A method for constructing and identifying the state of a fuel cell impedance domain

Abstract

The application discloses a kind of construction and state identification method of fuel cell impedance domain.Under multiple workload points, electrochemical impedance spectroscopy test is carried out, impedance data is preprocessed, quality is verified and feature is analyzed, impedance feature parameters are extracted and its association with operating state parameters is determined;Based on the associated parameters, a set of multi-dimensional discrete data points is constructed, a standard impedance surface is obtained by smoothing fitting, and a normal impedance domain is formed by combining the upper and lower limit impedance surfaces and the state parameter boundaries, and then a multi-element impedance domain database is established.When the fuel cell is running, the real-time operating state parameters and impedance feature parameters are mapped to a spatial state point, and the state is identified by its position relationship with the corresponding normal impedance domain, and the subsequent adjustment direction and amplitude can be determined by combining the hierarchical state space and the anchor point progressive method.

Description

Technical Field

[0001] This invention relates to the field of fuel cell condition monitoring and operation control technology, specifically to a method for constructing a fuel cell impedance domain and identifying its condition. Background Technology

[0002] During fuel cell operation, its internal electrochemical reactions, proton conduction, gas diffusion, and hydrothermal state change with conditions such as workload, temperature, gas supply, and pressure. Existing fuel cell systems typically use parameters such as voltage, current, temperature, pressure, and flow rate for condition monitoring. However, these parameters mainly reflect the external operating conditions of the system and have problems with insufficient characterization and difficulty in distinguishing between different abnormal states in the early stages of internal conditions such as membrane dryness, flooding, insufficient gas supply, and limited mass transfer.

[0003] Electrochemical impedance spectroscopy (EIS) can reflect the ohmic conduction, activation polarization, and mass transfer processes of a fuel cell, and therefore can be used for internal state analysis. However, the impedance characteristics of a fuel cell are also affected by operating parameters such as workload, temperature, flow rate, and pressure; the same impedance value may correspond to different states under different operating conditions. If only a single impedance parameter or a fixed threshold is used for judgment, it is difficult to fully reflect the correlation between impedance characteristics and actual operating conditions.

[0004] Therefore, there is an urgent need for a state identification method that can correlate fuel cell impedance characteristic parameters with external operating state parameters and establish corresponding normal state ranges for different workloads, so as to improve the adaptability of fuel cell internal state characterization, abnormal deviation judgment and subsequent operation adjustment under different operating conditions.

[0005] A search revealed a Chinese patent document disclosing a method and system for online monitoring of fuel cell impedance [Application No.: 202111599685.2, Publication No.: CN114264881B]. This method obtains ohmic impedance, activation polarization impedance, and mass transfer impedance by real-time measurement of the fuel cell's high-frequency impedance, low-frequency impedance, and single-cell voltage. These parameters are then used for online monitoring of the membrane's wet / dry state, catalyst activity state, and fuel supply state, respectively. Its main feature is the simplification of the electrochemical impedance spectroscopy, obtaining impedance parameters reflecting different polarization losses through a small number of characteristic frequencies to meet the requirements of online fuel cell condition monitoring.

[0006] While the comparative patent can monitor the internal operating state of a fuel cell online using ohmic impedance, activation polarization impedance, and mass transfer impedance, and features simplified impedance measurement using characteristic frequencies and direct determination of the corresponding internal state based on impedance components, this invention does not directly determine the state based on a single impedance component. Instead, it jointly maps impedance characteristic parameters with operating state parameters such as cooling temperature, cathode flow rate, and pressure, and constructs standard impedance surfaces, normal impedance domains, and multi-dimensional impedance domain databases for different workloads. This allows real-time impedance values ​​to be spatially determined in conjunction with their operating conditions. Furthermore, it can perform hierarchical state division and progressive adjustment based on the position of the state point relative to the impedance domain. The aforementioned state characterization and control method based on multi-dimensional impedance domains is a technical content not disclosed in the comparative patent. Summary of the Invention

[0007] In view of the problems existing in the prior art, the purpose of this invention is to provide a method for constructing the impedance domain and identifying the state of a fuel cell.

[0008] A method for constructing the impedance domain and identifying the state of a fuel cell, characterized by comprising: S1. Under multiple operating load points, adjust the operating status parameters based on standard operating conditions and perform electrochemical AC impedance frequency sweep test to obtain impedance data and corresponding status parameters. S2. Perform preprocessing, quality verification and analysis on the impedance data, extract impedance characteristic parameters and determine their correlation with state parameters; S3. Select the associated impedance characteristic parameters and state parameters to form an n-dimensional discrete data point set, where n≥2; S4. Perform smooth fitting on the discrete data point set to obtain the standard impedance surface that characterizes the change of impedance characteristic parameters with state parameters. S5. Obtain the upper and lower limit impedance surfaces according to ±δ%, and form the normal impedance domain of each working load point by the two and the boundary envelope of the state parameters. Then, store them in association according to the working load points to form a multi-element impedance domain database.

[0009] Preferably, in step S1, an AC current disturbance signal is applied to the fuel cell at each test frequency of the frequency sweep test, wherein the AC current disturbance signal is expressed as: ; The same-frequency response voltage generated by the fuel cell is expressed as: ; The complex forms of the alternating current disturbance signal and the same-frequency response voltage are respectively expressed as: ; ; The complex AC impedance at the corresponding angular frequency is expressed as: ; in: ; ; In the formula, For time; for The alternating current disturbance signal constantly applied to the fuel cell; For fuel cells in The same frequency response voltage generated at any given moment; The amplitude of the alternating current disturbance signal; This represents the amplitude of the voltage response at the same frequency. Let be the angular frequency of the alternating current disturbance signal, and ; The frequency of the alternating current disturbance signal; The initial phase of the alternating current disturbance signal; This represents the phase difference between the voltage response at the same frequency and the alternating current disturbance signal; For the phasor of the alternating current disturbance signal; For the phasor of the voltage response at the same frequency; It is a natural constant; It is the imaginary unit, and ; Angular frequency Complex AC impedance; This represents the AC impedance amplitude. Phase angle of AC impedance; The real part of the AC impedance; This represents the imaginary part of the AC impedance.

[0010] The above technical solution can obtain the complex AC impedance at the corresponding test frequency based on the same frequency response voltage generated by the fuel cell under AC current disturbance, and further obtain the AC impedance amplitude, AC impedance phase angle, AC impedance real part and AC impedance imaginary part, thereby forming electrochemical AC impedance data for characterizing the internal dynamic process of the fuel cell.

[0011] Specifically, at a certain test frequency, the response voltage generated by the fuel cell and the applied alternating current disturbance have the same frequency, but they differ in amplitude and phase. The amplitude of the alternating impedance is determined by the ratio of the response voltage amplitude to the disturbance current amplitude, and the phase angle of the alternating impedance is determined by the phase difference between the response voltage and the disturbance current. By changing the test frequency and obtaining the corresponding impedances sequentially, the electrochemical alternating impedance spectrum of the fuel cell can be formed.

[0012] In practical applications, the above frequency sweeping method can obtain the impedance response at different frequencies, enabling subsequent analysis of processes such as ohmic conduction, activation polarization, and mass transfer inside the fuel cell by combining the real part of the impedance, the imaginary part of the impedance, and the response characteristics of different frequency ranges, thus providing a basis for the extraction of impedance characteristic parameters.

[0013] Preferably, the frequency range of the electrochemical AC impedance sweep test is 0.1 Hz to 10 kHz, and the test process includes: The fuel cell system controller sends disturbance amplitude, disturbance frequency, and electrochemical AC impedance test enable signals to the DC / DC converter; The electrochemical AC impedance function module built into the DC / DC converter injects a disturbance signal into the fuel cell and detects the response signal. The disturbance signal and response signal are analyzed by Fast Fourier Transform to separate the effective AC component, calculate the AC impedance corresponding to each test frequency, and report the AC impedance result to the fuel cell system controller.

[0014] The above technical solution enables the application of AC disturbances, detection of response signals, and calculation of AC impedance using the DC / DC converter in the fuel cell system. This allows the electrochemical AC impedance test to be integrated with the fuel cell system control process, and the obtained impedance results to be directly provided to the fuel cell system controller.

[0015] Specifically, the fuel cell system controller sends corresponding disturbance parameters and test enable signals to the DC / DC converter according to the test requirements. The DC / DC converter injects disturbances into the fuel cell through its built-in electrochemical impedance spectroscopy (EIS) module and simultaneously detects the response. Then, it uses Fast Fourier Transform (FFT) to separate the corresponding effective AC components from the detection signal, thereby calculating the AC impedance at each test frequency. This process corresponds to the online EIS detection process described in the manual.

[0016] In practical applications, the above testing method can be used to obtain online impedance results with the help of the existing controller and DC / DC converter of the fuel cell system, and the impedance data can be reported to the system controller for subsequent impedance data processing, impedance characteristic analysis, impedance domain construction and state identification.

[0017] Preferably, step S2 includes: The Kramers-Kronig test was used to verify the quality of the impedance data in order to identify the data corresponding to instrument noise and fuel cell instability. A Nyquist plot is constructed with the real part of the impedance as the horizontal axis and the negative imaginary part of the impedance as the vertical axis. Based on the Nyquist plot, at least one of the following is extracted: ohmic impedance, anode activation polarization impedance, cathode activation polarization impedance, and mass transfer impedance. Relaxation time distribution analysis was performed on the impedance data that passed quality verification to obtain characteristic information corresponding to cathode activation polarization impedance and mass transfer impedance. Statistical merging is performed on repeated sampled data under the same combination of operating state parameters, and abnormal data that fails quality verification is excluded.

[0018] The above technical solution enables quality verification and impedance characteristic analysis of the original impedance data before impedance domain construction, reducing the impact of data generated by factors such as signal noise, test cable interference, system state drift, and electrode instability on subsequent impedance domain construction.

[0019] Specifically, the Kramers-Kronig test is used to identify data that do not meet the requirements of linearity, stability, and causality, and a Nyquist plot is constructed based on the data that has passed quality verification. The high-frequency intercept, high-frequency arc, mid-to-low-frequency arc, and low-frequency region in the Nyquist plot can be used to analyze different impedance processes; at the same time, relaxation time distribution analysis is combined to obtain corresponding characteristic information to help distinguish different impedance components.

[0020] In practical applications, combining quality verification, Nyquist plot analysis, relaxation time distribution analysis, and repeated sampling data statistics can reduce the possibility of abnormal test data causing standard impedance surface fitting distortion, and enable the impedance characteristic parameters used to construct discrete data point sets to better reflect the fuel cell impedance response under the corresponding operating conditions.

