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To solve the problem of unbalanced power supply and demand caused by the large-scale integration of intermittent renewable energy sources, this study presents a novel type of power device that integrates hydrogen energy storage. First, the composition and operation principle of the integrated hydrogen energy storage power device (IHESPD) are introduced. Then, the causal ordering graph is used to establish three sub-models of hydrogen production, hydrogen storage, and power generation of the IHESPD. Based on this foundation, a control-oriented electrochemistry model of the IHESPD is developed by connecting the inputs and outputs of each sub-model. Next, to ensure the stable operation of the IHESPD, a simple power and hydrogen flow control strategy is proposed considering the operation characteristics. In addition, according to the characteristics of the compressor map, high- and low-pressure hybrid hydrogen storage is used to improve the efficiency of compressed hydrogen storage. Finally, the effectiveness of the IHESPD is tested by conducting real-time hardware-in-the-loop experiments using RT-LAB. In the test case, the average efficiency of compressed hydrogen storage obtained is approximately 67%, with a minimum efficiency of 50%. Further, the average operating efficiency of the integrated power device is 35.89%. Compared with the single pressure hydrogen storage, the average operating efficiency is increased by more than 23.6% (23.6–28.3%) and the minimum operating efficiency is increased by more than 51% (51–400%).