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To guarantee a system stability and reliable operation of an inductor-capacitor-inductor (LCL)-filtered grid-connected inverter (GCI) under unexpected grid and system uncertainties, a linear matrix inequality (LMI)-based model predictive control (MPC) is presented in this paper. Even though the conventional MPC scheme is constructed by a simple concept, it is difficult to determine an optimized weighting matrix of the MPC cost function against parameter discrepancies. To overcome this problem, the MPC scheme is combined with LMI-based optimization. The system states are estimated by the LMI-based current-type observer in the stationary reference frame to implement the proposed scheme. Additionally, the MPC scheme is combined with the disturbance observer to eliminate offset error, which improves the reference tracking performance. In comparison with the other studies, the proposed control method ensures high robust control performance under grid voltage imbalance, parameter uncertainty, and frequency variation. In addition, the proposed approach achieves a robust active damping even for the grid impedance variation without the need of considering further damping method. The control design step is systematic and straightforward. Furthermore, unlike the conventional schemes, the proposed controller does not require an integral term and the 2nd harmonic compensation term to obtain a good reference tracking performance under grid imbalanced condition, which contributes to the reduction of the controller complexity by decreasing the order of the controller model. To verify the effectiveness of the proposed LMI-based MPC control scheme, the simulation and experiments are carried out by using prototype three-phase GCI. The comprehensive simulation and experimental results clearly demonstrate the robustness of the proposed current controller under various adverse test conditions with unexpected grid and system uncertainties.

LMI-Based Model Predictive Current Control for an LCL-Filtered Grid-Connected Inverter under Unexpected Grid and System Uncertainties