Method for analyzing electrochemical performance of solid oxide stack based on one-dimensional string-bead model

Abstract

This invention provides a method for analyzing the electrochemical performance of solid oxide battery stacks based on a one-dimensional beaded model, comprising: Step S1, discretizing the solid oxide battery stack into multiple beaded units along the flow channel direction and connecting them in series along the height direction to form a one-dimensional beaded model; Step S2, simulating the flow field and thermal field of the inlet region of the solid oxide battery stack using a three-dimensional finite element model and extracting initial boundary conditions; Step S3, obtaining multi-physics coupled solution results by coupling solutions in each beaded unit; Step S4, dividing the solid oxide battery stack into an end plate region and a uniform intermediate region based on the differential decay index threshold and differential decay index; Step S5, calculating the voltage distribution and thermal response characteristics of the solid oxide battery stack under dynamic load. The beneficial effect is that this invention can balance efficiency and accuracy and characterize the multi-physics spatiotemporal evolution characteristics of the solid oxide battery stack under dynamic load.

Description

Technical Field

[0001] This invention relates to the technical field of solid oxide batteries, and more specifically, to a method for analyzing the electrochemical performance of solid oxide battery stacks based on a one-dimensional beaded model. Background Technology

[0002] Solid oxide cell (SOC) stacks are core energy conversion devices in renewable energy systems. Their overall performance and service life are directly affected by the strong coupling effects of multiple physical field parameters, such as internal electrochemistry and heat and mass transfer, and these parameters exhibit significant spatiotemporal heterogeneity within the stack. To achieve performance evaluation and optimized design of SOC stacks, various multiphysics analysis models have been developed in this field. However, existing models all have significant technical limitations and are difficult to meet the engineering application requirements of industrial-grade stacks.

[0003] Zero-dimensional lumped parameter models treat the SOC (State of Charge) fuel cell stack as a homogeneous whole, characterizing its overall performance solely through macroscopic parameters at the inlet and outlet. This completely ignores the objectively existing voltage, temperature, and gaseous component concentration gradients along the flow path and stack height within the stack, failing to distinguish the performance differences between the endplate region and the central homogeneous region. When applying this model to the design of long-size, multi-unit industrial-grade fuel cell stacks, it is prone to misjudging operational risks such as localized overheating and fuel depletion, leading to deviations in the stack design safety margin setting.

[0004] To address the issue that zero-dimensional models cannot characterize parameter distribution characteristics, traditional one-dimensional analysis models have been developed. However, these models only discretize along a single spatial dimension (such as the flow channel direction) and often introduce isothermal assumptions or simplify mass transfer equations. They fail to realistically simulate the complex current transport paths formed by multiple repeating units connected in series via interconnects and the thermal coupling relationships between multiple units in a fuel cell stack. This oversimplification of the actual physical processes within the fuel cell stack leads to significant deviations in predicting performance distribution along the stack height, especially performance non-uniformity caused by endplate effects. The prediction accuracy cannot meet the engineering optimization requirements of industrial-grade fuel cell stacks.

[0005] Three-dimensional finite element models can finely depict the local distribution characteristics of multiple physical fields such as flow field, temperature field, and stress field under the local geometry of the fuel cell stack. The model has high prediction accuracy, but it has strict requirements for computing resources and computing power, making it difficult to apply to full-scale transient simulation of industrial-grade fuel cell stacks with 30 elements or more. Furthermore, it cannot support rapid analysis and design iteration under dynamic load conditions, resulting in technical problems such as high computing cost and low simulation efficiency.

[0006] In summary, existing multiphysics analysis models for SOC stacks struggle to balance computational efficiency and prediction accuracy, and generally lack effective methods for quantifying the spatiotemporal heterogeneity within the stack, particularly failing to accurately characterize the response mismatch of multiphysics fields under dynamic loads. These technical deficiencies have become key bottlenecks restricting the rapid and accurate design, operational parameter optimization, and scientific definition of safe operating windows for industrial-grade SOC stacks. Therefore, there is an urgent need to develop an electrochemical performance analysis method that balances computational efficiency and prediction accuracy, and can precisely characterize the spatiotemporal evolution of multiphysics parameters in SOC stacks under dynamic loads. Summary of the Invention

[0007] The technical problem to be solved by this invention is how to balance efficiency and accuracy and accurately characterize the spatiotemporal evolution characteristics of solid oxide battery stacks under dynamic load. In order to overcome the defects of the above-mentioned prior art (or related technology), this invention provides a method for analyzing the electrochemical performance of solid oxide battery stacks based on a one-dimensional beaded model.

