This paper proposes a control strategy of improving the power quality of the energy exchanged between a photovoltaic generator (PVG) and an unbalanced grid. A voltage source inverter (VSI) allowing the control of the zero-sequence during unbalanced regimes is proposed. A Second-Order Generalized Integrators-Based Approach (SOGI-BA), which suitably fits with the network's imbalances while ensuring the perfect isolation of the PVG from the adverse effects of the imbalance, is investigated. The investigation will focus mainly on three control objectives: the generation of a balanced current system, the active and reactive power's dependent control, and the elimination of the second frequency DC bus voltage fluctuations. The performance of this new approach is approved by various tests via MATLAB environment simulations.