## 1 Introduction
[12] proposed a \"sandwich\"-type thermally coupled structure in which phase change materials and MH materials are stacked on top of each other, and the results showed that this structure has a  
Figure 1: Installed capacity of fuel cells in recent years. larger heat transfer area, which is more beneficial to the hydrogen absorption and release of MH. Common active thermal coupling methods include air mass heating and coolant heating. For small power air-cooled fuel cells, a compact thermally coupled system using air mass heating is the best choice [13]. [PERSON] et al. [14] achieved system thermal coupling by transferring the heat from the waste air on the surface of the stack to the heat exchanger of the MH hydrogen storage unit by means of a fan, which heats the circulating coolant flowing through the MH hydrogen storage unit and the heat exchanger. Coolant heating utilises the circulating coolant flowing through the FC bipolar plates as well as the coolant flow channels in the MH bed to achieve heat transfer, and this thermal coupling method is more compact and has a higher heat exchange efficiency compared to air-mass heating, and it also reduces the workload of the radiator. [PERSON] et al. [15] considered the cold start process of a thermally coupled system when the initial temperature of FC and MHT was 25 \({}^{\circ}\)C but did not consider the cold start of the thermally coupled system in a low-temperature environment. [PERSON] et al. [16] based their study on an electric-hydrogen-electric system consisting of a battery, electrolyser, fuel cell, and MHT. Through the battery power supply, the electrolysis tank electrolysis water generates the hydrogen gas to be transferred to the MHT, and the waste heat of the electrolysis tank and the heat generated by MH hydrogen absorption are used to heat up the MHT together. The whole system can achieve low-temperature cold starting without an external heat source. Similarly, [PERSON] et al. [17] preheated the MHT by circulating water and hot air, which brought the equilibrium pressure of the MH up to the FC demand pressure and ensured a proper supply of hydrogen for the low-temperature cold start of the thermally coupled system. Although the method of preheating the MHT enables a cold start at low temperatures, this method has significant limitations and requires an external heat source to heat the MHT, increasing the cost and space occupation of the system. Although the thermal coupling between metal hydrogen storage and fuel cells can effectively utilise the MH hydrogen absorption as well as the waste heat generated during the operation in a supplementary way, it also puts forward greater requirements on the structure of the thermal management system and the control method of the system. In this paper, for PEMFCs, the design of a thermally coupled system with a parallel coolant-heated MHT is proposed based on the thermodynamic and dynamic properties of MH and the degree of matching with the operating conditions of PEMFCs. Parameters of the MHT and cooling system are designed based on the matched design of a 70 kW PEMFC system, and the heat balance of the thermally coupled system is analysed mechanistically. The limitations of the PEMFC-MH system with respect to its low-temperature start-up ability are analysed by comparing it with high-pressure gaseous hydrogen storage. A low-temperature cold start method combining internal self-heating and the external auxiliary preheating of the PEMFC is proposed, and a controller is designed according to the performance indexes of cold start time, energy consumption, and hydrogen consumption.