Lyapunov functions of lur'e-postnikov form for structure preserving models of power systems

Abstract

This paper improves the derivation of Lyapunov functions for power systems based on structure preserving models. Such models have been shown elsewhere to have considerable advantages over the usual models based on impedance loads and a reduced network. However, the development of energy functions for structure preserving models to date has largely proceeded by ad hoc means. Energy functions are shown to be cleanly derived (not guessed) and improved by a systematic application of the multivariable Popov stability criterion. This considerably extends an earlier analysis by Hill and Bergen (IEEE Trans. Circuits Syst., CAS-29, 840-848 (1982)). A fundamental limit to the class of non-linear load models allowed in the stability analysis is clarified. For the first time, a systematic study is made of refined energy functions corresponding to special generator and load damping properties. This exposes an interesting connection with the stability analysis of the usual reduced network model. © 1989.