A method of modeling a proton exchange membrane fuel cell

Abstract

The present disclosure is a kind of proton exchange membrane fuel cell modeling method, comprising: establishing anode, cathode activation voltage loss model;Establish ohmic voltage loss model;Establish concentration difference voltage loss model;According to the activation voltage loss model of anode, cathode, ohmic voltage loss model and concentration difference voltage loss model, the output voltage model of proton exchange membrane fuel cell is obtained.This embodiment proposes a kind of semi-empirical semi-mechanism modeling method of proton exchange membrane fuel cell, solves the problem that empirical model cannot effectively reflect the internal mechanism of PEMFC, mechanism model calculation is too complex, is not convenient for transient response observation and control strategy development.The model established in the present application can reflect part of the working mechanism of proton exchange membrane fuel cell, and compared with the traditional mechanism model, the calculation amount is greatly reduced, and can be used for transient response research and control strategy development.

Description

Technical Field

[0001] This invention relates to the field of new energy battery technology, and in particular to a proton exchange membrane fuel cell modeling method. Background Technology

[0002] The work on proton exchange membrane fuel cells (PEMFCs) involves a variety of physicochemical processes, typically including thermophysics, electrochemical reactions, and fluid dynamics. However, from both a technical and economic perspective, conducting extensive experiments on PEMFCs is impractical and unsuitable for the current state of development. Therefore, modeling PEMFCs and using these models as a substitute for experimentation has become an important approach to promoting the development of PEMFC technology.

[0003] Traditional empirical models cannot effectively represent the internal mechanism of PEMFC, and traditional mechanistic models are too complex to be computed efficiently.

[0004] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0006] The purpose of this invention is to provide a proton exchange membrane fuel cell modeling method, thereby overcoming, at least to some extent, one or more problems caused by the limitations and defects of related technologies.

[0007] This invention provides a method for modeling proton exchange membrane fuel cells, comprising:

[0008] S1, Establish the activation voltage loss model for the anode and cathode, as shown below:

[0009]

[0010]

[0011] in, This is the activation voltage loss of the anode. This is the activation voltage loss of the cathode. Represents the ideal gas constant. The temperature representing the fuel cell, Represents the charge transfer coefficient. Represents Faraday's constant. Represents current density, and These represent the exchange current densities of the anode and cathode, respectively.

[0012] S2, Establish the ohmic voltage loss model as follows:

[0013]

[0014] in, For ohmic voltage loss, The thickness of the plates representing the two poles. Represents the conductivity of the electrode plate. , , , These represent the thicknesses of the gas diffusion layer, microporous layer, catalyst layer, and proton exchange membrane in a proton exchange membrane fuel cell membrane assembly, respectively. , , These represent the effective electronic conductivity of the gas diffusion layer, the microporous layer, and the catalyst layer, respectively. This indicates the effective ionic conductivity of the catalyst layer. Represents the conductivity of the proton exchange membrane;

[0015] S3, Establish the concentration voltage loss model as follows:

[0016]

[0017] in, For concentration voltage loss, Instantaneous current density, The limiting current density;

[0018] S4. Based on the activation voltage loss model, ohmic voltage loss model, and concentration voltage loss model of the anode and cathode, the output voltage model of the proton exchange membrane fuel cell is obtained as follows:

[0019]

[0020] in, This refers to the output voltage of a proton exchange membrane fuel cell. This is the Nernst voltage.

[0021] In this invention, the exchange current density between the anode and the cathode and The expression is as follows:

[0022]

[0023]

[0024] in, These are the reference exchange current densities for the anode and cathode, respectively. , These represent the liquid saturation levels in the anode and cathode channels, respectively, assuming the anode is a dead-end anode and is not purged. It is the volume of liquid water in the anode divided by the volume of the anode; the cathode is an open cathode. It is a fixed value; , These represent the interface concentrations of hydrogen and oxygen, respectively. These are the reference interface concentrations for hydrogen and oxygen, respectively.

[0025] In this invention, the effective electronic conductivity is as follows:

[0026]

[0027] in, Represents the porosity of each layer. Represents the electrolyte volume fraction of each layer. p Represents a gas diffusion layer, microporous layer, or catalyst layer. Represents inherent electrical conductivity;

[0028] The effective ionic conductivity of the catalyst layer is shown below:

[0029]

[0030] in, This represents the volume fraction of the electrolyte in the catalyst layer.

