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

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 in state space, smaller is the estimate of the critical clearing time (CCT) 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.