A fuel cell impedance attribution method based on a physically interpretable impedance model

Abstract

This invention relates to the field of fuel cell technology and discloses a fuel cell impedance attribution method based on a physically interpretable impedance model. The method includes: performing impedance decomposition on the physically interpretable impedance model to obtain multiple sub-impedances of the fuel cell, including ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance; obtaining the frequency corresponding to the minimum value of the imaginary part of each sub-impedance, the inverse of the minimum value of the imaginary part, and the difference between the low-frequency real part value and the high-frequency real part value, as characteristic frequencies, imaginary peak values, and equivalent resistances; plotting the Nyquist plot, Bode plot, resistance ratio of the sub-impedance's equivalent resistance to the total equivalent resistance, and frequency-peak plot reflecting the relationship between the characteristic frequency and the imaginary peak value for each sub-impedance, to determine the contribution of each sub-impedance to the physically interpretable impedance model, thus realizing impedance attribution analysis under the physically interpretable impedance model.

Description

Technical Field

[0001] This invention relates to the field of fuel cell technology, and in particular to a fuel cell impedance attribution method, system, device, and medium based on a physically interpretable impedance model. Background Technology

[0002] Electrochemical impedance spectroscopy (EIS) enables impedance measurement during the operation of proton exchange membrane fuel cells, revealing various losses during operation. Traditional impedance analysis methods are based on equivalent circuit models (ECMs), analyzing the resistance changes at different characteristic frequencies using the resistance values ​​of resistive elements in the circuit, and empirically determining the phenomena that the resistance might correspond to based on the characteristic frequencies. Distribution of relaxation times (DRT) analysis does not require pre-setting the form and order of the equivalent circuit model; however, the decomposition of total impedance still relies on unit circuit structures such as RC parallel circuits, and the relationship between characteristic frequencies and actual physical phenomena occurring in the cell remains constrained by empirical interpretation.

[0003] Therefore, for stable operating devices such as lithium batteries and supercapacitors, electrochemical impedance spectroscopy data analysis methods based on ECM and DRT can obtain effective information. However, when faced with electrochemical systems such as proton exchange membrane fuel cells and electrolyzers, which have complex internal phenomena and multi-scale mass transfer processes coupled and intertwined, the characteristic frequencies corresponding to physical phenomena vary greatly under different operating conditions and structural designs. Judging phenomena based on experience may lead to incorrect judgments of physical phenomena, resulting in judgments with large deviations or even completely wrong conclusions.

[0004] To address the issue of traditional impedance analysis methods' strong reliance on experience, applying physically interpretable impedance models is an effective way to overcome empirical limitations by leveraging their inherent physical meaning. However, current physically interpretable impedance models for fuel cells lack effective methods for connecting with experimental data, and the theoretical foundation for further analyzing the impedance data characteristics of the model is also lacking. They are currently only used for calculating intrinsic parameters, leading to shortcomings in their practical applications. Summary of the Invention

[0005] The purpose of this invention is to provide a fuel cell impedance attribution method, system, device and medium based on a physically interpretable impedance model, which can solve the problem of the shortcomings of the physically interpretable impedance model in practical applications.

[0006] To address the aforementioned technical problems, embodiments of the present invention provide a fuel cell impedance attribution method based on a physically interpretable impedance model, comprising the following steps: Impedance decomposition is performed on the physically interpretable impedance model determined by the mass transfer control equation of the fuel cell to obtain multiple sub-impedances of the fuel cell. These multiple sub-impedances are the ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance of the fuel cell. Obtain the frequency corresponding to the minimum value of the imaginary part of each impedance, the negative of the minimum value of the imaginary part, and the difference between the low-frequency real part value and the high-frequency real part value, and use them as the characteristic frequency, imaginary peak value and equivalent resistance of each impedance in turn. Based on the characteristic frequency, imaginary peak value, and equivalent resistance of each impedance, draw the Nyquist plot, Bode plot, the resistance ratio of the equivalent resistance of the impedance to the total impedance equivalent resistance, and the frequency-peak plot reflecting the relationship between the characteristic frequency and the imaginary peak value for each impedance. Based on the Nyquist plot, Bode plot, resistance percentage plot, and frequency-peak plot of each impedance, determine the contribution of each impedance to the physically interpretable impedance model.

[0007] Furthermore, the ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance are respectively expressed by the following formulas: ; ; ; ; , , ; In the formula, R Ω , Z a , Z c-act , Z c-con-d , Z c-con-c These are, respectively, ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance. d m The thickness of the proton exchange membrane in a fuel cell. k m The equivalent conductivity of the proton exchange membrane is given by [value]. R T For thermal resistance, e The dielectric constant within the electric double layer, d SL The thickness of the double electric layer, ka This is the correction factor for the dielectric constant of the anodic double layer. oh Angular velocity, k c This is the correction factor for the dielectric constant of the cathode double layer. K Λ , K U and K c-d These represent the porous electrode diffusion correction factor, the velocity distribution correction factor, and the convection-diffusion interface correction factor, respectively. l This refers to the membrane water content in the proton exchange membrane. T For operating temperature, f The testing frequency for fuel cells, R Let be the ideal gas constant. F It is Faraday's constant. α The transfer coefficient of the electrochemical reaction, j 0 represents the steady current density.

[0008] Furthermore, when drawing the Nyquist plot of the impedance sub-plots, the Nyquist plot of the ohmic resistance is drawn first, and then the Nyquist plots of the remaining impedance sub-plots are drawn from large to small according to the characteristic frequency. When drawing the Nyquist plot of each of the remaining impedance sub-plots, the real part axis of the currently drawn Nyquist plot is translated according to the equivalent resistance of the impedance sub-plots corresponding to all the previously drawn Nyquist plots.

