Power system transient stability analysis via the concept of Lyapunov Exponents

Abstract

Transient stability of an electrical power system refers to the ability of the system to settle at the stable equilibrium point in the post-fault system subsequent to a specific fault scenario. This stability problem can be studied either as a system stability or a structural stability problem. In this paper, the concept of Lyapunov Exponents (LEs) is used to analyze the transient stability of IEEE 3-generator 9-bus and IEEE 16 generator 69 bus benchmark systems. A spectrum of LEs is calculated from the mathematical models and the Largest Lyapunov Exponent (LLE) being negative implies the exponential stability of the post-fault power system. The system stability regions for specific fault scenarios are determined using the invariance property of the LEs from the initial conditions. Furthermore, the structural stability regions in terms of parameters of the pre-fault system dynamic equations are also determined. This study demonstrates that the concept of LEs can be used as a novel method to determine if the post-fault power system is within the stability region of attraction of the new stable equilibrium point, and hence to determine the stability region. It is also proposed that the largest average exponential rate calculated over a short time window is a sound approach for early prediction of the stability.