This research work addresses the challenge of controlling a wind energy conversion system (WECS) connected to the grid, which incorporates a battery energy storage system and operates under varying real wind speed profiles. The system comprises a Doubly-Fed Induction Generator (DFIG) connected to the grid through an AC/DC/AC converter, along with a Li-ion battery pack storage unit linked to the Back-to-Back converter DC via a DC/DC converter. The study highlights that internal parametric variations and the non-linear behavior of the wind turbine negatively affect the energy quality produced, as well as the battery charging performance and its overall lifespan. To overcome these issues, the research proposes a robust control strategy based on Integral action Sliding Mode Control (ISMC) to independently manage the powers of the WECS, particularly the DFIG, to enhance dynamic performance. Furthermore, effective battery charging and discharging controllers are crucial for efficiently distributing the generated power to both the grid and the storage unit, ensuring proper energy extraction and battery charging/discharging. Depending on the battery's State of Charge (SOC), the available extracted energy, and the power injected into the grid, two current regulation modes are employed: buck charging mode and boost discharging mode. A storage system energy management algorithm is then utilized to determine the appropriate charging mode, ensuring battery safety. To validate the system's performance, a 1.5 MW wind power conversion system is tested using Matlab/Simulink simulations. The results demonstrate the robustness and efficiency of the proposed control approach in enhancing the overall system's performance.