Optimal LQR/LQG Output Feedback Control of Three-Phase Grid Connected Inverter with LCL Filter in dq Frame

This paper conducts a current control design method for three-phase voltage source inverter (VSI) grid-tied with LCL filter in the synchronous reference frame (SRF), based on the mathematical control theory optimal full states feedback linear quadratic regulator (LQR). Optimal set-point control is added for efficient tracking. The linear quadratic Gaussian minimum energy estimator LQG (MEE) is constructed for considering more practical system. Where the input disturbances and output noise are considered, the MEE minimizes the estimated error, and the LQG leads to cost reduction in the hardware design of the proposed controller. The explicit state-space model of the system is developed by using some averaging techniques to obtain the small modeling of the VSI grid connected with LCL. In order to verify the stability analysis precisely, the mathematical Lyapunov theorem is applied. A time-domain simulation model of a 3 kW grid-connected converter (GCC) is developed by PLECS to investigate the theoretical results. The proposed LQR/LQG controller is tested in steady state, dynamic regime, grid voltage SAG and Swell, and for parameter variations. The theoretical analysis is compared to the simulation results, and have demonstrated reliable performance and prove the robustness of the adopted controller.