Fuel cell anode impurity gas concentration on-line calculation method

Abstract

The invention relates to a fuel cell anode impurity gas concentration online calculation method. The method comprises the following steps: setting an anode impurity gas concentration test system of a fuel cell hydrogen path subsystem; when the test system runs, the concentration alpha of the anode impurity gas is calculated in real time; dynamically comparing the calculated concentration alpha of the anode impurity gas with an early warning value alpha max, and when the concentration alpha of the anode impurity gas is greater than or equal to the early warning value alpha max, opening a nitrogen discharge valve, discharging the impurity gas, reducing the concentration of the impurity gas, and stopping the nitrogen discharge valve when the concentration alpha of the anode impurity gas is greater than or equal to the early warning value alpha max. A temperature sensor, a humidity sensor and a pressure sensor which are mature and low in cost are used for collecting temperature, humidity and pressure data of all positions in a gas flow path of the fuel cell hydrogen path subsystem, and a mathematical model is established for analysis and calculation to accurately obtain the anode impurity gas concentration of the fuel cell hydrogen path subsystem. And the positive electrode impurity gas concentration is compared with an early warning value and a safety value of the positive electrode impurity gas concentration, and the opening and closing of the nitrogen removal valve are accurately controlled, so that the nitrogen removal strategy of the electric pile is more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of fuel cells, and in particular to an online calculation method for impurity gas concentration at anode of a fuel cell. Background Art

[0002] During the hydrogen circulation process of the fuel cell system, due to the difference in the concentration of the cathode and anode gas components, the nitrogen and water vapor in the cathode air will diffuse to the anode. Therefore, the gas in the anode cavity of the stack is a mixture of hydrogen, water vapor and nitrogen. After long-term operation, the hydrogen partial pressure will decrease, increasing the possibility of "lack of hydrogen". Local lack of hydrogen can promote cathode carbon corrosion under the reverse current mechanism, and overall lack of hydrogen can cause anode carbon corrosion and generate negative voltage, resulting in irreversible damage. Therefore, intermittently opening the drain valve to purge during operation to discharge the nitrogen accumulated in the anode is an important part of the fuel cell system structure design and strategy calibration. If the drain valve is opened too frequently or for a long time, it will cause a waste of hydrogen resources and low system efficiency; if the drain valve is opened too frequently or for a short time, there will be many impurities in the anode, which may cause the single-chip voltage to decrease and even affect the life of the stack.

[0003] At present, the monitoring and management of the anode hydrogen concentration of the fuel cell system is mainly carried out through model calculation, installation of vehicle-mounted hydrogen concentration sensors, experimental calibration and other methods. Due to the reliability, accuracy and cost of the sensor, the practice of installing vehicle-mounted hydrogen concentration sensors is not yet mature; the model estimation method has calculation errors, and the hydrogen concentration calculation is "distorted" under extreme working conditions. Therefore, it is urgent to propose an online calculation method for the impurity gas concentration of the anode of the fuel cell to simplify and accurately calculate the system nitrogen removal strategy. Summary of the invention

[0004] In view of this, the present invention provides an online calculation method for the impurity gas concentration at the anode of a fuel cell, the purpose of which is to establish a mathematical model to analyze and calculate the anode impurity gas concentration of the fuel cell hydrogen circuit system accurately, and to simplify and refine the system nitrogen removal strategy.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for online calculation of impurity gas concentration in a fuel cell anode comprises the following steps:

[0007] S1. A test system for the concentration of impurity gas at the anode of the hydrogen circuit subsystem of a fuel cell is set up, the test system includes a hydrogen source, an ejector, a plate heat exchanger, a fuel cell stack, a water separator and a gas flow path, the hydrogen source provides new hydrogen for the ejector, the hydrogen passes through the plate heat exchanger after being ejected from the ejector and then enters the fuel cell stack, the gas returning from the fuel cell stack passes through the water separator first, and then enters the ejector to mix with the new hydrogen; the test system also includes temperature sensors arranged at the hydrogen inlet newly entering the ejector, the water inlet and the water outlet of the plate heat exchanger, the gas inlet returning from the fuel cell stack to the ejector, the inlet and the outlet of the plate heat exchanger, the temperature sensor, the pressure sensor and the humidity sensor are arranged, and a flow meter is also arranged at the water outlet of the plate heat exchanger; the water separator is also provided with a nitrogen exhaust valve;

[0008] S2. When the test system is running, the proportion of the amount of impurity gas in the anode mixed gas, that is, the anode impurity gas concentration α, is calculated in real time;

[0009] S3. Set the anode impurity gas concentration warning value α max , the anode impurity gas concentration α calculated in step S2 is compared with the warning value α max Dynamic comparison: when the anode impurity gas concentration α is greater than or equal to the warning value α max When the nitrogen exhaust valve is opened, the impurity gas is discharged to reduce the concentration of impurity gas;

[0010] S4. Set the anode impurity gas concentration safety value α sf , safety value α sf Less than the warning value α max , the anode impurity gas concentration α calculated in step S2 is compared with the safety value α sf Dynamic comparison: when the anode impurity gas concentration α is less than the safety value α sf When the nitrogen is discharged, close the nitrogen exhaust valve.

[0011] Furthermore, the step S2 comprises:

[0012] S2-1. Calculate the mass flow rate of hydrogen at each point in the gas flow path;

[0013] The mass flow rate of hydrogen newly entering the ejector Calculated according to the following formula:

[0014]

[0015] In the formula, is the molar mass of hydrogen, N is the number of cells in the stack, I is the current generated by the fuel cell, F is the Faraday constant, and β is the correction parameter for hydrogen utilization, which is usually taken as 1.04;

[0016] The mass flow rate of hydrogen before it is ejected from the ejector and enters the plate heat exchanger is equal to the sum of the mass flow rate of hydrogen newly entering the ejector and the mass flow rate of hydrogen flowing back into the ejector from the fuel cell stack:

[0017]

[0018] Mass flow rate of hydrogen after leaving the plate heat exchanger The mass flow rate of hydrogen before it is ejected from the ejector and enters the plate heat exchanger are equal, so the following relationship exists:

[0019]

[0020] Furthermore, the step S2 further includes:

[0021] S2-2. Calculate the mass flow rate of impurity gas in the gas flow path, ie, the mass flow rate of nitrogen;

[0022] Mass flow rate of impurity gas in the gas flow path That is, the mass flow rate of nitrogen is calculated by the following formula:

[0023]

[0024] Where α is the anode impurity gas concentration, is the molar mass of nitrogen, is the molar mass of hydrogen, is the mass flow rate of hydrogen after leaving the plate heat exchanger.

