A Calibration Method for a Three-Dimensional Model of a PEM Fuel Cell at Low Current Densities

Abstract

The present invention discloses a calibration method for a three-dimensional model of a PEM fuel cell at low current density, including: respectively solving based on the gas-phase control equation and the liquid-phase control equation to construct a three-dimensional two-phase homogeneous PEM fuel cell model of the test object; based on the three-dimensional two-phase homogeneous PEM fuel cell model, using Comsol software for simulation to obtain polarization curves, overpotentials and open-circuit voltages under multiple sets of operating condition combinations; performing parameter sensitivity analysis on the model mass transfer parameters and electrochemical parameters by the single-factor method to obtain sensitive parameters of open-circuit loss, activation overpotential and ohmic overpotential at low current density; based on the sensitive parameters, separating the overpotential and the oxygen concentration calculated by the model from the polarization curve data at different temperatures and back pressures in the low current density range, performing open-circuit loss calibration based on the result of activation overpotential calibration, and performing ohmic overpotential calibration based on the result of open-circuit loss calibration to determine the model parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of fuel cells, and particularly relates to a method for calibrating a three-dimensional model of a PEM fuel cell at low current density. Background Technique

[0002] PEM fuel cells have the advantages of zero emissions, high efficiency, and fast start-stop speed, and have become one of the most promising sustainable energy solutions to replace fossil fuels, especially attracting wide attention in the field of new energy vehicles. A PEM fuel cell is a complex non-linear system involving multi-component reactions, multi-dimensional transport, and multi-physical fields. It is difficult to characterize the internal "water-gas-electricity-thermal" transport phenomena and distributions only by experiments. A high-precision mathematical model of a PEM fuel cell can deeply and thoroughly explore its internal transport and reaction processes, provide guidance for the optimal design of structures and operating conditions, and is beneficial to reducing product R & D costs and shortening the R & D cycle. However, the modeling mechanism of PEM fuel cells is complex and there are many model parameters. There will be situations where different parameter combinations can better fit the same polarization curve, greatly reducing the credibility of the model. Summary of the Invention

[0003] To solve the above technical problems, the present invention proposes a method for calibrating a three-dimensional model of a PEM fuel cell at low current density, achieving high model accuracy and credibility in the low current density range.

[0004] To achieve the above object, the present invention provides a method for calibrating a three-dimensional model of a PEM fuel cell at low current density, including:

[0005] Based on the gas-phase control equation and the liquid-phase control equation, solve respectively to construct a three-dimensional two-phase homogeneous PEM fuel cell model of the test object;

[0006] Based on the three-dimensional two-phase homogeneous PEM fuel cell model, use Comsol software to perform simulation to obtain polarization curves, overpotentials, and open circuit voltages under multiple sets of operating condition combinations;

[0007] Through the single-factor method, perform parameter sensitivity analysis on the model mass transfer parameters and electrochemical parameters to obtain the sensitive parameters of open circuit loss, activation overpotential, and ohmic overpotential at low current density;

[0008] Based on the sensitive parameters, separate the polarization curve data of different temperatures and back pressures in the low current density range to obtain the overpotential and the oxygen concentration calculated by the model. Based on the oxygen concentration, perform activation overpotential verification, based on the result of activation overpotential verification, perform open circuit loss verification, and based on the result of open circuit loss verification, perform ohmic overpotential verification to determine the model parameters.

[0009] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, the gas phase control equation solving equations include the mass conservation equation, the momentum conservation equation, the component conservation equation, and the energy conservation equation.

[0010] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, under steady-state conditions, the mass balance of the gas flow channels and porous media regions of the PEM fuel cell in the mass conservation equation is described as:

[0011] where ε is the porosity, ρ is the density of the gas mixture, p is the operating pressure, u is the gas viscosity, S m is the energy source term.

