Robust linear parameter varying frequency control for islanded hybrid AC/DC microgrids

•The LPV representation of a nonlinear isolated hybrid microgrid model is investigated.•The intermittent nature of the wind speed, solar irradiation, and loads, and several parameter uncertainties are considered in the frequency control design procedure.•A dynamic robust LPV controller synthesis based on the three-step algorithm is proposed for the nonlinear model.•The proposed secondary frequency control approach suggests a practical dynamic output feedback controller with lower order than the IHMG model.•The algorithm superiority is verified in various disturbance-based and uncertain parameter-based scenarios. The applicability of a robust linear parameter varying (LPV) control for frequency fluctuation damping in an islanded hybrid microgrid (IHMG) system (DEG/WTG /PV/FC/ESSs) is investigated in this paper. Due to the erratic behavior of the majority of the renewable energy sources (RESs) and the varying time nature of loads, frequency deviation from the nominal value is inevitable, especially in the islanded mode. Load variation, solar irradiation, and wind power disturbance, as well as system parametric uncertainties, can significantly disturb the system frequency operation. In this paper, the wind speed and rotated speed of the nonlinear wind turbine are highlighted as scheduling parameters, and the nonlinearity of the wind turbine is hidden by the LPV approach. In the proposed method, a dynamic output feedback controller is obtained based on the power balance equation, by solving three LMIs to minimize the upper bound of the L2-Norm of the uncertain IHMG in an algorithmic approach. For better evaluation, the ultimate LPV control approach is compared with two other methods on the understudy IHMG model. The result represents a noticeable advantage of the proposed robust method compared to other methods in terms of frequency stability based on time-domain and norms characteristics in presence of the simultaneous disturbances and parametric uncertainties.