Method for constructing fuel cell impedance spectrum analysis model based on electrochemical mechanism

Abstract

The present invention discloses a method for constructing a fuel cell impedance spectrum analysis model based on an electrochemical mechanism. The model includes four parts: solving the oxygen transport within the cathode; solving the activation overpotential and current density of the cathode; solving the transient response inside the PEMFC to obtain the output voltage of the proton exchange membrane fuel cell; and solving the electrochemical impedance spectrum. The modeling method proposed in the present invention can accurately reflect the reaction mechanism and battery performance of the fuel cell, and then interpret the electrochemical impedance spectrum data of the proton exchange membrane fuel cell through a mechanism model. The input parameters of the model cover multiple operating condition parameters and battery material design parameters in battery operation, making the model results more accurate and able to accurately reflect key parameters such as the activation performance and mass transfer efficiency inside the proton exchange membrane fuel cell, so as to achieve the simulation and interpretation of the electrochemical impedance spectrum of the proton exchange membrane fuel cell under different operating conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of electrochemical testing, and in particular relates to a method for constructing a quantitative calculation model of electrochemical impedance spectroscopy in a proton exchange membrane fuel cell. Background Art

[0002] Proton exchange membrane fuel cells (PEMFCs) are a key component of the new energy sector. With continuous technological advancements, PEMFCs have achieved significant improvements in multiple key performance indicators, gradually meeting diverse application needs. This type of power cell has achieved significant improvements in lifespan, energy density, safety, and affordability, demonstrating broad market potential in applications such as new energy vehicles.

[0003] In the development of PEMFCs, investigating cell activation performance and mass transfer efficiency is crucial. Improving activation performance reduces the energy required for the reaction, thereby increasing the cell's power output efficiency. Improving mass transfer efficiency ensures efficient flow of reactants and products within the cell, helping to maintain high power output and prevent performance degradation. However, practical research on these evaluations has limitations, including high experimental costs, difficulty in fully simulating the operating environment in real applications, and the lack of quantitative persuasiveness of existing analytical methods.

[0004] Electrochemical impedance spectroscopy (EIS) is an important non-destructive testing technology used to analyze the physical and chemical processes within PEMFC, including mass, momentum, energy and charge transfer. This technology is commonly used for factory inspection, fault diagnosis and internal state analysis of PEMFC during operation. EIS data is analyzed through an equivalent circuit model. Although it has the advantages of wide application, simple operation and strong applicability, it is considered uncertain, subjective and intangible because it compares the internal structure of the battery to related circuit elements. Based on the impedance physics model, PEMFC can be regarded as a multi-physical and chemical process. This makes the quantification of indicators such as the activation performance and mass transfer efficiency of PEMFC more physically meaningful, making up for the biggest shortcoming of the equivalent circuit method. The PEMFC electrochemical impedance spectroscopy analysis and calculation method based on the electrochemical mechanism model proposed in the present invention is mainly used for the quantitative analysis of the electrochemical impedance spectrum of fuel cells, and provides a method for designing relevant parameters of electrochemical impedance spectroscopy analysis of PEMFC. Summary of the Invention

[0005] To further address the limitations of PEMFC electrochemical impedance spectroscopy (EIS) data analysis, this paper aims to provide a method for constructing a fuel cell impedance spectroscopy analysis model based on electrochemical mechanisms, enabling EIS analysis and calculation for different cells and operating conditions. To ensure computational accuracy, the model is constructed using a quasi-two-dimensional approach. This model considers two dimensions, parallel to the flow path and perpendicular to the membrane electrode. This approach maintains a certain level of computational efficiency while maintaining a certain level of accuracy, and is widely used in PEMFC modeling.

[0006] A method for constructing a fuel cell impedance spectrum analysis model based on an electrochemical mechanism, wherein the steps of the model construction are as follows:

[0007] S1: Construct the oxygen transport control equations in the cathode flow channel and diffusion layer of the fuel cell, give the initial conditions and relevant boundary conditions of the relevant model, and solve the distribution of oxygen concentration on the cathode side.

[0008] S2: Based on the reaction rate equation and electrochemical conservation equation, solve the activation overpotential and current density of the fuel cell cathode.

[0009] S3: By inputting relevant frequency, amplitude, phase and current density into the electrochemical impedance spectroscopy analysis model, the transient response inside the proton exchange membrane fuel cell is solved, and the output voltage of the proton exchange membrane fuel cell is obtained.

