A rapid measurement system and method for fuel cell impedance spectrum

Abstract

The present application belongs to the technical field of fuel cell, and particularly relates to a kind of fuel cell impedance spectrum fast measurement system and measurement method, system is divided into excitation current injection part, data acquisition part and host computer, host computer uses DIBS signal with excellent peak suppression ability and flexible amplitude frequency design ability as test excitation, uses electronic load as excitation source.Host computer can control electronic load to generate current excitation waveform for impedance test based on DIBS signal, and electronic load injects excitation current into the output current of the measured stack, and host computer can also read the sampling data of data acquisition part, and the collected excitation current and response voltage data are subjected to fast Fourier transform to obtain electrochemical impedance spectrum.The present application improves the impedance measurement efficiency, the hardware structure is simple, has good on-site application prospect, and the measured object can be extended to other electrochemical systems including electrolytic cell, and has good expandability.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell related technology, and more specifically, relates to a rapid measurement system and method for fuel cell impedance spectrum. Background Technology

[0002] Electrochemical impedance spectroscopy (EIS) is a non-invasive method for characterizing the internal state and electrochemical behavior of fuel cells, and is commonly used for fuel cell stack fault diagnosis and health assessment. However, current EIS detection mainly relies on electrochemical workstations, which obtain broadband impedance information of the electrochemical system by "sweeping" a single-frequency sinusoidal signal applied to the fuel cell successively. Although this method can achieve high impedance measurement accuracy, its drawback is the long measurement time, making it difficult to obtain real-time information of the electrochemical system, which severely limits its function for real-time diagnosis and on-site monitoring.

[0003] Toyota's Miral product includes a DC / DC-based module for measuring fuel cell impedance. However, due to the bandwidth limitations of the DC / DC converter, the frequency of the excitation signal generated by the DC / DC converter is often difficult to reach a high value, thus affecting the measurement range of the impedance spectrum. Fortin et al. [P. Fortin, M.R. Gerhardt, ...] Ulleberg, F. Zenith, T. Holm. Multi-sine EIS for early detection of PEMFC failure modes. Frontiers in Energy Research, 2022, 10: 855-985. Using multiple sinusoidal signals as test excitation, a complete EIS with a frequency range from 0.5 Hz to 50 kHz is collected and analyzed within 50 seconds. However, the test time is insufficient to meet the requirements of real-time fault diagnosis.

[0004] Chinese patent CN 109459465 A uses two longest linear shift register sequences (M-sequences) to excite and measure the high-frequency and low-frequency regions of EIS, respectively. This can shorten the injected excitation signal to 16 seconds and ultimately shorten the measurement time to 21 seconds. However, this is still insufficient for the application of EIS technology in real-time fault diagnosis and needs to be further shortened. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a rapid measurement system and method for impedance spectrum of fuel cells, which aims to improve the efficiency of impedance measurement, shorten the impedance spectrum measurement time, and expand the application scenarios of impedance analysis.

[0006] To achieve the above objectives, according to one aspect of the present invention, a rapid measurement system for the impedance spectrum of a fuel cell is provided, comprising: a first electronic load, a second electronic load, a data acquisition unit, and a host computer;

[0007] The first electronic load is connected in series with the fuel cell stack under test to form a main circuit, which is used to operate in constant current mode to control the static operating point of the fuel cell stack under test; the second electronic load is connected in parallel across the two ends of the fuel cell stack under test to form a secondary circuit, which is used to generate the desired current excitation waveform and inject it into the output current of the fuel cell stack under test under the control command corresponding to the multi-frequency excitation signal designed by the host computer; the multi-frequency excitation signal is a wideband discrete range binary sequence signal.

[0008] The data acquisition unit is used to acquire the response voltage of the fuel cell stack under test to the current excitation waveform, and to sample the excitation current generated by the second electronic load; the host computer is also used to generate the electrochemical impedance spectrum of the fuel cell stack under test based on the response voltage and the sampled excitation current.

[0009] Furthermore, the host computer is also used to analyze the noise waveform of the fuel cell stack voltage under the stable state of the system based on the voltage across the fuel cell stack collected by the data acquisition unit under the stable state of the system, and to perform power spectrum analysis on the noise waveform of the stack voltage in order to generate a multi-frequency excitation signal with amplitude that meets the signal-to-noise ratio requirements.

[0010] Furthermore, when the host computer generates the multi-frequency excitation signal, it uses an AR model to perform the power spectrum estimation of the pile voltage noise. The optimal order of the AR model is determined based on the AIC criterion, and the parameters other than the order of the AR model are extracted by the Burg algorithm.

[0011] Furthermore, the optimal order of the AR model is 128.

[0012] Furthermore, the second electronic load operates in list mode. When the host computer controls the second electronic load, it controls the second electronic load through the programmable instrument standard command set according to the designed multi-frequency excitation signal to modulate the excitation current waveform for impedance testing.

