This paper presents the issue of the Sub-synchronous resonance (SSR) phenomenon in a series compensated DFIG-based wind power plant and its alleviation using a Battery Energy Storage-based Damping Controller (BESSDCL). A supplementary damping signal is developed considering the angular speed deviation and is incorporated into the BESS control system. Wide-area Measurement System data is used to determine the angular speed deviation. A linearized system model is developed to perform eigenvalue analysis, and to detect and examine unstable SSR modes. The variation of wind speed and three-phase fault are also taken into consideration to validate the robustness of the controller. To further verify the efcacy of the proposed damping controller, time-domain simulations are performed using MATLAB/Simulink. The application of the proposed BESSDCL stabilizes all the unstable system modes efectively at wind speeds of 7 m/s, 9 m/s, and 11 m/s, and at 40%, 50%, and 60% series compensation levels, as well three-phase fault conditions.