# An Analysis of the Altitude Impact on Roots Compressor Operation for a Fuel Cell System
## 1 Introduction  
As Earth's temperature has already risen by about 1 \({}^{\circ}\)C and may reach 1.5 \({}^{\circ}\)C if current trends continue, the need for decarbonization has become increasingly urgent [1]. The transition to zero-emission technologies across various sectors is vital for limiting global warming [2]. This includes road, air, and maritime transport, with road vehicles alone accounting for approximately 77% of transportation-related CO\({}_{2}\) emissions in 2020 [3]. Hydrogen fuel cell vehicles (FCNs) are emerging as a promising solution for reducing greenhouse gas emissions and addressing climate change as an alternative to traditional gasoline- and diesel-fueled vehicles [4]. This contribution can be particularly relevant thanks to the increasing availability of green hydrogen, which is produced from water electrolysis using electricity from renewable sources [5, 6]. On a life-cycle analysis basis, a reduction of up to 50% in greenhouse gas emissions can be achieved compared to a vehicle powered using a conventional engine [7, 8]. This contribution can be even higher by the application of technological improvements in the fuel cell stack and hydrogen storage systems, particularly in materials extraction and processing [9] and advancedfuel cell control strategies [10]. Additionally, fuel cell-powered vehicles do not produce other emissions such as nitrogen oxides, particulate matter, or incomplete combustion products typical of internal combustion engines [11]. While exhaust aftertreatment systems can largely mitigate these species [12], their cost and complexity are increasingly large to achieve current regulatory requirements. Therefore, hydrogen fuel cell vehicles can offer a competitive solution, especially if the production cost of hydrogen fuel and internal stack materials (mainly the membrane, catalyst layers, and bipolar plates) can be dropped from the current state [13]. Among various fuel cell types, proton-exchange membrane fuel cells (PEMFCs) are one of the most widely used, particularly in applications such as transportation and stationary power generation [14]. PEMFCs are favored for their high efficiency, low operating temperature, and scalability, making them suitable for a wide range of applications [15; 16]. The key reaction in a PEMFC occurs between hydrogen, which is supplied to the anode, and oxygen, which is supplied to the cathode, generally using environmental air as a source [17]. In this sense, the accurate control of the reactants' flow and distribution along the electrochemical surface area is critical to ensure high efficiency and durability. Inside the stack, this is achieved thanks to the use of gas diffusion layers, which consist of porous media like carbon paper or carbon cloth with porosities around 50% [18]. Additionally, the gas supplies for both the anode and cathode need to be accurately controlled and synchronized with the system power demand to ensure that the reactant content is enough for the electrochemical reaction to proceed efficiently [19]. In the anode stream, this control is particularly important due to the inclusion of a recirculation circuit for the hydrogen excess at the stack outlet, although the impact of this recirculation can be mitigated by the use of ejectors [20]. Instead, on the cathode side, the main driving factors are the oxygen concentration [21] and the addition of air compressors, normally electrically driven, which pressurize and supply air to the cathode in order to increase the fuel cell power density [22]. The compressor must deliver the air mass flow not only to maintain a proper stoichiometric ratio between the fuel (hydrogen) and oxygen, but also to avoid local oxygen starvation that can promote the degradation of the fuel cell [23; 24]. Therefore, a certain oxygen excess ratio (OER) is always included with respect to the stoichiometric requirements.