Method and device for analyzing maximum current density of SOEC stack tower under influence of non-uniformity

Abstract

The invention relates to the technical field of electrochemistry, in particular to a method and device for analyzing the maximum current density of an SOEC stack tower under the influence of non-uniformity. The method comprises the following steps: obtaining size data of an SOEC stack tower, wherein the size data comprises the number of battery pieces and the area of a single battery; according to the size data of the SOEC stack tower, the maximum current density of the SOEC stack tower is obtained through output of a preset equivalent circuit model, and the equivalent circuit model is used for indicating the relation between the size data and the maximum current density. The embodiment of the invention provides a method for quantitatively analyzing the influence of the size data on the maximum current density, and the SOEC stack tower can be more effectively designed by understanding the relationship between the size data and the performance of the stack tower so as to achieve higher hydrogen yield and system efficiency.

Description

Technical Field

[0001] The present disclosure relates to the field of electrochemical technology, and in particular to a method and device for analyzing the maximum current density of a solid oxide electrolysis cell (SOEC) stack under the influence of heterogeneity. Background Art

[0002] As the global energy and climate crises become increasingly prominent, exploring sustainable energy conversion, storage and utilization pathways has become critical and urgent. As a clean fuel and widely used chemical raw material, green hydrogen produced by water electrolysis is regarded as the backbone of sustainable energy development.

[0003] Among common electrolysis technologies, SOEC stands out for its high operating temperature, high energy efficiency, and reversible operation capabilities. However, there is still a gap between the scale of SOEC and its commercial application. Unlike low-temperature technologies such as alkaline electrolyzers, whose rated power has reached the megawatt level, the typical capacity of a single SOEC stack is still in the kilowatt level, which is limited by the inherent brittleness of the material and the increasingly serious thermal management problems. Typically, stacks are stacked together to form a stack tower, in which the stacks are connected in series. For example, 6 stacks are put together to form a 180-unit stack tower, and 10 such stack towers are integrated into a module. In addition, increasing the unit area of ​​each layer of the stack tower is another way to scale up.

[0004] At present, although there is a qualitative understanding of the limiting factors of the tower stack during the tower stack scale-up process, the relevant technology has not yet provided a reasonable and effective solution to conduct a clear quantitative analysis thereof. Summary of the invention

[0005] In view of this, the present disclosure proposes a method and device for analyzing the maximum current density of a SOEC stack under the influence of non-uniformity.

[0006] According to one aspect of the present disclosure, a method for analyzing the maximum current density of a SOEC stack under the influence of inhomogeneity is provided, the method comprising:

[0007] Obtaining the dimension data of the SOEC stack tower, wherein the dimension data includes the number of cells and the area of ​​a single cell;

[0008] According to the dimension data of the SOEC stack, a preset equivalent circuit model is used to output the maximum current density of the SOEC stack, and the equivalent circuit model is used to indicate the relationship between the dimension data and the maximum current density.

[0009] In one possible implementation, the equivalent circuit model includes a circuit sub-model and other sub-models, the other sub-models including a flow path sub-model and / or a thermal path sub-model, the flow path sub-model is used to predict the airflow distribution of the fuel side airflow of the SOEC stack tower, the thermal path sub-model is used to predict the temperature distribution of the batteries of the SOEC stack tower, and the circuit sub-model is used to predict the maximum current density of the SOEC stack tower based on the airflow distribution and / or the temperature distribution.

[0010] In another possible implementation, the input parameters of the flow path sub-model include the size data and the total air intake flow of the SOEC stack, and the output parameters of the flow path sub-model include the gas flow of each cell and the gas flow of each manifold section of the SOEC stack.

[0011] In another possible implementation, the input parameters of the thermal circuit model include the size data of the SOEC stack tower and the equivalent heat source of the electrochemical reaction heat release, and the output parameters of the thermal circuit model include the battery center temperature and battery edge temperature of the SOEC stack tower.

[0012] In another possible implementation, the input parameters of the circuit sub-model include the stack voltage of the SOEC stack tower and the battery voltage of a single battery, and the output parameters of the circuit sub-model include the maximum current density of the SOEC stack tower.

[0013] In another possible implementation, the equivalent circuit model is also used to indicate a first mapping relationship between the dimensional data and a non-uniformity index of the SOEC stack, and a second mapping relationship between the non-uniformity index and the maximum current density, wherein the non-uniformity index includes an airflow non-uniformity index and / or a thermal non-uniformity index.

[0014] In another possible implementation, the method further includes:

[0015] Determine the relationship between various size data of the SOEC stack and multiple maximum current densities through the equivalent circuit model;

[0016] According to the relationship between various size data of the SOEC tower and multiple maximum current densities, the target amplification path of the SOEC tower during the amplification process is determined. The target amplification path is to increase the number of cells in the SOEC tower in the first stage and to increase the single cell area of ​​the SOEC tower in the second stage. The first stage is earlier than the second stage.

[0017] According to another aspect of the present disclosure, there is provided a device for analyzing the maximum current density of a SOEC stack under the influence of inhomogeneity, the device comprising:

[0018] An acquisition module is used to acquire the size data of the SOEC stack, wherein the size data includes the number of cells and the area of ​​a single cell;

[0019] A processing module is used to obtain the maximum current density of the SOEC stack tower according to the size data of the SOEC stack tower using a preset equivalent circuit model output, wherein the equivalent circuit model is used to indicate the relationship between the size data and the maximum current density.

[0020] In one possible implementation, the equivalent circuit model includes a circuit sub-model and other sub-models, the other sub-models including a flow path sub-model and / or a thermal path sub-model, the flow path sub-model is used to predict the airflow distribution of the fuel side airflow of the SOEC stack tower, the thermal path sub-model is used to predict the temperature distribution of the batteries of the SOEC stack tower, and the circuit sub-model is used to predict the maximum current density of the SOEC stack tower based on the airflow distribution and / or the temperature distribution.

[0021] In another possible implementation, the input parameters of the flow path sub-model include the size data and the total air intake flow of the SOEC stack, and the output parameters of the flow path sub-model include the gas flow of each cell and the gas flow of each manifold section of the SOEC stack.

[0022] In another possible implementation, the input parameters of the thermal circuit model include the size data of the SOEC stack tower and the equivalent heat source of the electrochemical reaction heat release, and the output parameters of the thermal circuit model include the battery center temperature and battery edge temperature of the SOEC stack tower.

[0023] In another possible implementation, the input parameters of the circuit sub-model include the stack voltage of the SOEC stack tower and the battery voltage of a single battery, and the output parameters of the circuit sub-model include the maximum current density of the SOEC stack tower.

[0024] In another possible implementation, the equivalent circuit model is also used to indicate a first mapping relationship between the dimensional data and a non-uniformity index of the SOEC stack, and a second mapping relationship between the non-uniformity index and the maximum current density, wherein the non-uniformity index includes an airflow non-uniformity index and / or a thermal non-uniformity index.

[0025] In another possible implementation manner, the device further includes: a determining module, configured to:

[0026] Determine the relationship between various size data of the SOEC stack and multiple maximum current densities through the equivalent circuit model;

[0027] According to the relationship between various size data of the SOEC tower and multiple maximum current densities, the target amplification path of the SOEC tower during the amplification process is determined. The target amplification path is to increase the number of cells in the SOEC tower in the first stage and to increase the single cell area of ​​the SOEC tower in the second stage. The first stage is earlier than the second stage.

[0028] According to another aspect of the present disclosure, there is provided a device for analyzing the maximum current density of a SOEC stack under the influence of inhomogeneity, the device comprising:

[0029] processor;

[0030] a memory for storing processor-executable instructions;

[0031] The processor is configured to implement the above method when executing the instructions stored in the memory.

