Optimal Frequency Control for Virtual Synchronous Generator Based AC Microgrids via Adaptive Dynamic Programming

This paper proposes a novel virtual synchronous generator (VSG) controller for converters in AC microgrids (MGs). Such controller improves the control cost and DC-side energy requirements, while considering the system non-linearity for frequency support. First, the frequency dynamics of the MG, which are analytically studied based on the VSG with a secondary frequency controller, are formulated as a nonlinear state space representation. In this later, the reciprocal of the inertia is modeled as the control input. Correspondingly, a cost function is defined by comprehensively considering the angular deviation, frequency deviation, rate of change of the frequency (RoCoF), and a discount factor, which can retain a tradeoff between the critical frequency bounds and the required control energy. Following, the optimal frequency regulation problem is solved by using an online adaptive dynamic programming (ADP) method, where a single echo state network (ESN) is constructed to approximate the optimal cost function and the optimal control input to significantly reduce the computational burden and improve the real-time computation. Finally, simulation results demonstrate that the frequency response of the system is significantly improved, while also retaining more DC-side energy.