[0008] This invention provides a method for analyzing the electrochemical performance of solid oxide fuel cells based on a one-dimensional beaded model, comprising the following steps: Step S1: Discretize the solid oxide battery stack into multiple beaded units in the flow channel direction. Each beaded unit corresponds to a repeating unit in the solid oxide battery stack. Each beaded unit is connected in series along the height direction of the solid oxide battery stack to form a continuous current path to form a one-dimensional beaded model. Step S2: Model the solid oxide battery stack to obtain a three-dimensional finite element model and simulate the flow field and thermal field of the inlet region of the solid oxide battery stack using the three-dimensional finite element model. Extract the inlet gas composition, flow rate and temperature of each bead unit as the initial boundary conditions of the one-dimensional bead model. Step S3: In each of the beaded units, the electrochemical reaction model, mass conservation model, energy conservation model, and momentum conservation model are coupled and solved to obtain the multiphysics coupling solution result; Step S4: Calculate the voltage difference between two adjacent beaded units, and define the ratio of the voltage difference to the maximum voltage difference in the end plate region as the differential decay index. Based on the preset differential decay index threshold and the differential decay index, divide the solid oxide battery stack into the end plate region and the intermediate uniform region. Step S5: Based on the initial boundary conditions, combined with the multiphysics coupling solution results and the partitioning results, an iterative algorithm is used to calculate the voltage distribution and thermal response characteristics of the solid oxide battery stack under dynamic load.

[0009] Compared with existing technologies, the electrochemical performance analysis method for solid oxide fuel cells based on a one-dimensional beaded model of this invention has the following advantages: This invention, through the core architecture of constructing a one-dimensional beaded model, systematically applies the concept of distributed analysis to the performance evaluation of solid oxide battery stacks for the first time, realizing the distributed quantification of multi-physics parameters along the flow channel direction and the height direction of the solid oxide battery stack. By simulating the real continuous current path through the series-connected beaded units, the physical nature of the internal electrical connections of the solid oxide battery stack can be more realistically reflected, significantly improving the analysis accuracy. At the same time, the introduction of initial boundary conditions based on the three-dimensional finite element model and partitioning results based on the differential decay index distinguishes the endplate region that is significantly affected by the endplate effect, reducing the area involved in subsequent calculations and helping to improve computational efficiency. This allows for a clever balance between computational efficiency and model fidelity while ensuring accuracy, making it possible to conduct rapid analysis of industrial-grade large-size battery stacks under dynamic loads, achieving a balance between efficiency and accuracy and characterizing the multi-physics spatiotemporal evolution characteristics of solid oxide battery stacks under dynamic loads.

[0010] In one possible implementation, in step S1, each beaded unit is discretized into multiple control bodies of equal size along the flow channel direction using the finite volume method, wherein the parameters of each control body are obtained by solving the laws of conservation of mass, momentum, energy and charge.

[0011] Compared with existing technologies, the above-mentioned technical solution can ensure that the one-dimensional beaded model strictly follows the four conservation laws of mass, momentum, energy and charge at the microscopic discrete scale. This discretization method based on the control volume provides a solid mathematical and physical foundation for the subsequent accurate solution of multi-physics coupling equations, fundamentally guaranteeing the physical rationality and numerical stability of the model prediction results. It is the key technical cornerstone for improving the prediction accuracy of the entire method.

[0012] In one possible implementation, during the parameter solving process of each of the control bodies in step S1, the Newton-Raphson iteration algorithm is used to establish the electrical characteristic correlation between each of the control bodies so that the voltage within each of the control bodies is consistent, and the sum of the currents of all the control bodies is equal to the total current of the beaded unit to which they belong.

[0013] Compared with existing technologies, the above-mentioned technical solution can forcibly guarantee the consistency of the internal electrical characteristics of solid oxide battery stacks. The Newton iteration algorithm makes the voltage of all discrete control bodies in the same beaded unit equal through iteration, and the sum of their currents is strictly equal to the total current of the beaded unit. This effectively simulates the physical characteristics of a real bipolar plate as an equipotential body, avoids the problem of local charge non-conservation that may be introduced by discretization, and thus significantly improves the accuracy and reliability of the model in predicting voltage distribution and current density distribution.

[0014] In one possible implementation, in step S2, when simulating the flow field and thermal field of the inlet region of the solid oxide battery stack using the three-dimensional finite element model, the local physical quantities of the YZ cross section of the repeating unit air inlet are integrated globally using the plane averaging method, and then divided by the total area of ​​the YZ cross section to obtain a single scalar boundary parameter adapted to the one-dimensional beaded model. The flow field and thermal field of the inlet region are simulated based on the single scalar boundary parameter.

[0015] Compared with existing technologies, the above technical solution can achieve lossless and efficient transfer of key information between high-dimensional and low-dimensional models. The planar averaging method can reasonably condense the surface distribution parameters obtained from the three-dimensional simulation into a representative scalar value at the entrance of each bead unit. This not only makes full use of the advantages of the three-dimensional finite element model in capturing the complex distribution details of the entrance, providing a high-fidelity input starting point for the subsequent one-dimensional bead model, but also ensures the high efficiency and high accuracy of the overall solution.

