Method, device and equipment for determining operating point of solid oxide fuel cell

Abstract

This application relates to the field of fuel cell technology, and particularly to a method, apparatus, and equipment for determining the operating condition point of a solid oxide fuel cell. The method includes: acquiring source data of the cell's current-voltage characteristic curve at a target fuel supply flow rate; generating a criterion resistance characteristic curve and a measured resistance characteristic curve based on the source data; determining the operating condition boundary point corresponding to the target fuel supply flow rate based on the criterion resistance characteristic curve and the measured resistance characteristic curve; if either the power or efficiency corresponding to the operating condition boundary point does not meet user requirements, adjusting the target fuel supply flow rate to redetermine the operating condition boundary point; if both the power and efficiency corresponding to the operating condition boundary point meet user requirements, generating the target operating condition point based on the power and efficiency corresponding to the operating condition boundary point. This solves the problem in related technologies where the operating condition point of a solid oxide fuel cell is determined based on empirical values, resulting in poor universality of the ideal operating condition across different performance cells.

Description

Technical Field

[0001] This application relates to the field of fuel cell technology, and in particular to a method, apparatus and equipment for determining the operating point of a solid oxide fuel cell. Background Technology

[0002] Solid oxide fuel cells have attracted attention due to their ability to efficiently convert chemical energy into electrical energy with minimal pollution. They also offer advantages such as high efficiency and fuel flexibility, operating at high temperatures and possessing considerable potential for application in various energy systems.

[0003] In related technologies, numerical models can show the distribution of nickel oxidation, pointing out that the precise limitation of the safety boundary depends on the solution of the model, and cannot simply limit parameters such as fuel utilization rate or operating voltage as ideal operating conditions; physical information neural network surrogate models can quickly fit battery performance parameters and predict battery safety boundaries, but in actual engineering applications there are situations such as uneven fuel flow rate distribution in local gas leakage channels and fluctuations in fuel supply. Summary of the Invention

[0004] This application provides a method, apparatus, and equipment for determining the operating point of a solid oxide fuel cell, in order to solve the problem in the related art where the operating point of a solid oxide fuel cell is determined based on empirical values, resulting in poor universality of the ideal operating point of a solid oxide fuel cell across different performance cells.

[0005] The first aspect of this application provides a method for determining the operating condition point of a solid oxide fuel cell, comprising the following steps: acquiring source data of the cell volt-ampere characteristic curve of the solid oxide fuel cell at a target fuel supply flow rate; generating a criterion resistance characteristic curve and a measured resistance characteristic curve of the solid oxide fuel cell based on the source data of the cell volt-ampere characteristic curve; determining the operating condition boundary point corresponding to the target fuel supply flow rate based on the criterion resistance characteristic curve and the measured resistance characteristic curve; if either the power or efficiency corresponding to the operating condition boundary point does not meet the user's requirements, adjusting the target fuel supply flow rate to redetermine the operating condition boundary point; if both the power and efficiency corresponding to the operating condition boundary point meet the user's requirements, generating the target operating condition point of the fuel cell based on the power and efficiency corresponding to the operating condition boundary point.

[0006] Optionally, a battery model of a solid oxide fuel cell is fitted based on the source data of the battery current-voltage characteristic curve. The criterion resistance under different currents is calculated based on the fitted battery model and the target fuel supply flow rate. The criterion resistance characteristic curve is generated based on the criterion resistance under different currents. Discrete data differentiation calculation is performed on the source data of the battery current-voltage characteristic curve to obtain the differential curve of the source data of the battery current-voltage characteristic curve. The measured resistance characteristic curve is determined based on the differential curve.

[0007] Optionally, the fuel supply limit current value of the fuel cell is calculated based on the target fuel supply flow rate; the concentration data of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet location are calculated under each current condition in the source data of the battery current-voltage characteristic curve based on the fitted battery model; a data table is generated based on each current and the corresponding hydrogen and water vapor concentration data; the criterion potential of the fuel cell is calculated based on each row of data in the data table; and the criterion resistance characteristic curve is calculated based on the fuel supply limit current value and the criterion potential.

[0008] Optionally, the formula for calculating the fuel supply limiting current value is: , in, Represents the fuel supply limit current. F represents the fuel supply flow rate, and F represents the Faraday constant.

[0009] Optionally, the formula for calculating the criterion potential is: , in, The criterion potential is represented by R, the gas constant by T, and the battery operating temperature by T. This represents the mole fraction of hydrogen at the anode-electrolyte interface, where the battery fuel outlet is located. This represents the mole fraction of water vapor at the anode-electrolyte interface, where the battery fuel outlet is located.

[0010] Optionally, the formula for calculating the resistance characteristic curve is: , in, Represents the criterion resistor. Represents the criterion potential, This represents the fuel supply limit current.

[0011] Optionally, the differential calculation method for discrete data includes any one of the following: central difference, forward difference, backward difference, five-point difference, and polynomial fitting to obtain the differential.

[0012] A second aspect of this application provides an apparatus for determining the operating point of a solid oxide fuel cell, comprising: an acquisition module for acquiring source data of the cell's current-voltage characteristic curve at a target fuel supply flow rate; a generation module for generating a criterion resistance characteristic curve and a measured resistance characteristic curve of the solid oxide fuel cell based on the source data of the cell's current-voltage characteristic curve, and determining the operating point corresponding to the target fuel supply flow rate based on the criterion resistance characteristic curve and the measured resistance characteristic curve; and an adjustment module for adjusting the target fuel supply flow rate to redetermine the operating point if either the power or efficiency corresponding to the operating point does not meet user requirements, and generating the target operating point of the fuel cell based on the power and efficiency corresponding to the operating point if both the power and efficiency corresponding to the operating point meet user requirements.

[0013] Optionally, the generation module is further configured to: fit a solid oxide fuel cell model based on the battery current-voltage characteristic curve source data; calculate the criterion resistance under different currents based on the fitted battery model and the target fuel supply flow rate; generate a criterion resistance characteristic curve based on the criterion resistance under different currents; perform discrete data differentiation calculation on the battery current-voltage characteristic curve source data to obtain the differential curve of the battery current-voltage characteristic curve source data; and determine the measured resistance characteristic curve based on the differential curve.

[0014] Optionally, the generation module is further configured to: calculate the fuel supply limit current value of the fuel cell based on the target fuel supply flow rate; calculate the concentration data of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet location under each current condition in the source data of the battery current-voltage characteristic curve based on the fitted battery model; generate a data table based on each current and the corresponding hydrogen and water vapor concentration data; calculate the criterion potential of the fuel cell based on each row of data in the data table; and calculate the criterion resistance characteristic curve based on the fuel supply limit current value and the criterion potential.

[0015] Optionally, the formula for calculating the fuel supply limiting current value is: , in, Represents the fuel supply limit current. F represents the fuel supply flow rate, and F represents the Faraday constant.

[0016] Optionally, the formula for calculating the criterion potential is: , in, The criterion potential is represented by R, the gas constant by T, and the battery operating temperature by T. This represents the mole fraction of hydrogen at the anode-electrolyte interface, where the battery fuel outlet is located. This represents the mole fraction of water vapor at the anode-electrolyte interface, where the battery fuel outlet is located.

[0017] Optionally, the formula for calculating the resistance characteristic curve is: , in, Represents the criterion resistor. Represents the criterion potential, This represents the fuel supply limit current.

[0018] Optionally, the differential calculation method for discrete data includes any one of the following: central difference, forward difference, backward difference, five-point difference, and polynomial fitting to obtain the differential.

[0019] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the program to implement the method for determining the operating point of a solid oxide fuel cell as described in the above embodiments.

[0020] A fourth aspect of this application provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement the method for determining the operating point of a solid oxide fuel cell as described in the above embodiments.

