Method and apparatus for calculating ohmic resistance of a planar solid oxide cell stack

Abstract

This application discloses a method and apparatus for calculating the ohmic resistance of a planar solid oxide fuel cell stack, relating to the field of fuel cell and electrolysis device technology. The method includes: obtaining the geometric structural parameters, material conductivity parameters, and current collector structure parameters of a single cell in the planar solid oxide fuel cell stack; based on the current collector structure parameters, performing an equivalent reconstruction of the current conduction path in the electrodes to establish an equivalent current conduction model including the influence of the current collector path; based on the equivalent current conduction model, calculating the equivalent ohmic resistance of the single cell under operating conditions according to the geometric structural parameters and the material conductivity parameters; and using the equivalent ohmic resistance of the single cell as the ohmic resistance of the planar solid oxide fuel cell stack. This application can accurately calculate the ohmic resistance, improving the accuracy of stack structure optimization and performance analysis.

Description

Technical Field

[0001] This application relates to the field of fuel cell and electrolysis device technology, and in particular to a method and device for calculating the ohmic resistance of a planar solid oxide battery stack. Background Technology

[0002] Flat-panel solid oxide cell (SOC) stacks are widely used in solid oxide fuel cell (SOFC) and solid oxide electrolysis cell (SOEC) systems due to their compact structure and high power density. Ohmic resistance, as a crucial component of stack voltage loss, significantly impacts stack performance evaluation, structural design, and operational control.

[0003] In existing technologies, the calculation of ohmic resistance in planar SOC stacks typically employs simplified equivalent methods, often focusing primarily on the resistance contribution within the electrodes or electrolyte layer, while neglecting the current collector structure and the resulting changes in the current conduction path. In actual stacks, current is conducted through various structures, including electrodes, current collectors, and connecting components. The form, size, and layout of the current collector structure significantly affect the current conduction path, thus having a non-negligible impact on ohmic resistance. Existing literature indicates that this ohmic resistance caused by current collection has a significant impact on the overall performance of the SOC stack.

[0004] Due to the lack of a unified method for calculating ohmic resistance that can characterize the impact of current collection paths, existing technologies struggle to provide consistent and scalable ohmic resistance assessments across different fuel cell stack structures. This results in low accuracy in ohmic resistance calculations, limiting the accuracy of fuel cell stack structure optimization and performance analysis. Therefore, it is necessary to propose a novel method for calculating the ohmic resistance of planar SOC fuel cell stacks to overcome these problems. Summary of the Invention

[0005] The purpose of this application is to provide a method and device for calculating the ohmic resistance of a planar solid oxide battery stack. By equivalently reconstructing the current conduction path in the planar solid oxide battery stack, a unified modeling and calculation of the ohmic resistance can be achieved, so as to accurately calculate the ohmic resistance and improve the accuracy of stack structure optimization and performance analysis.

[0006] To achieve the above objectives, this application provides the following solution.

[0007] In a first aspect, this application provides a method for calculating the ohmic resistance of a planar solid oxide battery stack, comprising the following steps.

[0008] Obtain the geometric parameters, material conductivity parameters, and current collector structure parameters of individual cells in a planar solid oxide battery stack.

[0009] Based on the current collector structure parameters, the current conduction path in the electrode is equivalently reconstructed to establish an equivalent current conduction model that includes the influence of the current collector path.

[0010] Based on the current conduction equivalent model, the equivalent ohmic resistance of the single cell in the working state is calculated according to the geometric structural parameters and the material conductivity parameters.

[0011] The equivalent ohmic resistance of the single cell is used as the ohmic resistance of the planar solid oxide battery stack.

[0012] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method for calculating the ohmic resistance of a planar solid oxide battery stack.

[0013] According to the specific embodiments provided in this application, this application has the following technical effects: Based on the current collector structure parameters of a single cell in a planar solid oxide battery stack, this application performs equivalent reconstruction of the current conduction path in the electrodes, establishes an equivalent current conduction model that includes the influence of the current collector path, and can explicitly characterize the influence of the current collector structure on current conduction and ohmic resistance, thereby improving the rationality of ohmic resistance calculation; based on the equivalent current conduction model, according to the geometric structure parameters and material conductivity parameters, the equivalent ohmic resistance of the single cell in the working state is calculated, which is applicable to planar SOC stacks with different structural forms, realizes unified modeling and calculation of ohmic resistance, and has good scalability; the calculated equivalent ohmic resistance of the single cell is used as the ohmic resistance of the planar solid oxide battery stack, thereby accurately calculating the ohmic resistance and improving the accuracy of stack structure optimization and performance analysis. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments 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.