[0016] In one possible implementation, in step S3, the solution of the electrochemical reaction model includes the calculation of activation polarization loss, ohmic polarization loss, and concentration polarization loss; the solution of the mass conservation model describes the concentration changes of hydrogen, oxygen, and water vapor by coupling the electrochemical reaction rate; the solution of the energy conservation model integrates electrochemical reaction heat, ohmic-joule heat convection, and radiative heat transfer; the momentum conservation model is used to characterize the fluid flow law in the flow channel and porous electrode, which is described by the Navier-Stokes equation in the flow channel and manifold, and by the Brinkman equation with Darcy drag term correction in the porous electrode.

[0017] Compared with existing technologies, the above-mentioned technical solution can simultaneously solve the electrochemical reactions covering three types of polarization losses (activation, ohm, and concentration), the gas composition changes of coupled reaction rates, the energy conservation of multiple heat sources and heat transfer methods, and the description of fluid flow laws in the flow channels and porous electrodes. This can highly reproduce the complex process of strong coupling of multiple fields (electrochemical, thermal, and mass) in the actual operation of solid oxide battery stacks. This allows it not only to predict macroscopic performance but also to deeply reveal the mechanism of mutual influence and synergistic evolution of various internal physical quantities, providing profound insights for optimized design and fault diagnosis.

[0018] In one possible implementation, in step S3, the activation polarization loss is correlated with the average current density of each of the beaded units via the Butler-Wolmer equation.

[0019] Compared with existing technologies, the above-mentioned technical solution can provide an accurate first-principles-based mathematical description of electrochemical reaction kinetics. The Butler-Wolmer equation is the core equation of electrochemical kinetics. Using this equation instead of empirical formulas allows the model to more fundamentally reflect the relationship between the rate of charge transfer steps and the overpotential, which greatly improves the accuracy and universality of predicting electrochemical response characteristics under varying operating conditions.

[0020] In one possible implementation, in step S3, the ohmic polarization loss is calculated by multiplying the total ohmic resistance of a single beaded unit consisting of the fuel electrode electronic resistance, the air electrode electronic resistance, and the electrolyte ion resistance with the operating current.

[0021] Compared with existing technologies, the above-mentioned technical solution can achieve a refined consideration of multiple ohmic resistances such as electronic conduction, ion conduction and interfacial contact. By taking into account the electronic resistance of the fuel electrode and the air electrode and the ionic resistance of the electrolyte, the contribution of different component materials and microstructures to the total ohmic polarization loss can be distinguished. This helps to accurately locate performance bottlenecks and provides direct and quantitative guidance for the material selection and structural optimization of solid oxide battery stacks.

[0022] In one possible implementation, in step S3, the concentration polarization loss is calculated based on the functional electrode thickness, the effective diffusion coefficient of the gas component, and the concentration coefficient. The effective diffusion coefficient is determined by the ratio of tortuosity to porosity, the intrinsic molecular diffusion coefficient, and the Knudsen diffusion coefficient.

[0023] Compared with existing technologies, the above-mentioned technical solution can take into account the complex mass transfer process inside the porous electrode. By introducing a mass transfer model determined by the functional electrode thickness, effective diffusion coefficient and concentration coefficient, the concentration gradient of the reactant gas in the depth direction of the electrode and the resulting voltage loss can be accurately predicted. This is crucial for evaluating the impact of electrode microstructure on performance. In particular, when concentration polarization loss becomes the main limiting factor under high current density or low fuel utilization conditions, the predictive advantage of this model is more obvious.

[0024] In one possible implementation, in step S4, when the differential attenuation index is greater than the differential attenuation index threshold, the corresponding beaded unit is assigned to the end plate region; when the differential attenuation index is not greater than the differential attenuation index threshold, the corresponding beaded unit is assigned to the intermediate uniform region.

[0025] Compared with existing technologies, the above-mentioned technical solution can automatically identify non-uniform regions significantly affected by endplate effects and relatively uniform central regions in solid oxide battery stacks by setting a clear differential decay index threshold. This method of determination based on the degree of decay is more scientific and adaptive than the partitioning method that relies on experience or fixed positions, ensuring the rationality of the partitioning results and the effectiveness of the model simplification strategy. Attached Figure Description

[0026] Figure 1 This is a flowchart of the steps of the present invention; Figure 2 This is a schematic diagram illustrating the construction of the one-dimensional beaded model of the present invention, wherein, Figure 2 (a) in the text represents the SOC reaction mechanism. Figure 2 (b) in the diagram represents the finite volume discretization of a single beaded element along the flow direction. Figure 2 (c) in the figure represents a beaded unit connected in series along the height of the fuel cell stack; Figure 3 This is a schematic diagram illustrating the construction of the three-dimensional finite element model of the present invention, wherein, Figure 3 (a) in the text indicates the fuel cell stack assembly method. Figure 3 In the diagram, (b) represents the fuel cell stack geometry. Figure 3 (c) in the text indicates the fuel cell stack air intake method; Figure 4 This is a schematic diagram of the solid oxide electrochemical performance testing system of the present invention; Figure 5 This is a schematic diagram showing the results of the voltage test of the fuel cell stack region according to the present invention, wherein, Figure 5 (a) in the diagram represents a test schematic. Figure 5 (b) in the diagram represents the output voltage verification schematic in SOFC mode. Figure 5 (c) in the diagram represents the output voltage verification diagram in SOEC mode. Detailed Implementation

[0027] First, those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention. Those skilled in the art can make adjustments as needed to adapt to specific application scenarios.

