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

The objective of this work is to approximate the stability boundary of a power system without any integration using the normal form of the vector fields. This involves two steps: (1) first to test which unstable equilibrium point (UEP) lies on the stability boundary, and (2) the second step is to approximate the boundary by the second order approximated manifolds. The approximation is accomplished using the normal forms of vector fields. The stability boundary and its behavior under stressed system conditions are examined. The method is applied to an eleven-generator test system.