# An Analysis of the Altitude Impact on Roots Compressor Operation for a Fuel Cell System
## 1 Introduction
This parameter needs to be carefully calibrated as a function of the fuel cell power demand, working conditions, and hardware characteristics [25; 26], combined with the use of advanced control algorithms to avoid overshoots when operating in dynamic conditions [27]. However, compressors also consume a portion of the system's power, making their efficiency and power consumption key considerations in overall fuel cell system performance [28; 29]. For this reason, the addition of energy recuperation systems in the cathode exhaust, such as air expanders, can provide significant efficiency advantages, especially in highly boosted systems [30]. Previous studies have explored the role of the compressor in fuel cell systems for passenger car applications. [PERSON] [31] et al. studied a high-speed centrifugal compressor model for PEM fuel cells that was designed for automotive applications. A feedforward controller managed air mass flow, mitigating disturbances during dynamic load changes. This compressor maintained optimal oxygen levels, enhancing fuel cell efficiency and preventing oxygen starvation. It demonstrated efficient performance under varying load conditions. [PERSON] et al. [32] designed a magnetically levitated centrifugal compressor with forward-curved blades for automotive PEMFCs, achieving a pressure ratio of 1.10 and an isentropic efficiency of about 50%. Their approach integrated numerical simulations, experimental validation, and a novel algorithm to optimize blade profiles. This design addressed low-flow-rate challenges and emphasized stable operation, enhancing efficiency in PEMFC systems. [PERSON] et al. [33] studied a numerical model for a two-stage turbo compressor in a fuel cell system, achieving a pressure of 4.2 bar and a 70.8% efficiency. However, at very high overall pressure ratio values, the temperature of the air stream at the second-stage compressor outlet was very high, stressing the importance of the balance-of-plant thermal management system to control the temperature at the cathode inlet in order to avoid membrane dehydration and eventual material damage associated with an excessively high temperature level. [PERSON] et al. [34] conducted a comprehensive study on fuel cell compressors used in automotive applications, focusing on types like Roots, screw, centrifugal, and turbochargers. They discussed control strategies such as PID, fuzzy logic, and hybrid methods to manage the air supply. Key components like compressors and bypass valves played a vital role in optimizing fuel cell performance and durability. The mechanical and gas flow responses of compressors were also examined, emphasizing the need for precise control during operation. [PERSON] et al. [35] evaluated the use of twin-screw compressors with integrated water cooling for efficiency improvement. [PERSON] and [PERSON] [36] evaluated the effect of air compressor and cabin design for an open-cathode PEMFC, achieving a 9.4% power density improvement. The compressor operation can also be particularly relevant for multi-stack fuel cell systems, especially when all stacks are supplied by a unique compressor unit, affecting the optimal match between working pressure and power demand on each individual stack [37]. One of the aspects that can significantly affect both compressor and fuel cell performance is altitude [38; 39]. At higher altitudes, the atmospheric pressure decreases, which results in reduced air density [40]. If the fuel cell is not supercharged, this would imply a proportional decrease in fuel cell performance. However, in supercharged systems, the compressor can partially compensate for the lower environmental pressure by operating at higher pressure ratios, thus increasing its electrical power consumption and raising concerns about its durability and performance during prolonged use [41].