Calibration control method and system for solving multi-field coupling of solid oxide fuel cell

Abstract

The application provides a kind of solid oxide fuel cell multi-field coupling calibration control method and system, including building SOFC stack calibration experiment platform, obtaining internal state field data and corresponding external measurable parameters covering full calibration interval;Based on the calibration data, a calibration lookup table is established between the measurable parameters and the key internal state parameters, and a coupling correction coefficient matrix is constructed to represent the cross coupling effect between inputs;During online control, the current measurable parameters are collected, and the actual internal state is obtained by interpolation lookup table combined with coupling correction coefficient matrix decoupling calculation;To meet the voltage, temperature difference and concentration safety constraints as the target, the optimal control amount is calculated according to the actual internal state and the action is executed.The application offlines the complex multi-field coupling calculation, and only needs table lookup and simple operation during online control, realizes low complexity, high precision decoupling control, and significantly improves the real-time performance, engineering practicability and universality of SOFC control.

Description

Technical Field

[0001] This invention relates to the field of solid oxide fuel cell (SOFC) technology, and in particular to a calibration control method and system for solving multi-field coupling in solid oxide fuel cells. Background Technology

[0002] The operation of solid oxide fuel cells (SOFCs) involves strong nonlinear coupling of multiple physical processes, including electrochemical, temperature, flow, and concentration fields. Uneven internal state distribution can lead to localized thermal stress overload and performance degradation, which is the core issue restricting the long-term stable operation of SOFC systems.

[0003] Existing control methods mainly fall into two categories: one relies on numerical simulation models, which have high computational complexity and are difficult to implement in real-time control on embedded main controllers; the other relies on data-driven black-box models, which require a large amount of online training data, have poor universality for SOFC stacks with different structures and power ratings, and incur high model transfer costs. Furthermore, calibration methods, as a commonly used deterministic mapping relationship construction method in industrial fields, have not been effectively applied in SOFC multi-field coupled control. Existing technologies only calibrate single parameters and fail to establish multi-input, multi-output coupling mapping relationships, thus failing to solve the problem of multi-field cross-interference.

[0004] Therefore, how to reduce online computational complexity and improve engineering practicality while ensuring control accuracy is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This invention provides a calibration control method and system for solving multi-field coupling in solid oxide fuel cells, which can ensure control accuracy while reducing online computational complexity and improving engineering practicality.

[0006] On one hand, the present invention provides a calibration control method for solving multi-field coupling in solid oxide fuel cells, comprising: A calibration experimental platform for solid oxide fuel cell stacks was built to determine the control inputs and their calibration ranges, and the observable outputs were determined. By combining the calibration ranges of each control input, multiple calibration input combinations are obtained; For each calibration input combination, the temperature and reactant concentration inside the battery stack are measured to obtain internal state field distribution data, and the corresponding control input and observable output are recorded as external measurable parameters. The internal state field distribution data and external measurable parameters obtained under all calibration input combinations are used together as calibration data. Based on the calibration data, a calibration lookup table between external measurable parameters and internal state parameters is established, and a coupling correction coefficient matrix is ​​constructed. The coupling correction coefficient matrix is ​​used to characterize the cross-coupling effect of different control input quantities on the internal state parameters. During the control cycle, the current external measurable parameters are collected, and the first estimated value of the internal state parameters is obtained through the calibration lookup table. Then, the first estimated value is decoupled using the coupling correction coefficient matrix to obtain the actual internal state. With the control objectives of stable output voltage, maximum internal temperature difference not exceeding the safety threshold, and minimum reactant concentration not lower than the lower limit threshold, the optimal control input is calculated based on the actual internal state and the calibration lookup table, and the control action is executed.

[0007] On the other hand, the present invention also provides a calibration control system for solving multi-field coupling in solid oxide fuel cells, comprising: The experimental module is used to build a calibration experimental platform for solid oxide fuel cell stacks, determine the control input quantities and their calibration ranges, and determine the observable output quantities. The combination module is used to combine the calibration ranges of various control inputs to obtain multiple calibration input combinations; The measurement module is used to measure the temperature and reactant concentration inside the battery stack for each calibration input combination to obtain internal state field distribution data, and at the same time record the corresponding control input and observable output as external measurable parameters. A module is established to use the internal state field distribution data and external measurable parameters obtained under all calibration input combinations as calibration data. Based on the calibration data, a calibration lookup table between external measurable parameters and internal state parameters is established, and a coupling correction coefficient matrix is ​​constructed. The coupling correction coefficient matrix is ​​used to characterize the cross-coupling effect of different control input quantities on the internal state parameters. The analysis module is used to collect current external measurable parameters within the control cycle, obtain the first estimated value of the internal state parameters through the calibration lookup table, and then decouple the first estimated value using the coupling correction coefficient matrix to obtain the actual internal state. The control module is used to calculate the optimal control input based on the actual internal state and the calibration lookup table, and to execute the control action, with the control objectives being stable output voltage, maximum internal temperature difference not exceeding the safety threshold, and minimum reactant concentration not lower than the lower limit threshold.