[0012] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, the momentum conservation equation describes the pressure and velocity changes of the gas flow inside the PEM fuel cell and is simplified under steady-state conditions as:

[0013] where ε is the porosity, ρ is the density of the gas mixture, p is the operating pressure, μ is the dynamic viscosity of the gas phase mixture, is the gas velocity vector, is the pressure gradient of the gas flow inside the cell, is the velocity vector gradient of the gas flow inside the cell, S u is the momentum source term.

[0014] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, the component conservation equation is simplified to mixture-averaged calculation of diffusion using Maxwell-Stefan diffusion:

[0015]

[0016] where ρ is the density of the gas mixture, p is the operating pressure, ω i is the mass fraction of substance i, is the gas velocity vector, n is the number of component types, is the effective diffusion coefficient of substance i relative to substance j, is the gradient of the mole fraction of substance j, S i is the gas mass source term.

[0017] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, the heat transfer equation for the energy conservation equation under steady-state operation of the PEM fuel cell is calculated as follows:

[0018]

[0019] where ε is the porosity, s is the saturation of liquid water, ρ g is the density of the gas mixture, C p,g and C p,1 are the specific heat capacities of the gas mixture and liquid water, respectively, is the velocity vector of the gas, T is the temperature, ρ l is the density of liquid water, k eff is the effective thermal conductivity, is the temperature gradient of the reaction, S T is the energy source term.

[0020] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, when solving the liquid control equation under the steady-state operation conditions of the PEM fuel cell, the water content transport equation is:

[0021] where n d is the electroosmotic drag coefficient, i1 is the current density generated by proton movement, F is the Faraday constant, ρ mem is the dry membrane density, EW is the membrane equivalent weight, is the effective diffusion coefficient of water in the membrane state, λ is the water content, is the gradient of the water content, S νλ is the source term for water adsorption or desorption in the membrane state.

[0022] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, the method for checking the activation overpotential based on the oxygen concentration is:

[0023]

[0024] where, is the oxygen concentration at temperature T2, T2 and T1 are different reaction operating temperatures, α c is the charge transfer coefficient, F is the Faraday constant, is the cathode activation overpotential at temperature T2, R is the gas constant of the ideal gas, E ca is the magnitude of the activation energy required for the chemical reaction to occur, T ref is the temperature of the catalyst layer.

[0025] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, the method for checking the open circuit loss based on the result of checking the activation overpotential is:

[0026]

[0027] where i loss is the hydrogen permeation current density caused by hydrogen transmembrane, F is the Faraday constant, is the hydrogen transmembrane permeability coefficient, is the partial pressure of hydrogen, and δ m is the thickness of the proton exchange membrane, is the activation energy of hydrogen diffusion, R is the gas constant, and T is the reaction temperature.

[0028] According to the PEM fuel cell low current density three-dimensional model calibration method provided by the present invention, the method for checking the ohmic overpotential based on the open circuit loss check result is as follows:

[0029]

[0030] wherein, σ1 is the surface tension coefficient of liquid water, λ is the water content, ω1 is the proton conduction index, and T ref is the temperature of the catalyst layer, and T is the actual working temperature.

[0031] Technical effects of the present invention: The three-dimensional model calibration method for PEM fuel cells proposed by the present invention has certain advantages compared with the previously used calibration methods. The present invention conducts a sensitivity analysis of model parameters according to the modeling theory and uses the single factor method and parameter normalization, thereby obtaining a summary of the sensitivities of model parameters for open circuit voltage, activation overpotential, and ohmic overpotential under low current density conditions. And through the sensitivity parameters of the three-dimensional model under low current density, a parameter calibration process for the PEM fuel cell model is proposed. In order to obtain high-precision and highly reliable model parameters, a three-dimensional two-phase homogeneous PEM fuel cell model of the test object is established. A more detailed electrochemical parameter calibration method is proposed through the analysis of the Butler-Volmer equation, and the overpotential obtained by separating the polarization curve data of different temperatures and back pressures in the low current density range and the oxygen concentration calculated by the model uniquely determine the electrochemical parameters of the model, achieving high model accuracy and reliability in the low current density range. Brief Description of the Drawings

[0032] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0033] Figure 1 is the overall view of the PEM fuel cell parameter calibration process according to the embodiment of the present invention;

[0034] Figure 2 is the schematic flow chart of a method for calibrating a three-dimensional model of a PEM fuel cell at low current density according to an embodiment of the present invention. Detailed Embodiments

[0035] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail this application.

