An ellipsoidal expansion algorithm for estimating and representing regions of attraction for large power systems

This paper proposes an algorithm for efficient offline computation and representation of regions of attraction (RoA) to speed up assessing transient stability on-line of large lossy power systems. The RoAs are obtained for prescribed normal and post-fault circuit topologies in the form of unions of ellipsoids. The RoAs provide the basis of the decision support for a Secondary Protection (SP) scheme designed to recover from the Primary Protection (PP) misoperations. The algorithm iterates between a simulation step and an ellipsoidal expansion step. In the simulation step an electromechanical model of the system is utilized to generate state trajectories originating from randomly selected points on the surface of an ellipsoid, from which a new polyhedron is defined. In the expansion step, a convex optimization problem is solved to find the maximum volume inscribed ellipsoid on the polyhedron. The proposed algorithm is applied to the IEEE 68-bus test system for which the RoAs are obtained for all anticipated contingencies. One normal and forty- eight post-fault ellipsoidal RoAs are produced, with the estimated smallest critical clearing time at 131 milliseconds, sufficiently large for an SP to correct any of the anticipated cases of failure to trip or false trip by the PP.