[0028] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0029] See Figure 1 This invention discloses a method for analyzing the electrochemical performance of solid oxide fuel cells based on a one-dimensional beaded model, comprising the following steps: Step S1: Discretize the solid oxide battery stack into multiple beaded units in the flow channel direction. Each beaded unit corresponds to a repeating unit in the solid oxide battery stack. The beaded units are connected in series along the height direction of the solid oxide battery stack to form a continuous current path to form a one-dimensional beaded model. Step S2: Model the solid oxide battery stack to obtain a three-dimensional finite element model and simulate the flow field and thermal field of the inlet region of the solid oxide battery stack using the three-dimensional finite element model. Extract the inlet gas composition, flow rate and temperature of each bead unit as the initial boundary conditions of the one-dimensional bead model. Step S3: In each beaded unit, the electrochemical reaction model, mass conservation model, energy conservation model, and momentum conservation model are coupled and solved to obtain the multiphysics coupling solution result; Step S4: Calculate the voltage difference between two adjacent beaded units, and define the ratio of the voltage difference to the maximum voltage difference in the end plate region as the differential decay index. Based on the preset differential decay index threshold and differential decay index, divide the solid oxide battery stack into the end plate region and the intermediate uniform region. Step S5: Based on the initial boundary conditions, combined with the multiphysics coupling solution results and partitioning results, an iterative algorithm is used to calculate the voltage distribution and thermal response characteristics of the solid oxide battery stack under dynamic load.

[0030] See Figure 2 In this embodiment of the invention, the reaction mechanism of the solid oxide battery stack is as follows: Figure 2 As shown in (a), in the one-dimensional beaded model constructed in step S1, each bead unit represents a repeating unit, and spatial discretization needs to be performed using the finite volume method along the flow direction within the channel. Figure 2 As shown in (b), these beaded units are connected in series along the height direction of the solid oxide battery stack to form a complete stacked structure, as shown in [image]. Figure 2 As shown in (c) in the figure.

[0031] In this embodiment of the invention, a coupled model of electrochemical reactions and various transport processes within the repeating unit is established using the finite volume method. Given that the gas in the fuel channel and the air channel flows in the same direction, the repeating unit is discretized into control volumes of equal size along the gas flow direction. The computational domain of each control volume includes a single cell, a channel, and a bipolar plate. It should be noted that the control volume is the core unit for deriving the general model equation based on the conservation law. That is, the parameters of the control volume are mainly solved by the conservation law, and the output parameters of a certain control volume and the input parameters of the subsequent control volume all satisfy the continuity condition in terms of mass flow rate, pressure, component concentration, temperature, and current density.

[0032] In this embodiment of the invention, step S3 involves solving the electrochemical reaction model, including calculating activation polarization loss, ohmic polarization loss, and concentration polarization loss; solving the mass conservation model describes the concentration changes of hydrogen, oxygen, and water vapor by coupling the electrochemical reaction rate; solving the energy conservation model integrates electrochemical reaction heat, ohmic Joule heat convection, and radiative heat transfer; during actual operation, factors such as the diffusion resistance of reacting gases and contact resistance can cause the actual single-cell potential to deviate from the Nernst ideal electromotive force, and this potential deviation is specifically manifested in three types of polarization losses: activation polarization loss... (Caused by charge transfer resistance), Ohmic polarization loss (Including ohmic resistance to electron-ion transfer and interfacial contact resistance) and concentration polarization loss (Caused by mass transfer limitation of the reactant gas along the flow direction), total voltage of a single cell Equation (1) is defined as the result of the above-mentioned polarization loss, and the reversible electromotive force. The difference (i.e., the Nernst ideal electromotive force): ; It should be noted that the dual-mode operation of solid oxide fuel cells / electrolytes (SOFC / SOEC) is determined by the operating current. The decision, specifically, This corresponds to the SOFC runtime mode. This corresponds to the SOEC operating mode; The formula for calculating reversible electromotive force is: ; in, Represents the universal gas constant. Denotes Faraday's constant. Indicates temperature. Indicates the partial pressure of each component. Let represent the minimum Gibbs free energy change required to drive the reaction at a given temperature. In SOEC operation mode, the energy consumption per unit charge of the reaction is calculated according to equation (3): ; in, The molar Gibbs free energy change of a reaction is represented by the molar enthalpy change. Subtract temperature With the molar entropy change of the reaction The product of Indicates the number of electrons transferred in the reaction; In SOFC operating mode , The negative value is due to the heat released during the oxidation of hydrogen, i.e., molar enthalpy change. With negative values Together, they facilitated the spontaneous occurrence of hydrogen oxidation during fuel cell operation; It should be noted that the thermal neutral voltage The enthalpy change represents the amount of charge per unit of reaction and is used to determine the thermal state of a single cell. Its calculation formula is shown in equation (4): ; The Butler-Wolmer equation is used to characterize charge transfer dynamics, which establishes the relationship between activation polarization loss and average current density of a single cell. The quantitative relationship between them is expressed as follows: ; ; in, and These are the currents at the fuel electrode and the air electrode, respectively. Represents the exchange current density. This represents the charge transfer coefficient, with the subscripts fuel and air corresponding to the fuel flow path and air flow path, respectively. Indicates the number of electrons transferred in the reaction. Indicates activation polarization loss; Exchange current density at the fuel electrode Exchange current density with air electrode It can be expressed by the following formula: ; ; in, and An empirical constant used to fit numerical calculation results to experimental data. This represents the actual partial pressure of the corresponding gas component. It can represent or , This represents the reference partial pressure of each gas component. The formula for calculating this reference partial pressure is: ; in, It refers to the pre-factor. Indicates activation energy. Indicates surface site density, Indicates the adhesion probability. This indicates the molecular weight of the relevant gas.