[0015] Figure 1 A schematic diagram of the calculation method for the ohmic resistance of the planar solid oxide battery stack provided in this application.

[0016] Figure 2 This is a schematic diagram of a planar solid oxide battery structure.

[0017] Figure 3 This is a schematic diagram of the current vector of the air electrode in a two-dimensional model (after symmetry) of an air-supported SOC; where, Figure 3 (a) in the diagram is a schematic diagram of the actual current conduction path. Figure 3 (b) in the figure is a schematic diagram of the current conduction model based on the equivalent reconstruction of the current collection path.

[0018] Figure 4 This application provides a schematic diagram for verifying the I–V curve; wherein, Figure 4 In (a), the air electrode conductivity is 2000 Sm. -1 Below is a schematic diagram comparing the IV curves of Model 0 and Model 2. Figure 4 (b) represents the air electrode conductivity of 4000 Sm. -1 Below is a schematic diagram comparing the IV curves of Model 0 and Model 2. Figure 4 (c) represents the air electrode conductivity of 6000 Sm. -1 Below is a schematic diagram comparing the IV curves of Model 0 and Model 2.

[0019] Figure 5 A schematic diagram illustrating the sensitivity analysis of the effect of changes in current collector structure parameters on the equivalent ohmic resistance provided in this application; wherein, Figure 5 (a) is the best. A diagram illustrating how the value changes with pitch width. Figure 5 Option (b) is the best. A diagram illustrating how the value changes with airway width. Figure 5 (c) is the best. A schematic diagram showing how the value changes with the thickness of the air column. Figure 5 (d) is the best. A schematic diagram showing how the value changes with the conductivity of the air electrode. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] To make the objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] like Figure 1 As shown in the figure, this application provides a method for calculating the ohmic resistance of a planar solid oxide battery stack, including the following steps.

[0023] S1: Obtain the geometric parameters, material conductivity parameters, and current collector structure parameters of a single cell in a planar solid oxide battery stack.

[0024] S2: Based on the current collector structure parameters, the current conduction path in the electrode is equivalently reconstructed to establish an equivalent current conduction model that includes the influence of the current collector path. Here, the electrode is a single-cell electrode.

[0025] S3: Based on the current conduction equivalent model, calculate the equivalent ohmic resistance of the single cell in the working state according to the geometric structure parameters and the material conductivity parameters.

[0026] S4: Use the equivalent ohmic resistance of the single cell as the ohmic resistance of the planar solid oxide battery stack.

[0027] In one exemplary embodiment, the geometric parameters include: repeating unit width, airway width, and electrode thickness.

[0028] The electrical conductivity parameters of the material include: the electrical conductivity of the electrode material.

[0029] The flow collection structure parameters include the ratio between the width of the air passage and the width of the repeating unit.

[0030] In an exemplary embodiment, S2 specifically includes: S21: Based on the current collector structure parameters, determine the longest and shortest current conduction paths in the electrode; wherein the longest conduction path is equal to half the width of the airway and the thickness of the electrode; and the shortest conduction path is equal to the thickness of the electrode.

[0031] S22: Calculate the average conduction length of the current in the electrode based on the longest conduction path and the shortest conduction path.

[0032] S23: Based on the average conduction length, establish an equivalent current conduction model that includes the influence of the current collection path.

[0033] like Figure 2 As shown, a first fuel electrode layer 1, a battery repeating unit 2, and a second connector layer 3 are arranged sequentially from bottom to top. The battery repeating unit 2 includes a first connector layer 2-1, an air electrode layer 2-2, an electrolyte layer 2-3, and a second fuel electrode layer 2-4 stacked sequentially from bottom to top. Fuel 4 is introduced between the first fuel electrode layer 1 and the first connector layer 2-1, the second fuel electrode layer 2-4, and the second connector layer 3. Air 5 is introduced between the first connector layer 2-1 and the air electrode layer 2-2. The current direction 6 is from bottom to top.

