## 4 Case Analysis and Discussion
### Discussion
In terms of optimization objective functions, compared with the decreasing per unit hydrogen production cost of AWE, the PEME had a more significant effect on optimization objective \(J_{1}\), which exhibited monotonicity. As the proportion of PEME rose, the optimization objective function \(J_{2}\) declined substantially. In contrast, the optimization objective function \(J_{2}\) increased significantly. The makeup of the hydrogen production electrolyzer considerably influences the optimization objective function \(J_{2}\). Thus, the relative per unit hydrogen production cost of AWE and PEME is a key technical indicator determining the composition and hybrid ratio of hydrogen production. This relationship is critical, as it fundamentally affects the optimization objective function \(J_{2}\). Figure 7: The optimization results with changes in the efficiency of AWE and PEME. In Figure 9, when the per unit power investment cost of AWE ranged from 600 \(\forall\)/MW to 1600 \(\forall\)/MW, and that of PEME ranged from 3500 \(\forall\)/MW to 4500 \(\forall\)/MW, the hydrogen production electrolyzer operated under a hybrid electrolyzer framework. The planning results of the hybrid electrolyzer depend on the relative power investment cost of AWE and PEME; the rated power does not only show monotonicity in a single direction. For instance, as AWE's per unit power investment cost decreases, mainly when it falls below 1100 \(\forall\)/MW, the proportion of AWE increases. However, this increase is significantly impacted by the per unit power investment cost of PEME. Regarding the optimization objective functions, the per unit power investment costs of AWE and PEME exerted a substantial and monotonic effect on the optimization objective function \(j_{1}\). For example, if the AWE's per unit power investment cost is less than 850 \(\forall\)/MW, the proportion of AWE rises. This leads to a significant increase in hydrogen production resource losses. Conversely, if the per unit power investment cost of AWE exceeds 1200 \(\forall\)/MW, the proportion of PEME increases, significantly reducing the hydrogen production losses. Figure 8: The optimization results with changes in the producing cost of hydrogen by AWE and PEME. Under the stand-alone operation condition, the supply of new energy and the consumption of power loads significantly influence the hybrid electrolyzer's planning results. Therefore, Figure 10 examines the hybrid electrolyzer's configuration results based on varying the permissible abandonment rates of new energy sources and allowable cut-off rates of the load. Figure 10 illustrates that if the abandonment of new energy increases, the total rated power of hybrid electric generators will decrease. Consequently, a higher hydrogen production efficiency is required to satisfy the demand for hydrogen energy supply. As a result, the rated power of PEME in the hybrid electrolyzer remains relatively constant, while the rated power of AWE decreases. Moreover, with the permissible cut-off rate of load ascending, the rated power of PEME increases to remain steady, but AWE will slowly decrease and then be scaled up. This shows that if the electricity consumption of other loads is reduced, the total rated power of the hybrid electrolyzer will increase. In the newly added power of the hybrid electrolyzer, the proportion of AWE and PEME will be affected by the hydrogen production efficiency and cost parameters. Regarding the optimization objective functions, the abandonment rate of new energy had almost no effect on optimization objective function \(J_{1}\). However, as the permissible cut-off rate of load rose, the optimization objective function \(J_{2}\) showed a linear and rapid decline. This decrease can be attributed to the expansion of total rated power within the hybrid electrolyzer. The optimization objective function \(J_{2}\) is constrained by both the permissible abandonment rate of new energy and the permissible cut-off rate of load.