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This paper analyzes the electromechanical interaction in a flywheel system with a doubly fed induction machine, used for wind farm power smoothing or grid frequency response control. The grid-connected electrical machine is subject to power control, and this can cause it to produce negative damping to the shaft torsional vibration. Resonance must be prevented, and this paper proposes a solution by coordinating the design of the electrical controller and mechanical shaft. Computer simulations are used to demonstrate the problem and the proposed solution.