## 4 Cold Start Control Strategy for PEMFC-MH Coupling System
### Design of the Cold Start Controller
(3) MHT preheat control  
The source of hydrogen supply in the preheating stage is a gaseous hydrogen cylinder, a pressure-reducing valve is opened to maintain a constant pressure in the buffer tank, and the hydrogen in the buffer tank flows to the MHT for MH hydrogen absorption and the preheating of the circulating coolant. The preheating power of the MH to the coolant is related to the ambient temperature, coolant flow rate, and hydrogen supply pressure, and the preheating power can be calculated by the following equation [4]:  
\[\dot{Q}_{\rm preheat}=\dot{m}_{\rm cool}Cp_{\rm cool}(T_{\rm MHT,in}-T_{\rm MHT,out}) \tag{19}\]  
The effect of different pump openings on the MH preheating power is shown in Figure 8. The higher the flow rate of coolant flowing through the MHT, the higher the preheating power of the MHT on the heat transfer fluid, and the preheating power growth slows down as the flow rate increases. As the pump opening increased, the preheating completion times are 108 s, 108 s, 122 s, 138 s and 154 s, respectively. The effect of water pump opening on the preheating efficiency of the MHT is shown in Figure 9. The water pump speed is inversely proportional to the preheating efficiency of the MHT on the stack, mainly because the contact time between the coolant and the stack becomes shorter, resulting in less being heat absorbed by the stack per unit time. The higher the water pump speed, the higher the preheating power of the MHT to the coolant, and the preheating time appears to be extremely small at a water pump opening of 0.15. At water pump openings greater than 0.15, although the preheating power of the MHT is greater at higher coolant flow rates, the lower preheating efficiency results in longer overall preheating times. Figure 8: Effect of water pump opening on preheating power. Figure 7: Preheating efficiency at different compressor speeds and pressure ratios. In the preheating period, the pressure of the buffer tank is the hydrogen charging pressure of the MHT, and the preheating power at different buffer tank pressures when the initial SOC of the MHT is 10% is shown in \[\eta_{\text{AirHeat}}=\frac{W_{\text{FC,Air}}}{W_{\text{comp}}}\times 100\% \tag{17}\]0 As the buffer tank pressure increases, the preheating power increases and the preheating time decreases so that the hydrogen charging pressure of the MHT is increased as much as possible during the preheating period. In order to ensure that the pressure in the buffer tank at the end of the cold start to normal operation of the system does not fluctuate greatly during the excessive period, the buffer tank's desired pressure during the cold start phase is set to be 4 bar, which is the same as the working pressure of the system for normal operation. As the pressure decreases, the preheating completion times are 66 s, 72 s, 82 s, 103 s, and 177 s, respectively. The initial SOC has a great influence on the MHT preheating power, and it is known from the hydrogen absorption dynamics that the SOC has a higher rate of hydrogen absorption in the lower operating range, and therefore, the absorption of hydrogen releases a higher amount of heat. The preheating power for different SOCs when the water pump opening is 0.1 and the buffer tank pressure is controlled at 4 bar through a pressure-reducing valve is shown in \[\eta_{\text{AirHeat}}=\frac{W_{\text{FC,Air}}}{W_{\text{comp}}}\times 100\% \tag{17}\]1 From this figure, it can be seen that the lower the initial SOC of the cold start MHT, the higher the peak power of the MHT preheating and the shorter the preheating time required.