An overpotential solving method and device for an electrochemical system

Abstract

The application belongs to the field of electrochemistry, and discloses an overpotential solving method and device for an electrochemical system, which comprises the following steps: based on the mathematical relationship between the total current of the cathode catalytic layer and the total current of the anode catalytic layer in the target electrochemical system, constructing an inner iteration model with the proton potential bias as the variable to be solved and an outer iteration model with the plate voltage as the variable to be solved; coupling and iteration solving the inner iteration model with the proton potential bias as the variable to be solved and the outer iteration model with the plate voltage as the variable to be solved, obtaining the iteration solving result of the proton potential bias and the iteration solving result of the plate voltage; and calculating the overpotential of the target electrochemical system according to the iteration solving result of the proton potential bias and the iteration solving result of the plate voltage; the application can avoid the defects of long calculation time under low relaxation factor and the risk of voltage and current fluctuation under high relaxation factor, and can significantly improve the calculation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of electrochemical technology, and relates to the field of physical field solving for fuel cells and electrolyzers, and particularly to a method and apparatus for solving overpotential in electrochemical systems. Background Technology

[0002] With the rapid development of electrochemical technology, proton exchange membrane fuel cells (PEMFCs) and proton exchange membrane electrolyzer cells (PEMECs) play a crucial role in energy conversion and storage as major electrochemical systems or devices. The actual operation of fuel cells and electrolyzers involves multiple complex processes, including flow, heat and mass transfer, electrochemical reactions, two-phase flow, component transport, and three-phase water conversion, with extremely complex physical field coupling characteristics. To reduce equipment development costs and accelerate design and optimization processes, three-dimensional multiphysics simulation technology is widely used in the research and development of fuel cells and electrolyzers, playing a vital role.

[0003] In the three-dimensional multiphysics simulation of fuel cells and electrolyzers, it is usually necessary to solve the electronic potential equation and the proton potential equation to obtain the overpotential of the fuel cell and electrolyzer. Among them, the coupling of electronic and proton potentials is one of the key steps in solving the electronic potential equation and the proton potential equation, which has an important impact on the overall calculation speed and convergence of the three-dimensional multiphysics simulation. At present, explicit coupling strategy is generally adopted in the three-dimensional multiphysics simulation of fuel cells and electrolyzers. However, due to the strong nonlinear coupling of the electronic potential field and the proton potential field in the catalyst layer of the anode and cathode, the traditional explicit iterative algorithm faces serious numerical oscillation problems, which greatly affects the computational efficiency and stability.

[0004] Specifically, due to the lack of constant boundary conditions in the proton potential equation, when a high relaxation factor is adopted, abrupt changes in current density will cause significant fluctuations in the proton potential source term, leading to a high risk of high divergence or failure to converge to a stable solution in the simulation results. This is particularly true in operating conditions where fuel cells provide power for commercial / passenger vehicles and electrolyzers perform peak-shaving functions, requiring frequent load changes. While a high relaxation factor may result in faster simulation convergence, the drastic fluctuations in voltage and current pose a high risk of divergence or failure to converge to a stable solution. Conversely, while a low relaxation factor provides more stable computation, the computation time is too long to meet practical R&D needs. In summary, existing technologies for handling electron-proton potential coupling problems suffer from an inherent contradiction between computational stability and efficiency, becoming a core obstacle restricting the efficiency of engineering iterations and transient process simulations, such as flow field design and material selection. Summary of the Invention

[0005] To address the technical problems existing in the prior art, this invention provides a method and apparatus for solving overpotential in electrochemical systems. This method solves the problem that the traditional explicit iterative algorithm suffers from severe numerical oscillations due to the strong nonlinear coupling between the electron potential field and the proton potential field in the anode and cathode catalyst layers, which greatly affects the computational efficiency and stability.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention provides a method for solving the overpotential of an electrochemical system, characterized by comprising: Based on the mathematical relationship between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system, an internal iterative model with proton potential bias as the variable to be solved and an external iterative model with plate voltage as the variable to be solved are constructed. The inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved are coupled iteratively solved to obtain the iterative solution results of proton potential bias and plate voltage. The overpotential of the target electrochemical system is calculated based on the iterative solutions for the proton potential bias and the plate voltage.

[0007] Furthermore, an internal iterative model with proton potential bias as the variable to be determined is used to find a proton potential bias such that the total current of the cathode catalyst layer in the target electrochemical system is equal to the total current of the anode catalyst layer. Specifically, the internal iterative model with proton potential bias as the variable to be solved is as follows:

[0008] in, For the first Proton potential bias under the inner iteration step; For the first Proton potential bias under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step; For the first Proton potential bias under the inner iteration step.

[0009] Furthermore, an external iterative model with the plate voltage as the variable to be determined is used to find a plate voltage such that the average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system is equal to the preset total current. Specifically, the external iterative model with the plate voltage as the variable to be solved is as follows:

[0010] in, For the first Plate voltage under the outer iteration step; For the first Plate voltage under the outer iteration step; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; The preset total current; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; For the first Plate voltage under the outer iteration step.