[0025] Furthermore, the step S2 further includes:

[0026] S2-3. Calculate the mass flow rate of gaseous water and liquid water at each point in the gas flow path;

[0027] The step S2-3 is specifically divided into the following steps:

[0028] S2-3-1. Calculate the mass fraction of gaseous water at each point in the gas flow path

[0029] S2-3-2. Calculate the mass flow rate of gaseous water entering the stack

[0030] S2-3-3. Calculate the mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger

[0031] S2-3-4. Calculate the mass flow rate of gaseous water flowing back into the ejector from the stack

[0032] S2-3-5. Calculate the mass flow rate of liquid water flowing back from the stack into the ejector and the mass flow rate of liquid water before it is ejected from the ejector into the plate heat exchanger

[0033] Furthermore, the step S2-3-1 calculates the mass fraction of gaseous water at each point in the gas flow path. The details are as follows:

[0034] The gaseous water partial pressure at each point in the gas flow path is calculated according to the following formula:

[0035]

[0036] In the formula, is the gaseous water partial pressure at that location in the gas flow path, RH is the gas relative humidity at that location in the gas flow path, and T is the gas temperature at that location in the gas flow path. RH and T are measured by a humidity sensor and a temperature sensor arranged at that location in the gas flow path;

[0037] The mass fraction of gaseous water at each point in the gas flow path is calculated according to the following formula:

[0038]

[0039] In the formula, is the mass fraction of gaseous water at that point in the gas flow path, is the gaseous water partial pressure at that point in the gas flow path, is the molar mass of water, M is the mixed molar mass of hydrogen and impurities in the mixed gas at that location, and P is the gas pressure at that location in the gas flow path, and P is measured by a pressure sensor arranged at that location in the gas flow path.

[0040] Furthermore, the step S2-3-2 calculates the mass flow rate of gaseous water entering the fuel cell stack. The details are as follows:

[0041] The mixed gas ejected from the ejector is heated by the plate heat exchanger, and the liquid water in the mixed gas is vaporized and converted into gaseous water. The mass flow rate of gaseous water entering the fuel cell stack is Calculated by the following formula;

[0042]

[0043] Where m”” is the mass flow rate of hydrogen and impurities in the mixed gas after leaving the plate heat exchanger. is the mass fraction of gaseous water after passing through the plate heat exchanger, Calculated by formula (5) and formula (6);

[0044] The mass flow rate of hydrogen and impurities m"" in the mixed gas after leaving the plate heat exchanger is equal to the mass flow rate of hydrogen and impurities m"' in the mixed gas before being ejected from the ejector and entering the plate heat exchanger, so the following relationship exists:

[0045] m””=m”′ (8);

[0046] The mass flow rate of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger is equal to the mass flow rate of hydrogen newly entering the ejector. and the mass flow rate of hydrogen flowing back from the stack into the ejector and the mass flow rate of impurity gases in the gas flow path The sum is equal, so the following relationship exists:

[0047]

[0048] The mixed molar mass M” of hydrogen and impurities in the mixed gas after the plate heat exchanger is calculated by the following formula:

[0049]

[0050] Where α is the anode impurity gas concentration, is the molar mass of nitrogen, is the molar mass of hydrogen.

[0051] Furthermore, the step S2-3-3 calculates the mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger. The details are as follows:

[0052] The mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger Calculated by the following formula:

[0053]

[0054] Where m'' is the mass flow rate of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger. is the mass fraction of gaseous water before it is ejected from the ejector and enters the plate heat exchanger, Calculated by formula (5) and formula (6);

[0055] The mixed molar mass M'' of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger is equal to the mixed molar mass M'' of hydrogen and impurities in the mixed gas after it passes through the plate heat exchanger, so the following relationship exists:

[0056] M”′=M”” (12).

[0057] Furthermore, step S2-3-4 calculates the mass flow rate of gaseous water flowing back from the stack into the ejector. The details are as follows:

[0058] The mass flow rate of gaseous water flowing back from the stack into the ejector Calculated by the following formula:

[0059]

[0060] Where m” is the mass flow rate of hydrogen and impurities in the mixed gas flowing back from the fuel cell stack into the ejector. is the mass fraction of gaseous water flowing back from the stack into the ejector, Calculated by formula (5) and formula (6);

[0061] The mass flow rate m" of the mixed gas of hydrogen and impurities flowing back into the ejector from the stack is equal to the mass flow rate of the new hydrogen entering the ejector. The sum is equal to the mass flow rate m'' of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger, that is, there is the following formula:

[0062]

[0063] According to the law of conservation of matter, the following relationship exists:

[0064]

[0065] Wherein, M" is the mixed molar mass of hydrogen and impurities in the mixed gas flowing back from the stack into the ejector. Further, the step S2-3-5 calculates the mass flow rate of liquid water flowing back from the stack into the ejector and the mass flow rate of liquid water before it is ejected from the ejector into the plate heat exchanger The details are as follows:

[0066] Due to the conservation of mass of water at each location in the gas flow path, the following relationship exists:

[0067]

[0068] Furthermore, the step S2 further includes:

[0069] S2-4. Calculate the anode impurity gas concentration α;

[0070] According to the law of conservation of energy, the sum of the energy of the new hydrogen entering the ejector and the gas flowing back into the ejector from the fuel cell stack is equal to the energy of the gas before it is ejected from the ejector and enters the plate heat exchanger:

[0071]

[0072] The sum of the energy of the gas ejected from the ejector before entering the plate heat exchanger and the energy provided by the plate heat exchanger to convert liquid water into gaseous water is equal to the energy of the gas after passing through the plate heat exchanger:

[0073]

[0074] In the formula, is the specific heat capacity of hydrogen, is the specific heat of gaseous water, is the specific heat of liquid water, is the specific heat capacity of nitrogen, T 1 is the temperature of the new hydrogen entering the ejector, T 1 It is measured by the first temperature sensor arranged at the hydrogen inlet of the new ejector, T 2 is the temperature of the gas flowing back from the stack into the ejector, T 2 The temperature is measured by the second temperature sensor arranged at the gas inlet flowing back from the stack into the ejector, T 3 is the gas temperature before it is ejected from the ejector and enters the plate heat exchanger, T 3 The third temperature sensor placed at the inlet of the plate heat exchanger measures T 4 is the gas temperature after passing through the plate heat exchanger, T 4 Measured by the fourth temperature sensor arranged at the outlet of the plate heat exchanger; T 5 is the temperature of the liquid water at the outlet of the plate heat exchanger, T 5 Measured by the fifth temperature sensor arranged at the water outlet of the plate heat exchanger; T 6 is the temperature of liquid water at the inlet of the plate heat exchanger, T 6 Measured by a sixth temperature sensor arranged at the water inlet of the plate heat exchanger;

[0075] In the formula, m 板 is the mass flow rate of liquid water in the plate heat exchanger, measured by the flow meter arranged at the outlet of the plate heat exchanger;

[0076] Substitute the mass flow rate of hydrogen at each location in the gas flow path, the mass flow rate of gaseous water and liquid water at each location, and the mass flow rate of impurity gas nitrogen calculated in steps S2-1, S2-2, and S2-3 into formulas (17) and (18), and obtain two equations containing two unknown quantities, which are: and α, solve for the value of the anode impurity gas concentration α.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] (1) By adding a nitrogen exhaust valve to the water separator, the drain valve is only used to discharge water in the water separator, and the nitrogen exhaust valve is used to discharge impurity gases. When the water in the water separator is discharged to a level that meets the requirements, the drain valve can be closed, thereby greatly shortening the drainage time. At the same time, the calculation of the impurity gas concentration at the anode is combined to accurately control the opening and closing of the nitrogen exhaust valve, thereby improving the nitrogen exhaust efficiency and reducing the waste of hydrogen in the fuel cell system.

[0079] (2) By using relatively mature and low-cost temperature sensors, humidity sensors and pressure sensors to collect temperature, humidity and pressure data at various points in the gas flow path of the fuel cell hydrogen circuit system, a mathematical model is established to analyze and calculate the anode impurity gas concentration of the fuel cell hydrogen circuit system accurately, and it is compared with the warning value and safety value of the anode impurity gas concentration, and the opening and closing of the nitrogen exhaust valve is accurately controlled, making the nitrogen exhaust strategy of the fuel cell stack more accurate.

[0080] Other features and advantages of the present invention will be described in the following description, and partly become obvious from the description, or be understood by implementing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0082] Figure 1 A schematic diagram of an anode impurity gas concentration test system of a fuel cell hydrogen circuit system according to an embodiment of the present invention is shown;

[0083] In the figure: 1. Hydrogen source; 2. Ejector; 3. Plate heat exchanger; 4. Fuel cell; 5. Water separator; 6. Nitrogen exhaust valve. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0085] The embodiment of the present invention provides an online calculation method for the impurity gas concentration at the anode of a fuel cell. Figure 1As shown, the specific steps include:

[0086] S1. A test system for the anode impurity gas concentration of a fuel cell hydrogen circuit subsystem is set up, the test system includes a hydrogen source 1, an ejector 2, a plate heat exchanger 3, a stack 4, a water separator 5 and a gas flow path, the hydrogen source 1 provides new hydrogen for the ejector 2, the hydrogen passes through the plate heat exchanger 3 after being ejected from the ejector 2 and then enters the stack 4, the gas flowing back from the stack 4 passes through the water separator 5 first, and then enters the ejector 2 to mix with the new hydrogen; the test system also includes temperature sensors arranged at the inlet of the hydrogen entering the new ejector 2, the water inlet and the water outlet of the plate heat exchanger 3, the gas flowing back from the stack 4 into the ejector 2, the inlet and the outlet of the plate heat exchanger 3 are all arranged with temperature sensors, pressure sensors and humidity sensors, and a flow meter is also arranged at the water outlet of the plate heat exchanger 3; the water separator 5 is also provided with a nitrogen exhaust valve 6;

[0087] S2. When the test system is running, the proportion of the amount of impurity gas in the anode mixed gas, that is, the anode impurity gas concentration α, is calculated in real time;

[0088] S3. Set the anode impurity gas concentration warning value α max , the anode impurity gas concentration α calculated in step S2 is compared with the warning value α max Dynamic comparison: when the anode impurity gas concentration α is greater than or equal to the warning value α max When the nitrogen exhaust valve 6 is opened, the impurity gas is discharged to reduce the concentration of the impurity gas;

[0089] Specifically, the anode impurity gas concentration warning value α max It can be set to 5% based on experience.

[0090] S4. Set the anode impurity gas concentration safety value α sf , safety value α sf Less than the warning value α max , the anode impurity gas concentration α calculated in step S2 is compared with the safety value α sf Dynamic comparison: when the anode impurity gas concentration α is less than the safety value α sf When the nitrogen is discharged, close the nitrogen exhaust valve 6.

[0091] Specifically, the safe value of anode impurity gas concentration α sf It can be set to 1% based on experience.

