Method for determining a three-dimensional network model of a battery stack and related device
By constructing a multiphysics unit model and combining it with neural network training of source term equations, the problems of large computational scale and poor robustness of SOFC stacks were solved, and efficient and accurate stack simulation calculations were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA ENERGY INVESTMENT CORP LTD
- Filing Date
- 2022-02-17
- Publication Date
- 2026-07-14
AI Technical Summary
Existing multiphysics simulation models for solid oxide fuel cell (SOFC) stacks suffer from large computational scale, poor robustness, and low accuracy, making them difficult to implement in practice and commercialize.
A unit model with multiphysics is constructed. By modifying the multiphysics equations and using high-throughput solving, and combining neural network training of the source term equations, a three-dimensional network model of the fuel cell stack is established.
It improves computational stability and speed, enables accurate simulation of physicochemical phenomena within SOFC stacks, and supports efficient stack design and optimization.
Smart Images
Figure CN116665794B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of fuel cell development, and in particular to a method and related equipment for determining a three-dimensional network model of a fuel cell stack. Background Technology
[0002] Solid oxide fuel cells (SOFCs) boast energy conversion efficiencies as high as 70%, making them one of the most promising low-carbon power generation methods for the future. However, the compact metal-ceramic stack structure of SOFCs makes it difficult to practically measure internal electrochemical reactions, hindering the practical application and commercialization of SOFC technology. Computational simulation is currently the primary method for obtaining data on the physicochemical phenomena within SOFC stacks. However, existing multiphysics simulation models for SOFCs suffer from problems such as large computational scale, poor robustness, and low accuracy. Summary of the Invention
[0003] To address the aforementioned issues, this application provides a method and related equipment for determining a three-dimensional network model of a battery stack.
[0004] This application provides a method for determining a three-dimensional network model of a battery stack, including:
[0005] A unit model with multiphysics is constructed, wherein the unit model is used to characterize a cross section of a predetermined length in a single flow channel of a fuel cell stack, and the unit model includes multiphysics equations;
[0006] Based on the obtained reference parameters, the setting parameters of the multiphysics equation are modified so that the error between the calculated parameters obtained by the unit model through the modified multiphysics equation at different temperatures and the reference parameters is less than a preset threshold.
[0007] High-throughput solution is performed based on the acquired multiphysics input parameters and the modified multiphysics equations to determine the output parameters corresponding to the multiphysics input parameters.
[0008] The source equations of the multiphysics field are obtained by training a neural network based on the input parameters and corresponding output parameters of the multiphysics field.
[0009] A three-dimensional network model of the fuel cell stack is established based on the source term equations.
[0010] In some embodiments, the multiphysics equations include: a binary gas diffusion equation for describing gas diffusion and mass transfer, a Nernst equation for calculating the electromotive force of a battery, a Butler-Volmer equation for describing activation polarization, a composite porous dielectric conductivity equation for calculating ohmic polarization, and an equation for describing concentration polarization.
[0011] In some embodiments, the step of performing high-throughput solving based on the acquired multiphysics input parameters and the modified multiphysics equations to determine the output parameters corresponding to the multiphysics input parameters includes:
[0012] Obtain multiphysics input parameters, wherein the multiphysics input parameters include multiple parameters;
[0013] The value of each parameter is determined based on its range of values.
[0014] The input parameter matrix is determined by cross-combining the values corresponding to each parameter.
[0015] High-throughput solving is performed based on the input parameter matrix and the modified multiphysics equations to determine the output parameters corresponding to the multiphysics input parameters.
[0016] In some embodiments, the input layer of the neural network has multiple input units, each corresponding to an input parameter. The neural network has multiple sets of weight matrices and the same number of threshold matrices. The calculation process of each layer of the neural network can be represented as follows:
[0017]
[0018] Given the input parameters for the next layer of the neural network, the source term equation obtained from training the multi-layer neural network can be expressed as:
[0019]
[0020] S represents the corresponding source term, f(x) is the activation function, W1, W2…Wn are n sets of weight matrices, B1, B2…Bn are n sets of threshold matrices, and x… i This is the input parameter matrix.
[0021] In some embodiments, the plurality of parameters includes: voltage, temperature, and gas composition, and the method further includes:
[0022] The voltage range is determined based on the reference IV curve;
[0023] The temperature range is determined based on the gas inlet temperature and gas outlet temperature of the fuel cell stack.
[0024] The range of values for gas components is determined based on the inlet fuel gas composition and the exhaust gas composition of the fuel cell stack.
[0025] In some embodiments, the preset length is 0.25mm-1mm.
[0026] In some embodiments, a cross section of a predetermined length in the single flow channel can perform electrochemical reactions, gas flow, diffusion within porous media, heat transfer, and mass transfer.
[0027] This application provides a device for determining a three-dimensional network model of a battery stack, comprising:
[0028] The first construction module is used to construct a unit model with multiphysics, wherein the unit model is used to characterize a cross section of a predetermined length in a single flow channel of a fuel cell stack;
[0029] The modification module is used to modify the setting parameters of the multiphysics equation based on the acquired reference parameters, so that the error between the calculated parameters obtained by the unit model through the modified multiphysics equation at different temperatures and the reference parameters is less than a preset threshold.
[0030] The first calculation module is used to perform high-throughput solving on the unit model based on the acquired multiphysics input parameters, and determine the output parameters corresponding to the multiphysics input parameters.
[0031] The second calculation module is used to determine the source equation of the multiphysics field through neural network training based on the input parameters and corresponding output parameters of the multiphysics field.
[0032] The second construction module is used to establish a three-dimensional network model of the fuel cell stack based on the source term equations.
