## 3 Results
### PEMFC Powertrain Simulation  
To compare air supply systems, two different PEMFC stacks have been considered. Both have a 350 cm\({}^{2}\) active area and reach a 78 kW maximum output power. The first one is a 360-cell stack equipped with either an E-turbocharger or a single-stage compressor. The second one is a 315-cell stack equipped with a two-stage compressor. As a result, vehicles equipped with the 315-cell stack weigh 1850 kg, whereas the 360-cell stack vehicles have a five-kg excess weight [39].  
Figure 7: Example of a pressurised air supply system for an solid oxide fuel cell (SOFC) stack.  
The stack provides the entire power to propel the car and drive the air supply system. In each case, the air supply system has been optimised to reach the highest system electric efficiency, and thus it has the highest driving range with a 5.6-kg hydrogen storage tank [40]. Both stacks operate with a constant 3 bar pressure for the hydrogen supply system and operate at 80 \({}^{\circ}\)C. The overall model layout of the FCV is provided in Figure A3 in the appendices.  
The same compressor has been used for configurations 1 and 2. Only the performance map has been adapted for each configuration. The map is provided in the appendices (Figure A2). The single-stage compressor uses a backpressure, whereas the E-turbocharger has a turbine at the stack outlet. As seen in Table 3, the E-turbocharger system reaches a higher system electric efficiency average, and thus a 3.5% higher driving range. Due to the turbine, the average power that is required to drive the compressor in the E-turbocharger is 46% lower than the required average power for the single-stage compressor. During the maximum acceleration phase, the turbine recovers 2.4 kW, and thus required a relative power difference of 20%.  
By reducing the number of cells, the mass transfer losses increase, since it is harder for reactants to reach the catalysis area. As seen in Figure 8, the stack electric efficiency decreases. The two-stage compressor has been designed to reach 4.0 bar. During the WLTP driving cycle, the two-stage compressor average pressure is 4.9% higher than the E-turbocharger one, which could have compensated for the increase of mass transfer losses. However, the average power required for the two-stage compressor is 43% higher than the power required for the E-turbocharger. This leads to a 1.6% absolute change in the lower system electric efficiency average, and a 3.5% lower driving range than the E-turbocharger configuration.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Configuration number** & 1 & 2 & 3 \\ \hline
**Number of cells** & & 360 & 315 \\ \hline
**Air supply system** & E-turbocharger & Single-stage compressor & Two-stage compressor \\ \hline
**Pressure range (bar)** & [1.1–2.3] & [1.1–2.2] & [1.1–2.7] \\ \hline
**Average system electric** & & & \\
**efficiency (\%)** & & & \\ \hline
**Average stack electric** & & & \\
**efficiency (\%)** & & & \\ \hline
**Average compressor/turbine** & & & \\
**efficiency (\%)** & & & \\ \hline
**Driving range (km) for 5.6 kg** & & & \\
**of hydrogen** & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of the WLTP driving cycle simulation.  
Figure 8: Impact of the number of cells on the stack electric efficiency (operating at two bar).  
As seen in Figure 9, the model used for the PEMFC underestimated the output power when the operating pressure was between 1.0-1.7 bar, with an overestimation above this value. However, the results of the comparison between the different air supply systems were valid, even if the influence of the operating pressure was underestimated or overestimated.  
The single-stage compressor map outcome is provided in the appendices, in Figures A4 and A5.