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 determines the controlling UEP in the TEF method is based on the so-called exit 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 θ^egsa, where the first maximum of the potential energy along the fault-on trajectory is encountered. Second, the minimum gradient point θ ^mgp along the trajectory from θ^egsa is computed. The controlling UEP is then obtained by solving a system of nonlinear algebraic equations with θ^mgp as an initial guess. It has been observed that this method lacks robustness in the sense that the following two problems may occur: (1) there may be no detection of the minimum gradient point θ^mgp and hence, no determination of the controlling UEP, (2) if θ^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 algorithm used. Hence, another equilibrium point, possibly a stable equilibrium point, not the controlling UEP will be located. This results in a flawed transient stability assessment. The result of this research has been the development of a new numerical technique for determining the controlling UEP. With an initial starting point that is close to the exit point this technique efficiently produces a sequence of points. An analytical foundation for this method is given which shows that under 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 technique does not attempt to detect the point θ^mgp, (2) the technique can produce a point that is close to the controlling UEP thus avoiding a domain of convergence problem. The analytical foundation is provided for the unloaded gradient system, but an application of the technique to the IEEE 50-generator system shows that satisfactory stability assessment is also obtained for more general systems, for which the exit point method fails