GLOBAL BASIN STRUCTURE OF ATTRACTION OF TWO DEGREES OF FREEDOM SWING EQUATION SYSTEM

Abstract

A model of a simple electric power system consisting of two generators operating onto an infinite bus is studied by numerical simulations. In many practical situations the proper concern of the engineer is the extent of the basin of attraction of the safe operating condition in phase space. However traditional analysis using energy function method can capture only the regions of sufficient conditions, so that geometrical concepts and theories of dynamical systems are recognized to be necessary tools to understand power system stability. In this paper, all equilibrium points and limit cycles are listed, and their locations are investigated with relation to basins. It will be helpful to globally grasp the total structure of the basins of attractions in phase space. Periodic orbits correspond to one or both generators operating in a desynchronized steady state, and if realized, rotors are destroyed. However their basins concern the study of the basin of the stable equilibrium point. Focusing on one of the generators, that is, identifying states of another generator, the basin portrait is similar to that of the single degree of freedom swing equations system. And in this view, basin erosions of synchronized state are understood in connection with an escape phenomena. Global basin structures are studied by taking systematic basin portrait sections. Note that we do not treat situations where inertia ratio between generators is very large as is seen in some reports using Melnikov's method.