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In electrical islands, frequency excursions are sizeable and automatic load shedding is often required in response to disturbances. Moreover, the displacement of conventional generation with wind and solar plants, which usually do not provide inertial response, further weakens these power systems. Fast-acting storage, by injecting power within instants after the loss of a generating unit, can back up conventional generation assets during the activation of their primary reserve. This paper relies on dynamic simulations to study the provision of such a dynamic frequency control support by energy storage systems in the French island of Guadeloupe with large shares of wind or solar generation. The results show that fast-acting storage, by acting as a synthetic inertia, can mitigate the impact of these sources on the dynamic performance of the studied island grid in the case of a major generation outage. The other concerns raised by renewables (e.g., variability, forecast accuracy, low voltage ride-through, etc.) have not been addressed within this project.