Cooperative Differential Game-Based Optimal Control and Its Application to Power Systems

Differential games have been extensively applied to optimal control problems. Nash equilibrium captures the tradeoff among players' policies when every player independently tries to minimize a predefined index. When considering potential cooperation, Pareto equilibrium plays an important role in cooperative differential games. This article studies the cooperative control of multiplayer systems on the quadratic infinite horizon. First, by defining a joint cost function using a parameter set, a cooperative differential game is reformulated as a general optimal control problem, where all players form a grand coalition. Then, the joint cost function is approximated by a critic neural network, and for the first time, a novel adaptive dynamic programming algorithm with two learning stages is proposed to determine the parameter selection and then obtain Pareto optimal solutions. A numerical example demonstrates that this algorithm can achieve optimal policies and Pareto frontier. As for its application, the cooperative control of a two-area interconnected power system is investigated, where the primary frequency control and secondary frequency control are regarded as two players. Simulation results indicate that the proposed scheme can obtain binding cooperation agreements, such that cooperative control scheme can get better overall performance compared to Nash control method and another three control methods.