[0008] The present invention provides a calibration control method and system for solving multi-field coupling in solid oxide fuel cells. This method involves building a calibration experimental platform for a solid oxide fuel cell stack, determining the control inputs and their calibration intervals, and combining these intervals to obtain multiple calibration input combinations. For each calibration input combination, the method measures the temperature and reactant concentration values ​​inside the stack to obtain internal state field distribution data, while simultaneously recording the corresponding control inputs and observable outputs as external measurable parameters. Based on the calibration data obtained under all calibration input combinations, a calibration lookup table is established between external measurable parameters and internal state parameters, and a system is constructed to characterize the effect of different control inputs on the internal state field. The coupling correction coefficient matrix is ​​used to determine the cross-coupling effect of internal state parameters. During the control cycle, current external measurable parameters are collected, and the first estimated value of the internal state parameters is obtained through a calibration lookup table. Then, the coupling correction coefficient matrix is ​​used to decouple the first estimated value to obtain the actual internal state. With stable output voltage, maximum internal temperature difference not exceeding the safety threshold, and minimum reactant concentration not lower than the lower limit threshold as control objectives, the optimal control input is calculated based on the actual internal state and the calibration lookup table, and the control action is executed. This achieves low-complexity, high-precision, and highly versatile real-time decoupling control of multi-field coupling in solid oxide fuel cells, effectively ensuring the long-term stable operation of the stack. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0010] Figure 1 This is a flowchart illustrating the calibration control method for solving multi-field coupling in solid oxide fuel cells provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the calibration control system for solving multi-field coupling in solid oxide fuel cells provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0012] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0013] Figure 1 This is a flowchart illustrating the calibration control method for solving multi-field coupling in solid oxide fuel cells provided in this embodiment of the invention.

[0014] like Figure 1 As shown, the calibration control method for solving multi-field coupling in solid oxide fuel cells provided by this invention mainly includes the following steps: 101. Build a calibration experimental platform for solid oxide fuel cell stacks, determine the control input quantities and their calibration ranges, and determine the observable output quantities; In a specific implementation process, a dedicated calibration experimental platform can be built for the solid oxide fuel cell stack to be controlled. On this platform, fuel flow rate and air flow rate are determined as the main control inputs. At the same time, the stack's output voltage and inlet / outlet temperature difference are determined as observable outputs.

[0015] Specifically, when determining the calibration range of the control input quantity, based on the nonlinear sensitivity of the control input quantity to the internal state parameters, a first level of interval division is used within the range where the sensitivity is higher than a preset threshold, and a second level of interval division is used within the range where the sensitivity is lower than the preset threshold. In subsequent control processes, based on the real-time accumulated interpolation error statistics, sub-intervals are automatically added to intervals with persistently large errors, and intervals that have not been used for a long time are automatically merged. The first level of fineness is less than the second level of fineness.

[0016] In detail, during the calibration preparation phase, the range of all input quantities is not divided at equal intervals. Instead, prior knowledge or a small number of preliminary experiments are used to assess the nonlinear sensitivity of the control input (such as fuel flow rate) to key internal states (such as maximum internal temperature difference) across the entire range of variation. In regions of high sensitivity (e.g., where small fluctuations in flow rate can lead to drastic temperature changes within a certain flow range), a finer first level of granularity is used for interval division, i.e., more calibration points are set within this region to accurately capture nonlinear characteristics. Conversely, in flat regions with low sensitivity, a sparser second level of granularity is used for interval division to reduce the calibration workload.

[0017] During actual operation of the fuel cell stack, the system continuously monitors the accuracy of online condition estimation. Specifically, when more accurate offline analysis or periodic retest data becomes available, the system deduces the interpolation error generated by the lookup table interpolation in conventional control and accumulates it statistically according to different calibration intervals. For intervals with persistently large interpolation errors, it indicates that the original interval division is insufficient to describe the actual characteristics. The system automatically adds sub-intervals within these intervals, i.e., inserts new calibration points (the data of which can be obtained through interpolation of existing data or by arranging additional calibration). Conversely, for calibration intervals that have never been used in actual operation for a long time, the system automatically merges them with adjacent intervals to save storage resources. Through this dynamic adjustment, the calibration lookup table can maintain optimal mapping accuracy for the current actual operating conditions without occupying excessive storage space.

[0018] This embodiment achieves an optimal balance between calibration accuracy and resource consumption through non-uniform calibration interval division and online adaptive adjustment. This not only reduces unnecessary calibration workload but also automatically optimizes the lookup table structure to adapt to performance changes after long-term stack operation, thereby maintaining consistently high-accuracy state estimation.

[0019] 102. Combine the calibration ranges of each control input to obtain multiple calibration input combinations; Each sub-range of fuel flow can be combined with each sub-range of air flow to form multiple calibration input combinations covering the entire operating domain.