[0021] Preferably, the working load point is characterized by the working current or current density; The operating status parameters include at least one of cooling temperature, cathode metering ratio, cathode flow rate, cathode pressure, and anode pressure; The impedance characteristic parameters include at least one of ohmic impedance, anodic activation polarization impedance, cathodic activation polarization impedance, and mass transfer impedance; The associated impedance characteristic parameters and state parameters are determined by sensitivity test response amplitude, correlation coefficient threshold, or principal component analysis. The associated impedance characteristic parameters and state parameters include combinations of cathode activation polarization impedance and / or mass transfer impedance with at least one of cooling temperature, cathode flow rate, cathode pressure and anode pressure. The cathode activation polarization impedance and mass transfer impedance are used to decouple and characterize the internal state changes of the fuel cell stack, while the operating state parameters are used to characterize the external operating state of the fuel cell stack.

[0022] The above technical solution enables the correlation between impedance characteristic parameters, which reflect changes in the internal state of a fuel cell, and operating state parameters, which reflect the external operating state of a fuel cell. This allows impedance characteristics to be analyzed in conjunction with actual workload and operating conditions, rather than relying solely on a single impedance value for state judgment.

[0023] Specifically, under different operating currents or current densities, the electrochemical reaction rate, water production, heat production, gas consumption, and mass transfer requirements inside the fuel cell will all change. Therefore, the same operating state parameter may correspond to different impedance responses at different operating load points. Through sensitivity experiments and other methods, impedance characteristic parameters that have a clear correlation with the corresponding operating state parameters can be selected for impedance domain construction.

[0024] In practical applications, by combining the cathode activation polarization impedance, mass transfer impedance, and other parameters such as cooling temperature, cathode flow rate, and cathode pressure, the internal reaction kinetics and mass transfer state of the fuel cell can be integrated with external operating conditions, so that the same impedance value can be judged in combination with its corresponding load, temperature, flow rate, or pressure conditions.

[0025] Preferably, the cathode flow rate is calculated based on the cathode metering ratio, which is expressed as: ; The cathode oxygen molar consumption flow rate of the fuel cell stack is expressed as: ; The cathode oxygen mass consumption flow rate is expressed as: ; When air is used as the cathode reaction gas, the theoretical cathode air mass flow rate is expressed as: ; in: ; The actual cathode air mass flow rate is expressed as: ; In the formula, The cathode stoichiometric ratio is a dimensionless parameter; subscript... Indicates cathode; subscript Indicates the actual supply value; subscript Indicates the theoretical consumption value; The actual air mass flow rate supplied to the fuel cell cathode is expressed in g / s. This represents the theoretical air mass flow rate required for the electrochemical reaction at the cathode of a fuel cell, expressed in g / s. The oxygen molar consumption flow rate of the fuel cell stack is expressed in mol / s. This represents the operating current of the fuel cell stack, expressed in amperes (A). The number of individual cells contained in the fuel cell stack is a dimensionless positive integer; is the Faraday constant, with units of C / mol; the value 4 indicates the number of moles of electrons required for each mole of oxygen to participate in the cathodic reduction reaction. The cathode oxygen mass consumption flow rate is expressed in g / s. The molar mass of oxygen is 32 g / mol; The average molar mass of air is approximately 29 g / mol. Let be the volume fraction of oxygen in the air, a dimensionless parameter, taken as 0.21.

[0026] The above technical solution can convert the cathode metering ratio into the actual air mass flow rate supplied to the fuel cell cathode based on parameters such as the cathode metering ratio, the stack operating current, the number of individual cells in the stack, and the oxygen content in the air, thereby obtaining the cathode flow rate parameters corresponding to the current workload.

[0027] Specifically, the oxygen molar consumption corresponding to the cathode electrochemical reaction is first determined based on the working current of the fuel cell stack and the number of cells per cell. Then, the oxygen mass consumption is obtained based on the oxygen molar mass. When air is used as the cathode reaction gas, the theoretical cathode air mass flow rate is determined by combining the oxygen volume fraction in the air and the average molar mass of air. The actual cathode air mass flow rate is obtained based on the cathode metering ratio.

[0028] In practical applications, the cathode metering ratio can be used as a gas supply parameter in the fuel cell control process, while the cathode air mass flow rate calculated from the cathode metering ratio can be directly used as an operating state parameter in the impedance domain. The instruction manual also clearly states that the cathode air mass flow rate calculated from the cathode metering ratio is used together with the cooling temperature and impedance characteristic parameters to form a spatial point.

[0029] Preferably, in step S4, the running state parameter vector is represented as: ; The standard impedance surface is represented as: ; The parameter space formed by the recommended operating ranges of each operating state parameter is represented as follows: ; In step S5, the upper limit impedance surface and the lower limit impedance surface are respectively represented as: ; ; in: ; The normal impedance domain is represented as: ; In the formula, n is the spatial dimension of the normal impedance domain, and n≥2; X is the vector of operating state parameters; This refers to the i-th running status parameter; Recommend the lower limit of the operating range for the i-th operating status parameter; Recommend the upper limit of the operating range for the i-th operating status parameter; The parameter space is formed by recommending operating ranges for each operating state parameter; f(X) is the functional relationship obtained by smooth fitting based on the discrete data point set; The standard impedance value corresponding to the operating state parameter vector X; The upper limit impedance value corresponding to the operating state parameter vector X; X represents the lower limit impedance value corresponding to the operating state parameter vector; Z represents the impedance coordinate value within the normal impedance domain. The percentage of impedance deviation relative to the standard impedance value; The dimensionless relative impedance deviation rate; D is the normal impedance domain formed by the upper impedance surface, the lower impedance surface, and the parameter space boundary envelope; the... , , and The units are all the same as the units of the selected impedance characteristic parameters; The percentage of impedance deviation The impedance is determined based on repeated measurements under the same combination of operating parameters, and the corresponding impedance deviation value is made greater than the measurement error of the impedance testing equipment.

[0030] The impedance deviation percentage is determined based on the results of multiple repeated measurements under the same combination of operating parameters, and the corresponding impedance deviation value is made greater than the measurement error of the impedance testing equipment.

[0031] The above technical solution enables the establishment of a standard impedance surface based on discrete data point sets to reflect the variation of impedance characteristic parameters with operating state parameters. Furthermore, an upper and lower impedance surface are formed on the basis of the standard impedance surface, allowing the normal operating state of the fuel cell to be characterized by a spatial region with a certain range.

[0032] Specifically, by smoothing and fitting finite discrete experimental data, a continuous standard impedance surface can be formed, enabling combinations of operating state parameters not covered point-by-point by the experiment to obtain corresponding reference impedance values. This standard impedance surface is used to represent the benchmark relationship between impedance characteristic parameters and operating state parameters at the corresponding operating load point.

[0033] In practical applications, the actual impedance value of a fuel cell is affected by factors such as testing errors and fluctuations in operating conditions. Therefore, an allowable deviation is set based on the standard impedance surface, and a normal impedance domain is formed by the upper limit impedance surface, the lower limit impedance surface, and the boundaries of operating condition parameters. Setting the impedance deviation to be greater than the equipment measurement error can reduce the occurrence of normal measurement fluctuations being judged as abnormal deviations.

[0034] Preferably, during fuel cell operation, the real-time collected operating status parameters are represented as follows: ; The extracted impedance characteristic parameters and the operating state parameters are then mapped to real-time state points: ; When the following conditions are met: ; When the fuel cell is in normal operating condition at the corresponding operating load point, it is determined that the fuel cell is in normal operating condition at the corresponding operating load point; when the following conditions are met: ; When this occurs, it is determined that the real-time operating state of the fuel cell has shifted relative to the normal impedance domain; In the formula, This is a vector of real-time operating status parameters; the subscript rt represents the real-time measured value. This refers to the i-th running status parameter collected in real time. Impedance characteristic parameters extracted from real-time electrochemical AC impedance test data; This represents the real-time state point corresponding to the current operating state of the fuel cell in the n-dimensional space. This represents the normal impedance region at the kth working load point. The cathode activation polarization impedance domain and mass transfer impedance domain under different operating currents or different current densities are constructed and stored in association according to the operating load point to form the multi-element impedance domain database; the multi-element impedance domain database is iteratively updated by periodically recalibrating or reconstructing the normal impedance domain according to key operating state parameters.

[0035] The above technical solution can map the real-time operating status parameters and the real-time extracted impedance characteristic parameters of the fuel cell to the normal impedance domain corresponding to the current working load point. The positional relationship between the real-time status point and the normal impedance domain can be used to determine whether the current state of the fuel cell has deviated from the calibrated normal state.

[0036] Specifically, since the heat generation, water production, gas consumption, polarization loss and mass transfer state of fuel cells differ under different operating currents or current densities, this invention constructs normal impedance domains at multiple operating load points and stores them in association according to the operating load points and impedance characteristic parameters to form a multi-element impedance domain database.

[0037] In practical applications, the fuel cell system controller can call up the corresponding normal impedance domain based on the current operating current or current density, and then map the real-time state point to the called impedance domain for state judgment. Furthermore, as the fuel cell's operating time increases, the normal impedance domain can be reconstructed based on periodic recalibration results or key operating state parameters, allowing for iterative updates to the database.

[0038] Preferably, when the normal impedance domain consists of a three-dimensional space composed of two operating state parameters and one impedance characteristic parameter, it further includes constructing a hierarchical state space, specifically: Select a specific impedance value R, and intersect the normal impedance domain with the intersection plane that satisfies the following equation in the impedance coordinates: ; The intersection surface intersects with the standard impedance surface to form the core control line: ; The intersection surface intersects with the first lower deviation control surface and the first upper deviation control surface, forming the lower buffer boundary and the upper buffer boundary, respectively: ; ; The intersection surface intersects with the second lower deviation control surface and the second upper deviation control surface, forming the lower anomaly boundary and the upper anomaly boundary, respectively: ; ; in: ; In the formula, R is the specific impedance value used to cut off the normal impedance domain, and its unit is the same as the unit of the selected impedance characteristic parameter. This represents the intersection surface where the impedance coordinate value is constant at R; As the core control line; This is the lower buffer boundary; This serves as the upper buffer boundary. This is the lower anomaly boundary; This is the upper anomaly boundary; This represents the first percentage deviation of the buffer boundary from the standard impedance value. This represents the second percentage deviation of the abnormal boundary from the standard impedance value. This is the first relative impedance deviation rate; This is the second relative impedance deviation rate; Based on the core control line, lower buffer boundary, upper buffer boundary, lower abnormal boundary, and upper abnormal boundary, the intersection surface control area is divided into a core stable area, a buffer transition area, a dynamic adjustment area, and an abnormal state area.