[0021] Therefore, this application has the following beneficial effects: This application embodiment first obtains the volt-ampere characteristic curve source data of a solid oxide fuel cell under a target fuel supply flow rate, then generates a criterion resistance characteristic curve and a measured resistance characteristic curve based on this data, thereby determining the corresponding operating condition boundary point. Subsequently, the target fuel supply flow rate is dynamically adjusted based on whether the power and efficiency at the operating condition boundary point meet user requirements. The operating condition boundary point is repeatedly optimized until both the power and efficiency at the boundary point meet the standards, ultimately generating the target operating condition point. This achieves a compromise between the three core indicators of battery operation safety, high output power, and high power generation efficiency. The operating condition point determined by this application embodiment has... By clearly defining the physical meaning and accurately corresponding to the state where the current-voltage characteristic curve is about to enter the concentration polarization control region, and considering that the fuel utilization rate corresponding to the operating condition boundary point is lower than the critical operating condition point for anode nickel oxidation, an appropriate safety margin is provided for battery operation. This avoids power efficiency loss due to incomplete fuel utilization and prevents a surge in polarization loss from affecting operational safety. It can lock in the optimal operating condition according to user needs, and the derivation based on the physical model gives the method good universality, adapting to batteries with different performance characteristics. The safety margin design can also effectively cope with complex scenarios in practical engineering applications, simplifying the selection process of the ideal operating condition. Therefore, this solves the problem in related technologies where the operating condition point of solid oxide fuel cells is determined based on empirical values, resulting in poor universality of the ideal operating condition for solid oxide fuel cells across different performance levels.

[0022] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0023] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a method for determining the operating point of a solid oxide fuel cell according to an embodiment of this application; Figure 2 This is a schematic diagram illustrating the process of a method for determining the operating point of a solid oxide fuel cell according to an embodiment of this application. Figure 3 (a) Source data for a current-voltage characteristic curve under a fuel supply flow rate provided according to an embodiment of this application. Figure 3 (b) Source data for the volt-ampere characteristic curve under another fuel supply flow rate; Figure 4 (a) is a measured resistance characteristic curve under a fuel supply flow rate according to an embodiment of this application. Figure 4 (b) is the measured resistance characteristic curve under another fuel supply flow rate; Figure 5(a) A criterion resistance characteristic curve under a fuel supply flow rate according to an embodiment of this application. Figure 5 (b) is the criterion resistance characteristic curve under another fuel supply flow rate; Figure 6 (a) A comparison of the measured resistance characteristic curve and the criterion resistance characteristic curve under a fuel supply flow rate according to an embodiment of this application. Figure 6 (b) Comparison of the measured resistance characteristic curve and the criterion resistance characteristic curve under another fuel supply flow rate; Figure 7 This document describes the high-power / high-efficiency operating condition boundary points and their corresponding output power and efficiency under different fuel supply flow rates, obtained according to an embodiment of this application. Figure 8 This is an example diagram of an operating point determination device for a solid oxide fuel cell according to an embodiment of this application; Figure 9 This is an example diagram of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0024] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0025] Numerical models can depict the distribution of nickel oxidation, indicating that precise constraints on the safety boundary depend on the model's solution and cannot simply limit parameters such as fuel utilization rate or operating voltage as ideal operating conditions. Li Hangyue's physical information neural network surrogate model can quickly fit battery performance parameters and predict the battery safety boundary. However, in practical engineering applications, situations such as local gas leakage, uneven fuel flow rate distribution in the gas passage, and fuel supply fluctuations may exist, which can expand the range of operating conditions where oxidation occurs. Therefore, an appropriate safety margin should be reserved in the selection of operating conditions. The aforementioned model methods lack consideration for the safety margin issue, and currently, there is still a lack of a universal, physically meaningful method for selecting ideal operating conditions with an appropriate safety margin.

[0026] The following describes a method, apparatus, and device for determining the operating point of a solid oxide fuel cell according to embodiments of this application, with reference to the accompanying drawings. Addressing the problems mentioned in the background art, where the operating point of a solid oxide fuel cell is determined based on empirical values, resulting in poor universality of the ideal operating condition for solid oxide fuel cells across different performance levels, this application provides a method for determining the operating point of a solid oxide fuel cell. In this method, source data of the cell's current-voltage characteristic curve at a target fuel supply flow rate are obtained; a criterion resistance characteristic curve and a measured resistance characteristic curve of the solid oxide fuel cell are generated based on the source data; the operating point corresponding to the target fuel supply flow rate is determined based on the criterion resistance characteristic curve and the measured resistance characteristic curve; if either the power or efficiency corresponding to the operating point does not meet user requirements, the target fuel supply flow rate is adjusted to redetermine the operating point; if both the power and efficiency corresponding to the operating point meet user requirements, the target operating point of the fuel cell is generated based on the power and efficiency corresponding to the operating point. This solves the problem in related technologies where the operating conditions of solid oxide fuel cells are determined based on empirical values, resulting in poor universality of the ideal operating conditions of solid oxide fuel cells across different performance levels.

[0027] Specifically, Figure 1 This is a flowchart illustrating a method for determining the operating point of a solid oxide fuel cell, as provided in an embodiment of this application.

[0028] like Figure 1 As shown, the method for determining the operating point of this solid oxide fuel cell includes the following steps: In step S101, the source data of the cell current-voltage characteristic curve of the solid oxide fuel cell under the target fuel supply flow rate is obtained.

[0029] Among them, solid oxide fuel cells are electrochemical devices that directly convert the chemical energy of fuel into electrical energy; the target fuel supply flow rate is the volumetric or mass flow rate of fuel continuously supplied to the anode of the fuel cell during fuel cell performance testing or actual operation, in order to obtain the battery characteristics under specified operating conditions; the battery volt-ampere characteristic curve is a curve describing the relationship between the output voltage and the output current of the fuel cell under specific operating conditions.

[0030] It is understood that the embodiments of this application require obtaining source data of the battery current-voltage characteristic curve of the fuel cell under the target fuel supply flow rate. This data can accurately capture the dynamic law of the change of fuel cell output voltage with current under a specified fuel supply flow rate, clearly present the performance characteristics of the battery such as open circuit voltage, voltage decay trend and maximum power point. The obtained source data of the battery current-voltage characteristic curve has high accuracy and traceability, providing a real and reliable original basis for subsequent performance analysis.

[0031] Specifically, the battery current-voltage characteristic curve source data consists of the original values ​​of current and output voltage corresponding to the entire current range. It also includes supporting test condition parameter records to support the validity of the data, such as target fuel supply flow rate, oxidant supply flow rate, fuel cell operating temperature, operating pressure, as well as auxiliary information such as battery model and specifications, test environment conditions, data acquisition time points, and equipment accuracy parameters.

[0032] To obtain source data for the battery's current-voltage characteristic curve, a dedicated fuel cell test platform must first be built, consisting of a fuel supply system, a load regulating device, high-precision voltage and current acquisition equipment, and temperature and pressure control units. Pre-treatment operations such as activation and cleaning of the fuel cell sample are then performed. Subsequently, the target fuel supply flow rate and associated operating parameters such as oxidant flow rate, operating temperature, and pressure are set and stabilized according to test requirements. Starting from the open-circuit state, the output current is gradually adjusted according to a preset current gradient using the load regulating device. After maintaining stable operating conditions at each current node, the corresponding output voltage value is recorded in real time using the acquisition equipment, covering the entire range from open circuit to rated or maximum current. After data acquisition, abnormal data points caused by operating condition fluctuations and equipment errors are removed. Finally, the processed current-voltage values ​​are integrated and archived with the associated operating parameters to obtain complete source data for the battery's current-voltage characteristic curve.

