Proton exchange membrane fuel cell modeling method

Abstract

The invention discloses a proton exchange membrane fuel cell modeling method. The method comprises the following steps: establishing activation voltage loss models of an anode and a cathode; establishing an ohm voltage loss model; establishing a concentration difference voltage loss model; and obtaining an output voltage model of the proton exchange membrane fuel cell according to the activation voltage loss model, the ohm voltage loss model and the concentration difference voltage loss model of the anode and the cathode. The embodiment provides a semi-empirical semi-mechanism modeling method for a proton exchange membrane fuel cell, and solves the problems that an empirical model cannot effectively reflect the internal mechanism of the PEMFC, the calculation of a mechanism model is too complicated, and transient response observation and control strategy development are inconvenient. The model established by the invention can reflect part of the working mechanism of the proton exchange membrane fuel cell, and compared with a traditional mechanism model, the calculation amount is greatly reduced, and the model can be used for transient response research and control strategy development.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of new energy battery, and particularly relates to a proton exchange membrane fuel cell modeling method. BACKGROUND

[0002] The working of a proton exchange membrane fuel cell (PEMFC) covers various physical and chemical processes, usually including thermophysics, electrochemical reactions, fluid mechanics, etc., but it is not realistic to carry out a large number of experiments on the PEMFC from the technical and economic aspects, and it is not suitable for the current development status. Therefore, modeling the PEMFC to replace experiments has become an important way to promote the development of PEMFC technology.

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

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

[0005] It should be noted that this section aims to provide background or context to the technical solutions of the present disclosure stated in the claims. The description herein is not admitted to be prior art merely because it is included in this section. SUMMARY

[0006] The present application aims to provide a proton exchange membrane fuel cell modeling method, and to at least partially overcome one or more problems caused by the limitations and defects of the related art.

[0007] The present application provides a proton exchange membrane fuel cell modeling method, comprising: S1, an activation voltage loss model of an anode and a cathode is established, as shown below:

[0008]

[0009] wherein, is the activation voltage loss of the anode, is the activation voltage loss of the cathode, represents the ideal gas constant, represents the temperature of the fuel cell, represents the charge transfer coefficient, represents the Faraday constant, represents the current density, and respectively represent the exchange current density of the anode and the cathode. S2, establish ohmic voltage loss model, as shown below:

[0010] wherein, is ohmic voltage loss, represents the thickness of the electrode plate of the two poles, represents the conductivity of the electrode plate, , , , respectively represent the thickness of the gas diffusion layer, microporous layer, catalytic layer and proton exchange membrane in the membrane assembly of the proton exchange membrane fuel cell, , , respectively represent the effective electronic conductivity of the gas diffusion layer, microporous layer and catalytic layer, represent the effective ionic conductivity of the catalytic layer, represents the proton exchange membrane conductivity; S3, establish concentration voltage loss model, as shown below:

[0011] wherein, is concentration voltage loss, is instantaneous current density, is limiting current density; S4, according to 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 shown below:

[0012] wherein, is the output voltage of the proton exchange membrane fuel cell, is the Nernst voltage.

[0013] In the present application, the exchange current density of the anode and the cathode and The expression is as follows:

[0014]

[0015] wherein, respectively are the reference exchange current density of the anode and the cathode; , respectively represent the liquid saturation in the flow channel of the anode and the cathode, wherein it is assumed that the anode is a dead-end anode and does not perform purging, is the volume of liquid water in the anode divided by the volume of the anode; the cathode is an open cathode, for the fixed value; , are the interfacial concentrations of hydrogen and oxygen, respectively; are the reference interfacial concentrations of hydrogen and oxygen, respectively.

[0016] In the present invention, the effective electronic conductivity is given by:

[0017] where, represents the porosity of each layer, represents the electrolyte volume fraction of each layer, p represents the gas diffusion layer, microporous layer or catalytic layer, represents the intrinsic conductivity; In the present invention, the effective ionic conductivity of the catalytic layer is given by:

[0018] where, represents the electrolyte volume fraction of the catalytic layer.

