Cournot-model-based coordinated secondary voltage control considering reactive power coupling among multiple zones

Abstract To eliminate voltage violations resulting from load disturbances, this paper proposes a coordinated secondary voltage control (CSVC) method considering reactive power coupling among multiple zones. The novelty of this method lies in solving the CSVC problem from the perspective of game theory. Specifically, the CSVC model considering coupling reactive power is described as a Cournot model, where the players are the zone controllers with the objective to minimize voltage violations, and the strategy of each zone controller is the reactive power regulation vector of the controlled generators. Thus, the Nash-Cournot equilibrium is the best control strategy of CSVC. Furthermore, the payoff function is convex, and the constraints are linear. Such a CSVC game can guarantee that the Nash equilibrium always exists and is unique. As another contribution of this work, the best response functions of each control zone are derived based on Karush–Kuhn–Tucker optimality conditions, and then the Nash-Cournot equilibrium can be found quickly by using the Newton-Raphson method to solve all the best response functions simultaneously. Computational results on the IEEE 39-bus system and a real provincial power system show the good control performance and efficiency of CSVC in terms of regulating the voltage and avoiding control oscillation.