Robust Gain‐Tuning of the Primary Control for AC Islanded Microgrids Using an LMI‐Based P‐LPV/ <i> H _∞ </i> Control Structure and PCA Algorithm

ABSTRACT To address the issue of frequency regulation in AC‐islanded microgrids (MGs), this paper introduces a novel approach for adjusting primary controller gains for AC‐islanded MGs. The proposed approach uses the linear matrix inequality (LMI) for polytopic linear parameter varying (P‐LPV) modelling based on the H ∞ control theory and principal component analysis (PCA) algorithm. The objective is to regulate the MG frequency while considering the nonlinearity and uncertainty of the system. To achieve optimal control gains, the method considers all the system uncertainties in a P‐LPV modelling of the system. The PCA algorithm reduces the scheduling parameter region, and the optimal control gains are computed by solving the relevant LMIs defined on the obtained P‐LPV model based on H∞ performance and stability achievement. The primary control gains are optimised to minimise the errors between the optimal and actual control signals. Importantly, the suggested method preserves the order and structure of the primary control, making it applicable to implement on digital hardware devices. In addition, the MG is simulated in MATLAB/Simulink, and the simulation results demonstrate the authenticity, effectiveness, and efficiency of the proposed process for MG frequency regulation in the presence of uncertainties, disturbances, nonlinearity, and dynamic changes in MGs.