# Matching and Control Optimisation of Variable-Geometry Turbochargers for Hydrogen Fuel Cell Systems
## 1 Introduction
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Reference**} & **Low/Part Load** & **High Load** & **Compressor Power Offset** \\  & **Sys. Eff. Improvement** & **Sys. Eff. Improvement** & **by Turbine** \\ \hline [PERSON] et al., & & & \\
2023 [24] & +1\% & +8\% & Up to 60\% \\ \hline [PERSON] et al., 2021 [25] & +6\% (approx.) across the operating range. & 43.1–47.9\% (approx.) \\ \hline [PERSON] et al., 2021 [27] & & & 9–39.3\% \\ \hline [PERSON] et al., 2018 [13] & +3.3\% (WLTP avg.) vs. single-stage compressor & 45.8\% on average \\ +1.6\% (WLTP avg.) vs. two-stage compressor & & \\ \hline [PERSON] et al., 2017 [26] & +6.9\% (approx.) & 25–44.7\% (approx.) \\ \hline [PERSON] et al., 2006 [28] & +3\% (approx.) vs. single-stage compressor & \\  & +1\% (approx.) vs. two-stage compressor & \\ \hline [PERSON] et al., 2002 [29] & +1\% (approx.) & +5\% (approx.) & \\ \hline [PERSON] et al., 2000 [30] & “Largely unchanged” & +4\% (approx.) & \\ \hline \end{tabular}
\end{table} 
Table 1: Studies on the system efficiency benefits of FCEV turbine use compared. applications. Even at low mass flow rates where the absolute value of VGT power is greater than that of the FGT, the compressor consumes little power (6.3 kW vs. 25.4 kW for the highest load OP), so the proportion of power provided by the turbine is small and an FGT would be suitable. The main condition favouring VGTs is at high flow rates, where the VGT recovers more energy by utilising the full range of mass flow. But overall, the performances of the two are similar across the operating ranges, and an FGT with a wastegate is recommended as a suitable and less complex solution. [PERSON] et al. [15] also found that their bespoke VGT covers the full operating range whilst FGTs do not. Maximum energy recovery at low load was achieved using an FGT with a wastegate (WG) and at a high load with an FGT with a back pressure valve (BPV), but their VGT performs well enough across all loads to maximise average efficiency. Other studies conclude that VGTs should be redesigned for fuel cells to ensure that the full operating range is covered. For example, [PERSON] et al. [23] and the subsequent paper by [PERSON] et al. [35] found that a VGT without a wastegate can cover the entire operating range only if solidity (the ratio of blade chord to pitch) is reduced. They also found large performance improvements when doing so, reducing the inherent losses of VGTs' pivoting vanes and reducing gaps in the housings [35]. This is similar to the findings of [PERSON] et al. [36], who found a 13% increase in VGT efficiency by modifying turbine wheel geometry vs. using an unchanged VGT from an ICE vehicle. The combined findings above indicate the importance of correctly sizing turbomachinery for fuel cells, whilst the control optimisation work by [PERSON] et al. [28] and the influence of stoichiometry on system efficiency observed by [PERSON] et al. [37] illustrate the importance of optimising the operating points. [PERSON] et al. [38] explain that the operating parameters of the fuel cell must be established before considering the parameters of the turbine and compressor, for optimal matching. The mass flow rate and pressure demanded by the stack are fundamental parameters for matching [39], especially for mechanically coupled turbochargers, where the pressure ratio and mass flow rate ranges of the compressor and turbine must approximately correspond [40]. As the sizing of the turbomachinery will affect the optimal operating points for overall system efficiency, and the operating points will, in turn, determine the correct sizing of components, these factors are inherently coupled; however, no previous work has been identified that combines the optimisation of sizing and control concurrently. The aim of this work is therefore to determine the performance of a PEMFC system when used with a VGT against an FGT.