[0011] Furthermore, the process of coupling iteratively solving the inner iterative model with proton potential bias as the variable to obtain the iterative solution results for proton potential bias and plate voltage is as follows: S1. Determine whether the error between the average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system under the current external iteration step and the preset total current is less than the preset error setting value; if yes, the external iteration model with the plate voltage as the variable to be solved converges, and the plate voltage under the current external iteration step is output as the iterative solution result of the plate voltage; if no, jump to S2. S2, outer iteration step +1; S3. Obtain the average value of the plate voltage and the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the two external iteration steps before the current external iteration step; S4. Based on the plate voltages of the two previous external iteration steps and the average values ​​of the total current of the cathode catalyst layer and the total current of the anode catalyst layer, calculate the plate voltage under the current external iteration. S5. Set the inner iteration step to 0; S6. Determine whether the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system under the current internal iteration step is less than the preset difference setting value, or determine whether the current internal iteration step is greater than the maximum internal iteration step; if yes, output the proton potential bias under the current internal iteration step as the iterative solution result of the proton potential bias, and return to S1; if no, jump to S7. S7, Inner iteration step +1; S8. Obtain the proton potential bias and the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the two inner iteration steps before the current inner iteration step. S9. Based on the proton potential bias in the two internal iteration steps before the current internal iteration step and the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer, the proton potential bias in the current internal iteration is calculated. S10, Return to S6.

[0012] Furthermore, the overpotential of the target electrochemical system includes the anodic overpotential and the cathodic overpotential of the target electrochemical system; Based on the iterative solution results of the proton potential bias, the anodic overpotential of the target electrochemical system is calculated. Based on the iterative solution results of the proton potential bias and the plate voltage, the cathode overpotential of the target electrochemical system is calculated.

[0013] Furthermore, based on the iterative solution results of the proton potential bias, the process of calculating the anodic overpotential of the target electrochemical system is as follows:

[0014] in, The anodic overpotential of the target electrochemical system; The electronic potential is obtained based on computational fluid dynamics. The proton potential is obtained based on computational fluid dynamics. This is the result of the iterative solution for the proton potential bias.

[0015] Furthermore, based on the iterative solution results of the proton potential bias and the plate voltage, the cathode overpotential process of the target electrochemical system is calculated as follows:

[0016] in, The cathode overpotential of the target electrochemical system; The open-circuit voltage of the target electrochemical system; The electronic potential is obtained based on computational fluid dynamics. The proton potential is obtained based on computational fluid dynamics. The result of the iterative solution for the proton potential bias; This is the result of the iterative solution for the plate voltage.

[0017] The present invention also provides a system for solving overpotential in electrochemical systems, comprising: The iterative model construction module is used to construct an internal iterative model with proton potential bias as the variable to be solved and an external iterative model with plate voltage as the variable to be solved, based on the mathematical relationship between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system. The iterative solution module is used to perform coupled iterative solution of the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved, so as to obtain the iterative solution results of proton potential bias and plate voltage. The overpotential calculation module is used to calculate the overpotential of the target electrochemical system based on the iterative solution results of the proton potential bias and the iterative solution results of the plate voltage.

[0018] The present invention also provides an electronic device, comprising: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, performs the method for solving overpotentials for an electrochemical system.

[0019] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for solving overpotentials in an electrochemical system.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: The overpotential solution method for electrochemical systems provided by this invention, based on the mathematical relationship between the total current of the cathode catalyst layer and the total current of the anode catalyst layer, transforms the proton potential bias and plate voltage into parameters implicitly solved in the iterative model. By reshaping the coupling relationship between electron potential and proton potential, the proton potential can obtain a definite solution in any iteration step, avoiding the large fluctuations in source terms, numerical oscillations, and divergences in the proton potential equation under high relaxation factors in traditional explicit algorithms. Simultaneously, by reshaping the coupling relationship between electron potential and proton potential, the distribution ranges of cathode electron potential, anode electron potential, and proton potential are effectively constrained to a narrower range. This invention improves the stability of numerical calculations. Therefore, it allows for iteration using a high relaxation factor, avoiding the drawbacks of excessively long calculation times and inability to meet R&D needs under a low relaxation factor, while also avoiding the risk of drastic voltage and current fluctuations under a high relaxation factor. This significantly improves computational efficiency while ensuring simulation stability. The method is particularly suitable for frequent load variations in operating conditions, such as fuel cells powering commercial / passenger vehicles and electrolyzers performing peak-shaving functions. It effectively shortens the engineering iteration cycle for flow field design and material selection, overcoming the core obstacle to high efficiency in transient process simulation and providing reliable technical support for the rapid R&D and optimization of electrochemical systems.