[0092] Compared with the traditional water separator that discharges the impurity gas nitrogen through the drain valve, the nitrogen discharge valve is set on the water separator to discharge nitrogen, which improves the nitrogen discharge efficiency. Because the traditional water separator is only equipped with a drain valve, the drain valve has the dual functions of draining water and nitrogen. In order to discharge nitrogen, the drainage time is generally designed to be long enough to ensure that the water is completely drained before continuing to discharge nitrogen. Since the drain valve is opened for too long, the hydrogen in the fuel cell system will also be discharged, resulting in a waste of hydrogen. By adding a nitrogen discharge valve to the water separator, the drain valve is only used to discharge the water in the water separator, and the nitrogen discharge valve is used to discharge the impurity gas. When the water in the water separator is discharged to a level that meets the requirements, the drain valve can be closed, thereby greatly shortening the drainage time. At the same time, in conjunction with the calculation of the impurity gas concentration at the anode, the opening and closing of the nitrogen discharge valve can be accurately controlled, which improves the nitrogen discharge efficiency while reducing the waste of hydrogen in the fuel cell system.

[0093] It is enough to discharge the water to meet the requirements. It is not necessary to discharge it completely. The nitrogen discharge is precisely controlled to save the hydrogen that escapes with the nitrogen.

[0094] Specifically, in step S1, a first temperature sensor is arranged at the inlet of hydrogen newly entering the ejector 2, a second temperature sensor, a first pressure sensor and a first humidity sensor are arranged at the inlet of the gas flowing back from the fuel cell stack 4 into the ejector 2, a third temperature sensor, a second pressure sensor and a second humidity sensor are arranged at the inlet of the plate heat exchanger 3, and a fourth temperature sensor, a third pressure sensor and a third humidity sensor are arranged at the outlet of the plate heat exchanger 3; a fifth temperature sensor and a flow meter are arranged at the water outlet of the plate heat exchanger 3, and a sixth temperature sensor is arranged at the water inlet of the plate heat exchanger 3.

[0095] The specific steps of real-time calculation of the anode impurity gas concentration α in step S2 are as follows:

[0096] S2-1. Calculate the mass flow rate of hydrogen at each point in the gas flow path;

[0097] The mass flow rate of hydrogen newly entering the ejector Calculated according to the following formula:

[0098]

[0099] In the formula, is the molar mass of hydrogen, N is the number of cells in the stack, I is the current generated by the fuel cell, F is the Faraday constant, and β is the correction parameter for hydrogen utilization, which is usually taken as 1.04.

[0100] According to the law of mass conservation, the mass flow rate of hydrogen ejected from the ejector before entering the plate heat exchanger is equal to the sum of the mass flow rate of hydrogen newly entering the ejector and the mass flow rate of hydrogen returning from the fuel cell to the ejector:

[0101]

[0102] In the formula, is the mass flow rate of hydrogen newly entering the ejector, is the mass flow rate of hydrogen flowing back from the fuel cell stack into the ejector, is the mass flow rate of hydrogen ejected from the ejector and entering the plate heat exchanger.

[0103] Since after the mixed gas enters the plate heat exchanger, the liquid water vapor in the mixed gas vaporizes into gaseous water while hydrogen remains unchanged, that is, the mass flow rate of hydrogen after the plate heat exchanger is the same as the mass flow rate of hydrogen ejected from the ejector and entering the plate heat exchanger before, the following relationship exists:

[0104]

[0105] From formula (1), formula (2), and formula (3), it can be seen that the mass flow rate of hydrogen newly entering the ejector can be directly calculated, and the mass flow rate of hydrogen ejected from the ejector and entering the plate heat exchanger before and the mass flow rate of hydrogen after the plate heat exchanger are both expressed as functions of the mass flow rate of hydrogen flowing back from the fuel cell stack into the ejector.

[0106] S2-2. Calculate the mass flow rate of the impurity gas in the gas flow path, that is, the mass flow rate of nitrogen;

[0107] The mass flow rate of the impurity gas in the gas flow path that is, the mass flow rate of nitrogen can be calculated by the following formula:

[0108]

[0109] In the formula, α is the concentration of the anode impurity gas, is the molar mass of nitrogen, is the molar mass of hydrogen, is the mass flow rate of hydrogen after the plate heat exchanger.

[0110] According to the mass flow rate of hydrogen after the plate heat exchanger calculated in step S2-1 and substituting it into formula (4), it can be known that the mass flow rate of the impurity gas in the gas flow path is expressed as a function of the mass flow rate of hydrogen flowing back from the fuel cell stack into the ejector and the anode impurity gas concentration α.

[0111] S2-3. Calculate the mass flow rate of gaseous water and liquid water at each point in the gas flow path;

[0112] S2-3-1. Calculate the mass fraction of gaseous water at each point in the gas flow path

[0113] The gaseous water partial pressure at each point in the gas flow path is calculated according to the following formula:

[0114]

[0115] In the formula, is the gaseous water partial pressure at that point in the gas flow path, RH is the gas relative humidity at that point in the gas flow path, T is the gas temperature at that point in the gas flow path, and RH and T are measured by a humidity sensor and a temperature sensor arranged at that point in the gas flow path.

[0116] The mass fraction of gaseous water at each point in the gas flow path is calculated according to the following formula:

[0117]

[0118] In the formula, is the mass fraction of gaseous water at that point in the gas flow path, is the gaseous water partial pressure at that point in the gas flow path, is the molar mass of water, M is the mixed molar mass of hydrogen and impurities in the mixed gas at that location, and P is the gas pressure at that location in the gas flow path, and P is measured by a pressure sensor arranged at that location in the gas flow path.

[0119] S2-3-2. Calculate the mass flow rate of gaseous water entering the stack

[0120] The mixed gas ejected from the ejector is heated by the plate heat exchanger, and the liquid water in the mixed gas is vaporized and converted into gaseous water. The mass flow rate of gaseous water entering the fuel cell stack is Calculated by the following formula;

[0121]

[0122] Where m”” is the mass flow rate of hydrogen and impurities in the mixed gas after leaving the plate heat exchanger. is the mass fraction of gaseous water after passing through the plate heat exchanger.