[0033] In this embodiment of the invention, the concentration polarization of the fuel electrode Concentration polarization of air It can be calculated from the following equations (10) and (11): ; ; in, and For the thickness of the functional electrode, The effective diffusion coefficient of a gaseous component is determined by the ratio of tortuosity to porosity, the intrinsic molecular diffusion coefficient, and the Knudsen diffusion coefficient. Indicates penetration rate. This represents the concentration coefficient.

[0034] In this embodiment of the invention, ohmic polarization loss The calculation formula is as follows: ; in, This indicates the total ohmic resistance of a single bead unit, encompassing the electronic resistance of the fuel electrode, the electronic resistance of the air electrode, and the ion resistance of the electrolyte.

[0035] In this embodiment of the invention, step S1 uses the Newton-Raphson iterative algorithm to establish the electrical characteristic correlation between each control body, ensuring that the voltage within each control body is consistent, and that the sum of the currents of all control bodies equals the total current of their respective beaded units. This algorithm only needs to iterate over the unified target voltage of a single cell. The target voltage updated after the next iteration It can be calculated using the following formula: ; in, For the first During the nth iteration The voltage of each control unit; The mass conservation of each gaseous component is determined by the balance between the storage term and the convective inflow / outflow term affected by electrochemical reactions, and its expression is: ; in, and These are the inlet and outlet molar flow rates of the gas, respectively. and These represent the inlet and outlet mole fractions of the gas components, respectively. The electrochemical reaction rate of the gaseous component is the total amount of gas in the flow channel. The ideal gas law is satisfied, as shown in equation (15) below: ; The heat balance within the repeating unit is determined by both internal heat generation and external heat dissipation from the stack. This heat balance determines the dynamic temperature response characteristics of the repeating unit. For water electrolysis, the energy conservation equations for the gas in the fuel channel and air channel, the single cell, and the bipolar plate correspond to equations (16) to (19), respectively. ; ; The left-hand side of the equation above represents the rate of change of the temperature of the mixed gas in the flow channel with time; the first term on the right-hand side is the convective transport term of the mixed gas along the flow channel, the second term is the convective heat transfer term between the mixed gas and the single cell electrode, and the third term is the convective heat transfer term between the mixed gas and the bipolar plate. It should be noted that, Indicates the flow rate of the mixed gas. Indicates the convective heat transfer coefficient. Indicates the density of the mixed gas. This represents the specific heat capacity at constant pressure, while and The width and height of the flow channel are respectively represented by the subscripts fuel, air, cell, and cha, which correspond to the fuel flow channel, air flow channel, single cell, and flow channel, respectively. The following calculations are then performed: ; The first term on the right-hand side of the equation represents the internal heat conduction of a single-cell module (including electrodes and electrolyte layers); the second and third terms correspond to the convective heat transfer between the single cell and the mixed gas (fuel gas and air); the fourth term is the irreversible overpotential heat generation; and the fifth term is the radiative heat transfer between the single cell and the bipolar plates. Thermal conductivity, It is the Stefan-Boltzmann constant. For the emission rate, the following calculations are then performed: ; The first term on the right side of the equation represents the heat conduction of the bipolar plate; the second and third terms correspond to the convective heat transfer between the bipolar plate and the mixed gas (fuel gas and air), respectively; and the fourth term represents the radiative heat transfer between the bipolar plate and the single cell. It should be noted that in this invention, the radiative heat transfer between the bipolar plate and the single cell is regarded as a surface-to-surface heat transfer between adjacent parallel surfaces. The small distance between the two surfaces and their flat plate structure make this path the dominant radiative heat transfer mode between the two types of solid components.