[0021] The overpotential calculation system, electronic device, computer-readable storage medium, and computer program product for electrochemical systems provided by this invention possess all the advantages of the aforementioned overpotential calculation methods for electrochemical systems. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart of the overpotential calculation method for an electrochemical system provided in Example 1; Figure 2 This is a schematic diagram illustrating the distribution of electron and proton potentials in existing traditional electron-proton potential coupling methods. Figure 3 This is a schematic diagram showing the distribution of electron and proton potentials after the anode electron potential is shifted to the vicinity of the reference point in Example 1. Figure 4 This is a schematic diagram showing the distribution of electron and proton potentials after the anode electron potential and proton potential are shifted to the vicinity of the reference point in Example 1. Figure 5 This is a flowchart of the iterative solution process for the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved in Example 1. Figure 6 This is a comparison chart of the computational stability of the method described in Example 1 and the traditional explicit coupling algorithm; Figure 7 Here is a structural block diagram of the overpotential solving system for an electrochemical system provided in Example 2; Figure 8 This is a structural block diagram of the electronic device provided in Example 3. Detailed Implementation

[0024] To make the technical problems, technical solutions, and beneficial effects solved by this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0025] This invention provides a method for solving the overpotential of an electrochemical system, comprising the following steps: Step 100: Based on the mathematical relationship between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system, construct an internal iterative model with the proton potential bias as the variable to be solved and an external iterative model with the plate voltage as the variable to be solved.

[0026] Step 200: Perform coupled iterative solutions on the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved, and obtain the iterative solution results of proton potential bias and plate voltage.

[0027] Step 300: Calculate the overpotential of the target electrochemical system based on the iterative solution results of the proton potential bias and the plate voltage.

[0028] In the above embodiments, by constructing an internal iterative model with proton potential bias as the variable to be solved and an external iterative model with plate voltage as the variable to be solved, the plate voltage and proton potential bias are transformed into parameters implicitly solved in the model, thereby reconstructing a new coupling relationship between electron potential and proton potential. This ensures that the proton potential has a solution in any iteration step, and that the distribution ranges of cathode electron potential, anode electron potential, and proton potential are relatively narrow, thus improving the numerical stability during calculation. Therefore, this invention allows for the use of high relaxation factors in calculations, effectively resolving the contradiction between computational stability and efficiency, significantly improving computational efficiency, shortening the iteration cycle of engineering decisions such as flow field design and material selection, and providing strong support for the research and development of electrochemical systems.

[0029] Specifically, by constructing an inner iterative model with proton potential bias as the variable to be solved and an outer iterative model with plate voltage as the variable to be solved, and performing coupled iterative solutions, the numerical oscillation problem caused by the strong nonlinear coupling between electron potential and proton potential in the traditional explicit coupling strategy is fundamentally improved. Specifically, by introducing plate voltage and proton potential bias as implicit solution parameters into the iterative model, the proton potential bias has a clear solution benchmark in each iteration step, avoiding drastic fluctuations in the source term due to the lack of fixed boundary conditions, thereby effectively suppressing the divergence risk caused by sudden changes in current density. Simultaneously, through inner and outer iterative solutions... The iterative model's two-layer iterative mechanism achieves dynamic constraints on the balance between the total current in the cathode catalyst layer and the total current in the anode catalyst layer, keeping the distribution range of electron potential and proton potential stable and narrow, thus improving the stability of numerical calculations. Based on this, a higher relaxation factor can be safely used to accelerate iterations, significantly shortening the calculation cycle while ensuring convergence. This solves the technical contradiction of balancing computational efficiency and stability in traditional methods, making it particularly suitable for transient simulations under variable load conditions and high-frequency engineering optimization needs. It significantly improves the practicality and engineering application efficiency of multiphysics simulations for fuel cells and electrolyzers.

[0030] The following specific embodiments further explain the overpotential calculation method for electrochemical systems provided by this invention: Example 1 As attached Figure 1 As shown, this embodiment 1 provides a method for solving the electron-proton coupling potential of an electrochemical system, including the following steps: Step 1: Based on the mathematical relationship between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system, construct an internal iterative model with the proton potential bias as the variable to be solved and an external iterative model with the plate voltage as the variable to be solved.

[0031] An internal iterative model with proton potential bias as the variable to be determined is used to find a proton potential bias such that the total current of the cathode catalyst layer in the target electrochemical system is equal to the total current of the anode catalyst layer. An external iterative model with plate voltage as the variable to be determined is used to find a plate voltage such that the average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system is equal to the preset total current.

[0032] The internal iterative model with proton potential bias as the variable to be solved is as follows:

[0033] in, For the first Proton potential bias under the inner iteration step; For the first Proton potential bias under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step; For the first Proton potential bias under the inner iteration step.

[0034] The external iterative model with plate voltage as the variable to be determined is as follows:

[0035] in, For the first Plate voltage under the outer iteration step; For the first Plate voltage under the outer iteration step; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; The preset total current; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; For the first Plate voltage under the outer iteration step.

[0036] In this embodiment 1, taking a fuel cell as an example, the modeling principles of the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved are as follows: First, as attached Figure 2 As shown, attached Figure 2 The diagram below illustrates the distribution of electron and proton potentials using existing traditional electron-proton potential coupling methods; (Appendix) Figure 2 middle Defined as the electron potential under the traditional electron-proton potential coupling method. Defined as the proton potential under the traditional electron-proton potential coupling method. Defined as the plate voltage of the fuel cell.

[0037] From the appendix Figure 2 The calculation process for the anode overpotential and cathode overpotential of a fuel cell can be derived as follows:

[0038]

[0039] in, This represents the anode overpotential of the fuel cell; The electron potential under the traditional electron-proton potential coupling method; The proton potential under the traditional electron-proton potential coupling method; This represents the cathode overpotential of the fuel cell; This is the open-circuit voltage of the fuel cell.