[0020] 103. For each calibration input combination, measure the temperature and reactant concentration inside the battery stack to obtain internal state field distribution data, and record the corresponding control input and observable output as external measurable parameters. Specifically, for each calibration input combination, after the system reaches a stable operating state, embedded sensing units can be used to measure the temperature and hydrogen concentration values ​​at different locations inside the battery stack. These embedded sensing units employ miniature thermocouples and oxygen pump-type concentration sensors, arranged at nine characteristic locations across three cross-sections: the inlet, middle, and outlet sections of the stack. Specifically, three sets of sensors can be embedded on the anode side of the 5th, 15th, and 25th cells, covering the areas with the largest temperature and concentration gradients. After the system stabilizes, the temperature and hydrogen concentration values ​​at the nine measurement points are recorded to obtain the internal state field distribution data at the full calibration point. Simultaneously, the current control inputs (fuel flow rate, air flow rate) and observable outputs (output voltage, inlet and outlet temperatures) are recorded as external measurable parameters. Each calibration input combination is measured repeatedly multiple times, and the average value is taken. The data from all calibration input combinations together constitute the calibration dataset.

[0021] In a specific implementation, a low-amplitude frequency sweep excitation can be applied to the fuel cell stack periodically to obtain the response amplitude and phase changes at each measurement point. Based on the response amplitude and phase changes at each measurement point, the characterization capability of each measurement point for temperature and concentration gradients can be evaluated. When the characterization capability of a certain measurement point continues to decline, a second estimated value at the current maximum gradient location is reconstructed using the measured values ​​of other measurement points through spatial interpolation. The second estimated value includes a temperature estimate and a concentration estimate. The second estimated value replaces the measured value at the measurement location where the characterization capability continues to decline, and is used for subsequent calibration lookup table updates.

[0022] In detail, as the fuel cell stack operates for extended periods, some embedded sensors may age, drift, or become covered by contaminants, causing their measurements to fail to accurately reflect the actual physical quantities at that location, particularly reducing their ability to characterize temperature and concentration gradients. To identify this situation, the system periodically performs a diagnostic procedure: while the fuel cell stack is operating normally, a small, low-amplitude excitation signal with a continuously varying frequency within a certain range (frequency sweep) is superimposed. Then, the response signals from the sensors at all measurement points are acquired, and the changes in their response amplitude and phase relative to the excitation signal are analyzed.

[0023] For each measurement point, its ability to dynamically represent the current regional temperature and concentration gradients is comprehensively evaluated based on indicators such as the regularity of its response amplitude and phase changes, and its sensitivity. If the representation ability score of a certain point consistently falls below a preset effective threshold, the data for that point is considered unreliable. In this case, the point is not directly discarded. Instead, the measurements from multiple neighboring measurement points that are still valid after evaluation are used to estimate the temperature and concentration at the evaluated point or at the location of the maximum temperature / concentration gradient near that point in physical space using spatial interpolation algorithms (such as inverse distance weighted interpolation or Kriging interpolation). This second estimate, reconstructed through spatial interpolation, will then formally replace the original, inaccurate direct measurement at that point, serving as valid input data for subsequent calibration lookup table updates or online state estimation.

[0024] 104. Use the internal state field distribution data and external measurable parameters obtained under all calibration input combinations as calibration data. Based on the calibration data, establish a calibration lookup table between external measurable parameters and internal state parameters, and construct a coupling correction coefficient matrix. Based on the aforementioned calibration dataset, data extraction and relationship construction can be performed. Key internal state parameters, namely the maximum internal temperature, maximum internal temperature difference, and minimum internal hydrogen concentration, are extracted from the internal state field data of each calibration point. Then, three one-dimensional calibration lookup tables are established, corresponding to the mapping relationships between measurable parameters and the maximum internal temperature, the maximum internal temperature difference, and the minimum internal hydrogen concentration, respectively. Simultaneously, to handle the cross-coupling effect of fuel flow rate and air flow rate on the internal state, a coupling correction coefficient matrix is ​​constructed. This matrix characterizes the cross-coupling influence of different control inputs on the internal state parameters.

[0025] In a specific implementation, constructing the coupling correction coefficient matrix includes: Sequentially fix all control inputs except the target control input, change only the target control input and measure the change in each internal state parameter, calculate the local coupling gain of the target control input to each internal state parameter, and combine all local coupling gains into a matrix form.

[0026] In detail, we can take two control inputs (fuel flow rate and air flow rate) and three key internal state parameters (maximum internal temperature, maximum internal temperature difference, and minimum hydrogen concentration) as an example to construct a 3x2 matrix. The construction steps involve measuring the coupling gain of each input to each state.

[0027] First, the gain of fuel flow rate on each internal state is determined: the air flow rate is fixed at the midpoint of its calibration range, and then the fuel flow rate is changed stepwise from one calibration level to another. After the system stabilizes, the changes in the maximum internal temperature, the maximum internal temperature difference, and the minimum hydrogen concentration are measured respectively. The three ratios obtained by dividing the change in each state by the change in fuel flow rate are the local coupling gain of fuel flow rate on these three internal states.

[0028] Similarly, to measure the gain of airflow: keep the fuel flow rate constant, change the airflow rate, measure the changes in three internal states, and divide each change by the change in airflow rate to obtain the three local coupling gains of airflow rate.

[0029] Finally, these six calculated coupling gain values ​​are arranged into a matrix according to the organization of states and inputs, thus obtaining the required coupling correction coefficient matrix. Each element in this matrix quantitatively describes the strength of the influence of a specific input change on a specific state, ignoring changes in other inputs.

[0030] The formula for constructing the coupling correction coefficient matrix is ​​as follows: ; in, For input State The coupling correction coefficient, For state changes, Input the amount of change.

