## 2 Methodology
### Fuel Cell Vehicle Power System Modelling
#### 2.1.2 Fuel Cell Variable Load Cycle  
To optimize fuel cell and power battery collaboration, three key factors were considered as follows:  
(i) Fuel cell durability: The durability of a fuel cell is affected by the frequency and magnitude of load changes. Frequent and large load changes will accelerate the accumulation of mechanical and chemical stresses inside the fuel cell, affecting its life. The high variable load speed of the fuel cell will cause the membrane electrode assembly (MEA) to undergo greater mechanical stress and a greater chemical degradation rate, especially when the load changes frequently and greatly. By setting the appropriate variable load period \(T_{load}\), the frequency and amplitude of load change can be controlled. The variable load rate \(v_{load}\) is calculated as follows:  
\[v_{load}=\frac{\Delta P}{T_{load}} \tag{1}\]  
where \(\Delta P\) is the variable load amplitude. Long \(T_{load}\) can reduce the rate of reducing each variable load, thereby reducing the impact on the fuel cell membrane electrode assembly and improving its durability.  
(ii) Output characteristics of fuel cells: The output characteristics of fuel cells are soft and slow in response. In order to ensure that the fuel cell can supply the current steadily and avoid output instability or reduced efficiency due to frequent or drastic load changes, it is necessary to give the fuel cell sufficient time to adjust the output. The variable load cycle of the fuel cell should be long enough to ensure that its output can gradually adapt to new requirements when the load changes, avoiding the impact on system stability.  
\begin{table}
\begin{tabular}{c c} \hline
**Vehicle Type** & **49 Ton Fuel Cell Semi-Tractor** \\ \hline Rated power of drive motor (kW) & 236 \\ \hline Peak power of drive motor (kW) & 360 \\ \hline Fuel cell power rating (kW) & 125 \\ \hline Power battery total energy (kWh) & 141.312 \\ \hline Power battery nominal voltage (V) & 614.4 \\ \hline Power battery nominal capacity (Ah) & 230 \\ \hline Power battery pulse discharge ratio (C) & 2 \\ \hline Power battery pulse discharge time (s) & 30 \\ \hline \end{tabular}
\end{table}
Table 1: Power configuration of fuel cell vehicle.  
Figure 1: Structure of fuel cell and power battery.  
(iii) Pulse discharge time of the power battery: The power battery provides peak power when the car encounters high power demand (such as acceleration or climbing), and the pulse discharge time it can provide is usually 30-60 s. As an auxiliary energy source, the power battery can provide high currents in a short period of time, thereby reducing the instantaneous load demand of the fuel cell and extending the variable load cycle of the fuel cell to a certain extent. Therefore, in fuel cell commercial vehicles, during the peak power provided by the power cell, the fuel cell can gradually adjust the output to avoid drastic load changes affecting the durability of the fuel cell. For example, within 30 s of a power battery discharging, a fuel cell can gradually increase its output power without having to immediately reach maximum output in a short period of time.  
Based on the above three considerations, the variable load period of the fuel cell can be set to 15 s on the fuel cell commercial vehicle. In this cycle, only the variable load rate of the fuel cell is greater than 10 kW/s, that is, only a lower variable load rate can meet the power needs of the vehicle. This cycle length is combined with the 30-60 s pulse discharge time of the power battery to ensure that the fuel cell can change load in time during each cycle and effectively match the pulse discharge time of the power battery. Specifically, the 15 s variable load cycle is moderate, neither too frequent to cause fuel cell life attenuation, nor too slow to affect the vehicle power performance, to ensure the stable output of the fuel cell at the same time, to avoid damage caused by large variable load.