[0040] It should be noted that in existing traditional electron-proton potential coupling methods, when the anode electron potential of the fuel cell involved in the solution is around 0V, the proton potential involved in the solution is slightly less than 0V; while the cathode electron potential involved in the solution is related to the fuel cell plate voltage. When the proton potential involved in the solution is near the reference point, it is much greater than 0V. Therefore, in this embodiment 1, an electronic-proton potential coupling method based on the semi-implicit method is proposed. Its core lies in how to transfer the distribution range of the anode electronic potential, cathode electronic potential and proton potential involved in the solution to the vicinity of the same reference point. At the same time, the plate voltage and proton potential are converted from boundary conditions and explicit coupling relationship into model parameters.

[0041] The following example uses 0V as a reference point to illustrate the principle of the electronic-proton potential coupling method based on the semi-implicit method. It is worth noting that in actual implementation, any value can be used as the reference point.

[0042] As attached Figure 2 As shown, in existing traditional electron-proton potential coupling methods, the cathode electron potential differs significantly from the reference point, and the proton potential also differs to some extent, while the anode electron potential is very close to the reference point. Therefore, it is necessary to shift the cathode electron potential and proton potential to near the reference point, i.e., to construct a new cathode electron potential and a new proton potential; whereby the new cathode electron potential is denoted as... The new proton potential is denoted as .

[0043] Specifically, the process of constructing a new cathode electron potential and a new proton potential is as follows: First, the cathode electron potential is shifted to the vicinity of the reference point to construct a new cathode electron potential. Among them, the new cathode electron potential The definition is as follows:

[0044] in, This represents the new cathode electron potential.

[0045] At this point, under the new cathode electronic potential, the calculation process for the cathode overpotential of the fuel cell is as follows:

[0046] in, This represents the cathode overpotential of the fuel cell.

[0047] Meanwhile, the anode electron potential remains unchanged as the new proton potential, meaning there is no need to shift the anode electron potential to the vicinity of the reference point; at this point, the new proton potential is defined as follows:

[0048] in, This represents the new proton potential.

[0049] At this point, with the new cathode electron potential and anode electron potential remaining unchanged, the calculation process for the anode overpotential of the fuel cell is as follows:

[0050] in, This represents the anode overpotential of the fuel cell.

[0051] As attached Figure 3 As shown, attached Figure 3 The diagram shows the distribution of electron and proton potentials after the anode electron potential is shifted to the vicinity of the reference point.

[0052] Next, the proton potential is also shifted to the vicinity of the reference point to construct a new proton potential. Among them, the new proton potential The definition is as follows:

[0053] in, For the new proton potential; The proton potential bias is used to shift the proton potential to the reference point. The magnitude of the proton potential is the variable to be determined.

[0054] At this point, under the new cathode electron potential and the new proton potential, the calculation process of the anode overpotential and the cathode overpotential of the fuel potential in the fuel cell can be expressed as follows:

[0055]

[0056] in, This represents the anode overpotential of the fuel cell; This represents the cathode overpotential of the fuel cell.

[0057] As attached Figure 4 As shown, attached Figure 4 The diagram shows the distribution of electron and proton potentials after the anode electron potential and proton potential are shifted to the vicinity of the reference point.

[0058] Based on the above process of constructing new cathode electronic potentials and new proton potentials, the two physical quantities, plate voltage and proton potential bias, are transformed from boundary conditions and coupling relationships from the existing computational fluid dynamics perspective into two parameters to be solved in the model. At this point, by combining the two conditions that the total current of the cathode catalyst layer in the fuel cell is equal to the total current of the anode catalyst layer, and that the average value of the total current of the cathode catalyst layer in the fuel cell is equal to the preset total current, an algebraic equation containing plate voltage and an algebraic equation containing proton potential bias can be constructed. By solving the algebraic equations containing plate voltage and proton potential bias, the two physical quantities, plate voltage and proton potential bias, can be implicitly solved, ensuring that the potential field is globally coordinated and has a solution in each iteration step, thus improving the stability of the coupling algorithm.

[0059] Specifically, an algebraic equation including the plate voltage is used as the external iterative model with the plate voltage as the variable to be solved, and an algebraic equation including the proton potential bias is used as the internal iterative model with the proton potential bias as the variable to be solved. This allows for the reshaping of the coupling relationship between electron potential and proton potential. By dividing the internal and external iterative models, the internal iterative model establishes and solves the equation that the total current of the cathode catalyst layer is equal to the total current of the anode catalyst layer, i.e., the total reaction rates of the anode and cathode of the fuel cell are equal. The external iterative model ensures that the total current of the anode and cathode are equal to the preset value, i.e., the current calculated operating condition converges to the preset operating condition.

[0060] Step 2: Perform coupled iterative solutions on the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved, and obtain the iterative solution results of proton potential bias and plate voltage.