[0031] 105. During the control cycle, the current external measurable parameters are collected, and the first estimated value of the internal state parameters is obtained through the calibration lookup table. Then, the first estimated value is decoupled using the coupling correction coefficient matrix to obtain the actual internal state. During the actual operation and control phase of the fuel cell stack, the current fuel flow rate, air flow rate, output voltage, and inlet / outlet temperature are collected in real time within each control cycle (set to 1 second). First, using the current control input as an index, bilinear interpolation is performed in three offline calibration lookup tables to obtain preliminary estimates of the maximum internal temperature, maximum internal temperature difference, and minimum internal hydrogen concentration. Subsequently, a coupling correction coefficient matrix is ​​used to compensate for and eliminate the cross-coupling effects of these preliminary estimates, thereby calculating parameter values ​​that reflect the true internal state of the fuel cell stack.

[0032] 106. With stable output voltage, maximum internal temperature difference not exceeding the safety threshold, and minimum reactant concentration not lower than the lower limit threshold as control objectives, calculate the optimal control input based on the actual internal state and the calibration lookup table, and execute the control action.

[0033] In a specific implementation, the control strategy has three main control objectives: maintaining the output voltage stable near the setpoint, ensuring the maximum internal temperature difference does not exceed a safety threshold of 10 degrees Celsius, and setting a minimum internal hydrogen concentration of no less than 5%. Based on the actual internal state obtained after decoupling, and combined with the input-state mapping relationship described in the calibration lookup table, the optimal fuel flow and air flow control quantities that satisfy all constraints are solved in reverse. These control quantities are then sent to actuators such as the fuel flow regulating valve and air flow regulating valve to complete the closed-loop control of the solid oxide fuel cell system. During system operation, after each system start-up and shutdown or after 1000 hours of operation, three standard calibration conditions are selected for retesting to update the baseline values ​​of the calibration lookup table, thereby eliminating calibration errors caused by battery performance degradation.

[0034] This embodiment transforms complex multiphysics coupling relationships into simple lookup tables and correction matrices through offline calibration. Online control only requires interpolation and matrix operations, resulting in extremely short single-cycle control time and low computational load, facilitating real-time operation on embedded controllers. Simultaneously, the coupling correction coefficient matrix resolves cross-interference issues between multiple inputs, achieving high-precision decoupled control. This method does not rely on complex online learning or numerical iteration, ensuring high reliability in engineering implementation. Furthermore, the control framework can be reused for different fuel cell stacks simply by recalibration, demonstrating high versatility.

[0035] In a specific implementation, the optimal control input is calculated based on the actual internal state and the calibration lookup table, including: In the calibration lookup table, taking the current actual internal state as the center, multiple adjacent calibration points are selected, and a local linear mapping relationship of the internal state parameters changing with the control input is fitted based on the data of the multiple calibration points. Calculate the first deviation between the maximum internal temperature difference and the safety threshold, the second deviation between the minimum reactant concentration and the lower limit threshold, and the third deviation between the output voltage and the target voltage in the actual internal state. Using the local linear mapping relationship, the adjustment amount of eliminating the first deviation value, the second deviation value, and the third deviation value on the current control input is calculated respectively; The optimal control input is obtained by summing the adjustment values ​​according to preset weights and adding them to the current control input value. When the first deviation value or the second deviation value exceeds the corresponding emergency threshold, the adjustment weight corresponding to the first deviation value or the second deviation value is set to be higher than the adjustment weight corresponding to the third deviation value.

[0036] In detail, the estimated true internal state (such as the current maximum internal temperature difference) can be used as the central reference point. The calibration lookup table can then be used to find the nearest calibration points to this state. Using the data recorded at these adjacent calibration points, a simplified linear mathematical relationship can be fitted locally. This relationship describes how small changes in control inputs (such as fuel flow) linearly affect internal state parameters (such as the maximum internal temperature difference).

[0037] Three key control deviation values ​​can be further calculated: the first deviation value is the difference between the current maximum internal temperature difference and the preset 10-degree Celsius safety threshold; the second deviation value is the difference between the current minimum internal hydrogen concentration and the 5% flameout lower limit threshold; and the third deviation value is the difference between the current output voltage and the desired target voltage.

[0038] After obtaining the three deviation values, the previously obtained local linear mapping relationship can be used to independently estimate how much adjustment to the current control input is needed to eliminate each deviation value individually. For example, using the local linear gain of temperature difference on fuel flow, the amount of fuel flow reduction required to bring the temperature difference below the 10-degree Celsius safety threshold can be calculated.

[0039] These three independently calculated adjustment values ​​can be weighted and summed according to their respective preset weights. The summation result is then added to the current control input value to obtain the optimal control input value. The weighting strategy prioritizes the safe operation of the fuel cell stack. When the deviation of the maximum internal temperature difference exceeds the emergency threshold (indicating a risk of thermal runaway) or the deviation of the minimum internal hydrogen concentration exceeds the emergency threshold (indicating a risk of flameout), the weight of the corresponding deviation adjustment value is automatically increased, making it dominant in the weighted summation process. Conversely, the weight of maintaining voltage stability is reduced, ensuring that the safe operation of the fuel cell stack is prioritized under all circumstances, keeping the maximum internal temperature difference within the safe threshold.

