Abstract Hydrogen production from wind power can reduce wind abandonment and improve the utilization rate of wind power. However, both “source” turbulence caused by unstable wind speed and “load” turbulence caused by sudden load changes will adversely affect the stable operation of power‐to‐hydrogen systems and the grid connection stability of wind farms. A synergistic control strategy between a supercapacitor and power‐to‐hydrogen system is proposed to solve this problem. The strategy is based on the ensemble empirical‐mode decomposition algorithm. By using the supercapacitor to stabilize the high‐frequency component in the “source–load” turbulence, the stability of the power‐to‐hydrogen system is improved. An optimal allocation method of supercapacitor capacity suitable for the control strategy is then proposed. Considering the different states of each fan and supercapacitor, the unit inertia time constant variance is reduced by reasonably distributing the output of each unit. This effectively improves the inertia time constant and grid connection stability of the wind farm. Finally, the effectiveness of the strategy is verified by Simulink simulations.