Energy storage systems (ESS) can enhance the reliability of service in power systems with a high share of renewable energy sources. A converter topology that can integrate ESS directly into an HVDC system is presented in this work. The topology consists of a branch of energy storage submodules (ES-SMs) and an inductor. The ES-SMs are based on half-bridges, which are connected to a supercapacitor or a battery by means of a dc/dc converter. The topology is scalable to different voltage levels and since the energy storage elements are distributed among all submodules, it provides a high degree of redundancy. In this work, the converter topology is modelled using an average model and its control designed to regulate the injected dc power and the energy of the ES-SMs. A preliminary sizing of the main elements of the topology is also provided. The simulations show that the ES-SMs can both inject and absorb power from the HVDC system, while maintaining the desired energy in the ES-SMs capacitors.