[0010] S4: The frequency, amplitude, and phase of the response voltage are obtained through Fourier transform, and the electrochemical impedance spectrum of the fuel cell is solved by combining the complex impedance solution method and the complex number operation method.

[0011] Then specifically:

[0012] Solving the oxygen transport in the cathode flow channel and the oxygen transport in the cathode diffusion layer in step S1;

[0013] Solving the activation overpotential and current density of the fuel cell cathode in step S2;

[0014] Solving the voltage response of the initial conditions and transient iterations of the proton exchange membrane fuel cell transient calculation in step S3;

[0015] Solving the electrochemical impedance spectrum of the fuel cell in step S4.

[0016] The characteristics and beneficial effects of the present invention are: based on an in-depth analysis of the internal mechanism of proton exchange membrane fuel cells, a new method for constructing a fuel cell impedance spectrum analysis model based on electrochemical mechanism is provided. This method combines the electrochemical reaction mechanism of PEMFC and the AC characteristics of proton exchange membrane, while also being able to accurately depict the activation reaction and mass transfer phenomena inside the battery, and giving practical physical meaning to the quantitative analysis of electrochemical impedance. The main innovation of the present invention is that it provides an intuitive explanation of EIS data based on physical and electrochemical principles, rather than relying solely on the conventional equivalent circuit model. The new model covers a number of operating parameters and battery material design parameters, and can effectively predict the impact of these core parameters on the performance of the electrolytic cell. It can significantly improve the efficiency of fuel cell design and optimization, avoiding a large amount of experimental testing costs and time consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is the polarization curve of the PEMFC electrochemical mechanism model.

[0018] Figure 2 This is the amplitude Bode diagram of the PEMFC impedance calculated based on the electrochemical mechanism model analysis.

[0019] Figure 3 This is the Bode diagram of the PEMFC capacitive reactance characteristics obtained based on analysis and calculation of the electrochemical mechanism model. DETAILED DESCRIPTION

[0020] The following further illustrates the method steps of the present invention with reference to the accompanying drawings and through specific calculation examples. It should be noted that this calculation example is a narrative description for explaining the modeling steps, and is not restrictive, and does not limit the scope of protection of the present invention.

[0021] The method for constructing a fuel cell impedance spectrum analysis model based on the electrochemical mechanism is as follows:

[0022] S1: Construct the oxygen transport control equations in the cathode flow channel and diffusion layer of the fuel cell, give the initial conditions and relevant boundary conditions of the relevant model, and solve the distribution of oxygen concentration on the cathode side.

[0023] S2: Based on the reaction rate equation and electrochemical conservation equation, solve the activation overpotential and current density of the fuel cell cathode.

[0024] S3: By inputting relevant frequency, amplitude, phase and current density into the electrochemical impedance spectroscopy analysis model, the transient response inside the proton exchange membrane fuel cell is solved, and the output voltage of the proton exchange membrane fuel cell is obtained.

[0025] S4: The frequency, amplitude, and phase of the response voltage are obtained through Fourier transform, and the electrochemical impedance spectrum of the fuel cell is solved by combining the complex impedance solution method and the complex number operation method.

[0026] The step S1 is to solve the cathode oxygen concentration distribution, specifically including:

[0027] 1.1 Solving the oxygen transport in the cathode flow channel

[0028]

[0029] The oxygen concentration at the inlet at any time is only related to the operating conditions:

[0030]

[0031] Where v0 is the air flow rate, which depends on the stoichiometric ratio λ:

[0032]

[0033] is the oxygen concentration at the flow channel inlet, is the percentage of oxygen volume in the intake air, and the value in the atmosphere is 0.21;

[0034]

[0035] 1.2 Solving the oxygen transport in the cathode diffusion layer

[0036]

[0037] c(t,0)=c h (7)

[0038]

[0039] Effective oxygen diffusion coefficient Determined by the Bragmann relation:

[0040]

[0041] The solution for the activation overpotential and current density of the fuel cell cathode in step S2 specifically includes:

[0042] 2.1 Solving the cathode activation overpotential

[0043]

[0044] where ∈ is the dimensionless Newman penetration depth;

[0045]

[0046] γ is the solution of the following equation:

[0047]

[0048] 2.2 Solving the current density of proton exchange membrane fuel cells

[0049] This step is mainly used to solve the non-Faraday current formed by the double-layer capacitance, and the battery current is calculated by the following formula:

[0050]

[0051] Solving the transient voltage response of the proton exchange membrane fuel cell in step S3 specifically includes:

[0052] 3.1 Solving the initial conditions for transient calculations

[0053] Solve equations (1)-(14) in S2 and S3 simultaneously, combine the specific operating conditions and multiple geometric parameters of the stack (see Table 1), ignore the time term, and obtain J when the proton exchange membrane fuel cell reaches steady state. cell ,η, Related distribution parameters;

[0054] 3.2 Perform transient iterative solution

[0055] Obtaining the relationship between the perturbation and response of current and voltage requires electrochemical impedance spectroscopy data, and then obtaining a transient solution based on the steady-state solution. First, the differential equations (1), (5), and (14) are discretized to obtain the operating conditions when the battery is stable, and then the impedance of the battery is measured based on the premise of stable battery operation. The electrochemical impedance spectroscopy analysis model uses a quasi-two-dimensional method as the calculation domain, dividing n nodes in the direction parallel to the flow channel and k nodes in the direction perpendicular to the membrane electrode.

[0056] The oxygen transport in the diffusion layer is solved using the implicit format of formula (5), and formulas (1) and (14) are solved using the explicit format. The discrete form of formula (1) is as follows:

[0057]

[0058] The first term represents the time term, the second term represents the diffusion of gas along the flow channel, and the third term represents the gas entering the GDL from the flow channel.

[0059] The discretization method of formula (14) is:

[0060]

[0061] Formula (5) is discretized as follows:

[0062]

[0063] In the model, the current\voltage disturbance is given to obtain the voltage\current response. The relationship between current and voltage is obtained by formula (18). For a given J cell , the formula is used to solve E cell ,vice versa:

[0064] E cell =E oc -η-R ω ·J cell (18)

[0065] E oc is the open circuit voltage of PEMFC, and its calculation formula adopts the formula commonly used in the industry:

[0066]

[0067] R ω is the ohmic resistance of the proton exchange membrane fuel cell, reflecting the impedance value of the membrane resistance and the diffusion layer resistance:

[0068]

[0069] where l m and l d are the thicknesses of the proton exchange membrane and the diffusion layer, respectively; κ and σ correspond to their electrical conductivities, respectively.

[0070] Solving the electrochemical impedance spectrum of the fuel cell in step S4 is specifically solving the electrochemical impedance spectrum.

[0071] For functions that change periodically over time, the Fourier series expansion is used to represent them:

[0072]

[0073] The solution method of electrochemical impedance spectroscopy is similar to that of the experiment. After reaching steady state, Equation (21) will be subjected to a very small sinusoidal current perturbation formula (22). At this time, the voltage will also produce a perturbation of the same frequency. At this time, the potential signal and current signal are expressed as follows:

[0074] J(t)=ΔJ·cos(ωt) (22)

[0075] V(t)=ΔV·cos(ωt+φ) (23)

[0076] For linear sinusoidal input and output signals, the form of n = 1 is used to express them, such as (22) and (23). Through Fourier complex expression, the time domain signal can be converted to the frequency domain signal for plotting. For the signal represented by the cosine wave, the real part of its potential signal can be expressed as:

[0077]

[0078] The phase angle of its potential signal can be expressed as:

[0079]

[0080] The impedance can be calculated based on the complex ratio of the output and input signals, expressed mathematically as:

[0081]

[0082] The real and imaginary parts of the impedance correspond to the real and imaginary values ​​of the corresponding complex numbers.

[0083] By inputting alternating currents of different frequencies into the electrochemical impedance spectroscopy analysis model, responses at different frequencies are obtained, and then the impedances at different frequencies are obtained and represented on the Nyquist plot and Bode plot, and then the electrochemical impedance spectroscopy data are fitted and interpreted.