[0032] According to another aspect of the present disclosure, a non-volatile computer-readable storage medium is provided, on which computer program instructions are stored, wherein the computer program instructions implement the above method when executed by a processor.

[0033] According to another aspect of the present disclosure, a computer program product is provided, including a computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in a processor of a computing device, the processor in the computing device executes the above method.

[0034] The disclosed embodiment obtains the dimensional data of the SOEC tower, which includes the number of cells and the area of ​​a single cell; based on the dimensional data of the SOEC tower, a preset equivalent circuit model is used to output the maximum current density of the SOEC tower, and the equivalent circuit model is used to indicate the relationship between the dimensional data and the maximum current density; that is, a method is provided to quantitatively analyze the effect of the dimensional data on the maximum current density, and by understanding the relationship between the dimensional data and the tower performance, the SOEC tower can be designed more effectively to achieve higher hydrogen yields and system efficiency. Optimized tower design can reduce material usage and improve energy efficiency, thereby reducing the overall cost of the system. In short, this method provides a scientific and technical support for the design and operation of the SOEC tower, which helps to promote the development and application of solid oxide electrolysis technology.

[0035] Further features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the disclosure and, together with the description, serve to explain the principles of the disclosure.

[0037] Figure 1 A schematic diagram of the structure of a computing device provided by an exemplary embodiment of the present disclosure is shown.

[0038] Figure 2 A flow chart showing a method for analyzing the maximum current density of a SOEC stack under the influence of non-uniformity provided by an exemplary embodiment of the present disclosure.

[0039] Figure 3 A schematic diagram showing the scale-up process of the SOEC stack.

[0040] Figure 4 A schematic diagram of a flow path sub-model of a SOEC stack tower provided by an exemplary embodiment of the present disclosure is shown.

[0041] Figure 5 A schematic diagram of a thermal path model of a SOEC stack tower provided by an exemplary embodiment of the present disclosure is shown.

[0042] Figure 6 A schematic diagram of a circuit sub-model of a SOEC stack tower provided by an exemplary embodiment of the present disclosure is shown.

[0043] Figure 7 A schematic diagram showing the relationship between an equivalent path model and a multi-physics field model provided by an exemplary embodiment of the present disclosure.

[0044] Figure 8 A schematic diagram showing circuit equations, flux, potential, and resistance terms of an equivalent circuit model provided by an exemplary embodiment of the present disclosure is shown.

[0045] Fig. 9 A schematic diagram of a flow path sub-model provided by an exemplary embodiment of the present disclosure is shown.

[0046] Fig.10 A schematic plan view of a simplified thermal circuit model provided by an exemplary embodiment of the present disclosure is shown.

[0047] Fig.11 A schematic diagram showing test results provided by an exemplary embodiment of the present disclosure is shown.

[0048] Fig.12 A schematic diagram showing the relationship between the maximum current density and the area specific power provided by an exemplary embodiment of the present disclosure, and the influence of different single cell areas on the non-uniformity.

[0049] Fig.13A contour map of the maximum thermal gradient in the z direction and the xy plane provided by an exemplary embodiment of the present disclosure is shown.

[0050] Fig.14 A schematic diagram showing the maximum number of cells connected in series and their corresponding steam utilization and maximum thermal gradient under two conditions provided by an exemplary embodiment of the present disclosure is shown.

[0051] Fig.15 A schematic diagram showing a comparison between an explicit analytical expression provided by an exemplary embodiment of the present disclosure and a numerical result of a circuit equation is shown.

[0052] Fig.16 A design-performance diagram of a stack tower provided by an exemplary embodiment of the present disclosure is shown.

[0053] Fig.17 A schematic structural diagram of a device for analyzing the maximum current density of a SOEC stack under the influence of heterogeneity provided by an exemplary embodiment of the present disclosure is shown.

[0054] Fig.18 It is a block diagram of a device for analyzing the maximum current density of a SOEC stack under the influence of non-uniformity according to an exemplary embodiment. DETAILED DESCRIPTION

[0055] Various exemplary embodiments, features and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0056] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0057] In addition, in order to better illustrate the present disclosure, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present disclosure can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the subject matter of the present disclosure.

[0058] SOEC has the characteristics of high energy efficiency, but the current module (kW, tens of kW level) and system (hundreds of kW level) scale are still far from supporting commercial use in the field of electric-hydrogen coupling. Modularization is an important path for SOEC to scale up. The series integrated stack tower formed by stacking multiple batteries and stacks is the general idea in the early stage of SOEC module scale-up. The module scale can be enlarged by increasing the single cell area and the number of cells. Limited by materials and high temperatures, the integrated scale-up of single hot zone stack tower modules is an important engineering problem, and the enhanced non-uniformity after integration is the main limiting factor. There is a qualitative understanding of this, but there is a lack of in-depth quantitative analysis and law revelation. Multi-physics models widely used in stack-level research can accurately simulate the non-uniformity of stack towers. However, their complex form and high computational cost hinder the investigation of the effects of various operating and geometric parameters (such as current density, number of series batteries, and single cell area).

[0059] In order to solve the above technical problems, the embodiment of the present disclosure analyzes the impact of inhomogeneity on performance during the SOEC tower amplification process and reveals the target amplification path. To this end, an equivalent circuit sub-model (coupled fluid-thermal-electric equivalent circuit sub-model) is proposed, which reduces the computational cost of the model by more than three orders of magnitude compared to the multi-physics model in the related art, with an error of less than 0.8%. The circuit elements of the model are identified and extended to towers of different sizes and operating conditions. In addition, using this model, explicit analytical expressions for inhomogeneity indicators (i.e., airflow and thermal gradient) and corresponding maximum current density are derived, which quantify the relationship between the maximum current density and the size data. The accuracy is verified by experimental results and 3D simulation results. According to the model, the maximum current density of the SOEC tower will decrease during the amplification process due to enhanced fluid and thermal inhomogeneity. That is, the embodiment of the present disclosure quantifies the relationship between the maximum current density and the size of the SOEC tower, and also reveals the target amplification path to improve the economy, providing an optimized combination of the number of series cells and the area of ​​a single cell for towers of different sizes.

[0060] First, the execution subject involved in this disclosure is introduced. Figure 1 , which shows a schematic diagram of the structure of a computing device provided by an exemplary embodiment of the present disclosure.

[0061] The computing device can be a terminal or a server. The terminal includes a mobile terminal or a fixed terminal, such as a mobile phone, a tablet computer, a laptop computer, a desktop computer, etc. The server can be a server, a server cluster consisting of several servers, or a cloud computing service center.

[0062] The computing device includes a processor 10, a memory 20, and a communication interface 30. Those skilled in the art will appreciate that Figure 1 The structure shown in the figure does not constitute a limitation on the computing device, and may include more or fewer components than shown in the figure, or combine certain components, or arrange the components differently.

[0063] The processor 10 is the control center of the computing device, and uses various interfaces and lines to connect various parts of the entire computing device. By running or executing software programs and / or modules stored in the memory 20, and calling data stored in the memory 20, the processor 10 performs various functions of the computing device and processes data, thereby controlling the computing device as a whole. The processor 10 can be implemented by a central processing unit (CPU) or a graphics processing unit (GPU).

[0064] The memory 20 can be used to store software programs and modules. The processor 10 executes various functional applications and data processing by running the software programs and modules stored in the memory 20. The memory 20 may mainly include a program storage area and a data storage area, wherein the program storage area may store an operating system 21, an acquisition module 22, a processing module 23, and an application 24 required for at least one function, etc.; the data storage area may store data created according to the use of the computing device, etc. The memory 20 may be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as a static random access memory (SRAM), an electrically erasable programmable read-only memory (EEPROM), an erasable programmable read-only memory (EPROM), a programmable read-only memory (PROM), a read-only memory (ROM), a magnetic memory, a flash memory, a magnetic disk or an optical disk. Accordingly, the memory 20 may further include a memory controller to provide the processor 10 with access to the memory 20 .