[0036] In this embodiment of the invention, to address the non-uniformity of the stack along its height, a Differential Decay Index (DDI) is further proposed as a partitioning method. This method constructs an evaluation strategy that combines refined modeling of the endplate region with simplified merging of the central uniform region. This strategy can capture the non-uniform voltage distribution caused by endplate edge effects and adapt to the characteristics of the central region of the stack, thereby further optimizing the beaded connection model. Compared to other empirical partitioning methods, DDI can establish a quantitative partitioning standard based on the relative decay of the voltage difference between adjacent cells. Compared to the absolute voltage difference method, this index provides a unified evaluation benchmark for voltage distribution analysis of stacks of different sizes through normalization, eliminating the inconsistency in evaluation standards caused by differences in the total voltage of the stack or the number of stacked cells. Unlike global statistical indicators such as the coefficient of variation, DDI is more sensitive to local voltage gradients and can effectively characterize the transition characteristics from significant voltage fluctuations in the endplate region to voltage decay in the central region, rather than simply quantifying the overall voltage dispersion of the stack. As mentioned above, DDI is defined as the ratio of the voltage difference between adjacent cells to the maximum inter-cell voltage difference near the endplate, and its calculation formula is as follows: ; ; in, It is the maximum inter-cell voltage difference observed within the area affected by the bottom plate. The first in the fuel cell stack The voltage of a single cell should be noted; taking the absolute value can eliminate the influence of positive and negative voltage differences. When DDI≤0.1 (the difference attenuation index threshold is set to 0.1), the beaded unit is determined to belong to the uniform region, indicating that the influence of the end plate edge effect has been attenuated to an acceptable level, and this judgment standard conforms to mature engineering practices. Therefore, the total voltage of the fuel cell stack It can be calculated using the following formula: ; in, It is the first Repeating units (counted from bottom to top). It is the total number of repeating units. ; The number of repeating units in the bottom plate region, the middle uniform region, and the top plate region, respectively.

[0037] In this embodiment of the invention, the assumptions of the one-dimensional beaded model are as follows: gas transport in the flow channel is mainly dominated by convection along the flow direction (x direction), and diffusion and mass transfer processes in the transverse plane (y, z directions) of the single cell are ignored; it is assumed that the flow is a fully developed laminar flow; it is assumed that the bipolar plate is an ideal conductor, so the potential is uniformly distributed in all finite volumes (i.e., single cells) of a single repeating unit along the flow direction; at the same time, it is assumed that the spatial average parameters (such as mass flow rate and temperature) at the intake manifold are derived from the three-dimensional finite element stack model and used as the input conditions for each repeating unit in the one-dimensional beaded model. The performance difference of the solid oxide battery stack along the height direction mainly stems from the non-uniformity of the inlet state of each repeating unit, including the spatial non-uniformity of the intake components, flow rate and temperature.

[0038] In this embodiment of the invention, the overall boundary conditions of the one-dimensional beaded model are set as follows: the global input conditions (including stack operating current, gas pressure, total mass flow rate, and inlet temperatures of fuel-side and air-side gases) are all taken from experimentally set parameters; in addition, the inlet boundary parameters (including inlet gas component mole fraction, gas flow rate, and temperature) of each beaded unit (or single cell) in the one-dimensional beaded model are all derived from the prediction results of the three-dimensional finite element model. This three-dimensional finite element model is used to simulate the inlet gas distribution and heat transfer process under the initial steady state before the stack load changes, capture the local gas component and temperature distribution characteristics, and then obtain the detailed state parameters of the inlet of each repeating unit at different positions along the height direction of the solid oxide battery stack.

[0039] In this embodiment of the invention, the one-dimensional beaded model is a lumped performance mapping model, which can achieve efficient evaluation and analysis at the stack level; the three-dimensional finite element model in step S2 is constructed with reference to the actual structure of a solid oxide battery stack, as shown below. Figure 3 As shown in (b) above, the assembly method is as follows: Figure 3 As shown in (a) above, the air intake method is as follows: Figure 3 As shown in (c), the geometric parameters are completely consistent with the 39-cell solid oxide battery experimental stack from Elcogen in Estonia. The stack is assembled by stacking basic repeating units step by step. Each repeating unit contains a single cell, a metal frame, bipolar plates, and seals. The materials of each component of the stack are as follows: the bipolar plates are made of Crofer 22 APU alloy, the end plates and structural frame are made of SUS 310 stainless steel, the seals are made of Flexitallic 866 gaskets, and the single cell is a multi-layer ceramic structure: a dense 8% molar yttrium-stabilized zirconium oxide (8YSZ) electrolyte layer with a nickel-8YSZ fuel electrode on one side and gadolinium-doped cerium dioxide on the other side. (GDC) diffusion barrier layer and strontium-doped lanthanum cobalt oxide ( The core electrochemical reactions of the solid oxide battery stack (LSC) air electrode (hydrogenation reaction in SOFC mode and steam electrolysis reaction in SOEC mode) all occur at the three-phase interface within the porous electrode of a single cell. It should be noted that the solid oxide battery stack in this invention adopts a co-current arrangement.

