## 1 Introduction
### Hydrogen Energy Technology  
Hydrogen energy, with its green and carbon-free characteristics, is well-suited for long-term storage and is a key medium for building a low-carbon and efficient modern energy system. Hydrogen energy technology has the potential to participate in the flexible interaction and regulation of the power grid at multiple stages, including hydrogen production, storage, and utilization. Electrolytic hydrogen production can act as a highly adjustable load, effectively enhancing the flexibility and security of the power system and promoting the consumption and utilization of new energy sources. It can also be combined with hydrogen storage equipment, hydrogen combustion units, or fuel cells to achieve the large-scale, long-duration storage and conversion of new energy, effectively ensuring the sustainable and large-scale development and utilization of new energy sources. In terms of hydrogen storage, high-pressure gaseous storage has low energy consumption but a relatively low storage efficiency of about 3-38 kg/m\({}^{3}\). Low-temperature liquid storage has an extremely high efficiency of 71-120 kg/m\({}^{3}\), but its energy consumption is 1-2 times that of the former. In terms of hydrogen utilization, fuel cells have a high power generation efficiency of approximately 60-80% and excellent flexible regulation performance. However, they are currently constrained by technological breakthroughs and high costs. In the long term, they have the broadest potential to participate in flexible grid regulation. The development trends of hydrogen energy technology in the future are shown in Table 3, where proton exchange membrane (PEM) electrolysis for hydrogen production, high-pressure gaseous hydrogen storage, and proton exchange membrane fuel cell technology are all key development directions for hydrogen energy technology. In the future low-carbon transformation of the power sector, the development scale of hydrogen energy technology will mainly be determined by the demand for hydrogen production electricity and the flexibility regulation needs of the power system. The specific mathematical model is shown in the following formula:  
\[\left\{ \begin{array}{l}S^{P2H}=\sum\limits_{t=1}^{8760}P_{t}^{P2H}\bullet \Delta T\\ P_{\min}^{P2H}\leq P_{t}^{P2H}\leq P_{\max}^{P2H}\\ \left|P_{t}^{P2H}-P_{t-1}^{P2H}\right|\leq\Delta P^{P2H}\\ P_{\max}^{P2H}\leq P_{\max}^{P2H}\leq P_{\max,\max}^{P2H}\\ \left|P_{\text{Not},t}^{P2H}-P_{\text{Not},t-1}^{P2H}\right|\leq\Delta P_{ \text{stop}}^{P2H}\\ P_{\text{slot},t}^{P2H}\leq P_{\text{Not},t}^{P2H}\\ \left|S_{\text{slot},t}^{P2H}=S_{\text{slot},t-1}^{P2H}+P_{\text{slot},t}^{P2H }\bullet T\\ S_{\text{slot},\min}^{P2H}\leq S_{\text{slot},t}^{P2H}\leq S_{\text{slot}, \max}^{P2H}\end{array} \right. \tag{3}\]  
In the formula, \(S^{P2H}\) represents the annual electricity demand for hydrogen production. \(P_{t}^{P2H}\) represents the power of electrolytic hydrogen production at time \(t\). \(P_{\min}^{P2H}\), \(P_{\max}^{P2H}\) represent the upper and lower limits of the electrolytic hydrogen production power variation at time \(t\). \(\Delta P^{P2H}\) represents the maximum rate of change of the electrolytic hydrogen production power. \(P_{\text{slot},t}^{P2H}\) represents the charging and discharging power of the hydrogen energy storage at time \(t\). If \(P_{\text{slot},t}^{P2H}\) is less than 0, it indicates charging, and if greater than 0, it indicates discharging. \(P_{\text{slot},\min}^{P2H}\), \(P_{\text{slot},\max}^{P2H}\) represent the maximum charging and discharging power limits of hydrogen energy storage. \(\Delta P_{\text{slot}}^{P2H}\) represents the maximum rate of change of hydrogen energy storage power. \(S_{\text{slot},t}^{P2H}\) represents the amount of hydrogen energy stored at time \(t\). \(S_{\text{slot},\min}^{P2H}\), \(S_{\text{slot},\max}^{P2H}\) represent the upper and lower limits of the hydrogen energy storage capacity.