[0065] Among them, the processor 10 performs the following functions by running the acquisition module 22: obtaining the size data of the SOEC stack tower, the size data including the number of battery cells and the area of ​​a single battery; the processor 10 performs the following functions by running the processing module 23: according to the size data of the SOEC stack tower, the maximum current density of the SOEC stack tower is obtained by using the preset equivalent circuit model output, and the equivalent circuit model is used to indicate the relationship between the size data and the maximum current density.

[0066] Below, several exemplary embodiments are used to introduce the analysis method of the maximum current density of the SOEC tower under the influence of non-uniformity provided by the embodiments of the present disclosure, the structure of the SOEC tower, the equivalent circuit sub-model, the derivation of explicit expressions, the model verification results, the influence of non-uniformity on the tower performance during the amplification process, and the target amplification path of the SOEC tower.

[0067] Please refer to Figure 2 , which shows a flow chart of a method for analyzing the maximum current density of a SOEC stack under the influence of non-uniformity provided by an exemplary embodiment of the present disclosure. This embodiment uses this method for Figure 1 The method is illustrated by using the computing device shown in FIG.

[0068] Step 201, obtaining the dimension data of the SOEC stack, the dimension data including the number of cells and the area of ​​a single cell.

[0069] The SOEC stack is an integrated system consisting of multiple solid oxide electrolysis units (cells), which is formed into a highly efficient hydrogen generation device by stacking these individual stacks and installing distribution manifolds on the inlet and outlet sides.

[0070] The number of cells in a SOEC stack is also called the number of cells in series, which is directly related to the ability of the entire system to produce hydrogen, that is, the magnitude of the current. Generally speaking, the more cells there are, the greater the current generated by the system, and the higher the amount of hydrogen that can be produced. Increasing the number of cells can increase the total power, but it will also bring higher costs and more complex system integration issues.

[0071] The single cell area refers to the effective electrolysis area of ​​a single electrolyzer, which affects the electrolysis efficiency and the rate of hydrogen production. In theory, the larger the single cell area, the more hydrogen is produced per unit time. However, in practice, the design of the single cell area needs to consider a variety of factors including material properties, thermal management, and mechanical stability. An excessively large single cell area may lead to uneven temperature distribution and increase manufacturing costs.

[0072] Multiple SOC batteries are stacked to form a single SOC battery stack. There are conductive end plates on the top and bottom of the battery stack. Multiple battery stacks are stacked and distribution manifolds are installed on the inlet and outlet sides to form a multi-stack integrated stack tower module, namely the SOEC stack tower. Figure 3 As shown, it shows the enlarged process of the SOEC stack. Figure 3 (a) shows the geometry of a single cell and a cross-section of a flow channel unit, (b) shows the geometry of a single stack, and (c) shows the geometry of a SOEC tower with a manifold.

[0073] The SOEC stack tower involved in the embodiment of the present disclosure is a planar co-flow design. A single battery can be composed of 23 flow channel units in the y direction. Figure 3 As shown in (a), a flow channel unit includes an interconnector, a flow channel, an air electrode, a fuel electrode and a solid electrolyte. A stack is obtained by stacking several cells and connecting them in series. Repeating the same process can obtain a stack tower with N cells, N is a positive integer. In order to achieve gas distribution, the intake and exhaust manifolds are arranged on each side of the stack tower. The flow path adopts a design where the gas enters and exits from the bottom, such as Figure 3 (c). Assume that the height and width of the manifold are consistent with the stack. Finally, the stack is placed in a hot box to form a module. The lower surface of the stack is directly in contact with the insulating layer or base of the hot box. The hot box is electrically heated to the operating temperature and maintained constant. Schematically, the values ​​of the geometric parameters of the SOEC stack can be shown in Table 1 below.

[0074] Table 1

[0075]

[0076]

[0077] Step 202, according to the size data of the SOEC tower, a preset equivalent circuit model output is used to obtain the maximum current density of the SOEC tower, and the equivalent circuit model is used to indicate the relationship between the size data and the maximum current density.

[0078] The computing device inputs the dimension data of the SOEC stack into the preset equivalent circuit model and outputs the maximum current density of the SOEC stack. The maximum current density of the SOEC stack is a key parameter in the performance evaluation of SOEC, which characterizes the amount of current passing through a unit area. In practical applications, the maximum current density is directly related to the electrolysis efficiency and energy conversion efficiency of the SOEC stack. Therefore, understanding and optimizing the maximum current density is crucial for designing and manufacturing efficient and stable SOEC stacks.

[0079] It should be noted that the input parameters and output parameters of the equivalent circuit model can be swapped, that is, the input parameter can be the maximum current density of the SOEC tower, and the output parameter is the size data of the SOEC tower. The computing device inputs the maximum current density of the SOEC tower into the preset equivalent circuit model, and outputs the size data of the SOEC tower. The design of the model allows the interchange of input and output parameters, which means that both the size data of the SOEC tower and its maximum current density can be used as the starting input parameters, and the corresponding output parameters can be obtained after model processing. This ability to swap parameters greatly improves the flexibility and applicability of the model.

[0080] The equivalent circuit model is a model used to simulate and analyze the performance of the SOEC stack. Optionally, the equivalent circuit model includes a circuit sub-model and other sub-models, the other sub-models including a flow sub-model and / or a thermal sub-model, the flow sub-model is used to predict the gas flow distribution of the fuel side gas flow of the SOEC stack, the thermal sub-model is used to predict the temperature distribution of the battery of the SOEC stack, and the circuit sub-model is used to predict the maximum current density of the SOEC stack based on the gas flow distribution and / or temperature distribution.

[0081] For the convenience of explanation, the equivalent path model of the SOEC stack is only introduced as an example, including the flow path sub-model, the thermal path sub-model and the circuit sub-model. These three sub-models can be coupled with each other through interfaces such as flow, temperature and heat.

[0082] The flow path sub-model is used to predict the gas flow distribution of the fuel side gas flow of the SOEC stack, that is, the flow path sub-model aims to predict the distribution of the fuel side gas flow in the SOEC stack, and characterizes the gas flow distribution with the pressure difference distribution.

[0083] Optionally, the input parameters of the flow path sub-model include the size data of the SOEC tower and the total air intake flow rate, and the output parameters of the flow path sub-model include the gas flow rate of each cell and the gas flow rate of each manifold section of the SOEC tower.

[0084] Figure 4 FIG. 1 is a schematic diagram of a flow path sub-model of a SOEC stack provided by an exemplary embodiment of the present disclosure, wherein the SOEC stack is a SOEC stack having N battery cells, where N is a positive integer. The pressure p along the feed manifold fed , p fed is assumed to be constant (i.e., the flow resistance of the feed manifold is zero). Therefore, the pressure difference distribution of the cell is completely determined by the exhaust manifold pressure Dominant. Pressure at the exhaust manifold outlet is the atmospheric pressure p atm . represents the flow resistance of the battery, which is assumed to be equal between different batteries. represents the flow resistance of each part of the exhaust manifold, and for simplicity, it is also assumed to be equal between different parts. The flow rate of gas flowing through the i-th battery and the manifold is respectively expressed as and Indicates that is the gas flow rate per cell in the SOEC stack, It is the gas flow rate of each manifold section of the SOEC tower. represents the flow rate of a given total gas into the stack, that is, is the total air inlet flow rate of the SOEC stack.

[0085] Since the pressure drop in the stack is very small compared to the atmospheric pressure, the steady-state flow in the stack is assumed to be incompressible. In addition, the effects of temperature distribution and composition changes are neglected.

[0086] According to the Hagen-Poiseuille law, the gas flow rate is proportional to the pressure drop, which can be expressed as formula (1).