[0013] Furthermore, the data acquisition unit includes a voltage divider resistor and a data acquisition card; the voltage divider resistor is connected in parallel across the two ends of the fuel cell stack under test to form a voltage divider circuit, which is used to meet the measurement voltage range of the data acquisition card; the data acquisition card is used to read the voltage across the voltage divider resistor and sample the excitation current generated by the second electronic load;

[0014] The host computer is also used to analyze the voltage across the fuel cell stack under test based on the voltage across the voltage divider resistor, and further subtract the DC component to obtain the response voltage of the current excitation waveform.

[0015] Furthermore, the host computer communicates with the second electronic load via USB to transmit multi-frequency excitation signal control commands; the data acquisition card communicates with the host computer via Ethernet to transmit the voltage across the voltage divider resistor and the excitation current.

[0016] Furthermore, the voltage divider resistor is divided into two parts with a resistance ratio of 10:1; the data acquisition card acquires the voltage across the voltage divider resistor with the smaller resistance value.

[0017] According to another aspect of the present invention, a method for rapid measurement of fuel cell impedance spectrum is provided, wherein the measurement is performed using a rapid fuel cell impedance spectrum measurement system as described above.

[0018] In summary, compared with the prior art, the solutions conceived by this invention have the following main advantages:

[0019] 1. This invention proposes a rapid impedance spectrum measurement system for fuel cells, comprising an excitation current injection section, a data acquisition section, and a host computer. The host computer uses a DIBS signal with excellent peak suppression and flexible amplitude-frequency design capabilities as the test excitation, and a common electronic load as the excitation source. The host computer can control the electronic load to generate the desired current excitation waveform based on the test excitation. The electronic load injects the excitation current into the output current of the electrochemical system under test. The host computer can also read the sampling data from the data acquisition unit and perform a fast Fourier transform on the acquired excitation current and response voltage data to obtain the electrochemical impedance spectrum. This measurement system, by injecting an alternating current for only 8.2 seconds, can acquire wideband impedance information of 0.5–1 kHz from a fuel cell in a single measurement, greatly improving the efficiency of impedance measurement. Combined with its simple hardware structure, it has good prospects for field application. Furthermore, the measurement range of this system can be extended to other electrochemical systems, including lithium batteries and electrolyzers, demonstrating good adaptability and scalability.

[0020] 2. This invention proposes a rapid measurement system for fuel cell impedance spectrum. The excitation signal is designed by the host computer based on the power spectrum estimation of the system noise under steady-state conditions, ensuring sufficient frequency component amplitude to reduce noise interference. At the same time, the overall peak value is limited to maintain the linear characteristics of the tested system and avoid strong nonlinear distortion, thus achieving a relatively accurate fuel cell impedance spectrum in a single test.

[0021] 3. This invention also proposes that the host computer uses an AR model to perform voltage noise power spectrum estimation when generating multi-frequency excitation signals, resulting in low computational complexity. The optimal order of the AR model is determined by the sampling AIC criterion, which balances model complexity and goodness of fit, thus selecting a model that is neither too simple nor too complex. Furthermore, the AIC criterion is relatively simple, unaffected by specific data distributions or sample sizes, and possesses objectivity and consistency. Therefore, this invention uses the AIC criterion to determine the optimal order of the AR model. In addition, parameters other than the order of the AR model are extracted using the Burg algorithm. The Burg algorithm solves the AR model parameters based on a recursive process of the data sequence, avoiding the need to solve the computationally intensive autocorrelation function, and has high frequency resolution, enabling high-precision excitation. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of a rapid impedance spectrum measurement system for fuel cells provided in an embodiment of the present invention;

[0023] Figure 2 This invention provides the fluctuation of the output voltage of a fuel cell stack and the power spectrum estimation for noise. Among them, (a) and (b) are the voltage noise signals when the stack is not started and when it is running at a constant current of 10A, respectively; (c) is the AIC index under different orders; and (d) is the power spectrum obtained by estimating the voltage noise in (b) using the periodogram method and AR models of different orders.

[0024] Figure 3 These are the time-domain and frequency-domain distributions of the low-frequency and high-frequency signals provided in this embodiment of the invention; wherein, (a) is the designed DIBS signal, (b) is the sampled actual current data and the corresponding frequency-domain distribution, and (c) is the sampled actual stack voltage data and the corresponding frequency-domain distribution;

[0025] Figure 4 The present invention provides the calculation results and analysis of impedance spectrum; wherein, (a) and (b) are impedance spectra obtained by repeated measurements when running at constant current of 10A and 8A, respectively, and (c) and (d) are the deviation and root mean square error of repeated measurements when running at constant current of 10A and 8A, respectively.

[0026] Figure 5 This is a diagram illustrating the filtering process for invalid data points in coarse impedance data provided in an embodiment of the present invention.