[0033] This application provides a device including a memory and a processor. The memory stores a computer program, which, when executed by the processor, performs the method for determining the three-dimensional network model of the battery stack described above.
[0034] This application provides a storage medium storing a computer program that can be executed by one or more processors and can be used to implement the method for determining the three-dimensional network model of the battery stack described in any of the above claims.
[0035] This application provides a method, apparatus, device, and storage medium for determining a three-dimensional network model of a battery stack. By constructing a unit model with multiphysics, modifying the setting parameters of the multiphysics equations based on the obtained reference parameters, performing high-throughput computation and neural network computation to obtain the source term equations, and then determining the three-dimensional network model of the battery stack based on the source term equations, the obtained three-dimensional network model of the battery stack has high computational stability and fast computation speed during simulation. Attached Figure Description
[0036] The present application will be described in more detail below based on embodiments and with reference to the accompanying drawings.
[0037] Figure 1 A schematic diagram illustrating the implementation process of a method for determining a three-dimensional network model of a battery stack, provided in an embodiment of this application;
[0038] Figure 2 A schematic diagram of a unit model provided in an embodiment of this application;
[0039] Figure 3 A schematic diagram illustrating the implementation process of a method for determining a three-dimensional network model of a battery stack, provided in an embodiment of this application;
[0040] Figure 4 This is a schematic diagram of the structure of a neural network model provided in an embodiment of this application;
[0041] Figure 5 A schematic diagram illustrating the implementation process for determining a three-dimensional network model of a battery stack, as provided in an embodiment of this application;
[0042] Figure 6 A schematic diagram showing the relative error between the IV curves obtained from the 5-cell fuel cell stack experiment and the IV calculated by the model.
[0043] Figure 7 A schematic diagram showing the relative error between the IV curves obtained from experiments with 30 fuel cell stacks and the IV calculated by the model.
[0044] Figure 8 This is a cloud map showing the molar concentration distribution of hydrogen at the anode within the fuel cell stack.
[0045] Figure 9 A schematic diagram of the structure of a device for determining a three-dimensional network model of a battery stack provided in an embodiment of this application;
[0046] Figure 10 This is a schematic diagram of the composition structure of the device provided in the embodiments of this application.
[0047] In the accompanying drawings, the same parts are referred to by the same reference numerals, and the drawings are not drawn to scale. Detailed Implementation
[0048] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. The described embodiments should not be regarded as limitations on this application. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0049] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.
[0050] If the application documents contain similar descriptions such as "first, second, third", the following explanation shall be added: In the following description, the terms "first, second, third" are used only to distinguish similar objects and do not represent a specific order of objects. It is understood that "first, second, third" may be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.
[0051] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.
[0052] To address the problems existing in related technologies, this application provides a method for determining a three-dimensional network model of a battery stack. The method is applied to a device, which is an electronic device, such as a computer or mobile terminal. The function implemented by the method for determining the three-dimensional network model of a battery stack provided in this application can be achieved by the device's processor calling program code, wherein the program code can be stored in a computer storage medium.
[0053] Example One
[0054] This application provides a method for determining a three-dimensional network model of a battery stack. Figure 1 This application provides a schematic diagram illustrating the implementation process of a method for determining a three-dimensional network model of a battery stack, as shown in the embodiments below. Figure 1 As shown, it includes:
[0055] Step S101: Construct a unit model with multiphysics, wherein the unit model is used to characterize a cross section of a predetermined length in a single flow channel of a fuel cell stack, and the unit model includes multiphysics equations.
[0056] In this embodiment, the multiphysics equations include equations for phenomena such as electrochemical reactions, gas flow, diffusion within porous media, heat transfer, and mass transfer. A multiphysics-based unit model can be constructed using COMSOL 5.3. This unit model characterizes a cross-section of a predetermined length within a single flow channel of the fuel cell stack. The predetermined length can be 0.25-1 mm, preferably 0.5-1 mm.
[0057] In this embodiment, the element model can simulate all possible operating conditions within the fuel cell stack. This element model is a complete multiphysics model. Since the element model only represents a 0.25-1mm cross-section in a single flow channel of the fuel cell stack, the scale span of the element cell is reduced from four to five orders of magnitude for a typical stack to three orders of magnitude between ten micrometers and one millimeter. This significantly reduces the mesh requirements for computation and improves the solution speed of the element model.
[0058] Figure 2 This is a schematic diagram of the structure of a unit model provided in an embodiment of this application, such as... Figure 2 As shown, the reactant gas in each channel of an SOFC can be considered as flowing through each unit cell in a specific order. Each unit cell, when considered individually, has a specific inlet gas composition, and its temperature varies little within its corresponding scale range, thus it can be considered isothermal. Simultaneously, the diffusion of the reactant gas within the porous medium is primarily perpendicular to the PEN direction and towards the electrolyte, with a diffusion path on the order of tens of micrometers. Secondly, there is diffusion laterally along the unit cell from the channel space towards the porous medium region corresponding to the channel ridge, and diffusion along the channel direction, with diffusion paths on the order of approximately 0.25 mm to several millimeters, which is tens to hundreds of times longer than the vertical diffusion distance. Therefore, choosing a unit cell scale of 0.25-1 mm is sufficient to simultaneously meet the requirements of adequate computational accuracy and a moderate computational scale. Furthermore, the unit cell does not include bipolar channel ridges or other metal structures because considering channel ridge structures within the unit cell would make heat conduction between the unit and the external environment anisotropic, increasing the complexity of the data interface between units and expanding the number of parameters that need to be set and the scale of high-throughput computation. The flow channel ridge has high electrical conductivity and large size, and its ohmic heat is not significant. Therefore, removing the flow channel ridge part from the element model, performing isothermal treatment, and exporting the PEN heat source term as the heat source term of the fuel cell stack model is an effective method to maintain accuracy and reduce computational load.
