Newton methods for the fast computation of the periodic steady-state solution of systems with nonlinear and time-varying components

The periodic steady-state solution of electric networks with nonlinear and time-varying components is efficiently solved in the time domain with the use of novel Newton methods for the acceleration of the convergence of state variables to the limit cycle. The Newton techniques are based on the direct approach and the numerical differentiation procedures, respectively. Electric networks having linear transmission lines, nonlinear loads and time-varying components such as electric arc furnaces and TCR components are analyzed. Comparisons are made between case studies of systems solved in the time domain with the conventional brute force approach and with two Newton methods of natural quadratic convergence, in terms of the number of full periods of time and CPU time required by the different algorithms, code implementation and computer platform used.