[0039] The above technical solution enables the construction of a normal impedance domain, which can be truncated with specific impedance values ​​to transform the impedance domain in three-dimensional space into a parametric control region under the corresponding impedance conditions. Furthermore, it can form hierarchical regions with different state meanings based on different deviation ranges.

[0040] Specifically, the intersection of the intercept surface and the standard impedance surface forms the core control line, which corresponds to the baseline state under the current impedance value. The intersection surface intersects with different deviation control surfaces to form buffer boundaries and abnormal boundaries, respectively. Therefore, based on the position of the real-time state point relative to the core control line and different boundaries, the fuel cell state can be divided into different levels. The manual uses this hierarchical state space to further convert the impedance domain judgment results into corresponding control regions and control actions.

[0041] In practical applications, when the real-time status point is located in the core stable zone, buffer transition zone, dynamic adjustment zone, or abnormal state zone, it can correspond to different degrees of operating state deviation. This allows the system to distinguish between normal state, small deviation, state requiring active adjustment, and abnormal state requiring further diagnosis and calming, rather than simply using normal and abnormal states for judgment.

[0042] Preferably, the real-time state point of the fuel cell on the intersection surface is represented as: ; Select the anchor point closest to the real-time state point from the core control line as the convergence target: ; The adjustment direction and adjustment range of the operating status parameters are determined based on the direction and distance between the real-time status point and the anchor point. When the real-time status point is in the core stable region, it maintains the current operating state; when the real-time status point is in the buffer transition region, it enters the observation state; when the real-time status point is in the dynamic adjustment region, it adjusts the operating state parameters to make the real-time status point converge toward the buffer transition region or the core control line; when the real-time status point is in the abnormal state region, it initiates multi-dimensional diagnosis and calming control.

[0043] The above technical solution enables the determination of the real-time state point region after the real-time state point region is determined from the core control line, and the adjustment direction and adjustment range of the operating state parameters are determined according to the positional relationship between the real-time state point and the anchor point, so that the fuel cell state can be adjusted step by step according to the hierarchical state space.

[0044] Specifically, the system controller selects the point closest to the real-time state point from the core control line as the anchor point, and determines the adjustment direction of the operating state parameters based on the direction between the real-time state point and the anchor point, and determines the corresponding adjustment degree based on the distance between the two. For cases with large state deviations, the state point can be converged towards the buffer transition region first, and then a decision can be made on whether to continue gradual adjustment towards the core stable region based on the subsequent operating state of the fuel cell.

[0045] In practical applications, when the real-time state point is in the core stable region, it maintains the current operating state; when it is in the buffer transition region, it enters the observation state; when it is in the dynamic adjustment region, the operating state parameters are adjusted according to the deviation between the state point and the target region; and when it is in the abnormal state region, multi-dimensional diagnosis and calming control are initiated. In this way, control overshoot or large fluctuations in actuators that may be caused by a one-step adjustment of the state point from the abnormal region to the core stable region can be avoided.

[0046] Compared with the prior art, the present invention has the following advantages: 1. This invention combines impedance characteristic parameters, such as cathode activation polarization impedance and mass transfer impedance, which reflect the internal reaction and mass transfer state of a fuel cell, with external operating state parameters such as cooling temperature, cathode flow rate, and pressure to jointly characterize the fuel cell and construct a normal impedance domain in a multi-dimensional space. Compared to judging solely based on a single impedance value or a fixed threshold, this method can analyze impedance changes in conjunction with actual operating conditions, enabling more targeted state determination of the same impedance characteristic under different operating conditions.

[0047] 2. This invention establishes corresponding impedance domains for different operating currents or current densities, and stores the normal impedance domains formed under each load point as a multi-element impedance domain database. When the fuel cell is running, the corresponding normal impedance domain can be called according to the current load, and the real-time operating state parameters and impedance characteristic parameters are mapped together to spatial state points, thereby reducing the impact of differences in reaction rate, heat generation, gas supply demand, and mass transfer state under different load conditions on the unified threshold judgment.

[0048] 3. This invention further divides the normal impedance domain into a core stable region, a buffer transition region, a dynamic adjustment region, and an abnormal state region. It determines the adjustment direction and amplitude of operating parameters based on the direction and distance between the real-time state point and the target anchor point. This method can link the state identification results of the impedance domain with control actions such as those of the air compressor, cooling system, and pressure regulation. Furthermore, through phased and gradual adjustments, it reduces the possibility of control overshoot and frequent fluctuations in actuators when the state point changes across regions. Attached Figure Description

[0049] Figure 1 This is a schematic diagram illustrating the principle of the electrochemical AC impedance testing of fuel cells according to the present invention; Figure 2 This is a schematic diagram of the Nyquist plot and impedance characteristic analysis of the electrochemical AC impedance spectrum of the fuel cell of this invention; Figure 3 This is a schematic flowchart of the fuel cell impedance domain construction method of the present invention; Figure 4 This is a comparison chart of the cooling temperature sensitivity EISNyquist under a current density of 600mA / cm² according to the present invention; Figure 5 This is a comparison chart of the cathode metric sensitivity EISNyquist at a current density of 600 mA / cm² according to the present invention; Figure 6 This is a three-dimensional discrete data point plot of cathode activation polarization impedance related to cooling temperature and cathode flow rate, as presented in this invention. Figure 7 This is the standard cathode activation polarization impedance surface plot of the present invention regarding cooling temperature and cathode flow rate; Figure 8 This is a schematic diagram of the normal impedance domain formed by the standard impedance surface and the upper and lower limit impedance envelopes of the present invention; Figure 9 This is a schematic diagram of the multi-element impedance domain database construction process under multiple workload points according to the present invention; Figure 10 This is a schematic diagram of the online electrochemical AC impedance detection process based on a DC / DC converter according to the present invention; Figure 11 This is a schematic diagram of the present invention based on impedance domain truncation to form a parametric control region; Figure 12 This is a schematic diagram of the hierarchical state space construction process based on the impedance domain of the present invention; Figure 13 This is a schematic diagram of the path point asymptotic control process based on the impedance domain of the present invention; Figure 14 This is a schematic diagram of the hierarchical anchor point progressive control strategy based on impedance domain of the present invention. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. All equivalent substitutions, improvements, and variations made within the spirit and principles of the present invention should fall within the scope of protection of the present invention.

[0051] Working principle This invention relates to a method for constructing an impedance domain and identifying the state of a fuel cell. The basic idea is to utilize the characteristics of electrochemical AC impedance spectroscopy, which can reflect the internal electrochemical reactions, ohmic conduction, gas diffusion, hydrothermal state, and mass transfer state of a fuel cell, and to integrate the impedance characteristic parameters with the external measurable and controllable operating state parameters of the fuel cell to construct a multidimensional impedance domain that can characterize the normal operating state range of the fuel cell.

[0052] Existing fuel cell systems typically rely on conventional sensors such as voltage, current, temperature, pressure, flow rate, and humidity for condition monitoring. However, when problems such as membrane dryness, flooding, undergassing, limited mass transfer, or abnormal thermal management are in their early stages, conventional sensors often fail to reflect changes in the internal state of the fuel cell stack in a timely manner. By the time a significant voltage drop or system alarm occurs, substantial performance degradation may have already occurred within the stack. Electrochemical impedance spectroscopy (EIS) can obtain the impedance response of the fuel cell at different frequencies through small AC perturbations, thus reflecting changes in the internal reaction kinetics, proton conduction, gas transport, and water distribution of the fuel cell stack at an earlier stage.

[0053] This invention does not rely solely on a single impedance value as a fixed threshold for judgment. Instead, it establishes a mapping relationship between impedance characteristic parameters and operating state parameters such as cooling temperature, cathode metering ratio, cathode flow rate, cathode pressure, anode pressure, and current density, forming a multi-dimensional space of "operating state parameters - impedance characteristic parameters." Within this multi-dimensional space, a standard impedance surface is obtained by fitting experimental data, and an upper and lower impedance surface are constructed based on the standard impedance surface, thus forming a normal impedance domain. During real-time operation of the fuel cell, the real-time operating state parameters and real-time impedance characteristic parameters are mapped to spatial state points. If the state point falls within the normal impedance domain, the fuel cell is determined to be in a normal state; if the state point deviates from the normal impedance domain, the internal state of the fuel cell is determined to have shifted relative to the normal calibration state.

[0054] Electrochemical AC impedance measurement principle like Figure 1 As shown, electrochemical AC impedance testing of fuel cells typically includes the system under test, a perturbation application system, and a response signal acquisition system. The system under test is a fuel cell stack or fuel cell system; the perturbation application system is used to apply AC current perturbation or AC voltage perturbation to the fuel cell; and the response signal acquisition system is used to collect the voltage or current response generated by the fuel cell under the perturbation.

[0055] Taking the application of alternating current perturbation as an example, at a certain test frequency in the frequency sweep test, an alternating current perturbation signal is applied to the fuel cell: ; In the formula, The alternating current disturbance signal applied to the fuel cell at time t; The amplitude of the alternating current disturbance signal; The angular frequency of the alternating current disturbance signal; This represents the initial phase of the alternating current disturbance signal.

[0056] Because a fuel cell is not a purely resistive system, but rather involves processes such as ohmic impedance, charge transfer impedance, double-layer capacitance, and diffusion impedance, the in-frequency response voltage generated by the fuel cell will experience a phase shift relative to the disturbance current. This in-frequency response voltage can be expressed as: ; In the formula, Let be the same-frequency response voltage generated by the fuel cell at time t; This refers to the voltage amplitude of the same frequency response. This represents the phase difference between the voltage response at the same frequency and the alternating current disturbance signal.

[0057] Converting the AC current disturbance signal and the same-frequency response voltage into complex form, they can be expressed as follows: ; ; The complex AC impedance at the corresponding angular frequency is: ; in: ; ; Therefore, at a certain test frequency, the AC impedance amplitude of a fuel cell is determined by the ratio of the response voltage amplitude to the disturbance current amplitude, and the AC impedance phase angle is determined by the phase difference between the response voltage and the disturbance current. By performing frequency sweep tests within a preset frequency range, the impedance amplitude, impedance phase angle, real part of impedance, and imaginary part of impedance at different frequencies can be obtained, thus forming the electrochemical AC impedance spectrum of the fuel cell.

