## 4 Cold Start Control Strategy for PEMFC-MH Coupling System
### Analysis of PEMFC-MH System Cold Start Results  
The heat sources for the preheating process include air compression preheating, radiator heating, and MHT hydrogen absorption preheating. The preheating power output of different preheating sources during preheating is shown in Figure 12. From the figure, it can be seen that the preheating power of MHT at a lower initial SOC is significantly higher than the preheating power of the heater and air compressor, which are the main heat sources in the preheating period. Due to the constant operating parameters of the radiator as well as the air compressor during the preheating period, the preheating power output from the heater and the air compressor is constant at 9 kW and 5.7 kW, while the MHT reaches a maximum peak preheating power of 39 kW at an initial SOC of 10% and a hydrogen charging pressure of 4 bar. During the cold start period, the preheating of the stack by the radiator and the MHT uses thermal convection, while the preheating of the  
Figure 11: Effect of initial SOC on preheating power. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Actuator Parameters** & **Preheating** & **Self-Heating** \\ \hline Stack current/A & 0 & 0-300 \\ Thermostat opening/\% & 0 & 0 \\ Air compressor/rpm & 6000 & \(LUT(I_{req})\) \\ Air compressor pressure ratio & 2 & \(LUT(I_{req})\) \\ Radiator power/kW & 10 & 10 \\ Pump opening/\% & 10 & 10 \\ Pressure-reducing valve/bar & 4 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Cold start parameters. stack by air is a heat exchange between the air and the stack. There is some heat loss with different preheating methods, and the overall preheating time is 75 s.  
In order to investigate the effect of the initial SOC on the preheating process, this paper analyses the percentage of heat provided by different heat sources for the preheating of the stack during preheating. As shown in Figure 13, the lower the initial SOC, the more heat is released by the MHT to absorb hydrogen, with the highest percentage being 65% of the total preheat. When the temperature is lower than 20 \({}^{\circ}\)C, the balance pressure of the MH is significantly lower than the hydrogen charging pressure of 4 bar; therefore, the rate of hydrogen absorption and the amount of heat released by the MH are high in the lower SOC range. As the SOC rises, limited by the hydrogen absorption dynamics, the hydrogen absorption rate of MH decreases significantly, and the amount of preheat provided gradually decreases. When the initial SOC of the MH is 100%, the MH is saturated and cannot absorb hydrogen; at this time, the MHT cannot provide preheat and even absorbs heat from the coolant, which leads to an increase in the preheating time. When the heat source of the preheating process is only air compression preheating and heater heating, the overall preheating time reaches 222 s, while the preheating time after adding the MHT is as low as 75 s, which reduces the preheating time by 66.2%. The heat sources in the self-heating process include the hot air compressed by the air compressor, the radiator, the heat released from the hydrogen absorption of the MHT, and the waste heat generated during the operation of the electric stack. The preheating power of different heat sources throughout the cold start phase is shown in Figure 14, with the  
Figure 12: Comparison of preheating powers of different heat sources. Figure 13: Preheating percentages of different heat sources. preheating stage before 76 s and the self-heating stage after 76 s. After the preheating, the air compressor is switched on to the normal operating mode, which results in it providing less thermal power in the self-heating phase due to the smaller pressure ratio and rotational speed and even cools down the stack as the temperature of the stack rises. The heat generated by the fuel cell gradually increases as the load current increases, but as the temperature rises, the efficiency of the stack increases and the thermal power of the stack decreases.