This work examines the operation of the autonomous power system of a geographical island assuming the integration of significant generation shares from renewable energy sources and the installation of the required storage systems. The frequency stability of the system is investigated considering different operating conditions, in terms of load demand and renewable power generation. The main focus of the work is an original control strategy specifically designed for power converters interfacing storage units to the grid. The proposed strategy is based on an extended frequency droop control, which selects specific droop settings depending on the operating mode—charge or discharge—of the storage unit. A simulation model of the whole electrical system is developed for dynamic analysis. The model also implements the possibility of including specific auxiliary frequency controls for synthetic inertia and primary reserve. The results of the simulation and analysis indicate that the proposed control strategy has a significant positive effect, making the storage units able to provide a fundamental and more effective support to the frequency stability of the system. The application of the proposed control strategy to storage units also reduces the need for a contribution to the frequency control from intermittent and variable sources, making the whole system more robust, stable and reliable.