[0040] This embodiment utilizes local linearization to apply a nonlinear lookup table for online optimization, resulting in simple and efficient computation. By introducing a safety-priority-based dynamic weight allocation mechanism, it can prioritize the adjustment of control variables to ensure safety when the fuel cell stack faces high-risk conditions such as thermal runaway or fuel depletion, significantly improving the system's safety and robustness.

[0041] In some embodiments, the adjustment amount required to eliminate the first deviation value, the second deviation value, and the third deviation value is calculated using the local linear mapping relationship, including: Extract the partial derivative of the maximum internal temperature difference with respect to the current control input from the local linear mapping relationship, and divide the first deviation value by the partial derivative to obtain the adjustment amount required to eliminate the first deviation value. Extract the partial derivative of the minimum reactant concentration with respect to each control input from the local linear mapping relationship, and divide the second deviation value by the partial derivative to obtain the adjustment amount required to eliminate the second deviation value; Extract the partial derivatives of the output voltage with respect to each control input from the local linear mapping relationship, and divide the third deviation value by the partial derivatives to obtain the adjustment amount required to eliminate the third deviation value.

[0042] In detail, the partial derivative of the maximum internal temperature difference with respect to fuel flow rate or air flow rate can be extracted from this local linear relationship. This partial derivative represents approximately how much the maximum internal temperature difference will change for each unit adjustment of fuel flow rate under the current operating conditions. Then, the calculated first deviation value (i.e., the portion of the temperature difference exceeding the 10-degree Celsius safety threshold) is divided by this partial derivative, and the result is the adjustment amount required to adjust the fuel flow rate (or air flow rate) to eliminate the temperature difference deviation. Similarly, the partial derivative of the minimum internal hydrogen concentration with respect to each input quantity can be extracted, and the second deviation value (i.e., the value where the concentration is below the 5% lower limit) can be divided by this partial derivative to obtain the adjustment amount required to eliminate the concentration deviation. In the same way, the partial derivative of the output voltage with respect to each input quantity can be extracted, and the third deviation value (voltage deviation) can be divided by the partial derivative to obtain the adjustment amount required to eliminate the voltage deviation.

[0043] In a specific implementation process, for a 1kW flat-plate SOFC stack, the specific implementation steps are as follows: Calibration Platform and Interval Division: A calibration experimental platform was built. In a 1kW (30 single-cell) planar SOFC stack, three sets of miniature thermocouples and hydrogen concentration sensors were embedded on the anode side of the 5th, 15th, and 25th single cells, respectively, for a total of 9 measurement points. The input quantities were determined as fuel flow rate Q_f (range 0.5~5.0NL / min, divided into 10 calibration intervals at 0.5NL / min intervals) and air flow rate Q_a (range 2~20NL / min, divided into 10 calibration intervals at 2NL / min intervals), resulting in a total of 10×10=100 calibration input combinations.

[0044] Offline calibration data acquisition: Set each input combination in sequence. After the system has been running stably for 30 minutes, record the temperature and hydrogen concentration at 9 measuring points. At the same time, record the stack output voltage and inlet and outlet temperatures. Repeat the measurement 3 times for each input and take the average value. Finally, obtain the input-output dataset of all calibration points.

[0045] Calibration mapping and coupling coefficient construction: Based on calibration data, extract the maximum internal temperature T_max and maximum temperature difference at each calibration point. For T_max and minimum hydrogen concentration C_(H_2,min), two-dimensional lookup tables are constructed with fuel flow rate and air flow rate as inputs, respectively. Then, by changing the air flow rate while keeping the fuel flow rate constant and changing the fuel flow rate while keeping the air flow rate constant, the effect of each input change on the three internal states is measured, resulting in a 3×2 coupling correction coefficient matrix. ; Online control operation: The control cycle is set to 1 second. Within each cycle, the current fuel flow rate, air flow rate, output voltage, and inlet / outlet temperature are collected. An initial internal state estimate is obtained by bilinear interpolation of a lookup table. Then, the actual internal state is obtained by eliminating cross-coupling effects using a coupling correction coefficient matrix. Subsequently, the output voltage is stabilized at the set value ±0.05V. With constraints of T_max≤10℃ and C_(H_2,min)≥5%, the optimal control quantity for regulating the flow valve was calculated.

[0046] Calibration update: Every 1000 hours of operation, retesting is performed under three standard operating conditions: 0.3kW, 0.6kW, and 1kW. The reference temperature and concentration values ​​in the lookup table are updated to eliminate deviations caused by attenuation.

[0047] In some embodiments, after obtaining the actual internal state, the method further includes: Calculate the nearest neighbor calibration point of the current operating point in the calibration lookup table; Determine the distance between the current working point and the nearest neighbor calibration point; If the distance exceeds the preset reliable extrapolation boundary, the correction weight of the coupling correction coefficient matrix is ​​reduced, and a prediction compensation term based on the historical state change trend is introduced. The predicted and compensated internal state replaces the original actual internal state for the calculation of the optimal control input.

[0048] In detail, since the calibration lookup table only covers a limited range of operating conditions, when the fuel cell stack starts up, stops, or undergoes drastic changes in operating conditions, the current operating point may temporarily fall outside the range covered by the calibration table. In this case, direct extrapolation may produce a large error.

