This paper investigates hybrid energy storage systems (HESS) in wind turbine applications to simultaneously address power quality and grid support requirements. Unlike conventional dispatch approaches, a modified mean-value strategy with a regulation band is proposed to limit wind power fluctuations while reducing storage capacity needs. The required HESS power and energy ratings are determined using peak power mismatch and cumulative energy analysis under different dispatch methods, including mean-value, min–max, and ramp-rate-limited strategies. In addition, the sizing framework is extended to consider low-voltage ride-through (LVRT) and frequency support requirements based on grid-code scenarios. The performance of different configurations, including standalone HESS and HESS combined with a braking chopper (BC), is also evaluated. A hierarchical control structure is developed, including supervisory, power allocation, and converter control layers, allowing dynamic mode selection and effective power sharing between the battery and supercapacitor while respecting state-of-charge (SOC) limits. The results show that the modified method significantly reduces the required HESS size while maintaining reliable performance during grid disturbances. Overall, the proposed multi-objective sizing and control framework offers a practical solution for integrating HESS in modern wind turbine systems.