[0033] This application embodiment requires obtaining source data of the battery volt-ampere characteristic curve of the fuel cell under the target fuel supply flow rate. It can accurately capture the dynamic law of the change of the fuel cell output voltage with the current under the specified fuel supply flow rate, and clearly present the performance characteristics of the battery such as open circuit voltage, voltage decay trend and maximum power point. The obtained source data of the battery volt-ampere characteristic curve has high accuracy and traceability, and provides a real and reliable original basis for subsequent performance analysis.

[0034] In step S102, the criterion resistance characteristic curve and the measured resistance characteristic curve of the solid oxide fuel cell are generated based on the source data of the battery current-voltage characteristic curve. The operating condition boundary point corresponding to the target fuel supply flow rate is determined based on the criterion resistance characteristic curve and the measured resistance characteristic curve.

[0035] Among them, the criterion resistance characteristic curve is a resistance reference curve generated based on the theoretical model of the fuel cell under the extreme mass transfer state; the measured resistance characteristic curve is the curve of the change of the actual equivalent resistance of the battery with the current, calculated by the corresponding electrochemical data processing method based on the source data of the battery current-voltage characteristic curve; the operating condition boundary point is the dividing boundary node of the battery under different operating states under the target fuel supply flow rate.

[0036] It is understood that the embodiments of this application generate the fuel cell criterion resistance characteristic curve and the measured resistance characteristic curve from the source data of the battery volt-ampere characteristic curve and determine the operating condition boundary point corresponding to the target fuel supply flow rate. The criterion resistance characteristic curve reflecting the change law of the ideal equivalent resistance of the battery is obtained through theoretical calculation. At the same time, based on the source data of the volt-ampere characteristic curve, the measured resistance characteristic curve that reflects the actual operating state of the battery is calculated. The two curves are then compared and analyzed. By capturing the intersection points and deviation change nodes of the curve trends, the operating condition boundary point under the target fuel supply flow rate is finally determined. This achieves accurate analysis of the change law of the battery equivalent resistance with current under the target fuel supply flow rate, clearly delineates the dominant range of different polarization effects, and achieves a trade-off between the three indicators of battery operation safety, high output power and high power generation efficiency. The determined operating condition boundary point has clear physical meaning and verifiability, providing an intuitive and accurate basis for the evaluation of the battery operating state.

[0037] Specifically, to generate the criterion resistance characteristic curve of a solid oxide fuel cell based on the source data of the battery current-voltage characteristic curve, firstly, the fuel supply limiting current value needs to be calculated based on the source data of the battery current-voltage characteristic curve. Then, the mole fractions of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet location need to be obtained based on the source data of the battery current-voltage characteristic curve. Finally, the criterion resistance characteristic curve needs to be calculated based on the fuel supply limiting current obtained in the above steps and the data table consisting of the current and criterion potential columns.

[0038] The acquired voltage-current characteristic curve source data is preprocessed to filter and remove abnormal voltage-current data points caused by instantaneous fluctuations in operating conditions and equipment acquisition errors, ensuring that the remaining data are valid measured values ​​that correspond one-to-one. Subsequently, with current as the independent variable and output voltage as the dependent variable, a mathematical differential transformation is performed on the preprocessed continuous data to calculate the voltage change rate corresponding to each current node. The voltage change rate value is the actual equivalent resistance of the battery under the corresponding current condition. This resistance integrates the combined effects of ohmic resistance, activation polarization equivalent resistance, and concentration polarization equivalent resistance. Finally, the current and the corresponding actual equivalent resistance data in the entire current range are systematically integrated and plotted as a continuous function curve to obtain the measured resistance characteristic curve of the fuel cell. The criterion is that the resistance characteristic curve and the measured resistance characteristic curve have one and only one intersection point. The operating current value corresponding to this intersection point is the boundary point between high power / high efficiency operating conditions under the target fuel supply flow rate.

[0039] Furthermore, in the embodiments of this application, generating the criterion resistance characteristic curve and the measured resistance characteristic curve of the solid oxide fuel cell based on the battery current-voltage characteristic curve source data includes: fitting a battery model of the solid oxide fuel cell based on the battery current-voltage characteristic curve source data; calculating the criterion resistance under different currents based on the fitted battery model and the target fuel supply flow rate; generating the criterion resistance characteristic curve based on the criterion resistance under different currents; performing discrete data differentiation calculation on the battery current-voltage characteristic curve source data to obtain the differential curve of the battery current-voltage characteristic curve source data; and determining the measured resistance characteristic curve based on the differential curve.

[0040] Among them, the battery model is a mathematical correlation model obtained by fitting data based on the battery current-voltage characteristic curve source data, combined with the electrochemical polarization theory, inherent structural parameters, and operating condition parameters such as the target fuel supply flow rate of the fuel cell; the criterion resistance is the theoretical equivalent resistance calculated under different current conditions based on the fitted fuel cell electrochemical mathematical model and the target fuel supply flow rate; the discrete data differential calculation is a numerical operation performed using the discrete numerical differential method for the corresponding points of discrete current and voltage in the battery current-voltage characteristic curve source data; the differential curve is a characteristic curve reflecting the rate of change of fuel cell output voltage with current, obtained by discrete data differential calculation based on the battery current-voltage characteristic curve source data.

[0041] It is understood that this application embodiment is based on the source data of the battery current-voltage characteristic curve. A battery model that fits the electrochemical characteristics of the fuel cell is constructed through data fitting. The fitted battery model is then combined with the target fuel supply flow rate parameter, and the relevant theoretical equations of polarization effect are substituted to calculate the criterion resistance corresponding to different current conditions in the full current range. The data is then integrated to generate the criterion resistance characteristic curve. At the same time, the source data of the battery current-voltage characteristic curve is preprocessed to remove abnormal discrete points. The effective data is calculated using the discrete data differential calculation method to obtain the differential curve reflecting the rate of change of voltage with current. Based on the differential curve, the actual equivalent resistance corresponding to each current node is extracted, and the measured resistance characteristic curve is finally determined. The complete generation of two resistance characteristic curves is completed, realizing the construction of a core curve that corresponds to theory and reality. The criterion resistance characteristic curve clearly presents the change law of the theoretical equivalent resistance of the battery under the target fuel supply flow rate. The measured resistance characteristic curve can truly restore the comprehensive resistance characteristics of the battery in actual operation, fully exploring the value of the existing current-voltage characteristic curve source data. The combination of model fitting and discrete differential calculation improves the accuracy and reliability of curve generation.

[0042] Specifically, to fit a solid oxide fuel cell model to the source data of the battery's current-voltage characteristic curve, the source data needs to be preprocessed first. Abnormal current-voltage discrete data points caused by operating condition fluctuations and equipment acquisition errors are screened and removed. At the same time, the inherent structural parameters of the fuel cell and basic information on the test operating conditions are collected. Then, based on the electrochemical polarization theory of fuel cells, the equations are integrated to construct a theoretical equation framework that includes current, voltage, and polarization effect parameters. The preprocessed source data is then substituted into this theoretical framework, and the undetermined parameters in the framework are iteratively solved and optimized to obtain a mathematical model of the fuel cell that fits the target fuel supply flow conditions.

[0043] To calculate the criterion resistance at different currents based on the fitted battery model and the target fuel supply flow rate, the target fuel supply flow rate parameters need to be substituted into the fitted fuel cell model. The parameters related to fuel mass transfer in the model need to be corrected. Then, the full current range covered by the source data needs to be determined. Multiple calculation nodes are selected according to the preset current gradient. For each current node, the corresponding theoretical polarization voltage is calculated through the model. Then, the theoretical equivalent resistance of the battery at that current is solved by combining the correlation between the equivalent resistance and the polarization effect. That is, the criterion resistance.

