AN IMPROVED TECHNIQUE TO DETERMINE THE CONTROLLING UNSTABLE EQUILIBRIUM-POINT IN A POWER-SYSTEM

The accuracy of stability assessment provided by the transient energy function (TEF) method depends on the determination of the controlling unstable equilibrium point (UEP), The technique that currently determi nes the controlling UEP in the TEF method is based on the so-called ex it point method and has also been recently labeled the BCU method, The exit point method consists of two basic steps, First, the exit point is approximated by the point theta(egsa), where the first maximum of t he potential energy along the fault-on trajectory is encountered, Seco nd, the minimum gradient point theta(mgp) along the trajectory from th eta(egsa) is computed, The controlling UEP is then obtained by solving a system of nonlinear algebraic equations with theta(mgp) as an initi al guess, It has been observed that this method lacks robustness in th e sense that the following two problems may occur, 1) There may be no detection of the minimum gradient point theta(mgp) and hence, no deter mination of the controlling UEP, 2) if theta(mgp) is found, then based on the definition of the controlling UEP, it may not be in the domain of convergence of the controlling UEP for the particular solving algo rithm used, Hence, another equilibrium point, possibly a stable equili brium paint, not the controlling UEP will be located, This results in a flawed transient stability assessment, The result of this research h as been the development of a new numerical technique for determining t he controlling UEP, With an initial starting point that is close to th e exit point this technique efficiently produces a sequence of points, An analytical foundation for this method is given which shows that un der certain assumptions this sequence will converge to the controlling UEP, Hence this new technique exhibits a substantial improvement over the exit point method because of the following reasons: (1) the techn ique does not attempt to detect the point theta(mgp), (2) the techniqu e can produce a point that is close to the controlling UEP thus avoidi ng a domain of convergence problem, The analytical foundation is provi ded for the unloaded gradient system, but an application of the techni que to the IEEE 50-generator system shows that satisfactory stability assessment is also obtained for more general systems, for which the ex it point method fails.