[0031] In this invention, the limiting current density The expression is as follows:

[0032]

[0033] in, Indicates the oxygen transfer coefficient. This indicates the partial pressure of oxygen at the cathode.

[0034] In this invention, the interfacial concentration of hydrogen and oxygen... , They are respectively:

[0035]

[0036]

[0037] in, This indicates the partial pressure of hydrogen gas at the anode.

[0038] In this invention, the empirical aging models for multiple mechanistic parameters of the proton exchange membrane fuel cell are as follows:

[0039] Activation area :

[0040] Charge transfer coefficient :

[0041] Reference exchange current density :

[0042] Gas diffusion layer porosity :

[0043] Oxygen transfer coefficient :

[0044] in, , , , , These represent the initial activated area, initial charge transfer coefficient, initial reference exchange current density, initial gas diffusion layer porosity, and initial oxygen transfer coefficient, respectively. This indicates the operating time of the proton exchange membrane fuel cell; , , , , These represent the degradation coefficients of the activated area, charge transfer coefficient, reference exchange current density, gas diffusion layer porosity, and oxygen transfer coefficient, respectively.

[0045] In this invention, the method further includes:

[0046] S5. SOBOL parameter sensitivity analysis was performed on the output voltage model of the proton exchange membrane fuel cell to obtain the sensitivity parameters of multiple mechanistic parameters of the proton exchange membrane fuel cell.

[0047] The technical solution provided by this invention may include the following beneficial effects:

[0048] This invention discloses a proton exchange membrane fuel cell (PEMFC) modeling method, which is a semi-empirical, semi-mechanistic modeling approach. It addresses the problems of empirical models failing to effectively represent the internal mechanisms of PEMFCs, and mechanistic models being computationally too complex and inconvenient for transient response observation and control strategy development. The model established in this application can reflect part of the working mechanism of PEMFCs and significantly reduces the computational load compared to traditional mechanistic models, making it suitable for transient response research and control strategy development. Attached Figure Description

[0049] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0050] Figure 1 A flowchart illustrating a proton exchange membrane fuel cell modeling method in an exemplary embodiment of this disclosure is shown;

[0051] Figure 2 A comparison chart showing the output characteristics of a proton exchange membrane fuel cell simulation model and the output characteristics of the tested cell.

[0052] Figure 3 For the output voltage model and the empirical model of aging mechanism parameters, durability testing is conducted. , The simulation experiment of durability test conducted under the condition of 1016h shows the comparison of the output characteristics of the proton exchange membrane fuel cell with the output characteristics of the tested cell at time nodes of 182h, 343h, 515h, 666h, 830h and 1016h. Detailed Implementation

[0053] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0054] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0055] This example implementation first provides a proton exchange membrane fuel cell modeling method; please refer to [reference needed]. Figure 1 This method may include: S1-S4, as follows:

[0056] S1, Establish the activation voltage loss model for the anode and cathode, as shown below:

[0057]

[0058]

[0059] in, This is the activation voltage loss of the anode. This is the activation voltage loss of the cathode. Represents the ideal gas constant. The temperature representing the fuel cell is taken as 353K. Represents the charge transfer coefficient. Represents Faraday's constant. Represents current density, and These represent the exchange current densities of the anode and cathode, respectively.

[0060] S2, Establish the ohmic voltage loss model as follows:

[0061]

[0062] in, For ohmic voltage loss, The thickness of the plates representing the two poles. Represents the conductivity of the electrode plate. , , , These represent the thicknesses of the gas diffusion layer, microporous layer, catalyst layer, and proton exchange membrane in a proton exchange membrane fuel cell membrane assembly, respectively. , , These represent the effective electronic conductivity of the gas diffusion layer, the microporous layer, and the catalyst layer, respectively. This indicates the effective ionic conductivity of the catalyst layer. Represents the conductivity of the proton exchange membrane;

[0063] S3, Establish the concentration voltage loss model as follows:

[0064]

[0065] in, For concentration voltage loss, Instantaneous current density, The limiting current density;

[0066] S4. Based on the activation voltage loss model, ohmic voltage loss model, and concentration voltage loss model of the anode and cathode, the output voltage model of the proton exchange membrane fuel cell is obtained as follows:

[0067]

[0068] in, This refers to the output voltage of a proton exchange membrane fuel cell. The Nernst voltage is calculated as follows:

[0069]

[0070] in, The temperature of the proton exchange membrane fuel cell is represented by 353K. and The partial pressure of hydrogen and oxygen in a proton exchange membrane fuel cell.