[0044] To generate the criterion resistance characteristic curve based on the criterion resistance under different currents, the current data and the corresponding criterion resistance data within the entire current range need to be organized in an orderly manner to form a one-to-one corresponding dataset. With current as the horizontal axis and criterion resistance as the vertical axis, the organized dataset is mapped to a two-dimensional coordinate system. A smooth curve fitting algorithm is used to connect each data node, and finally, a criterion resistance characteristic curve that reflects the change law of equivalent resistance with current under theoretical conditions is generated.

[0045] To obtain the differential curve of the battery's current-voltage characteristic curve source data, discrete data differentiation calculations are performed on the source data. First, the source data needs to undergo secondary preprocessing to ensure that the data consists of continuous discrete points arranged according to the current gradient. Then, the finite difference method is used for discrete data differentiation calculation. For two adjacent current nodes, the ratio of voltage change to current change is calculated; this ratio is the voltage change rate for the corresponding current interval. This method is applied to all adjacent nodes across the entire current interval to obtain the voltage change rate data for each node. Finally, the calculated voltage change rate data is plotted as a curve with current as the x-axis and voltage change rate as the y-axis, which is the differential curve of the battery's current-voltage characteristic curve source data.

[0046] To determine the measured resistance characteristic curve based on the differential curve, it is necessary to extract the voltage change rate values ​​corresponding to each current node within the full current range from the differential curve. The voltage change rate values ​​are the actual equivalent resistance of the fuel cell under the corresponding current conditions. The extracted equivalent resistance data is then calibrated to remove outliers at edge nodes introduced by the differential calculation. The calibrated current and actual equivalent resistance data are then organized, and a curve is plotted with current as the abscissa and actual equivalent resistance as the ordinate. Finally, a measured resistance characteristic curve that reflects the true operating state of the battery is obtained.

[0047] Furthermore, in the embodiments of this application, the fuel supply limit current value of the fuel cell is calculated based on the target fuel supply flow rate; the concentration data of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet position are calculated under each current condition in the source data of the battery current-voltage characteristic curve based on the fitted battery model; a data table is generated based on each current and the corresponding hydrogen and water vapor concentration data, and the criterion potential of the fuel cell is calculated based on each row of data in the data table; the criterion resistance characteristic curve is calculated based on the fuel supply limit current value and the criterion potential.

[0048] Among them, the fuel supply limit current value is the maximum current value corresponding to the fuel supply amount that the fuel cell anode can provide for the electrochemical reaction to reach saturation under the specific operating condition of the target fuel supply flow rate; the battery model is the electrochemical mathematical model of the fuel cell obtained by fitting the source data of the battery current-voltage characteristic curve; the data table is a parameter correlation table containing hydrogen concentration and water vapor concentration at the interface between the fuel cell anode and electrolyte, arranged in order according to current conditions; the criterion potential is the theoretical output potential of the fuel cell calculated by fitting the battery model based on the current and corresponding hydrogen and water vapor concentration data of each row in the data table.

[0049] It is understood that this application embodiment relies on the target fuel supply flow rate and the fitted battery model. Each current condition in the source data of the battery volt-ampere characteristic curve is substituted into the fitted battery model and arranged in order of current to generate a corresponding data table containing three parameters: current, hydrogen concentration, and water vapor concentration. Based on the data table, the battery model is substituted into the polarization effect and reaction thermodynamic formulas to calculate the criterion potential corresponding to each current condition. Finally, combined with the fuel supply limit current value, the criterion resistance of each node is calculated throughout the entire current range to generate the criterion resistance characteristic curve. This constructs a correlation chain from macroscopic fuel flow rate to microscopic interface concentration, and then to the theoretical potential and resistance curve. It accurately reflects the change law of the theoretical equivalent resistance of the battery with current under the target fuel supply flow rate, and achieves a trade-off between the three indicators of battery operation safety, high output power, and high power generation efficiency. It improves the accuracy of the criterion resistance characteristic curve, leaves an appropriate safety margin for the method of determining operating conditions, and can be well adapted to practical engineering applications.

[0050] Specifically, to calculate the fuel supply limit current value of a fuel cell based on the target fuel supply flow rate, the following steps are required: First, collect the necessary basic parameters, including the target fuel supply flow rate, the effective reaction area of ​​the fuel cell anode electrode, the electrode porosity, the molar mass of hydrogen, the stoichiometric ratio of the electrochemical reaction, and the diffusion coefficient of the fuel within the electrode. Then, based on the theoretical equations for calculating the fuel supply limit current value, substitute the target fuel supply flow rate into the equations to clarify the balance between the fuel transport rate from the anode inlet to the outlet and the electrochemical reaction consumption rate. Finally, by calculating the current value corresponding to when the hydrogen concentration at the anode-electrolyte interface at the fuel outlet approaches zero, the fuel supply limit current value under the target fuel supply flow rate can be obtained.

[0051] To obtain the mole fractions of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet location using a modeling method, a two-dimensional numerical model of the fuel cell needs to be established. Then, based on the source data of the current-voltage characteristic curve, all the parameters to be fitted in the two-dimensional numerical model are determined. Subsequently, the concentration data of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet location under each current condition in the current-voltage characteristic curve source data are calculated using the model. Finally, a data table consisting of current and the mole fractions of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet location is obtained.

[0052] The fuel supply limit current is used as the boundary to define the calculation range of the criterion resistance. Data for operating conditions exceeding the limit current are eliminated. Then, for each current node within the calculation range, the criterion resistance under that current condition is calculated using the correlation formula between equivalent resistance, potential, and current, combined with its corresponding criterion potential. The current values ​​and corresponding criterion resistance values ​​across the entire range are organized to form a current-criterion resistance dataset. Finally, the dataset is mapped to a two-dimensional coordinate system with current as the x-axis and criterion resistance as the y-axis. A smooth curve fitting algorithm is used to connect the data nodes to generate a complete criterion resistance characteristic curve.

[0053] Furthermore, in the embodiments of this application, the formula for calculating the fuel supply limiting current value is as follows: , in, Represents the fuel supply limit current. F represents the fuel supply flow rate, and F represents the Faraday constant.

[0054] It is understood that the calculation formula for the fuel supply limit current value in the fuel cell system proposed in this application directly converts the fuel supply flow rate into the corresponding limit current through the Faraday constant, establishing a precise quantitative correlation between the mass flow rate of the fuel supply and the current output of the electrochemical reaction. This clearly reflects the limiting effect of the fuel supply capacity on the maximum output current of the battery, and also allows the system design and operation to quickly determine the upper limit of the current directly through the fuel flow rate. This provides a theoretical basis for the performance matching, safety protection and optimized control of the fuel cell, and achieves a trade-off between the three indicators of battery operation safety, high output power and high power generation efficiency. It ensures the stable operation of the battery under fuel supply constraints and can be well adapted to practical engineering applications.

[0055] Furthermore, in the embodiments of this application, the formula for calculating the criterion potential is: , in, The criterion potential is represented by R, the gas constant by T, and the battery operating temperature by T. This represents the mole fraction of hydrogen at the anode-electrolyte interface, where the battery fuel outlet is located. This represents the mole fraction of water vapor at the anode-electrolyte interface, where the battery fuel outlet is located.

[0056] It is understood that the criterion potential calculation formula proposed in this application is based on the mole fraction of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet of the fuel cell, combined with the gas constant, battery operating temperature and Faraday constant, to calculate the criterion potential. The criterion potential can quantitatively reflect the critical potential state of the fuel cell under specific operating temperature and fuel outlet interface gas composition conditions, clarify the physical meaning of the high-power operating condition point, and provide a quantitative basis for judging whether the fuel cell is in a critical state of insufficient fuel or performance degradation. It realizes real-time monitoring and early warning, and facilitates timely adjustment of operating strategies to avoid performance degradation or failure caused by insufficient fuel, thereby improving the stability and reliability of system operation.