[0027] Figure 6 Is using Figure 5 The impedance spectrum of the second-order R-CPE equivalent circuit fitting model obtained by the corresponding impedance data processing method;

[0028] Figure 7This is a specific result diagram of a rapid impedance spectrum measurement system for fuel cells provided in an embodiment of the present invention;

[0029] Figure 8 This is a flowchart of the operation of the fast impedance testing system provided in the embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0031] Example 1

[0032] A rapid measurement system for the impedance spectrum of a fuel cell, such as Figure 1 As shown, it includes: a first electronic load, a second electronic load, a data acquisition unit, and a host computer;

[0033] The first electronic load is connected in series with the fuel cell stack under test to form the main circuit, which is used to operate in constant current mode to control the static operating point of the fuel cell stack under test; the second electronic load is connected in parallel across the fuel cell stack under test to form the secondary circuit, which is used to generate the desired current excitation waveform and inject it into the output current of the fuel cell stack under test under the control command corresponding to the multi-frequency excitation signal designed by the host computer; the multi-frequency excitation signal is a wide-band discrete-range binary sequence signal; the fuel cell under test is a proton exchange membrane fuel cell (PEMFC).

[0034] The data acquisition unit is used to acquire the response voltage of the fuel cell stack under test to the current excitation waveform, and to sample the excitation current generated by the second electronic load; the host computer is also used to generate the electrochemical impedance spectrum of the fuel cell under test based on the response voltage and the sampled excitation current.

[0035] In this embodiment, the multi-frequency excitation signal is a wideband discrete-interval binary sequence (DIBS) signal with excellent peak suppression capability and flexible amplitude-frequency design capability.

[0036] As a preferred implementation, the host computer is also used to analyze the noise waveform of the fuel cell stack voltage under stable conditions based on the voltage across the fuel cell stack collected by the data acquisition unit under stable conditions, and to perform power spectrum analysis on the noise waveform of the stack voltage in order to generate a multi-frequency excitation signal with amplitude that meets the signal-to-noise ratio requirements.

[0037] Regarding the multi-frequency excitation signal whose amplitude meets the signal-to-noise ratio (SNR) requirement, it should be noted that this multi-frequency excitation signal contains multiple frequency components, which can significantly improve test efficiency. For proton exchange membrane fuel cells (PEMFCs), the impedance spectrum in the range of 0.5Hz-1000Hz can reflect sufficient impedance information. Therefore, this frequency range of 0.5Hz-1000Hz is selected as the measurement range of electrochemical impedance spectroscopy. Furthermore, since PEMFCs are typical nonlinear time-varying systems, using a smaller perturbation amplitude makes it easier to ensure that the system operates within a linear range during measurement, avoiding strong nonlinear distortion. However, this may lead to a decrease in the signal-to-noise ratio (SNR), making it difficult to distinguish interference from noise. On the other hand, excessively high amplitudes may violate the quasi-linearity requirement of the system and even affect the normal operation of the system under test. Therefore, the excitation signal needs to have appropriate frequency component amplitudes. In this embodiment, the frequency component amplitude is designed to be within 3% of the current amplitude in a steady state.

[0038] As a preferred implementation, the signal can be designed based on voltage noise power spectrum estimation to ensure sufficient frequency component amplitude to reduce noise interference, while limiting the overall peak value to maintain the linearity of the system under test. Voltage noise power spectrum estimation is performed using a 128th-order AR model. The optimal order of the AR model is determined using the AIC criterion, and the Burg algorithm is selected for parameter extraction.

[0039] In other words, the excitation current signal for testing is dynamically generated based on the frequency range required for measurement and the power spectrum estimation of voltage noise, minimizing disturbance to the system while ensuring measurement accuracy. Power spectrum estimation of voltage noise is mainly divided into classical power spectrum estimation and parametric model power spectrum estimation. The periodogram method and the autocorrelation method are two widely used representative methods in classical power spectrum estimation. Parametric model power spectrum estimation mainly includes AR model method, MA model method, and ARMA model method. AR model parameter estimation is based on linear equations, making the calculation relatively simple and direct. In contrast, MA model and ARMA model parameter estimation involve solving nonlinear equations, making the calculation relatively complex. Moreover, according to Wold's theorem, any ARMA model or MA model can be represented by an infinite-order AR model. This means that even if an unsuitable model is chosen in practical applications, a reasonable approximation can still be obtained using a high-order AR model. Therefore, when choosing an AR model for power spectrum estimation of the electrochemical noise of a battery, the first step is to determine the model order, and then solve for the corresponding model parameters. The specific steps are as follows:

[0040] (1) The choice of AR model order has a significant impact on the accuracy of power spectrum estimation. An AR model with too low an order may lead to inaccurate power spectrum estimation and omission of important frequency components; while an AR model with too high an order may introduce spurious spectral peaks, distorting the power spectrum estimation and increasing computational complexity. Methods for determining the order of AR models mainly include the autocorrelation and partial correlation function method, statistical hypothesis testing, and the information criterion method. The AIC (Akaike Information Criterion) method for determining the AR model order can balance the model's complexity and goodness of fit, thus selecting a model that is neither too simple nor too complex. It is relatively simple, unaffected by specific data distributions or sample sizes, and possesses objectivity and consistency. Therefore, preferably, this embodiment uses the AIC criterion to determine the optimal AR model order.