[0084] The geometric parameters and operating conditions for PEMFC modeling in this embodiment are shown in Table 1:

[0085] Table 1 Model geometric parameters and operating conditions

[0086]

[0087] Specific implementation examples

[0088] 1. The steady-state conditions are obtained by calculating the following equations simultaneously:

[0089]

[0090] E cell =E oc -η-R ω ·J cell (18)

[0091] J cell =J r (30)

[0092] Steady-state equations (28), (29), and (30) are all obtained by ignoring the time term in the transient equations. The specific calculation method is as follows: first, based on the given operating conditions (oxygen concentration at the inlet, battery temperature, pressure, current density, etc.), combined with the general calculation method for oxygen diffusion coefficient in the field, the oxygen concentration distribution of the battery is calculated by formulas (28) and (29), and then the oxygen concentration c in the catalyst layer is obtained. t Then, combine formulas (10), (12), and (13) to calculate the overpotential η, and finally combine formulas (18) and (30) to obtain the operating voltage of the battery.

[0093] To form the polarization curve, the current density J cell Range setting 0 to 20000A / m 2 In the following description of this embodiment, J cell =10000A / m 2 For example, the average oxygen concentration in the catalytic layer is 6.689 mol / m 2 , the battery voltage is 0.5203V.

[0094] 2. Solve battery transient changes

[0095] Obtaining electrochemical impedance spectroscopy data requires understanding the relationship between the perturbation and response of current and voltage. This model requires obtaining a transient solution based on the steady-state solution. Solving the transient process requires discretizing differential equations (1), (5), and (14). The significance of solving the steady-state solution in the above section is to obtain the operating conditions when the battery is stable, and then to be able to measure the battery impedance based on the premise of stable battery operation. This model uses a quasi-two-dimensional method as the calculation domain of the model, that is, dividing n nodes in the direction parallel to the flow channel and k nodes in the direction perpendicular to the membrane electrode.

[0096] After the steady-state solution is completed, the current needs to be input into the model in the form of a sine wave, and the iterative solution is divided into the following 5 steps. To form the electrochemical impedance spectroscopy, the current vibration frequency is set to 1Hz-2000Hz, and the amplitude will be 0.02A / cm 2 , take the AC current input with a frequency of 100 Hz and an initial phase of 0 as an example:

[0097] (1) Calculate the oxygen concentration in the flow channel at the next moment

[0098] According to the conditions at the current moment, combined with equation (15), the oxygen concentration of each node in the flow channel at the next moment is calculated. The boundary conditions are:

[0099]

[0100] (2) Calculate the oxygen transport in the GDL perpendicular to the membrane at the next moment

[0101] The oxygen concentration in the flow channel obtained in the previous step is the concentration at the interface between the GDL and the flow channel, that is, the oxygen concentration on the GDL side, which is used as the boundary condition. Solve equation (17)

[0102]

[0103] After the equation is discretized, the boundary conditions between the CL layer and the GDL layer are:

[0104]

[0105] The method for solving equation (17) is the Thomas algorithm, which is widely used in solving linear equations. For the Faraday current generated by the reaction at the next moment in equation (31), It cannot be solved alone and needs to be solved by combining step (3).

[0106] (3) Calculate the battery's output voltage, current density, and various losses at the next moment

[0107] The activation overpotential at the next moment is obtained by formula (11):

[0108]

[0109] The current density generated by the redox reaction at the next moment The oxygen concentration distribution in the GDL layer in step (2) can be obtained by combining formulas (10), (12):

[0110]

[0111] Finally, according to formula (18), the voltage variation relationship is obtained. When the amplitude is 200A / m 2 When an AC current with a frequency of 100 Hz and an initial phase of 0 is input, the output voltage amplitude is 0.00501 V and the phase difference is 0.1709 (radians).

[0112] At this time, the frequency domain representation of the voltage is obtained by combining the following Fourier transform related formula:

[0113] The real part of its voltage signal can be expressed as:

[0114]

[0115] The phase angle of its voltage signal can be expressed as:

[0116]

[0117] Then the impedance is solved by the following formula:

[0118]

[0119] The real and imaginary parts of the impedance correspond to the real and imaginary values ​​of the corresponding complex numbers.

[0120] The current and voltage under different frequency excitation are solved according to formulas (26) and (27) to obtain the impedance at that frequency, and then plotted as a Bode plot or Nyquist plot, thus completing the electrochemical impedance spectrum simulation of the model under that working condition.

