An approach to compute stable solution based on stability constraints in power systems

This paper presents a new method based on stability constraints to directly calculating static stable solutions of power systems, in order to deal with the difficulty in getting stable operating points. In this discussion, the concept of stability functions is defined. This technique avoids computing critical points and judging stability of equilibrium points, through using stable constraints to exclude the unstable solutions, and therefore gets the stable solution conveniently. According to various instability types, many kinds of stability constraints could be constructed. A saddle-node bifurcation is taken for example to illustrate how to construct stability constraints. In order to design effective mathematical methods to compute solution, some techniques of equivalent transformation for the stability constraints have been studied, such as using smoothing technology and reformulating constraints into equations. The usage of proposed method to compute static stable solution is shown in the typical two-generator example here and the effect is also analyzed.