[0087] p in -p out =R flow ×Q g (1)

[0088] Among them, R flow represents the flow resistance, p in -p out represents the pressure drop across the flow resistance, Q g Indicates the gas flow rate.

[0089] The fluid circuit equations corresponding to the flow path submodel are shown in equations (2a)-(2b). Equation (2a) is a KVL equation, indicating that the pressure drop on the loop formed by adjacent units is zero. The mass conservation is expressed as a KCL equation, as shown in equations (2b)-(2c). Subscripts i=1, 2, ..., N are used similarly hereafter. cell , N cell is the number of cells.

[0090]

[0091] The thermal path model is used to predict the temperature distribution of the battery in the SOEC stack. Since the center and corner of the cell will have extreme temperatures when the convection effect is not significant, the center and corner temperatures of cell i are modeled as two temperature nodes. and Right now is the central temperature of the battery in the SOEC stack, is the battery edge temperature of the SOEC tower. Three heat transfer effects are considered: heat conduction between units, heat convection, and heat radiation between the tower and the hot box chamber. When the excess air ratio is not too high, the heat convection in the gas flow channel between units is ignored because it has little effect on the temperature distribution. Generally, SOEC requires a high excess air ratio to avoid temperature runaway. However, due to the relatively low heat release of SOEC and the fact that excess air increases the energy consumption of the balancing plant, the excess air ratio in the SOEC system is typically between 0.7 and 1.5. The disclosed embodiment can be verified using an excess air ratio of 1.

[0092] Optionally, the input parameters of the thermal circuit model include the size data of the SOEC stack tower and the equivalent heat source of the electrochemical reaction heat release, and the output parameters of the thermal circuit model include the battery center temperature and battery edge temperature of the SOEC stack tower.

[0093] Figure 5 A schematic diagram of a thermal path model of a SOEC stack tower provided by an exemplary embodiment of the present disclosure is shown. The lateral heat conduction within a single unit is modeled as a thermal resistance Longitudinal heat conduction between elements is modeled as thermal resistance The heat convection and radiation between the unit and the heat box chamber are modeled as equivalent heat sources and They are connected to and Electrochemical heat source given by the model and is also covered. arrive The heat flux of thermal conductivity is Indicates. and The transverse heat conduction heat flux is express.

[0094] According to Fourier's law of heat conduction, the heat flux is proportional to the temperature difference, as shown in formula (3).

[0095] T (i) -T (i+1) =R th ×Q h (3)

[0096] Among them, R th Represents thermal resistance, T (i) -T (i+1) represents the temperature difference across the flow resistance, Q h represents the heat flux.

[0097] The thermal circuit equations corresponding to the thermal circuit model are shown in formulas (4a)-(4c). Kirchhoff's theorem for analog circuits uses KVL and KCL type equations to describe the thermal circuit equations.

[0098]

[0099] The circuit sub-model is used to predict the electrochemical performance and thermal effect of the SOEC stack based on the gas flow distribution and / or temperature distribution. Optionally, the input parameters of the circuit sub-model include the stack voltage of the SOEC stack and the cell voltage of a single cell, and the output parameters of the circuit sub-model include the maximum current density of the SOEC stack.

[0100] In the thermal circuit model, the area of ​​a single cell is also a key parameter. In order to adapt to the calculation of thermal resistance of different sizes, the value of thermal resistance can be determined by using the area of ​​a single cell according to Fourier's law of heat conduction. This process involves an extended calculation of thermal resistance, and the specific calculation formula can be flexibly selected according to actual conditions, and the embodiments of the present disclosure do not limit this. Figure 6 A schematic diagram of a circuit sub-model of a SOEC stack tower provided by an exemplary embodiment of the present disclosure is shown. The voltage of a single cell in the SOEC stack tower is composed of equilibrium potential, activation overpotential, concentration difference overpotential, and ohmic overpotential, which are modeled as a voltage source, a nonlinear resistor, a nonlinear resistor, and a linear resistor, respectively. The single cells are connected in series, and the circuit can be described by KVL and KCL equations. Formulas (5a)-(5c) show the decomposition process of the SOEC stack tower and the solution cell voltage.

[0101]

[0102] 0=JJ (i) ,i=1,2,…,N cell (5c)

[0103] Among them, V ST (J) is the voltage of the SOEC stack, J is the current density of the stack, J (i) is the current density of the ith cell, and V (i) is the voltage of a single cell. represents the equilibrium potential and is modeled as a voltage source. and They represent activation overpotential, concentration overpotential and ohmic overpotential respectively. and is modeled as a nonlinear resistor, and is modeled as a linear resistor.

[0104] In addition, the heat release per unit area of ​​the battery is shown in formula (6).

[0105]

[0106] Among them, q ec(i) is the heat release per unit area of ​​the battery, Represents the thermal neutral voltage.

[0107] The equivalent path model is constructed by extracting the key spatial nodes, and the circuit elements are identified from the multiphysics model. Figure 7 A schematic diagram showing the relationship between an equivalent circuit model and a multi-physics field model provided by an exemplary embodiment of the present disclosure includes equations and resistance terms. The mass and momentum balance, charge balance, and energy balance equations correspond to fluid, circuit, and thermal circuit equations, respectively. At the same time, Figure 7It also shows that the three sub-models (flow path sub-model, thermal path sub-model and circuit sub-model) have a one-way or two-way coupling relationship. The gas flow rate of each cell in the stack tower Given by the flow path sub-model, it determines the steam utilization and affects V in the circuit model (i) The thermal circuit sub-model and the circuit sub-model are coupled to each other. Therefore, the output of the circuit sub-model and is the input of the thermal circuit model. The output of the thermal circuit model is and is the input to the circuit sub-model.

[0108] The disclosed embodiment models the flow field, temperature field and electric field of the SOEC stack in a unified way, and proposes an expandable identification method for key resistive parameters. The model is analogous to the circuit, using linear and nonlinear resistive elements and source elements to model physical phenomena such as flow, heat transfer, and electrochemical reactions, and using KVL or KCL equations to describe the distribution of physical quantities such as flow, heat, and electricity, which has the characteristics of unified form and easy expansion.

[0109] Figure 8 A schematic diagram of the circuit equations, flux, potential and resistance terms of an equivalent circuit model provided by an exemplary embodiment of the present disclosure is shown. Numerical results can be obtained by solving the above-mentioned equations (2a)-(2c), (4a)-(4c) and (5a)-(5c). The unified modeling method allows the sub-models to have similar mathematical forms. At the same time, the resistance parameters can be well extended to various sizes and operating conditions of the stack.

[0110] In addition to obtaining numerical results by solving algebraic equations, the equivalent circuit model also facilitates the derivation of explicit analytical expressions. Based on the fluid and simplified thermal circuit, the following analytical expressions can give the distribution of the non-uniformity index (air flow non-uniformity and thermal non-uniformity index) and the corresponding maximum current density. The battery center temperature and edge temperature nodes are merged, and the local linearization method is used to model the heat exchange between the battery and the hot box as a linear thermal resistance.

[0111] Optionally, the equivalent circuit model is also used to indicate a first mapping relationship between the dimension data and the non-uniformity index of the SOEC tower, and a second mapping relationship between the non-uniformity index and the maximum current density, the non-uniformity index including an airflow non-uniformity index and / or a thermal non-uniformity index. During the tower amplification process, the spatial uneven distribution of gas flow and temperature inside the module is the most critical issue. For example, thermal non-uniformity has been shown to be a direct cause of performance degradation and battery failure, and fluid non-uniformity may cause uneven heating and cooling effects, leading to potential damage. The airflow non-uniformity index and the thermal non-uniformity index are two important parameters for evaluating the performance of the SOEC tower. The airflow non-uniformity index is used to indicate the uniformity of the airflow distribution inside the SOEC tower, and the thermal non-uniformity index is used to indicate the uniformity of the temperature distribution inside the SOEC tower.