[0036] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. And although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0037] As Figure 1-2 shown, in this embodiment, a method for calibrating a three-dimensional model of a PEM fuel cell at low current density is provided, including: respectively solving based on the gas-phase control equation and the liquid-phase control equation to construct a three-dimensional two-phase homogeneous PEM fuel cell model of the test object;

[0038] Based on the three-dimensional two-phase homogeneous PEM fuel cell model, use Comsol software to perform simulation to obtain polarization curves, overpotentials and open-circuit voltages under multiple sets of operating condition combinations;

[0039] Perform parameter sensitivity analysis on the model mass transfer parameters and electrochemical parameters by the single-factor method to obtain sensitive parameters of open-circuit loss, activation overpotential and ohmic overpotential at low current density;

[0040] Based on the sensitive parameters, separate the polarization curve data of different temperatures and back pressures in the low current density range to obtain the overpotential and the oxygen concentration calculated by the model. Based on the oxygen concentration, perform activation overpotential verification, based on the result of activation overpotential verification, perform open-circuit loss verification, and based on the result of open-circuit loss verification, perform ohmic overpotential verification to determine the model parameters.

[0041] The modeling theory establishes a three-dimensional two-phase model. The two-phase flow model of the fuel cell adopted is mainly the two-fluid method. The two-fluid method requires separate solutions of the gas-phase control equation and the liquid-phase control equation. The interaction between different phases is reflected by the phase transfer term. The gas-phase solution equations include the mass conservation equation, the momentum conservation equation, and the component conservation equation. The liquid phase mainly solves the liquid water transport theory, and the gas phase and the liquid phase jointly solve the energy conservation equation. Specifically:

[0042] The mass conservation equation is expressed as the continuity equation of a continuous medium fluid. Under steady-state conditions, the mass balance of the gas flow channel and the porous medium region of the PEM fuel cell is described as: In the formula, ρ is the density of the gas mixture, u is the gas viscosity, S m is the energy source term, ε is the porosity, defined as the ratio of the pore volume of the porous medium material to the total volume of the material under standard conditions. The main influencing parameters of this part are the porosity ε, the working pressure p, the working temperature T, and the current density i.

[0043] The momentum conservation equation uses the Navier-Stokes equation to describe the changes in gas flow pressure and velocity inside the PEM fuel cell, which is simplified under steady-state conditions to The main influencing parameters of this part are porosity ε, operating pressure p, gas viscosity μ, and gas permeability K i , ρ is the density of the gas mixture, is the velocity vector of the gas, is the pressure gradient of the gas flow inside the cell, is the velocity vector gradient of the gas flow inside the cell, S u is the momentum source term.

[0044] The component conservation equation is simplified to mixture-averaged diffusion using Maxwell-Stefan diffusion: In the formula, ω i is the mass fraction of substance i, n is the number of component types, is the gradient of the mole fraction of substance j, S i is the gas mass source term, is the effective diffusion coefficient of substance i relative to substance j. The effective diffusion coefficient needs to add the reference diffusion coefficient of substance i relative to j Correction of porosity, pressure, temperature, and liquid water: The main influencing parameters are operating pressure p, operating temperature T, current density i, porosity ε, reference diffusion coefficient and liquid water saturation s.

