This paper presents the design of a robust proportional integral derivative (PID) controller for the control of a single phase microgrid voltage. A microgrid consists of loads, distributed generation units and several power‐electronics interfaced LC filter and voltage source inverter. These loads are unknown and parameters are uncertain which produce unmodeled load dynamics. This unmodeled load dynamics reduces the voltage tracking performance of the microgrid. The proposed controller gives the robustness of the system with unmodeled load dynamics. Under different kinds of uncertainties, PID controller guarantees the stability and provides zero steady‐state error and fast transient response. The robustness and optimal performance of the controller is obtained by using linear matrix inequality approach. The performance of the controller under different uncertainties is studied. Results indicate the robustness and high voltage tracking performance of the microgrid system.

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This paper proposes a high-performance and robust linear quadratic regulator-proportional integral derivative (LQR-PID) controller for frequency regulation in a two-area interconnected smart grid with a population of plug-in hybrid electric vehicles. Controller robustness is achieved using a linear matrix inequality approach. The proposed control framework is tested in a simulated two-area interconnected smart grid integrated with plug-in hybrid electric vehicles under load disturbances and wind power fluctuations. The performance of the proposed controller is simulated using Matlab and compared with that of a conventional linear quadratic regulator controller. Simulation results show that the proposed controller provides reliable smart grid frequency control.INDEX TERMS Smart grid, frequency control, linear matrix inequality.

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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