[0121] The above process calculates Jcell =1.0A·cm -2 The output voltage of the fuel cell when . The current density I is calculated in the range of 0 to 2.5 A·cm -2 When the corresponding fuel cell output voltage is , the fuel cell polarization curve is formed, and the performance of PEMFC under different working conditions can be simulated by using this model. Figure 1 The model polarization curve plot describes the fuel cell's performance under different operating conditions. This curve shows how the cell output voltage changes with increasing current density, providing important information about the fuel cell's efficiency. This information is not available in the equivalent circuit model.

[0122] Furthermore, by using the transient model and discretely solving the equation, the voltage response of the fuel cell under current excitation of different frequencies under certain working conditions can be obtained, and then the electrochemical impedance spectrum of the fuel cell can be obtained.

[0123] In J cell =10000A / m 2 In the example, the average oxygen concentration in the catalyst layer is 6.690 mol / m 3 , the battery voltage is 0.5203V. The oxygen concentration at the inlet is 8.838mol / m 3 In contrast, the mass transfer performance of oxygen in the membrane electrode and the flow channel is better, but the voltage drops more. Observing the internal output parameters of the model, its activation overpotential reaches 0.4642V, which indicates that the activation performance of the battery is not good. This phenomenon is reflected in Figure 3 In the imaginary capacitive reactance diagram, the peak in the low-frequency region (1Hz-10Hz) is smaller, while the peak in the high-frequency region (100Hz-1000Hz) is larger. Figure 2 The figure shows a Bode plot of the impedance amplitude of a PEMFC. The amplitude plot shows a decreasing trend with increasing frequency. This indicates the capacitive effect within the cell. At low frequencies, the electrochemical capacitor can accumulate more charge, providing greater resistance to the AC signal, resulting in a higher amplitude. As the frequency increases, the capacitor has less time to charge and discharge, and its impedance effect weakens, causing the amplitude to decrease.

[0124] Electrochemical mechanism models can directly link features in EIS spectra to key fuel cell parameters such as activation performance and mass transfer efficiency, and interpret them based on the model's physical foundations. This approach avoids the subjectivity and abstraction that can be introduced by equivalent circuit methods when fitting components, thus providing a new, more objective and physically interpretable approach to the quantitative analysis of electrochemical impedance spectroscopy.

[0125] This model can be used to analyze and interpret electrochemical impedance spectroscopy (EIS), thereby exploring the electrical, thermal, and mass transport within fuel cells, and is useful for rapid fuel cell testing, fault diagnosis, and other related practices. The model's input parameters encompass various PEM fuel cell operating parameters (such as temperature and pressure), as well as cell material design parameters (such as PEM physical properties and porous electrode physical properties). This effectively simulates the impact of these core parameters on electrolytic cell performance, thus avoiding the significant economic and time costs of experimental testing. This model provides supportive interpretation of EIS data and improves the efficiency of fuel cell design and optimization.

Claims

1. A method for constructing a fuel cell impedance spectrum analysis model based on an electrochemical mechanism, characterized by: The steps to build the model are as follows: S1: Construct the oxygen transport control equations in the fuel cell cathode flow channel and diffusion layer, provide the initial conditions and relevant boundary conditions of the relevant model, and solve the distribution of oxygen concentration on the cathode side; S2: Based on the reaction rate equation and electrochemical conservation equation, solve the activation overpotential and current density of the fuel cell cathode; S3: Input frequency, amplitude, phase, and current density into the electrochemical impedance spectroscopy analysis model to solve the transient response inside the proton exchange membrane fuel cell and obtain the output voltage of the proton exchange membrane fuel cell; S4: The frequency, amplitude, and phase of the response voltage are obtained through Fourier transform, and the electrochemical impedance spectrum of the fuel cell is solved by combining the complex impedance solution method and the complex number operation method.

2. The method for constructing a fuel cell impedance spectrum analysis model based on an electrochemical mechanism according to claim 1, characterized in that: Solving the cathode side oxygen concentration distribution in S1 specifically includes: (1) Solving the oxygen transport in the cathode flow channel where c h is the oxygen concentration in the flow channel. The oxygen concentration at the inlet at any time is only related to the operating conditions: Where v0 is the air flow rate, which depends on the stoichiometric ratio λ: is the oxygen concentration at the flow channel inlet, is the percentage of oxygen volume in the intake air, and the value in the atmosphere is 0.21; (2) Solving the oxygen transport in the cathode diffusion layer c(t,0)=c h (7) Effective oxygen diffusion coefficient Determined by the Bragg-mann relation, ε is the porosity of the material.