[0123] After the mixed gas enters the plate heat exchanger, the liquid water in the mixed gas vaporizes into gaseous water, and the hydrogen and impurity gases do not change. That is, the mass flow rate m'' of hydrogen and impurities in the mixed gas after leaving the plate heat exchanger is equal to the mass flow rate m'' of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger. Therefore, the following relationship exists:

[0124] m””=m”′ (8);

[0125] According to the law of mass conservation, the mass flow rate of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger is equal to the mass flow rate of hydrogen newly entering the ejector. and the mass flow rate of hydrogen flowing back from the stack into the ejector and the mass flow rate of impurity gases in the gas flow path The sum is equal, so the following relationship exists:

[0126]

[0127] In the formula, is the mass flow rate of hydrogen newly entering the ejector, is the mass flow rate of hydrogen flowing back from the stack into the ejector, The mass flow rate of impurity gas in the gas flow path.

[0128] Substituting the mass flow calculated in step S2-1 and step S2-2 into formula (9), it can be seen that the mass flow rate of hydrogen and impurities in the mixed gas before being ejected from the ejector into the plate heat exchanger is expressed as: and a function of the anode impurity gas concentration α.

[0129] Mass fraction of gaseous water after passing through the plate heat exchanger Then it is calculated according to formula (5) and formula (6), as follows:

[0130]

[0131] In the formula, is the gaseous water partial pressure after the plate heat exchanger, RH 3 is the relative humidity of the gas after passing through the plate heat exchanger, T 4 is the gas temperature after passing through the plate heat exchanger, RH 3 and T 4 The humidity is measured by the third humidity sensor and the fourth temperature sensor arranged at the outlet of the plate heat exchanger.

[0132] Mass fraction of gaseous water after passing through the plate heat exchanger Calculated according to the following formula:

[0133]

[0134] In the formula, is the gaseous water partial pressure after passing through the plate heat exchanger, is the molar mass of water, M”” is the mixed molar mass of hydrogen and impurities in the mixed gas after passing through the plate heat exchanger, P 3 is the gas pressure of the mixed gas after passing through the plate heat exchanger, P 3 It is measured by a third pressure sensor arranged at the outlet of the plate heat exchanger.

[0135] The mixed molar mass M” of hydrogen and impurities in the mixed gas after the plate heat exchanger is calculated by the following formula:

[0136]

[0137] Where α is the anode impurity gas concentration, is the molar mass of nitrogen, is the molar mass of hydrogen.

[0138] From formula (5-1), formula (6-1) and formula (10), it can be seen that the mass fraction of gaseous water after passing through the plate heat exchanger is It is expressed as a function of the anode impurity gas concentration α as the independent variable.

[0139] In summary, the mass flow rate of gaseous water entering the stack is The independent variable is the mass flow rate of hydrogen flowing back from the stack into the ejector. and a function of the anode impurity gas concentration α.

[0140] S2-3-3. Calculate the mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger

[0141] The mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger Calculated by the following formula:

[0142]

[0143] Where m'' is the mass flow rate of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger. It is the mass fraction of gaseous water before being ejected from the ejector and entering the plate heat exchanger.

[0144] The mass flow rate m″′ of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger is expressed by formula (9).

[0145] The mass fraction of gaseous water before it is ejected from the ejector and enters the plate heat exchanger Then it is calculated according to formula (5) and formula (6), as follows:

[0146]

[0147] In the formula, RH is the gaseous water pressure before it is ejected from the ejector and enters the plate heat exchanger. 2 is the relative humidity of the gas before it is ejected from the ejector and enters the plate heat exchanger, T 3 RH is the gas temperature before it is ejected from the ejector and enters the plate heat exchanger. 2 and T 3 The humidity is measured by a second humidity sensor and a third temperature sensor arranged at the gas inlet ejected from the ejector and entering the plate heat exchanger.

[0148]

[0149] In the formula, is the gaseous water pressure before it is ejected from the ejector and enters the plate heat exchanger. is the molar mass of water, M'' is the mixed molar mass of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger, P 2 P is the gas pressure of the mixed gas before it is ejected from the ejector and enters the plate heat exchanger. 2 It is measured by a second pressure sensor arranged at the gas inlet ejected from the ejector into the plate heat exchanger.

[0150] After the mixed gas enters the plate heat exchanger, the liquid water in the mixed gas vaporizes into gaseous water, and the hydrogen and impurity gases do not change, so the following relationship exists:

[0151] M”′=M”” (12);

[0152] In the formula, M'' is the mixed molar mass of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger, and M'' is the mixed molar mass of hydrogen and impurities in the mixed gas after it passes through the plate heat exchanger. That is, the mixed molar mass M'' of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger is expressed by formula (10).

[0153] From formula (5-2), formula (6-2), formula (10) and formula (12), we can know that the mass fraction of gaseous water before it is ejected from the ejector and enters the plate heat exchanger is It is expressed as a function of the anode impurity gas concentration α as the independent variable.

[0154] In summary, the mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger is The independent variable is the mass flow rate of hydrogen flowing back from the stack into the ejector. and a function of the anode impurity gas concentration α.

[0155] S2-3-4. Calculate the mass flow rate of gaseous water flowing back into the ejector from the stack

[0156] The mass flow rate of gaseous water flowing back from the stack into the ejector Calculated by the following formula:

[0157]

[0158] Where m” is the mass flow rate of hydrogen and impurities in the mixed gas flowing back from the fuel cell stack into the ejector. is the mass fraction of gaseous water flowing back from the stack into the ejector.

[0159] According to the law of mass conservation, the mass flow rate m" of the mixed gas of hydrogen and impurities flowing back into the ejector from the stack is equal to the mass flow rate of hydrogen newly entering the ejector. The sum is equal to the mass flow rate m'' of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger, that is, there is the following formula:

[0160]

[0161] From formula (1) and formula (9), it can be seen that the mass flow rate m' of the mixed gas of hydrogen and impurities in the fuel cell flowing back into the ejector is expressed as the independent variable is the mass flow rate of hydrogen flowing back into the ejector from the fuel cell and a function of the anode impurity gas concentration α.