[0071] This embodiment proposes a semi-empirical, semi-mechanistic modeling method for proton exchange membrane fuel cells (PEMFCs). This addresses the problems of empirical models failing to effectively represent the internal mechanisms of PEMFCs, and mechanistic models being computationally too complex and inconvenient for transient response observation and control strategy development. The model established in this application can reflect part of the working mechanism of PEMFCs and significantly reduces the computational load compared to traditional mechanistic models, making it suitable for transient response research and control strategy development.

[0072] The calculation process for some parameters in the above steps is as follows:

[0073] In S1, the exchange current density between the anode and cathode and The expression is as follows:

[0074]

[0075]

[0076] in, These are the reference exchange current densities for the anode and cathode, respectively. , These represent the liquid saturation levels in the anode and cathode channels, respectively, assuming the anode is a dead-end anode and is not purged. This is the volume of liquid water in the anode divided by the volume of the anode; the cathode is an open cathode, and it is assumed that the liquid water content in the cathode is small and can be ignored. This is a fixed value; for ease of calculation, it is set to 0.00001. , These represent the interface concentrations of hydrogen and oxygen, respectively. The reference interface concentrations for hydrogen and oxygen are respectively set to a constant value of 41. .

[0077] Furthermore, the interfacial concentration of hydrogen and oxygen , They are respectively:

[0078]

[0079]

[0080] in, This indicates the partial pressure of hydrogen gas at the anode.

[0081] In S2, the effective electronic conductivity is shown below:

[0082]

[0083] in, Represents the porosity of each layer. Represents the electrolyte volume fraction of each layer. p Represents a gas diffusion layer, microporous layer, or catalyst layer. Represents inherent electrical conductivity;

[0084] The effective ionic conductivity of the catalyst layer is shown below:

[0085]

[0086] in, This represents the volume fraction of the electrolyte in the catalyst layer.

[0087] In S3, the limiting current density The expression is as follows:

[0088]

[0089] in, Indicates the oxygen transfer coefficient. This indicates the partial pressure of oxygen at the cathode.

[0090] In this invention, the method further includes:

[0091] S5. SOBOL parameter sensitivity analysis was performed on the output voltage model of the proton exchange membrane fuel cell to obtain the sensitivity parameters of multiple mechanistic parameters of the proton exchange membrane fuel cell. A sensitivity parameter value greater than or equal to 0.1 was considered a high-sensitivity parameter, and a value less than 0.1 was considered a low-sensitivity parameter. Then, the degradation coefficient of each mechanistic parameter was derived based on its sensitivity parameter.

[0092] In addition, based on the activated area Charge transfer coefficient Reference exchange current density Porosity of the gas diffusion layer and oxygen transfer coefficient Taking the mechanistic parameters as the objects of decline, empirical aging models are established for them, as follows:

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] in, , , , , These represent the initial activated area, initial charge transfer coefficient, initial reference exchange current density, initial gas diffusion layer porosity, and initial oxygen transfer coefficient, respectively. This indicates the operating time of the proton exchange membrane fuel cell; , , , , These represent the degradation coefficients of the activated area, charge transfer coefficient, reference exchange current density, gas diffusion layer porosity, and oxygen transfer coefficient, respectively.

[0099] when When = 0, the values ​​of each initial mechanism parameter are obtained by fitting the experimentally measured polarization curve, as follows:

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] Working hours Determined by experimental data, for example, it can be 182h, 343h, 515h, 666h, 830h, or 1016h. Activation area. Used for calculating current density, which is obtained by dividing the current by the activated area.

