Current Balancing Control for a Grid-Connected Inverter Under Grid Voltage Sag Using LMI

The increasing integration of renewable energy sources into smart grids demands the use of efficient and reliable grid-connected inverters to ensure stable and uninterrupted power delivery. These inverters face significant challenges, particularly in maintaining a balanced current during grid voltage sags, which can disrupt power delivery and damage equipment. This paper presents a systematic optimal control design using linear matrix inequality (LMI) techniques for a three-phase grid-connected inverter equipped with an L-filter. The proposed control strategy employs state feedback to ensure system stability and integral control to eliminate offset errors. By solving the LMI problem, the optimal stabilizing gain is determined, minimizing convergence time and simplifying the gain-tuning process. Simulation results demonstrate the proposed method's ability to provide a fast dynamic response with zero offset error, highlighting its efficiency and robustness compared to a state feedback control with a negative sequence compensator. Additionally, the current unbalance factor of the proposed control is 0.5% which is significantly better compared to the one without a negative sequence compensator 15%.