[0061] Specifically, taking fuel cells as an example again, the principle of coupling iterative solution of the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved is explained as follows: (1) Iterative solution principle of the internal iterative model with proton potential bias as the variable to be solved Because in the internal iterative model where the proton potential bias is the variable to be determined, the proton potential bias... As the variable to be determined, it is necessary to find a proton potential bias. This ensures that the total current in the cathode catalyst layer of the fuel cell is equal to the total current in the anode catalyst layer.

[0062] Based on the electrochemical reaction equation, specifically taking the BV equation as an example, the current source terms on each grid node within the catalyst layer are as follows:

[0063]

[0064] in, This refers to the current source terms on the grid nodes within the anode catalyst layer; This represents the specific surface area of ​​the catalyst layer. The anode reference exchange current density; This represents the molar concentration of hydrogen gas. This is a reference concentration for hydrogen reactants; The transfer coefficient of the anode; The number of electrons at the anode; It is Faraday's constant; It is the gas constant; For temperature; The cathode transfer coefficient; For current source terms on the grid nodes within the cathode catalyst layer; The cathode reference exchange current density; This represents the molar concentration of oxygen. Reference concentration for oxygen reactants; The number of electrons in the cathode; subscript Indicates the anode; subscript Indicates cathode; subscript Indicates hydrogen gas, subscript It represents oxygen.

[0065] Therefore, the calculation process for the total current of the anode catalyst layer and the total current of the cathode catalyst layer can be obtained as follows:

[0066]

[0067] in, This represents the total current in the anode catalyst layer. This represents the total current in the cathode catalyst layer. The volume of the grid cells in the catalyst layer.

[0068] Furthermore, the calculation process for the difference between the total current in the anode catalyst layer and the total current in the cathode catalyst layer is as follows:

[0069] in, This is the difference between the total current in the anode catalyst layer and the total current in the cathode catalyst layer.

[0070] It should be noted that the anode overpotential of a fuel cell For proton potential bias The monotonically decreasing function of the total current in the anode catalyst layer For the anode overpotential of the fuel cell The current is a monotonically increasing function; therefore, the total current in the anode catalyst layer is... For proton potential bias The monotonically decreasing function; due to the cathode overpotential of the fuel cell. For proton potential bias The monotonically decreasing function of the total current in the cathode catalyst layer For the anode overpotential of the fuel cell The current is a monotonically decreasing function; therefore, the total current of the cathode catalyst layer is... For proton potential bias The monotonically increasing function; therefore, the difference between the total current in the anode catalyst layer and the total current in the cathode catalyst layer. For proton potential bias It is a monotonically decreasing function.

[0071] Therefore, based on the idea of ​​Newton's iteration method, the inner iteration model with proton potential bias as the variable to be solved is solved, so that the difference between the total current of the anode catalyst layer and the total current of the cathode catalyst layer is... The root that is 0 can be obtained; the specific solution process is as follows: Proton potential bias In a certain iteration step of the internal iterative model with proton potential bias as the variable to be solved, according to the principle of Newton's iteration method, we have the following:

[0072] in, For the first Proton potential bias under the inner iteration step; For the first Proton potential bias under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step.

[0073] Due to the difference between the total current of the anode catalyst layer and the total current of the cathode catalyst layer The form of the tangent is complex and its differentiation is difficult. Therefore, a secant is used to approximate the tangent, i.e., the tangent has passed through the point. and the Point corresponding to the proton potential bias under the inner iteration step The secant line then has:

[0074] in, For the first Proton potential bias under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step.

[0075] Therefore, we have:

[0076] in, For the first Proton potential bias under the inner iteration step.

[0077] At this point, the proton potential bias can be obtained through iteration. .

[0078] (2) Iterative solution principle of the external iterative model with plate voltage as the variable to be solved Because in the external iterative model where the plate voltage is the variable to be determined, the plate voltage... As the variable to be determined, it is necessary to find a plate voltage. This ensures that the average value of the total current in the cathode catalyst layer and the total current in the anode catalyst layer is equal to the preset total current, i.e., finding the function... The plate voltage corresponding to the zero point; where, the function In This represents the average of the total current in the cathode catalyst layer and the total current in the anode catalyst layer. The total current is a preset value, calculated based on the preset current density.

[0079] Based on the monotonicity of the polarization curves, the average values ​​of the total current in the cathode catalyst layer and the total current in the anode catalyst layer are also monotonic functions of the plate voltage. Therefore, the solution can also be obtained using the Newton-Raphson iteration method; specifically as follows: Regarding plate voltage Within a certain iteration step of the external iterative model with the plate voltage as the variable to be solved, according to the principle of Newton's iteration method, we have the following:

[0080] Among them, among them, For the first Plate voltage under the outer iteration step; For the first Plate voltage under the outer iteration step; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; This is the preset total current.

[0081] Similarly, the secant is used to approximate the tangent, i.e., the point has been passed. and the Point corresponding to the plate voltage under the outer iteration step The secant line then has:

[0082] in, For the first Plate voltage under the outer iteration step; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step.

[0083] Therefore, we have:

[0084] in, For the first Plate voltage under the outer iteration step.

[0085] At this point, the plate voltage can be obtained through iteration. .

[0086] Therefore, based on the Newton iteration method, by coupling the internal iteration model with the proton potential bias as the variable to be solved and the external iteration model with the plate voltage as the variable to be solved, the iterative solution results of the proton potential bias and the plate voltage can be obtained.

