Estimating Relevant Portion of Stability Region using Lyapunov Approach and Sum of Squares

TL;DR

This paper introduces a novel Lyapunov and sum of squares based method to more accurately estimate the relevant portion of the stability region in power systems, reducing conservativeness in transient stability assessment.

Contribution

It proposes a data-driven approach that leverages disturbance trajectory data and sum of squares techniques to improve Lyapunov-based stability region estimation.

Findings

Enhanced stability region estimates with less conservativeness

Demonstrated effectiveness on a classical power system model

Potential for more accurate transient stability assessments

Abstract

Traditional Lyapunov based transient stability assessment approaches focus on identifying the stability region (SR) of the equilibrium point under study. When trying to estimate this region using Lyapunov functions, the shape of the final estimate is often limited by the degree of the function chosen, a limitation that results in conservativeness in the estimate of the SR. More conservative the estimate is in a particular region of state space, smaller is the estimate of the critical clearing time for disturbances that drive the system towards that region. In order to reduce this conservativeness, we propose a methodology that uses the disturbance trajectory data to skew the shape of the final Lyapunov based SR estimate. We exploit the advances made in the theory of sum of squares decomposition to algorithmically estimate this region. The effectiveness of this technique is demonstrated on a power systems classical model.