[0059] The unit model contains a complete multiphysics model, which mainly includes the following parts:
[0060] Gas mass transfer models include the flow continuity of multi-component gases and the diffusion of multi-component gases in porous media.
[0061] Electrochemical reaction models, including theoretical potential, activation, ohmic, and concentration overpotential;
[0062] The current conduction model in porous media, including the conductivity of multi-component porous media materials;
[0063] The mass and energy source term model includes source terms for the gaseous components involved in the reaction and heat source terms for each layer in the PEN due to various polarizations.
[0064] Step S102: Modify the setting parameters of the multiphysics equation based on the obtained reference parameters, so that the error between the calculated parameters obtained by the unit model through the modified multiphysics equation at different temperatures and the reference parameters is less than a preset threshold.
[0065] The multiphysics equations may include: a binary gas diffusion equation describing gas diffusion and mass transfer; the Nernst equation for calculating the electromotive force of a battery; the Butler-Volmer equation describing activated polarization; an equation for calculating the conductivity of porous composite materials with ohmic polarization; and an equation describing concentration polarization. In this embodiment, the multiphysics equations can be experimentally calibrated using reference parameters to modify their set parameters, which may include exchange current density, transfer coefficient, etc.
[0066] The reference parameters can be obtained through experiments on the fuel cell stack, and the reference parameters can be IV curves, etc.
[0067] In this embodiment, the preset threshold can be set based on experience; for example, the preset threshold can be 4%. Exemplarily, the IV curve calculated by the multiphysics equations can be compared with a reference IV curve to determine the error. Then, the error is compared with the preset threshold. When the error is less than the preset threshold, the setting parameters of the multiphysics equations are modified. If the error is greater than the preset threshold, the setting parameters of the multiphysics equations need to be modified further until the error is less than the preset threshold.
[0068] Step S103: Based on the acquired multiphysics input parameters and the modified multiphysics equations, perform high-throughput solving to determine the output parameters corresponding to the multiphysics input parameters.
[0069] In this embodiment, the multiphysics input parameters may include: gas composition, operating temperature, and operating voltage. In some embodiments, the multiphysics input parameters may further include: location information. The gas composition includes: anode hydrogen mass concentration and cathode oxygen mass concentration.
[0070] Because the unit model is very small, the changes in composition and temperature of the gas during flow due to electrochemical reactions and heat transfer are minimal. Therefore, these input parameters can be considered constant within the unit model. The selection of input parameters needs to cover all possible operating conditions within the stack. For example, temperature should cover the range from gas inlet temperature to gas outlet temperature, gas composition should cover the range from fresh fuel gas to exhaust components, and voltage should cover the range of operating points on the required IV curve. Within the value range of each parameter, several values at different levels are taken and cross-combined to form the input parameter matrix required for high-throughput calculations. The calculated output parameters can be extracted from the corresponding positions in the unit model. For example, statistical analysis of the hydrogen reaction source terms within the anode can yield the distribution of the hydrogen reaction rate along different positions in the flow channel and flow channel ridge. This distribution corresponds to a certain combination of input parameters. From another perspective, if the phenomena occurring within the SOFC are considered as a function, then the calculation of all reaction equations within the SOFC can be expressed as a mapping process of calculating output parameters (range, source terms) based on a certain combination of input parameters (domain). In the unit model stage, we know the domain of the function (input parameters) and its mapping form (multiphysics equations), but we don't know its range (output parameters). High-throughput computing is the process of using these multiphysics equations to map the input parameters to the output parameters, that is, calculating the range based on the domain.
[0071] In this embodiment, high-throughput calculations can be performed using the software COMSOL 5.3. COMSOL, as a partial differential equation solver based on the finite element method, has advantages such as high accuracy and high parameterization. It can also output the correspondence between multiphysics input and output parameters.
[0072] Step S104: Based on the input parameters and corresponding output parameters of the multiphysics field, the source equation of the multiphysics field is obtained by training a neural network.
[0073] In this embodiment, the multiphysics input parameters and corresponding output parameters can be input into the BP neural network model for training and learning. The BP neural network model is established using MATLAB 2017a, and the source term equation for each source term is obtained after training.
[0074] In this embodiment, through the training and learning of the BP neural network model, another equivalent expression of the mapping relationship represented by the multiphysics equations in the SOFC stack is obtained. This expression is presented in the form of a transition matrix and a bias matrix. Through certain linear matrix operations, the combination of input parameters in the domain can be mapped into the combination of output parameters in the range within a certain accuracy range, thereby achieving accurate and fast calculation.
[0075] Step S105: Establish a three-dimensional network model of the fuel cell stack based on the source term equation.
[0076] In this embodiment, a three-dimensional network model of the fuel cell stack can be constructed based on source term equations as component and heat source terms. In some embodiments, this three-dimensional network model of the fuel cell stack can also be called a multiphysics computational model. In this multiphysics computational model, the electrolyte, anode, and cathode, which are thin layers at the ten-micrometer level, can be represented by only one or a few simplified mesh layers. Since the various mass and heat transfer source terms in the PEN layer are directly calculated from the gas parameters in the flow channel, the computational requirements for problems such as mass transfer of multi-component gases in porous media can be appropriately reduced without affecting the accuracy of the calculation results. In this way, the number of meshes and equations required to solve the multiphysics computational model is greatly reduced. The solution of the multiphysics computational model can be regarded as a pure mass and heat transfer process with several custom source terms, without complex nonlinear reaction equations. At the same time, since the process of calculating the source term equations from the obtained linear matrix is very stable, the computational stability of the multiphysics computational model is also greatly improved. The reduction in the number of equations and grids, along with the improvement in computational stability, further enhances the convergence performance and speed of multiphysics computational models, thereby enabling computational capabilities for complex structures and dynamic characteristics that are not achievable by traditional algorithms.