[0009] Furthermore, the characteristic frequencies of the sub-impedances, from largest to smallest, are ohmic resistance, cathode activation impedance, anode impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance. Each impedance on the Nyquist plot is: ; In the formula, Z a,plot ( f ), Z c-act,plot ( f ), Z c-con-d,plot ( f ), Z c-con-c,plot ( f The following are expressions for the anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance on the Nyquist plot, respectively. R Ω ( f ), Z a ( f ), Z c-act (f ), Z c-con-d ( f )and Z c-con-c ( f The expressions for ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance are respectively. R eq,Za , R eq,Zc-act , R eq,Zc-con-d These are the equivalent resistances of the anode impedance, the cathode activation impedance, and the cathode mass transfer diffusion impedance, respectively.

[0010] Furthermore, the characteristic frequency, imaginary peak value, and equivalent resistance of each impedance sub-impedance are as follows: ; In the formula, f 0,k For impedance k The characteristic frequencies, argmin(·), are used to solve the function Im( Z k The frequency at which the minimum value is obtained f ; ; In the formula, A im,k For impedance k The peak value of the imaginary part, Z k For impedance k The impedance values ​​at different frequencies are functions, and min(·) and Im(·) are functions for calculating the minimum and imaginary parts, respectively. ; In the formula, R eq,k For impedance k The equivalent resistance, Re(·) is a function for calculating the real part of the impedance. f →∞ and f →0 represents frequency f The cases when it approaches infinity and when it approaches 0.

[0011] Furthermore, before performing impedance decomposition on the physically interpretable impedance model determined by the mass transfer control equations based on the fuel cell, the method further includes: Based on the resistance and reactance of the fuel cell obtained from electrochemical impedance spectroscopy, the surface specific impedance of the fuel cell is determined using the following formula: ; In the formula,Z exp Surface impedance, i For imaginary numbers, A ACT This represents the activation area of ​​a single cell within a fuel cell stack. N This refers to the number of individual cells in a fuel cell stack. R exp,stack and X exp,stack These are the fuel cell resistance and reactance, respectively. Using the internal state parameters of the fuel cell as state variables, the impedance values ​​corresponding to the state variables are obtained through a physically interpretable impedance model. The single-objective optimization problem for inverting the internal state parameters of the fuel cell is constructed with the goal of minimizing the difference between the impedance value and the surface specific impedance. The single-objective optimization problem is solved to obtain all the state parameters inside the fuel cell, and the value of each impedance is determined based on the state parameters of the fuel cell.

[0012] Furthermore, the diffusion correction coefficient of the porous electrode K Λ for: ; , ; In the formula, d M and d G These represent the thicknesses of the microporous layer and the gas diffusion layer of the fuel cell, respectively. l M and l G These are the characteristic transport lengths of the microporous layer and the gas diffusion layer, respectively. l M Characteristic length of electrochemical reaction, k s This is the ratio of interlayer diffusion coefficients. n is the correction coefficient for the Bruggeman equation, and tanh(·) is the hyperbolic tangent function; D Let be the diffusion coefficient of oxygen under standard conditions. e M and e G The porosity of the microporous layer and the gas diffusion layer are respectively. s M and s G The liquid water saturation levels of the microporous layer and the gas diffusion layer are respectively. n c This is the oxygen concentration index, reflecting the effect of oxygen concentration on the electrochemical reaction process; The oxygen concentration is for a steady-state reaction. Velocity distribution correction factor K U for: ; , ; In the formula, L GC The length of the gas flow channel of the bipolar plate in the fuel cell. u The inlet velocity of air in the gas flow channel. d * The thickness of the membrane electrode is dimensionless. i M The characteristic phase angle of the membrane electrode; d CG Let be the height of the gas flow path of the bipolar plate in the fuel cell, and arctanh(·) be the inverse function of the hyperbolic tangent function; ; In the formula, sech(·) is the hyperbolic secant function.

[0013] Embodiments of the present invention also provide a fuel cell impedance attribution system based on a physically interpretable impedance model, comprising: The total impedance decomposition module is used to decompose the physically interpretable impedance model determined by the mass transfer control equation of the fuel cell to obtain multiple sub-impedances of the fuel cell. The multiple sub-impedances are the ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance and cathode mass transfer convection impedance of the fuel cell. The feature extraction module is used to obtain the frequency corresponding to the minimum value of the imaginary part of each impedance, the inverse of the minimum value of the imaginary part, and the difference between the low-frequency real part value and the high-frequency real part value, which are used as the characteristic frequency, imaginary peak value and equivalent resistance of each impedance in turn. The characteristic plotting module is used to plot the Nyquist plot, Bode plot, resistance ratio of the equivalent resistance of the sub-impedance to the total impedance equivalent resistance, and frequency-peak plot reflecting the relationship between the characteristic frequency and the imaginary peak value of each sub-impedance based on the characteristic frequency, imaginary peak value, and equivalent resistance of each sub-impedance. The impedance attribution module is used to determine the contribution of each sub-impedance to the physically interpretable impedance model based on the Nyquist plot, Bode plot, resistance percentage plot, and frequency-peak plot of each sub-impedance.

[0014] Embodiments of the present invention also provide a computer device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the above-described fuel cell impedance attribution method based on a physically interpretable impedance model.

[0015] Embodiments of the present invention also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described fuel cell impedance attribution method based on a physically interpretable impedance model.

