Foundations of the potential energy boundary surface method for power system transient stability analysis

A theoretical foundation is provided for the potential energy boundary surface (PEBS) method for power system transient stability analysis. First, a theory of stability boundaries for two classes of dynamical systems: generalized gradient systems and systems described by a second-order vector differential equation. A complete characterization of the stability boundaries of these two dynamical system classes is given, and a qualitative analysis is conducted of the stability boundary when the vector field of the system is under a certain kind of perturbation. Using these results, the PEBS method is evaluated. Conditions under which the PEBS method gives good stability assessments are derived. A modified PEBS method is suggested.<>