Distributed sampled-data PID control for voltage regulation in inverter-based islanded microgrids using artificial delays

This paper addresses and solves the secondary voltage regulation control problem in inverter-based islanded Microgrids (MGs) via a fully distributed delayed sampled-data PID controller, whose derivative action is approximated using finite difference. By choosing a small enough sampling period and leveraging artificial delays approach, the proposed strategy ensures the secondary voltage regulation with closed-loop performances similar to ones achievable via a continuous-time PID controller, but with a significant reduction of the communication burden, while improving the efficiency of the entire MG. Exponential stability of the closed-loop MG network is analytically proved via Lyapunov-Krasovskii theory and the derived sampling-dependent stability conditions are expressed as a set of LMIs, whose solution allows finding the weighted L₂ gain. Finally, a detailed simulation analysis confirms the effectiveness and the robustness of the proposed approach.