## 2 PEMFC-MH System Matching Design  
### Solid Metal Hydrogen Storage Material Selection  
When choosing a solid metal for the hydrogen storage method for the PEMFC hydrogen subsystem, it is important to consider that the PEMFC is characterised by low operating temperatures and fast start-up. The hydrogen absorption/release performance of the hydrogen storage material will directly affect the output power of the PEMFC, so it is necessary to select a suitable solid-state hydrogen storage material based on the thermodynamic and dynamic properties of the metal hydride and the operating conditions. The thermodynamic properties of metal hydrogen storage materials are the relationship between the temperature and pressure at which the metal material is exposed and the concentration of hydrogen contained in the metal material, i.e., the Pressure, Concentration, and Temperature (PCT) curve. Hydrogen absorption and release in metal hydrogen storage materials depends on the temperature and pressure of the metal hydride, as well as the concentration of the hydrogen contained. Hydrogen absorption and release is a reversible process, and the equilibrium state in this reversible reaction process can be expressed by the Van 't Hoff equation:  
\[\ln P_{\text{eq}}=-\frac{\Delta S}{R}+\frac{\Delta H}{RT}, \tag{1}\]  
where \(P_{\text{eq}}\) denotes the balancing pressure of the MH, bar; \(\Delta S\) denotes the entropy changes in reversible reactions, J/(mol\(\cdot\)K); \(\Delta H\) denotes the enthalpy changes in reversible reactions, J/mol; \(R\) denotes the gas constant; and \(T\) denotes the temperature of the MH. The ability of the selected hydrogen storage material to be properly integrated with the fuel cell also requires the consideration of whether the reaction enthalpy change and the operating conditions of the metal hydrogen storage material are compatible with the operating conditions of the fuel cell, as described below. (1) Requirements for reaction enthalpy changes  
Metal materials need to absorb a certain amount of heat when releasing hydrogen, and the heat absorbed is the enthalpy change of the hydrogen release reaction. If additional heat exchange devices are not considered and only the waste heat from the stack is used to heat the hydrogen storage device, the heat that needs to be absorbed by the MH to discharge the hydrogen needs to be lower than the heat loss from the stack, as in Equation (2); otherwise, additional heating devices need to be added. \[|\Delta H|\leq Q_{loss}=HHV(1-\eta), \tag{2}\]  
where \(Q_{loss}\) denotes the heat generated by fuel cells, \(HHV\) denotes the high thermal value of hydrogen, and \(\eta\) denotes the efficiency of the PEMFC. (2) Requirements for working conditions  
The ideal hydrogen storage material has a hydrogen absorption/release temperature near the operating temperature of the fuel cell so that it can work efficiently when coupled with the fuel cell system. For the PEMFC system, the maximum operating temperature of the MH material is 80 \({}^{\circ}\)C, and the balance pressure at this operating temperature must be higher than the maximum hydrogen supply pressure required for the stack [18], so the operating temperature of the MH material must be satisfied:  
\[T_{\text{op}}\geq\frac{\Delta H}{\Delta S+R\cdot\text{In}P_{\text{supply}}}, \tag{3}\]  
where \(T_{\text{op}}\) denotes the operating temperature of the MH material; \(P_{\text{supply}}\) denotes the hydrogen pressure for the stack requirements. In addition, when hydrogen storage devices supply hydrogen to power reactors, they need to meet the hydrogen flow rate required for the operation of power reactors under different operating conditions. Therefore, it is necessary that the hydrogen release flow rate of the hydrogen storage material at the operating temperature can satisfy the maximum demand flow rate of the stack.