On the mechanism of transient instability of power systems

In recent studies, it has been verified heuristically and experimentally (via simulations) that instability in power systems due to a fault occurs when one machine or a group of machines, called the critical group, loses synchronism with the remaining machines. Using energy functions associated with a critical group (rather than system-wide functions), transient stability results which are less conservative than other existing results, have been obtained. The existence and identity of a critical group is ascertained in these studies by off-line simulations. In this paper, we present results, for power systems with uniform damping, which establish analytically the existence and the identity of the critical group of machines due to a given fault. We also present a result to determine estimates of the domain of attraction of asymptotically stable equilibrium points in power systems. The results presented herein can potentially be used on-line to determine which machines belong to a critical group, and to use this information for corrective action (e.g., shedding of the critical generators or fast valving for these generators). The applicability of the present results is demonstrated by means of a specific example (a 162-bus, 17-generator model of the power network of the State of Iowa).