[0016] The fuel cell impedance attribution method based on a physically interpretable impedance model provided by this invention has at least the following beneficial effects: First, impedance decomposition is performed on the physically interpretable impedance model to obtain multiple sub-impedances of the fuel cell. These sub-impedances correspond one-to-one with five physical phenomena: ohmic loss, anode loss (or anode activation loss, with anode concentration loss ignored), cathode activation loss, cathode mass transfer diffusion loss, and cathode mass transfer convection loss. In other words, the total impedance of the fuel cell is decomposed into sub-impedances with clear physical meanings representing different physical phenomena. Then, each sub-impedance is described by three characteristic quantities: characteristic frequency, imaginary peak value, and equivalent resistance. The characteristic frequency, imaginary peak value, and equivalent resistance of each sub-impedance are plotted, along with Nyquist plots, Bode plots, a resistance ratio plot of the sub-impedance's equivalent resistance to the total impedance's equivalent resistance, and a frequency-peak plot reflecting the relationship between the characteristic frequency and the imaginary peak value. This can show the variation of different sub-impedance characteristic quantities under different conditions (e.g., different operating conditions or different structural parameters), and thus reflect the contribution of different sub-impedances to the total impedance of the fuel cell (the contribution of resistance value and the contribution during dynamic changes). This achieves fuel cell impedance attribution based on the physically interpretable impedance model. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0018] Figure 1 A flowchart illustrating a fuel cell impedance attribution method based on a physically interpretable impedance model provided by this invention. Figure 2 A schematic diagram illustrating the implementation principle of this invention; Figure 3 A calculation flowchart provided for this invention; Figure 4A Bode plot of the imaginary part of the impedance provided by the present invention; Figure 5 A Nyquist plot of impedance breakdown provided by the present invention; Figure 6 This invention provides a histogram of equivalent resistance for partial impedance and a graph showing the contribution ratio of total impedance. Figure 7 This invention provides a frequency-peak diagram that reflects the relationship between the characteristic frequency and the peak value of the imaginary part of the impedance. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0020] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0021] One embodiment of the present invention relates to a fuel cell impedance attribution method based on a physically interpretable impedance model. The specific process of the fuel cell impedance attribution method based on a physically interpretable impedance model in this embodiment can be as follows: Figure 1 As shown, it includes: Step 101: Perform impedance decomposition on the physically interpretable impedance model determined based on the mass transfer control equation of the fuel cell to obtain multiple sub-impedances of the fuel cell. The multiple sub-impedances are the ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance of the fuel cell.

[0022] Specifically, a physically interpretable impedance model of a proton exchange membrane fuel cell is constructed, consisting of multiple sub-impedances. Through physically meaningful impedance decomposition, the total impedance is constructed as the sum of five sub-impedances:

[0023] ; In the formula, Z PIIE The total impedance of the physically interpretable impedance model. R Ω , Z a , Z c-act , Z c-con-d , Z c-con-cThese are, respectively, ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance.

[0024] Ohm resistor R Ω It can be calculated as: ; In the formula, d m The thickness of the proton exchange membrane is expressed in meters (m), and in a specific embodiment, it is taken as 12 μm. k m The equivalent conductivity of the proton exchange membrane, expressed in S / m, is calculated using empirical correlations: ; In the formula, l The membrane water content in the proton exchange membrane is 3.98 in a specific embodiment; T The operating temperature is expressed in K, and in one specific embodiment it is 353.15 K.

[0025] Anode impedance is modeled as the gain and loss of charge within the electric double layer on the electrode surface. The effect of hydrogen concentration on anode impedance is ignored, and the impedance is calculated using physical quantities within the electric double layer. ; In the formula, R T Resistance temperature measurement (RTD), unit is Ω·m 2 ; e is the dielectric constant within the electric double layer, expressed in F / m, and in a specific embodiment, it is taken as 6.95 × 10⁻⁶. -10 F / m; d SL The thickness of the double electric layer is expressed in meters (m), and in this example it is taken as 0.9 nm. k a This is the dielectric constant correction factor for the anodic double layer, which is taken as 57.7 in a specific embodiment; oh The angular velocity of the input current excitation (sine wave), in rad / s, is related to the test frequency as follows: ; In the formula, f The test frequency is in Hz, and in a specific embodiment, it is taken as 0.032 Hz ~ 100 kHz.

[0026] The thermal resistance is only related to the operating conditions of the fuel cell being tested, and is calculated as follows: ; In the formula, Ris the ideal gas constant, with units of J / (mol·K). In a specific embodiment, it is taken as the commonly estimated value of 8.314 J / (mol·K). F is the Faraday constant, with units of C / mol. In this example, the commonly estimated value of 96487 C / mol is used. α The transfer coefficient for the electrochemical reaction is denoted as 0.5 in a specific embodiment; j The steady current density under the tested operating conditions is expressed in A / m. 2 In one specific embodiment, the value is taken as 2.0 A / cm. 2 .

[0027] Cathode activation impedance Z c-act Its form is close to that of the anode impedance, and it is the cathode impedance without considering the mass transfer process: ; In the formula, k c This is the correction factor for the dielectric constant of the cathode double layer, which is taken as 21.6 in a specific embodiment.

[0028] Cathode mass transfer diffusion impedance Z c-con-d The effect of oxygen diffusion and transport in porous electrodes, cathode mass transfer convection resistance Z c-con-c Representing the effect of oxygen convective transport in the cathode gas flow channel, the two partial impedances are calculated as follows: ; In the formula, K Λ , K U and K c-d These represent the porous electrode diffusion correction factor, the velocity distribution correction factor, and the convection-diffusion interface correction factor, respectively.

