Small-Signal Stability Analysis of Numerical Integration Methods

TL;DR

This paper introduces a new matrix pencil-based framework to analyze the accuracy and stability of various numerical integration methods used in power system simulations, providing insights into their comparative performance.

Contribution

It presents a systematic, general approach for evaluating the dynamic mode errors of numerical methods in power system simulations, applicable to any numerical scheme.

Findings

The framework effectively compares different numerical methods.

Simulation results validate the approach on real power system models.

Insights into method stability and accuracy are provided.

Abstract

The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error between the dynamic modes of the power system and the modes of the approximated discrete-time system arising from the application of the numerical method. The proposed approach can provide meaningful insights on how different methods compare to each other when applied to a power system, while being general enough to be systematically utilized for, in principle, any numerical method. The framework is illustrated for a handful of well-known explicit and implicit methods, while simulation results are presented based on the WSCC 9-bus system, as well as on a 1, 479-bus dynamic model of the All-Island Irish Transmission System.