[0045] The energy conservation equation The heat transfer equation under steady-state operation of the PEM fuel cell can be expressed as the following formula: In the formula, ε is the porosity, s is the saturation of liquid water, ρ g is the density of the gas mixture, C p,g and C p,1 are the specific heat capacities of the gas mixture and liquid water respectively, is the velocity vector of the gas, T is the temperature, ρ l is the density of liquid water, k eff is the effective thermal conductivity, is the temperature gradient of the reaction, S T is the energy source term. Membrane water exists in the electrolyte and proton exchange membrane of the catalyst layer, and the transport mechanism mainly considers the electroosmotic drag effect and reverse diffusion caused by concentration difference. Under the steady-state operation conditions of the PEM fuel cell, the water content transport equation is: In the formula, n d is the electroosmotic drag coefficient, i1 is the current density generated by proton movement, that is, the electrolyte current density, ρ mem is the dry membrane density, EW is the membrane equivalent, is the effective diffusion coefficient of the membrane water, λ is the water content, is the gradient of the water content, S νλ is the source term for the adsorption or desorption of the membrane water. In the catalyst layer, the correction of the effective diffusion coefficient in the concentration difference diffusion of the membrane water is as follows: In the formula, ε1 is the volume fraction of the electrolyte in the catalyst layer, which is the ratio of the volume of the electrolyte in the catalyst layer to the total volume. The direction of water adsorption / desorption is determined by the difference between the water content and the average water content. The mutual conversion rate between the membrane water and the gaseous water is called the adsorption / desorption rate, which is expressed as: In the formula, γ νλ is the adsorption rate constant for the conversion of gaseous water to membrane water, γ λν is the desorption rate constant for the conversion of membrane water to gaseous water. The main influencing parameters are the water content λ, the volume fraction of the electrolyte in the catalyst layer ε1, the adsorption / desorption rate constants γ νλ and γ λν , the liquid water saturation s, the operating temperature T, the relative humidity RH, and the current density i.

[0046] The liquid water transport equation under steady-state operating conditions is: In the formula, K is the absolute permeability of the porous medium, k1 is the relative permeability of the liquid water, μ1 is the viscosity of the liquid water, and p1 is the liquid pressure.

[0047] Among them,

[0048] In the formula, θ is the contact angle, and is the surface tension of the liquid water.

[0049] Under the homogeneous assumption model of the PEM fuel cell catalyst layer, the modified Butler-Volmer equation can be used to describe the influence of factors such as temperature, polarization, and concentration on the electrochemical reaction:

[0050]

[0051] In the formula, a CL is the reaction surface area density, are the reference exchange current densities of the anode and cathode respectively, are the hydrogen concentration and oxygen concentration respectively, are the reference hydrogen concentration and reference oxygen concentration respectively, E a 、E c are the activation energy barriers for the anode hydrogen reaction and the cathode oxygen reaction respectively, α a 、α c are the charge transfer coefficients of the anode and cathode respectively, are the activation overpotentials of the anode and cathode respectively.

[0052] The hydrogen permeation loss in PEM fuel cells mainly occurs in the permeation loss caused by hydrogen transmembrane: where i loss is the hydrogen permeation current density caused by hydrogen transmembrane, δ m is the thickness of the proton exchange membrane, is the hydrogen transmembrane permeation coefficient, is the activation energy of hydrogen diffusion.

[0053] Sensitivity analysis is to study the degree of influence of the change of uncertain parameters in the model on the output results. The single-factor method is one of the simplest and most commonly used methods. Each time only one quantity is changed, and other variables are fixed at the base value. It is simple to operate, fast to calculate, and the comparability of the results is good. Normalizing the model parameters can compare the sensitivities between different parameters. Combining with the single-factor analysis method, the sensitivity of the parameters is quantified as a scalar S for comparison. The higher the sensitivity, the more sensitive the output result is to the fluctuation of the parameter.