[0106] The process of deriving the degradation coefficient of each mechanistic parameter based on its sensitivity parameters includes: using SOBOL parameter sensitivity analysis to obtain the sensitivity parameters of multiple mechanistic parameters of the proton exchange membrane fuel cell; calculating the voltage decay caused by the corresponding mechanistic parameter over a certain operating time based on the sensitivity parameters; obtaining the real-time mechanistic parameter for that operating time based on the voltage decay; and then calculating the degradation coefficient of the mechanistic parameter using an empirical aging model. An example is provided below to illustrate this process.

[0107] It should be noted that the total voltage decay is the sum of the voltage decay caused by all the mechanistic parameters.

[0108] For example, if a fuel cell operates for 1016 hours, the total voltage decay is 13V. First, using SOBOL parameter sensitivity analysis, the sensitivity parameter for the activated area is found to be 0.4019. Therefore, the voltage decay caused by the activated area over 1016 hours is 13V × 0.4019 = 5.2247V. Then, to achieve a voltage decay of 5.2247V, the activated area needs to be increased from 276.5330 cm². 2 Attenuation to 261.188cm 2 Finally, the degradation coefficient of the activated area was obtained as 6.8453886e from the empirical aging model of the activated area. -5 h -1 .

[0109] The decay coefficients of other mechanistic parameters follow the same principle as described above and will not be repeated here. It should be noted that the dimensions of the decay coefficients of the charge transfer coefficient, reference exchange current density, gas diffusion layer porosity, and oxygen transfer coefficient are determined according to the formulas of their corresponding empirical aging models.

[0110] This application establishes a proton exchange membrane fuel cell output voltage model using the MATLAB software SIMULINK platform, conducts durability tests, and fits the experimental data from the durability tests. The fitting results are as follows: Figure 2 As shown. Figure 2 After modeling the output voltage model, a comparison chart of the output characteristics of the simulation model after adjusting the mechanism parameters and the output characteristics of the tested battery is generated, referencing the durability test of the proton exchange membrane fuel cell.

[0111] from Figure 2 As can be seen, the small root mean square error (RMSE) indicates that the output voltage model of the proton exchange membrane fuel cell in this application can accurately reflect the output characteristics of the proton exchange membrane fuel cell under test.

[0112] After modeling, referencing the output voltage drop over 1016 hours of durability testing, the attenuation amount was determined based on the sensitivity parameters of each mechanistic parameter, thus deriving the degradation coefficient for each mechanistic parameter. Please refer to... Figure 3 Durability testing was simulated using a built model. The simulation conditions were 353K and the durability test current density was [value missing]. Polarization curves were compared at six time points, and the results are shown in [the table below]. Figure 3 .

[0113] Figure 3 For the output voltage model and the empirical model of aging parameters, durability testing was conducted at 353K, 0.7A / cm. 2 A 1016-hour durability test simulation was conducted under specific conditions. Time points of 182h, 343h, 515h, 666h, 830h, and 1016h were selected. A comparison graph of the simulated proton exchange membrane fuel cell output characteristics (represented by dashed lines) and the tested battery output characteristics (represented by solid lines) was generated. Figure 3 It can be seen that the small root mean square error proves that the output voltage model of the proton exchange membrane fuel cell in this application can realize the health status monitoring of the proton exchange membrane fuel cell.

[0114] It should be noted that, Figure 2 and Figure 3 In this context, MSE represents the mean squared error.

[0115] The semi-empirical, semi-mechanistic model proposed in this application can selectively represent the internal mechanism of proton exchange membrane fuel cells, while also reducing computational load to facilitate transient response research and control strategy development. Furthermore, by adding an empirical aging formula with highly sensitive parameters, the model can also be equipped with health status monitoring capabilities. Durability tests have demonstrated that the modeling method presented in this application can accurately reflect the output characteristics of the modeled object and also achieve health status monitoring.

