## 3 The Impact of Size and Dynamic Limitations
### Impact on the Durability of Fuel Cells  
In this section, we will analyze the impact of fuel cell rated power and current density variation rate on the durability of the fuel cell. Durability refers to the ability of the fuel cell to maintain its performance and lifespan during long-term operation.  
Based on the analysis results from the previous section, we can infer that the rated power and current density variation rate also have an impact on the degradation rate of fuel cells. Figure 10 illustrates the variations in degradation factors of fuel cells under different rated powers and current density variation rates. By considering the analysis in Figure 11, we can observe their combined effects. According to the lifespan termination criteria established by the Department of Energy, the fuel cell's lifespan reaches its endpoint when the power relative to the nominal voltage decreases by 10%. In this experiment, the fuel cell's nominal power was used, corresponding to a current density of 1.6 A/cm\({}^{2}\).  
When increasing the rated power of the fuel cell system there is a significant impact on the degradation distribution of the fuel cell. From Figure 11, it can be observed that, in the absence of dynamic limitations, the 100 kW designed fuel cell has a 15% increase in lifespan compared to the 200 kW fuel cell. Combining this with Figure 10, it becomes apparent that this is due to lower degradation caused by load variations in the lower-power fuel cell. Figure 8a indicates that higher-power fuel cells exhibit more pronounced load variations in the unrestricted state, leading to an increased proportion of degradation caused by load changes. The proportion of degradation caused by load variations increases from 43.1% to 48.1%. Additionally, from Figure 10, it can be seen that start-stop events are the second-largest contributing factor to degradation, and they are not influenced by cycling conditions but rather by the number of start and stop cycles. As the rated power of the fuel  
Figure 9: Normalized comparison of equivalent hydrogen consumption.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Power (kW)** & **100** & **160** & **200** \\ \hline H\({}_{2}\) Consumption (g) & 3401.7 & 3380.4 & 3386.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Equivalent hydrogen consumption at a current density change rate of 0.01 A/cm\({}^{2}\).  
cell system increases, the proportion of low-power operation increases while the duration of high-power operation decreases.  
From Figure 10, it can be observed that as the restriction on current density variation rate becomes more stringent, the proportion of degradation caused by load variations increases. Therefore, imposing dynamic variation restrictions on the fuel cell system is the most effective way to increase its lifespan. Figure 11 also demonstrates that reducing the current density variation rate can effectively extend the fuel cell's lifespan. Comparing the working conditions of the fuel cell with no dynamic restrictions to the most stringent dynamic restriction, the durability of the 100 kW and 200 kW fuel cells increases by 106% and 101%, respectively. Although it may not be feasible to apply such strict restrictions in practical situations, limiting the current density to 0.1 A/cm\({}^{2}\)-s and 0.01 A/cm\({}^{2}\)-s can still yield improvements of approximately 20% and 50%, respectively. This increase in lifespan is primarily attributed to the reduction in degradation caused by load variations. Under a rated power of 160 kW, the degradation caused by load variations ranges from 5.7% to 43.9% of the total degradation. Combining this with Figure 11, it can be observed that  
Figure 11: Normalization of fuel cell lifecycle.  
Figure 10: The effect of current density on degradation.  
the projected lifespan of the fuel cell increases incrementally, with a maximum increase of 106%.