[0040] In this embodiment of the invention, a three-dimensional finite element model of a 39-cell single-cell fuel cell stack is first constructed in COMSOL Multiphysics software, and a corresponding computational mesh is generated. By solving the coupled fluid dynamics and conjugate heat transfer equations, the velocity distribution and temperature gradient within the intake manifold are quantified. Subsequently, the local physical quantities of the YZ cross-section of the intake port of each repeating unit are analyzed. The planar averaging algorithm (see Equation (24)) is used to process the local physical quantities distributed in two-dimensional space. The dimensionality is reduced to a single scalar value, which serves as the entry boundary parameter for the previously discussed one-dimensional beaded model. This scalar value is obtained using the following formula: ; in, This represents the total cross-sectional area of ​​the intake section in the yz plane of the repeating unit. and These are the differential length elements along the y and z directions in the yz plane, respectively. In this embodiment of the invention, the one-dimensional beaded model is implemented in MATLAB / Simulink software. It should be noted that each beaded unit embeds partial differential equations (PDEs) describing the multiphysics coupling process. A variable-step rigid solver is used for time integration, implicitly satisfying algebraic constraints such as current conservation within each time step. This one-dimensional beaded model can obtain the time-varying parameters of each repeating unit at different positions along the flow channel axis. Under a given total current constraint, the Newton-Raphson iteration method is used to solve for the unified terminal voltage of the stack. Through iteration, the sum of the local currents of each repeating unit is matched with the given total current. The final output total voltage of the stack is the series summation of the terminal voltages of each repeating unit.

[0041] In this embodiment of the invention, a solid oxide battery experimental testing system was built to verify the method of the invention. After the system was built, an airtightness test was first carried out. Based on the airtightness test results, the assembly load was determined and an appropriate clamping force was applied to avoid component leakage or structural failure during the operation of the battery stack. The compression airtightness test was completed by calibrating the cylinder pressure. If no continuous bubbles were generated within 10 seconds, the seal was deemed to be intact. The battery stack adopts a frame-type vertical (i.e., in the height direction of the battery stack) pre-tightening assembly system. This system consists of a rectangular metal constraint frame, a double compression spring assembly, and end support components. Specifically, the battery stack is placed in the fitting cavity of the rectangular metal constraint frame, and the double compression spring assembly arranged at both ends of the frame applies a vertical pre-tightening force to the battery stack. Electrochemical testing systems such as Figure 4 As shown, the system mainly includes a mass flow controller, a gas preheater, and a temperature-controlled furnace; current and voltage leads are arranged in a cross pattern, connecting to the electronic load and the potentiostat respectively; during the test, the fuel cell stack is heated to the target temperature at a rate of 2 K / min in the temperature-controlled furnace and maintained at a constant temperature; the system initially uses 5% [temperature missing]. The mixture is used as a protective atmosphere, and then the fuel polar gas source is switched to 50%. The mixed gas was discharged and activated for 60 minutes in the range of 0.9 to 1.0 V average voltage of a single cell through an electronic load. To characterize the performance of the stack and the distribution of internal parameters, the inter-cell voltage was measured at nine typical locations in the 39-cell stack under both SOFC and SOEC modes. The corresponding locations are single cells No. 1, No. 2-7, No. 8-13, No. 14-19, No. 20, No. 21-26, No. 27-32, No. 33-38, and No. 39. Because the stack is compactly assembled and the functional layers are micron-scale structures, the spatial distribution of key internal parameters such as stress distribution and gas phase composition is difficult to determine directly through experiments. Therefore, the model validation focuses on the measurable electrochemical performance of the stack. Specifically, the validation content includes the regional voltage distribution of the 39 stacks in SOFC and SOEC modes predicted by the one-dimensional beaded model. The operating parameters for the stack area voltage test are set as follows: In SOFC mode, the stack operating current is 29.50 A, the hydrogen flow rate at the fuel electrode is 14.50 L / min, and the air electrode inlet flow rate is 70.00 L / min; after switching to SOEC mode, the air electrode flow rate is adjusted to 50.00 L / min, and the fuel electrode atmosphere is switched to contain 2.50 L / min. With 20.00 g / min The wet gas mixture was tested with an operating current set to 61.00 A. The polarization curve was measured using a stepped current regulation + synchronous pressure sampling method. The current change rate was 0.50 A every 20 seconds in SOFC mode and 1.00 A every 20 seconds in SOEC mode. Model validation results show that the root mean square error (RMSE) of the one-dimensional beaded model for predicting the regional voltage is 4.05% in SOFC mode and 3.92% in SOEC mode. Specific data can be found in [link to relevant documentation]. Figure 5 ,in Figure 5 (a) in the diagram represents a test schematic. Figure 5 (b) in the diagram represents the output voltage verification schematic in SOFC mode. Figure 5 (c) in the diagram represents the output voltage verification schematic in SOEC mode. The formula for calculating the root mean square error (RMSE) is as follows: ; in, This indicates relative error.