[0058] In one embodiment, the AC impedance test can be performed using a dedicated electrochemical impedance spectroscopy instrument; in another embodiment, it can also be performed using a DC / DC converter in the fuel cell system. When using a DC / DC converter for impedance testing, the fuel cell system controller sends the disturbance amplitude, disturbance frequency, and electrochemical AC impedance test enable signal to the DC / DC converter. The built-in electrochemical AC impedance function module of the DC / DC converter injects the disturbance signal into the fuel cell and detects the response signal. Then, it separates the effective AC component through a fast Fourier transform, calculates the AC impedance corresponding to each test frequency, and reports the AC impedance result to the fuel cell system controller.

[0059] Impedance data preprocessing and impedance characteristic analysis principles like Figure 2 As shown, Figure 2 (a) is the Nyquist plot of the impedance spectrum. Figure 2 (b) is a schematic diagram of impedance characteristic analysis. After frequency sweep testing, the impedance data that has passed quality verification is plotted with the real part of the impedance as the horizontal axis and the negative imaginary part of the impedance as the vertical axis to obtain the Nyquist plot of the electrochemical AC impedance spectrum of the fuel cell. A typical fuel cell Nyquist plot usually includes characteristic regions such as high-frequency intercept, high-frequency semicircle, mid-to-low-frequency semicircle, and low-frequency diffusion tail.

[0060] In the Nyquist plot, the high-frequency intercept on the left side relative to the real axis reflects ohmic impedance, primarily corresponding to the ohmic polarization losses formed by the proton exchange membrane, catalyst layer, gas diffusion layer, bipolar plates, current collectors, and connecting components. The high-frequency semicircle typically corresponds to the anode activation polarization process, and its diameter can be used to characterize the anode activation polarization impedance. The mid-to-low-frequency semicircle typically corresponds to the cathode activation polarization process, and its diameter can be used to characterize the cathode activation polarization impedance. The appearance of sloping lines, diffusion tails, or tail-end deformations in the low-frequency region usually indicates a certain mass transfer polarization loss in the fuel cell, which can be used to extract mass transfer impedance.

[0061] Before impedance characteristic analysis, the raw impedance data needs to be preprocessed and its quality verified. Due to potential issues in actual testing, such as signal noise, test cable interference, excessive AC disturbances, system state drift, and electrode instability, directly using the raw data to construct the impedance domain may lead to distorted fitting surfaces or abnormal misjudgments. Therefore, this invention employs the Kramers-Kronig test to verify the reasonableness of the impedance data, identifying data that does not meet the requirements of linearity, stability, and causality.

[0062] After quality verification, impedance characteristic parameters can be extracted through equivalent circuit fitting, Nyquist plot geometric feature analysis, relaxation time distribution analysis, or a combination of methods. The impedance characteristic parameters include at least one of ohmic impedance, anodic activation polarization impedance, cathodic activation polarization impedance, and mass transfer impedance.

[0063] To improve the reliability of impedance characteristic parameter assignment, this invention does not rely solely on a single half-circle of the Nyquist plot or the position of a peak in the relaxation time distribution. Instead, it comprehensively determines impedance characteristic parameters based on the following factors: first, the time scale differences corresponding to different impedance processes; second, the contribution of the corresponding impedance component to the total impedance; third, the law of impedance component variation with current density; and fourth, the response law of impedance component to changes in operating state parameters such as cooling temperature, cathode stoichiometry, and cathode pressure. Through the above multi-factor cross-validation, ohmic impedance, anode activation polarization impedance, cathode activation polarization impedance, and mass transfer impedance can be more accurately distinguished.

[0064] Among these, cathode activation polarization impedance and mass transfer impedance are particularly sensitive to changes in the operating state of a fuel cell. Cathode activation polarization impedance reflects changes in cathode oxygen reduction reaction kinetics, catalyst layer reaction state, temperature state, and local water state; mass transfer impedance reflects changes in oxygen transport capacity, flow channel gas supply state, diffuser layer patency, liquid water blockage, and flooding tendency. Therefore, when constructing the impedance domain, cathode activation polarization impedance and mass transfer impedance can be preferentially selected as core impedance characteristic parameters.

[0065] The correlation principle between operating state parameters and impedance characteristic parameters The impedance characteristics of a fuel cell do not exist in isolation, but are closely related to the operating load point and operating parameters. Under different operating currents or current densities, the internal electrochemical reaction rate, water production, heat production, gas consumption, and mass transfer requirements of the fuel cell are all different. Therefore, the same change in operating parameters may produce different impedance responses at different load points.

[0066] This invention first conducts sensitivity experiments at multiple operating load points. The operating load points can be characterized by operating current or current density; the operating state parameters can include at least one of cooling temperature, cathode metering ratio, cathode flow rate, cathode pressure, and anode pressure. Preferably, the cooling temperature is the cooling inlet temperature; the cathode flow rate can be the actual cathode air mass flow rate, or it can be calculated from the cathode metering ratio, stack operating current, number of stack sections, and oxygen volume fraction in the air. During the experiments, using standard operating condition parameters as a benchmark, one or more operating state parameters are adjusted upwards or downwards, and electrochemical AC impedance frequency sweep tests are performed under each parameter combination to obtain impedance data and corresponding state parameters.

[0067] like Figure 4As shown, at a current density of 600 mA / cm², both the activation polarization impedance arc and the mass transfer impedance arc in the EISNyquist plot of the fuel cell undergo significant changes when the cooling temperature changes. With increasing cooling temperature, the arcs representing activation polarization impedance and mass transfer impedance generally show a shrinking trend. This phenomenon indicates that, within a certain temperature range, increasing the cooling temperature is beneficial for improving the electrochemical reaction rate, enhancing catalytic reaction kinetics, and reducing some polarization losses. Simultaneously, temperature also affects membrane water content, gas diffusion, and water evaporation states; therefore, temperature changes are directly reflected in the impedance spectrum characteristics.

[0068] like Figure 5 As shown, at a current density of 600 mA / cm², the activation polarization impedance and mass transfer impedance arcs in the EISNyquist plot change to varying degrees when the cathode stoichiometry changes. With increasing cathode stoichiometry, the cathode's oxygen supply capacity increases, concentration polarization caused by insufficient oxygen concentration weakens, and the mass transfer process improves. Therefore, the arcs related to activation polarization impedance and mass transfer impedance generally show a decreasing trend. Ohmic impedance, on the other hand, is mainly related to film resistance, contact resistance, and material conductivity, and is not sensitive to changes in the cathode stoichiometry, with relatively small changes.

[0069] Figure 4 and Figure 5 Taking the test results at a current density of 600 mA / cm² as an example, the influence of cooling temperature and cathode stoichiometry on the impedance spectrum is shown; the same method can be used to obtain the corresponding sensitivity characteristics at other current density points or other operating current ranges.

[0070] This demonstrates that different impedance characteristic parameters exhibit varying sensitivities to different operating state parameters. Based on sensitivity experiment results, this invention selects impedance characteristic parameters and operating state parameters with clear correlations to construct an impedance domain. For example, the correlation between cathode activation polarization impedance, mass transfer impedance, current density, cooling temperature, and cathode flow rate can be analyzed. Specifically, cathode activation polarization impedance and mass transfer impedance characterize the internal state changes of the fuel cell stack; current density, cooling temperature, and cathode flow rate characterize the external load and externally controllable operating state.

[0071] The significance of this correlation analysis lies in the fact that fuel cell condition assessment no longer relies on a single absolute impedance value, but rather on judging whether the impedance value is reasonable in conjunction with the current external operating conditions. For example, the same impedance value may be within the normal range under low temperature and low flow conditions, but may represent an abnormal deviation under high temperature and high flow conditions. Therefore, only by integrating impedance characteristic parameters with operating state parameters can the actual state of the fuel cell be determined more accurately.

[0072] Principles of constructing discrete data point sets like Figure 3As shown, after determining the impedance characteristic parameters and operating state parameters used to construct the impedance domain, each set of experimental data is mapped into a multidimensional space to form a discrete data point set.

[0073] The following uses the cathode activation polarization impedance domain as an example to illustrate the impedance domain construction process; the mass transfer impedance domain can be constructed using the same method. Taking cooling temperature, cathode flow rate, and cathode activation polarization impedance as examples, the cooling temperature can be denoted as... The cathode flow rate is denoted as The cathode activation polarization impedance is denoted as At a given workload point, each set of experimental data can be represented as a discrete point in space: ; In the formula, The cooling temperature corresponding to the i-th group of experiments. Let i be the cathode flow rate corresponding to the i-th group of experiments. The cathode activation polarization impedance is extracted from the i-th group of experiments.

[0074] like Figure 6 As shown, multiple experimental points are discretely distributed in three-dimensional space. This discrete data set reflects the experimental correlation between cooling temperature, cathode flow rate, and cathode activation polarization impedance at a certain operating load point. Since experimental data typically only covers a limited number of parameter combinations, directly using discrete points for state judgment results in limited coverage and cannot provide continuous judgment for untested parameter points. Therefore, further spatial fitting of the discrete data points is needed to form a continuous impedance surface.

[0075] If m operating state parameters are selected, the operating state parameter vector can be represented as: ; The corresponding discrete data points can be represented as: ; in, Let be the impedance characteristic parameters corresponding to the i-th group of experiments. The dimension of the constructed impedance domain space is . ,and .when When, a two-dimensional impedance domain can be constructed; when When m is greater than 2, a three-dimensional impedance domain can be constructed; when m is greater than 2, a high-dimensional impedance domain can be constructed.

[0076] Standard impedance surface construction principle like Figure 7 As shown, a standard impedance surface can be obtained by performing spatial surface smoothing fitting on a discrete data point set. This standard impedance surface is used to describe the baseline relationship between impedance characteristic parameters and operating state parameters at a given operating load point.

[0077] The running state parameter vector is represented as: ; The standard impedance surface can then be represented as: ; In the formula, This is the standard impedance value. This is a functional relationship obtained by fitting a discrete set of data points. This is a vector of running state parameters.

[0078] In practical implementation, spatial surface smoothing can be achieved using methods such as polynomial fitting, spline surface fitting, radial basis function fitting, local weighted regression, interpolation fitting, or lookup table interpolation. If the controller has sufficient computing power, a continuous function model can be used to represent the standard impedance surface; if the controller has limited computing power, the fitted surface can be stored in the controller as a two-dimensional table, a three-dimensional table, or a multi-dimensional lookup table, and the standard impedance value under the corresponding state parameters can be obtained through interpolation.

[0079] The purpose of a standard impedance surface is to extend finite experimental data into a continuous state space, enabling fuel cells to obtain corresponding reference impedance values ​​even for parameter combinations not covered point-by-point by experiments. This standard impedance surface can be understood as the reference operating state surface of the fuel cell at the corresponding operating load point.