[0077] This application provides a method for determining a three-dimensional network model of a battery stack. The method involves constructing a unit model with multiphysics, then modifying the setting parameters of the multiphysics equations based on the obtained reference parameters, performing high-throughput computation and neural network computation to obtain the source term equations, and then determining the three-dimensional network model of the battery stack based on the source term equations. The resulting three-dimensional network model of the battery stack has high computational stability and fast computation speed during simulation.
[0078] Example Two
[0079] Based on the foregoing embodiments, this application further provides a method for determining a three-dimensional network model of a battery stack. Figure 3 This application provides a schematic diagram illustrating the implementation process of a method for determining a three-dimensional network model of a battery stack, as shown in the embodiments below. Figure 3 As shown, it includes:
[0080] Step S301: Construct a unit model with multiphysics, wherein the unit model is used to characterize a cross section of a preset length in a single flow channel of a fuel cell stack, and the unit model includes multiphysics equations.
[0081] Step S302: Modify the setting parameters of the multiphysics equation based on the obtained reference parameters, so that the error between the calculated parameters obtained by the unit model through the modified multiphysics equation at different temperatures and the reference parameters is less than a preset threshold.
[0082] In this embodiment, a reference current-voltage (IV) curve is used, which is obtained experimentally. The multiphysics equations include: a binary gas diffusion equation for describing gas diffusion mass transfer, a Nernst equation for calculating the battery electromotive force, a Butler-Volmer equation for describing activation polarization, a composite porous medium conductivity equation for calculating ohmic polarization, and an equation for describing concentration polarization. The set parameters of the multiphysics equations are modified based on the obtained reference parameters so that the error between the calculated parameters obtained by the unit model through the modified multiphysics equations at different temperatures and the reference parameters is less than a preset threshold. For example, taking the Butler-Volmer equation as an example, the set parameters of the Butler-Volmer equation are modified based on the obtained reference IV curve so that the error between the IV curve obtained by the unit model through the modified Butler-Volmer equation at different temperatures and the reference IV curve is less than a preset threshold.
[0083] In this embodiment of the application, other physical field equations can also be modified in this way to change the calculation parameters of each multiphysics field equation.
[0084] Step S303: Obtain multiphysics input parameters, wherein the multiphysics input parameters include multiple parameters.
[0085] In this embodiment, the multiphysics input parameters can be user-inputted or obtained directly from a database. These parameters may include voltage, temperature, and gas composition.
[0086] Step S304: Determine the value of each parameter based on the range of values for each parameter.
[0087] In this embodiment of the application, after determining the various parameters, the value range of each parameter can be determined. In this embodiment of the application, the voltage value range can be determined based on the reference IV curve; the temperature value range can be determined based on the gas inlet temperature and gas outlet temperature of the fuel cell stack; and the gas component value range can be determined based on the inlet fuel gas component and the outlet gas component of the fuel cell stack.
[0088] Once the range of values for each parameter is determined, several different levels of values can be selected within each parameter's range.
[0089] Step S305: Combine the values corresponding to each parameter to determine the input parameter matrix.
[0090] In this embodiment of the application, the values corresponding to each parameter are cross-combined to form the input parameter matrix required for high-throughput computing.
[0091] Step S306: Perform high-throughput solving based on the input parameter matrix and the modified multiphysics equations to determine the output parameters corresponding to the multiphysics input parameters.
[0092] In this embodiment, the output parameters can be extracted from the corresponding positions in the unit model. For example, by statistically analyzing the hydrogen reaction source terms within the anode, the distribution of the hydrogen reaction rate along different positions of the flow channel and the flow channel ridge can be obtained. This distribution corresponds to a certain combination of input parameters. From another perspective, if the phenomena occurring within the SOFC are considered as a function, then the calculation of all reaction equations within the SOFC can be expressed as a mapping process of calculating the output parameters (range, source terms) based on a certain combination of input parameters (domain). At the unit model stage, we know the domain of the function (input parameters) and its mapping form (multiphysics equations), but we do not know its range (output parameters). High-throughput computing utilizes these combinations of multiphysics equations to map the input parameters to the output parameters, that is, calculating the range based on the domain.
[0093] Step S307: Based on the input parameters and corresponding output parameters of the multiphysics field, the source equation of the multiphysics field is obtained by training a neural network.
[0094] The input layer of the neural network has multiple input units, each corresponding to an input parameter. The neural network has multiple sets of weight matrices and the same number of threshold matrices. The calculation process of each layer of the neural network can be represented as follows:
[0095]
[0096] Given the input parameters for the next layer of the neural network, the source term equation obtained from training the multi-layer neural network can be expressed as:
[0097]
[0098] S represents the corresponding source term, f(x) is the activation function, W1, W2…Wn are n sets of weight matrices, B1, B2…Bn are n sets of threshold matrices, and x… i This is the input parameter matrix.
[0099] Step S308: Establish a three-dimensional network model of the fuel cell stack based on the source term equation.
[0100] This application provides a method for determining a three-dimensional network model of a fuel cell stack. The method involves constructing a unit model with multiphysics, then modifying the setting parameters of the multiphysics equations based on the obtained reference parameters, performing high-throughput computation and neural network computation to obtain the source term equations, and then determining the three-dimensional network model of the fuel cell stack based on the source term equations. The resulting three-dimensional network model of the fuel cell stack has high computational stability and fast computation speed during simulation.
