With the expansion of islanded hydrogen production systems, the randomness and volatility of renewable energy pose higher requirements for the power supply reliability of energy storage systems (ESS). This paper presents an adaptive hierarchical control (AHC) strategy for parallel energy storage units (ESUs) in electrolytic hydrogen production systems to improve the reliability of power supply. In this strategy, each ESU is considered an agent and a dynamic average consensus algorithm is used to obtain the average value of the observed quantities. In the primary control layer, a sigmoid function is proposed to improve the droop coefficient, enabling the state of charge (SoC) of each ESU to converge to the average value. On this basis, a novel acceleration factor based on a normal distribution function is designed to accelerate the speed of SoC balancing in the later stage. In the secondary control layer, a unit virtual voltage drop balancing term and an average voltage compensation term are used to distribute the output current of ESUs proportionally according to their capacity and restore the average bus voltage deviation. The stability analysis confirms that the proposed method is strongly stable. Finally, a photovoltaic hydrogen production simulation model and a StarSim HIL experimental platform are established. The results show that the proposed control strategy can achieve rapid SoC balancing and accurate load current distribution with excellent average bus voltage compensation under various complex operating conditions.