[0034] In practical applications, in a planar SOC design, the fuel electrode (including the first fuel electrode layer 1 and the second fuel electrode layer 2-4), electrolyte, and air electrode form a three-layer sandwich structure. The first connector layer 2-1 and the second connector layer 3 have air channels that separate the fuel electrode and air electrode layer 2-2 within the fuel cell stack. Since the air channels are non-conductive, the current flowing from the electrodes to the connectors for collection must be irregularly curved, such as... Figure 3 As shown in (a), the length through which the current flows cannot be explicitly represented and needs to be approximated.

[0035] Based on the distribution characteristics of the current path, in Figure 3 (b) briefly illustrates several of the main different paths.

[0036] This embodiment uses the air electrode as an example; the calculation method for the ohmic resistance on the fuel electrode side follows the same logic. The longest current path in the air electrode... l max The red arrow indicates that the electron's initial position is at the leftmost part of the connector, i.e., the point of contact with the airway, and its value is approximately equal to... l max = w channel / 2+ d ai The subscript "ai" is an abbreviation for air electrode. w channel This refers to the airway width. (Shortest path) l min Represented by the blue arrow (the electron's initial position is on the far right of the connector), it is approximately... l min = d ai .

[0037] Assuming the current path increases uniformly and linearly from shortest to longest, the starting position of the current traverses from the rightmost to the leftmost edge of the connector, thus covering the entire current path of the air electrode. Therefore, the average conduction length of electrons within the entire air electrode is... l ave =( l max + l min ) / 2= w channel / 4+ d ai .

[0038] In an exemplary embodiment, S3 specifically includes: S31: Based on the current conduction equivalent model, an analytical expression for the electrode surface resistance is constructed according to the electrode thickness, the conductivity of the electrode material, and the average conduction length. The analytical expression for the electrode surface resistance includes at least a path extension factor, a cross-sectional area reduction factor, and a current distribution scaling factor. The path extension factor is determined based on the ratio of the average conduction length to the electrode thickness. The cross-sectional area reduction factor is determined based on the ratio of the width of the repeating unit to the electrode thickness. The current distribution scaling factor is determined based on the ratio of the airway width to the width of the repeating unit.

[0039] S32: Calculate the equivalent ohmic resistance of the single cell in the working state according to the analytical expression of the electrode surface resistance.

[0040] In an exemplary embodiment, the analytical expression for the electrode surface resistance further includes fitting parameters, which characterize the approximation of the analytical expression for the electrode surface resistance. These fitting parameters refer to the degree to which the mathematical expression (analytical expression) used to describe the electrode surface resistance (or resistivity) approximates the actual physical phenomenon, i.e., the magnitude of the deviation between the theoretical model and the actual situation.

[0041] Since the electrode thickness (micrometers) is much smaller than the electrode width (millimeters), the cross-sectional width through which the current flows can be approximated as... d ai Previous studies have shown that most of the current at the electrolyte-electrode interface is concentrated below the airway, with only a small proportion of the current below the connector; therefore, a current distribution ratio factor also exists. w channel / w pitch Therefore, the equivalent ohmic resistance ASR ai This can be achieved by adjusting the original ohmic resistor ASR0=d ai / σ ai To obtain the path extension factor, multiply by three factors: l ave / d ai ), cross-sectional reduction factor ( w pitch / d ai ) and current distribution scaling factor ( w channel / w pitch ).

[0042] In an exemplary embodiment, the analytical expression for the electrode surface resistance is: (1) in, Equivalent ohmic resistance; These are the fitting parameters; Airway width; Width of the repeating unit; Electrode thickness; The conductivity of the electrode material is denoted as .

[0043] The analytical expression for the electrode surface resistance is introduced. As fitting parameters, this characterizes the approximation used in the expression. If the formula accurately captures the underlying physical characteristics of the resistor, then... The value should be around 1.

[0044] Furthermore, when the electrode has a double-layer structure, the equivalent ohmic resistance of the single cell is determined by calculating the electrode surface resistance of each layer. The double-layer structure includes a functional layer and a current collection layer, and the resistors in the double-layer structure are connected in parallel.