[0057] Specifically, the calculation formula for the criterion potential first determines the basic parameters such as the gas constant, Faraday constant, and battery operating temperature. Then, for different current values, the mole fractions of hydrogen and water vapor at the anode-electrolyte interface at the battery fuel outlet are obtained. Subsequently, these parameters are substituted into the criterion potential calculation formula to obtain the criterion potential corresponding to each current value. Finally, each set of current values ​​and the corresponding criterion potential results are compiled into a data table containing these two columns of data.

[0058] Furthermore, in the embodiments of this application, the formula for calculating the criterion resistance characteristic curve is as follows: , in, Represents the criterion resistor. Represents the criterion potential, This represents the fuel supply limit current.

[0059] It is understood that the calculation of the criterion resistance characteristic curve in this application embodiment is achieved by calculating the ratio of the calculated criterion potential to the fuel supply limit current to obtain the criterion resistance under different current conditions. By combining the current value to construct the criterion resistance characteristic curve, the correlation between the potential and the fuel supply limit current can be transformed into a physical quantity that reflects the system impedance characteristics. This can more intuitively reflect the impact of fuel supply limitations on the critical state of the battery under different currents. The resistance characteristic curve can more clearly quantify the critical impedance state of the fuel cell under different current outputs, providing a more interpretable physical indicator for the monitoring and evaluation of the system's operating status. It can help determine whether the fuel supply matches the current current demand and also provide support for improving the system's operational stability and reliability.

[0060] Specifically, the criterion resistance characteristic curve is obtained by first acquiring or calculating the criterion potential for different current values, and simultaneously determining the fuel supply limit current under that operating condition. Then, the criterion potential corresponding to each set of currents is divided by the corresponding fuel supply limit current to obtain the criterion resistance corresponding to each current value. Finally, all current values ​​are correlated with the corresponding criterion resistance results and organized into a data table containing two columns of data: current and criterion resistance, thus obtaining the criterion resistance characteristic curve.

[0061] Furthermore, in the embodiments of this application, the discrete data differential calculation method includes any one of central difference, forward difference, backward difference, five-point difference, and polynomial fitting to obtain the differential.

[0062] Among them, central difference is a discrete differential approximation method that uses the difference between the function values ​​of the current data point and the previous and next points to calculate the derivative; forward difference is a discrete differential approximation method that uses the difference between the function values ​​of the current data point and the next point to approximate the derivative; backward difference is a discrete differential approximation method that uses the difference between the function values ​​of the current data point and the previous point to approximate the derivative; five-point difference is a discrete differential approximation method that uses the function values ​​of five points before and after the current data point to construct a fourth-order precision difference formula to calculate the derivative; polynomial fitting for differentiation is a discrete differential method that first performs polynomial fitting on local discrete data points to obtain a continuous polynomial function, then differentiates the polynomial to obtain the derivative of the original function at the corresponding point, and uses this as the derivative approximation of the original function.

[0063] It is understood that the embodiments of this application, based on the characteristics of discrete data, select appropriate methods such as central difference, forward difference, backward difference, five-point difference, or polynomial fitting to calculate the derivative. By constructing an approximate formula through the difference of function values ​​of adjacent data points or by first fitting a local polynomial and then taking the derivative, the approximate calculation of the derivative of discrete data is achieved. This enables the obtaining of derivative results with corresponding accuracy according to different needs, adapts to diverse data scenarios, and provides a variety of discrete differential solutions. Appropriate methods can be selected according to actual accuracy requirements and data conditions, balancing computational efficiency and result reliability.

[0064] Specifically, central difference first determines the uniform sampling step size of the discrete data, and for the target data point xi in the data sequence excluding the first and last points, selects its preceding neighbor xi. 1 and the next adjacent point xi+1, obtain the function value f(xi) corresponding to the three points. 1) Substitute the corresponding values ​​of f(xi) and f(xi+1) into the approximate formula of the first derivative of the central difference: f′(xi)≈2hf(xi+1) f(xi 1) Calculate the approximate value of the derivative of the target point. If a higher-order derivative is required, it can be calculated using the corresponding higher-order central difference formula.

[0065] Forward differencing first determines the uniform sampling step size of the discrete data. For the target data point xi in the data sequence, it selects its next neighboring point xi+1 and obtains the function values ​​f(xi) and f(xi+1) corresponding to the two points. The corresponding values ​​are then substituted into the approximate formula of the first derivative of forward differencing: f′(xi)≈hf(xi+1). f(xi) is used to calculate the approximate value of the derivative of the target point. This method can be directly applied to the starting point of the data sequence. Higher-order derivatives can be calculated using the corresponding higher-order forward difference formula.

[0066] Backward differencing first determines the uniform sampling step size of the discrete data, and then selects the previous neighboring point xi for the target data point xi in the data sequence. 1. Obtain the function value f(xi) corresponding to two points. 1) f(xi), substitute the corresponding value into the backward difference first derivative approximation formula f′(xi)≈hf(xi). f(xi 1) The approximate value of the derivative of the target point is calculated. This method can be directly applied to the end point of the data sequence. Higher-order derivatives can be calculated by the corresponding higher-order backward difference formula.

[0067] Five-point difference sampling first determines the uniform sampling step size h of the discrete data, and then selects the first two points xi of the target data point xi in the data sequence, excluding the first two and last two points. 2. xi 1 and the next two points xi+1 and xi+2, together with the target point, make a total of five points. Obtain the function value f(xi) corresponding to each point. 2) f(xi) 1) Substitute the corresponding values ​​of f(xi), f(xi+1), and f(xi+2) into the five-point difference first derivative approximation formula f′(xi)≈12h f(xi+2)+8f(xi+1) 8f(xi 1)+f(xi 2) Calculate the approximate value of the derivative of the target point. Higher-order derivatives can be calculated using the corresponding higher-order five-point difference formula.

[0068] Polynomial fitting for differentiation involves first selecting several adjacent discrete points around the target data point to form a fitting dataset based on the noise level and sampling characteristics of the discrete data. Then, a suitable polynomial order, such as a quadratic or cubic polynomial, is determined based on the data characteristics. A fitting method, such as least squares, is used to fit the fitting dataset using a polynomial to obtain a continuous polynomial function P(x). Next, the derivative of the polynomial function P(x) is calculated to obtain the corresponding derivative function P′(x). Finally, the x-coordinate of the target data point is substituted into the derivative function P′(x) to calculate the approximate value of the derivative at that point. If it is necessary to calculate the derivative of multiple points, the above local fitting and differentiation steps can be repeated for each target point.

[0069] This application embodiment generates a fuel cell criterion resistance characteristic curve and a measured resistance characteristic curve from source data of the battery volt-ampere characteristic curve, and determines the operating condition boundary point corresponding to the target fuel supply flow rate. The criterion resistance characteristic curve, which reflects the change law of the ideal equivalent resistance of the battery, is obtained through theoretical calculation. At the same time, based on the source data of the volt-ampere characteristic curve, the measured resistance characteristic curve, which reflects the actual operating state of the battery, is calculated. The two curves are then compared and analyzed. By capturing the intersection points and deviation change nodes of the curve trends, the operating condition boundary point under the target fuel supply flow rate is finally determined. This achieves accurate analysis of the change law of the battery's equivalent resistance with current under the target fuel supply flow rate, clearly delineates the dominant range of different polarization effects, and the determined operating condition boundary point has clear physical meaning and verifiability, providing an intuitive and accurate basis for the evaluation of the battery's operating state.

[0070] In step S103, if either the power or efficiency corresponding to the operating condition boundary point does not meet the user's requirements, the target fuel supply flow rate is adjusted to redetermine the operating condition boundary point. If both the power and efficiency corresponding to the operating condition boundary point meet the user's requirements, the target operating condition point of the fuel cell is generated based on the power and efficiency corresponding to the operating condition boundary point.