[0087] It needs to be explained in detail, as shown in the attached document. Figure 5 As shown in Example 1, the process of coupling the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved to obtain the iterative solution results of proton potential bias and plate voltage is as follows: S1. Determine whether the error between the average value of the total current in the cathode catalyst layer and the total current in the anode catalyst layer of the target electrochemical system under the current external iteration step and the preset total current is less than the preset error setting value; if yes, the external iteration model with the plate voltage as the variable to be solved converges, and the plate voltage under the current external iteration step is output as the iterative solution result of the plate voltage; if not, jump to S2. The outer iteration step is the current outer iteration step; the outer iteration step refers to the number of iterations of the outer iteration model with the plate voltage as the variable to be solved.

[0088] S2, External Iteration Step +1. That is, the number of iterations of the external iteration model with the plate voltage as the variable to be solved is increased by 1.

[0089] S3. Obtain the average value of the plate voltage and the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the two outer iteration steps prior to the current outer iteration step. Specifically, obtain the... Plate voltage under external iteration step , No. Plate voltage under external iteration step , No. The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step. and the The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step. .

[0090] S4. Based on the plate voltages of the two previous external iteration steps and the average of the total currents of the cathode and anode catalyst layers, calculate the plate voltage under the current external iteration. The process for calculating the plate voltage under the current external iteration is as follows:

[0091] in, For the first Plate voltage under the outer iteration step; For the first Plate voltage under the outer iteration step; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; The preset total current; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; For the first Plate voltage under external iteration step S5. Set the inner iteration step to 0. The inner iteration step refers to the number of iterations in the inner iteration model with proton voltage as the variable to be solved.

[0092] S6. Determine whether the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system under the current inner iteration step is less than the preset difference setting value, or determine whether the current inner iteration step is greater than the maximum inner iteration step; if yes, output the proton potential bias under the current inner iteration step as the iterative solution result of the proton potential bias, and return to S1; if no, jump to S7. Wherein, the first... The outer iteration step is used as the current inner iteration step.

[0093] It should be noted that when the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system at the current inner iteration step is less than the preset difference setting value, the inner iteration model with the proton potential bias as the variable to be solved converges; when the current inner iteration step is greater than the maximum inner iteration step, the inner iteration model with the proton potential bias as the variable to be solved diverges.

[0094] S7, Inner Iteration Step +1. That is, the number of iterations of the inner iterative model with proton potential bias as the variable to be solved is increased by 1.

[0095] S8. Based on the iterative solution results of the proton potential bias and the iterative solution results of the plate voltage, the overpotential of the target electrochemical system is calculated.

[0096] S9. Obtain the total current of the cathode catalyst layer and the total current of the anode catalyst layer.

[0097] S10. Obtain the proton potential bias and the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the two inner iteration steps prior to the current inner iteration step. Specifically, obtain the first... Proton potential bias under inner iteration step , No. Proton potential bias under inner iteration step , No. Total current of cathode catalyst layer under internal iteration step The difference between the current and the total current of the anode catalyst layer and the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step .

[0098] S11. Based on the proton potential bias and the difference between the total current in the cathode catalyst layer and the total current in the anode catalyst layer in the two previous internal iteration steps, the proton potential bias in the current internal iteration is calculated. The process for calculating the proton potential bias in the current internal iteration is as follows:

[0099] in, For the first Proton potential bias under the inner iteration step; For the first Proton potential bias under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step; For the first Proton potential bias under the inner iteration step.

[0100] S12, Return to S6.

[0101] Step 3: Based on the iterative solution results of the proton potential bias and the plate voltage, calculate the overpotential of the target electrochemical system. The overpotential of the target electrochemical system includes the anodic and cathodic overpotentials.

[0102] Specifically, the steps are as follows: Step 31: Based on the iterative solution results of the proton potential bias, calculate the anodic overpotential of the target electrochemical system; the process of calculating the anodic overpotential of the target electrochemical system is as follows:

[0103] in, The anodic overpotential of the target electrochemical system; The electronic potential is obtained based on computational fluid dynamics. The proton potential is obtained based on computational fluid dynamics. This is the result of the iterative solution for the proton potential bias.

[0104] Step 32: Based on the iterative solution results of the proton potential bias and the plate voltage, the cathode overpotential of the target electrochemical system is calculated; the process of calculating the cathode overpotential of the target electrochemical system is as follows:

[0105] in, The cathode overpotential of the target electrochemical system; The open-circuit voltage of the target electrochemical system; The electronic potential is obtained based on computational fluid dynamics. The proton potential is obtained based on computational fluid dynamics. The result of the iterative solution for the proton potential bias; This is the result of the iterative solution for the plate voltage.

[0106] Stability test: Taking a certain fuel cell as an example, the stability test of the electronic-proton potential coupling algorithm based on the semi-implicit method mentioned in Example 1 was carried out using a preset high relaxation factor, and the traditional explicit coupling algorithm was used as a control. The preset high relaxation factor includes pressure of 0.3, momentum of 0.7, energy of 0.95, composition of 0.95, electronic potential of 1, proton potential of 1, membrane water content of 0.99 and liquid water pressure of 0.99.