[0041] (2) For parameter extraction of AR model, Burg algorithm is preferred because it solves AR model parameters based on the recursive process of data sequence, without having to solve the computationally intensive autocorrelation function, and has high frequency resolution.

[0042] Furthermore, in order to analyze the fluctuation of the output voltage of the fuel cell stack when no alternating current excitation is injected (operating with constant current), the stack was set to operate with a constant current of 10A, and the stack terminal voltage was sampled using a data acquisition card with a sampling frequency of 2048Hz and a sampling time of 16s. Figure 2 Images (a) and (b) show the sampled voltage noise signals when the fuel cell stack is not started and when it is running at a constant current of 10A, respectively. It can be seen that the amplitude of voltage fluctuations during fuel cell stack operation is several orders of magnitude higher than the background noise of the measuring instrument. Considering that the order of the AR model directly affects the accuracy and computational efficiency of the Burg algorithm in spectral estimation, the Burg algorithm from order 1 to 256 is applied to fit AR models of voltage fluctuations, obtaining AIC indices for different orders, such as... Figure 2 As shown in (c), the decay trend of AIC with increasing order gradually slows down, and AIC tends to stabilize after the order exceeds 150. Periodogram method and AR models of different orders (32, 64, 128, 192) were used to estimate... Figure 2 The power spectrum of voltage noise in (b) is shown in the figure. Figure 2 As shown in (d) of the figure, several peaks are observed in the power spectrum of both the voltage fluctuation and the background noise during constant current operation of the fuel cell stack. These peaks have fundamental frequencies of 15Hz and 50Hz, which are likely noise introduced by electronic loads or other equipment. These frequencies should be avoided when designing the amplitude-frequency distribution of the impedance test excitation signal. Figure 2Figure (d) further shows that for power spectrum estimation of stack operating voltage fluctuations, the AR model method can obtain a smoother curve compared to the periodogram method. This means that a smoother amplitude-frequency distribution can be obtained when designing the test excitation current based on noise power and required signal-to-noise ratio. Since DIBS is only an approximation of the desired amplitude-frequency distribution, the amplitude-frequency of the generated sequence signal will always deviate from the desired value to some extent. A smoother amplitude-frequency distribution design can make the actual amplitude-frequency line of the signal closer to the desired value. Considering the above, this embodiment preferably uses a 128th-order AR model for power spectrum estimation of voltage noise.

[0043] After the excitation current signal is generated, the host computer sends a current control command to the electronic load to inject current. Simultaneously, it activates the current sampling channel of the data acquisition card and synchronizes it with the voltage sampling channel across the previously opened voltage divider resistor. Since the electronic load requires a certain amount of time to respond to the command, the sampling time of the acquisition card can be set slightly longer than the duration of the excitation current to ensure that complete excitation and response signals are sampled. After the test is completed, the host computer determines the start time of the excitation in the sampled data based on the preset excitation signal and truncates the sampled data according to the designed duration of the excitation signal. The next step is to calculate the impedance of the system under test at the corresponding test frequency point based on the current excitation and voltage response signals.

[0044] In one embodiment, the first electronic load is an IT9715 electronic load, the second sampling load is a DL3021 electronic load, and the data acquisition unit is implemented by a data acquisition card and voltage divider resistors. The IT9715 electronic load is connected in series with the fuel cell stack under test to form a main circuit, which is used to operate in constant current mode to control the static operating point of the fuel cell stack under test. The DL3021 electronic load is connected in parallel across the fuel cell stack under test to form a secondary circuit, which is used to generate the desired current excitation waveform and inject it into the output current of the fuel cell stack under test under the control command corresponding to the multi-frequency excitation signal of the host computer. The multi-frequency excitation signal is a wide-band discrete-range binary sequence signal. The voltage divider resistors are connected in parallel across the fuel cell stack under test to form a voltage divider circuit to meet the measurement voltage range of the data acquisition card. The data acquisition card is used to read the voltage across the voltage divider resistors and sample the excitation current generated by the DL3021 electronic load. The host computer is also used to analyze the voltage across the fuel cell stack under test based on the voltage across the voltage divider resistors as the response voltage to the current excitation waveform, and combine it with the excitation current sampled by the data acquisition card to generate the electrochemical impedance spectrum of the fuel cell stack under test.

[0045] As a preferred implementation, the DL3021 electronic load operates in list mode, which allows for a maximum of 512 steps. The current value and duration of each step can be set individually. The host computer, based on the manufacturer's programming manual, uses Standard Commands for Programmable Instruments (SCPI) to control the DL3021 electronic load to execute the current waveform designed by the host computer, thereby modulating the excitation current for impedance testing and injecting it into the output current of the fuel cell stack.

[0046] Furthermore, considering the acquisition range of the data acquisition card, the current magnitude in the DL3021 can be converted for acquisition. The acquisition card is used to acquire the voltage across the resistor with the smaller resistance value, and the response voltage of the fuel cell stack is calculated according to the corresponding ratio. Since the electronic load response command requires a certain amount of time, the sampling time of the acquisition card is set to be slightly longer than the duration of the excitation current to ensure that the complete excitation and response signals can be sampled.