[0071] Among them, user requirements are specific quantitative requirements and constraints on the power and efficiency of fuel cell system operation proposed by the user in combination with the actual application scenarios of fuel cells; the target operating condition point is the specific operating state point that the fuel cell system must follow in actual operation, with the power and efficiency at the qualified operating condition point as the core parameters, provided that the power and efficiency at the corresponding operating condition boundary point meet the user requirements.

[0072] It is understood that the embodiments of this application take whether the power and efficiency corresponding to the operating condition boundary point meet the user's needs as the core judgment criterion, and dynamically optimize the fuel cell operating condition boundary point and determine the target operating condition point. By adjusting the fuel supply flow, closed-loop optimization of the operating condition boundary point is achieved, ensuring that the final target operating condition point meets the preset requirements in terms of power and efficiency performance indicators. This fundamentally avoids the situation where a single indicator meets the standard but the overall operating state does not meet the application expectations, ensuring the dual compliance of the target operating condition point performance parameters, providing an optimization means for adjusting the fuel supply flow, and ensuring that the determination of the target operating condition point always revolves around the performance requirements of the user's actual application. This ensures a high degree of matching between the operating condition point and the actual application requirements, guiding the fuel cell system to achieve coordinated operation of power and efficiency under the premise of fuel supply matching, and providing specific execution basis for subsequent fuel cells, effectively improving the adaptability and practicality of fuel cell system operation.

[0073] Specifically, this application embodiment evaluates whether the operating condition boundary point obtained under the fuel supply flow rate meets the user's needs, and evaluates the power and efficiency corresponding to the operating condition boundary point. If the evaluation result meets the user's needs, the operating condition boundary point corresponding to the target fuel supply flow rate is taken as the target operating condition point. If the evaluation result does not meet the user's needs, it is necessary to change the fuel supply flow rate. For example, if the power corresponding to the operating condition boundary point does not meet the user's needs, the fuel supply flow rate is appropriately increased; if the power generation efficiency corresponding to the operating condition boundary point does not meet the user's needs, the fuel supply flow rate is appropriately decreased. After changing the fuel supply flow rate, the steps of generating the criterion resistance characteristic curve and the measured resistance characteristic curve of the solid oxide fuel cell based on the battery volt-ampere characteristic curve source data are repeated. The operating condition boundary point corresponding to the target fuel supply flow rate is determined based on the criterion resistance characteristic curve and the measured resistance characteristic curve. The operating condition boundary points under different fuel supply flow rates are obtained. The output power and efficiency of the operating condition boundary points under different fuel supply flow rates are compared to select the fuel supply flow rate and its corresponding operating current that meet the user's needs as the final ideal operating condition point.

[0074] This application embodiment uses whether the power and efficiency corresponding to the operating condition boundary point meet user needs as the core judgment criterion. It dynamically optimizes the fuel cell operating condition boundary point and determines the target operating condition point. By adjusting the fuel supply flow, it achieves closed-loop optimization of the operating condition boundary point, ensuring that the final target operating condition point meets the preset requirements in both power and efficiency performance indicators. This fundamentally avoids the situation where a single indicator meets the standard but the overall operating state does not meet the application expectations, ensuring the dual compliance of the target operating condition point performance parameters. It provides an optimization means for adjusting the fuel supply flow, and at the same time, it ensures that the determination of the target operating condition point always revolves around the performance requirements of the user's actual application, ensuring a high degree of matching between the operating condition point and the actual application requirements. This not only guides the fuel cell system to achieve coordinated power and efficiency compliance under the premise of fuel supply matching, but also provides specific execution basis for subsequent fuel cells, effectively improving the adaptability and practicality of fuel cell system operation.

[0075] To better understand the solution of this application, the following specific embodiment describes the method or execution process for determining the operating point of the solid oxide fuel cell of this application, as follows: like Figure 2 As shown, the method for determining the high-power / high-efficiency operating conditions of a fuel cell includes the following steps: (1) Select the fuel supply flow rate for experimental testing to obtain the source data of the battery volt-ampere characteristic curve; (2) Based on the obtained battery current-voltage characteristic curve source data, establish and fit the battery model to obtain the mole fraction of hydrogen and water vapor at the three-phase interface at the anode outlet under different current conditions; then calculate the criterion resistance under different currents using the analytical formula proposed in this method to form the criterion resistance characteristic curve. (3) Perform appropriate mathematical transformations on the obtained battery current-voltage characteristic curve source data to obtain the measured resistance characteristic curve; (4) Compare the measured resistance characteristic curve with the criterion resistance characteristic curve to obtain the high power / high efficiency operating condition boundary point under the fuel supply flow rate; (5) Assess whether the operating condition boundary point obtained under this fuel supply flow rate meets the user's needs; (6) Change the fuel supply flow rate and repeat steps (1)-(5) to obtain the high power / high efficiency operating condition boundary point under different fuel supply flow rates; (7) Compare the output power and efficiency at the high power / high efficiency operating point under different fuel supply flow rates to determine the ideal operating point.

[0076] According to one embodiment of the present invention, before performing step (1) above, it is necessary to determine the desired operating conditions of the battery, specifically including: the ambient temperature of the battery operation, the air supply flow rate, and the fuel composition supplied. Step (1) above is then performed under these operating conditions.

[0077] When performing step (1) above, the fuel supply flow rate needs to be specified; the battery current-voltage characteristic curve refers to a set of continuous current-voltage data. According to one embodiment of the present invention, the current-voltage curve is sampled at equal current intervals of 1 ampere starting from 0 ampere until the obtained current-voltage characteristic curve contains the peak power operating point. Figure 3 (a) schematically represents source data of the current-voltage characteristic curve obtained according to an embodiment of the present invention.

[0078] According to one aspect of the present invention, a battery model is established and parameter fitting is completed using the selected fuel supply flow rate and the source data of the current-voltage characteristic curve; the mole fraction of hydrogen and water vapor at the three-phase interface at the anode outlet under different current conditions is obtained using the fitted model. According to one aspect of the embodiments of the present invention, by utilizing the obtained mole fractions of hydrogen and water vapor at the three-phase interface of the anode outlet under different current conditions, the criterion resistance under different currents is calculated using the analytical formula proposed in this method, thereby forming a set of criterion resistance characteristic curve data.

[0079] When performing step (2) above, it is necessary to calculate the fuel supply limit current value based on the fuel supply flow rate specified in step (1). The calculation formula is as follows:

[0080] in, Represents the fuel supply limit current. F represents the fuel supply flow rate, and F represents the Faraday constant. According to one embodiment of the present invention, when performing step (2) above, it is also necessary to obtain the mole fraction of hydrogen and water vapor at the anode-electrolyte interface at the battery fuel outlet position based on the source data of the volt-ampere characteristic curve obtained in step (1).

[0081] According to one embodiment of the present invention, when performing step (2) above, the mole fractions of hydrogen and water vapor at the interface between the anode and electrolyte at the fuel outlet of the battery can be obtained using a model method. First, a two-dimensional numerical model of the fuel cell is established; then, based on the source data of the current-voltage characteristic curve obtained in step (1), all the parameters to be fitted in the two-dimensional numerical model are determined; then, the concentration data of hydrogen and water vapor at the interface between the anode and electrolyte at the fuel outlet of the battery under each current condition in the source data of the current-voltage characteristic curve obtained in step (1) are calculated using the model; finally, a data table is obtained consisting of three columns of data: current, mole fraction of hydrogen and water vapor at the interface between the anode and electrolyte at the fuel outlet of the battery.

[0082] When performing step (2) above, it is necessary to calculate the criterion potential of each row of data based on the data table consisting of three columns of data. The calculation formula is as follows:

[0083] in, The criterion potential is represented by R, the gas constant by T, and the battery operating temperature by T. and These represent the mole fractions of hydrogen and water vapor at the anode-electrolyte interface, respectively, at the battery fuel outlet. Based on the above calculations, a data table consisting of two columns of data: current and criterion potential, was obtained.

