Frequency controller design for islanded microgrid by multi-objective LMI based approach

One of the main problems in the islanded microgrids is the frequency regulation. Moreover, there are several uncertainties and disturbances in the islanded microgrids that may lead to the instability. To solve this problem, this paper proposes the design of a multi-objective Linear Matrix Inequalities (LMIs) based regulator. It considers the LMI conditions in such a way that the design criterion holds. It also considers the disturbances, including solar radiation, wind speed, and load demand variations. With extracting microgrid state space model, it builds a framework to synthesize the controller. Next, it presents the mixed robust design criteria to set up the multi-objective function. The controller design process includes two steps: state feedback and observer designs. With considering weighing functions in the design process, it determines the optimal solution of the objective function. The obtained solution is the state feedback matrix, and it forms the controller by combining the state feedback matrix with a state observer. We have applied the designed controller to the islanded microgrid, and the effect of disturbances is evaluated together with parametric uncertainties. The proposed regulator is compared with the traditional PI method. The results show that the designed regulator has robust performance as well as robust stability.