Multiagent-Based Consensus Optimal Control for Microgrid With External Disturbances via Zero-Sum Game Strategy

Abstract

Due to the fact that the external disturbances are unavoidable in nonlinear microgrids (MGs) systems, which could induce the oscillate of controller, leading to the excessive line loss, and the nonlinear could also result in the controller design difficulty in MGs. Therefore, based on the distributed consensus algorithm of multi-agent systems, this paper studies the distributed voltage recovery consensus optimal control problem for the MGs with nonlinear item and external disturbances. Firstly, the distributed secondary voltage restoration consensus control problem can be transformed into a distributed zero-sum (ZS) differential game problem of the voltage restoration consensus tracking error dynamics via applying the adaptive command-filtered backstepping technique, in which the auxiliary system and neural networks (NNs) are introduced to solve the unknown nonlinearities and external disturbances. Subsequently, the distributed voltage restoration consensus optimal control protocol is constructed via ZS differential game algorithm to achieve the voltage recovery of island MGs, in which a critic network is proposed to estimate the associated cooperative cost function online with a designed weight update law. Further, the consensus optimal control protocol proposed not only ensures the cooperative cost function to be minimized, but also ensures in the closed-loop systems all signals to be cooperatively uniformly ultimately bounded (CUUB). In addition, based on the Lyapunov stability theory, it is proved that the voltage recovery synchronization error can converge to an arbitrarily small range near the origin. Finally, simulation results verify the effectiveness of the proposed controller in island MG.