Mixed $\mathrm{H}_{2}/\mathrm{H}_{\infty}$ State-Feedback Control for Islanded DC Microgrids: An LMI Based Approach

This paper addresses a robust control strategy for a DC microgrid in the presence of both perturbations in load current and the voltage of distributed resource. The DC Microgrid system is comprised of two distributed generation units feeding unknown loads. The main objective in each DG unit is to design a decentralized controller to minimize the effect of disturbance while tracking the reference voltage signal. To accomplish the objective, a mixed H ₂ /H _∞ state-feedback control strategy based on linear matrix inequality (LMI) techniques has been fully developed. Firstly, a nonlinear model of each DG unit is formulated and then it is linearized around an operating point. Secondly, the control designed problem is transformed into a convex LMI optimization problem which can be easily solved by MATLAB solvers. Furthermore, by using integral control strategy, output voltage of each DG unit tracks the desired reference output voltage. To evaluate the effectiveness of the proposed control strategy, the electrical model of DC Microgrid is analyzed in MATLAB/SimPower System.