[0080] Normal impedance domain construction principle A standard impedance surface alone cannot be directly used as a boundary for judging normal operation. In actual operation, fuel cell systems are affected by factors such as ambient temperature, hydrogen quality, air humidity, sensor errors, actuator response errors, test noise, and slight aging of the fuel cell stack. Real-time impedance values ​​typically fluctuate within a certain range around the standard impedance surface. Therefore, this invention, based on the standard impedance surface, sets allowable deviation ranges to construct upper and lower impedance surfaces.

[0081] Let the percentage of deviation be ,make: ; The upper and lower impedance surfaces are then represented as follows: ; ; The recommended operating ranges for each operating status parameter form the parameter space: ; in, Recommend the lower limit of the operating range for the i-th operating status parameter. Recommend the upper limit of the operating range for the i-th operating status parameter.

[0082] The normal impedance domain is formed by the combined envelope of the upper impedance surface, the lower impedance surface, and the state parameter boundary. ; like Figure 8 As shown, the normal impedance domain is an envelope region with spatial thickness, rather than a single curved surface. During fuel cell operation, if the state point formed by the combination of the real-time measured cooling temperature, cathode flow rate, and impedance characteristic parameters falls within this envelope space, it indicates that the current fuel cell state is still within the normal range; if the state point deviates from this envelope space, it indicates that the current fuel cell state has abnormally shifted relative to the calibrated normal state.

[0083] The percentage deviation δ can be determined based on the statistical results of repeated measurements, the measurement error of the impedance testing equipment, the fluctuation range of operating conditions, and fuel cell aging or fault injection experiments. δ needs to be greater than the equipment measurement error to avoid normal measurement fluctuations being misjudged as abnormal; at the same time, δ should not be set too large to avoid incorrectly including early abnormal states in the normal impedance range.

[0084] Principles of constructing a multivariable impedance domain database Fuel cells exhibit varying heat generation, water production, gas consumption, polarization losses, and internal mass transfer states under different operating currents or current densities. Consequently, the impedance response corresponding to the same operating state parameter differs at different operating load points. To improve the accuracy of state determination, this invention constructs normal impedance domains at multiple operating load points and stores these multiple impedance domains in association, forming a multi-element impedance domain database.

[0085] like Figure 9 As shown, normal impedance domains related to cooling temperature, cathode flow rate, and cathode activation polarization impedance can be constructed separately under multiple current densities or multiple operating current levels; cathode activation polarization impedance domains and mass transfer impedance domains can also be constructed separately under the same load point. Multiple operating load points, multiple impedance characteristic parameters, and multiple state parameter combinations together constitute the multivariate impedance domain database of the fuel cell system.

[0086] The multivariable impedance domain database can be represented as: ; In the formula, This represents the normal impedance domain corresponding to the type p impedance characteristic parameter at the k-th operating load point.

[0087] During fuel cell operation, the system controller retrieves the corresponding normal impedance domain from the multivariate impedance domain database based on the current operating current or current density. If the current operating load point is located between two calibrated load points, the corresponding standard impedance surface or normal impedance domain can be obtained through interpolation. As the fuel cell operating time increases, the multivariate impedance domain database can also be iteratively updated based on periodic recalibration results or long-term operating data to adapt to stack aging and system state changes.

[0088] Real-time state mapping and anomaly recognition principles like Figure 10 As shown, during the actual operation of a fuel cell, online electrochemical AC impedance detection can be achieved through a DC / DC converter; subsequently, the system controller combines real-time operating status parameters and impedance characteristic parameters to map the current state to the corresponding impedance domain.

[0089] The real-time collected runtime status parameter vector is represented as follows: ; The impedance characteristic parameters extracted in real time are expressed as follows: Then the current state point of the fuel cell can be represented as: ; When the following conditions are met: ; At that time, it is determined that the fuel cell is in normal operating condition under the corresponding working load point and corresponding impedance characteristic parameters.

[0090] When the following conditions are met: ; When this occurs, it is determined that the current operating state of the fuel cell has shifted relative to the normal impedance domain.

[0091] This method of judgment can identify fuel cell anomalies before a fault occurs. For example, when the mass transfer impedance is significantly higher than the upper limit of the normal impedance range at the current cathode flow rate, cooling temperature, and load point, it can be considered that the fuel cell has a tendency for insufficient cathode gas supply, limited gas diffusion, liquid water blockage, or flooding. When the cathode activation polarization impedance is significantly higher than the upper limit of the normal impedance range, it can be considered that the fuel cell has a tendency for limited reaction kinetics, low temperature, poor catalytic reaction conditions, or abnormal membrane water state.

[0092] Therefore, this invention can not only determine whether a fuel cell is abnormal, but also combine the type of deviation impedance characteristics and the direction of operating state parameters to provide a basis for subsequent control strategies.

[0093] Hierarchical state space construction principle like Figure 11 and Figure 12As shown, based on the already constructed normal impedance domain, the present invention can further construct a hierarchical state space in order to transform the impedance domain judgment result into a more specific control region and control action.

[0094] Taking a three-dimensional impedance domain consisting of two operating state parameters and one impedance characteristic parameter as an example, let the two operating state parameters be cooling temperature. and cathode flow The impedance characteristic parameters are When a specific impedance value R is measured in real time for a fuel cell, it can be intersected by an intersection plane with the impedance domain, where the impedance coordinates are constant at R: ; The intersection surface successively passes through the standard impedance surface and the control surfaces at different deviation ratios. The intersection surface and the standard impedance surface form the core control line: ; The core control line is a baseline control line obtained experimentally. Points on this line correspond to optimal operating state combinations for the current impedance value R. Using the core control line as a reference, a first deviation percentage can be further set. Second deviation percentage ,and: ; in, Used to define buffer boundaries Used to define exception boundaries. Let: ;

[0095] The intersection surface intersects with the first lower deviation control surface and the first upper deviation control surface, forming the lower buffer boundary and the upper buffer boundary, respectively: ; ; The intersection surface intersects with the second lower deviation control surface and the second upper deviation control surface, forming the lower anomaly boundary and the upper anomaly boundary, respectively: ; ; Based on the core control line, upper and lower buffer boundaries, and upper and lower abnormal boundaries, the control area of ​​the intersection surface can be divided into the core stable area, the buffer transition area, the dynamic adjustment area, and the abnormal state area.

[0096] The core stability region is defined by the core control line and its adjacent area. When the real-time state point is located within the core stability region, it indicates that the fuel cell is in an operating state with excellent overall performance or close to the calibration reference. The system does not need to actively adjust and can maintain the current operating condition.

[0097] The buffer transition zone is located outside the core stability zone and inside the buffer boundary. When the real-time state point is located in the buffer transition zone, it indicates that the fuel cell state has a slight deviation from the calibration reference state, but it is still within an acceptable range. The system can enter observation mode and increase the monitoring frequency, but does not immediately change the output of the actuators.

[0098] The dynamic adjustment zone is located between the buffer boundary and the abnormal boundary. When the real-time state point is in the dynamic adjustment zone, it indicates that the fuel cell state has deviated significantly and it is necessary to actively adjust the operating state parameters, such as adjusting the cooling water pump, cooling fan, air compressor, back pressure valve, hydrogen circulation device, or drain valve, so that the state point gradually converges towards the buffer transition zone or the core stable zone.

[0099] The abnormal state zone is located outside the abnormal boundary. When the real-time state point is located in the abnormal state zone, it indicates that the fuel cell may have membrane dryness, flooding, undergassing, thermal runaway tendencies, or other abnormal risks. The system should initiate multi-dimensional diagnostics and stabilization control, and can record abnormal data, issue alarms, or reduce the load to prioritize the safety of the fuel cell.

[0100] To avoid frequent switching of real-time state points near region boundaries due to measurement noise or minor fluctuations in operating conditions, hysteresis loops can be set at each region boundary. The hysteresis width can be set to ±σ% of the corresponding region size. If σ is too small, the hysteresis effect will be insignificant, and frequent switching may still occur; if σ is too large, the control response will become sluggish, and real anomalies may be delayed in processing. Therefore, the value of σ can be determined based on the normal fluctuation range of the state variables under dynamic operating conditions, and the hysteresis width should cover the normal fluctuation range.

[0101] Anchor point progressive control principle like Figure 13 and Figure 14 As shown, in the hierarchical state space, in order to avoid control overshoot or large fluctuations in the actuators caused by the fuel cell state point jumping directly from the abnormal region to the core stable region, the present invention can adopt an anchor point progressive control method.

[0102] The real-time state point of the fuel cell at the intersection surface is represented as: ; Select the point closest to the real-time status point from the core control line as the anchor point: ; In the formula, For the nearest anchor point, This represents the Euclidean distance.

[0103] The system controller determines the direction and magnitude of adjustment for operating status parameters based on the direction and distance between the real-time status point and the nearest anchor point. For example, when the real-time status point shows a lower cooling temperature relative to the anchor point, the target temperature of the cooling system can be appropriately increased or the thermal management actuators can be adjusted; when the real-time status point shows insufficient cathode flow, the air compressor speed can be increased or the cathode back pressure can be adjusted; when the real-time status point shows an abnormally high mass transfer impedance, comprehensive adjustments can be made by combining cathode flow, pressure, and drainage strategies.

[0104] For abnormal state regions, the system can avoid directly targeting the core control line as the immediate goal. Instead, it can first use the buffer transition region as a short-term target to quickly pull the state point back into a controllable range. Once the state point enters the buffer transition region, the system then determines whether to continue gradual adjustment towards the core stable region based on the fuel cell's operating status. This approach reduces control overshoot and improves system robustness while ensuring safety.

[0105] Therefore, this invention transforms fuel cell control from traditional single-target point control to spatial region judgment, hierarchical state division, and anchor point gradual adjustment, which can enhance the system's adaptability to dynamic operating conditions, measurement noise, and early abnormal states.

[0106] Example The following embodiments are used to further illustrate the present invention, but should not be construed as limiting the scope of protection of the present invention. Equivalent substitutions made by those skilled in the art for fuel cell power levels, operating load points, frequency sweep ranges, fitting algorithms, impedance feature extraction methods, or control execution components without departing from the concept of the present invention should all fall within the scope of protection of the present invention.

[0107] Example 1: Impedance characteristic parameter screening based on standard operating conditions and sensitivity experiments of a 150kW fuel cell stack This embodiment illustrates how to select suitable impedance characteristic parameters for constructing an impedance domain from electrochemical AC impedance test data of a fuel cell stack, and demonstrates that there is a stable correlation between the impedance characteristic parameters and the operating state parameters that can be used for domain construction.

