This letter presents a new control strategy of threephase grid-connected inverter for the positive sequence voltage recovery and negative sequence voltage reduction under asymmetrical grid faults. Unlike the conventional control strategy based on an assumption that the network impedance is mainly inductive, the proposed control strategy is more flexible and effective by considering the network impedance impact, which is of great importance for the high penetration of grid-connected renewable energy systems into low-voltage grids. The experimental tests are carried out to validate the effectiveness of the proposed solution for the flexible voltage support in a low-voltage grid, where thenetwork impedance is mainly resistive.