[0101] Example Three
[0102] Based on the foregoing embodiments, this application further provides a neural network model. Figure 4 This is a schematic diagram of the structure of a neural network model provided in an embodiment of this application, such as... Figure 4 As shown, the input layer of the neural network has six input units, each corresponding to an input parameter, such as... Figure 4 In this neural network, the six input units are 6 nodes, the first hidden layer has 16 units, the second hidden layer has 6 units, and the output layer has 1 unit, used to output the heat source term. The neural network has three sets of weight matrices and three sets of threshold matrices, with dimensions as shown in Table 1.
[0103] Table 1 shows the dimensions of the weight and threshold matrix obtained by training a BP neural network according to an embodiment of this application.
[0104]
[0105] Example Four
[0106] Based on the foregoing embodiments, this application further provides a method for determining a three-dimensional network model of a battery stack. Figure 5 A schematic diagram illustrating the implementation process for determining a three-dimensional network model of a battery stack, as provided in this application embodiment, is shown below. Figure 5 As shown, the method includes:
[0107] Step S501: Construct the unit model.
[0108] A scaled-down, multiphysics-based element model is established. An element model is a 0.5-1 mm cross-section extracted from a single flow channel out of hundreds of flow channels in a SOFC (SOFC) stack, representing all possible operating conditions within the SOFC stack. The element model encompasses complete electrochemical reactions, gas flow, diffusion within the porous medium, and various heat and mass transfer phenomena, making it a complete multiphysics model. However, its scale is reduced from four to five orders of magnitude in a typical SOFC stack to three orders of magnitude between ten micrometers and one millimeter, significantly reducing the required mesh size and improving the solution speed.
[0109] Step S205, experimental data correction.
[0110] In this embodiment of the application, when the corrected error is less than a preset threshold, step S503 is executed, and when the corrected error is greater than the preset threshold, step S501 is executed.
[0111] Experimental calibration of the multiphysics equations in the unit cell model is performed. For example, taking the Butler-Volmer equation as an example, the parameters of the Butler-Volmer equation are corrected based on the experimental data such as the IV curves of the unit cell. This ensures that the IV curves calculated by the multiphysics equations in the unit cell model at different temperatures are consistent with the experimental results, and the error is within the allowable range.
[0112] Step S503, high-throughput calculation.
[0113] In this embodiment of the application, high-throughput computation is performed by acquiring input parameters, and the input parameter sequence and the corresponding output parameter sequence are obtained through high-throughput computation.
[0114] Input parameters include the gas composition, operating temperature, and operating voltage of the anode and cathode. Because the unit model is very small, the changes in gas composition and temperature due to electrochemical reactions and heat transfer are minimal during gas flow; therefore, these input parameters can be considered constant within the unit model. The selection of input parameters needs to cover all possible operating conditions within the fuel cell stack. For example, temperature should cover the range from gas inlet temperature to gas outlet temperature; gas composition should cover the range from fresh fuel gas to exhaust components; and voltage should cover the range of operating points on the required IV curve. Within the value range of each parameter, several values at different levels are selected and cross-combined to form the input parameter matrix required for high-throughput calculations. The calculated output parameters can be extracted from the corresponding positions in the unit model. For example, statistical analysis of the hydrogen reaction source term within the anode can yield the distribution of the hydrogen reaction rate along different positions in the flow channel and flow channel ridge; this distribution corresponds to a specific combination of input parameters. From another perspective, if we consider the phenomena occurring within a SOFC as a function, then the calculation of all reaction equations within a SOFC can be expressed as a mapping process to obtain output parameters (range, source terms) based on a certain combination of input parameters (domain). In the unit model stage, we know the domain of the function (input parameters) and its mapping form (multiphysics equations), but we don't know its range (output parameters). High-throughput computing utilizes these combinations of multiphysics equations to map input parameters to output parameters; that is, it calculates the range based on the domain.
[0115] Step S504, BP neural network training.
[0116] In this embodiment, the source term equation is obtained by performing a BP neural network calculation on the input parameter sequence and the corresponding output parameter sequence.
[0117] Based on the one-to-one correspondence between the domain and the range obtained from the unit model calculation, another equivalent expression of the mapping relationship represented by the multiphysics equations in the SOFC stack can be obtained through the training and learning of the BP neural network. This expression is presented in the form of a transition matrix and a bias matrix. Through certain linear matrix operations, the combination of input parameters in the domain can be mapped to the combination of output parameters in the range within a certain accuracy range, thereby achieving accurate and fast calculation.
[0118] Step S505: Construct a multiphysics model (same as the fuel cell model in the figure).
[0119] In this embodiment, the multiphysics model (similar to the fuel cell stack model in other embodiments) uses thin layers of about ten micrometers, such as the electrolyte, anode, and cathode, which can be represented by only one or a few simplified meshes. The mapping relationships obtained in step four are introduced as component and heat source terms. Furthermore, since the various mass and heat transfer source terms in the PEN layer are directly calculated from the gas parameters within the flow channel, the computational requirements for problems such as mass transfer of multi-component gases in porous media can be appropriately reduced without affecting the accuracy of the calculation results. This significantly reduces the number of meshes and equations required to solve the fuel cell stack model (i.e., the multiphysics model). The solution to the fuel cell stack model can be viewed as a pure mass and heat transfer process with several custom source terms, without complex nonlinear reaction equations. Simultaneously, the computational stability of the fuel cell stack model is greatly improved because the process of calculating source terms using the linear matrix obtained in step four is very stable. The reduction in the number of equations and meshes, along with the improved computational stability, further improves the convergence performance and speed of the fuel cell stack calculation, thereby enabling computational capabilities for complex structures and dynamic characteristics that are impossible with traditional algorithms.
