Quadratic form of stable sub‐manifold for power systems

Abstract

AbstractThe stable sub‐manifold of type‐1 unstable equilibrium point is fundamental in determining the region of attraction of a stable working point for power systems, because such sub‐manifolds form the boundary of the region (IEEE Trans. Automat. Control 1998; 33(1):16–27; IEEE Trans. Circuit Syst. 1988; 35(6):712–728). The quadratic approximation has been investigated in some recent literatures (Automatica 1997; 33(10):1877–1883; IEEE Trans. Power Syst. 1997; 12(2):797–802). First, the paper reports our recent result: a precise formula is obtained, which provides the unique quadratic approximation with the error of 0(∣∣x∣∣3). Then the result is applied to differential–algebraic systems. The real form of practical large scale power systems are of this type. A detailed algorithm is obtained for the quadratic approximation of the stable sub‐manifold of type‐1 unstable equilibrium points of such systems. Some examples are presented to illustrate the algorithm and the application of the approximation to stability analysis of power systems. Copyright © 2004 John Wiley & Sons, Ltd.