[0045] In practical applications, the air electrode likely comprises a functional layer (FL) and a current-collecting layer (CCL), and the resistances within these two layers can be considered as being in parallel. Therefore, the formula can be adapted to apply to the case of a double-layer air electrode: (2) and The equivalent ohmic resistances of the functional layer and the current collection layer are respectively, and can be calculated using equation (1).

[0046] in, and The electrode thicknesses are respectively those of the functional layer and the current collection layer; and The conductivity of the electrode materials for the functional layer and the current collection layer are respectively.

[0047] To verify the accuracy of equation (1), this application used COMSOL Multiphysics finite element software to establish three-dimensional models of three single-layer SOEC stacks for comparison. The basic parameters of the models were set as follows: pitch =4mm, channel =2mm, d ai =0.025mm.

[0048] Using Model 0 as a baseline, Model 0 completely solves the charge transfer equation to ensure a realistic current conduction path, such as... Figure 3 As shown in (a) in the figure. Model 1 is the equivalent model, using the ASR of equation (1). ai It is used to characterize the resistance of the electrode surface, that is, the equivalent ohmic resistance.

[0049] Except for the electrochemical field being equivalent, the flow field and mass transport field of Model 0 and Model 1 are kept the same, and the corresponding boundary conditions are also the same.

[0050] To demonstrate ASR ai It inherently possesses a good fit to the actual model, and the fitting parameters The value is set to 1. Model 2 has the same settings as Model 1, but uses the value d. ai / σ ai The electrode surface resistance.

[0051] The I–V curve of the above model is in Figure 4 A comparison was made between (a) and (c) in the figure, where I is the current density and V is the voltage. It can be seen that for the air electrode conductivity at 2000 Sm -1 Up to 6000Sm -1 Within a broad range, Model 1 ( Figure 4 The fit between the black line in the middle and model 0 is very accurate, confirming that... Figure 3 The simple image in (b) captures well the physical nature of current conduction in the electrode. That is, for different electrode materials, the resistance caused by the current path can also be effectively characterized by equation (1).

[0052] However, from Figure 4 Similarly, it can be observed that as the current density increases, Model 2 ( Figure 4 The difference between the model (red line in the middle) and model 0 gradually widens. With... As the value decreases, this difference tends to increase. Clearly, using the commonly used surface resistivity value d... ai / σ ai Characterizing the electrode resistance in a planar SOC stack is not accurate. Considering the resistance caused by the current bending path due to current collection is crucial for obtaining accurate simulation results.

[0053] To further evaluate the universality of this improved resistance model, this application has conducted optimal... Values ​​of design parameters pitch , channel , d ai as well as Sensitivity analysis test. Best The value is obtained by fitting Model 1 and Model 0 so that the IV curves of the two models completely overlap.

[0054] Figure 5 (a)-(d) in the table show one of the parameters from its default value: pitch =4mm, channel =2mm, d ai =0.025mm and ai =4000Sm -1 When changes occur, the best The values ​​vary. The testing range essentially covers all possible values ​​that conform to the SOC (State of Charge) material and structural properties. For all considered cases, the optimal... The value remains around 1, or in the range of 1 ± 0.3. Considering that the analytical solution uses a certain approximation, the result is sufficient to justify the expression.

[0055] It is worth noting that, A slight deviation from its optimal value will only cause minor inaccuracies in the derived I–V relationship. For example, as Figure 5 As shown in (d) in the figure, ai =2000Sm -1 The best time The value is 0.72. ai =6000Sm -1 The best time The value is 1.1. From Figure 4 It can be seen from this that for current densities below 8000 Am -2 Under the operating condition where λ is 1, ai =2000Sm -1 and ai =6000Sm -1 The maximum errors are 3.3% and 0.35%, respectively. Therefore, the previous assumption of a linear increase in the current path length has an acceptable impact on the final result. In other words, the value of λ = 1 can be applied to a wide range of situations, making equation (1) effective for prediction. w pitch , w channel , d ai and ai Finding the optimal choice is very useful.