[0042] In the description of this invention, the references to "one embodiment," "some embodiments," "in this embodiment," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0043] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for analyzing electrochemical performance of a solid oxide stack based on a one-dimensional string-bead model, characterized in that, Includes the following steps: Step S1: Discretize the solid oxide battery stack into multiple beaded units in the flow channel direction. Each beaded unit corresponds to a repeating unit in the solid oxide battery stack. Each beaded unit is connected in series along the height direction of the solid oxide battery stack to form a continuous current path to form a one-dimensional beaded model. Step S2: Model the solid oxide battery stack to obtain a three-dimensional finite element model and simulate the flow field and thermal field of the inlet region of the solid oxide battery stack using the three-dimensional finite element model. Extract the inlet gas composition, flow rate and temperature of each bead unit as the initial boundary conditions of the one-dimensional bead model. Step S3: In each of the beaded units, the electrochemical reaction model, mass conservation model, energy conservation model, and momentum conservation model are coupled and solved to obtain the multiphysics coupling solution result; Step S4: Calculate the voltage difference between two adjacent beaded units, and define the ratio of the voltage difference to the maximum voltage difference in the end plate region as the differential decay index. Based on the preset differential decay index threshold and the differential decay index, divide the solid oxide battery stack into the end plate region and the intermediate uniform region. Step S5: Based on the initial boundary conditions, combined with the multiphysics coupling solution results and the partitioning results, an iterative algorithm is used to calculate the voltage distribution and thermal response characteristics of the solid oxide battery stack under dynamic load.

2. The method according to claim 1, wherein, In step S1, each beaded unit is discretized into multiple control bodies of equal size along the flow channel using the finite volume method. The parameters of each control body are obtained by solving the laws of conservation of mass, momentum, energy, and charge.

3. The method according to claim 2, wherein the one-dimensional string-bead model is based on the following equation: ###0001### where, I is the current, R is the resistance, n is the number of electrons, F is the Faraday constant, C is the concentration of the reactant, A is the electrode area, and v is the reaction rate. In step S1, during the parameter solving process of each control body, the Newton-Raphson iteration algorithm is used to establish the electrical characteristic correlation between each control body so that the voltage within each control body is consistent, and the sum of the currents of all control bodies is equal to the total current of the beaded unit to which they belong.

4. The method for analyzing the electrochemical performance of solid oxide fuel cells based on a one-dimensional beaded model according to claim 1, characterized in that, In step S2, when simulating the flow field and thermal field of the inlet region of the solid oxide battery stack using the three-dimensional finite element model, the local physical quantities of the YZ cross section of the repeating unit air inlet are integrated globally using the plane averaging method and then divided by the total area of ​​the YZ cross section to obtain a single scalar boundary parameter that fits the one-dimensional beaded model. The flow field and thermal field of the inlet region are then simulated based on the single scalar boundary parameter.

5. The method for analyzing the electrochemical performance of solid oxide fuel cells based on a one-dimensional beaded model according to claim 1, characterized in that, In step S3, the solution of the electrochemical reaction model includes the calculation of activation polarization loss, ohmic polarization loss, and concentration polarization loss; the solution of the mass conservation model describes the concentration changes of hydrogen, oxygen, and water vapor by coupling the electrochemical reaction rate; the solution of the energy conservation model integrates electrochemical reaction heat, ohmic-joule heat convection, and radiative heat transfer; the momentum conservation model is used to characterize the fluid flow law in the flow channel and porous electrode. The flow channel and manifold are described by the Navier-Stokes equation, and the porous electrode is characterized by the Brinkman equation with the introduction of Darcy drag term correction.

6. The method for analyzing the electrochemical performance of solid oxide fuel cells based on a one-dimensional beaded model according to claim 5, characterized in that, In step S3, the activation polarization loss is correlated with the average current density of each bead unit via the Butler-Wolmer equation.

7. The method for analyzing the electrochemical performance of solid oxide fuel cells based on a one-dimensional beaded model according to claim 5, characterized in that, In step S3, the ohmic polarization loss is calculated by multiplying the total ohmic resistance of the single beaded unit composed of the fuel electrode electronic resistance, the air electrode electronic resistance, and the electrolyte ion resistance with the operating current.

8. The method for analyzing the electrochemical performance of solid oxide fuel cells based on a one-dimensional beaded model according to claim 5, characterized in that, In step S3, the concentration polarization loss is calculated based on the functional electrode thickness, the effective diffusion coefficient of the gas component, and the concentration coefficient. The effective diffusion coefficient is determined by the ratio of tortuosity to porosity, the intrinsic molecular diffusion coefficient, and the Knudsen diffusion coefficient.

9. The method for analyzing the electrochemical performance of solid oxide fuel cells based on a one-dimensional beaded model according to claim 1, characterized in that, In step S4, when the differential attenuation index is greater than the differential attenuation index threshold, the corresponding beaded unit is assigned to the end plate region; when the differential attenuation index is not greater than the differential attenuation index threshold, the corresponding beaded unit is assigned to the intermediate uniform region.

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