[0112] Maximum current density limited by fluid inhomogeneity: The flow path submodel can be abstracted as an N-cell resistor network, such as Fig. 9 The gas flow rate of each cell is shown in formula (7).

[0113]

[0114] in, is the gas flow rate of the kth cell, is the input equivalent resistance of the k-order network, YesN cell -k-order network input equivalent resistance, It is the Nth cell Gas flow rate of the cell.

[0115] The ratio of the gas flow rate in the top unit to the average gas flow rate in the stack is defined as the flow inhomogeneity index IH. f , the index is shown in formula (8).

[0116]

[0117] Assume J max,theo For the corresponding The theoretical maximum current density. In order to avoid damage to the battery due to steam starvation, the actual maximum current density J max Received The restriction is shown in formula (9).

[0118] J max =J max,theo ×IH f (9)

[0119] Maximum current density limited by thermal inhomogeneities: The thermal circuit model is simplified for explicit analysis. Fig.10A schematic diagram of a simplified thermal circuit model provided by an exemplary embodiment of the present disclosure is shown. First, the temperature nodes at the center and corner of each battery and Merged into one node Second, the effect of temperature distribution on electrochemical performance is neglected, and the gas flow rate into each cell is assumed to be the same. Therefore, the electrochemical heat source for each cell is the same and is determined by the current density. Third, the heat convection and radiation between the stack tower and the hot box are remodeled as thermal resistances. As shown in formula (10).

[0120]

[0121] in, is the surface area of ​​the ith battery exposed in the furnace, k conv is the convective heat transfer coefficient, T hb is the furnace temperature, ε rad is the emissivity, σ rad is the Stefan-Boltzmann constant, is the surface area of ​​the battery center node exposed to the furnace, is the surface area of ​​the cell edge node exposed to the furnace, It is the Nth cell The thermal resistance of heat transfer between the battery cell and the furnace.

[0122] The heat flux distribution is shown in equations (11) and (12).

[0123]

[0124] Among them, α and β are characteristic roots, and C1 and C2 are coefficients. is a fitting formula used to simulate the electrochemical reaction heat source of the battery. yes Fig.10 The heat flux between the kth battery and the furnace in the simplified heat circuit is yes Fig.10 The Nth simplified thermal circuit cell The heat flux between the cell and the furnace, yes Fig.10 Heat flux between the kth battery and the k+1th battery in the simplified thermal circuit.

[0125] The thermal gradient quantifies the local thermal non-uniformity. Since the thermal gradient is proportional to the heat flow through the thermal resistance according to Fourier's law of heat conduction, its distribution can be obtained simultaneously, as shown in formula (13a). The maximum thermal gradient as a function of current density is defined as the thermal non-uniformity index IH th(J), as shown in formula (13b).

[0126]

[0127] Typically, the maximum thermal gradient is 10°C·cm -1 is considered as an acceptable limit for safe operation. Therefore, the maximum current density J affected by thermal non-uniformity is max It can be obtained by formula (14).

[0128]

[0129] It can be seen that the above-mentioned flow path sub-model: the air flow distribution under different size data and intake flow rate can be accurately predicted. The manifold flow resistance changes significantly and has strong nonlinearity; the battery flow channel flow resistance changes insignificantly. The flow path modeling assumptions are reasonable. The thermal path sub-model: the temperature distribution of the SOEC stack module under the heat absorption and release state can be accurately predicted. The three-dimensional simulation shows that there is no significant asymmetric temperature distribution of the stack along the airflow direction, and the thermal path modeling assumptions are reasonable. The circuit sub-model: the electrochemical performance of the SOEC stack, especially the change trend of the concentration difference overvoltage, can be accurately predicted.

[0130] Based on the equivalent path model provided above, Fig.11 (a)-11(b) show the predicted cell pressure drop distribution on the test set (30 and 60 cells), Δp cell =p fed -p ex . The model was trained using data from a 3D model of 30 units. For different flow rates and different numbers of units in series, the model was able to effectively predict the pressure drop and airflow distribution within an error of 0.6%, showing good generalization ability. It was observed that the airflow in the top unit was less than that in the bottom. In addition, the unit flow resistance varied little, i.e., the unit flow resistance showed good linearity. In contrast, although the runner flow resistance is much smaller than the unit flow resistance, it increases rapidly with increasing gas flow rate, indicating that it plays a more important role in determining the airflow distribution of stack towers of various sizes and operating conditions.

[0131] The effectiveness of the equivalent circuit model is verified by comparing the temperature curves of the equivalent circuit model and the 3D model provided by the embodiment of the present disclosure. The heat sources for the heat absorption and heat release conditions generated by the fluid and circuit sub-models are applied to the equivalent circuit model and the 3D model. Fig.11 (c)-11(d) compare the temperature curves of the two models. The equivalent path model can effectively predict the temperature distribution of the stack tower with an error of less than 0.8%. In addition, the 3D temperature curve with an excess air ratio of 1 reveals that there is no obvious asymmetric temperature distribution along the airflow direction, as shown in Figure 1. Fig.11(g) This finding supports the hypothesis that air convection in the stack tower plays only a minor role in heat transfer. The modeling approach adopted is reasonable.

[0132] Furthermore, to validate the parameters of the circuit sub-model, the simulated IV curves of SOECs at constant temperature were compared with other reported experimental results. The experiments were conducted on a SOEC stack with a structure similar to the fuel electrode support described above. Fig.11 (e) shows that the IV curves match the experimental results well, which indicates that the parameters of the circuit model are appropriate. In addition, the trend of concentration overpotential as a function of steam utilization SU is specially considered, because the airflow distribution directly affects the steam utilization of different units. Fig.11 (f) shows the good match between the proposed circuit model results and the 3D model results.

[0133] Fig.11 (h) Comparison of the degrees of freedom and computational time of the equivalent path model and the 3D model. The equivalent path model significantly reduces the computational cost by three orders of magnitude while maintaining accuracy, making it a reliable method for studying the scale-up of stack towers.

[0134] In order to study the effect of non-uniformity on the performance of the stack during the scale-up process, different numbers of series cells N were selected. cell (range from 30 to 150) and single cell area A cell (Range from 68cm 2 To 544cm 2 ) for case studies. For example, a SOEC tower with 30-150 cells (A cell =136cm 2 ) and the case with A cell =68-544cm 2 Battery Case (N cell = 60), and for better visualization, not all cases are shown in the diagram. The total steam flow into the stack is fixed, that is, the area-specific gas flow rate is constant, and J max,theo =0.8A·cm 2 The temperature of the hot box chamber was set at 700°C.

[0135] During the scale-up process, the maximum current density of the stack is limited, which indicates that the economics are reduced. The area-specific power at different sizes is also compared. The maximum current density decreases as the number of cells in series increases. Fig.12 (a) shows the JV relationship for towers with 30, 60, and 90 cells. cell As the current density increases, the maximum current density and area-specific power decrease. The decrease in the maximum current density can be explained by the steam starvation of the cells at the top of the stack. Fig.12 (c) shows that at the same current density (J = 0.6 A cm 2 ), the steam utilization of the top cell increases rapidly with the increase in the number of cells in series. In contrast, the steam utilization of the bottom cell decreases. The difference in steam utilization between the top and bottom cells increases with the increase in the number of cells in series, causing the top cell to suffer from steam starvation earlier. Therefore, the reduction in total steam utilization and maximum current density will reduce the efficiency and economy of the system. On the contrary, if Fig.12 As shown in (b), the maximum current density does not change with the increase of the single cell area. Since the difference between the battery flow resistance and the channel flow resistance reaches four orders of magnitude, the effect of the single cell area on the fluid heterogeneity can be ignored. Fig.12 (d) also shows that increasing the cell area does not significantly exacerbate fluid inhomogeneity.

