Synchronous solutions of power systems: existence, uniqueness and stability

Abstract

Abstract. This paper contains a study of the asymptotic stability and uniqueness of equilibrium solutions of multi-dimensional Hamiltonian-like systems. The results are applied to the swing equations, the classical model for power systems. By developing some results in matrix theory, it is shown that asymptotically stable equilibrium solutions may exist even though most rotor angle pairs are more than 90°, some even 180°, out of phase. In contrast to the numerical criteria usually used, an analytic criterion for the existence of asymptotically stable equilibrium solutions of the swing equations is given.1. Introduction. Most authors studying the stability of the swing equations for power systems have investigated only those equilibrium solutions for which all the rotor angles are less than 90° out of phase with each other. In this paper we develop examples of swing equations for which asymptotically stable equilibrium solutions exist even though most of the rotor angle differences are greater than 90° in magnitude; some such