[0107] As attached Figure 6 As shown, attached Figure 6 The appendix provides a comparison of the computational stability of the method described in Example 1 with that of the traditional explicit coupling algorithm; from the appendix... Figure 6 It can be seen from this that at 0.8 A / cm 2 At current densities of , the traditional explicit coupling algorithm exhibits significant current density oscillations under high relaxation factors; in contrast to the traditional explicit coupling algorithm, the semi-implicit coupling algorithm proposed in this embodiment 1 completely eliminates current density oscillations.

[0108] It should be noted that the above only uses the operating conditions of a fuel cell as an example, but this Example 1 is applicable to various electrochemical systems that include electron-proton potential coupling; the principle in the electrolyzer is similar to that of the fuel cell described above, and will not be repeated here.

[0109] The overpotential solution method for electrochemical systems described in Example 1 constructs an internal iterative model with proton potential as the variable to be solved and an external iterative model with plate voltage as the variable to be solved. This transforms the reference point in the coupling relationship between electron and proton potentials into implicit solution parameters, ensuring that the proton potential has a solution in any iteration step. This not only effectively alleviates the numerical oscillation problem caused by strong nonlinear coupling in traditional explicit iterative algorithms, improving computational stability, but also allows for the use of higher relaxation factors, significantly improving computational efficiency. Simultaneously, it can significantly shorten the iteration cycle of engineering decisions such as flow field design and material selection while ensuring the accuracy of simulation results, providing a more efficient and stable solution for the development of fuel cells and electrolyzers. Furthermore, by introducing an implicit reference point transformation strategy, the coupling between electron and proton potentials becomes smoother, reducing proton potential source term fluctuations caused by sudden changes in current density, thereby avoiding the risk of high divergence or failure to converge to a stable solution, achieving a dual improvement in computational efficiency and stability.

[0110] Example 2 As attached Figure 7 As shown in the figure, this embodiment 2 provides a method for solving the overpotential of an electrochemical system, including an iterative model construction module, an iterative solution module, and an overpotential solution module.

[0111] The iterative model construction module is used to construct an internal iterative model with proton potential bias as the variable to be solved and an external iterative model with plate voltage as the variable to be solved, based on the mathematical relationship between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system.

[0112] The iterative solution module is used to perform coupled iterative solutions on the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved, so as to obtain the iterative solution results of proton potential bias and plate voltage.

[0113] The overpotential calculation module is used to calculate the overpotential of the target electrochemical system based on the iterative solution results of the proton potential bias and the iterative solution results of the plate voltage.

[0114] Example 3 As attached Figure 8 As shown, this embodiment 3 provides an electronic device, including: a memory for storing a computer program; a processor for executing the computer program to implement the steps of the overpotential solution method for an electrochemical system; or, the processor for executing the computer program to implement the functions of each module in the above-mentioned overpotential solution system for an electrochemical system.

[0115] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a preset function, the instruction segments describing the execution process of the computer program in the electronic device.

[0116] The electronic device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The electronic device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above are examples of electronic devices and do not constitute a limitation on the electronic device. It may include more components than described above, or combine certain components, or different components. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0117] The processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor, or any conventional processor, etc. The processor is the control center of the electronic device, connecting various parts of the entire electronic device through various interfaces and lines.

[0118] The memory can be used to store the computer program and / or module. The processor implements various functions of the electronic device by running or executing the computer program and / or module stored in the memory and by calling the data stored in the memory.

[0119] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function (such as sound playback, image playback, etc.). The data storage area may store data created based on the use of the mobile phone (such as audio data, phonebook, etc.). Furthermore, the memory may include high-speed random access memory and non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart memory cards, secure digital cards, flash memory cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0120] Example 4 This embodiment 4 also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method for solving the overpotential of an electrochemical system.

[0121] If the modules / units of the overpotential solving system for the electrochemical system are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0122] Based on this understanding, the present invention can implement all or part of the process in the above-described method for solving the overpotential of an electrochemical system, or it can be accomplished by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the above-described method for solving the overpotential of an electrochemical system. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or a preset intermediate form, etc.

[0123] The computer-readable storage medium may include any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electrical carrier signal, telecommunication signal, and software distribution medium, etc.

[0124] The overpotential solution method for electrochemical systems described in this invention transforms the plate voltage and proton potential bias into implicit solution parameters of the iterative model within the coupling relationship between electronic and proton potentials. This yields a new coupling relationship between electronic and proton potentials, ensuring that the proton potential has a solution in any iteration step. Furthermore, the distribution ranges of the cathode electronic potential, anode electronic potential, and proton potential are relatively narrow, thus significantly improving the numerical stability during calculation. Consequently, a high relaxation factor can be used for calculation, significantly improving computational efficiency and shortening the iterative cycle for engineering decisions such as flow field design and material selection.

[0125] The above embodiments are merely one of the implementation methods for achieving the technical solution of the present invention. The scope of protection claimed by the present invention is not limited to this embodiment, but also includes any variations, substitutions and other implementation methods that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention.

