## 2 Modeling of Fuel Cell Systems
### Fuel Cell Single Cell Modeling  
The fuel cell temperature calculation is divided into five layers--the negative/positive end plate layer, negative/positive plate layer, and MEA layer. The MEA layer can be divided into the proton exchange layer, gas diffusion layer, and the MPL (Micro-porous layer) and catalyst layer [17]. However, it is very difficult to model the energy change of each layer inside the MEA layer, therefore it was essential to determine the heat generation of the internal layers and the energy changes caused by the material flow. The material flow inside the MEA layer is particularly complex compared with other layers, and it is difficult to quantify their relationship with the simulink model. Due to the frequent material exchange of the gas diffusion layer, catalyst layer, and proton exchange membrane layer, their temperature differences are small, and are therefore combined into the MEA layer for modeling. The temperature calculation of each layer is different [18; 19]. Fuel cells have a symmetrical structure, and the temperature in the main area of electrochemical reaction at the cathode side varies greatly, which also has a great influence on the overall temperature of the battery [20]. To simplify the model, a fuel cell model from the cathode side end plate layer to the MEA layer will be established here.  
Figure 2 is a schematic diagram of the fuel cell temperature model. The end plate layer is the outermost part of the fuel cell, and its main function is to make the fuel cell fit inside. Its heat change mainly comes from two sources, heat exchange with air Q\({}_{\text{air}}\) and heat exchange with the bipolar plate layer Q\({}_{\text{L2}}\). The main function of the bipolar plate between the end plate layer and the MEA layer is to separate the \"Yin and Yang\" poles of the battery. There is a gas flow channel near the MEA layer for gas to penetrate the MEA layer for the next reaction. The main ways of heat exchange are the heat transfer Q\({}_{\text{L3}}\) between solid and solid within the MEA layer, the heat convection Q\({}_{\text{L3R}}\) between solid and fluid, the heat change H\({}_{\text{H}_{\text{2}}\text{O,L2}}\), and Q\({}_{\text{gas,in}}\) of material flowing into the bipolar plate from the MEA layer. The other side of the bipolar plate is adjacent to the end plate layer, and the main heat change mode is heat transfer, Q\({}_{\text{L1}}\). Some bipolar plates will be provided with a coolant runner for cooling. The heat change brought to the bipolar plate by the air runner and coolant runner is Q\({}_{\text{gas}}\) and Q\({}_{\text{H}_{\text{2}}\text{O}}\). The bipolar plate will also produce heat, Q\({}_{\text{int1}}\), due to its own resistance. The main function of the MEA layer is to provide the conditions for chemical reaction, converting chemical energy into electrical energy. Both sides of the MEA layer are in contact with the bipolar plate, and the source of heat change caused by the external environment is similar to that of the bipolar plate layer. The internal heat change is the resistance heat production and voltage polarization, totaling Q\({}_{\text{int2}}\).  
Figure 2: Diagram of fuel cell temperature model.