Region of Stability in Power Systems

Abstract

The stability problem in power systems was mathematically formulated in Chapter I as one of ensuring that the state of the power system at the instant of clearing the fault is inside the region of stability (ROS) of the post-fault stable equilibrium point. Computation of ROS is perhaps the most difficult task in successfully using the Lyapunov/energy functions for stability analysis. In this chapter we explain the foundation of the theory underlying the characterization of the stability boundary of nonlinear autonomous dynamical systems and then indicate its application to power systems. We also provide a theoretical foundation to the potential energy boundary surface method. Both these theoretical results are due to Chiang et al. [1988]. A parallel development in characterizing ROS in the entire state space is due to Zaborsky et al. [1988]. In terms of application to realistic systems, three basic methods have proved to be successful in application.