## 4 Cold Start Control Strategy for PEMFC-MH Coupling System
### Design of the Cold Start Controller  
The actuators in the preheating stage mainly include an air compressor, a circulating water pump, and a radiator. According to the technical requirements proposed by DOE [29], the start-up time and start-up energy consumption are the main performance indexes of cold start-up, and it is necessary to reasonably design the controller to make the system have a lower cold start-up time and low start-up energy consumption. In addition, since the PEMFC-MH system requires an external hydrogen source during the cold start phase, the cold start hydrogen consumption is also an important indicator of the cold start process of the system. (1) Valve opening control  
During the cold start-up period, in order to increase the temperature of the incoming air and to reduce the humidity of the incoming air, the bypass valve of the intercooler is usually closed to reduce the cooling of the incoming air. In order to utilise the heat released from the MHT hydrogen absorption reaction during cold start-up, the MHT bypass valve is opened, and the MHT is connected in series throughout the thermal management  
Figure 5: Comparison of MHT between simulation and experiment. (**a**) Hydrogen storage change curve; (**b**) temperature in MHT. subsystem. Opening the coolant mini-circulation loop rapidly increases the circulating coolant temperature and reduces the cold start time. (2) Air compressor speed and pressure ratio control  
The preheating time under different air compressor speeds and pressure ratios was plotted using a thermodynamic diagram, as shown in Figure 6 (colourful zone). The speed and pressure ratio of the air compressor determine the flow rate and temperature of the preheated air, and it can be seen from Figure 6 that the preheating time decreases significantly with the increase in the speed and pressure ratio of the air compressor, and the increase in the speed has a more significant effect on the reduction in the preheating time. In order to study the energy consumption for air preheating, the air preheating efficiency is defined as follows:  
\[\eta_{\text{AirHeat}}=\frac{W_{\text{FC,Air}}}{W_{\text{comp}}}\times 100\% \tag{17}\]  
where \(W_{\text{FC,Air}}\) denotes the heat absorbed by the stack when the air is preheated alone; \(W_{\text{comp}}\) denotes the energy consumption of the air compressor to compress the gas. The total heat required to preheat the stack from \(-20\)\({}^{\circ}\)C to \(5\)\({}^{\circ}\)C can be calculated by the following equation:  
\[W_{\text{FC,Iotle}}=m_{\text{st}}Cp_{\text{st}}\Delta T \tag{18}\]  
where \(m_{\text{st}}\) denotes the mass of the stack; \(Cp_{\text{st}}\) denotes the specific heat capacity of the stack. Due to the material of the stack, the specific heat capacity of the stack increases slightly with the temperature of the stack. It is calculated that the total heat to be absorbed by the stack to preheat from \(-20\)\({}^{\circ}\)C to \(5\)\({}^{\circ}\)C is 1640 kJ. Since the total heat required in the preheating stage of the electric stack is certain, the higher the preheating efficiency, the lower the energy consumption of the air compressor in the preheating stage, and the air preheating efficiencies at different air compressor pressure ratios and speeds plotted using a thermodynamic diagram are shown in Figure 7. With the increase in air compressor speed and pressure ratio, the preheating efficiency also increases, and increasing the pressure ratio of the air compressor can significantly improve the preheating efficiency. Considering the preheating time and preheating efficiency, the air compressor speed is set to 6000 rpm and the pressure ratio to 2 during the cold start preheating. Figure 6: Preheating time at different compressor speeds and pressure ratios.