The Navier-Stokes equation, neglecting the viscosity and gravity terms, can be used to simply calculate the total number of moles of purge gas. As shown in the figure above, only the pressure difference between the hydrogen supply system and the air supply system manifold will cause the gas mixture in the hydrogen supply system pipeline to exit the hydrogen supply system. In order to discharge the gas mixture in the hydrogen pipeline, the pressure of the hydrogen supply system pipeline is usually controlled to be higher than the pressure of the outlet manifold of the air supply system. Based on the concept of mole fraction during purge, the total moles of the mixture can be divided into the sum of the moles of each component. The mole fraction of each component is defined as follows (ni is the number of moles of component i, n is the total number of moles of the hydrogen supply system). The higher the mole fraction, the greater the discharge of component i.

　　yi=ni/n(4)

　　Initial estimate of hydrogen concentration

　　After the fuel cell vehicle is started, it is difficult to estimate the initial value of hydrogen concentration because the CPU in the controller is powered off during parking. But the controller can know the parking time of the vehicle with the help of the timer chip. It is known that the longer the shutdown time and the higher the operating temperature of the system during shutdown, the lower the hydrogen concentration. Therefore, drawing a map of two parameters (parking time and operating temperature at shutdown) is a good way to estimate the initial hydrogen concentration value at the start of a fuel cell vehicle.

　　The relationship between anode hydrogen concentration and operating temperature

　　estimator calibration

　　Simplifying the complex hydrogen flow in the fuel supply system can lead to an estimation error, which is defined as the difference between the hydrogen concentration estimate and the hydrogen concentration value measured by the hydrogen concentration analyzer. Hyundai Motor Company has designed the following three calibration parameters, as shown in the figure above. The three calibration parameters are: (1) Nitrogen penetration gain. Calibration parameter of estimated hydrogen concentration decay rate at normal operating temperature; (2) Activation energy. Calibration parameter that minimizes the estimation error caused by operating temperature; (3) Purge gain, a calibration parameter that increases the estimated hydrogen concentration value during purging at normal operating temperature.

　　Adjust the three calibration parameters of the estimator (based on the hydrogen concentration value measured by the concentration analyzer)

　　Hydrogen concentration estimator validity

　　After adding the hydrogen concentration estimator to the NEXO fuel cell controller, Hyundai Motor Company conducted extensive tests to verify the effectiveness of the hydrogen concentration estimator. Based on the measurement data of UDDS, HWFET and US06 operating conditions (wide load range from low load to high load), Hyundai Motor Company adjusted three calibration parameters to reduce estimation errors. After adjusting the three calibration parameters, the error size of the hydrogen concentration estimator changes slightly in different driving conditions, but remains within a reasonable range, indicating that it is sufficient to be used as an estimator, as shown in the figure below. The variation in estimation error comes from the assumption of homogeneity of the mixture. Under low load conditions of the hydrogen supply system, due to the low hydrogen consumption of the stack and the small amount of hydrogen recirculation, the gaseous mixture in the hydrogen supply system is more uneven. As shown in the figure below, this effect shows that the error is smaller under the UDDS operating condition, but the error is slightly larger under the HWFET and US06 operating conditions.

　　Validity experiment of hydrogen concentration estimator for NEXO fuel cell system

　　Feedback control based on hydrogen concentration estimator

　　There are two methods to control the hydrogen concentration in the hydrogen supply system pipeline. One is to increase the pressure of hydrogen flowing from the hydrogen storage bottle through the hydrogen supply system pipeline, and the other is to control the nitrogen and water vapor in the hydrogen supply system pipeline. Perform a purge operation. Using a hydrogen concentration estimator that functions in the same way as a hydrogen concentration sensor, a feedback control as shown in the figure below can be constructed to resist internal disturbances (such as manufacturing process deviations) and external disturbances (such as changes in environmental pressure). The reference signal is the optimal hydrogen concentration at the operating point, and the reference signal is compared with the output of the hydrogen concentration estimator to obtain the error signal. When the fuel cell system suddenly enters the power generation state from the shutdown state, the purge controller sends a purge command, and the pressure controller sends a pressure reference signal to the hydrogen supply valve. The purge controller and pressure controller are designed to reduce signal errors independent of stack load conditions, meaning the hydrogen concentration estimator output signal follows the reference signal.

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