[0108] This embodiment uses a 150kW fuel cell stack as the test object. The stack comprises 290 individual cells, each with an electrochemical active area of ​​380 cm². The test system includes the fuel cell stack, a fuel cell stack test bench, a regenerative electronic load, a high-power electrochemical impedance spectroscopy (EIS) meter, a low-voltage power supply, a cooling circulation system, a hydrogen supply system, an air supply system, and a host computer data acquisition system. The fuel cell stack test bench is used to control the stack's operating current, cooling inlet temperature, cathode metering ratio, cathode pressure, and anode pressure; the regenerative electronic load provides stable load conditions under different current densities; and the EIS meter applies AC disturbances to the fuel cell stack and acquires voltage and current response signals.

[0109] In this embodiment, the 150kW fuel cell stack is first subjected to standard operating condition EIS testing. As a specific testing method, the frequency sweep range is set to 0.1Hz to 10kHz, and frequency points are selected at logarithmic intervals. The AC disturbance amplitude at different current density points is set according to the stack operating current to avoid excessive disturbance causing stack state deviation.

[0110] After completing the standard operating condition frequency sweep test, the raw impedance data is preprocessed. This includes: removing data with abnormal imaginary parts in the high-frequency band due to the influence of test cables, inductive coupling, or current collectors; performing Kramers-Kronig tests on the impedance data to determine if it meets the requirements for linearity, stability, and causality; and normalizing the quality-verified impedance data by the number of stack sections and the active area of ​​a single chip, so that impedance values ​​at different current densities can be compared in mΩ·cm².

[0111] Reference Figure 2 The Nyquist graph analysis method shown is as follows: Figure 2 (a) is the Nyquist plot of the impedance spectrum. Figure 2 (b) is a schematic diagram of impedance characteristics. Under standard operating conditions, the impedance spectra corresponding to different current densities all exhibit typical capacitive impedance characteristics of a fuel cell stack. The intersection of the high-frequency region and the real axis corresponds to ohmic impedance, which is mainly affected by the proton exchange membrane, electrode materials, bipolar plates, current collectors, and interface contact resistance. The high-frequency intercept does not change significantly with varying current density, indicating that ohmic impedance is not the most sensitive characteristic under short-term operating conditions. The mid-to-high frequency and mid-to-low frequency arcs in the Nyquist plot show varying degrees of contraction or expansion with changes in current density, indicating that the activation polarization and mass transfer processes inside the fuel cell change significantly with the workload.

[0112] To further avoid subjective judgments based solely on the semi-circular shape of the Nyquist plot, this embodiment performs relaxation time distribution analysis on the impedance data that has passed quality verification. For impedance characteristic peaks appearing in the relaxation time distribution analysis, this embodiment does not assign them solely based on the "time constant range of the peak," but rather determines their physical meaning by comprehensively considering the following four criteria: First, the speed of the process can be determined based on the relaxation time scale. Peaks within a shorter relaxation time range correspond to faster charge transfer processes, while peaks within a longer relaxation time range correspond to slower reactant transport or product removal processes. Inside a fuel cell, the anode reaction is typically faster, the cathode oxygen reduction reaction is slower, and gas diffusion and water removal are even slower. Therefore, the order of relaxation times can serve as a preliminary criterion.

[0113] Second, the impedance contribution can be determined based on the peak area or peak intensity. If a relaxation peak has a small peak area and a low contribution to the total impedance, it usually does not constitute the main source of the stack impedance; if a relaxation peak has a large peak area and a significant contribution to the total impedance under different current densities, it can be used as the key object for impedance domain construction.

[0114] Third, the judgment is made based on the trend of change with current density. If a certain peak changes significantly with the increase of current density, it indicates that it is closely related to the electrochemical reaction rate, reactant consumption, or water production; if a certain peak does not change significantly with current density, it indicates that the process is not sensitive to load changes and is not suitable as a key state identification feature.

[0115] Fourth, verification is performed based on the sensitivity test response. For candidate impedance characteristic parameters, their response to changes in cooling temperature, cathode stoichiometry, and cathode pressure is further observed. If the impedance component can produce a clear and repeatable change with changes in temperature, cathode gas supply, or pressure, it indicates that there is a correlation between it and externally controllable operating state parameters that can be used to construct an impedance domain.

[0116] Based on the above criteria, this embodiment decomposes the impedance components obtained under standard operating conditions into ohmic impedance, anode activation polarization impedance, cathode activation polarization impedance, and mass transfer impedance. The anode activation polarization impedance has a relatively small value and its variation with current density is not significant, indicating that although it can reflect the reaction process on the anode side, it is not suitable as the primary monitoring object in impedance domain construction. The ohmic impedance shows some variation in the low current density range and remains relatively stable in the medium to high current density range, indicating that it is more suitable for auxiliary judgment of membrane resistance, contact resistance, or long-term degradation status. The cathode activation polarization impedance has a relatively large value in the low current density range, decreases with increasing current density, and contributes significantly to the overall impedance, indicating that it can reflect the kinetic state of the cathode oxygen reduction reaction. The mass transfer impedance shows a trend of first decreasing and then increasing with current density, or increasing again under high load, and is closely related to reactant supply, permeate discharge, and gas diffusion status, making it suitable for judging insufficient cathode gas supply, flooding, or limited mass transfer trends.

[0117] Based on this, this embodiment further conducts parameter sensitivity testing. First, a cooling temperature sensitivity test is performed. For example... Figure 4 As shown, at the same current density, the arcs representing activation polarization impedance and mass transfer impedance in the Nyquist plot decrease overall with increasing cooling temperature. Combined with impedance characteristic analysis results, it can be seen that the ohmic impedance decreases only slightly with increasing temperature, while the cathode activation polarization impedance and mass transfer impedance change more significantly with temperature. This phenomenon indicates that within a certain temperature range, increasing the cooling temperature can improve electrochemical reaction kinetics, reduce cathode reaction resistance, and help improve hydrothermal conditions and gas transport conditions; however, if the temperature is too high, it may cause a decrease in membrane water content, leading to the risk of membrane drying. Therefore, cooling temperature is not only an important operating parameter affecting impedance response but also an important adjustable parameter in the fuel cell control system.

[0118] Then, a cathode metrological sensitivity test is performed. For example... Figure 5 As shown, the EIS Nyquist plots and impedance changes were obtained by changing the cathode stoichiometry ratio under different current densities. The experiment revealed that when the cathode stoichiometry ratio was low, the arc in the low-frequency region of the Nyquist plot significantly increased, indicating insufficient oxygen supply, a decrease in oxygen concentration at the reaction interface, and enhanced concentration polarization. As the cathode stoichiometry ratio increased, the low-frequency mass transfer-related impedance decreased, indicating that the degree of mass transfer limitation was reduced after the cathode gas supply was improved. Meanwhile, the ohmic impedance was not sensitive to changes in the cathode stoichiometry ratio, suggesting that the cathode stoichiometry ratio mainly affects the reactant supply and mass transfer process on the cathode side, rather than directly affecting the ohmic conduction of the fuel cell stack.

[0119] Furthermore, under high cathode stoichiometric ratio conditions, although oxygen supply capacity is enhanced, excessive airflow may remove moisture from the membrane, increasing the risk of localized membrane dryness. Therefore, a higher cathode stoichiometric ratio is not always better. This principle suggests that the cathode stoichiometric ratio, or the cathode air mass flow rate derived from it, is suitable as a key operating state parameter in impedance domain construction, while mass transfer impedance and cathode activation polarization impedance are suitable as corresponding impedance characteristic parameters.

[0120] Next, cathode pressure sensitivity tests were conducted. The results showed that at both low and high current densities, changes in cathode pressure had a weak effect on ohmic impedance and anode activation polarization impedance, but a significant impact on mass transfer impedance. This phenomenon indicates that cathode pressure primarily affects the mass transfer process by altering reactant partial pressures, gas diffusion conditions, and water discharge status. Therefore, cathode pressure can be used as a supplementary operating parameter when constructing mass transfer impedance domains or assisting in the determination of abnormal causes.

[0121] In summary, this embodiment does not directly identify a specific impedance component based on the position of a single impedance peak. Instead, it combines the Nyquist plot arc position, relaxation time sequence, peak area contribution, variation with current density, and sensitivity responses to temperature, stoichiometry, and pressure to determine impedance characteristic parameters. Based on these results, this embodiment preferentially selects cathode activation polarization impedance and mass transfer impedance as the objects for impedance domain construction, and selects at least one of cooling temperature, cathode flow rate, and cathode pressure as operating state parameters, thereby forming a multidimensional impedance domain capable of characterizing the internal reaction kinetics and mass transfer states of the fuel cell.

[0122] The technical advantages of this embodiment are as follows: through standard operating condition testing and sensitivity experiments on a 150kW fuel cell stack, it is demonstrated that the cathode activation polarization impedance and mass transfer impedance have higher responsiveness to changes in the internal state of the fuel cell and can serve as core features for impedance domain construction; at the same time, it is demonstrated that cooling temperature, cathode stoichiometry, and cathode pressure have a clear impact on impedance response, so that impedance domain construction has an experimental basis, rather than relying solely on theoretical assumptions.

[0123] Example 2: Construction of a multivariate impedance domain database based on a 180kW fuel cell system This embodiment illustrates how to use the impedance characteristic parameters and operating state parameters determined in Embodiment 1 for the construction of a system-level impedance domain database, and demonstrates that the present invention is applicable to online operation scenarios of fuel cell systems.

[0124] This embodiment uses a 180kW fuel cell system as the example. The fuel cell system comprises 370 individual cells, each with an electrochemical active area of ​​380 cm². The system includes a fuel cell stack, a fuel cell system controller, a DC / DC converter, an air compressor, a hydrogen supply device, a cooling circulation device, a humidification device, an air filtration device, an electronic load, and a data acquisition module. The DC / DC converter has a built-in electrochemical impedance spectroscopy (EIS) testing module, which can inject AC disturbances into the fuel cell stack during operation and detect the response signal.

[0125] In this embodiment, five operating current ranges—750A, 570A, 380A, 190A, and 76A—were selected for impedance database construction. At each operating current range, based on the system's calibrated recommended operating conditions, the cooling temperature and cathode metering ratio were varied to obtain impedance data under different combinations of operating parameters. Specific experimental conditions are shown in the table below: 750A 67～76℃ 1.8～2.2 40 groups 570A 67～73℃ 1.8～2.2 36 groups 380A 66～72℃ 2.0～2.4 47 groups 190A 63～69℃ 2.4～3.0 49 groups 76A 60～66℃ 3.2～3.8 19 groups A total of 191 frequency sweep tests were conducted across the five operating current levels. This experimental design ensures that the impedance database covers not only high-power, medium-power, and low-power operating conditions, but also different temperature ranges and different cathode gas supply levels. For fuel cell systems, heat generation, water production, oxygen consumption, and mass transfer requirements vary under different current levels. Therefore, this embodiment establishes domains separately for each operating current level, rather than using a uniform threshold to cover all operating conditions.