[0120] The fuel cell stack model comprises three parts: a fluid-structure interaction (FSI) structural model, mass and energy source terms, and voltage regulation under constant current. The model includes a complete stack structure, encompassing not only the PEN structure (anode, cathode, electrolyte, and diffusion layers), but also the unit model representing the anode and cathode flow channels, as well as the bipolar plates and sealing material layers. The bipolar plates, made of Crofer APU22 metal, provide the gas flow boundaries for the anode and cathode on both sides of the PEN, and include detailed structures such as the gas headers and distribution pipes for the anode and cathode. Through the thermal conductivity of the metal and the convective heat transfer between the metal and the gas flow, a heat transfer network is formed within the stack. Therefore, the fuel cell stack model is a FSI model containing all detailed structural information of the stack. The calculations required are for the convection and diffusion of the multi-component mixed gas within the flow channels and porous medium, as well as the heat conduction and convection calculations for the transfer of reaction heat from the PEN to the gas in the flow channels and the bipolar plates. Due to the inherent long flow channels and small cross-sections in SOFC structures, radiative heat transfer in the flow channels is not significant along the flow channel direction because the angular coefficient is very small. Therefore, only conduction and convection are considered in the heat transfer calculation.
[0121] In this embodiment, the multiphysics model implementation requires the collaboration of three software programs to complete the solution process. COMSOL 5.3 is used for the establishment of the SOFC unit model and high-throughput parameterized calculations. As a partial differential equation solver based on the finite element method, COMSOL has the advantages of high accuracy and high parameterization. The calculation results of COMSOL can be output and organized into the required correspondence data between the six source terms and gas components, temperature, and voltage, i.e., the domain and range required for BP neural network training. Each source term has approximately 7.5 million data points. A BP neural network model is established using MATLAB 2017a, and after training, the transition matrix and bias matrix of each source term are obtained. The multiphysics model is solved in AnsysFluent, and then a UDF file expressing the source term equations is written based on it, with a code size of approximately 1200 lines, as well as functions such as source term import and current-voltage adjustment for the stack model.
[0122] To verify the reliability of the fuel cell stack model, we selected experimental results from fuel cell stacks with two different stacking numbers of 5 and 30 layers for verification. The experimental test conditions are shown in Table 2.
[0123] Table 2. Experimental and Model Calculation Conditions for the Fuel Cell Stack
[0124]
[0125] Figure 6 A schematic diagram illustrating the relative error between the IV curves obtained from the five-chip fuel cell stack experiment and the IV calculated from the model, as shown below. Figure 6 As shown. Within the 2.5A-30A range, the stack voltage decreases from 5.31V to 3.9V, equivalent to a decrease in the average voltage per chip from 1.062V to 0.78V. Within this range, the model calculation error ranges from -0.438% to +3.634%. In terms of error distribution, within the main operating range of the stack (10-25A, corresponding to an average power of approximately 10-20W per chip), the error is only -0.438% to +0.474%, i.e., less than ±0.5%. The error on the low-current side (below 5A) mainly stems from the accuracy of the Butler-Volmer description of activation polarization in this region; the error on the high-current side (above 30A) mainly comes from concentration polarization.
[0126] Figure 7 This is a schematic diagram illustrating the relative error between the IV curves obtained from experiments with 30 fuel cell stacks and the IV calculated by the model, as shown below. Figure 7As shown, the trend is consistent with that of the 5-cell stack, but the relative error widens to -1.618% to -0.046% within the 5A-20A range. This change is related to the temperature distribution within the stack and the IV curve fitting error. The 5-cell stack is smaller and generates less heat itself; its temperature is mainly affected by the external heating source, resulting in better temperature uniformity and a more uniform gas flow distribution between the cells. This leads to a very small voltage difference between the cells, only 0.05% at 20A. The 30-cell stack has more internal reaction heat and greater thermal conductivity resistance with the external constant-temperature furnace wall. This results in a temperature distribution where the core temperature is controlled by the electrochemical reaction, while the outer wall temperature is significantly affected by the electric furnace temperature. Within the 10-20A operating current range, the core temperature exceeds the surrounding environment's 750℃. Simultaneously, the gas distribution in the 30-cell stack is more complex, and the voltage difference between the cells is larger, reaching 1.14% at 20A. The errors in the experimental and model calculation results for 30-cell fuel cell stacks can be attributed to the influence of the accuracy of the IV curve fitting at 800℃. The calculation errors of less than ±2% between the model calculation results and experimental results for 5-cell and 30-cell fuel cell stacks are sufficient for the research and engineering applications of SOFC fuel cell stacks.
[0127] Figure 8 This is a cloud map showing the hydrogen molar concentration distribution at the anode within the fuel cell stack, such as... Figure 8 As shown, with the increase in the number of layers in the fuel cell stack, the gas flow velocity under standard conditions gradually decreases in that layer. In other words, in a fuel cell stack with parallel gas paths, the larger the number of layers, the smaller the gas flow rate to that layer. Under the premise of electrical series connection, the current in each layer is exactly the same, meaning that the amount of hydrogen consumed by the electrochemical reaction in each layer is the same. The combination of these two factors results in a gradual decrease in hydrogen concentration at the outlet of each layer of the fuel cell stack. Simultaneously, due to the non-uniformity of gas flow within a single layer of the fuel cell stack, the outlet hydrogen concentration of the flow channel in the middle of each layer is higher than that of the flow channels on both sides, forming a layer-specific concentration distribution that is high in the middle and low on the sides.
