Polynomial approximation of the damping-ratio-based small-signal security region boundaries of power systems

The small-signal security region (SSSR) is an important concept in the security analysis of power systems, especially for the problems of low-frequency oscillation. In this paper, a polynomial approximation method is proposed to construct an analytical expression of the boundaries of the damping-ratio-based small-signal security region (D-SSSR) by using the implicit function approach. Compared with the conventional small-signal security region based on the Hopf bifurcation, our method is more practical and suitable for the dispatching of power systems, since it directly depicts the weak damped boundaries in the high-dimensional parameter space. The formulations of the linear and quadratic approximation are presented in detail. The effectiveness and accuracy of the algorithm is verified through case studies on a rudimentary power system.