Use of Polytopic Convexity in Developing an Adaptive Interarea Oscillation Damping Scheme

An adaptive control scheme based on the convexity property of polytopes for damping interarea oscillations is developed here. A polytopic control guarantees requisite damping when the current operating point lies inside it. Multiple polytopes increase the robustness of the control provided the polytope inside which the operating point lies after a disturbance is correctly identified. In this paper, the identification of the correct polytope is performed using Kalman-filters and the mean-chi square variable. A 29-machine 127-bus model of the Western Electricity Coordinating Council (WECC) system is used as the test system for this analysis. The simulation results demonstrate that the proposed adaptive control is able to provide adequate damping to the interarea modes of oscillation under changing operating conditions without any prior knowledge of the postdisturbance operating state. It is also found to be more robust than some of the modern controllers proposed previously.