As the penetration of renewable energy generation increases, the importance of energy storage systems becomes evident since these systems can contribute for the preservation of the power system stability. Wind turbine owners can also benefit from having energy storage systems as they can increase their revenues. The fast growth of wind turbine power ratings will eventually lead to the requirement of higher voltage levels as well. Proper power electronic converters will be required to drive these systems. Converters with a modular multilevel structure are considered the state-of-the-art solution for high-power applications. These topologies allow for a flexible integration of energy storage systems in both centralized and decentralized ways. This article presents a new converter solution with a modular multilevel structure and decentralized energy storage integration suitable to drive high-power medium-voltage wind turbines. This converter presents important structural and control characteristics that allows for a straightforward integration of an energy storage system in such a way that the wind turbine driven by it can operate with high flexibility and in a dispatchable fashion, benefiting both the power system operator and the wind-power-plant owner.