[0056] In one exemplary embodiment, the planar solid oxide battery stack is suitable for solid oxide fuel cells or solid oxide electrolyzers.

[0057] In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments. The computer device can be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (I / O), and a communication interface. The processor, memory, and I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device stores data to be processed. The I / O interface of the computer device is used for exchanging information between the processor and external devices. The communication interface of the computer device is used for communicating with an external terminal via a network connection. When the computer program is executed by the processor, it implements the above-described methods.

[0058] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0059] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method of calculating the ohmic resistance of a planar solid oxide cell stack, characterized in that, include: Obtain the geometric parameters, material conductivity parameters, and current collector structure parameters of a single cell in a planar solid oxide battery stack; The geometric parameters include: repeating unit width, airway width, and electrode thickness; the material conductivity parameters include: the conductivity of the electrode material; the current collection structure parameters include: the ratio between the airway width and the repeating unit width. Based on the current collector structure parameters, the current conduction path in the electrodes is equivalently reconstructed, and an equivalent current conduction model incorporating the influence of the current collector path is established, specifically including: Based on the current collector structure parameters, the longest and shortest current conduction paths in the electrodes are determined; wherein, the longest conduction path is equal to half the width of the airway and the thickness of the electrode; and the shortest conduction path is equal to the thickness of the electrode. Based on the longest and shortest conduction paths, calculate the average conduction length of the current in the electrode; Based on the average conduction length, an equivalent current conduction model incorporating the influence of the current collection path is established; Based on the current conduction equivalent model, the equivalent ohmic resistance of the single cell in the working state is calculated according to the geometric structure parameters and the material conductivity parameters. The equivalent ohmic resistance of the single cell is used as the ohmic resistance of the planar solid oxide battery stack.

2. The method of calculating the ohmic resistance of a planar solid oxide cell stack according to claim 1, characterized in that, Based on the current conduction equivalent model, and according to the geometric parameters and the material conductivity parameters, the equivalent ohmic resistance of the single cell in the operating state is calculated, specifically including: Based on the current conduction equivalent model, an analytical expression for the electrode surface resistance is constructed according to the electrode thickness, the conductivity of the electrode material, and the average conduction length. The analytical expression for the electrode surface resistance includes at least a path extension factor, a cross-sectional area reduction factor, and a current distribution scaling factor. The path extension factor is determined based on the ratio of the average conduction length to the electrode thickness; the cross-sectional area reduction factor is determined based on the ratio of the width of the repeating unit to the electrode thickness; and the current distribution scaling factor is determined based on the ratio of the airway width to the width of the repeating unit. The equivalent ohmic resistance of the single cell in the operating state is calculated based on the analytical expression of the electrode surface resistance.

3. The method of calculating the ohmic resistance of a planar solid oxide cell stack according to claim 2, characterized in that, The analytical expression for the electrode surface resistance also includes fitting parameters, which are used to characterize the approximation of the analytical expression for the electrode surface resistance.

4. The method for calculating the ohmic resistance of a planar solid oxide battery stack according to claim 3, characterized in that, The analytical expression for the electrode surface resistance is: in, Equivalent ohmic resistance; These are the fitting parameters; Airway width; Electrode thickness; The conductivity of the electrode material; The width of the repeating unit.

5. The method for calculating the ohmic resistance of a planar solid oxide battery stack according to claim 3, characterized in that, When the electrode has a double-layer structure, the equivalent ohmic resistance of the single cell is determined by calculating the electrode surface resistance of each layer. The double-layer structure includes a functional layer and a current collection layer, and the resistors in the double-layer structure are connected in parallel.

6. The method for calculating the ohmic resistance of a planar solid oxide battery stack according to claim 5, characterized in that, When the electrode has a double-layer structure, the equivalent ohmic resistance of the single cell is: in, The equivalent ohmic resistance of the functional layer; This is the equivalent ohmic resistance of the current collecting layer.

7. The method for calculating the ohmic resistance of a planar solid oxide battery stack according to any one of claims 1 to 6, characterized in that, The flat-plate solid oxide battery stack is suitable for solid oxide fuel cells or solid oxide electrolyzers.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the method for calculating the ohmic resistance of a planar solid oxide battery stack according to any one of claims 1-7.

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