# Matching and Control Optimisation of Variable-Geometry Turbochargers for Hydrogen Fuel Cell Systems
## 1 Introduction  
Hydrogen fuel cell systems (FCSs) provide a power source for a variety of applications, including rail [1], marine [2], aircraft [3] (including smaller UAVs [4]), road vehicle [5], and stationary power [6] applications. Fuel cells can reduce pollution due to zero tailpipe emissions [7] and the possibility of being powered by 'green' hydrogen, which is generated using renewable energy and feedstock [8]. As the automotive industry seeks to move away from fossil-fuel-powered vehicles and towards electrified powertrains, fuel cell electric vehicles (FCEVs) provide a promising alternative for the heavy-duty vehicle market [9]. In particular, proton exchange membrane fuel cells (PEMFCs) are favoured for automotive applications due to their high efficiency, high current density, and low operating temperature, providing quick start-up [10, 11]. To achieve maximum power density from the fuel cell stack, PEMFCs are commonly operated under pressurised conditions (up to \(\sim\)4 bar [12]), allowing for better performance [13, 14] and a reduction in stack size [15]. Fuel cell performance and efficiencyincrease as the pressure of the reactant gases increases, as described by the Nernst equation [16] and as can be observed experimentally [17; 18; 19]. Although there is an increase in stack power output, pressurising the system leads to significant parasitic loss when powering the compressor. This can account for up to 80% of all parasitic losses experienced [20] and can require 15-35% of all power output from the stack [10; 12; 21; 22; 14]. To compensate for some of the losses from powering the compressor, a turbine can be used to recover some of the exhaust energy at the cathode outlet to drive the compressor shaft, reducing the power requirements from the e-motor. In contrast to an internal combustion engine (ICE), there is not enough energy in the exhaust flow to fully power the compressor [23]. However, up to 60% of the compressor power can be offset depending on operating conditions, resulting in increases in full system efficiency by up to 8% [24; 25; 26; 13; 27]. Existing findings are summarised in Table 1.  
In ICE applications, fixed-geometry turbochargers (FGTs) can experience lag in transient conditions such as low-speed operation, due to the size of the turbine and its inertia [31]. Variable-geometry turbochargers (VGTs) overcome this by manipulating the effective aspect ratio of the turbine to reduce lag and increase the turbocharger's operating range, particularly increasing boost at low speeds and reducing over-boosting [32]. VGT use with diesel engines can improve matching, enhance fuel economy, and reduce soot emissions [33] by increasing charge air mass by up to 20% compared to an FGT with a wastegate [34]. For FCEVs, the reduction in lag and management of exhaust gas recirculation (EGR) for emission reductions are no longer concerns. However, VGTs still offer potential benefits, with recent studies aiming to leverage the extended operating range of VGTs for enhancing vehicle efficiency across a wider range of loads [27; 23; 15; 23]. Several studies have found that VGTs can cover the full fuel cell operating range. [PERSON] et al. [27] compared FGTs and VGTs at nominal air mass flow rates across a range of pressure ratios, as well as compromised (low and high) air mass flow rate conditions. At the nominal operating points (OPs), they showed that FGTs recover more power due to their superior efficiency, but at the compromised, low and high mass flow rates, the VGT exhibited greater efficiency. The VGT appears to provide reasonable efficiency across the range, while the FGT peaks in the middle and drops at the extremes. Despite their improved performance at the extremes, the authors do not recommend VGTs for most