-state solution of electric networks containing nonlinear and time-varying components. This Newton method is based on the Numerical Differentiation process. An electric system is solved in the time domain using this Newton method for the acceleration of the convergence to the limit cycle and a conventional Brute Force procedure. An harmonic analysis is carried-out for the electric network containing nonlinear magnetising branches, electric arc furnaces and TCRs. Comparisons are made between these approaches in terms of the required number of full cycles to obtain the periodic steady-state solution.