This paper presents the design of an extended parameterisations of H ∞ controller for off grid operation of a microgrid. The microgrid consists of distributed generation units, filters and local loads. The filters are used to achieve accurate sinusoidal output voltage. However, loads which are connected to the microgrid are parametrically uncertain. Hence, it undergoes with unknown loads uncertainties. These unknown loads may create unknown loads harmonics, non-linearities which may reduce the voltage and current profile of the microgrid. As a result, the sudden rise and fall of voltage current profile damages the domestic and commercial loads. The proposed controller provides robust stability against various unknown loads and uncertainties. The design of the controller is presented using linear matrix inequality approach and satisfies the Lyapunov stability criterion. Moreover, it provides lower closed-loop H ∞ norm and has better tracking accuracy than other. For justification, several load conditions have been tested in MATLAB/SimPowerSystem Toolbox to ensure the robust stability of the proposed controller. All the results presented in the paper indicate high performance of the controller.

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