Precision analysis of the integration rules used for transient simulation in electric networks

Abstract

The adequate selection of the integration rule and time step is crucial to ensure accurate results in the simulation of an electric network. For this reason, this work has two main objectives: to analyze the distortion of the waves due to the integration rule and integration time step, and to provide guidelines for new circuit simulators’ users on how to properly choose an integration rule and a time step according to a desired precision. When discretizing a continuous system, the frequency response of the discrete system can be used to evaluate the precision of the mentioned rule, since a discrete system can be viewed as a filter. However, the frequency response provides the accuracy of the discrete system during the steady state; the transient-state accuracy can be analysed by evaluating the pole distortion due the discretization. This work focuses on the analysis of the steady-state accuracy and the transient-state accuracy of two discrete systems: an RL branch used as a fist order system and an RLC branch used as a second order system. For this analysis, two commonly used discretization rules are considered, backward Euler and trapezoidal rules.