The paper presents a control method for a grid-following inverter with improved power quality under unbalanced grid voltage and uncertain grid impedance operation. For grid-connected inverters, unbalanced grid voltage operation results in negative sequence components of the grid voltage, and consequently, double frequency components of the instantaneous real and imaginary power, resulting in power oscillations. The proposed method addresses the problem of power oscillations and maintains power delivery stability under unbalanced grid voltage operation by using a dual current control structure with separate control of the positive and negative sequence components of the grid current. By controlling both sequence components of the grid current, the method eliminates power oscillations and maintains power delivery stability under unbalanced grid voltage operation.

To improve the robustness of the proposed method under uncertain grid impedance operation, the control method is formulated as a state feedback integral control method, and the gains of the state feedback integral control method are synthesized using a linear matrix inequality optimization method. The optimization method formulates the control problem as a convex optimization problem, and the closed-loop stability and robustness of the control method under uncertain grid impedance operation are guaranteed.

The proposed method, with the aid of dual sequence current control and robust control design using LMI, is able to suppress power oscillations of double frequency and improve the power quality of the grid-connected inverter system. The simulation results under various operating conditions, such as unbalanced grid voltage and uncertain grid impedance, validate the proposed control method.