[0136] Thermal safety is the most critical factor limiting the design and operation of SOECs due to the inherent fragility of the material. Fig.13 (a) and 13(b) show the temperature extremes of the stack under different sizes and current densities. As the current density increases, the trend of the temperature extremes shows two stages. The first stage (I) is the endothermic stage, when both the maximum and minimum temperatures are below 700°C. The valley point increases with the size (N cell or A cell ) increases. The second stage (II) is the exothermic stage, when both the maximum and minimum temperatures are above 700°C. The peak value increases with increasing size. In addition, in the endothermic and exothermic stages, the peak temperature difference increases with increasing size data. Scaling up the tower will intensify the temperature extremes due to higher thermal resistance and may threaten the thermal safety of the tower. Thermal gradient is a common indicator for measuring thermal safety. During operation, the maximum thermal gradient of the SOEC module cannot exceed a certain threshold. Fig.13 (c)-13(f) show the contour plots of the maximum thermal gradient in the z direction and in the xy plane. Fig.13 (c) and 13(e) show the maximum thermal gradients in the z direction and xy plane for stacks with different numbers of cells in series. The upper right corner of the color-filled contour plot is blank due to fluid inhomogeneity, and the boundary represents the steam starvation constraint. As the current density increases, the two gradients first increase, then decrease, and finally continue to increase, which is consistent with Fig.13 The trend is consistent with that in (a). It is also noted that the maximum thermal gradient in the z direction is much larger than the thermal gradient in the xy plane. This can be attributed to the tendency of the stack to transfer heat through the upper surface and accumulate heat flux at the top, which is determined by the thermal circuit topology and thermal resistance distribution. The contour lines representing the temperature gradient of 10℃·cm-1 are bolded to distinguish them from other contour lines. The corresponding maximum current density decreases with the increase of the number of cells in series.

[0137] Fig.13 (d) and 13(f) show the maximum thermal gradients in the z direction and xy plane for stacked towers with different cell areas. As mentioned before, both gradients increase first, then decrease, and continue to increase with increasing current density. The maximum thermal gradient in the z direction is much larger than that in the xy plane. One difference is that the latter is more sensitive to changes in the cell area. Fig.13 In (f), a thick line also appears in the endothermic region. However, when discussing the maximum current density of steady-state operation, the maximum thermal gradient under endothermic conditions can be ignored because the load variation range is less interesting. From the thick line in the exothermic region, it can be seen that the maximum current density decreases with the increase of the single cell area. Fig.13 The angle between the thick line in (f) and the J axis is less than Fig.13 From the angle in (e), it can be concluded that the thermal gradient is more sensitive to the single cell area.

[0138] The maximum achievable current density is usually determined by the manufacturing technology and the electrode material. For a given maximum current density, the scale-up of the stack tower is limited due to the above-mentioned non-uniformity. The disclosed embodiment shows the results of two cases to discuss and summarize the contradiction between the stack tower size and the maximum current density and its corresponding mechanism:

[0139] Case 1: With a given cell area A cell =136cm 2 The stack tower was operated at different current densities to investigate the cell upper limit.

[0140] Case 2: With a given number of series connected cells N cell = 60 stack towers were operated at different current densities to investigate the cell In both cases, the hot box temperature is T hb =700℃, and the stack tower is at a given steam flow rate of 0.8[A·cm-2]×A cell N cell / (2F). The scaling-up limit of the number of cells in series shows a two-stage decrease in the maximum current density. When the current density is lower than 0.62A·cm-2, steam starvation limits the maximum number of cells in series. As the current density increases further, thermal safety limits the maximum number of cells in series.

[0141] Fig.14 (a) and 14(c) show the maximum number of series cells and their corresponding steam utilization and maximum thermal gradient for Case 1. The red and yellow shaded areas represent the N caused by steam starvation and thermal safety, respectively. cell The blue shaded area indicates the number of cells that can be connected in series. Fig.14In (a), the results of considering only steam starvation constraints and only thermal safety constraints are represented by solid and dashed lines, respectively. As the current density increases, the maximum number of series cells decreases in two stages, I and II. In stage I, the solid line coincides with the dashed line, and the maximum number of series cells is limited by steam starvation. This can be seen from Fig.14 (c) is shown in stage I. The maximum thermal gradient does not exceed 10℃·cm-1, while the steam utilization of the top cell is close to 100%. In stage II, the dotted line is lower than the solid line, which means that thermal safety limits the maximum number of series cells. Fig.14 (c) In stage II, the steam utilization of the top cell is less than 100%, and the maximum thermal gradient is close to 10℃·cm-1. The cost of increasing the maximum current density is the loss of NcellNcell. Considering two constraints, J max From 0.54A·cm-2 to 0.69A·cm-2, N cell It decreases from 150 to 30. This also shows that when N cell When expanding from 30 to 150, J max A decrease of 21.7%.

[0142] The expansion of single cell area is mainly limited by thermal safety constraints. Fig.14 (b) and 14(d) show the maximum single cell area and its corresponding steam utilization and maximum thermal gradient for Case 2. The red and yellow shaded areas represent the A caused by steam starvation and thermal safety, respectively. cell The blue shaded area indicates the achievable single cell area. Fig.14 In (b), the solid line and the dashed line represent the results under steam starvation and thermal safety constraints, respectively. As shown by the solid line, when thermal safety constraints are not considered, the single cell area can be expanded almost infinitely. As mentioned above, the change of the single cell area has little effect on the airflow distribution. Fig.14 The corresponding maximum steam utilization in (d) is close to 100%. However, as the maximum current density increases, the maximum single cell area decreases due to thermal safety constraints, as shown by the dotted line. The corresponding maximum thermal gradient is close to 10℃·cm-1.

[0143] Similarly, there is a contradiction between the maximum current density and the single cell area. max From 0.62A·cm-2 to 0.72A·cm-2, A cell From 544cm 2 Reduced to 68cm 2 This also means that when A cell From 544cm 2 Expanded to 68cm 2 When J max A decrease of 13.9%.

[0144] The explicit analytical expressions for the fluid circuit agree well with the numerical results for the circuit equations. Fig.15 (a) shows that the airflow distribution given by the explicit analytical expression is consistent with the numerical results. The top cell (No. 60) has the least steam flow and is the most critical. Fig.15 (c) shows that the explicit analytical expression accurately predicts the maximum number of cells in series at different current densities. Although the thermal safety assessment is more conservative, the explicit analytical expression of the thermal circuit is consistent with the numerical results. Fig.15 As shown in (b), the trend of the thermal gradient in the z direction is similar to the numerical result. The weakest point of thermal safety appears at the top of the stack. However, the explicit analytical expression overestimates the value of the maximum gradient Tz. To solve this problem, Fig.15 The result in (d) is multiplied by a compensation factor of 1.07. The results show that the explicit analytical results are consistent with the numerical results both qualitatively and quantitatively.

[0145] After the above verification, the following conclusions can be drawn: Comparing the number of degrees of freedom and calculation time of the equivalent path model with the manifold-battery flow channel three-dimensional model containing only the flow field, the degrees of freedom and calculation time of the equivalent path model are significantly lower than those of the three-dimensional model of a single physical field.