3. The method for constructing a fuel cell impedance spectrum analysis model based on an electrochemical mechanism according to claim 1, characterized in that: The solution for the activation overpotential and current density of the fuel cell cathode in S2 specifically includes: (1) Solve the activation overpotential of the cathode Among them, c t is the oxygen concentration in the catalyst layer, which is obtained from S1, and ∈ is the dimensionless Newman penetration depth: γ is the solution of the following equation: (2) Solving the current density of proton exchange membrane fuel cells The battery current density is calculated from the following formula: J r is the Faraday current density generated by the reaction, C dl is the double layer capacitance of the battery, and η is the activation overpotential of the battery.

4. The method for constructing a fuel cell impedance spectrum analysis model based on an electrochemical mechanism according to claim 1, characterized in that: Solving the transient voltage response of the proton exchange membrane fuel cell in S3 specifically includes: (1) Solving the initial conditions for transient calculations By solving equations (1)-(14) together, combined with specific operating conditions and multiple geometric parameters of the stack, and ignoring the time term, we can obtain the equation when the proton exchange membrane fuel cell reaches steady state: distribution parameters, (2) Perform transient iterative solution To obtain the relationship between the disturbance and response of current and voltage, it is necessary to obtain the electrochemical impedance spectroscopy data, and then obtain the transient solution based on the steady-state solution. First, the differential equations (1), (5), and (14) are discretized to obtain the working conditions when the battery is stable. Then, the impedance of the battery is measured based on the premise of stable operation of the battery. The electrochemical impedance spectroscopy analysis model uses a quasi-two-dimensional method as the calculation domain, dividing n nodes in the direction parallel to the flow channel and k nodes in the direction perpendicular to the membrane electrode. The oxygen transport in the diffusion layer is solved using the implicit format of formula (5), and formulas (1) and (14) are solved using the explicit format. The discrete form of formula (1) is as follows: The first term represents the time term, the second term represents the diffusion of gas along the flow channel, and the third term represents the gas entering the GDL from the flow channel. is the effective diffusion coefficient of oxygen, v0 is the flow velocity at the flow channel inlet, The discretization method of formula (14) is: Formula (5) is discretized as follows: In the model, the current\voltage disturbance is given to obtain the voltage\current response. The relationship between current and voltage is obtained by formula (18). For a given J cell , the formula is used to solve E cell ,vice versa: E cell JE oc -η-R ω ·J cell (18) E oc is the open circuit voltage of PEMFC, and its calculation formula adopts the formula commonly used in the industry: R ω is the ohmic resistance of the proton exchange membrane fuel cell, reflecting the impedance value of the membrane resistance and the diffusion layer resistance: where l m and l d are the thicknesses of the proton exchange membrane and the diffusion layer, respectively; κ and σ correspond to their electrical conductivities, respectively.

5. The method for constructing a fuel cell impedance spectrum analysis model based on an electrochemical mechanism according to claim 1, characterized in that: Solve the electrochemical impedance spectrum of the fuel cell in S4, specifically: Electrochemical impedance spectroscopy solution For functions that change periodically over time, the Fourier series expansion is used to represent them: After reaching steady state, a very small sinusoidal current perturbation (equation (22)) will be applied to Equation (21). At this time, the voltage will also produce a perturbation of the same frequency. At this time, the potential signal and current signal are expressed as follows: J(t)=ΔJ·cos(ωt) (22) V(t)=ΔV·cos(ωt+φ) (23) For the input and output signals of linear sinusoidal waves, according to the form of expression when n=1, such as (24) and (25), the time domain signal can be converted to the frequency domain signal for plotting through Fourier complex expression. For the signal represented by the cosine wave, the real part of its potential signal can be expressed as: The phase angle of its potential signal can be expressed as: The impedance can be calculated based on the complex ratio of the output and input signals, expressed mathematically as: The real and imaginary parts of the impedance correspond to the real and imaginary values ​​of the corresponding complex numbers, By inputting alternating currents of different frequencies into the electrochemical impedance spectroscopy analysis model, responses at different frequencies are obtained, and then the impedances at different frequencies are obtained and represented on the Nyquist plot and Bode plot, and then the electrochemical impedance spectroscopy data are fitted and interpreted.

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