## 2 Analysis of the Operating Mechanism of a Hybrid Plant Station Primary Frequency Regulation
### Mathematical Model and Dynamic Characteristics Analysis of the Electric Hydrogen Production Device
In summary, because of its operating and dynamic features, the electric hydrogen generation device cannot fully respond to the frequency regulation power when it participates in the system's frequency regulation. The electric hydrogen generation and energy storage devices complement each other regarding frequency regulation features. Facilitate the recovery of system frequency by using rapid power correction. Comparative Analysis of the Electrical Characteristics of Different Energy Storage Devices Combined with the P2H Device  
Select from three distinct categories of energy storage apparatuses. Relevant research findings on flywheel energy storage, batteries, and supercapacitor energy storage systems (SCESS) are included in Appendix B, along with projections for potential future development scenarios. To improve frequency control effects in the hybrid power station, choose the right kind of energy storage device based on the information in the figure and the electrical properties of each energy storage device [34]. A schematic depiction of the findings comparing different energy storage systems can be found in Figure 3.  
The electric hydrogen generation device has great power control capabilities on medium and long time scales, as demonstrated in Figure 3a. It also boasts a good capacity economy. However, the flexibility and performance of short-time high-frequency power regulation are lacking. The storage battery's electric properties indicate a medium level, meaning it cannot work with the electric hydrogen production unit to produce complementary advantages. Flywheels and supercapacitors have a high charging and discharging economy and can adapt flexibly to short-term high-frequency power demands. As shown in Figure 3b, the energy storage devices, both flywheel and supercapacitor, can make up for the deficiency of dynamic characteristics of electric hydrogen production devices. After combining the two devices with electric hydrogen production devices, the system presents higher electrical parameter indices. However, flywheel energy storage is still in the early commercialization stage and has yet to be applied in large-scale engineering. Therefore, the supercapacitor is combined with the electric hydrogen production device to assist a hybrid plant station in participating in the primary frequency regulation. Influence of the P2H and SCESS Dynamic Characteristics on the Frequency Regulation Effect of the Hybrid Plant Station  
The P2H device and the SCESS are the power sources of a hybrid plant station that is taking part in the system frequency regulation; so, the frequency regulation outcomes will be impacted by the dynamic response characteristics of the two. Taking into account the  
Figure 3: Comparison of parameters for various energy storage devices and combined with P2H. P2H device's operating characteristics, when a hybrid plant station engages in the primary frequency regulation of the system, the P2H device can assume the following frequency regulation power through load shedding:  
\[\Delta P=P_{\rm P2 Hreal}-N\times P_{\rm min} \tag{12}\]  
Among them, \(P_{\rm P2 Hreal}\) is the operating state of the P2H device; \(N\) is the number of electrolyzers opened; and \(P_{\rm min}\) is the minimum working limit of the electrolyzer. The actual load-shedding power of electric hydrogen production is limited by climbing ability, as shown in Equation (13):  
\[\lim_{\Delta t\to 0}\frac{P_{\rm P2H}(t)-P_{\rm P2H}(t-\Delta t)}{\Delta t} \leq N\times\Delta P_{\rm max} \tag{13}\]  
Therefore, when \(\Delta P=P_{\rm wsp}\), the SCESS needs to compensate for the energy as shown in Equation (14):  
\[E_{\rm SC}=\int_{0}^{t_{1}}{(\Delta P-N\Delta P_{\rm max}t)dt} \tag{14}\]  
In the equation, \(t_{1}\) is the time when the actual load reduction power of the P2H device reaches \(\Delta P\). Equations (12)-(14) show that the number of electrolyzers opened has an impact on the P2H device's load-shedding power.