Chapter 11
Controlling UEP Method: Theory
11.1 INTRODUCTION
Several methods are available for determining critical energy values for direct stability analysis. The classical closest unstable equilibrium point (UEP) method has been found to yield unduly conservative results when applied to power system transient stability analysis. The potential energy boundary surface (PEBS) method gives fairly fast stability assessments, but it can be inaccurate (i.e., giving overestimated and unduly underestimated stability assessments). A desirable method for determining the critical energy value is one that can provide the most accurate approximation of the relevant stability boundary towards which the fault-on trajectory is heading. This is the spirit of the controlling UEP method (Chiang, 1991; Chiang et al., 1987).
It is now well recognized that among several methods for determining the critical energy value, the controlling UEP method is the most viable for direct stability analysis of practical power systems. The controlling UEP method uses the constant energy surface passing through the controlling UEP to approximate the relevant part of the stability boundary towards which the fault-on trajectory is heading. If, when the fault is cleared, the system state lies inside the energy surface passing through the controlling UEP, then the postfault system is stable (i.e., the postfault trajectory will settle down to a stable operating point); otherwise, the postfault system may be unstable. ...
