Foundations of direct methods for power system transient stability analysis

Considerable progress has been made in recent years in the application of direct methods to power system transient stability analysis. The methods are derived largely based on heuristics and simulations. In this paper, a theoretical foundation for the direct methods is presented. A complete topological characterization of the stability boundary of a stable equilibrium point is derived. The closest u.e.p. method and the controlling u.e.p. method are interpreted and justified in terms of this result. Improvements of these methods are proposed. Characterizations of the closest u.e.p. and the controlling u.e.p. are provided. The stability region is shown to be unbounded.