[0019] In the present invention, the limiting current density is given by:

[0020] where, denotes the oxygen transfer coefficient, denotes the cathode oxygen partial pressure.

[0021] In the present invention, the interfacial concentrations of hydrogen and oxygen , are given by:

[0022]

[0023] where, denotes the anode hydrogen partial pressure.

[0024] In the present invention, the empirical aging models for the various mechanism parameters of the proton exchange membrane fuel cell are given by: the activation area :

[0025] the charge transfer coefficient :

[0026] the reference exchange current density :

[0027] the gas diffusion layer porosity :

[0028] oxygen transfer coefficient :

[0029] wherein, , , , , respectively represent initial activation area, initial charge transfer coefficient, initial reference exchange current density, initial gas diffusion layer porosity, initial oxygen transfer coefficient; represent the working time of the proton exchange membrane fuel cell; , , , , respectively represent the activation area decay coefficient, the charge transfer coefficient decay coefficient, the reference exchange current density decay coefficient, the gas diffusion layer porosity decay coefficient, and the oxygen transfer coefficient decay coefficient.

[0030] In the present application, the method further comprises: S5, the SOBOL parameter sensitivity analysis of the output voltage model of the proton exchange membrane fuel cell is carried out, and the sensitivity parameters of the multiple mechanism parameters of the proton exchange membrane fuel cell are obtained.

[0031] The technical scheme provided by the present application can include the following beneficial effects: The proton exchange membrane fuel cell modeling method in the present application is a semi-empirical and semi-mechanism modeling method, which solves the problems that the empirical model cannot effectively reflect the internal mechanism of the PEMFC, the mechanism model calculation is too complex, and it 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 the proton exchange membrane fuel cell, and greatly reduces the calculation amount compared with the traditional mechanism model, and can be used for transient response research and control strategy development. BRIEF DESCRIPTION OF DRAWINGS

[0032] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the disclosure. Obviously, the drawings in the following description are only some embodiments of the present disclosure, and other drawings can be obtained according to these drawings without creative labor for those skilled in the art.

[0033] Figure 1 A flow chart of the proton exchange membrane fuel cell modeling method in the exemplary embodiment of the present disclosure is shown; Figure 2 A comparison chart of the output characteristics of the proton exchange membrane fuel cell simulation model and the output characteristics of the measured cell. Figure 3 The output voltage model and the mechanism parameter aging empirical model are referenced to the durability test , The simulation experiment of 1016h durability test is carried out under the condition, and the comparison chart of the output characteristics of the proton exchange membrane fuel cell at the time nodes of 182h, 343h, 515h, 666h, 830h and 1016h and the output characteristics of the measured battery. DETAILED DESCRIPTION

[0034] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations may, however, be implemented in many different forms and should not be construed as limited to the examples set forth herein; rather, these implementations are provided so that this disclosure will be thorough and complete, and will fully convey the inventive concept to those skilled in the art. The described features, structures, or characteristics can be combined in one or more implementations.

[0035] In addition, the accompanying drawings are only schematic and are non-limiting precise representations of embodiments of the disclosure. Identical components have been given the same reference numerals in the various drawings and will not be described again in detail. Some of the blocks in the drawings are functional blocks that do not necessarily have to be physically or logically implemented in the illustrated form.

[0036] In the present example implementation, a modeling method of a proton exchange membrane fuel cell is first provided, please refer to Figure 1 The method can include S1-S4, specifically as follows: S1, an activation voltage loss model of an anode and a cathode is established, as shown below:

[0037]

[0038] wherein, is the activation voltage loss of the anode, is the activation voltage loss of the cathode, represents the ideal gas constant, represents the temperature of the fuel cell, and is 353K, represents the charge transfer coefficient, represents the Faraday constant, represents the current density, and represent the exchange current density of the anode and the cathode, respectively; S2, an ohmic voltage loss model is established, as shown below:

[0039] wherein, for ohmic voltage loss, representing the thickness of the electrode plate, representing the conductivity of the electrode plate, respectively represent the thickness of the gas diffusion layer, microporous layer, catalytic layer and proton exchange membrane in the proton exchange membrane fuel cell membrane assembly, respectively represent the effective electronic conductivity of the gas diffusion layer, microporous layer and catalytic layer, representing the effective ionic conductivity of the catalytic layer, representing the proton exchange membrane conductivity; S3, the concentration voltage loss model is established, as follows:

[0040] wherein, is the concentration voltage loss, is the instantaneous current density, is the limiting current density; S4, according to the activation voltage loss model of the anode and the cathode, the ohmic voltage loss model and the concentration voltage loss model, the output voltage model of the proton exchange membrane fuel cell is obtained, as follows:

[0041] wherein, is the output voltage of the proton exchange membrane fuel cell, is the Nernst voltage, and the calculation method is as follows:

[0042] wherein, represents the temperature of the proton exchange membrane fuel cell, and is taken as 353K, and hydrogen partial pressure and oxygen partial pressure of the proton exchange membrane fuel cell.

[0043] In this embodiment, a semi-empirical and semi-mechanism modeling method of the proton exchange membrane fuel cell is proposed, which solves the problems that the empirical model cannot effectively reflect the internal mechanism of the PEMFC, and the mechanism model is too complex to be convenient for transient response observation and control strategy development. The model established in this application can reflect part of the working mechanism of the proton exchange membrane fuel cell, and greatly reduces the calculation amount compared with the traditional mechanism model, and can be used for transient response research and control strategy development.

[0044] The calculation process of part of the parameters in the above steps is as follows: In S1, the exchange current density of the anode and the cathode​​​​​ With The expression of is as follows:

[0045]

[0046] where, are the reference exchange current densities of the anode and cathode, respectively; , and represent the liquid saturations in the anode and cathode flow channels, respectively, where the anode is assumed to be a dead-end anode and no purge is performed, is the volume of liquid water in the anode divided by the volume of the anode; the cathode is an open cathode, and the liquid water content in the cathode is assumed to be small and can be ignored, is a fixed value, and for ease of calculation, the value is 0.00001; , are the interfacial concentrations of hydrogen and oxygen, respectively; are the reference interfacial concentrations of hydrogen and oxygen, respectively, and are fixed values, both of which are 41 .

[0047] Further, the interfacial concentrations of hydrogen and oxygen are , respectively:

[0048]

[0049] where, represents the hydrogen partial pressure in the anode.

[0050] In S2, the effective electronic conductivity is as follows:

[0051] where, represents the porosity of each layer, represents the electrolyte volume fraction of each layer, p represents the gas diffusion layer, microporous layer, or catalytic layer, represents the intrinsic conductivity; The effective ionic conductivity of the catalytic layer is as follows:

[0052] where, represents the electrolyte volume fraction of the catalytic layer.

[0053] In S3, the expression of the limiting current density is as follows:

[0054] in, Indicates the oxygen transfer coefficient. This indicates the partial pressure of oxygen at the cathode.

[0055] In this invention, the method further includes: 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.

[0056] 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:

[0057]

[0058]

[0059]

[0060]

[0061] 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.

[0062] when When = 0, the values ​​of each initial mechanism parameter are obtained by fitting the experimentally measured polarization curve, as follows:

[0063]

[0064]

[0065]

[0066]

[0067] 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.

[0068] 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.

[0069] It should be noted that the total voltage decay is the sum of the voltage decay caused by all the mechanistic parameters.

[0070] 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 .

[0071] 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.

[0072] 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.

[0073] 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.

[0074] 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 .

[0075] 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.

[0076] It should be noted that, Figure 2 and Figure 3 In this context, MSE represents the mean squared error.

[0077] 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.

[0078] 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.

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 3, characterized in that, limiting current density The expression is as follows: in, Indicates the oxygen transfer coefficient. This indicates the partial pressure of oxygen at the cathode.

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

6. The proton exchange membrane fuel cell modeling method according to claim 5, characterized in that, 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.

7. The proton exchange membrane fuel cell modeling method according to any one of claims 1 to 6, characterized in that, The method further includes: 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.

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