[0084] When performing step (2) above, it is necessary to calculate the criterion resistance characteristic curve based on the fuel supply limit current obtained in the above steps and the data table consisting of the current and criterion potential columns. The calculation formula is as follows:

[0085] in, This represents the criterion resistor. Through the above calculations, a data table consisting of two columns of data—current and criterion resistor—is obtained, which is the criterion resistor characteristic curve. Figure 4 (a) Schematic representation of a criterion resistance characteristic curve obtained according to an embodiment of the present invention.

[0086] When performing step (3) above, it is necessary to perform appropriate mathematical transformations on the source data of the volt-ampere characteristic curve obtained in step (1). Specifically, appropriate mathematical transformations refer to performing discrete data differential calculations on the source data of the volt-ampere characteristic curve (differential calculation methods include, but are not limited to: central difference, forward difference, backward difference, five-point difference, and polynomial fitting to obtain the differential). Differential calculations use the current data as the independent variable to obtain the differential curve of the source data of the volt-ampere characteristic curve, i.e., the measured resistance characteristic curve. Figure 5(a) Schematic representation of a measured resistance characteristic curve obtained according to an embodiment of the present invention.

[0087] When performing step (4) above, it is necessary to compare the measured resistance characteristic curve with the criterion resistance characteristic curve. Figure 6 (a) Schematic representation of a comparison between a measured resistance characteristic curve and a criterion resistance characteristic curve obtained according to an embodiment of the present invention. The two characteristic curves have one and only one intersection point, and the operating current value corresponding to this intersection point is the high-power / high-efficiency operating condition boundary point under the target fuel supply flow rate condition.

[0088] When performing step (5) above, it is necessary to evaluate the high-power / high-efficiency operating condition boundary point obtained from step (4) above. Specifically, evaluate the battery output power and efficiency corresponding to this operating condition point. If the evaluation result meets the user's requirements, skip steps (6) and (7), and the high-power / high-efficiency operating condition boundary point obtained from step (4) is the ideal operating condition point. If the evaluation result does not meet the user's requirements, steps (6) and (7) need to be performed.

[0089] According to one embodiment of the present invention, when performing step (6) above, it is necessary to change the fuel supply flow rate. The direction of the change is determined by the evaluation result of step (5). Specifically, if the output power corresponding to the high power / high efficiency operating condition boundary point obtained by step (4) does not meet the user's needs, the fuel supply flow rate is appropriately increased; if the power generation efficiency corresponding to the high power operating condition point obtained by step (4) does not meet the user's needs, the fuel supply flow rate is appropriately decreased. After changing the fuel supply flow rate, steps (1)-(5) are repeated to obtain the high power / high efficiency operating condition boundary points under different fuel supply flow rates.

[0090] According to one embodiment of the present invention, when performing step (7) above, the output power and efficiency at the high-power / high-efficiency operating condition boundary point under different fuel supply flow rates are compared. The fuel supply flow rate that meets the user's needs and its corresponding operating current are selected as the final ideal operating condition point. Figure 7 This illustration schematically shows the high-power / high-efficiency operating condition boundary points and their corresponding output power and efficiency under different fuel supply flow rates obtained according to an embodiment of the present invention.

[0091] In summary, the method for determining the operating point of a solid oxide fuel cell proposed in this application first acquires the source data of the volt-ampere characteristic curve of the solid oxide fuel cell at the target fuel supply flow rate, then generates a criterion resistance characteristic curve and a measured resistance characteristic curve based on this data, thereby determining the corresponding operating point boundary. Subsequently, the target fuel supply flow rate is dynamically adjusted based on whether the power and efficiency at the operating point boundary meet user requirements, and the operating point boundary is repeatedly optimized until both the power and efficiency at the operating point boundary meet the standards, ultimately generating the target operating point. This achieves a compromise between the three core indicators of battery operation safety, high output power, and high power generation efficiency. The operating point determined in the application embodiment has a clear physical meaning and accurately corresponds to the state when the current-voltage characteristic curve is about to enter the concentration polarization control region. At the same time, the fuel utilization rate corresponding to the operating point is lower than the critical operating point of nickel oxidation of the anode, leaving an appropriate safety margin for battery operation. This avoids power efficiency loss caused by insufficient fuel utilization and prevents the surge in polarization loss from affecting operational safety. It can lock in the optimal operating condition according to user needs, and the derivation based on the physical model makes the method have good universality and can be adapted to batteries with different performance. The safety margin design can also well cope with the complex scenarios in actual engineering applications and simplify the selection process of the ideal operating condition.

[0092] Next, referring to the accompanying drawings, the device for determining the operating point of a solid oxide fuel cell according to an embodiment of this application is described.

[0093] Figure 8 This is a block diagram of the solid oxide fuel cell operating condition point determination device 800 according to an embodiment of this application.

[0094] like Figure 8 As shown, the solid oxide fuel cell operating condition point determination device 800 includes: an acquisition module 801, a generation module 802, and an adjustment module 803.

[0095] The module 801 is used to acquire source data of the volt-ampere characteristic curve of the solid oxide fuel cell under the target fuel supply flow rate; the generation module 802 is used to generate the criterion resistance characteristic curve and the measured resistance characteristic curve of the solid oxide fuel cell based on the source data of the volt-ampere characteristic curve, and to determine the operating condition boundary point corresponding to the target fuel supply flow rate based on the criterion resistance characteristic curve and the measured resistance characteristic curve; the adjustment module 803 is used to adjust the target fuel supply flow rate to redetermine the operating condition boundary point if either the power or efficiency corresponding to the operating condition boundary point does not meet the user's requirements, and to generate the target operating condition point of the fuel cell based on the power and efficiency corresponding to the operating condition boundary point if both the power and efficiency corresponding to the operating condition boundary point meet the user's requirements.

[0096] Furthermore, in this embodiment, the generation module 802 is further configured to: fit a battery model of a solid oxide fuel cell based on the battery current-voltage characteristic curve source data; calculate the criterion resistance under different currents based on the fitted battery model and the target fuel supply flow rate; generate a criterion resistance characteristic curve based on the criterion resistance under different currents; perform discrete data differentiation calculation on the battery current-voltage characteristic curve source data to obtain the differential curve of the battery current-voltage characteristic curve source data; and determine the measured resistance characteristic curve based on the differential curve.

[0097] Furthermore, in this embodiment, the generation module 802 is further configured to: calculate the fuel supply limit current value of the fuel cell based on the target fuel supply flow rate; calculate the concentration data of hydrogen and water vapor at the anode-electrolyte interface at the fuel outlet position under each current condition in the source data of the battery current-voltage characteristic curve based on the fitted battery model; generate a data table based on each current and the corresponding hydrogen and water vapor concentration data; calculate the criterion potential of the fuel cell based on each row of data in the data table; and calculate the criterion resistance characteristic curve based on the fuel supply limit current value and the criterion potential.

[0098] Furthermore, in this embodiment, the formula for calculating the fuel supply limit current value is as follows: , in, Represents the fuel supply limit current. F represents the fuel supply flow rate, and F represents the Faraday constant.

[0099] Furthermore, in the embodiments of this application, the formula for calculating the criterion potential is as follows: , in, The criterion potential is represented by R, the gas constant by T, and the battery operating temperature by T. This represents the mole fraction of hydrogen at the anode-electrolyte interface, where the battery fuel outlet is located. This represents the mole fraction of water vapor at the anode-electrolyte interface, where the battery fuel outlet is located.

[0100] Furthermore, in the embodiments of this application, the formula for calculating the criterion resistance characteristic curve is as follows: , in, Represents the criterion resistor. Represents the criterion potential, This represents the fuel supply limit current.