[0126] like Figure 10 As shown, a single online EIS test is jointly performed by the fuel cell system controller, the DC / DC converter, and the fuel cell stack. The fuel cell system controller sends the disturbance amplitude, disturbance frequency, and EIS enable signal to the DC / DC converter; the DC / DC converter's built-in EIS module injects the disturbance into the fuel cell stack and detects the response; the effective AC component is separated by a fast Fourier transform, and the impedance amplitude and phase at the corresponding frequency are calculated; the DC / DC converter reports the impedance results to the fuel cell system controller. To avoid the AC disturbance affecting the stability of the system power level, the disturbance current amplitude is set to 5A in this embodiment. For this 180kW fuel cell system, the effective detection frequency range of the DC / DC converter's EIS module can be taken as 2Hz to 500Hz. This frequency range can cover the main characteristic frequency range of cathode activation polarization impedance and mass transfer impedance, making it suitable for online detection.

[0127] Taking the 380A operating current setting as an example, the cooling temperature range is 66–72℃, and the cathode metering ratio ranges from 2.0 to 2.4. A total of 47 sweep frequency tests were conducted. Based on the cathode metering ratio, fuel cell operating current, number of fuel cell sections, and oxygen volume fraction in the air, the cathode metering ratio was converted into cathode air mass flow rate. Therefore, each set of test data can be represented as a spatial point composed of cooling inlet temperature, cathode air mass flow rate, and impedance characteristic parameters.

[0128] In one specific construction method, the cathode activation polarization impedance is selected as the impedance characteristic parameter, and each set of valid data is expressed as: ; in, The cooling inlet temperature corresponding to the i-th test group. Let be the cathode air mass flow rate corresponding to the i-th test group. The cathode activation polarization impedance corresponds to the i-th test group.

[0129] like Figure 6 As shown, taking a specific operating load point, such as the 380A operating current range, as an example, the three-dimensional discrete points cover the corresponding cooling inlet temperature range, cathode flow range, and cathode activation polarization impedance range. This three-dimensional point plot is not a simple data stacking, but rather unifies the "controllable external state quantity" and the "internal impedance response quantity" into the same space, making each steady-state test result a sample point in the impedance domain.

[0130] By performing a spatial surface smoothing fit on the above three-dimensional discrete points, the standard cathode activation polarization impedance surface with respect to cooling temperature and cathode flow rate at the 380A operating current setting is obtained: ; like Figure 7 As shown, the standard impedance surface represents the reference cathode activation polarization impedance of the fuel cell system under different combinations of cooling temperature and cathode flow rate at a 380A operating current setting. This surface expands a finite number of experimental points into a continuous state judgment surface, enabling the system to obtain the corresponding standard impedance value even under temperature-flow rate combinations that are not tested point by point.

[0131] Considering the normal fluctuations during fuel cell operation and the measurement errors in the DC / DC converter EIS detection module, this embodiment sets an allowable deviation range based on the standard impedance surface. Specifically, the measurement error of the DC / DC converter EIS functional module is less than 3.5%, therefore, this embodiment sets the allowable impedance deviation to ±5%. This deviation range is greater than the equipment measurement error, which can avoid misjudgments caused by measurement noise; at the same time, it is not so large as to cover obvious abnormal states. In other embodiments, the deviation percentage δ can also be determined based on equipment error, repeated measurement statistics, aging experiments, or fault injection experiments.

[0132] Therefore, the upper limit impedance surface and the lower limit impedance surface are respectively: ; ; The normal cathode activation polarization impedance domain at the 380A operating current level is formed by the combined envelope of the upper limit impedance surface, the lower limit impedance surface, the cooling temperature boundary, and the cathode flow boundary. Figure 8 As shown. When the fuel cell system is running online, if the state point formed by the real-time measured cooling inlet temperature, cathode flow rate, and cathode activation polarization impedance falls within this spatial domain, it indicates that the current fuel cell system is in normal operating range; if the state point exceeds this spatial domain, it indicates that the current internal reaction kinetic state of the fuel cell has deviated from the normal calibration state.

[0133] Similarly, at the 380A operating current range, mass transfer impedance can be selected as the impedance characteristic parameter to construct a normal mass transfer impedance domain with respect to cooling temperature, cathode flow rate, and mass transfer impedance. This mass transfer impedance domain can be used to identify insufficient cathode gas supply, water accumulation in the flow channel, restricted gas diffusion, or flooding trends. For the 750A, 570A, 190A, and 76A operating current ranges, repeating the above steps will yield the corresponding cathode activation polarization impedance domain and mass transfer impedance domain.

[0134] Ultimately, as Figure 9 As shown, the normal impedance domains corresponding to different operating current levels, different impedance characteristic parameters, and different combinations of state parameters are associated and stored to form a multi-element impedance domain database. During operation, the fuel cell system controller calls the corresponding impedance domain according to the current operating current level and maps the real-time state point to that impedance domain to complete the state judgment.

[0135] The technical advantages of this embodiment are as follows: Through 191 sets of system-level frequency sweep tests, the temperature-flow-impedance response relationship of the fuel cell system at five typical operating current levels is transformed into a multi-dimensional impedance domain database that can be accessed by the controller. Compared with methods that rely solely on a single impedance threshold, this database can distinguish the normal impedance range under different loads, temperatures, and flow rates, improving the accuracy of state judgment in dynamic operating scenarios. Compared with methods that rely solely on laboratory impedance meters, this embodiment utilizes a DC / DC converter to complete online EIS testing, making it more suitable for engineering applications of vehicle-mounted or distributed generation fuel cell systems.

[0136] Example 3: Anomaly Identification and Hierarchical Anchor Point Progressive Control Based on Impedance Domain Database In one optional implementation, the multi-element impedance domain database constructed in Example 2 is used to illustrate the state identification and control adjustment during fuel cell operation. This example mainly illustrates the combination of the impedance domain database and the fuel cell system control strategy.

[0137] During the operation of the fuel cell system, the system controller determines the corresponding operating load point based on the current operating current or current density, and retrieves the normal impedance domain corresponding to that operating load point from the multivariate impedance domain database. Simultaneously, the system obtains the current impedance data of the fuel cell through the online electrochemical AC impedance detection function of the DC / DC converter, and extracts impedance characteristic parameters such as cathode activation polarization impedance and / or mass transfer impedance according to the aforementioned impedance characteristic analysis method; at least one operating status parameter among cooling temperature, cathode flow rate, cathode pressure, and anode pressure is simultaneously acquired.

[0138] The real-time collected operating status parameters are represented as a real-time operating status parameter vector. The impedance characteristic parameters extracted in real time are expressed as The two together constitute the real-time state point. The system controller maps the real-time status point to the normal impedance domain corresponding to the current working load point. When the real-time status point is within the normal impedance domain, it is determined that the current operating state of the fuel cell is within the normal range of the corresponding working load point, and the current operating state is maintained; when the real-time status point exceeds the normal impedance domain, it is determined that the current state of the fuel cell has deviated from the normal calibration state, and further hierarchical state space judgment is performed.

[0139] When the normal impedance domain consists of a three-dimensional space composed of two operating state parameters and one impedance characteristic parameter, the real-time impedance characteristic parameter is used. The corresponding impedance value is used as the cutoff value to cut the normal impedance domain, thereby obtaining the corresponding parametric control region. Based on the intersection of the intersection surface with the standard impedance surface and different deviation control surfaces, the parametric control region is divided into a core stability region, a buffer transition region, a dynamic adjustment region, and an abnormal state region.

[0140] When the real-time state point is located in the core stable region, the system maintains the current control input; when the real-time state point is located in the buffer transition region, the system enters the observation state, which can increase the state detection frequency without immediately changing the output of the actuators; when the real-time state point is located in the dynamic adjustment region, the system gradually adjusts the corresponding operating state parameters according to the offset direction and offset distance of the real-time state point relative to the core control line or buffer boundary; when the real-time state point is located in the abnormal state region, the system initiates multi-dimensional diagnosis and stabilization control, and prioritizes the convergence of the real-time state point towards the buffer transition region.

[0141] During incremental adjustments, the point closest to the real-time state point from the core control line is selected as the target anchor point. Alternatively, when the real-time state point deviates significantly, the corresponding point on the boundary of the buffer transition zone is used as a stage anchor point. The system determines the adjustment direction of each operating state parameter based on the direction between the real-time state point and the target anchor point, and determines the adjustment magnitude based on the distance between them.

[0142] For example, when the offset direction of the state point indicates insufficient cathode gas supply, the cathode flow rate or cathode gas supply can be increased or improved by increasing the air compressor speed or adjusting the cathode back pressure. When the offset direction of the state point indicates that the cooling temperature deviates from the normal range, the cooling state of the fuel cell can be changed by adjusting the cooling fan speed or cooling water pump speed. When the mass transfer impedance deviates abnormally, it can be comprehensively adjusted by combining the cathode flow rate, cathode pressure, and drainage status.

[0143] During the adjustment process, the system periodically reacquires real-time impedance characteristic parameters and operating status parameters, and redetermines the position of the real-time state point in the hierarchical state space. As the real-time state point gradually approaches the buffer transition zone or the core stable zone, the adjustment range of the operating status parameters is reduced accordingly; when the real-time state point enters the buffer transition zone, it can switch from active adjustment to observation; when the real-time state point further enters the core stable zone, the current operating state is maintained.

[0144] In the above way, the state judgment results of the multivariate impedance domain database can be further transformed into the adjustment direction and adjustment range of the operating state parameters of the fuel cell system. This allows the impedance domain to not only be used for fuel cell operating state identification, but also to provide control basis for the gradual adjustment and abnormal state handling of the fuel cell system.

