Construction of Lur'e Type Lyapunov Function with Effect of Magnetic Flux Decay

Abstract

In this paper a generalized stability criterion for a system with multi-argument non-linearities is derived. The new criterion is based on M. A. Pai's work, and is proved along B. D. O. Anderson's criterion. The new criterion enables us to construct a Lur'e type Lyapunov function in a systematic way. The new criterion is applied to a multi-machine power system with magnetic flux decays of generators. A new Lyapunov function is constructed in a well known manner established by J. L. Willems and other researchers. The new Lyapunov function is similar to the one which has already been obtained for a system without the magnetic flux decays, except for a few points which will affect a transient stability of the system.