[0047] As a preferred option, the voltage divider resistors are divided into two, with a resistance ratio of 10:1; the data acquisition card acquires the voltage across the voltage divider resistor with the smaller resistance value.

[0048] The output voltage of a fuel cell stack is typically tens of volts, which is greater than the sampling range of the data acquisition card. Two ohmic resistors with a resistance ratio of 10:1 are connected in parallel with the stack to form a voltage divider circuit to meet the measurement voltage range of the acquisition card.

[0049] Preferably, the host computer communicates with the DL3021 electronic load via USB to transmit the excitation signal control commands; the data acquisition card communicates with the host computer via Ethernet (LAN) to transmit the voltage across the voltage divider resistor and the sampled excitation current.

[0050] In one example of this embodiment, the VK701NW data acquisition card is a 4-channel Ethernet high-speed synchronous data acquisition card manufactured by Shenzhen Micro-Precision Technology Co., Ltd. It features 4 channels of true differential input, 24-bit resolution to ensure measurement accuracy, a maximum sampling rate of 100kHz, and a maximum voltage input range of ±10V. Communication with the data acquisition card is based on the TCP protocol. Using the dynamic library functions (.dll) provided by the manufacturer, the input range, sampling channels, sampling time, and sampling frequency of the acquisition card are configured to achieve the corresponding data sampling functions.

[0051] In practical applications, the host computer can be developed using Python in the PySide environment. Its program design includes two main tasks: communicating with the instrument and processing the collected data.

[0052] In one example, the host computer determines the start time of the excitation in the sampled data based on a preset excitation signal, and truncates the sampled data according to the designed duration of the excitation signal. Then, a Fast Fourier Transform is performed on the acquired excitation current and response voltage data to obtain the transformed current FI(w) and the transformed voltage FU(w). The following formula is then used to extract the broadband impedance under the desired harmonic components:

[0053]

[0054] Where n is the desired number of harmonics in the designed broadband signal, FU=F[U(t)], FU=F[I(t)], Z k The impedance test point corresponds to the k-th desired harmonic component. Appropriate impedance data processing methods are then used to improve the robustness of impedance spectrum measurements.

[0055] To verify the feasibility of the impedance testing system and the accuracy of the EIS measurement in this embodiment, a repeated test experiment was designed. Specifically, the PEMFC stack was set to operate under the same steady-state conditions, and its EIS was repeatedly measured multiple times. The dispersion of the measurement results reflected the accuracy of the measurement. For the EOS1000 stack used in the experiment, the two electronic loads were first adjusted so that the main circuit current was 10A and the secondary circuit current was 0.74A. The secondary circuit was set with a DC bias because the electronic loads could not generate negative current; the minimum value of the alternating current excitation must be greater than 0. Subsequently, the electronic loads in the secondary circuit were used to modulate and generate the excitation current for the impedance test. The DIBS signal used in the test was divided into low-frequency and high-frequency segments, with durations of 8s and 0.2s respectively. The designed frequency distribution consisted of 24 frequency points from 0.5 to 1000Hz, distributed proportionally.

[0056] Figure 3 (a) shows the design value of the DIBS signal, which is less than 3% of the steady-state operating current of the fuel cell. Similarly, the same test was performed by adjusting the main circuit current to 8A. Figure 3 Images (b) and (c) show the sampled current and voltage data and their corresponding frequency domain distributions obtained after injecting two DIBS test excitations into the PEMFC stack. Due to the effective bandwidth of the electronic load and the noise introduced during the modulation current process, the actual current excitation is somewhat distorted compared to the design value. However, the frequency analysis results show that the harmonic distribution of the excitation current is roughly consistent with the design value. Furthermore, the frequency components corresponding to the response voltage and excitation current also have high resolution, indicating that the test has a sufficient signal-to-noise ratio.

[0057] Since the test frequency is basically consistent with the design value, the amplitude and phase of the corresponding harmonic components can be directly extracted from the Fourier transform of the sampled current and voltage signals at the design frequency to calculate the impedance spectrum. Under 10A and 8A operating conditions, the measurements were repeated 13 times consecutively, and the results are as follows: Figure 4 As shown in (a) and (b) above, the impedance spectrum of the fuel cell at this operating point can be represented by the average of these 13 tests. The average curve shows that the shape of the impedance spectrum is mainly determined by the frequency points below 260 Hz, while the impedance points at higher frequencies are only slightly different from each other. Figure 4 Figures (c) and (d) visualize the dispersion of repeated impedance spectrum measurements. The left vertical axis represents the deviation of a single measurement point from the average value, while the right vertical axis represents the root mean square error of repeated measurements at each frequency. The figures show that the dispersion of test points is generally greater in the low-frequency region than in the high-frequency region. Of particular note are the significantly higher root mean square errors at several frequency points between 10 and 100 Hz compared to their neighboring frequencies, indicating potential anomalous noise interference at these frequencies.