[0029] Porous electrode diffusion correction factor K Λ The calculation is as follows: ; In the formula, d M and d G These are the thicknesses of the microporous layer and the gas diffusion layer, respectively, in meters (m). In a specific embodiment, these values ​​are 25 μm and 150 μm, respectively. l M and l GThese are the characteristic transport lengths of the microporous layer and the gas diffusion layer, respectively, in meters; l M The characteristic length of the electrochemical reaction is expressed in meters (m). k s This represents the ratio of interlayer diffusion coefficients. n is the correction coefficient for the Bruggeman equation, which is taken as 1.8 in a specific embodiment; tanh(·) is the hyperbolic tangent function.

[0030] The characteristic transport lengths of the microporous layer and the gas diffusion layer are calculated as follows: ; In the formula, D The diffusion coefficient of oxygen under standard conditions is given in meters (m). 2 / s, in a specific embodiment, is taken as 1.46 × 10 -5 m 2 / s; e M and e G The porosities of the microporous layer and the gas diffusion layer are respectively 0.4 and 0.8 in a specific embodiment; s M and s G The values ​​are the liquid water saturation of the microporous layer and the gas diffusion layer, respectively, and in a specific embodiment, they are 0.20 and 0.69.

[0031] Electrochemical reaction characteristic length l M Ratio of interlayer diffusion coefficient k s The calculation method is as follows: ; In the formula, n c The oxygen concentration index reflects the effect of oxygen concentration on the electrochemical reaction process, and in a specific embodiment, it is set to 1.8. The oxygen concentration for a steady-state reaction is expressed in mol / m³. 3 This typically refers to the oxygen concentration at the catalyst reaction site under stable operating conditions; in a specific embodiment, it is taken as 0.76 mol / m³. 3 .

[0032] Velocity distribution correction factor K U The calculation is as follows: ; In the formula, L GCThe length of the gas flow channel of the fuel cell bipolar plate is expressed in meters (m), and in a specific embodiment, it is taken as 0.48 m. u The inlet velocity of air in the gas flow channel is expressed in m / s, and in a specific embodiment, it is taken as 13.6 m / s. d * The thickness of the membrane electrode is dimensionless. i M This represents the characteristic phase angle of the membrane electrode.

[0033] Dimensionless thickness of membrane electrode d * and the characteristic phase angle of the membrane electrode i M The calculation formula is: ; ; In the formula, d CG is the height of the gas flow channel of the fuel cell bipolar plate, in meters, and is taken as 0.2 mm in a specific embodiment; arctanh(·) is the inverse function of the hyperbolic tangent function.

[0034] Convection-diffusion interface correction factor K c-d The calculation is as follows: ; In the formula, sech(·) is the hyperbolic secant function, and the other variables are related to... K U and K Λ The variables remain consistent throughout the calculation process.

[0035] In some embodiments, to calculate the impedance breakdown, it is necessary to first determine the state parameters inside the fuel cell, i.e., the parameter values ​​of the complete physically interpretable impedance model. Methods for obtaining these parameter values ​​may include pre-determining them or obtaining them from experimental data through fitting methods. If pre-determined, no special processing is required; commonly used or empirical values ​​can be substituted into step 101 to obtain the impedance information.

[0036] If obtained from experimental data through fitting methods, the surface impedance of the fuel cell is determined based on the resistance and reactance obtained from the electrochemical impedance spectroscopy test. The internal state parameters of the fuel cell are used as state variables. The impedance values ​​corresponding to the state variables are obtained through a physically interpretable impedance model. With the goal of minimizing the difference between the impedance value and the surface impedance, a single-objective optimization problem for the inversion of the internal state parameters of the fuel cell is constructed. The single-objective optimization problem is solved to obtain all the internal state parameters of the fuel cell.

[0037] In practical implementation, the first step is to process the experimental impedance data. The experimental surface impedance of the fuel cell stack is calculated using the stack resistance and reactance obtained experimentally. ; In the formula, Z exp The required experimental surface impedance, in Ω·m. 2 ; i The imaginary number is the unit. A ACT The activated area of ​​a single cell within a fuel cell stack, expressed in m². 2 ; N This represents the number of individual cells in the tested fuel cell stack. When the test object is a single cell, N = 1; R exp,stack and X exp,stack These are the stack resistance and reactance values ​​from the electrochemical impedance spectroscopy information of the measured fuel cell stack, respectively, in Ω.

[0038] To supplement the parameters of the physically interpretable impedance model from experimental data, an optimization scheme for solving the state variables needs to be constructed. The optimization scheme includes an optimization problem and an optimization algorithm. The mathematical expression of the single-objective optimization problem for solving the state variables can be written as:

[0039] ; In the formula, x state For state variables in a physically interpretable impedance model; F Here is the specific expression for the objective function, where Z exp,k For the first k The specific impedance of each experimental surface, in Ω·m 2 ; Z exp,k The corresponding operating frequency is f k The unit is Hz.

[0040] State variables x state Options include: ; In the formula, l The content of membrane water; k a and k c These are the correction factors for the dielectric constants of the anode and cathode double layers, respectively; s Mand s G The liquid water saturation levels are respectively those of the microporous layer and the gas diffusion layer; The oxygen concentration for a steady-state reaction is expressed in mol / m³. 3 ; u The inlet velocity of air in the gas flow channel is expressed in m / s.

[0041] In addition, the state parameters can also be any combination of the following physical quantities or a combination of these physical quantities in their dimensionless form: ; In the formula, x state,k State variables x state The k One component; the definitions of all other physical quantities are consistent with the definitions of physical quantities in the first step.

