On the nature of unstable equilibrium points in power systems

The application of direct methods for transient stability analysis of stressed power systems is considered. One of the most important issues in this area is to find the controlling unstable equilibrium point for the disturbance under consideration. A conceptual framework for discussing stable and unstable equilibrium points in power systems based on simple topological arguments is provided. It is shown that every conceivable case of system separation can be related to a specific unstable equilibrium point (UEP) in an unloaded system. This result can be seen as a verification of the soundness of the often-used corrected corner point approximation and ray point approximation, since these two approximations would give the same unstable equilibrium points in an unloaded system. Moreover, an example is given to show that some of the unstable equilibrium points can disappear when the loading of the system increases. The implications of the findings are discussed for the so-called MOD method of finding the controlling UEP, which is used in some software packages. A method based on a combination of the MOD method and the BCU method is outlined and proposed as the subject of future investigation