[0058] Furthermore, under ideal conditions, the impedance spectrum would be the same if the fuel cell operating state is identical. However, maintaining complete stability of the fuel cell's operating state in actual measurements is impossible, and the instruments used for measurement also introduce random noise. Therefore, the impedance data obtained from experimental measurements will inevitably deviate. By keeping the fuel cell operating parameters the same and repeatedly measuring the impedance spectrum, and plotting the impedance data from multiple measurements on the same graph, the dispersion of the test points can visually reflect the interference encountered in the measurement. In practical applications, due to limited testing time, it is not advisable to repeat the test dozens of times; instead, the goal is to obtain sufficiently accurate impedance spectrum information in a single test. Achieving this goal requires appropriate data processing methods. The processing of the original impedance test points includes removing ionized bad points and correcting some effective deviation points. The specific steps are as follows:

[0059] 1) Defect Filtering: The KK test can be approximated using a fitted RC equivalent circuit model, but it is only suitable for handling impedance data with low noise. In actual testing, with shortened test time and constrained test excitation signal amplitude, the measured signal-to-noise ratio often cannot be very high, meaning that the obtained impedance data is mostly coarse. Considering that the ideal impedance spectrum is usually a highly smooth curve, the continuity criterion can be used to identify defect points in the test impedance data. To characterize the continuity between impedance points, a Savitzky-Golay filter is first used to obtain smooth impedance interpolation points Z. smooth (w). The SG filter is a filtering method based on local polynomial least squares fitting, where each interpolation point is formed by the neighboring N... SGThe data points were obtained using second-order polynomial estimation. The real part of the smoothed impedance point is given here; the imaginary part is calculated similarly.

[0060] Z Smooth，re (ω j ) = a re，1 +a re，2 ln(ω j )+a re，3 ln 2 (ω j j = 1, 2, ..., n

[0061] Where n is the number of data points. Choose N. SG =4, the coefficients a of the interpolation polynomial re =[a re,1 a re,2 a re,3 ] T Determined through least squares regression

[0062] a re =(X T X) -1 X T Z re

[0063]

[0064]

[0065] Is with ω j Four adjacent impedance data points, and The discontinuity of a data point is defined as the difference from the smooth interpolation point:

[0066] ε(ω j )=|Z(ω j )-Z smooth (ω j )|

[0067] To avoid filtering out "normal" data points, only one data point with the highest discontinuity is deleted at a time. After deleting a data point, the discontinuity of its neighboring points is recalculated, excluding the deleted point. This process of iteratively deleting the data point with the highest discontinuity continues until the overall discontinuity is reached. If the rate of decrease is less than a set threshold, the free defective pixels can be removed.

[0068]

[0069] In the formula, it represents the number of iterations. Figure 5The process of filtering invalid data points in coarse impedance data is demonstrated, and the continuity of data points gradually increases as bad points are removed.

[0070] 2) Deviation correction is achieved by assigning different weight values ​​to the data points. The KK test can be used to obtain the fit residuals and weighted mean square error for each point:

[0071]

[0072] Weight adjustment is to correct w(ω) j The value of ) makes ε less than the set threshold. First, calculate the suggested adjustment value w for the weights based on the relative "significance" of the residuals from the KK test. s (ω j ):

[0073]

[0074] And through high-pass filtering h q = [-0.25 0.5 -0.25] T To prevent data points that deviate from their intended purpose from affecting nearby normal data points. s (ω j Update the KK test iteratively:

[0075] w it (ω j ) -1 =ζ·(w s (ω j )) -2 +(1-ζ)·(max(w min ,w it-1 (ω j ))) -1

[0076] In the formula, w it (ω j ) represents the frequency ω after the it-th iteration. j The weight value of the impedance point, ζ = 0.5, w min =10 -6 It is the lower limit value to prevent zero from being a divisor.

[0077] Furthermore, because the RC equivalent circuit model's fit to experimental data is unstable, the RC fitting model used in the deviation point correction stage was changed to the distribution of relaxation times (DRT) model. The DRT method treats the electrochemical system as an ohmic resistance connected in series with an infinite number of polarization processes, avoiding uncertainties introduced by prior model assumptions and approximating the impedance model of any electrochemical system. The DRT analysis is based on the following integral formula:

[0078]

[0079] Among them, Z DRT (ω) is the complex impedance calculated by the DRT model at angular frequency ω, R inf It is a series resistance characterizing a process with negligible relaxation time (infinite characteristic frequency), where τ is the relaxation time. The core problem of the DRT method is to obtain the Z... DRT Impedance Z measured by model fitting experiment exp (w), deconvolve to calculate the relaxation time distribution function γ(τ). Solving for γ(τ) is an inverse problem, which can be expressed as a linear combination of the weight parameters and the corresponding basic functions, i.e.:

[0080]

[0081] In the formula, N represents the number of relaxor elements; a larger number results in higher accuracy but also a greater computational burden; x j The weight parameters for the estimated basis functions; φ j (lnτ) is a radial basis function.

