## 3 The Impact of Size and Dynamic Limitations
### Impact on Fuel Cell Performance  
The maximum power and dynamic response of a fuel cell system can significantly impact the performance output of the fuel cell, leading to different trends in current density variations. Therefore, considering the degradation and output performance of the fuel cell system under real-world operating conditions, this section analyzes the trends in fuel cell output performance with changes in power and dynamic response. Figure 8 illustrates the current density variations for fuel cells rated at 100 kW and 200 kW. In the figure, the analysis of maximum power and minimum power design for fuel cell stack performance and degradation is conducted by introducing the change rate of fuel cell current density as a comparative condition. The study selects current density change rates of 0.001 A/cm\({}^{2}\), 0.01 A/cm\({}^{2}\), 0.1 A/cm\({}^{2}\), and 1 A/cm\({}^{2}\), corresponding to strict power limitations and ideal conditions with no limitations. In Figure 8a, where the fuel cell current density change rate is controlled at 1 A/(cm\({}^{2}\cdot\)s), it corresponds to no control over the fuel cell's output performance (only existing in the simulation). The energy management strategy aims for power performance and charge maintenance without considering the fuel cell's aging and dynamic response. When increasing the fuel cell power, it can be observed that the time for the fuel cell to reach its rated power output decreases. This is because high-power fuel cells can instantly deliver a large amount of power to meet the power demand and energy storage requirements of the power battery, whereas low-power fuel cells need to sustain themselves at high power \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline Vehicle Mass & kg & 12,150 \\ Windward area & m\({}^{2}\) & 8.32 \\ Radius & mm & 542.5 \\ Air drag coefficient & - & 0.6 \\ Rolling resistance coefficient & - & 0.015 \\ Battery capacity & kW.h & 123.1 \\ Initial SOC & \% & 72 \\ Battery voltage & V & 600 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: FCHEV parameters. Figure 7: Simulation and experimental comparison of polarization curves of fuel cells before and after durability. levels for a longer time to meet the power demand. Since fuel cell systems are primarily composed of individual fuel cells, the shorter the time they operate at maximum power, the higher their efficiency and economic performance. Therefore, fuel cells with lower rated power cannot simultaneously balance efficiency and economic performance while meeting power requirements. Figure 8b represents setting the fuel cell's current density change rate to 0.1 A/(cm\({}^{2}\cdot\)s). Although this limitation is still low compared to the actual dynamic characteristics of the fuel cell, a comparison between Figure 8a,b reveals that some high-power points in Figure 8a cannot be achieved. In order to meet the power demand, the fuel cell also tends to reduce the time spent operating at minimum power. These phenomena are more pronounced in the fuel cell curve with a maximum power of 100 kW. In addition, due to this dynamic limitation, the power changes of 200 kW and 100 kW fuel cells become relatively stable. Combined with the fuel cell degradation model, it can be seen that a gentle load change in fuel cells will increase durability. Figure 8c,d illustrate the variations in fuel cell output power when the current change rate is limited to 0.01 A/(cm\({}^{2}\cdot\)s) and 0.001 A/(cm\({}^{2}\cdot\)s), respectively. In these cases, due to the stringent restrictions on the fuel cell's dynamic response, it can be clearly seen that the power output of the fuel cell becomes smoother. In Figure 8c, both fuel cells with different maximum power settings reduce the time spent operating at the minimum power point. As the power demand increases, the 100 kW fuel cell increases the time spent operating at the rated power point. At this higher current density, the fuel cell generates more heat, leading to noticeable high-power degradation.