[0042] In one example, the objective function of the above application F (·) can be selected to describe the average distance between two sets of vectors with the same dimension. Minimizing the objective function is usually chosen as the solution objective of the optimization problem. For example, it can be selected as the correlation coefficient. R 2 Root mean square error (RMSE) and weighted quadratic error x 2 Or the functional form related to the mean absolute percentage error (MAPE):

[0043] ; In the formula, cov( A , B ) is the function to calculate the covariance of two sets of vectors A and B, var(·) is the function to calculate the variance of the vectors, and |·| is the function to calculate the absolute value.

[0044] Here Z exp The vector is formed by calculating the surface impedance and resistance at each frequency point in the experiment. Z PIIE This is a vector formed by substituting the impedance value calculated in the physically interpretable impedance model using each frequency point in the experiment as input. The dimension of both vectors is the total number of frequency points in the experiment. N f ; Z exp,k For the first k The specific impedance of each experimental surface, in Ω·m 2 The corresponding operating frequency is f k The unit is Hz; mFor example, choosing the dimension of the state variable. When used as a state variable, the dimensions of the state variable m = 7; Re(·) and Im(·) are functions for calculating the real and imaginary parts of the impedance, respectively.

[0045] The optimization methods are single-objective optimization methods, including least squares method, conjugate gradient method, simulated annealing algorithm, genetic algorithm and particle swarm optimization algorithm.

[0046] Step 102: Obtain the frequency corresponding to the minimum value of the imaginary part of each impedance, the negative of the minimum value of the imaginary part, and the difference between the low-frequency real part value and the high-frequency real part value, and use them as the characteristic frequency, imaginary peak value and equivalent resistance of each impedance in turn.

[0047] Specifically, a method for extracting impedance characteristics based on partial impedances is constructed. After solving the state variables, all parameters within the impedance model can be interpreted as known. Based on this, a method for extracting partial impedance characteristics is constructed to achieve characteristic analysis of partial impedances. The characteristics constructed in this embodiment include: characteristic frequency. f 0. Peak value of the imaginary part A im and equivalent resistance R eq .

[0048] The peak value of the imaginary part is taken as the negative of the minimum value of the imaginary part of the impedance: ; In the formula, A im,k For impedance k The peak value of the imaginary part; Z k For impedance k The impedance values ​​at different frequencies are functions; min(·) and Im(·) are functions for calculating the minimum and imaginary parts, respectively.

[0049] The characteristic frequency is defined as the frequency at which the imaginary part of the impedance reaches its minimum value, and the calculation formula is: ; In the formula, f 0,k For impedance k The characteristic frequency; argmin(·) is the function that calculates the independent variable when the function within the parentheses reaches its minimum value, used here to solve the function Im( Z k The frequency at which the minimum value is obtained f .

[0050] The equivalent resistance is used to analyze the proportion of individual impedances to the total impedance, and its calculation formula is: ; In the formula, R eq,k For impedance k The equivalent resistance; Re(·) is a function for calculating the real part of the impedance; f →∞ and f →0 represents frequency f The cases when it approaches infinity and when it approaches 0.

[0051] Step 103: Based on the characteristic frequency, imaginary peak value, and equivalent resistance of each impedance, draw the Nyquist plot, Bode plot, the resistance ratio of the equivalent resistance of the impedance to the total impedance equivalent resistance, and the frequency-peak plot reflecting the relationship between the characteristic frequency and the imaginary peak value for each impedance.

[0052] Specifically, for each impedance sub-impedance, a Bode plot is drawn with the frequency of the fuel cell on the x-axis and the imaginary part of the impedance sub-axis on the y-axis. Next, regarding the Nyquist plot, the Nyquist plot of the ohmic resistance is drawn first, and then the Nyquist plots of the remaining impedance sub-impedances are drawn from largest to smallest according to the characteristic frequency. When drawing the Nyquist plot of each of the remaining impedance sub-impedances, the real part axis of the currently drawn Nyquist plot is shifted according to the equivalent resistance of the impedance sub-impedances corresponding to all the previously drawn Nyquist plots. Finally, a graph showing the ratio of the equivalent resistance of the impedance sub-impedances to the equivalent resistance of the total impedance and a frequency-peak graph reflecting the relationship between the characteristic frequency and the peak value of the imaginary part are drawn.

[0053] This step provides a method for creating charts describing the characteristics of partial impedances. The charts include Nyquist plots, Bode plots, resistance percentage plots reflecting the equivalent resistance, and frequency-peak plots reflecting the relationship between characteristic frequencies and the imaginary part peak value. The Bode plot used for analysis is an imaginary Bode plot with frequency on the x-axis and the imaginary part of the impedance on the y-axis. This is achieved by substituting multiple frequency points into the partial impedance expression and then applying the result using the function Im( Z k The imaginary part is obtained for plotting. The Nyquist plot representing the impedance characteristics differs from traditional methods. First, the characteristic frequencies of the obtained impedances need to be sorted in descending order. The characteristic frequency of the ohmic impedance can be considered as +∞. Ohmic impedances are plotted first, followed by those in descending order of characteristic frequency. When plotting each impedance, the equivalent resistance of all previous impedances needs to be added to shift the real part axis of the Nyquist plot. The resistance ratio reflecting the equivalent resistance is obtained by calculating the ratio of the equivalent resistance of the impedances to the equivalent resistance of the total impedance. Due to testing conditions, the extreme values ​​of the total experimental impedance, where the frequency approaches ∞ and 0, are difficult to obtain. Therefore, the extreme values ​​are calculated using impedance calculations. Z PIIEThe equivalent resistance of the total impedance is obtained by obtaining the characteristic frequency and the imaginary peak value. The frequency-peak plot, which reflects the relationship between the characteristic frequency and the imaginary peak value, is plotted by using the calculated characteristic frequency as the horizontal axis and the imaginary peak value as the vertical axis.