[0082] Therefore, solving for γ(τ) can be transformed into minimizing the fitted model Z. DRT (ω) and test data Z exp Error between (w):

[0083]

[0084] Due to the influence of noise in experimental data, directly solving for the loss often results in ill-posed optimization results (underfitting, overfitting, and difficulty in improving accuracy). Therefore, regularization methods are often used to add penalty terms to the equations to smooth noisy data. The EISART software package developed by Li Hangyue uses regularization calculation methods and can automatically select basic functions and regularization parameters based on data type, achieving high-precision DRT model fitting. This invention chooses to use the EISART open-source tool to achieve equivalent EIS model fitting for impedance measurement data. EISART can not only calculate the fitted model for data points but also output confidence references for data points in the 0-1 interval. Measurement confidence references not only reflect the deviation of data points but can also be incorporated into the impedance spectrum feature extraction calculations to improve the accuracy of feature parameter identification.

[0085] Furthermore, the above impedance data processing method was applied to the PEMFC impedance spectrum under steady-state conditions for repeated measurements. The impedance spectrum of the fitted model (2nd order R-CPE) obtained from each set of test data is as follows: Figure 6 As shown. Compared to Figure 4 The impedance spectra of each fitted model at the original test points are quite close to the average value of the test points. If the average value of multiple repeated measurements is regarded as the true impedance of the fuel cell, then with the help of impedance data processing methods, even if some impedance test points are significantly deviated due to noise interference, a relatively accurate impedance spectrum can still be obtained through a single test.

[0086] Example 2

[0087] A rapid method for measuring the impedance spectrum of a fuel cell is provided, which uses a rapid measurement system for the impedance spectrum of a fuel cell as described in Example 1.

[0088] In actual measurement, the following steps can be followed:

[0089] (1) Build an impedance spectroscopy rapid testing system and initialize each component; the rapid impedance spectroscopy measurement system includes components such as a fuel cell stack, IT9715 electronic load, DL3021 electronic load, data acquisition card, host computer, and voltage divider resistors, with the structure as follows: Figure 7 As shown.

[0090] (2) The host computer determines whether the system is in a stable state where impedance testing can be performed by monitoring the voltage of the fuel cell stack in real time, and generates an excitation signal with appropriate amplitude and spectrum distribution based on the power spectrum analysis of the collected voltage waveform.

[0091] (3) The host computer communicates with the DL3021 programmable electronic load via USB, controls the electronic load to generate the desired current excitation waveform, and injects it into the output current of the electrochemical system under test. At the same time, it reads the sampling data in the data acquisition card buffer via Ethernet (LAN) communication. Since the electronic load requires a certain amount of time to respond to the command, the sampling time of the data acquisition card is set to be slightly longer than the duration of the excitation current to ensure that the complete excitation and response signals can be sampled.

[0092] (4) Based on the actual excitation signal generated by the electronic load, determine the start time of the excitation in the sampled data, and truncate the sampled data according to the duration of the excitation signal. Then, perform a fast Fourier transform on the acquired excitation current and response voltage data to obtain the electrochemical impedance spectrum, and use the corresponding impedance data processing method to improve the robustness of the impedance spectrum measurement.

[0093] During testing, the IT9715 electronic load operated in constant current mode to control the static operating point of the fuel cell stack. The fuel cell stack is an air-cooled, self-humidifying type, and the hydrogen required for its operation is supplied from a high-pressure hydrogen cylinder through a pressure reducing valve to approximately 0.5 bar. The host computer was developed using Python in the PySide environment, and its program design includes two main tasks: communicating with the instrument and processing the acquired data.

[0094] Figure 8 The operation flow of the rapid impedance testing system is demonstrated. After the EIS measurement module is enabled in the program, the voltage sampling channel of the acquisition card is started to continuously monitor the voltage of the fuel cell. The stability conditions of the EIS test are determined by estimating the power spectrum of the voltage noise. When the operator manually issues a test request through the graphical user interface (GUI), and the voltage fluctuation is less than the set threshold (determined by the peak value constraint of the test signal and the test signal-to-noise ratio), the module enters the test state. The excitation current signal for the test is dynamically generated according to the frequency range required for the measurement and the power spectrum estimation of the voltage noise, minimizing disturbance to the system while ensuring measurement accuracy.

[0095] In summary, this invention relates to a rapid impedance spectrum measurement system and method for fuel cells. The constructed rapid impedance spectrum testing system consists of an excitation current injection section, a data acquisition section, and a host computer. A wideband discrete binary sequence (DIBS) signal is used as the test excitation. The host computer determines whether the system is in a stable state suitable for impedance testing by real-time monitoring of the fuel cell stack voltage, and generates an excitation signal with an amplitude that meets the signal-to-noise ratio requirements based on power spectrum analysis of the acquired voltage waveform. Then, communication with a programmable electronic load is established via USB, controlling the electronic load to generate the desired current excitation waveform and injecting it into the output current of the electrochemical system under test. Simultaneously, the host computer reads the sampled data from the acquisition card cache via Ethernet (LAN) communication. A fast Fourier transform is performed on the acquired excitation current and response voltage data to obtain the electrochemical impedance spectrum, and corresponding impedance data processing methods are used to improve the robustness of the impedance spectrum measurement. This invention employs the DIBS signal, which boasts excellent peak suppression and flexible amplitude-frequency design capabilities, as the test excitation. Using a common electronic load as the excitation source, and injecting an alternating current lasting only 8.2 seconds, it can acquire a wideband impedance information of 0.5–1 kHz for the battery in a single measurement, significantly improving the efficiency of impedance measurement. Coupled with its simple hardware structure, it has promising prospects for field applications. Furthermore, the measurement range of this system can be extended to other electrochemical systems, including lithium batteries and electrolytic cells, demonstrating good adaptability and scalability.

