Power System Transient Stability Analysis Using Sum of Squares Programming

Transient stability is an important issue in power systems but difficult to quantify analytically. Most of the approaches use a simplified model of the generators, that often reduces to the swing equation. In this work, a more detailed model which includes voltage dynamics and both voltage and frequency regulators is considered to get more realistic results. The proposed analysis framework uses an algebraic reformulation technique that recasts the system's dynamics into a set of polynomial differential algebraic equations in conjunction with a sum of squares method to search for a Lyapunov function and to estimate the region of attraction of the stable operating point. The results are checked against a numerical evaluation of the region of attraction.