Power system transient stability analysis: Formulation as nearly Hamiltonian systems

In this paper we formulate power systems as nonlinear nearly Hamiltonian systems. Using the invariance principle for ordinary differential equations, necessary and sufficient conditions for asymptotic stability are established and a new method of estimating the domain of attraction of the stable equilibrium point is developed. The present results constitute a novel approach to stability analysis and involve the following three steps: a. Given a system with dissipation, the stability of its equilibrium is ascertained by determining the stability of the associated conservative system. b. Attractivity of the stable equilibrium of the entire system (with dissipation) is determined from the system topology. c. An estimate of the domain of attraction of the asymptotically stable equilibrium is obtained by making use of results obtained in (a) and (b). The stability criterion developed in this paper sheds new light on the mechanism of instability in power systems and it provides analytical verification to the concept of the potential-energy boundary surface (PEBS). The PEBS is a hypersurface which makes up a part of the boundary of the domain of attraction of the stable equilibrium in a power system. The existence and properties of the PEBS have thus far been deduced primarily via simulations and heuristic methods.