ON THE NATURE OF UNSTABLE EQUILIBRIUM POINTS IN POWER-SYSTEMS

This paper concerns the application of direct methods for transient st ability analysis of stressed power systems. One of the most important issues in this area is to find the controlling unstable equilibrium po int for the disturbance under consideration. This paper provides a con ceptual framework for discussing stable and unstable equilibrium point s in power systems based on simple topological arguments. It is for in stance shown that every conceivable case of system separation can be r elated to a specific unstable equilibrium point (u.e.p.) in an unloade d system. This result can be seen as a verification of the soundness o f the often used corrected comer point approximation and ray point app roximation [1], since these two approximations would give the same uns table equilibrium points in an unloaded system. Moreover, it is shown, by an example, that some of these unstable equilibrium points can dis appear when the loading of the system increases. The implications of t he findings of this paper are discussed for the so-called MOD method o f finding the controlling u.e.p. [1,2,3], which is used in some softwa re packages. Finally, a method based on a combination of the MOD metho d and the BCU method [4] is outlined and proposed as the subject of fu ture investigation.