[0054]

[0055] where ΔR / R is the change rate of the output quantity, and ΔA / A is the change rate of the model parameter. By comparing the magnitudes of the sensitivity index S, the sensitivity classification principle of the model parameters can be quantitatively determined. 10% of the maximum value of the sensitivity index corresponding to each output quantity is used as the demarcation value of the parameter sensitivity of the output quantity

[0056] (1) The maximum value of S for the open-circuit voltage is 0.35. S > 0.035 is a highly sensitive parameter, and S < 0.035 is a low-sensitive parameter;

[0057] (2) The maximum value of S for the activation overpotential is 1.04. S > 0.104 is a highly sensitive parameter, and S < 0.104 is a low-sensitive parameter

[0058] (3) The maximum value of S for the ohmic overpotential is 0.41. S > 0.041 is a highly sensitive parameter, and S < 0.041 is a low-sensitive parameter.

[0059] Using the single-factor method to conduct parameter sensitivity analysis on the mass transfer parameters and electrochemical parameters of the model, the sensitive parameters of the open-circuit loss, activation overpotential, and ohmic overpotential at a low current density (0.2 A / cm 2 ) are obtained, as shown in Table 1.

[0060] Table 1

[0061]

[0062]

[0063] It is found that: (1) the number of sensitive parameters is small at low current density; (2) the number of sensitive parameters of ohmic overpotential is the least, and there is only one coincidence with the sensitive parameters of activation overpotential and open-circuit voltage; (3) the sensitive parameters of open-circuit voltage cover the sensitive parameters of cathode activation overpotential at low current density. In summary, the parameter calibration process of the PEM fuel cell model can be determined.

[0064] The parameter calibration process of the fuel cell model is as Figure 2 shown, and the method description is as follows:

[0065] Specifically, since the sensitive parameters of open-circuit voltage loss cover the sensitive parameters of cathode activation loss at low current density. Therefore, when calibrating the two sensitive parameters that dominate the performance loss of PEM fuel cells, the sensitive parameters of cathode activation overpotential should be calibrated first.

[0066] The hydrogen transmembrane permeation coefficient in open-circuit loss and the hydrogen diffusion activation energy barrier can be verified after the activation overpotential.

[0067] The ohmic overpotential accounts for a relatively small proportion in the performance loss of the fuel cell, and at the model level, its sensitive parameters are relatively independent, with only one sensitive parameter at low current density. Therefore, the verification of the ohmic overpotential at low current density is relatively easy.

[0068] Subsequently, a three-dimensional two-phase homogeneous PEM fuel cell model of the test object was established, and a more detailed electrochemical parameter calibration method was proposed through the analysis of the Butler-Volmer equation:

[0069] Through the analysis of the experimental object, the oxygen concentration was obtained from the overpotential separated by using the polarization curve data of different temperatures and back pressures in the low current density range and the model calculation.

[0070] Then, the activation overpotential verification is carried out:

[0071] The magnitude of the activation overpotential of the fuel cell depends on three aspects, namely the current density, the reaction conditions, and the catalytic ability of the catalyst. The Butler-Volmer equation describes this process in detail:

[0072]

[0073] The analysis of the equation is as follows: in the formula, i 0,c represents the local reaction rate, and T represent the reaction conditions, and the remaining parameters represent the catalytic ability of the catalyst. and T ref refer to the catalyst surface area per unit volume as a CL , the catalyst oxygen concentration and temperature are With T ref (Reference condition), the reaction current density of the electrode when the overpotential is 0 is It characterizes the basic intrinsic activity of the catalyst. When the reactant conditions deviate from the reference conditions, the first half of the Butler-Volmer equation can be used to correct the intrinsic activity, E ca is the magnitude of the activation energy required for the chemical reaction, which is highly correlated with the composition of the catalyst layer and the crystal plane structure of the catalyst. The key parameter in the second half of the Butler-Volmer equation - the charge transfer coefficient α c , describes the influence of the electronic effect on the change in Gibbs free energy in the electrochemical reaction. At low current densities, the sensitive parameters of the activation overpotential of the fuel cell are E ca , α c and

[0074] Through theoretical analysis, it is found that the parameters E ca and α c can be solved through the overpotentials at different operating pressures and different temperatures.

