# Matching and Control Optimisation of Variable-Geometry Turbochargers for Hydrogen Fuel Cell Systems
## 3 Results  
### One-Dimensional Modelling  
The results from the 1D modelling indicate that fuel cell stack power is very similar whether an FGT or a VGT is used. This is shown in Figure 6, the lower left portion of which shows a less than 0.5% difference in stack power across the range of current density operating points with the use of an FGT or a VGT. The data also show that the choice of an FGT or a VGT subsequently has a negligible effect on overall system efficiency: Figure 6 shows a less than 0.25% increase in system efficiency when using a VGT, as shown in the lower right of the figure.  
The very similar system performance data--fuel cell power and overall system efficiency--when using either turbocharger are due to two main factors: fundamental turbo design, such as size, and turbine operating point, such as speed. The fundamental turbine design was purposefully kept the same in this study to ensure the effect of a variable nozzle gap was isolated. However, the turbine operating points were found by the  
Figure 6: Comparison of fuel cell system performance parameters when using VGT and FGT.  
boundary condition optimisation exercise, aiming to maximise overall system efficiency. This was conducted independently for the FGT and VGT to assess if their optimal operation differs because of their different air system controls. It was found that the optimised operating points for the two turbos are similar despite their different control capabilities, as shown in Figure 7, where the FGT and VGT operate along the same curve for much of the operating range. A slight divergence is noticeable at the final two points, representing 1.6 A/cm\({}^{2}\) and 1.7 A/cm\({}^{2}\), where the VGT begins to curve downward, more closely following the peak efficiency curve of the compressor. It is also noticeable from these plots that the operating curve closely follows the peak efficiency curves of both the compressor and turbine, demonstrating that the compressor and turbine are well matched to each other as well as to the fuel cell requirements.  
Subsequently, this results in little difference in turbine power, as shown in Figure 8, which also presents the turbine inlet pressure and turbocharger shaft speed. The e-motor provides the remaining compressor power that is not provided by the turbine. Since the optimisation of the two turbines did not result in significantly different operating points, and because they have the same fundamental geometry and efficiency characteristics, they recover similar power across the range. Therefore, the remaining compressor power provided by the e-motor power is also very similar for the vast majority of the operating range. As in Figure 7, however, a slight divergence is seen for the final two operating points, resulting in the slightly higher system efficiency observed in the lower right of Figure 6.  
Similar FGT and VGT operating conditions also result in a very similar utilisation of the air system controls. For both turbos, Figure 9 shows that the magnitude of the controls used is very small, indicating negligible wastegate use by the FGT (\(<\)1% of flow through wastegate) and a minimal change in rack position by the VGT. There was no use of the back pressure valve for either, so this is not plotted. As explained in the methodology, the VGT model was able to use the wastegate and back pressure valve if its rack position limits were reached. However, according to these data, the optimised rack position remains very close to the centre of the rack, comfortably between 45% and 60%, and exactly 51% for much of  
Figure 7: Optimised operating points overlaid onto compressor and turbine efficiency maps.  
the current density range. Similarly, the FGT, represented by a constant rack position at the flush gap (51%), required little wastegate use to meet its optimised operating points.