[0054] Among them, the characteristic frequencies of all impedance components, from largest to smallest, are typically: ohmic resistance, cathode activation impedance, anode impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance, i.e. R Ω > Z c-act > Z a > Z c-con-d > Z c-con-c Taking this magnitude relationship as an example, the impedance calculation for each component when plotted on a Nyquist plot is as follows:

[0055] ; In the formula, Z a,plot ( f ), Z c-act,plot ( f ), Z c-con-d,plot ( f ), Z c-con-c,plot ( f The following are expressions for the anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance on the Nyquist plot, respectively. R Ω ( f ), Z a ( f ), Z c-act ( f ), Z c-con-d ( f )and Z c-con-c ( f The expressions for ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance are respectively. R eq,Za , R eq,Zc-act , R eq,Zc-con-d These are the equivalent resistances of the anode impedance, the cathode activation impedance, and the cathode mass transfer diffusion impedance, respectively.

[0056] In this embodiment, impedance analysis based on a physically interpretable impedance model is achieved through physically meaningful impedance decomposition. This allows for quantitative analysis of the internal physical processes of the fuel cell stack, building upon the state variables obtained through the physically interpretable impedance model. By decomposing the total impedance of the fuel cell into five single-peak impedances, impedances corresponding one-to-one with five physical phenomena—ohmic loss, anode loss (or anode activation loss, with anode concentration loss ignored), cathode activation loss, cathode mass transfer diffusion loss, and cathode mass transfer convection loss—are formed to describe the fuel cell impedance. Furthermore, three characteristic quantities—characteristic frequency, imaginary peak value, and equivalent resistance—are constructed within the framework of the physically interpretable impedance model to describe the impedances, forming a plotting scheme to represent the contribution of the impedances to the total impedance. This impedance attribution method transfers physical concepts widely used in impedance analysis based on equivalent circuit models to impedance analysis within the framework of physically interpretable impedance models. It overcomes the shortcomings of equivalent circuit model-based analysis methods, which are highly empirical and may contain far-fetched interpretations of phenomena. Simultaneously, it overcomes the limitations of difficulty in connecting physically interpretable impedance models with experimental data and the scarcity of means for conducting phenomenological analysis. By combining the low comprehension barrier of equivalent circuit models with the endogenous physical interpretability of physically interpretable impedance models, it achieves experimental impedance analysis that is both easy to understand and highly physically interpretable. This embodiment can provide a transferable theoretical basis and technical guidance for the analysis of electrochemical impedance spectroscopy data and the application of physically interpretable impedance models in most electrochemical systems.

[0057] To further understand the fuel cell impedance attribution method based on a physically interpretable impedance model of the present invention, Figure 2 A schematic diagram illustrating the implementation principle is provided, demonstrating the function and characteristics of this impedance attribution method. In practical implementation, it can be used... Figure 3 The calculation process.

[0058] In one embodiment, Figure 4 to Figure 7 A graph describing the characteristic quantities of partial impedance obtained by the fuel cell impedance attribution method based on a physically interpretable impedance model of the present invention is shown, wherein the impedance model parameters are supplemented in advance. The input model parameters include: proton exchange membrane, microporous layer, gas diffusion layer, and gas channel heights of 12 μm, 25 μm, 150 μm, and 0.2 mm, respectively; gas channel length of 0.48 m; porosities of the microporous layer and gas diffusion layer of 0.4 and 0.8, respectively; operating temperature of 353.15 K; and steady-state operating current density of 2.0 A / cm³. 2 The diffusion coefficient of oxygen under standard conditions is taken as 1.46 × 10⁻⁶. -5 m 2 / s; the dielectric constant within the electric double layer is 6.95 × 10⁻⁶. -10F / m; double layer thickness is taken as 0.9 nm; ideal gas constant is taken as the commonly estimated value of 8.314 J / (mol·K); Faraday constant is taken as the commonly estimated value of 96487 C / mol; electrochemical reaction transfer coefficient is taken as 0.5; correction factor for the Bruggeman equation and oxygen concentration exponent are both taken as 1.8; input frequency is 0.032 Hz ~ 100 kHz. Pre-defined supplementary parameters (state variables) are: membrane water content is taken as 3.98; dielectric constant correction factors for the anode and cathode double layers are taken as 57.7 and 21.6, respectively; liquid water saturation in the microporous layer and gas diffusion layer are taken as 0.20 and 0.69, respectively; steady-state reaction oxygen concentration is taken as 0.76 mol / m. 3 The inlet velocity of air in the gas flow channel is taken as 13.6 m / s.

[0059] Figure 4 The Bode plot of the imaginary part of the impedance calculated in this embodiment is shown in detail. Figure 5 The Nyquist plot of the partial impedance calculated in this embodiment is shown in detail. Figure 6 The diagram specifically illustrates the calculated equivalent resistance histogram and contribution ratio graph of the partial impedances obtained in this embodiment. Figure 7 The frequency-peak diagram showing the relationship between the characteristic frequency and the peak value of the imaginary part calculated in this embodiment is specifically illustrated.