[0049] To address this issue, after each internal state estimate is obtained, a calibration lookup table is searched for the calibration point with the closest Euclidean distance to the current operating point (e.g., a coordinate point composed of the current fuel flow rate and air flow rate). The spatial distance between the current operating point and this closest calibration point is calculated. A threshold for a reliable extrapolation boundary can be pre-stored. The specific method for setting this threshold is as follows: the average spacing between adjacent calibration points is determined based on the grid density of the calibration experiment (e.g., a fuel flow rate interval of 0.5 standard liters per minute and an air flow rate interval of 2 standard liters per minute). Half of the grid spacing in each direction (i.e., 0.25 and 1) is taken as the basic extrapolation radius. Then, through small-range deviation experiments, it is verified whether the internal state error (e.g., the maximum internal temperature difference error) of linear extrapolation within this radius is within the allowable range. If it exceeds the allowable range, the radius is appropriately reduced. Finally, an Euclidean distance value that can guarantee extrapolation accuracy is determined as the threshold.

[0050] If the calculated distance is less than this threshold, the current operating point is considered to be within the reliable extrapolation range of the calibration table, and the original decoupling estimation result is used. Conversely, if the distance exceeds the threshold, it indicates that the current operating point is far from all calibration data, and directly using the coupling correction coefficient matrix for correction may no longer be accurate. In this case, a fault-tolerant strategy is implemented: on the one hand, the weight of the coupling correction coefficient matrix in the state estimation is reduced, and its correction magnitude is decreased to avoid erroneous cross-coupling compensation amplifying the estimation error; on the other hand, a predictive compensation term based on historical state change trends is introduced, for example, using the internal state change rate of the previous few control cycles to linearly predict the state of the current cycle. Finally, this state value predicted by historical trends is used as the main basis to replace the original estimate based on extrapolation and weak correction for subsequent optimal control quantity calculations until the operating point returns to the reliable extrapolation boundary.

[0051] In some embodiments, after establishing the calibration lookup table, the method further includes: For multiple repeated measurements under the same calibration input combination, calculate the dispersion of the obtained internal state parameter measurements; If the dispersion exceeds the preset consistency threshold, the abnormal measurement value with the largest deviation will be removed and the measurement will be retested. If the dispersion still exceeds the consistency threshold after retesting, the control mode corresponding to the calibration input combination is switched to the weighted extrapolation mode of adjacent valid calibration points, and the calibration point is marked as an untrusted point in the calibration lookup table.

[0052] In detail, during offline calibration, to eliminate random errors, measurements for each combination of calibration inputs are typically repeated multiple times. Statistical analysis can then be performed on the internal state parameters (such as temperature at a point) of these measurements. First, the dispersion of these measurements, such as the standard deviation or range, is calculated. Then, this dispersion is compared to a preset consistency threshold.

[0053] If the dispersion is less than or equal to the threshold, it indicates that multiple measurements are consistent and the data is reliable; the average value is then stored in the lookup table. If the dispersion exceeds the threshold, it indicates that there are significant outliers in the data. The measurement with the largest deviation from the average can be automatically identified and removed, and then the calibration point is remeasured. After the remeasurement, the dispersion of the remaining measurements and the newly remeasured values ​​is recalculated. If the dispersion recovers to within the threshold, the average value is then stored in the lookup table. If the dispersion still exceeds the consistency threshold after the remeasurement, it indicates that the SOFC operation under this condition may be extremely unstable, and reliable consistent calibration data cannot be obtained. In this case, unreliable data will not be forcibly used. Instead, the control mode of this calibration point is marked as "weighted extrapolation mode". In actual control, when the operating point falls within this area, its internal state is not given by the local lookup table, but is estimated by the data of adjacent, reliable calibration points through a weighted extrapolation algorithm. At the same time, this unreliable calibration point can be clearly marked in the calibration lookup table to remind operators or to pay special attention to it in subsequent updates.

[0054] This embodiment effectively eliminates the impact of random errors and abnormal operating conditions on calibration data by introducing data consistency verification and anomaly handling mechanisms, ensuring the accuracy and reliability of the calibration lookup table. For special operating conditions where consistent data cannot be obtained, switching to extrapolation mode and marking unreliable points avoids interference from erroneous calibration data with control, thus improving the overall robustness of the system.

[0055] Based on the same general inventive concept, this invention also protects a calibration control system for solving multi-field coupling in solid oxide fuel cells. The calibration control system for solving multi-field coupling in solid oxide fuel cells provided by this invention will be described below. The calibration control system for solving multi-field coupling in solid oxide fuel cells described below can be referred to in correspondence with the calibration control method for solving multi-field coupling in solid oxide fuel cells described above.

[0056] Figure 2 This is a schematic diagram of the calibration control system for solving multi-field coupling in solid oxide fuel cells provided in an embodiment of the present invention, as shown below. Figure 2 As shown, the calibration control system for solving multi-field coupling in solid oxide fuel cells in this embodiment includes an experimental module 21, a combination module 22, a measurement module 23, a setup module 24, an analysis module 25, and a control module 26.

