Stability boundary approximation of a power system using the real normal form of vector fields

This paper presents a method to approximate the stability boundary of the post-fault stable equilibrium point of a power system using the real normal form of vector fields. We first explain the method of approximating the invariant manifolds of an equilibrium point via second order normal forms, and present an instructive example. The proposed method is then used to analyze an 11 generator test system. For two different fault scenarios and different loading conditions, we determine the controlling unstable equilibrium point (UEP), study the change of this UEP under increased loading, find the approximation to the stability boundary, and discuss the change of its shape. Finally, the behavior of system trajectories near the UEP and the stability boundary is described