A large-capacity low-speed flywheel energy storage system based on a doubly-fed induction machine (DFIM) basically consists of a wound-rotor induction machine, and a back-to-back converter for rotor excitation. It has been promoted as a challenging storage system for power system applications such as grid frequency support/control, power conditioning, and voltage sag mitigation. This paper presents a power control strategy to charge/discharge a flywheel doubly-fed induction machine storage system (FW-DFIM) to obtain a constant power delivered to the grid. The proposed controller is based on conventional vector control, where an artificial neural network (ANN) is used to develop the required rotor current component based on the required grid power level and the flywheel instantaneous speed. This technique is proposed for power levelling and frequency support to improve the quality of the electric power delivered by wind generators, where a constant power level can be delivered to the grid for a predetermined time depending on the required power level and the storage system inertia. The controller is designed to avoid overloading stator as well as rotor circuits while the flywheel charges/discharges. The validity of the developed concept in this paper, along with the effectiveness and viability of the control strategy, is confirmed by computer simulation using Matlab/Simulink for a medium voltage 10MJ/1000hp FW-DFIM example.