Predicting unstable modes in power systems: theory and computations

Prediction of the (critical) unstable mode of a power system due to a fault cleared immediately after the critical clearing time is useful, for example, in transient stability analysis and in relay setting. However, the existing methods of predicting (critical) unstable modes were derived mostly on heuristics and simulations; these methods were derived for the classical power system model. In this paper, theoretical results for predicting unstable modes for general power system models are presented. It is shown that the unstable manifold of the controlling u.e.p. (instead of the coordinate of the controlling u.e.p.) determines the unstable mode. It is also shown that the unstable modes due to different fault-on trajectories with the same type-one controlling u.e.p. are the same. A computational scheme is developed to predict unstable modes for general power system models. To confirm the theoretical results developed in this paper, the scheme has been tested on a 50-generator, 145-bus system with promising results. Also, one application of the unstable mode predictions to transient stability analysis is illustrated