A Dynamic Theory-Based Method for Computing Unstable Equilibrium Points of Power Systems

In this paper, anew theory-based dynamic method for computing unstable equilibrium points is proposed. This dynamic method is a combination of a dynamic transformation method and a trajectory-unified method for the computation of unstable equilibrium points (UEPs) of power system models. The transformation method converts a UEP into a stable equilibrium point (SEP) to expand its convergence region by creating a quotient gradient system (QGS). The resulting SEP is then calculated using a quasi-Newton form of the pseudo-transient continuation method (ψtc) that exploits the structure of the quotient gradient system for fast and reliable computation. Itis shown that the proposed QGS-based ψtc can have local q-superlinear or even local quadratic convergence under certain conditions. These conditions for convergence are presented and analyzed. The proposed method is tested on the WSCC 9-bus system and the IEEE 145-bus 50-machine system. The results show that the proposed method gives accurate results, is sufficiently fast, numerically stable, and enlarges the convergence region of computed UEPs.