[0128] The distribution of oxygen concentration in each cathode layer within the fuel cell stack exhibits a similar trend to the distribution of hydrogen concentration in the anode. Since the cathode air, in addition to supplying oxygen, also plays a role in controlling the stack temperature, its flow rate far exceeds the requirements of the electrochemical reaction. Therefore, the rate of change in oxygen concentration between cathode layers is less than that of hydrogen concentration in the anode. The lowest outlet oxygen molar concentration and the highest cathode gas utilization rate both occur between the twentieth and twenty-fifth layers within the stack. The variation of cathode oxygen molar concentration along the flow channel direction is consistent with the trend of anode hydrogen molar concentration along the flow channel direction, indicating that the gas flow characteristics influence both the inlet and outlet sections of the flow channel.
[0129] The method for determining the three-dimensional network model of the battery stack provided in this application adopts a separate solution process. Although it adds the process of pre-preparing high-throughput calculations of unit models and training of BP neural networks, it significantly improves the computational stability and speed of the stack-level model, making multiphysics simulation calculations at the stack level and thermal zone level, which were previously impossible, a reality. Simultaneously, in the stack calculation, operating parameters such as gas inlet temperature, operating temperature, and gas composition can be flexibly adjusted in the SOFC stack to perform parametric calculations under various operating conditions, improving the speed of stack-scale calculations, gaining a thorough understanding of various operating characteristics of the stack, reducing the resource and effort consumed in exploratory experiments, and continuously improving the stack's performance.
[0130] Example 5
[0131] Based on the foregoing embodiments, this application provides a device for determining a three-dimensional network model of a battery stack. The various modules and units included in the device can be implemented by a processor in a computer device; of course, they can also be implemented by specific logic circuits. In the implementation process, the processor can be a central processing unit (CPU), a microprocessor (MPU), a digital signal processor (DSP), or a field programmable gate array (FPGA), etc.
[0132] This application provides a device for determining a three-dimensional network model of a battery stack. Figure 9 This is a schematic diagram of the structure of a device for determining a three-dimensional network model of a battery stack, as provided in an embodiment of this application. Figure 9 As shown, the device 900 for determining the three-dimensional network model of the battery stack includes:
[0133] The first construction module 901 is used to construct a unit model with multiphysics, wherein the unit model is used to characterize a cross section of a preset length in a single flow channel of a fuel cell stack, and the unit model includes multiphysics equations.
[0134] Modification module 902 is used to modify the setting parameters of the multiphysics equation based on the acquired reference parameters, so that the error between the calculated parameters obtained by the unit model through the modified multiphysics equation at different temperatures and the reference parameters is less than a preset threshold.
[0135] The first calculation module 903 is used to perform high-throughput solving based on the acquired multiphysics input parameters and the modified multiphysics equations, and to determine the output parameters corresponding to the multiphysics input parameters.
[0136] The second calculation module 904 is used to obtain the source term equation of the multiphysics field by training a neural network based on the input parameters and corresponding output parameters of the multiphysics field.
[0137] The second construction module 905 is used to establish a multiphysics calculation model of the electric stack based on the source term equation.
[0138] In some embodiments, the multiphysics equations include: a binary gas diffusion equation for describing gas diffusion and mass transfer, a Nernst equation for calculating the electromotive force of a battery, a Butler-Volmer equation for describing activation polarization, a composite porous dielectric conductivity equation for calculating ohmic polarization, and an equation for describing concentration polarization.
[0139] In some embodiments, the first calculation module is specifically used to obtain multiphysics input parameters, wherein the multiphysics input parameters include multiple parameters; determine the value corresponding to each parameter based on the value range of each parameter; perform cross-combination of the values corresponding to each parameter to determine the input parameter matrix; and perform high-throughput solving based on the input parameter matrix and the modified multiphysics equation to determine the output parameters corresponding to the multiphysics input parameters.
[0140] In some embodiments, the input layer of the neural network has multiple input units, each corresponding to an input parameter. The neural network has multiple sets of weight matrices and the same number of threshold matrices. The calculation process of each layer of the neural network can be represented as follows:
[0141]
[0142] Given the input parameters for the next layer of the neural network, the source term equation obtained from training the multi-layer neural network can be expressed as:
[0143]
[0144] S represents the corresponding source term, f(x) is the activation function, W1, W2…Wn are n sets of weight matrices, B1, B2…Bn are n sets of threshold matrices, and x… i This is the input parameter matrix.
[0145] In some embodiments, the plurality of input parameters include: voltage, temperature, and gas composition, and the device 900 for determining the three-dimensional network model of the battery stack further includes:
[0146] The first determining module is used to determine the range of voltage values based on the reference IV curve;
[0147] The second determining module is used to determine the range of temperature values based on the gas inlet temperature and gas outlet temperature of the fuel cell stack.
[0148] The third determining module is used to determine the range of values for gas components based on the inlet fuel gas components and the outlet gas components of the fuel cell stack.
[0149] In some embodiments, the preset length is 0.25mm-1mm.
[0150] In some embodiments, a cross section of a predetermined length in the single flow channel can perform electrochemical reactions, gas flow, diffusion within porous media, heat transfer, and mass transfer.
[0151] It should be noted that, in the embodiments of this application, if the method for determining the three-dimensional network model of the battery stack described above is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiments of this application, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), magnetic disks, or optical disks. Thus, the embodiments of this application are not limited to any specific hardware and software combination.
[0152] Accordingly, this application provides a storage medium storing a computer program, characterized in that the computer program, when executed by a processor, implements the steps in the method for determining the three-dimensional network model of the battery stack provided in the above embodiments.
[0153] Example 6
[0154] This application provides an electronic device; Figure 10 This is a schematic diagram of the composition structure of the device provided in the embodiments of this application, such as... Figure 10As shown, the electronic device 1000 includes: a processor 1001, at least one communication bus 1002, a user interface 1003, at least one external communication interface 1004, and a memory 1005. The communication bus 1002 is configured to enable communication between these components. The user interface 1003 may include a display screen, and the external communication interface 1004 may include standard wired and wireless interfaces. The processor 1001 is configured to execute a program for determining a three-dimensional network model of a battery stack stored in the memory, to implement the steps in the method for determining a three-dimensional network model of a battery stack provided in the above embodiment.