[0146] Taking the fixed steam inlet of the theoretical maximum current density (for example, 0.8A / cm2) as the operation mode, considering the steam starvation constraint, the maximum load (power density and yield density) of the tower stacks of different sizes is analyzed by example. The following conclusions can be drawn: As the number of cells increases, the maximum current density of the tower stack decreases significantly. The loss of maximum current density is caused by steam starvation. Under the same current density, the steam utilization rate of the bottom and top cells shows an opposite trend, that is, the increase in the number of cells exacerbates the unevenness of airflow distribution. However, as the area of ​​a single cell increases, the maximum load of the tower stack does not change significantly. Because the battery flow resistance is 4 orders of magnitude higher than the manifold flow resistance, the change in battery flow resistance caused by the change in the area of ​​a single cell has little effect on the airflow distribution. Still taking the fixed steam inlet as the operation mode, considering the thermal safety constraint, the maximum current density of the tower stacks of different sizes is analyzed by example. The following conclusions can be drawn: As the size data (number of cells and single cell area) increases, the temperature difference and temperature gradient increase significantly, which may pose a challenge to the safety performance of steady-state operation. The longitudinal gradient is greater than the lateral gradient, and both are more sensitive to the area of ​​a single cell. Indicatively, the maximum temperature gradient of a preset value (such as 10°C / cm) is used as a thermal safety constraint: when the stack size increases, the maximum safe current density decreases significantly. By fixing the single cell area and the number of cells, the amplification limit of the SOEC stack under different maximum current densities can be obtained. Under the fixed steam feed mode, two effects limit the amplification limit of the stack.

[0147] When the single cell area is fixed, in the first stage of the amplification process: the maximum temperature gradient is not clamped, the maximum steam utilization rate is clamped, and the airflow distribution is dominant; in the second stage of the amplification process: the maximum temperature gradient is clamped, the maximum steam utilization rate is not clamped, and the temperature gradient is dominant. When the number of cells is fixed, the steam starvation constraint curve is perpendicular to the horizontal axis, and the thermal safety constraint curve is located to the left of the steam starvation constraint curve, indicating that the change in the cell area mainly limits the amplification limit by affecting thermal safety.

[0148] The explicit analytical expression of the above flow path is consistent with the numerical calculation in both qualitative trends and quantitative results. Although the thermal path overestimates the temperature gradient after simplification, a consistent quantitative result can be obtained by multiplying it by the compensation coefficient.

[0149] As mentioned above, there is a contradiction between the stack size and the maximum current density of the SOEC stack tower due to fluid and thermal heterogeneity. In some cases, system designers require a single module to reach a specific size for economic or safety reasons. In order to maximize the hydrogen production of the SOEC stack tower and reduce the system cost, it is necessary to determine the optimal combination of single cell area and stack tower height to achieve the scale-up of the stack tower. The total cell area is used to measure the size of the stack tower. The stack tower operates at a given steam flow rate and a given hot box chamber temperature. For the same size stack tower, a higher maximum current density is more advantageous.

[0150] Indicative, Fig.16 (a) shows the design-performance diagram of the stack tower. The x-axis, y-axis, and z-axis are the number of cells in series, N. cell 、Single battery area A cell and the total battery area A cell,tot The color map shows the maximum current density of the stack tower. The contour lines represent the different sizes of the stack tower. As the size of the stack tower increases, the maximum current density decreases. At small sizes, the maximum current density is more sensitive to the area of ​​the single cell. As the size increases, the maximum current density becomes less sensitive to the area of ​​the single cell, while becoming more sensitive to the number of cells in series. This result is also consistent with Fig.16 (b) shows the maximum total steam utilization. Thermal safety limits the maximum current density at small sizes, while the scaling of the single cell area has a greater impact on thermal inhomogeneity than the number of cells in series. When the number of cells in series is high enough, the fluid inhomogeneity will increase rapidly. In this case, steam starvation limits the maximum current density.

[0151] Different combinations will lead to different maximum current densities at the same size. The target amplification path shows the optimal combination of the number of series cells and the single cell area at the same size, such as Fig.16(a). The results show that the number of cells in series should be increased preferentially because thermal inhomogeneities limit the maximum current density when the size is small. As the size increases, the scaling space of the single cell area should also be fully explored. This can be attributed to the dominance of fluid inhomogeneities at larger heights, at which point increasing the number of cells in series is not the best option. However, even following the optimal path, increasing the total cell area from 5000cm 2 Expanded to 25000cm 2 It will also reduce the total battery area from 0.75A·cm-2 to 0.63A·cm-2.

[0152] Therefore, the proper combination of the number of cells and the area of ​​a single cell can improve the maximum load and economy of the module. Optionally, the equivalent circuit model is also used to indicate the target amplification path of the SOEC tower during the amplification process, that is, the relationship between the various size data of the SOEC tower and the multiple maximum current densities is determined by the equivalent circuit model; according to the relationship between the various size data of the SOEC tower and the multiple maximum current densities, the target amplification path of the SOEC tower during the amplification process is determined, and the target amplification path is to increase the number of cells of the SOEC tower in the first stage, and increase the single cell area of ​​the SOEC tower in the second stage, and the first stage is earlier than the second stage. In other words, based on the established equivalent circuit model, the design performance diagram of the SOEC tower can be traversed to obtain the target amplification path of the SOEC tower amplification. That is, the target amplification path can be roughly divided into two stages: the first stage (stage I): the scale is small, and the number of cells is increased first; the second stage (stage II): the scale is slightly larger, and the single cell area needs to be fully enlarged at the same time.

[0153] In summary, the equivalent circuit model provided by the embodiment of the present disclosure can simultaneously perform gas, heat, and electricity characteristic analysis of multi-heat zone multi-module and single heat zone module, reflect key information, significantly reduce the amount of calculation, and facilitate explicit analysis in the parameter space. The embodiment of the present disclosure provides a gas-heat-electric equivalent circuit model of a multi-stack integrated tower module, explicitly analyzes the restrictions of the number of tower cells and the single cell area on the maximum current density of the tower under the influence of airflow and thermal inhomogeneity, and quantitatively reveals the relationship between size data and maximum current density, and the optimal integrated amplification path to improve technical economy. On the one hand, the embodiment of the present disclosure establishes a gas-heat-electric coupling equivalent circuit model for the scale-up problem of multi-stack integrated towers in a single heat zone. The model has the characteristics of concise and unified form, low calculation cost, and expandable parameters. On the other hand, based on the proposed equivalent circuit model, the embodiment of the present disclosure derives the key indicators of airflow and thermal inhomogeneity, as well as the analytical expression corresponding to the maximum current density, and quantitatively reveals the contradiction between size data and maximum current density. On the other hand, based on the proposed equivalent path model, the disclosed embodiment proposes a target scale-up path for a multi-stack integrated tower module in a single hot zone. The path presents two stages: in the initial stage of scale-up, priority should be given to increasing the number of battery cells in the tower, and when it is scaled up to a certain extent, priority should be given to increasing the single battery area.

[0154] The following is an apparatus embodiment of the present disclosure. For parts not described in detail in the apparatus embodiment, reference may be made to the technical details disclosed in the above method embodiment.

[0155] Please refer to Fig.17 , which shows a schematic diagram of the structure of an analysis device for the maximum current density of a SOEC stack under the influence of inhomogeneity provided by an exemplary embodiment of the present disclosure. The device can realize all or part of a so-called computing device through software, hardware, or a combination of the two. The device includes: an acquisition module 22 and a processing module 23.

[0156] An acquisition module 22 is used to acquire the size data of the SOEC stack, the size data including the number of cells and the area of ​​a single cell;

[0157] The processing module 23 is used to obtain the maximum current density of the SOEC tower according to the size data of the SOEC tower by using a preset equivalent circuit model output, and the equivalent circuit model is used to indicate the relationship between the size data and the maximum current density.

[0158] In one possible implementation, the equivalent circuit model includes a circuit sub-model and other sub-models, the other sub-models include a flow path sub-model and / or a thermal path sub-model, the flow path sub-model is used to predict the gas flow distribution of the fuel side airflow of the SOEC stack tower, the thermal path model is used to predict the temperature distribution of the batteries of the SOEC stack tower, and the circuit sub-model is used to predict the maximum current density of the SOEC stack tower based on the gas flow distribution and / or temperature distribution.

