## 4 Results and Discussion
### Fuel Economic  
Figure 3 illustrates the variation in economic costs concerning battery capacity and the weighting factor. As illustrated in Figure 3a, as the battery capacity increases, the economic cost initially decreases and rises, demonstrating a non-linear trend. Additionally, it can be observed that, as the weighting factor increases, the turning point gradually shifts to a smaller value. As illustrated in Figure 4, the increase in economic costs under an insufficient battery capacity arises from the critical role of the battery in regenerative braking and dynamic power supply. A limited battery capacity prevents the system from fully utilizing braking energy and providing adequate dynamic power, reducing energy efficiency and incurring higher economic costs. In Figure 4a, it is evident that, during certain periods, the FCS does not maintain its minimum output, but rather shuts down. This occurs because the battery, due to an insufficient capacity, cannot absorb additional regenerative braking energy, preventing the fuel cell from recharging, and, thus, it must be deactivated. In contrast, as the battery capacity increases, as shown in Figure 4b, the fuel cell remains operational without shutting down. An increase in battery capacity enhances the maximum charge and discharge power, enabling the battery to absorb more regenerative braking energy and provide an improved dynamic response. While the increased absorption of braking energy reduces costs, the improved dynamic response incurs additional costs. This combined effect initially leads to a net reduction in economic costs. As shown in Figure 4b,c, although the 33 Ah battery outputs slightly more than the 22 Ah version, this difference is marginal and does not significantly affect the overall trend. Figure 4: _Cont._  
Figure 3: Relationship between economic cost, battery capacities and weighting factor: (**a**) economic cost vs. battery capacities and (**b**) economic cost vs. weighting factor. Figure 4: Different EMS power distributions for PEMFC and battery under different battery capacities (weighting factor = 0.5): (**a**) battery capacity: 11 Ah, (**b**) battery capacity: 22 Ah, (**c**) battery capacity: 33 Ah, (**d**) battery capacity: 44 Ah, and (**e**) battery capacity: 55 Ah. However, once the battery capacity exceeds a certain threshold, the system reaches a point where the battery can fully absorb all braking energy, and its dynamic response performance is optimized. Beyond this point, further increases in battery capacity contribute to additional system weight, leading to a higher power demand and ultimately increasing the total economic cost. Additionally, it is important to note that, in the final stages of braking, where rapid deceleration occurs, the battery does not fully absorb all of the regenerative braking energy. This is due to the high braking power in these final moments, which exceeds the battery's maximum power output, limiting its ability to absorb the full amount of regenerative energy. As shown in Figure 2(b), economic cost exhibits a relatively lower sensitivity to variations in battery capacity compared to changes in the weighting coefficient. The figure reveals a significant reduction in economic cost with an increasing weighting factor, driven by the EMS's prioritization of routes with a lower hydrogen consumption. Although both the weighting coefficient and battery capacity influence energy distribution by altering the FC output power, their underlying mechanisms are fundamentally different. An insufficient battery capacity restricts dynamic power supply, limiting the system's ability to meet transient demands and forcing the FC to deliver high power to compensate. Conversely, a low weighting factor drives the EMS to prioritize fuel economy by favoring FC operation within higher-efficiency regions. This strategy also requires the FC to sustain a high power output, even under less favorable operating conditions. These contrasting mechanisms underscore their distinct impacts on energy management strategies.