[0116] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for modeling a proton exchange membrane fuel cell, characterized in that, include: S1, Establish the activation voltage loss model for the anode and cathode, as shown below: in, This is the activation voltage loss of the anode. This is the activation voltage loss of the cathode. Represents the ideal gas constant. The temperature representing the fuel cell, Represents the charge transfer coefficient. Represents Faraday's constant. Represents current density, and These represent the exchange current densities of the anode and cathode, respectively. S2, Establish the ohmic voltage loss model as follows: in, For ohmic voltage loss, The thickness of the plates representing the two poles. Represents the conductivity of the electrode plate. , , , These represent the thicknesses of the gas diffusion layer, microporous layer, catalyst layer, and proton exchange membrane in a proton exchange membrane fuel cell membrane assembly, respectively. , , These represent the effective electronic conductivity of the gas diffusion layer, the microporous layer, and the catalyst layer, respectively. This indicates the effective ionic conductivity of the catalyst layer. Represents the conductivity of the proton exchange membrane; S3, Establish the concentration voltage loss model as follows: in, For concentration voltage loss, Instantaneous current density, The limiting current density; S4. Based on the activation voltage loss model, ohmic voltage loss model, and concentration voltage loss model of the anode and cathode, the output voltage model of the proton exchange membrane fuel cell is obtained as follows: in, This refers to the output voltage of a proton exchange membrane fuel cell. This is the Nernst voltage; S5. SOBOL parameter sensitivity analysis was performed on the output voltage model of the proton exchange membrane fuel cell to obtain the sensitivity parameters of multiple mechanistic parameters of the proton exchange membrane fuel cell. The process of deriving the decay coefficient of each mechanistic parameter based on its sensitivity parameter includes: The sensitivity parameters of multiple mechanistic parameters of proton exchange membrane fuel cells are obtained by using SOBOL parameter sensitivity analysis. The voltage decay caused by the corresponding mechanistic parameter under a certain working time is calculated based on the sensitivity parameters. The real-time mechanistic parameter under the working time is obtained based on the voltage decay. Then, the decay coefficient of the mechanistic parameter is calculated based on the empirical aging model. S6, combining the output voltage model of proton exchange membrane fuel cells and the empirical aging model of highly sensitive mechanism parameters to monitor the health status of the battery; In the empirical aging model of mechanistic parameters, the values ​​of initial activated area, initial charge transfer coefficient, initial reference exchange current density, initial gas diffusion layer porosity, and initial oxygen transfer coefficient are 276.5330 cm². 2 0.6464, 1489.944 A / cm 2 0.8033, 6.4279×10 -7 m 2 / s; limiting current density The expression is as follows: in, Indicates the oxygen transfer coefficient. Indicates the partial pressure of oxygen at the cathode; The empirical aging models for several mechanistic parameters of proton exchange membrane fuel cells are as follows: Activation area : Charge transfer coefficient : Reference exchange current density : Gas diffusion layer porosity : Oxygen transfer coefficient : in, , , , , These represent the initial activated area, initial charge transfer coefficient, initial reference exchange current density, initial gas diffusion layer porosity, and initial oxygen transfer coefficient, respectively. This indicates the operating time of the proton exchange membrane fuel cell; , , , , These represent the degradation coefficients of the activated area, charge transfer coefficient, reference exchange current density, gas diffusion layer porosity, and oxygen transfer coefficient, respectively.

2. The proton exchange membrane fuel cell modeling method according to claim 1, characterized in that, Exchange current density between anode and cathode and The expression is as follows: in, , These are the reference exchange current densities for the anode and cathode, respectively. , These represent the liquid saturation levels in the anode and cathode channels, respectively, assuming the anode is a dead-end anode and is not purged. It is the volume of liquid water in the anode divided by the volume of the anode; the cathode is an open cathode. It is a fixed value; , These represent the interface concentrations of hydrogen and oxygen, respectively. , These are the reference interface concentrations for hydrogen and oxygen, respectively.

3. The proton exchange membrane fuel cell modeling method according to claim 2, characterized in that, The effective electronic conductivity is shown below: in, Represents the porosity of each layer. Represents the electrolyte volume fraction of each layer. p Represents a gas diffusion layer, microporous layer, or catalyst layer. Represents inherent electrical conductivity; The effective ionic conductivity of the catalyst layer is shown below: in, This represents the volume fraction of the electrolyte in the catalyst layer.

4. The proton exchange membrane fuel cell modeling method according to claim 1, characterized in that, Interfacial concentration of hydrogen and oxygen , They are respectively: in, This indicates the partial pressure of hydrogen gas at the anode.

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