[0075] For fuel cells with the same current density and temperature but different operating pressures, the activation overpotential can be expressed as:

[0076]

[0077] Since α c < 1, after simplification and transformation, it can be obtained: In the low current density stage, the gas is far in excess, and the internal pressure difference of the fuel cell is also small. That is to say, it can be roughly considered that the oxygen concentration distribution inside the fuel cell is uniform in the low current density stage, and the corresponding overpotential distribution should also be uniform, so the experimental data can be used instead. The oxygen concentration inside the fuel cell can be calculated theoretically or obtained through a model. The required flow model has been verified and can obtain a more accurate average oxygen concentration. Then, for a determined operating temperature, through the activation loss between different operating pressures, the value of α c can be determined.

[0078] Similarly, for fuel cells operating at the same current density and pressure but different operating temperatures, the activation overpotential is written and after simplification and transformation, it is obtained:

[0079]

[0080] In the low current density stage, for a determined operating pressure, through the experimental values of the activation loss between different operating temperatures and the calculated values of the oxygen concentration, as well as the already determined value of α c , the value of E caValues. Thus, a calibration method for the homogeneous model of PEM fuel cells is obtained. Determine the value of α c and the value of E ca After determining the values, the parameter α c = 7.0×10 7 l / m,

[0081] Open-circuit voltage check:

[0082] The open-circuit loss depends on the magnitude of the hydrogen permeation current and the catalyst activity. The higher the hydrogen permeation current, the lower the catalyst activity, and the lower the open-circuit voltage.

[0083]

[0084] After the parameter check of the activation overpotential is completed, the α c and i 0,c The remaining parameters to be checked are the activation energy of hydrogen diffusion and the hydrogen transmembrane permeability coefficient The required parameter values can be calculated using the open-circuit voltage and hydrogen partial pressure at different temperatures.

[0085] Ohmic overpotential check:

[0086] This formula is an empirical formula for the modified electrolyte conductivity, adding a proton conduction index ω1. Its core is to correct the dependence of conductivity on water content. The smaller this index, the less the conductivity is affected by water content; when ω1 = 1, the conductivity and water content are linearly related.

[0087] The three-dimensional model calibration method of PEM fuel cells proposed by the present invention has certain advantages compared with the previously used calibration methods. The present invention conducts a sensitivity analysis of model parameters according to the modeling theory and uses the single-factor method and parameter normalization, thus obtaining a summary of the sensitivities of the open-circuit voltage, activation overpotential, and ohmic overpotential to model parameters under low current density conditions. And through the sensitivity parameters of the three-dimensional model under low current density, a parameter calibration process for the PEM fuel cell model is proposed. In order to obtain high-precision and highly reliable model parameters, a three-dimensional two-phase homogeneous PEM fuel cell model of the test object is established. A more detailed electrochemical parameter calibration method is proposed through the analysis of the Butler-Volmer equation, and the overpotential obtained by separating the polarization curve data of different temperatures and back pressures in the low current density range and the oxygen concentration calculated by the model uniquely determine the electrochemical parameters of the model, achieving higher model accuracy and reliability in the low current density range.

[0088] The above are only the preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for calibrating a low current density three-dimensional model of a PEM fuel cell, characterized in that: include: Based on solving the gas phase control equation and the liquid phase control equation respectively, a three-dimensional two-phase homogeneous PEM fuel cell model of the test object is constructed; Based on the three-dimensional two-phase homogeneous PEM fuel cell model, COMSO software was used for simulation to obtain polarization curves, overpotentials and open circuit voltages under multiple combinations of operating conditions. The single factor method was used to analyze the sensitivity of the model mass transfer parameters and electrochemical parameters, and the sensitive parameters of open circuit loss, activation overpotential and ohmic overpotential at low current density were obtained. Based on the sensitive parameters, the overpotential and the oxygen concentration calculated by the model are obtained by separating the polarization curve data at different temperatures and back pressures in the low current density range, and the activation overpotential is calibrated based on the oxygen concentration. The open circuit loss is calibrated based on the result of the activation overpotential calibration, and the ohmic overpotential is calibrated based on the result of the open circuit loss calibration to determine the model parameters.

2. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 1, characterized in that: The equations to be solved in the gas phase include the mass conservation equation, momentum conservation equation, and component conservation equation; the liquid phase is mainly used to solve the liquid water transport theory, and the gas and liquid phases jointly solve the energy conservation equation.

3. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 2, characterized in that: The mass conservation equation under steady-state conditions, the mass balance of the gas flow channel and porous medium region of the PEM fuel cell is described as: Where ε is the porosity, ρ is the density of the gas mixture, is the velocity vector of the gas, S m is the energy source term.

4. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 2, characterized in that: The momentum conservation equation describes the changes in gas flow pressure and velocity inside the PEM fuel cell and is simplified to: Where ε is the porosity, ρ is the density of the gas mixture, p is the working pressure, μ is the gas viscosity, is the velocity vector of the gas, is the pressure gradient of the gas flow inside the battery, is the velocity vector gradient of the gas flow inside the battery, S u is the momentum source term.

5. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 2, characterized in that: The species conservation equations are simplified to mixture-averaged diffusion using Maxwell-Stephen diffusion: Where ρ is the density of the gas mixture, ω i is the mass fraction of substance i, is the velocity vector of the gas, n is the number of components, is the effective diffusion coefficient of substance i relative to substance j, is the gradient of the mole fraction of substance j, S i is the gas mass source term.

6. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 2, characterized in that: The energy conservation equation is calculated as follows when the heat transfer equation is used in the steady-state operation of the PEM fuel cell: Among them, ε is the porosity, s is the saturation of liquid water, and ρ g is the density of the gas mixture, C p,g and C p,1 are the specific heat capacities of the gas mixture and liquid water, respectively, is the velocity vector of the gas, T is the temperature, ρ l is the density of liquid water, k eff is the effective thermal conductivity, is the temperature gradient of the reaction, S T is the energy source term.

7. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 1, characterized in that: The solution of the liquid phase control equation under the steady-state operation condition of the PEM fuel cell is: Among them, n d is the electric drag coefficient, i1 is the current density generated by proton movement, F is the Faraday constant, ρ mem is the dry film density, EW is the film equivalent, is the effective diffusion coefficient of membrane water, λ is the water content, is the gradient of water content, S νλ is the membrane water adsorption or desorption source term.

8. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 1, characterized in that: The method for checking the activation overpotential based on the oxygen concentration is: in, is the oxygen concentration at temperature T2, T2 and T1 are different reaction operating temperatures, α c is the charge transfer coefficient, F is the Faraday constant, is the cathode activation overpotential at T2 temperature, R is the gas constant of an ideal gas, E ca T is the activation energy required for a chemical reaction to occur. ref is the catalyst layer temperature.

9. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 1, characterized in that: The method for open circuit loss verification based on the results of activation overpotential verification is: Among them, i loss is the hydrogen permeation current density caused by hydrogen crossing the membrane, F is the Faraday constant, is the hydrogen transmembrane permeability coefficient, is the hydrogen partial pressure, δ m is the thickness of the proton exchange membrane, is the activation energy of hydrogen diffusion, R is the gas constant, and T is the reaction temperature.

10. The method for calibrating a low current density three-dimensional model of a PEM fuel cell according to claim 1, characterized in that: The method for ohmic overpotential verification based on the open circuit loss verification result is: Among them, σ1 is the surface tension coefficient of liquid water, λ is the water content, ω1 is the proton conductivity index, T ref is the catalyst layer temperature, and T is the actual working temperature.

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