[0057] Among them, experimental module 21 is used to build a calibration experimental platform for solid oxide fuel cell stacks, determine the control input quantities and their calibration ranges, and determine the observable output quantities. Combination module 22 is used to combine the calibration ranges of various control input quantities to obtain multiple calibration input combinations; Measurement module 23 is used to measure the temperature and reactant concentration inside the battery stack for each calibration input combination to obtain internal state field distribution data, and at the same time record the corresponding control input and observable output as external measurable parameters. Module 24 is established to use the internal state field distribution data and external measurable parameters obtained under all calibration input combinations as calibration data. Based on the calibration data, a calibration lookup table between external measurable parameters and internal state parameters is established, and a coupling correction coefficient matrix is ​​constructed. The coupling correction coefficient matrix is ​​used to characterize the cross-coupling effect of different control input quantities on internal state parameters. Analysis module 25 is used to collect current external measurable parameters within the control cycle, obtain the first estimated value of the internal state parameters through the calibration lookup table, and then decouple the first estimated value using the coupling correction coefficient matrix to obtain the actual internal state; The control module 26 is used to calculate the optimal control input based on the actual internal state and the calibration lookup table, and execute the control action, with the control objectives being stable output voltage, maximum internal temperature difference not exceeding the safety threshold, and minimum reactant concentration not lower than the lower limit threshold.

[0058] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. The electronic device may include: a processor 310, a communication interface 320, a memory 330, and a communication bus 340. The processor 310, communication interface 320, and memory 330 communicate with each other via the communication bus 340. The processor 310 can call logic instructions stored in the memory 330 to execute a calibration control method for resolving multi-field coupling in solid oxide fuel cells.

[0059] Furthermore, the logical instructions in the aforementioned memory 330 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0060] It should be noted that all relevant information that may be involved in the various embodiments of the present invention is processed in strict accordance with the requirements of laws and regulations, following the principles of legality, legitimacy, and necessity, based on the reasonable purpose of the business scenario, and is information that users actively provide or generate during the use of the product / service, as well as information obtained with user authorization.

[0061] The information processed by this invention may vary depending on the specific product / service scenario and should be based on the specific scenario in which the user uses the product / service. This may involve user account information, device information, or other related information. This invention will treat the relevant information and its processing with the utmost diligence.

[0062] This invention places great emphasis on the security of relevant information and has adopted reasonable and feasible security protection measures that comply with industry standards to protect user information and prevent unauthorized access, public disclosure, use, modification, damage or loss of relevant information.

[0063] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0064] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A calibration control method for solving multi-field coupling in solid oxide fuel cells, characterized in that, include: A calibration experimental platform for solid oxide fuel cell stacks was built to determine the control inputs and their calibration ranges, and the observable outputs were determined. By combining the calibration ranges of each control input, multiple calibration input combinations are obtained; For each calibration input combination, the temperature and reactant concentration inside the battery stack are measured to obtain internal state field distribution data, and the corresponding control input and observable output are recorded as external measurable parameters. The internal state field distribution data and external measurable parameters obtained under all calibration input combinations are used together as calibration data. Based on the calibration data, a calibration lookup table between external measurable parameters and internal state parameters is established, and a coupling correction coefficient matrix is ​​constructed. The coupling correction coefficient matrix is ​​used to characterize the cross-coupling effect of different control input quantities on the internal state parameters. During the control cycle, the current external measurable parameters are collected, and the first estimated value of the internal state parameters is obtained through the calibration lookup table. Then, the first estimated value is decoupled using the coupling correction coefficient matrix to obtain the actual internal state. With the control objectives of stable output voltage, maximum internal temperature difference not exceeding the safety threshold, and minimum reactant concentration not lower than the lower limit threshold, the optimal control input is calculated based on the actual internal state and the calibration lookup table, and the control action is executed.

2. The calibration and control method for solving multi-field coupling in solid oxide fuel cells according to claim 1, characterized in that, Calculating the optimal control input based on the actual internal state and the calibration lookup table includes: In the calibration lookup table, taking the current actual internal state as the center, multiple adjacent calibration points are selected, and a local linear mapping relationship of the internal state parameters changing with the control input is fitted based on the data of the multiple calibration points. Calculate the first deviation between the maximum internal temperature difference and the safety threshold, the second deviation between the minimum reactant concentration and the lower limit threshold, and the third deviation between the output voltage and the target voltage in the actual internal state. Using the local linear mapping relationship, the adjustment amount of eliminating the first deviation value, the second deviation value, and the third deviation value on the current control input is calculated respectively; The optimal control input is obtained by summing the adjustment values ​​according to preset weights and adding them to the current control input value. When the first deviation value or the second deviation value exceeds the corresponding emergency threshold, the adjustment weight corresponding to the first deviation value or the second deviation value is set to be higher than the adjustment weight corresponding to the third deviation value.

