The brief architecture of the modern NEXO fuel cell system is shown in the figure below. One of the basic functions of the hydrogen supply system is hydrogen fuel pressure regulation and control. When the stack current changes according to the power demand of the driver (vehicle), the controller maintains the pressure sensor value within the set range by operating the fuel supply system. And the pressure drop is compensated by purging operation. The purge valve outlet is connected to the cathode outlet manifold. The unreacted hydrogen at the stack anode outlet is recycled to the hydrogen supply valve through the ejector to improve hydrogen utilization.

　　Hyundai NEXO fuel cell system architecture simplified

　　For accurate evaluation, it is necessary to model the parts with ejector, pipeline and anode flow channel and hydrogen supply valve. However, it is difficult to develop real-time embedded software models due to complexity and computational time cost. Therefore, the processing model is simplified and the entire hydrogen supply system is regarded as a cube with the same volume as its volume, and all gas components are assumed to be homogeneous, as shown in the figure below.

　　Hydrogen supply system and air supply system cube model

　　The estimation error caused by model simplification can be compensated by appropriate calibration parameter design. Since the hydrogen concentration is compared between the measured value of the hydrogen concentration analyzer and the estimated value of the estimator in the study, and the hydrogen concentration analyzer uses hydrogen and nitrogen to calculate the hydrogen concentration after removing water vapor, the hydrogen concentration can be expressed as the following formula (nH2 and nN2 are the moles of hydrogen and nitrogen respectively). Therefore, if the moles of hydrogen and nitrogen can be calculated in real time, the hydrogen concentration can be easily calculated.

　　Hydrogen concentration=nH2/(nH2+nN2)(1)

　　Hydrogen concentration estimation strategy

　　According to the ideal gas equation of state, the total number of moles of the gas mixture in the hydrogen supply system pipeline can be calculated from the total pressure and temperature in the pipeline. According to the mass conservation equation, the number of moles of a gas mixture is equal to the sum of the moles of hydrogen, nitrogen and water vapor, that is

　　n=nH2+nN2+nV(2)

　　To simplify the model, the mole number of water vapor nV can be determined by the two-dimensional map constructed between the stack current and the operating temperature in the experiment. The mole number of water vapor nV under specific working conditions is calculated by the interpolation method. Therefore, the initial values can be integrated over time using the permeation model and the purge model to obtain the moles of hydrogen and nitrogen, that is

　　nN2=initial moles of nitrogen+nitrogen permeability integrated over time-nitrogen purge rate integrated over time (3)

　　Nitrogen permeation model

　　The composition of the gaseous mixture between the cathode and anode of the fuel cell changes over time, so there are concentration gradients of different components on both sides of the proton membrane. On a microscopic scale, there is a phenomenon of mass transfer (diffusion) from high concentration areas to low concentration areas on both sides of the proton membrane. Fick's law was used in this study, which states that the mass diffusion flux of each component per unit area is proportional to the concentration gradient, as shown in the figure above. Among them, the diffusion coefficient is a semi-empirical formula related to a specific proton membrane, which increases as the operating temperature increases. Note that for hydrogen concentration calculations, only the nitrogen permeation model is required.

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