# An Analysis of the Altitude Impact on Roots Compressor Operation for a Fuel Cell System
## 4 Conclusions  
In the current paper, an investigation of the altitude effects on the operation of a super-charged heavy-duty fuel cell powerplant equipped with a roots compressor is performed. For this purpose, the complete balance-of-plant model is developed in the Simscape platform. For the fuel cell stack, a one-dimensional physical and chemical model extracted from the literature is calibrated against experimental data at different temperatures and pressures at the single-cell polarization curve level. Then, the number of cells and effective areas are scaled up to provide a maximum net power of 200 kW, which is representative of the requirements of a heavy-duty vehicle. The roots compressor, characterized by a maximum pressure ratio of 2.9 and a maximum corrected flow of 0.55 kg/s, is calculated using information from the efficiency and corrected speed maps. The model is completed by including an air filter, which is characterized with a pressure drop of up to 2% for the maximum mass flow conditions, the anode recirculation system, membrane humidifiers for both anode and cathode streams, and a simplified thermal management system aimed at maintaining a constant temperature of 73 \({}^{\circ}\)C, where the maximum proton conductivity is found. The model is explored in an altitude range between sea level and 5 km, optimizing the compressor and fuel cell stack working points to achieve the highest balance-of-plant efficiency for a net power range between 10 and 200 kW (or the maximum achievable value at a given altitude). With this methodology, the following conclusions can be made:  
Figure 8: Fuel cell stack operation as a function of altitude: (**A**) cathode inlet pressure; (**B**) fuel cell stack efficiency. * The pressure in the fuel cell stack helps to extend the current density operating range and therefore increase the achievable fuel cell power. However, the sensitivity to pressure starts reducing when the pressure exceeds 2 bar, where the minimum differences are achieved from 2.45 bar on. * At sea-level operations, a minimum compressor power consumption is seen at low-to-mid fuel cell power (i.e., air mass flow) operations, which are dominated by the isentropic efficiency evolution. This minimum power increases nearly exponentially with the pressure ratio. * At mid-to-high-power conditions, the Roots compressor efficiency is nearly constant and close to the highest efficiency, and the compressor power consumption is dominated by the air mass flow. * As altitude increases, the maximum corrected air mass flow tends to increase as a consequence of the lower ambient pressure. However, thanks to the characteristics of the Roots compressor, it operates with minimal changes in efficiency (between 60 and 70%) for a wide range of altitude and mass flow conditions. * For the highest altitude and power operating conditions, the combined increase in corrected mass flow and pressure ratio makes the compressor leave the best efficiency area, consequently increasing the power consumption and limiting the maximum balance-of-plant performance. Particularly, the peak net power produced is lowered from 200 kW at sea level to 135 kW at a 5 km altitude, which represents a 32.5% deterioration. Additionally, the balance-of-plant efficiency is also impaired, reaching up to a 7% reduction. * At mid-to-low net power operations, the best efficiency values are reached for nearly constant (and low) pressure ratios, with a slight increase as a function of the altitude. Consequently, the fuel cell stack operating pressure is reduced, inducing a penalty in efficiency of up to 3%. Conceptualization, P.P. and J.d.l.M. ; methodology, P.P. ; software, E.J.S. and I.S. ; validation, J.d.l.M. and E.J.S. ; formal analysis, P.P. ; investigation, J.d.l.M. ; resources, P.P. ; data curation, I.S. ; writing--original draft preparation, J.d.l.M. and I.S. ; writing--review and editing, P.P. and E.J.S. ; visualization, E.J.S. ; supervision, P.P. ; project administration, J.d.l.M. ; funding acquisition, J.d.l.M.