Relaxed Large-Scale Systems Stability Analysis Applied to Power Systems

Abstract

The use of standard scalar Liapunov functions for stability investigations of power systems imposed consideration of very simplified mathematical models. Attempts to get rid of this and some other related drawbacks have led to the decomposition-aggregation method, based on vector Liapunov functions. Within this framework, questions of great importance from an engineering point of view are the relaxation of stability requirements and a suitable estimation of the stability domain, The theoretical part of the present paper is essentially devoted to these questions; they are embedded and solved in the general context of the stability of autonomous nonlinear large-scale systems. The second part of the paper deals with the application of the obtained theoretical results to power system transient stability analysis. The power systems are described here by more refined mathematical models than in all previous related studies. A simple numerical example illustrates the theoretical developments.