[0101] Furthermore, in the embodiments of this application, the discrete data differential calculation method includes any one of central difference, forward difference, backward difference, five-point difference, and polynomial fitting to obtain the differential.

[0102] It should be noted that the explanation of the aforementioned embodiment of the method for determining the operating point of a solid oxide fuel cell also applies to the device for determining the operating point of a solid oxide fuel cell in this embodiment, and will not be repeated here.

[0103] In summary, the solid oxide fuel cell operating condition point determination device proposed in this application first acquires the source data of the solid oxide fuel cell's volt-ampere characteristic curve at the target fuel supply flow rate, then generates a criterion resistance characteristic curve and a measured resistance characteristic curve based on this data, thereby determining the corresponding operating condition boundary point. Subsequently, based on whether the power and efficiency at the operating condition boundary point meet user requirements, the target fuel supply flow rate is dynamically adjusted, and the operating condition boundary point is repeatedly optimized until both the power and efficiency at the operating condition boundary point meet the standards, ultimately generating the target operating condition point. This achieves a compromise between the three core indicators of battery operation safety, high output power, and high power generation efficiency. The operating point determined in the application embodiment has a clear physical meaning and accurately corresponds to the state when the current-voltage characteristic curve is about to enter the concentration polarization control region. At the same time, the fuel utilization rate corresponding to the operating point is lower than the critical operating point of nickel oxidation of the anode, leaving an appropriate safety margin for battery operation. This avoids power efficiency loss caused by insufficient fuel utilization and prevents the surge in polarization loss from affecting operational safety. It can lock in the optimal operating condition according to user needs, and the derivation based on the physical model makes the method have good universality and can be adapted to batteries with different performance. The safety margin design can also well cope with the complex scenarios in actual engineering applications and simplify the selection process of the ideal operating condition.

[0104] Figure 9 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: The memory 901, the processor 902, and the computer program stored on the memory 901 and capable of running on the processor 902.

[0105] When the processor 902 executes the program, it implements the method for determining the operating point of a solid oxide fuel cell provided in the above embodiments.

[0106] Furthermore, electronic devices also include: Communication interface 903 is used for communication between memory 901 and processor 902.

[0107] The memory 901 is used to store computer programs that can run on the processor 902.

[0108] The memory 901 may include high-speed RAM (Random Access Memory) memory, and may also include non-volatile memory, such as at least one disk storage.

[0109] If the memory 901, processor 902, and communication interface 903 are implemented independently, then the communication interface 903, memory 901, and processor 902 can be interconnected via a bus to complete communication between them. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, or an EISA (Extended Industry Standard Architecture) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 5 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0110] Optionally, in a specific implementation, if the memory 901, processor 902, and communication interface 903 are integrated on a single chip, then the memory 901, processor 902, and communication interface 903 can communicate with each other through an internal interface.

[0111] The processor 902 may be a CPU (Central Processing Unit), an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of this application.

[0112] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described method for determining the operating point of a solid oxide fuel cell.

[0113] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. 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.

[0114] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0115] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0116] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any of the following techniques known in the art, or a combination thereof: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (FPGAs), field-programmable gate arrays (FPGAs), etc.

[0117] Those skilled in the art will understand that all or part of the steps of the methods implementing the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0118] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A method of determining an operating point of a solid oxide fuel cell, characterized by, Includes the following steps: Obtain source data of the volt-ampere characteristic curve of a solid oxide fuel cell at a target fuel supply flow rate; The criterion resistance characteristic curve and the measured resistance characteristic curve of the solid oxide fuel cell are generated based on the source data of the battery current-voltage characteristic curve. The operating condition boundary point corresponding to the target fuel supply flow rate is determined based on the criterion resistance characteristic curve and the measured resistance characteristic curve. If either the power or efficiency corresponding to the operating condition boundary point does not meet the user's requirements, the target fuel supply flow rate is adjusted to redetermine the operating condition boundary point. If both the power and efficiency corresponding to the operating condition boundary point meet the user's requirements, the target operating condition point of the fuel cell is generated based on the power and efficiency corresponding to the operating condition boundary point.

2. The method of determining an operating condition point of a solid oxide fuel cell according to claim 1, characterized by, The process of generating the criterion resistance characteristic curve and the measured resistance characteristic curve of the solid oxide fuel cell based on the source data of the battery current-voltage characteristic curve includes: The battery model of the solid oxide fuel cell is fitted based on the source data of the battery current-voltage characteristic curve. The criterion resistance under different currents is calculated based on the fitted battery model and the target fuel supply flow rate. The criterion resistance characteristic curve is generated based on the criterion resistance under different currents. Discrete data differentiation calculations are performed on the source data of the battery current-voltage characteristic curve to obtain the differential curve of the source data of the battery current-voltage characteristic curve, and the measured resistance characteristic curve is determined based on the differential curve.

3. The method of determining an operating condition point of a solid oxide fuel cell according to claim 2, characterized by, The step of calculating the criterion resistance under different currents based on the fitted battery model and the target fuel supply flow rate includes: Calculate the fuel supply limit current value of the fuel cell based on the target fuel supply flow rate; The concentration data of hydrogen and water vapor at the anode-electrolyte interface at the battery fuel outlet location are calculated under each current condition in the source data of the battery current-voltage characteristic curve based on the fitted battery model. A data table is generated based on each current and the corresponding concentration data of hydrogen and water vapor. The criterion potential of the fuel cell is calculated based on each row of data in the data table. The criterion resistance characteristic curve is calculated based on the fuel supply limit current value and the criterion potential.

4. The method of determining an operating condition point of a solid oxide fuel cell according to claim 3, characterized by, The formula for calculating the fuel supply limit current value is as follows: ， wherein, represents a fuel supply limit current, represents a fuel supply flow rate, F represents a Faraday constant.

5. The method of determining an operating condition point of a solid oxide fuel cell according to claim 3, characterized by, The formula for calculating the criterion potential is as follows: ， wherein, R represents the gas constant, T represents the cell operating temperature, XH2represents the mole fraction of hydrogen gas at the anode-electrolyte interface at the fuel outlet location of the cell, XH2Orepresents the mole fraction of water vapor at the anode-electrolyte interface at the fuel outlet location of the cell.

6. The method for determining the operating point of a solid oxide fuel cell according to claim 3, characterized in that, The formula for calculating the criterion resistance characteristic curve is as follows: ， in, Represents the criterion resistor. Represents the criterion potential, This represents the fuel supply limit current.

7. The method for determining the operating point of a solid oxide fuel cell according to claim 2, characterized in that, The methods for calculating the differential of discrete data include any one of the following: central difference, forward difference, backward difference, five-point difference, and polynomial fitting to obtain the differential.

8. A device for determining the operating point of a solid oxide fuel cell, characterized in that, include: The acquisition module is used to acquire source data of the current-voltage characteristic curve of a solid oxide fuel cell under a target fuel supply flow rate; The generation module is used to generate the criterion resistance characteristic curve and the measured resistance characteristic curve of the solid oxide fuel cell based on the source data of the battery current-voltage characteristic curve, and to determine the operating condition boundary point corresponding to the target fuel supply flow rate based on the criterion resistance characteristic curve and the measured resistance characteristic curve. The adjustment module is used to adjust the target fuel supply flow rate to redetermine the operating condition boundary point if either the power or efficiency corresponding to the operating condition boundary point does not meet the user's requirements; if both the power and efficiency corresponding to the operating condition boundary point meet the user's requirements, the target operating condition point of the fuel cell is generated based on the power and efficiency corresponding to the operating condition boundary point.

9. An electronic device, characterized in that, include: The method for determining the operating point of a solid oxide fuel cell according to any one of claims 1-7 includes a memory, a processor, and a computer program stored in the memory and executable on the processor.

10. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed, they implement the method for determining the operating point of a solid oxide fuel cell according to any one of claims 1-7.

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