Hydrogen energy storage (HES) has attracted renewed interest as a means to enhance the flexibility of power balancing to achieve the goal of a low-carbon grid. This paper presents an innovative data-driven HES model that reflects the interactive operations of an electrolyzer, a fuel cell, and hydrogen tanks. A model predictive control strategy is then developed, in which HES units support the frequency regulation (FR) of a microgrid (MG). In the proposed strategy, an MG-level controller is designed to optimize power sharing, to allow the HES units to respond quickly to power supply-and-demand imbalances, while distributed generators compensate for any remaining imbalance. The MG-level controller cooperates with the HES-level controll- ers, which change the operating modes and override the FR supports based on the hydrogen levels. Small-signal analysis is conducted to evaluate the contribution and sensitivity of the FR supports. Comparative case studies are also carried out, wherein HES model accuracy is verified and a hardware-in-the-loop simulation is implemented. The results of the small-signal analysis and case studies confirm that the proposed strategy is effective for reducing frequency deviations under various MG conditions, characterized by the net load demand, line congestion, plug-and- play, model parameters, and communication time delays.