[0155] The descriptions of the display device and storage medium embodiments above are similar to those of the method embodiments above, and have similar beneficial effects. For technical details not disclosed in the computer device and storage medium embodiments of this application, please refer to the descriptions of the method embodiments of this application for understanding.
[0156] It should be noted that the descriptions of the storage medium and device embodiments above are similar to the descriptions of the method embodiments above, and have similar beneficial effects. For technical details not disclosed in the storage medium and device embodiments of this application, please refer to the descriptions of the method embodiments of this application for understanding.
[0157] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of this application, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. The sequence numbers of the above-described embodiments are merely descriptive and do not represent the superiority or inferiority of the embodiments.
[0158] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.
[0159] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.
[0160] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.
[0161] In addition, each functional unit in the various embodiments of this application can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.
[0162] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as mobile storage devices, read-only memory (ROM), magnetic disks, or optical disks.
[0163] Alternatively, if the integrated units described above are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a controller to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROMs, magnetic disks, or optical disks.
[0164] The above description is merely an embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for determining a three-dimensional network model of a battery stack, characterized in that, include: A multiphysics-based unit model is constructed, which is used to characterize a cross-section of a predetermined length in a single flow channel of a fuel cell stack. The unit model includes multiphysics equations. The unit model can simulate all possible operating conditions that may occur in the fuel cell stack. The reactant gas in each flow channel of the SOFC is regarded as flowing through each unit model in a certain order. Based on the obtained reference parameters, the setting parameters of the multiphysics equation are modified so that the error between the calculated parameters obtained by the unit model through the modified multiphysics equation at different temperatures and the reference parameters is less than a preset threshold. Based on the acquired multiphysics input parameters and the modified multiphysics equations, high-throughput solving is performed to determine the output parameters corresponding to the multiphysics input parameters. The source equations of the multiphysics field are obtained by training a neural network based on the input parameters and corresponding output parameters of the multiphysics field. A three-dimensional network model of the fuel cell stack is established based on the source term equation.
2. The method according to claim 1, characterized in that, The multiphysics equations include: a binary gas diffusion equation for describing gas diffusion and mass transfer; the Nernst equation for calculating the electromotive force of a battery; the Butler-Volmer equation for describing activation polarization; the composite porous dielectric conductivity equation for calculating ohmic polarization; and an equation for describing concentration polarization.
3. The method according to claim 2, wherein the step of performing high-throughput solving based on the acquired multiphysics input parameters and the modified multiphysics equations to determine the output parameters corresponding to the multiphysics input parameters includes: Obtain multiphysics input parameters, wherein the multiphysics input parameters include multiple parameters; The value of each parameter is determined based on its range of values. The input parameter matrix is determined by cross-combining the values corresponding to each parameter. High-throughput solving is performed based on the input parameter matrix and the modified multiphysics equations to determine the output parameters corresponding to the multiphysics input parameters.
4. The method according to claim 3, characterized in that, The input layer of the neural network has multiple input units, each corresponding to an input parameter. The neural network has multiple sets of weight matrices and the same number of threshold matrices. The calculation process of each layer of the neural network can be represented as follows: ； Given the input parameters for the next layer of the neural network, the source term equation obtained from training the multi-layer neural network can be expressed as: ； S is the corresponding source term. Let W1, W2…Wn be the activation function, W1, W2…Wn be n sets of weight matrices, and B1, B2…Bn be n sets of threshold matrices. This is the input parameter matrix.
5. The method according to claim 3, characterized in that, The parameters include: voltage, temperature, and gas composition. The method also includes: The voltage range is determined based on the reference IV curve; The temperature range is determined based on the gas inlet temperature and gas outlet temperature of the fuel cell stack. The range of values for gas components is determined based on the inlet fuel gas composition and the exhaust gas composition of the fuel cell stack.
6. The method according to any one of claims 1 to 5, characterized in that, The preset length is 0.25mm-1mm.
7. The method according to claim 6, characterized in that, A cross section of a predetermined length in the single flow channel can perform electrochemical reactions, gas flow, diffusion within porous media, heat transfer, and mass transfer.
8. A device for determining a three-dimensional network model of a battery stack, characterized in that, include: The first construction module is used to construct a unit model with multiphysics. The unit model is used to characterize a cross section of a preset length in a single flow channel of a fuel cell stack. The unit model includes multiphysics equations. The unit model can simulate all possible operating conditions that may occur in the fuel cell stack. The reactant gas in each flow channel of the SOFC is regarded as flowing through each unit model in a certain order. The modification module is used to modify the setting parameters of the multiphysics equation based on the acquired reference parameters, so that the error between the calculated parameters obtained by the unit model through the modified multiphysics equation at different temperatures and the reference parameters is less than a preset threshold. The first calculation module is used to perform high-throughput solving based on the acquired multiphysics input parameters and the modified multiphysics equations, and to determine the output parameters corresponding to the multiphysics input parameters. The second calculation module is used to obtain the source equation of the multiphysics field by training a neural network based on the input parameters and corresponding output parameters of the multiphysics field. The second building module is used to establish a multiphysics calculation model of the electric stack based on the source term equation.
9. A device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program that, when executed by the processor, performs a method for determining a three-dimensional network model of the battery stack as described in any one of claims 1 to 7.
10. A storage medium, characterized in that, The computer program stored in the storage medium can be executed by one or more processors and can be used to implement the method for determining the three-dimensional network model of the battery stack as described in any one of claims 1 to 7.