[0060] This method can effectively analyze electrochemical impedance spectroscopy data of fuel cells, obtain characteristic quantities of partial impedance corresponding to physical phenomena in the fuel cell, and thus achieve quantitative analysis of the physical process. This method can provide guidance for the state observation and extraction of internal information during operation of various fuel cells and further extended to other electrochemical systems.

[0061] The steps of the various methods described above are only for clarity. In practice, they can be combined into one step or some steps can be split into multiple steps. As long as they include the same logical relationship, they are all within the protection scope of this invention. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the protection scope of this invention.

[0062] Another embodiment of the present invention relates to a fuel cell impedance attribution system based on a physically interpretable impedance model. The implementation details of this embodiment's fuel cell impedance attribution system based on a physically interpretable impedance model are described below. The following details are provided for ease of understanding and are not essential for implementing this solution. This embodiment's fuel cell impedance attribution system based on a physically interpretable impedance model includes: The total impedance decomposition module is used to decompose the physically interpretable impedance model determined by the mass transfer control equation of the fuel cell to obtain multiple sub-impedances of the fuel cell. The multiple sub-impedances are the ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance and cathode mass transfer convection impedance of the fuel cell. The feature extraction module is used to obtain the frequency corresponding to the minimum value of the imaginary part of each impedance, the inverse of the minimum value of the imaginary part, and the difference between the low-frequency real part value and the high-frequency real part value, which are used as the characteristic frequency, imaginary peak value and equivalent resistance of each impedance in turn. The characteristic plotting module is used to plot the Nyquist plot, Bode plot, resistance ratio of the equivalent resistance of the sub-impedance to the total impedance equivalent resistance, and frequency-peak plot reflecting the relationship between the characteristic frequency and the imaginary peak value of each sub-impedance based on the characteristic frequency, imaginary peak value, and equivalent resistance of each sub-impedance. The impedance attribution module is used to determine the contribution of each sub-impedance to the physically interpretable impedance model based on the Nyquist plot, Bode plot, resistance percentage plot, and frequency-peak plot of each sub-impedance.

[0063] It is not difficult to see that this embodiment is a system embodiment corresponding to the above method embodiments, and this embodiment can be implemented in conjunction with the above method embodiments. The relevant technical details and technical effects mentioned in the above embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above embodiments.

[0064] It is worth mentioning that all modules involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this invention, this embodiment does not introduce units that are not closely related to solving the technical problem proposed by this invention; however, this does not mean that other units are absent from this embodiment.

[0065] Another embodiment of the present invention relates to a computer device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the fuel cell impedance attribution method based on the physically interpretable impedance model in the above embodiments.

[0066] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0067] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0068] Another embodiment of the present invention relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the method embodiments described above.

[0069] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0070] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of the present invention.

Claims

1. A fuel cell impedance attribution method based on a physically interpretable impedance model, characterized in that, The method includes: Impedance decomposition is performed on the physically interpretable impedance model determined by the mass transfer control equation of the fuel cell to obtain multiple sub-impedances of the fuel cell. These multiple sub-impedances are the ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance of the fuel cell. Obtain the frequency corresponding to the minimum value of the imaginary part of each impedance, the negative of the minimum value of the imaginary part, and the difference between the low-frequency real part value and the high-frequency real part value, and use them as the characteristic frequency, imaginary peak value and equivalent resistance of each impedance in turn. Based on the characteristic frequency, imaginary peak value, and equivalent resistance of each impedance, draw the Nyquist plot, Bode plot, the resistance ratio of the equivalent resistance of the impedance to the total impedance equivalent resistance, and the frequency-peak plot reflecting the relationship between the characteristic frequency and the imaginary peak value for each impedance. Based on the Nyquist plot, Bode plot, resistance percentage plot, and frequency-peak plot of each impedance, determine the contribution of each impedance to the physically interpretable impedance model.

2. The fuel cell impedance attribution method based on a physically interpretable impedance model according to claim 1, characterized in that, The ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance are expressed by the following formulas: ； ； ； ； ， ， ； In the formula, R Ω , Z a , Z c-act , Z c-con-d , Z c-con-c These are, respectively, ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance. δ m The thickness of the proton exchange membrane in a fuel cell. κ m The equivalent conductivity of the proton exchange membrane is given by [value]. R T For thermal resistance, ε The dielectric constant within the electric double layer, δ SL The thickness of the double electric layer, k a This is the correction factor for the dielectric constant of the anodic double layer. ω Angular velocity, k c This is the correction factor for the dielectric constant of the cathode double layer. K Λ , K U and K c-d These represent the porous electrode diffusion correction factor, the velocity distribution correction factor, and the convection-diffusion interface correction factor, respectively. λ This refers to the membrane water content in the proton exchange membrane. T For operating temperature, f For fuel cell testing frequency, R Let be the ideal gas constant. F It is Faraday's constant. α The transfer coefficient of the electrochemical reaction, j 0 represents the steady current density.

3. The fuel cell impedance attribution method based on a physically interpretable impedance model according to claim 2, characterized in that, When drawing the Nyquist plot of the impedance sub-plots, the Nyquist plot of the ohmic resistance is drawn first, and then the Nyquist plots of the remaining impedance sub-plots are drawn from large to small according to the characteristic frequency. When drawing the Nyquist plot of each of the remaining impedance sub-plots, the real part axis of the currently drawn Nyquist plot is translated according to the equivalent resistance of the impedance sub-plots corresponding to all the previously drawn Nyquist plots.

