Power System Transient Stability Analysis Using Sum Of Squares Programming

International audienceTransient stability is an important issue in power systems but difficult to quantify analytically. Most of the approaches in this case lie on a very simplified model of the generators, usually reduced 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 used methodology for algorithmic construction of Lyapunov functions is based on recent advances in the field of positive polynomials. This analysis framework uses an algebraic reformulation technique that recasts the systems dynamics into a set of polynomial differential algebraic equations in conjunction with a sum of Squares method to search for a Lyapunov function. Next, linear matrix inequalities are used to expand the region of attraction of the considered equilibrium point. The results are checked against an experimental (by extensive numerical simulations) evaluation of the region of attraction. Index Terms-Lyapunov theory, nonlinear systems, power systems analysis, region of attraction, sum of squares