3. The calibration and control method for solving multi-field coupling in solid oxide fuel cells according to claim 2, characterized in that, Using the local linear mapping relationship, the adjustment amounts required to eliminate the first deviation value, the second deviation value, and the third deviation value are calculated respectively, including: Extract the partial derivative of the maximum internal temperature difference with respect to the current control input from the local linear mapping relationship, and divide the first deviation value by the partial derivative to obtain the adjustment amount required to eliminate the first deviation value. Extract the partial derivative of the minimum reactant concentration with respect to each control input from the local linear mapping relationship, and divide the second deviation value by the partial derivative to obtain the adjustment amount required to eliminate the second deviation value; Extract the partial derivatives of the output voltage with respect to each control input from the local linear mapping relationship, and divide the third deviation value by the partial derivatives to obtain the adjustment amount required to eliminate the third deviation value.

4. The calibration and control method for solving multi-field coupling in solid oxide fuel cells according to claim 1, characterized in that, After obtaining the actual internal state, it also includes: Calculate the nearest neighbor calibration point of the current operating point in the calibration lookup table; Determine the distance between the current working point and the nearest neighbor calibration point; If the distance exceeds the preset reliable extrapolation boundary, the correction weight of the coupling correction coefficient matrix is ​​reduced, and a prediction compensation term based on the historical state change trend is introduced. The predicted and compensated internal state replaces the original actual internal state for the calculation of the optimal control input.

5. The calibration control method for solving multi-field coupling in solid oxide fuel cells according to claim 1, characterized in that, When determining the calibration range of the control input quantity, based on the nonlinear sensitivity of the control input quantity to the internal state parameters, a first level of interval division is used within the range where the sensitivity is higher than a preset threshold, and a second level of interval division is used within the range where the sensitivity is lower than the preset threshold. In subsequent control processes, based on the real-time accumulated interpolation error statistics, sub-intervals are automatically added to intervals with persistently large errors, and intervals that have not been used for a long time are automatically merged. The first level of fineness is less than the second level of fineness.

6. The calibration control method for solving multi-field coupling in solid oxide fuel cells according to claim 1, characterized in that, Constructing the coupling correction coefficient matrix includes: Sequentially fix other control inputs except the target control input, change only the target control input and measure the change in each internal state parameter, and calculate the local coupling gain of the target control input to each internal state parameter; Combine all local coupling gains into a matrix form.

7. The calibration control method for solving multi-field coupling in solid oxide fuel cells according to claim 1, characterized in that, After establishing the calibration lookup table, the following is also included: For multiple repeated measurements under the same calibration input combination, calculate the dispersion of the obtained internal state parameter measurements; If the dispersion exceeds the preset consistency threshold, the abnormal measurement value with the largest deviation will be removed and the measurement will be retested. If the dispersion still exceeds the consistency threshold after retesting, the control mode corresponding to the calibration input combination is switched to the weighted extrapolation mode of adjacent valid calibration points, and the calibration point is marked as an untrusted point in the calibration lookup table.

8. The calibration control method for solving multi-field coupling in solid oxide fuel cells according to claim 1, characterized in that, The sensing units used to measure the internal temperature and reactant concentration of the battery stack employ miniature thermocouples and oxygen pump-type concentration sensors. The miniature thermocouples and oxygen pump-type concentration sensors are respectively arranged at the inlet section, middle section, and outlet section of the battery stack, with multiple measurement points arranged at each section to ensure that the measurement data covers the areas with the largest temperature and concentration gradients.

9. The calibration control method for solving multi-field coupling in solid oxide fuel cells according to claim 8, characterized in that, Also includes: Low-amplitude frequency sweep excitation was periodically applied to the fuel cell stack to obtain the response amplitude and phase changes at each measurement point; Based on the response amplitude and phase changes at each measurement point, the ability of each measurement point to characterize the temperature gradient and concentration gradient is evaluated. When the characterization capability of a certain measurement point continues to decline, the second estimated value at the current maximum gradient location is reconstructed by spatial interpolation using the measurement values ​​of other measurement points; the second estimated value includes temperature estimate and concentration estimate. The second estimate replaces the measurement values ​​at the measurement locations where the characterization capability continues to decline, and is used for subsequent calibration lookup table updates.

10. A calibration control system for solving multi-field coupling in solid oxide fuel cells, characterized in that, include: The experimental module is used to build a calibration experimental platform for solid oxide fuel cell stacks, determine the control input quantities and their calibration ranges, and determine the observable output quantities. The combination module is used to combine the calibration ranges of various control inputs to obtain multiple calibration input combinations; The measurement module is used to measure the temperature and reactant concentration inside the battery stack for each calibration input combination to obtain internal state field distribution data, and at the same time record the corresponding control input and observable output as external measurable parameters. A module is established to use the internal state field distribution data and external measurable parameters obtained under all calibration input combinations as calibration data. Based on the calibration data, a calibration lookup table between external measurable parameters and internal state parameters is established, and a coupling correction coefficient matrix is ​​constructed. The coupling correction coefficient matrix is ​​used to characterize the cross-coupling effect of different control input quantities on the internal state parameters. The analysis module is used to collect current external measurable parameters within the control cycle, obtain the first estimated value of the internal state parameters through the calibration lookup table, and then decouple the first estimated value using the coupling correction coefficient matrix to obtain the actual internal state. The control module is used to calculate the optimal control input based on the actual internal state and the calibration lookup table, and to execute the control action, with the control objectives being stable output voltage, maximum internal temperature difference not exceeding the safety threshold, and minimum reactant concentration not lower than the lower limit threshold.

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