Power systems transient stability analysis via optimal rational Lyapunov functions

Transient stability analysis is a traditional yet significant topic in power systems. In order to obtain the stability domain of the post-fault equilibrium point, the Lyapunov method is proven to be effective and efficient once a Lyapunov function has been found. The main innovation of this paper consists in the use of rational Lyapunov functions to compute the largest estimate of the Region of Attraction (ROA) of an equilibrium point for power systems. Firstly, the non-polynomial power systems are reconstructed to uncertain differential algebraic systems via the multi-variate truncated Taylor expansion. An iteration procedure is proposed to compute the largest estimate of the ROA by exploiting the Sum of Squares (SOS) technique and the Squared Matrix Representation (SMR). A classical power system with transfer conductances is studied to demonstrate the effectiveness of the proposed approach.