[0162] Mass fraction of gaseous water flowing back into the ejector from the stack Then it is calculated according to formula (5) and formula (6), as follows:

[0163]

[0164] In the formula, RH is the partial pressure of gaseous water flowing back into the ejector from the stack, 1 is the relative humidity of the gas flowing back from the stack into the ejector, T 2 RH is the temperature of the gas flowing back from the stack into the ejector, 1 and T 2 The humidity is measured by a first humidity sensor and a second temperature sensor arranged at the gas inlet flowing back from the fuel cell stack into the ejector.

[0165]

[0166] In the formula, is the partial pressure of gaseous water flowing back into the ejector from the stack, is the molar mass of water, M” is the mixed molar mass of hydrogen and impurities in the mixed gas flowing back into the ejector from the stack, P1 is the gas pressure of the mixed gas flowing back from the stack into the ejector, P 1 The pressure is measured by a first pressure sensor arranged at the gas inlet flowing back from the fuel cell stack into the ejector.

[0167] According to the law of conservation of matter:

[0168]

[0169] Wherein, m" is the mass flow rate of hydrogen and impurities in the mixed gas flowing back from the stack into the ejector, M" is the mixed molar mass of hydrogen and impurities in the mixed gas flowing back from the stack into the ejector, m"' is the mass flow rate of hydrogen and impurities in the mixed gas before it is ejected from the ejector into the plate heat exchanger, M"' is the mixed molar mass of hydrogen and impurities in the mixed gas before it is ejected from the ejector into the plate heat exchanger, is the mass flow rate of hydrogen newly entering the ejector, is the molar mass of hydrogen.

[0170] Substituting formula (1), formula (9), formula (10), formula (12) and formula (14) into formula (15), the mixed molar mass M' of hydrogen and impurities in the mixed gas flowing back into the ejector from the stack is expressed as: and a function of the anode impurity gas concentration α.

[0171] From formula (5-3), formula (6-3) and formula (15), it can be seen that the mass fraction of gaseous water flowing back from the stack into the ejector is The independent variable is the mass flow rate of hydrogen flowing back from the stack into the ejector. and a function of the anode impurity gas concentration α.

[0172] In summary, the mass flow rate of gaseous water flowing back from the stack into the ejector is The independent variable is the mass flow rate of hydrogen flowing back from the stack into the ejector. and a function of the anode impurity gas concentration α.

[0173] S2-3-5. Calculate the mass flow rate of liquid water flowing back from the stack into the ejector and the mass flow rate of liquid water before it is ejected from the ejector into the plate heat exchanger

[0174] Due to the conservation of mass of water at each location in the gas flow path, the following relationship exists:

[0175]

[0176] In the formula, is the mass flow rate of gaseous water entering the stack, is the mass flow rate of liquid water before it is ejected from the ejector and enters the plate heat exchanger, is the mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger, is the mass flow rate of liquid water flowing back from the stack into the ejector, is the mass flow rate of gaseous water flowing back from the stack into the ejector.

[0177] Since steps S2-3-2, S2-3-3, and S2-3-4 have been respectively indicated and Substituting into formula (16), the mass flow rate of liquid water flowing back from the stack into the ejector is and the mass flow rate of liquid water before it is ejected from the ejector into the plate heat exchanger The independent variables are respectively expressed as the mass flow rate of hydrogen flowing back from the stack into the ejector and a function of the anode impurity gas concentration α.

[0178] S2-4. Calculate the anode impurity gas concentration α;

[0179] According to the law of conservation of energy, the sum of the energy of the new hydrogen entering the ejector and the gas flowing back into the ejector from the fuel cell stack is equal to the energy of the gas before it is ejected from the ejector and enters the plate heat exchanger:

[0180]

[0181] The sum of the energy of the gas ejected from the ejector before entering the plate heat exchanger and the energy provided by the plate heat exchanger to convert liquid water into gaseous water is equal to the energy of the gas after passing through the plate heat exchanger:

[0182]

[0183] In the formula, is the specific heat capacity of hydrogen, is the specific heat of gaseous water, is the specific heat of liquid water, is the specific heat capacity of nitrogen, T 1 is the temperature of the new hydrogen entering the ejector, T 1 It is measured by the first temperature sensor arranged at the hydrogen inlet of the new ejector, T 2 is the temperature of the gas flowing back from the stack into the ejector, T 2 The temperature is measured by the second temperature sensor arranged at the gas inlet flowing back from the stack into the ejector, T 3 is the gas temperature before it is ejected from the ejector and enters the plate heat exchanger, T 3The third temperature sensor placed at the inlet of the plate heat exchanger measures T 4 is the gas temperature after passing through the plate heat exchanger, T 4 Measured by the fourth temperature sensor arranged at the outlet of the plate heat exchanger; T 5 is the temperature of the liquid water at the outlet of the plate heat exchanger, T 5 Measured by the fifth temperature sensor arranged at the water outlet of the plate heat exchanger; T 6 is the temperature of liquid water at the inlet of the plate heat exchanger, T 6 Measured by a sixth temperature sensor arranged at the water inlet of the plate heat exchanger;

[0184] In the formula, is the mass flow rate of hydrogen newly entering the ejector, is the mass flow rate of hydrogen flowing back from the stack into the ejector, is the mass flow rate of hydrogen before it is ejected from the ejector and enters the plate heat exchanger, is the mass flow rate of hydrogen after leaving the plate heat exchanger;

[0185] In the formula, is the mass flow rate of gaseous water flowing back from the stack into the ejector, is the mass flow rate of liquid water flowing back from the stack into the ejector, is the mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger, is the mass flow rate of liquid water before it is ejected from the ejector and enters the plate heat exchanger, is the mass flow rate of gaseous water entering the fuel cell stack;

[0186] In the formula, is the mass flow rate of nitrogen in the mixed gas, m 板 It is the mass flow rate of liquid water in the plate heat exchanger, which is measured by the flow meter arranged at the outlet of the plate heat exchanger.

