Robust Controller Synthesis and Analysis in Inverter-Dominant Droop-Controlled Islanded Microgrids

This work investigates the problem of controller design for the inverters in an islanded microgrid. Robust μ-synthesis controllers and local droop controllers are designed to regulate the output voltages of inverters and share power among them, respectively. The designed controllers alleviate the need for additional sensors to measure the states of the system by relying only on output feedback. It is shown that the designed μ-synthesis controller properly damps resonant oscillations, and its performance is robust to the control-loop time delay and parameter uncertainties. The stability of a droop-controlled islanded microgrid including multiple distributed generation（DG） units is analyzed by linearizing the nonlinear power flow model around the nominal operating point and applying theorems from linear algebra. It is indicated that the droop controller stabilizes the microgrid system with dominantly inductive tie-line impedances for all values of resistive-inductive loads, while for the case of resistive-capacitive loads the stability is conditioned on an upper bound on the load susceptances. The robust performance of the designed μ-synthesis controller is studied analytically, compared with the similar analysis in an H∞ control（benchmark） framework, and verified by simulations for a four DG benchmark microgrid. Furthermore, the robustness of the droop controllers is analyzed by Monte Carlo simulations in the presence of local voltage fluctuations and phase differences among neighboring DGs.