This paper presents a planning framework to investigate the impact of different levels of integration of large-scale energy storage on the development plan of a meshed HVDC grid in a power system with large-scale offshore wind. In our problem formulation, the charge/discharge schedules of energy storage are modeled in such a way that market conditions in the succeeding hours are taken into account in the power dispatch at present. Both unlimited and limited energy storage capacity scenarios are considered, and compared to a no-storage reference case. The optimal plan includes grid topology, transmission capacities, energy storage capacities and optimal energy storage schedules. The optimization model sets the transmission capacities in such a way that transmission congestion revenue collected throughout the lifetime of the infrastructure pays off the investment cost of building the grid. The proposed model is applied to study the future development of an offshore grid in the North Sea. Simulation results are assessed according to various economic indicators. Investing in energy storage is shown to be economically effective for windy offshore regions.