[0096] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A system for rapid measurement of impedance spectra of a fuel cell, characterized by, The application relates to a fuel cell impedance spectrum measurement system, which comprises a first electronic load, a second electronic load, a data acquisition unit and a host computer. The first electronic load is connected in series with a fuel cell stack to be measured to form a main circuit, which is used to work in a constant current mode to control a static working point of the fuel cell stack to be measured; the second electronic load is connected in parallel across the fuel cell stack to be measured to form a sub-circuit, which is used to generate an expected current excitation waveform under a control instruction corresponding to a multi-frequency excitation signal designed by the host computer and inject the current excitation waveform into an output current of the fuel cell stack to be measured; the multi-frequency excitation signal is a wide-frequency discrete interval binary sequence signal. The data acquisition unit is used to collect a response voltage of the fuel cell stack to the current excitation waveform and sample an excitation current generated by the second electronic load; the host computer is further used to generate an electrochemical impedance spectrum of the fuel cell stack to be measured according to the response voltage and the sampled excitation current. The host computer is configured to perform the following operations to realize fast measurement of the impedance spectrum: step one, signal generation: before the multi-frequency excitation signal is generated, a noise waveform of a voltage across the fuel cell stack to be measured under a stable state of the system is analyzed according to a voltage across the fuel cell stack to be measured collected by the data acquisition unit under the stable state of the system, and a power spectrum analysis is performed on the noise waveform of the voltage across the fuel cell stack to be measured by using an autoregressive (AR) model to generate the multi-frequency excitation signal with each frequency component amplitude satisfying a signal-to-noise ratio requirement; wherein the optimal order of the AR model is determined based on an Akaike information criterion (AIC), and parameters of the AR model other than the order are extracted by using a Burg algorithm; step two, impedance data processing: after the response voltage and the excitation current collected by the data acquisition unit are obtained, an original impedance spectrum is first calculated, and then data post-processing is performed on test points of the original impedance spectrum, the data post-processing includes removing free bad points and correcting part of valid deviating points to obtain a final electrochemical impedance spectrum. The optimal order of the AR model is 128.

2. The system for rapid measurement of impedance spectrum of a fuel cell according to claim 1, wherein The working mode of the second electronic load is a list mode, and the host computer controls the second electronic load by using a programmable instrument standard command set according to the designed multi-frequency excitation signal to modulate an excitation current waveform for impedance test.

3. The system for rapid measurement of impedance spectrum of a fuel cell according to claim 1, wherein The data acquisition unit comprises a voltage dividing resistor and a data acquisition card; the voltage dividing resistor is connected in parallel across the fuel cell stack to be measured to form a voltage dividing circuit, which is used to satisfy a measurement voltage range of the data acquisition card; and the data acquisition card is used to read a voltage across the voltage dividing resistor and sample the excitation current generated by the second electronic load.

4. The system for rapid measurement of impedance spectrum of a fuel cell according to claim 1, wherein The host computer is further used to analyze a voltage across the fuel cell stack to be measured according to the voltage across the voltage dividing resistor and further subtract a direct current component from the voltage across the fuel cell stack to be measured to obtain the response voltage of the current excitation waveform. The host computer communicates with the second electronic load by using a USB to realize transmission of the multi-frequency excitation signal control instruction; and the data acquisition card communicates with the host computer by using an Ethernet to realize transmission of the voltage across the voltage dividing resistor and the excitation current.

5. The system for rapid measurement of impedance spectrum of a fuel cell according to claim 4, wherein ​ 6. The system for rapid measurement of impedance spectrum of a fuel cell according to claim 4, wherein The voltage dividing resistor is divided into two, and the resistance ratio is 10:1; the data acquisition card collects the voltage between the two voltage dividing resistors with smaller resistance.

7. A rapid measurement system of impedance spectroscopy of a fuel cell according to any one of claims 1 to 6, characterized in that, The host computer avoids the peak frequency point in the voltage noise power spectrum in the constant current operation state of the electric pile when designing the amplitude-frequency distribution of the impedance test excitation signal, so that a smoother amplitude-frequency distribution is obtained when designing the test excitation current according to the noise power and the required signal-to-noise ratio.

8. A method for rapid measurement of impedance spectrum of a fuel cell, characterized by, The measurement is performed by using a fuel cell impedance spectrum rapid measurement system according to any one of claims 1 to 7.

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