## 4 Results and Discussion
### System Durability Cost  
From a durability perspective, a limited battery capacity intensifies the dynamic power demands on the FCS, as the reduced power output from the battery is insufficient to effectively buffer these fluctuations. Consequently, the FCS is forced to operate under suboptimal conditions, accelerating its degradation. In contrast, when the battery has suffi  
Figure 5: Different EMS power distributions for PEMFC and battery under different weighting factors (battery capacity = 44 Ah): (**a**) weighting factor: 0.1, (**b**) weighting factor: 0.3, (**c**) weighting factor: 0.5, (**d**) weighting factor: 0.7, and (**e**) weighting factor: 0.9.  
cient capacity to accommodate dynamic power demands, the durability cost is significantly reduced and eventually stabilizes.  
From the perspective of durability costs, the primary concern is the specific degradation of energy sources. Increasing the battery capacity helps to mitigate this issue by reducing the duration for which the FCS operates under unfavorable conditions, thereby significantly lowering fuel cell degradation, as shown in Figure 6a. At a battery capacity of 11 Ah, fuel cell degradation is particularly pronounced. When the battery capacity is too small, the fuel cell must frequently shut down, and the associated start-stop cycles lead to substantial degradation, making the degradation at 11 Ah significantly higher than that in other scenarios.  
At a battery capacity of 44 Ah, the fuel cell system operates under near-optimal conditions, where degradation is minimized. Beyond this point, further increases in battery capacity result in diminishing returns in terms of reducing degradation. Additionally, larger battery capacities reduce the current demand per cell for equivalent power outputs, leading to lower discharge rates and further mitigating battery degradation costs, as shown in Figure 6b.  
As previously mentioned, increasing the weighting coefficient reduces economic costs. However, this comes at the expense of higher durability costs. FC degradation is the primary contributor to durability costs, as shown in Figure 7a. In contrast, BAT degradation exhibits a declining trend at lower weighting factors, as shown in Figure 7b. This behavior arises because, under these conditions, the EMS prioritizes system durability. Given the higher cost of the FC compared to the BAT, the EMS minimizes unfavorable operating conditions for the FC, resulting in the BAT handling more dynamic power demands. Consequently, the BAT experiences relatively higher degradation, as its power output is ultimately derived from the FC, incurring additional economic costs. As the weighting factor increases, the emphasis on economic costs grows. Compared to durability degradation, the economic losses associated with the BAT power output change more rapidly. In the intermediate range of weighting factors, the BAT power output increases to balance economic and durability trade-offs, leading to a slight rise in durability degradation. However, at higher weighting factors, where economic cost considerations dominate, the EMS places a greater emphasis on minimizing the economic losses associated with the BAT power output. As a result, the BAT power output decreases, and the FC assumes a greater share of the dynamic power demands.  
Figure 6: Per kilometer performance degeneration percentage of fuel cell and battery under different battery capacities: (**a**) fuel cell and (**b**) battery.