# An Analysis of the Altitude Impact on Roots Compressor Operation for a Fuel Cell System
## 2 Materials and Methods
### Balance-of-Plant Model  
The current work explores the altitude effects on compressor and fuel cell performance for a heavy-duty vehicle. For this purpose, the balance-of-plant proposed sketch in Figure 1 is modeled using the MATLAB Simscape platform v24.1. On the anode side, the hydrogen from the fuel tank goes through a controlled valve that is used to set the operational pressure at the fuel cell inlet \(p_{in,a}\) and afterwards to a heat exchanger to control the temperature \(T_{in,a}\), particularly during the warm-up phase. After this heat exchanger, the flow coming from the fuel tank is mixed with the hydrogen excess flow recirculated from the anode exhaust by means of a recirculation pump (P). Finally, a membrane humidifier is used to set the final humidity content of the anode stream. In the cathode side, the first element in the line is an air filter, which is necessary to ensure that no impurities arrive at the cathode gas channels and is characterized by a 2% pressure drop at the maximum mass flow conditions. Afterwards, an electrically driven compressor is used to control the mass flow and pressure of the air arriving at the fuel cell (\(p_{in,c}\)), where a second heat exchanger is used to control the inlet temperature \(T_{in,c}\). Finally, a second membrane humidifier sets the humidity level of the cathode gas stream, using water recuperated from the cathode exhaust as the water source. It has to be considered that, in addition to these elements, a real system would also include two additional elements that are not considered in the current simulations. First, a thermal management system is used to maintain the PEMFC stack at the optimal working temperature (around 70 \({}^{\circ}\)C) once the system's warm-up phase is completed. Second, a hydrogen purge circuit derives the hydrogen from the recirculation line to the cathode exhaust when the hydrogen purity reaches a certain minimum value due to nitrogen crossover across the stack. However, in the current work, these systems are not considered since they have no direct relation with the system performance in altitude conditions, which is the main scope of the activity. One of the key elements in this model, together with the electrical compressor (which will be described in the next subsection), is the fuel cell stack itself. Given the nature of the study, it is critical that the selected submodel for the fuel cell stack provides physical sensitivity to the working pressure in the anode and cathode, which has a direct impact on both activation and mass transfer losses. In the current work, the open-source model developed by [PERSON] et al. [45] is selected. This model has been developed using experimental data from the literature [46; 47] including different temperature and pressure conditions, up to a maximum pressure of 2.5 bar. For this purpose, the model was calibrated using data from a single polarization curve at 1.3 bar and 346 K, with the rest of the available data being used for model validation. Figure 2 shows the comparison between experimental and simulated polarization curves for three of the conditions extracted from previous studies. As can be seen, the model is well capable of reproducing the fuel cell performance in the whole current density range, not only for the curve used for the calibration, but also when inducing variations in pressure and temperature conditions. This points out that the physical model is capable of capturing pressure and temperature effects, a critical aspect for the evaluation of different altitude conditions proposed in the current study. Once the fuel cell electrochemical response is validated at the cell level, its operation is scaled up to be representative of a PEMFC-based powertrain system in a heavy-duty vehicle [48]. Particularly, a total of 1000 cells with an active area of 280 cm\({}^{2}\) each are considered in order to provide a maximum fuel cell power of 225 kW.