Research of the stability region in a power system

A power system is employed to illustrate how we can apply singular perturbation theory to decompose a full system into two subsystems, slow and fast subsystems. Then, we study the qualitative properties of their solutions and finally obtain the stability region and an analytical expression of the approximate stability boundary of the operation point of the full system by numerical simulation and by computing the local quadratic approximation of the one-dimensional stable manifold at the saddle point. Furthermore, we consider the effects of changing the parameters on the size of the stability region.