An Approach to Evaluating Accuracy of Numerical Simulation of Linear Network Transients

This paper discusses an approach to evaluating accuracy of numerical integration in simulation of linear electrical network transients. Both modes of the free motion of a linear network (i.e. modes of the general solution of the differential equations) and modes of the forced motion (particular solution) are distorted independently when numerical integration is performed. The distortions of the modes are considered as accuracy characteristics of the method applied. For the free motion modes the quantities used are damping and frequency distortions, while for the forced motion modes of sinusoidal form the quantities used are amplitude and phase distortions. Each distortion is defined as the relative error when reproducing the corresponding parameter. Discussed are cases of extreme distortions that determine principal numerical distorting mechanisms in simulations of network transients by Runge-Kutta and multi-step methods. Evaluating the distortions of the free motion modes brings understanding of the accuracy and stability of a method and simulations, unachievable when using truncation error estimations.