Investigation of the applicability of Lyapunov exponents for transient stability assessment

Abstract

Lyapunov Exponents (LEs) measure the exponential rates of divergence or convergence of nearby trajectories in state-space models. The study presented in this paper investigates the applicability of this concept to power system transient stability analysis. It is shown that the Largest Lyapunov Exponent (LLE) of the post-fault system subsequent to a given fault scenario is independent of the fault clearing time up to the Critical Clearing Time (CCT). Furthermore, the set of exponentially stable equilibrium points of the post-fault system corresponding to different load-generation combinations of the pre-fault system can also be characterized by this LLE. The study compares the LEs with the conventional Time Domain Simulation (TDS), Extended Equal Area Criterion (EEAC) and Potential Energy Boundary Surface (PEBS) methods. It is shown that LEs give reliable results. Further, the power system stability regions can be determined using the invariance of LEs within the same stability region.