Hybrid Numerical Integration Scheme Based on Exponential Time Differencing for Transient Stability Analysis

A Transient Stability Study (TSS) focuses on the analysis of the ability of an Electric Power System (EPS) to remain close to their steady-state operation after the occurrence of a perturbance. To perform a TSS, EPSs are described using dynamic models expressed by ordinary differential equations (ODEs), which are solved with numerical integration schemes. Selecting numerical integration algorithms and step-sizes severely affects computational effort, accuracy and numerical stability, which are often contradictory requirements that need to be balanced for each practical case. This paper presents a novel numerical integration scheme based on matrix exponential time differencing (ETD) for TSSs. This approach allows using high-order step sizes to decrease the computational effort without compromising accuracy and numerical stability. The proposed scheme is validated on the IEEE 39-bus test system and compared with a classic 4th order Runge-Kutta (RK4) algorithm. The test results show that the proposed scheme is more accurate than the classic numerical integration algorithms when high-size steps are used, indicating promising potential for real-life application.