## 4 Case Analysis and Discussion  
### Parameter Description  
Based on the structure of the stand-alone wind-photovoltaic-battery system with the hybrid electrolyzer comprising both AWE and PEME that is shown in Figure 1, a simulation model was constructed to validate the efficacy of the proposed methodology. This simulation case incorporated a PVG, WTG, a lithium-ion BESS, AWE unit, PEME unit, and HST. The system parameters are detailed in Table 1[31, 33, 34]. The unit of hydrogen production cost refers to the Chinese CNY, \(\forall\). Figure 3 shows the power curves of the load, PVGs, and WTGs in a day. The time interval was \(\Delta t=1\) h, resulting in a total simulation time of T = 24 h. In this study, the HST was assumed to possess sufficient capacity, and the purity of hydrogen and the form of hydrogen produced remained consistent across different electrolyzer configurations. These ensured equivalent conditions for both single-type electrolyzers and hybrid electrolyzer configurations within the proposed framework. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Simulation Parameter** & **Value** & **Simulation Parameter** & **Value** \\ \hline Rated power of the PVGs & 100 MW & Maximum power of AWE & 100 MW \\ Cost per kW/h of the PVGs & 0.359 \(\forall\)\(\times\)kWh & Efficiency of AWE & 60\% \\ Rated power of the WTGs & 100 MW & The investment cost of AWE & 1233.33 \(\forall\)\(\times\)kWh \\ Cost per kW/h of the WTGs & 0.242 \(\forall\)\(\times\)kWh & The hydrogen production cost of AWE & 22.425 \(\forall\)\(\times\)kg \\ Rated power of the BESS & 20 MW & Energy consumption of AWE & 55.56 kWh/kg \\ Rated capacity of the BESS & 40 MWh & Operation life of AWE and PEME & 20 years \\ Cost per kW/h of the BESS & 0.7 \(\forall\)\(\times\)kWh & Maximum power of PEME & 100 MW \\ Charging efficiency of the BESS & 95\% & Efficiency of PEME & 90\% \\ Discharging efficiency of the BESS & 92\% & Investment cost coefficient of PEME & 4000 \(\forall\)\(\times\)kWh \\ SOE range of the BESS & 10–90\% & The hydrogen production cost of PEME & 29.903 \(\forall\)\(\times\)kg \\ Initial SOE of the BESS & 50\% & Energy consumption of PEME & 48.89 kWh/kg \\ Capacity of the HST & 20,000 m\({}^{3}\) & Maximum hydrogen sales rate & 10,000 m\({}^{3}\)/h \\ SOH range of the HST & 10–90\% & Hydrogen sales revenue & 50.4 \(\forall\)\(\times\)kg \\ Initial SOH of the HST & 50\% & Discount rate \(\gamma\) & 8\% \\ The abandonment rate of new energy & 5\% & Initial stepper parameter \(\Delta c\) & \(10^{-3}\) \\ source \(\delta_{1}\) & 5\% & Initial stepper parameter \(\Delta c\) & \(10^{-3}\) \\ Cut-off rate of load \(\delta_{2}\) & 3\% & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. Table 1 illustrates various energy types in this simulation case including PVGs, WTGs, BESS, and hydrogen energy. The hybrid electrolyzer in this system comprised both AWE and PEME. AWE offers significant advantages regarding investment and hydrogen production costs; however, PEME is notably more efficient. Consequently, a hybrid electrolyzer will leverage the advantages of both AWE and PEME, enhancing the economic viability and energy utilization efficiency. Figure 3 shows that for most of the day (areas A, C and E), the output power of the new energy source exceeded the power required by the load. The peak surplus power occurred at 12 h, demonstrating an excess power generation capacity exceeding 90 MW. Under stand-alone conditions, this discrepancy can lead to a significant waste of wind and photovoltaic energy. However, this issue can be addressed by producing and selling hydrogen energy. Conversely, there were times when the power consumption of the load surpassed that of the new energy source such as area B (6:00-9:00) and area D (19:00-22:00). In particular, at 20:00, the demand exceeded 30 MW. To ensure that the power consumption of the load is met, a BESS should be integrated into this energy system. Meanwhile, this study compared the proposed method with other standard multi-objective optimization methods.