[0187] Substituting the mass flow rate of hydrogen at each location in the gas flow path, the mass flow rate of gaseous water and liquid water at each location, and the mass flow rate of impurity gas nitrogen calculated in steps S2-1, S2-2, and S2-3 into formulas (17) and (18), two binary linear equations are obtained, and the two unknowns are the mass flow rate of hydrogen flowing back from the stack into the ejector, The two equations are used to solve two unknowns and calculate the value of the anode impurity gas concentration α.

[0188] By using relatively mature and low-cost temperature sensors, humidity sensors and pressure sensors to collect temperature, humidity and pressure data at various points in the gas flow path of the fuel cell hydrogen subsystem, a mathematical model is established to analyze and calculate the anode impurity gas concentration of the fuel cell hydrogen subsystem accurately, and it is compared with the warning value and safety value of the anode impurity gas concentration, and the opening and closing of the nitrogen exhaust valve is accurately controlled to make the nitrogen exhaust strategy of the fuel cell stack more accurate.

[0189] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent substitutions for some of the technical features therein; and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An online calculation method for the impurity gas concentration of anode of a fuel cell, It is characterized in that The steps include: S1. A test system for the anode impurity gas concentration of a fuel cell hydrogen circuit subsystem is set up, the test system includes a hydrogen source, an ejector, a plate heat exchanger, a fuel cell stack, a water separator and a gas flow path, the hydrogen source provides new hydrogen for the ejector, the hydrogen passes through the plate heat exchanger after being ejected from the ejector and then enters the fuel cell stack, the gas returning from the fuel cell stack passes through the water separator first, and then enters the ejector to mix with the new hydrogen; the test system also includes temperature sensors arranged at the hydrogen inlet newly entering the ejector, the water inlet and the water outlet of the plate heat exchanger, the gas inlet returning from the fuel cell stack to the ejector, the inlet and the outlet of the plate heat exchanger, the temperature sensor, the pressure sensor and the humidity sensor are arranged, and a flow meter is also arranged at the water outlet of the plate heat exchanger; the water separator is also provided with a nitrogen exhaust valve; S2. When the test system is running, the proportion of the amount of impurity gas in the anode mixed gas, that is, the anode impurity gas concentration α, is calculated in real time; S3. Set the anode impurity gas concentration warning value α max , the anode impurity gas concentration α calculated in step S2 is compared with the warning value α max Dynamic comparison: when the anode impurity gas concentration α is greater than or equal to the warning value α max When the nitrogen exhaust valve is opened, the impurity gas is discharged to reduce the concentration of impurity gas; S4. Set the anode impurity gas concentration safety value α sf , safety value α sf Less than the warning value α max , the anode impurity gas concentration α calculated in step S2 is compared with the safety value α sf Dynamic comparison: when the anode impurity gas concentration α is less than the safety value α sf When the nitrogen is discharged, close the nitrogen exhaust valve.

2. The method for online calculation of impurity gas concentration at anode of a fuel cell according to claim 1, It is characterized in that The step S2 comprises: S2-1. Calculate the mass flow rate of hydrogen at each point in the gas flow path; The mass flow rate of hydrogen newly entering the ejector is m' H2 Calculated according to the following formula: In the formula, is the molar mass of hydrogen, N is the number of cells in the stack, I is the current generated by the fuel cell, F is the Faraday constant, and β is the correction parameter for hydrogen utilization, which is usually taken as 1.04; The mass flow rate of hydrogen before it is ejected from the ejector and enters the plate heat exchanger is equal to the sum of the mass flow rate of hydrogen newly entering the ejector and the mass flow rate of hydrogen flowing back into the ejector from the fuel cell stack: Mass flow rate of hydrogen after leaving the plate heat exchanger The mass flow rate of hydrogen before it is ejected from the ejector and enters the plate heat exchanger are equal, so the following relationship exists:

3. The method for online calculation of impurity gas concentration at anode of a fuel cell according to claim 2, It is characterized in that The step S2 further comprises: S2-2. Calculate the mass flow rate of impurity gas in the gas flow path, ie, the mass flow rate of nitrogen; Mass flow rate of impurity gas in the gas flow path That is, the mass flow rate of nitrogen is calculated by the following formula: Where α is the anode impurity gas concentration, is the molar mass of nitrogen, is the molar mass of hydrogen, is the mass flow rate of hydrogen after leaving the plate heat exchanger.

4. The method for online calculation of impurity gas concentration at anode of a fuel cell according to claim 3, It is characterized in that The step S2 further comprises: S2-3. Calculate the mass flow rate of gaseous water and liquid water at each point in the gas flow path; The step S2-3 is specifically divided into the following steps: S2-3-1. Calculate the mass fraction of gaseous water at each point in the gas flow path S2-3-2. Calculate the mass flow rate of gaseous water entering the stack S2-3-3. Calculate the mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger S2-3-4. Calculate the mass flow rate of gaseous water flowing back into the ejector from the stack S2-3-5. Calculate the mass flow rate of liquid water flowing back from the stack into the ejector and the mass flow rate of liquid water before it is ejected from the ejector into the plate heat exchanger 5. The method for online calculation of impurity gas concentration at anode of a fuel cell according to claim 4, It is characterized in that Step S2-3-1 calculates the mass fraction of gaseous water at each location in the gas flow path The details are as follows: The gaseous water partial pressure at each point in the gas flow path is calculated according to the following formula: In the formula, is the gaseous water partial pressure at that location in the gas flow path, RH is the gas relative humidity at that location in the gas flow path, and T is the gas temperature at that location in the gas flow path. RH and T are measured by a humidity sensor and a temperature sensor arranged at that location in the gas flow path; The mass fraction of gaseous water at each point in the gas flow path is calculated according to the following formula: In the formula, is the mass fraction of gaseous water at that point in the gas flow path, is the gaseous water partial pressure at that point in the gas flow path, is the molar mass of water, M is the mixed molar mass of hydrogen and impurities in the mixed gas at that location, and P is the gas pressure at that location in the gas flow path, and P is measured by a pressure sensor arranged at that location in the gas flow path.