[0159] In another possible implementation, the input parameters of the flow path sub-model include size data and the total air inlet flow rate of the SOEC stack, and the output parameters of the flow path sub-model include the air flow rate of each cell and each manifold of the SOEC stack.

[0160] In another possible implementation, the input parameters of the thermal circuit model include the size data of the SOEC tower and the equivalent heat source of the electrochemical reaction heat release, and the output parameters of the thermal circuit model include the battery center temperature and battery edge temperature of the SOEC tower.

[0161] In another possible implementation, the input parameters of the circuit sub-model include the stack voltage of the SOEC stack and the cell voltage of a single cell, and the output parameters of the circuit sub-model include the maximum current density of the SOEC stack.

[0162] In another possible implementation, the equivalent circuit model is also used to indicate a first mapping relationship between the dimension data and the non-uniformity index of the SOEC stack, and a second mapping relationship between the non-uniformity index and the maximum current density, wherein the non-uniformity index includes an airflow non-uniformity index and / or a thermal non-uniformity index.

[0163] In another possible implementation, the device further includes: a determining module, configured to:

[0164] The relationship between various size data of SOEC stack and multiple maximum current densities is determined by equivalent circuit model;

[0165] According to the relationship between various size data of the SOEC tower and multiple maximum current densities, the target amplification path of the SOEC tower in the amplification process is determined. The target amplification path is to increase the number of cells in the SOEC tower in the first stage and to increase the single cell area of ​​the SOEC tower in the second stage, and the first stage is earlier than the second stage.

[0166] It should be noted that the device provided in the above embodiment only uses the division of the above-mentioned functional modules as an example to implement its functions. In practical applications, the above-mentioned functions can be assigned to different functional modules according to actual needs, that is, the content structure of the device can be divided into different functional modules to complete all or part of the functions described above.

[0167] Regarding the device in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0168] An embodiment of the present disclosure also provides an analysis device for the maximum current density of a SOEC tower under the influence of non-uniformity, the device comprising: a processor; a memory for storing processor executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0169] The embodiment of the present disclosure further provides a non-volatile computer-readable storage medium having computer program instructions stored thereon, wherein the computer program instructions implement the method as claimed above when executed by a processor.

[0170] The embodiment of the present disclosure also provides a computer program product, including a computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in a processor of a computing device, the processor in the computing device executes the above method.

[0171] Fig.18 1 is a block diagram of an apparatus 1900 for analyzing the maximum current density of a SOEC stack under the influence of non-uniformity according to an exemplary embodiment. For example, the apparatus 1900 may be provided as a server or a terminal device. Fig.18 , the apparatus 1900 includes a processing component 1922, which further includes one or more processors, and a memory resource represented by a memory 1932 for storing instructions, such as an application, that can be executed by the processing component 1922. The application stored in the memory 1932 may include one or more modules, each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute instructions to perform the above method.

[0172] The device 1900 may also include a power supply component 1926 configured to perform power management of the device 1900, a wired or wireless network interface 1950 configured to connect the device 1900 to a network, and an input / output interface 1958 (I / O interface). The device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server™, MacOS X™, Unix™, Linux™, FreeBSD™ or the like.

[0173] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions, which can be executed by the processing component 1922 of the device 1900 to perform the above method.

[0174] The present disclosure may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0175] A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples of computer-readable storage media (a non-exhaustive list) include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination of the foregoing. As used herein, a computer-readable storage medium is not to be interpreted as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through a wire.

[0176] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0177] The computer program instructions for performing the operation of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed completely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be customized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0178] Various aspects of the present disclosure are described herein with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer-readable program instructions.

[0179] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, so that when these instructions are executed by the processor of the computer or other programmable data processing device, a device that implements the functions / actions specified in one or more boxes in the flowchart and / or block diagram is generated. These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions cause the computer, programmable data processing device, and / or other equipment to work in a specific manner, so that the computer-readable medium storing the instructions includes a manufactured product, which includes instructions for implementing various aspects of the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0180] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operating steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0181] The flow chart and block diagram in the accompanying drawings show the possible architecture, function and operation of the system, method and computer program product according to multiple embodiments of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and a part of the module, program segment or instruction includes one or more executable instructions for realizing the specified logical function. In some alternative implementations, the function marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous square boxes can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or action, or can be implemented with a combination of special hardware and computer instructions.

[0182] The embodiments of the present disclosure have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A method for analyzing the maximum current density of a solid oxide electrolytic cell SOEC stack under the influence of heterogeneity, characterized in that: The method comprises: Obtaining the dimension data of the SOEC stack tower, wherein the dimension data includes the number of cells and the area of ​​a single cell; According to the dimension data of the SOEC stack, a preset equivalent circuit model is used to output the maximum current density of the SOEC stack, and the equivalent circuit model is used to indicate the relationship between the dimension data and the maximum current density.

2. The method according to claim 1, characterized in that The equivalent circuit model includes a circuit sub-model and other sub-models, and the other sub-models include a flow path sub-model and / or a thermal path sub-model. The flow path sub-model is used to predict the airflow distribution of the fuel side airflow of the SOEC stack tower, and the thermal path sub-model is used to predict the temperature distribution of the batteries of the SOEC stack tower. The circuit sub-model is used to predict the maximum current density of the SOEC stack tower based on the airflow distribution and / or the temperature distribution.

3. The method according to claim 2, characterized in that The input parameters of the flow path sub-model include the size data and the total air intake flow rate of the SOEC stack tower, and the output parameters of the flow path sub-model include the gas flow rate of each cell and the gas flow rate of each manifold section of the SOEC stack tower.

4. The method according to claim 2, characterized in that: The input parameters of the thermal circuit model include the size data of the SOEC stack tower and the equivalent heat source of the electrochemical reaction heat release, and the output parameters of the thermal circuit model include the battery center temperature and battery edge temperature of the SOEC stack tower.

5. The method according to claim 2, characterized in that: The input parameters of the circuit sub-model include the stack voltage of the SOEC stack tower and the cell voltage of a single cell, and the output parameters of the circuit sub-model include the maximum current density of the SOEC stack tower.

6. The method according to any one of claims 1 to 5, characterized in that: The equivalent circuit model is also used to indicate a first mapping relationship between the dimension data and a non-uniformity index of the SOEC stack, and a second mapping relationship between the non-uniformity index and the maximum current density, wherein the non-uniformity index includes an airflow non-uniformity index and / or a thermal non-uniformity index.

7. The method according to any one of claims 1 to 5, characterized in that: The method further comprises: Determine the relationship between various size data of the SOEC stack and multiple maximum current densities through the equivalent circuit model; According to the relationship between various size data of the SOEC tower and multiple maximum current densities, the target amplification path of the SOEC tower during the amplification process is determined. The target amplification path is to increase the number of cells in the SOEC tower in the first stage and to increase the single cell area of ​​the SOEC tower in the second stage. The first stage is earlier than the second stage.

8. An analysis device for the maximum current density of a SOEC stack under the influence of inhomogeneity, characterized in that: The device comprises: An acquisition module is used to acquire the size data of the SOEC stack, wherein the size data includes the number of cells and the area of ​​a single cell; A processing module is used to obtain the maximum current density of the SOEC stack tower according to the size data of the SOEC stack tower using a preset equivalent circuit model output, wherein the equivalent circuit model is used to indicate the relationship between the size data and the maximum current density.

9. An analytical device for the maximum current density of a SOEC stack under the influence of inhomogeneity, characterized in that: The device comprises: processor; a memory for storing processor-executable instructions; The processor is configured to implement the method described in any one of claims 1 to 7 when executing the instructions stored in the memory.

10. A non-volatile computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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