Claims

1. A method for solving the overpotential of an electrochemical system, characterized in that, include: Based on the mathematical relationship between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system, an internal iterative model with proton potential bias as the variable to be solved and an external iterative model with plate voltage as the variable to be solved are constructed. The inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved are coupled iteratively solved to obtain the iterative solution results of proton potential bias and plate voltage. The overpotential of the target electrochemical system is calculated based on the iterative solutions for the proton potential bias and the plate voltage.

2. The method for solving the overpotential of an electrochemical system according to claim 1, characterized in that, An internal iterative model with proton potential bias as the variable to be determined is used to find a proton potential bias such that the total current of the cathode catalyst layer in the target electrochemical system is equal to the total current of the anode catalyst layer. Specifically, the internal iterative model with proton potential bias as the variable to be solved is as follows: in, For the first Proton potential bias under the inner iteration step; For the first Proton potential bias under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step; For the first The difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the inner iteration step; For the first Proton potential bias under the inner iteration step.

3. The method for solving the overpotential of an electrochemical system according to claim 1, characterized in that, An external iterative model with plate voltage as the variable to be determined is used to find a plate voltage such that the average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system is equal to the preset total current. Specifically, the external iterative model with the plate voltage as the variable to be solved is as follows: in, For the first Plate voltage under the outer iteration step; For the first Plate voltage under the outer iteration step; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; The preset total current; For the first The average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer under the outer iteration step; For the first Plate voltage under the outer iteration step.

4. The method for solving the overpotential of an electrochemical system according to claim 1, characterized in that, The process of coupling iteratively solving the inner iterative model with proton potential bias as the variable to obtain the iterative solution results for proton potential bias and plate voltage is as follows: S1. Determine whether the error between the average value of the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system under the current external iteration step and the preset total current is less than the preset error setting value; if yes, the external iteration model with the plate voltage as the variable to be solved converges, and the plate voltage under the current external iteration step is output as the iterative solution result of the plate voltage; if no, jump to S2. S2, outer iteration step +1; S3. Obtain the average value of the plate voltage and the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the two external iteration steps before the current external iteration step; S4. Based on the plate voltages of the two previous external iteration steps and the average values ​​of the total current of the cathode catalyst layer and the total current of the anode catalyst layer, calculate the plate voltage under the current external iteration. S5. Set the inner iteration step to 0; S6. Determine whether the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system under the current internal iteration step is less than the preset difference setting value, or determine whether the current internal iteration step is greater than the maximum internal iteration step; if yes, output the proton potential bias under the current internal iteration step as the iterative solution result of the proton potential bias, and return to S1; if no, jump to S7. S7, Inner iteration step +1; S8. Obtain the proton potential bias and the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the two inner iteration steps before the current inner iteration step. S9. Based on the proton potential bias in the two internal iteration steps before the current internal iteration step and the difference between the total current of the cathode catalyst layer and the total current of the anode catalyst layer, the proton potential bias in the current internal iteration is calculated. S10, Return to S6.

5. The method for solving the overpotential of an electrochemical system according to claim 1, characterized in that, The overpotential of the target electrochemical system includes the anodic overpotential and the cathodic overpotential of the target electrochemical system; Based on the iterative solution results of the proton potential bias, the anodic overpotential of the target electrochemical system is calculated. Based on the iterative solution results of the proton potential bias and the plate voltage, the cathode overpotential of the target electrochemical system is calculated.

6. The method for solving the overpotential of an electrochemical system according to claim 5, characterized in that, Based on the iterative solution results of the proton potential bias, the process of calculating the anodic overpotential of the target electrochemical system is as follows: in, The anodic overpotential of the target electrochemical system; The electronic potential is obtained based on computational fluid dynamics. The proton potential is obtained based on computational fluid dynamics. This is the result of the iterative solution for the proton potential bias.

7. The method for solving the overpotential of an electrochemical system according to claim 5, characterized in that, Based on the iterative solutions for the proton potential bias and the plate voltage, the cathode overpotential of the target electrochemical system is calculated as follows: in, The cathode overpotential of the target electrochemical system; The open-circuit voltage of the target electrochemical system; The electronic potential is obtained based on computational fluid dynamics. The proton potential is obtained based on computational fluid dynamics. The result of the iterative solution for the proton potential bias; This is the result of the iterative solution for the plate voltage.

8. A system for solving overpotential in electrochemical systems, comprising: The iterative model construction module is used to construct an internal iterative model with proton potential bias as the variable to be solved and an external iterative model with plate voltage as the variable to be solved, based on the mathematical relationship between the total current of the cathode catalyst layer and the total current of the anode catalyst layer in the target electrochemical system. The iterative solution module is used to perform coupled iterative solution of the inner iterative model with proton potential bias as the variable to be solved and the outer iterative model with plate voltage as the variable to be solved, so as to obtain the iterative solution results of proton potential bias and plate voltage. The overpotential calculation module is used to calculate the overpotential of the target electrochemical system based on the iterative solution results of the proton potential bias and the iterative solution results of the plate voltage.

9. An electronic device, characterized in that, include: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, performs the overpotential calculation method for an electrochemical system as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the overpotential calculation method for electrochemical systems as described in any one of claims 1-7.

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