6. The method for online calculation of impurity gas concentration in anode of a fuel cell according to claim 5, It is characterized in that The step S2-3-2 calculates the mass flow rate of gaseous water entering the fuel cell stack. The details are as follows: The mixed gas ejected from the ejector is heated by the plate heat exchanger, and the liquid water in the mixed gas is vaporized and converted into gaseous water. The mass flow rate of gaseous water entering the fuel cell stack is Calculated by the following formula; Where m”” is the mass flow rate of hydrogen and impurities in the mixed gas after leaving the plate heat exchanger. is the mass fraction of gaseous water after passing through the plate heat exchanger, Calculated by formula (5) and formula (6); The mass flow rate of hydrogen and impurities m"" in the mixed gas after leaving the plate heat exchanger is equal to the mass flow rate of hydrogen and impurities m"' in the mixed gas before being ejected from the ejector and entering the plate heat exchanger, so the following relationship exists: m””=m″′ (8); The mass flow rate of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger is equal to the mass flow rate of hydrogen newly entering the ejector. and the mass flow rate of hydrogen flowing back from the stack into the ejector and the mass flow rate of impurity gases in the gas flow path The sum is equal, so the following relationship exists: The mixed molar mass M” of hydrogen and impurities in the mixed gas after the plate heat exchanger is calculated by the following formula: Where α is the anode impurity gas concentration, is the molar mass of nitrogen, is the molar mass of hydrogen.

7. The method for online calculation of impurity gas concentration at anode of a fuel cell according to claim 6, It is characterized in that The step S2-3-3 calculates the mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger. The details are as follows: The mass flow rate of gaseous water before it is ejected from the ejector and enters the plate heat exchanger Calculated by the following formula: Where m″′ is the mass flow rate of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger. is the mass fraction of gaseous water before it is ejected from the ejector and enters the plate heat exchanger, Calculated by formula (5) and formula (6); The mixed molar mass M'' of hydrogen and impurities in the mixed gas before being ejected from the ejector and entering the plate heat exchanger is equal to the mixed molar mass M'' of hydrogen and impurities in the mixed gas after passing through the plate heat exchanger, so the following relationship exists: M″′=M”” (12).

8. The method for online calculation of impurity gas concentration at anode of a fuel cell according to claim 7, It is characterized in that Step S2-3-4 calculates the mass flow rate of gaseous water flowing back into the ejector from the stack The details are as follows: The mass flow rate of gaseous water flowing back from the stack into the ejector Calculated by the following formula: Where m” is the mass flow rate of hydrogen and impurities in the mixed gas flowing back from the fuel cell stack into the ejector. is the mass fraction of gaseous water flowing back from the stack into the ejector, Calculated by formula (5) and formula (6); The mass flow rate m" of the mixed gas of hydrogen and impurities flowing back into the ejector from the stack is equal to the mass flow rate of the new hydrogen entering the ejector. The sum is equal to the mass flow rate m'' of hydrogen and impurities in the mixed gas before it is ejected from the ejector and enters the plate heat exchanger, that is, there is the following formula: According to the law of conservation of matter, the following relationship exists: Where M” is the mixed molar mass of hydrogen and impurities in the mixed gas flowing back from the fuel cell stack into the ejector.

9. The method for online calculation of impurity gas concentration in anode of a fuel cell according to claim 8, It is characterized in that Step S2-3-5 calculates the mass flow rate of liquid water flowing back from the stack into the ejector and the mass flow rate of liquid water before it is ejected from the ejector into the plate heat exchanger The details are as follows: Due to the conservation of mass of water at each location in the gas flow path, the following relationship exists:

10. The method for online calculation of impurity gas concentration in anode of a fuel cell according to claim 9, It is characterized in that The step S2 further comprises: S2-4. Calculate the anode impurity gas concentration α; According to the law of conservation of energy, the sum of the energy of the new hydrogen entering the ejector and the gas flowing back into the ejector from the fuel cell stack is equal to the energy of the gas before it is ejected from the ejector and enters the plate heat exchanger: The sum of the energy of the gas ejected from the ejector before entering the plate heat exchanger and the energy provided by the plate heat exchanger to convert liquid water into gaseous water is equal to the energy of the gas after passing through the plate heat exchanger: In the formula, is the specific heat capacity of hydrogen, is the specific heat of gaseous water, is the specific heat of liquid water, is the specific heat capacity of nitrogen, T 1 is the temperature of the new hydrogen entering the ejector, T 1 It is measured by the first temperature sensor arranged at the hydrogen inlet of the new ejector, T 2 is the temperature of the gas flowing back from the stack into the ejector, T 2 The temperature is measured by the second temperature sensor arranged at the gas inlet flowing back from the stack into the ejector, T 3 is the gas temperature before it is ejected from the ejector and enters the plate heat exchanger, T 3 The third temperature sensor placed at the inlet of the plate heat exchanger measures T 4 is the gas temperature after passing through the plate heat exchanger, T 4 Measured by the fourth temperature sensor arranged at the outlet of the plate heat exchanger; T 5 is the temperature of the liquid water at the outlet of the plate heat exchanger, T 5 Measured by the fifth temperature sensor arranged at the water outlet of the plate heat exchanger; T 6 is the temperature of liquid water at the inlet of the plate heat exchanger, T 6 Measured by a sixth temperature sensor arranged at the water inlet of the plate heat exchanger; In the formula, m 板 is the mass flow rate of liquid water in the plate heat exchanger, measured by the flow meter arranged at the outlet of the plate heat exchanger; Substitute the mass flow rates of hydrogen at various locations, the mass flow rates of gaseous water and liquid water at various locations, and the mass flow rate of the impurity gas nitrogen calculated in steps S2-1, S2-2, and S2-3 into formula (17) and formula (18) to obtain two equations containing two unknowns. The two unknowns are and α, and solve for the value of the anode impurity gas concentration α.

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