4. The fuel cell impedance attribution method based on a physically interpretable impedance model according to claim 3, characterized in that, The characteristic frequencies of the sub-impedances, from largest to smallest, are ohmic resistance, cathode activation impedance, anode impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance. Each impedance on the Nyquist plot is: ； In the formula, Z a,plot ( f ), Z c-act,plot ( f ), Z c-con-d,plot ( f ), Z c-con-c,plot ( f The following are expressions for the anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance on the Nyquist plot, respectively. R Ω ( f ), Z a ( f ), Z c-act ( f ), Z c-con-d ( f )and Z c-con-c ( f The expressions for ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance, and cathode mass transfer convection impedance are respectively. R eq,Za , R eq,Zc-act , R eq,Zc-con-d These are the equivalent resistances of the anode impedance, the cathode activation impedance, and the cathode mass transfer diffusion impedance, respectively.

5. The fuel cell impedance attribution method based on a physically interpretable impedance model according to claim 1, characterized in that, The characteristic frequency, imaginary peak value, and equivalent resistance of each impedance are as follows: ； In the formula, f 0,k For impedance k The characteristic frequencies, argmin(·), are used to solve the function Im( Z k The frequency at which the minimum value is obtained f ; ； In the formula, A im,k For impedance k The peak value of the imaginary part, Z k For impedance k The impedance values ​​at different frequencies are functions, and min(·) and Im(·) are functions for calculating the minimum and imaginary parts, respectively. ； In the formula, R eq,k For impedance k The equivalent resistance, Re(·) is a function for calculating the real part of the impedance. f →∞ and f →0 represents frequency f The cases when it approaches infinity and when it approaches 0.

6. The fuel cell impedance attribution method based on a physically interpretable impedance model according to claim 1, characterized in that, Before performing impedance decomposition on the physically interpretable impedance model determined by the mass transfer control equations based on the fuel cell, the method further includes: Based on the resistance and reactance of the fuel cell obtained from electrochemical impedance spectroscopy, the surface specific impedance of the fuel cell is determined using the following formula: ； In the formula, Z exp Surface impedance, i For imaginary numbers, A ACT This represents the activation area of ​​a single cell within a fuel cell stack. N This refers to the number of individual cells in a fuel cell stack. R exp,stack and X exp,stack These are the fuel cell resistance and reactance, respectively. Using the internal state parameters of the fuel cell as state variables, the impedance values ​​corresponding to the state variables are obtained through a physically interpretable impedance model. The single-objective optimization problem for inverting the internal state parameters of the fuel cell is constructed with the goal of minimizing the difference between the impedance value and the surface specific impedance. The single-objective optimization problem is solved to obtain all the state parameters inside the fuel cell, and the value of each impedance is determined based on the state parameters of the fuel cell.

7. The fuel cell impedance attribution method based on a physically interpretable impedance model according to claim 2, characterized in that, The diffusion correction coefficient of the porous electrode K Λ for: ； ， ； In the formula, δ M and δ G These represent the thicknesses of the microporous layer and the gas diffusion layer of the fuel cell, respectively. λ M and λ G These are the characteristic transport lengths of the microporous layer and the gas diffusion layer, respectively. l M Characteristic length of electrochemical reaction, k s This is the ratio of interlayer diffusion coefficients. n is the correction coefficient for the Bruggeman equation, and tanh(·) is the hyperbolic tangent function; D Let be the diffusion coefficient of oxygen under standard conditions. ε M and ε G The porosity of the microporous layer and the gas diffusion layer are respectively. s M and s G The liquid water saturation levels of the microporous layer and the gas diffusion layer are respectively. n c This is the oxygen concentration index, reflecting the effect of oxygen concentration on the electrochemical reaction process; The oxygen concentration is for a steady-state reaction. Velocity distribution correction factor K U for: ； ， ； In the formula, L GC The length of the gas flow channel of the bipolar plate in the fuel cell. u The inlet velocity of air in the gas flow channel. δ * The thickness of the membrane electrode is dimensionless. θ M The characteristic phase angle of the membrane electrode; δ CG Let be the height of the gas flow path of the bipolar plate in the fuel cell, and arctanh(·) be the inverse function of the hyperbolic tangent function; ； In the formula, sech(·) is the hyperbolic secant function.

8. A fuel cell impedance attribution system based on a physically interpretable impedance model, characterized in that, The system includes: The total impedance decomposition module is used to decompose the physically interpretable impedance model determined by the mass transfer control equation of the fuel cell to obtain multiple sub-impedances of the fuel cell. The multiple sub-impedances are the ohmic resistance, anode impedance, cathode activation impedance, cathode mass transfer diffusion impedance and cathode mass transfer convection impedance of the fuel cell. The feature extraction module is used to obtain the frequency corresponding to the minimum value of the imaginary part of each impedance, the inverse of the minimum value of the imaginary part, and the difference between the low-frequency real part value and the high-frequency real part value, which are used as the characteristic frequency, imaginary peak value and equivalent resistance of each impedance in turn. The characteristic plotting module is used to plot the Nyquist plot, Bode plot, resistance ratio of the equivalent resistance of the sub-impedance to the total impedance equivalent resistance, and frequency-peak plot reflecting the relationship between the characteristic frequency and the imaginary peak value of each sub-impedance based on the characteristic frequency, imaginary peak value, and equivalent resistance of each sub-impedance. The impedance attribution module is used to determine the contribution of each sub-impedance to the physically interpretable impedance model based on the Nyquist plot, Bode plot, resistance percentage plot, and frequency-peak plot of each sub-impedance.

9. A computer device, characterized in that, include: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the fuel cell impedance attribution method based on a physically interpretable impedance model as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the fuel cell impedance attribution method based on a physically interpretable impedance model as described in any one of claims 1 to 7.

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