This paper proposes a grid-connected power control strategy for a hydrogen storage device integrated on the DC side of a double fed induction generator. In order to compensate for the slow dynamic response of hydrogen energy, the priority of the control signal is set: supercapacitor > hydrogen storage system. The signal conversion module is used to select the working mode to reduce the probability of returning of the supercapacitor and ensure the constant power operation of the electrolyzer. Each unit of the system is controlled by the power control strategy and the DC/DC converter to balance the power fluctuations on the DC bus, and the DC/AC grid-connected inverter is used to sink into the low-voltage AC network. In the case of grid impact, load fluctuations, and uneven wind speed output, the load requirements are met, and the controllable flexible connection is realized, and the wind curtailment is effectively solved. The effectiveness of the model and its control strategy is proved by simulation.