[0145] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0146] 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 one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0147] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for constructing the impedance domain and identifying the state of a fuel cell, characterized in that, include: S1. Under multiple operating load points, adjust the operating status parameters based on standard operating conditions and perform electrochemical AC impedance frequency sweep test to obtain impedance data and corresponding status parameters. S2. Perform preprocessing, quality verification and analysis on the impedance data, extract impedance characteristic parameters and determine their correlation with state parameters; S3. Select the associated impedance characteristic parameters and state parameters to form an n-dimensional discrete data point set, where n≥2; S4. Perform smooth fitting on the discrete data point set to obtain the standard impedance surface that characterizes the change of impedance characteristic parameters with state parameters. S5. Obtain the upper and lower limit impedance surfaces according to ±δ%, and form the normal impedance domain of each working load point by the two and the boundary envelope of the state parameters. Then, store them in association according to the working load points to form a multi-element impedance domain database.

2. The method for constructing and identifying the impedance domain of a fuel cell according to claim 1, characterized in that, In step S1, an AC current disturbance signal is applied to the fuel cell at each test frequency of the frequency sweep test. The AC current disturbance signal is expressed as follows: ； The same-frequency response voltage generated by the fuel cell is expressed as: ； The complex forms of the alternating current disturbance signal and the same-frequency response voltage are respectively expressed as: ； ； The complex AC impedance at the corresponding angular frequency is expressed as: ； in: ； ； In the formula, For time; for The alternating current disturbance signal constantly applied to the fuel cell; For fuel cells in The same frequency response voltage generated at any given moment; The amplitude of the alternating current disturbance signal; This represents the amplitude of the voltage response at the same frequency. Let be the angular frequency of the alternating current disturbance signal, and ; The frequency of the alternating current disturbance signal; The initial phase of the alternating current disturbance signal; This represents the phase difference between the voltage response at the same frequency and the alternating current disturbance signal; For the phasor of the alternating current disturbance signal; For the phasor of the voltage response at the same frequency; It is a natural constant; It is the imaginary unit, and ; Angular frequency Complex AC impedance; This represents the AC impedance amplitude. Phase angle of AC impedance; The real part of the AC impedance; This represents the imaginary part of the AC impedance.

3. The method for constructing and identifying the impedance domain of a fuel cell according to claim 2, characterized in that, The frequency range of the electrochemical AC impedance sweep test is 0.1 Hz to 10 kHz, and the test procedure includes: The fuel cell system controller sends disturbance amplitude, disturbance frequency, and electrochemical AC impedance test enable signals to the DC / DC converter; The electrochemical AC impedance function module built into the DC / DC converter injects a disturbance signal into the fuel cell and detects the response signal. The disturbance signal and response signal are analyzed by Fast Fourier Transform to separate the effective AC component, calculate the AC impedance corresponding to each test frequency, and report the AC impedance result to the fuel cell system controller.

4. The method for constructing and identifying the state of a fuel cell impedance domain according to claim 1, characterized in that, Step S2 includes: The Kramers-Kronig test was used to verify the quality of the impedance data in order to identify the data corresponding to instrument noise and fuel cell instability. A Nyquist plot is constructed with the real part of the impedance as the horizontal axis and the negative imaginary part of the impedance as the vertical axis. Based on the Nyquist plot, at least one of the following is extracted: ohmic impedance, anode activation polarization impedance, cathode activation polarization impedance, and mass transfer impedance. Relaxation time distribution analysis was performed on the impedance data that passed quality verification to obtain characteristic information corresponding to cathode activation polarization impedance and mass transfer impedance. Statistical merging is performed on repeated sampled data under the same combination of operating state parameters, and abnormal data that fails quality verification is excluded.

5. The method for constructing and identifying the impedance domain of a fuel cell according to claim 1, characterized in that, The operating load point is characterized by the operating current or current density; The operating status parameters include at least one of cooling temperature, cathode metering ratio, cathode flow rate, cathode pressure, and anode pressure; The impedance characteristic parameters include at least one of ohmic impedance, anodic activation polarization impedance, cathodic activation polarization impedance, and mass transfer impedance; The associated impedance characteristic parameters and state parameters are determined by sensitivity test response amplitude, correlation coefficient threshold, or principal component analysis. The associated impedance characteristic parameters and state parameters include combinations of cathode activation polarization impedance and / or mass transfer impedance with at least one of cooling temperature, cathode flow rate, cathode pressure and anode pressure. The cathode activation polarization impedance and mass transfer impedance are used to decouple and characterize the internal state changes of the fuel cell stack, while the operating state parameters are used to characterize the external operating state of the fuel cell stack.

6. The method for constructing and identifying the impedance domain of a fuel cell according to claim 5, characterized in that, The cathode flow rate is calculated based on the cathode metering ratio, which is expressed as: ； The cathode oxygen molar consumption flow rate of the fuel cell stack is expressed as: ； The cathode oxygen mass consumption flow rate is expressed as: ； When air is used as the cathode reaction gas, the theoretical cathode air mass flow rate is expressed as: ； in: ； The actual cathode air mass flow rate is expressed as: ； In the formula, The cathode stoichiometric ratio is a dimensionless parameter; subscript... Indicates cathode; subscript Indicates the actual supply value; subscript Indicates the theoretical consumption value; The actual air mass flow rate supplied to the fuel cell cathode is expressed in g / s. This represents the theoretical air mass flow rate required for the electrochemical reaction at the cathode of a fuel cell, expressed in g / s. The oxygen molar consumption flow rate of the fuel cell stack is expressed in mol / s. This represents the operating current of the fuel cell stack, expressed in amperes (A). The number of individual cells contained in the fuel cell stack is a dimensionless positive integer; is the Faraday constant, with units of C / mol; the value 4 indicates the number of moles of electrons required for each mole of oxygen to participate in the cathodic reduction reaction. The cathode oxygen mass consumption flow rate is expressed in g / s. The molar mass of oxygen is 32 g / mol; The average molar mass of air is approximately 29 g / mol. Let be the volume fraction of oxygen in the air, a dimensionless parameter, taken as 0.

21.

7. The method for constructing and identifying the impedance domain of a fuel cell according to claim 1, characterized in that, In step S4, the running state parameter vector is represented as follows: ； The standard impedance surface is represented as: ； The parameter space formed by the recommended operating ranges of each operating state parameter is represented as follows: ； In step S5, the upper limit impedance surface and the lower limit impedance surface are respectively represented as: ； ； in: ； The normal impedance domain is represented as: ； In the formula, n is the spatial dimension of the normal impedance domain, and n≥2; X is the vector of operating state parameters; This refers to the i-th running status parameter; Recommend the lower limit of the operating range for the i-th operating status parameter; Recommend the upper limit of the operating range for the i-th operating status parameter; The parameter space is formed by recommending operating ranges for each operating state parameter; f(X) is the functional relationship obtained by smooth fitting based on the discrete data point set; The standard impedance value corresponding to the operating state parameter vector X; The upper limit impedance value corresponding to the operating state parameter vector X; X represents the lower limit impedance value corresponding to the operating state parameter vector; Z represents the impedance coordinate value within the normal impedance domain. The percentage of impedance deviation relative to the standard impedance value; The dimensionless relative impedance deviation rate; D is the normal impedance domain formed by the upper impedance surface, the lower impedance surface, and the parameter space boundary envelope; the... , , and The units are all the same as the units of the selected impedance characteristic parameters; The percentage of impedance deviation The impedance is determined based on repeated measurements under the same combination of operating parameters, and the corresponding impedance deviation value is made greater than the measurement error of the impedance testing equipment.

8. The method for constructing and identifying the impedance domain of a fuel cell according to claim 7, characterized in that, During fuel cell operation, the real-time collected operating status parameters are represented as follows: ； The extracted impedance characteristic parameters and the operating state parameters are then mapped to real-time state points: ； When the following conditions are met: ； When the fuel cell is in normal operating condition at the corresponding operating load point, it is determined that the fuel cell is in normal operating condition at the corresponding operating load point; when the following conditions are met: ； When this occurs, it is determined that the real-time operating state of the fuel cell has shifted relative to the normal impedance domain; In the formula, This is a vector of real-time operating status parameters; the subscript rt represents the real-time measured value. This refers to the i-th running status parameter collected in real time. Impedance characteristic parameters extracted from real-time electrochemical AC impedance test data; This represents the real-time state point corresponding to the current operating state of the fuel cell in the n-dimensional space. This represents the normal impedance region at the kth working load point. The cathode activation polarization impedance domain and mass transfer impedance domain under different operating currents or different current densities are constructed respectively, and stored in association according to the operating load point to form the multi-element impedance domain database. The multivariate impedance domain database is iteratively updated by periodically recalibrating or reconstructing the normal impedance domain based on key operating state parameters.

9. The method for constructing and identifying the impedance domain of a fuel cell according to claim 7, characterized in that, When the normal impedance domain consists of a three-dimensional space composed of two operating state parameters and one impedance characteristic parameter, it also includes constructing a hierarchical state space, specifically: Select a specific impedance value R, and intersect the normal impedance domain with the intersection plane that satisfies the following equation in the impedance coordinates: ； The intersection surface intersects with the standard impedance surface to form the core control line: ； The intersection surface intersects with the first lower deviation control surface and the first upper deviation control surface, forming the lower buffer boundary and the upper buffer boundary, respectively: ； ； The intersection surface intersects with the second lower deviation control surface and the second upper deviation control surface, forming the lower anomaly boundary and the upper anomaly boundary, respectively: ； ； in: ； In the formula, R is the specific impedance value used to cut off the normal impedance domain, and its unit is the same as the unit of the selected impedance characteristic parameter. This represents the intersection surface where the impedance coordinate value is constant at R; As the core control line; This is the lower buffer boundary; This serves as the upper buffer boundary. This is the lower anomaly boundary; This is the upper anomaly boundary; This represents the first percentage deviation of the buffer boundary from the standard impedance value. This represents the second percentage deviation of the abnormal boundary from the standard impedance value. This is the first relative impedance deviation rate; This is the second relative impedance deviation rate; Based on the core control line, lower buffer boundary, upper buffer boundary, lower abnormal boundary, and upper abnormal boundary, the intersection surface control area is divided into a core stable area, a buffer transition area, a dynamic adjustment area, and an abnormal state area.

10. The method for constructing and identifying the impedance domain of a fuel cell according to claim 9, characterized in that, The real-time state point of the fuel cell on the intersection surface is represented as: ； Select the anchor point closest to the real-time state point from the core control line as the convergence target: ； The adjustment direction and adjustment range of the operating status parameters are determined based on the direction and distance between the real-time status point and the anchor point. Maintain the current operating state when the real-time status point is located in the core stable region; The system enters observation mode when the real-time status point is located in the buffer transition zone. When the real-time status point is in the dynamic adjustment zone, adjust the operating status parameters to make the real-time status point converge toward the buffer transition zone or the core control line. When the real-time status point is in the abnormal state zone, multi-dimensional diagnosis and calming control are initiated.

Images