Method for estimating state of charge of flow battery based on electrochemical impedance spectroscopy

Abstract

The invention discloses a flow battery state-of-charge estimation method based on an electrochemical impedance spectrum, and belongs to the technical field of flow batteries. According to the method, a flow battery mechanism model and an electrochemical impedance spectrum model considering an electrochemical reaction process are established, electrochemical impedance spectrums under different SOCs are measured, and the models are utilized to carry out fitting analysis on impedance spectrum data; impedance characteristic parameters such as ohmic impedance, charge transfer impedance, diffusion resistance, diffusion time constant, constant phase angle element constant and diffusion coefficient are extracted; by calculating the Pearson's correlation coefficient between the SOC and each impedance characteristic parameter, the characteristic parameter with strong correlation with the SOC is screened out, and the mapping relation between the SOC and the impedance characteristic parameter is established, so that the accurate estimation of the SOC of the flow battery is realized. According to the method, the physical model of the electrochemical process in the battery is combined, the method has the advantages of high physical significance, high real-time performance, wide applicability and the like, the SOC estimation precision and reliability are improved, and the method is suitable for flow battery systems under different working conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of flow batteries, and particularly relates to a method for estimating the state of charge (SOC) of a flow battery based on electrochemical impedance spectroscopy (EIS). Background Art

[0002] With the rapid development of renewable energy, flow batteries have received extensive attention as an efficient energy storage technology. Flow batteries are considered a highly potential energy storage system due to their advantages such as low cost, high safety, and environmental friendliness. However, the complex electrochemical reactions and non-linear characteristics inside flow batteries make it difficult to accurately estimate the state of charge (SOC) of the battery. SOC is the ratio of the battery capacity at time t of the nth cycle to the maximum battery capacity during the nth cycle, expressed as:

[0003] SOC = Q n,t / Q n

[0004] In the formula, Q n,t is the battery capacity at time t of the nth cycle, and Q n is the maximum battery capacity during the nth cycle.

[0005] Traditional SOC estimation methods such as Coulomb counting method, open circuit voltage method, etc. have problems such as cumulative measurement errors and inability to perform real-time online monitoring. Electrochemical impedance spectroscopy (EIS) is an electrochemical measurement method with a small-amplitude sinusoidal wave potential or current as the perturbation signal, which does not damage the internal state structure of the battery and has characteristics such as in-situ non-destructive. At present, the EIS measurement results are often fitted and analyzed using an equivalent circuit model, and equivalent circuit elements are used to represent each electrochemical step occurring in the battery, which can be used for battery state estimation measurement. However, the impedance values obtained by fitting cannot be associated with the actual physical parameters in the electrochemical steps, and there is a lack of a direct analytical formula.

[0006] Therefore, there is an urgent need for a method for estimating the state of charge of a zinc-iron flow battery based on EIS to achieve accurate estimation of the SOC of the flow battery. Summary of the Invention

[0007] The purpose of the present invention is to overcome the defects in the prior art and provide a method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy. By establishing a mechanism and impedance spectrum model considering the electrochemical reaction process, and using the proposed model to perform fitting analysis on the EIS results to propose a functional relationship between the model parameters and SOC, accurate estimation of the battery SOC is achieved.

[0008] The specific technical solution adopted by the present invention is as follows:

[0009] The present invention provides a method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy, specifically as follows:

[0010] S1. Establish a mechanism model of the flow battery considering the electrochemical reaction process;

[0011] S2. Based on the results of S1, establish an electrochemical impedance spectroscopy model of the flow battery;

[0012] S3. Measure the electrochemical impedance spectroscopy of the flow battery under different states of charge;

[0013] S4. For the electrochemical impedance spectroscopy measured in S3, use the electrochemical impedance spectroscopy model described in S2 for fitting analysis to extract impedance characteristic parameters;

[0014] S5. Based on the results of S4, by calculating the Pearson correlation coefficient between the state of charge and each impedance characteristic parameter, screen out the characteristic parameters with strong correlation with the state of charge, establish the mapping relationship between the state of charge and the impedance characteristic parameters, and complete the estimation of the state of charge.

[0015] Preferably, in S1, the mechanism model of the flow battery includes:

[0016] The Faraday impedance Z caused by the Faraday current: F :

[0017]

[0018] In the formula, both f and g are functions of the interfacial potential V and the active substance concentration c, j is the imaginary number, and ω is the frequency;

[0019] The charge transfer impedance R t :

[0020]

[0021] The diffusion impedance Z D :

[0022]

[0023] The double-layer impedance Zc caused by the charging current:

[0024]

[0025] In the formula, C dl is the interfacial capacitance;

[0026] The ohmic impedance R caused by the proton transfer resistance in the membrane, the electrolyte solution resistance, the current collector resistance, and the contact resistance between different battery components ohm .

[0027] Preferably, in S2, the electrochemical impedance spectroscopy model includes:

[0028] The ohmic impedance R that is independent of frequency, with a constant real part and a zero imaginary part ohm and the charge transfer impedance R t ;

[0029] The constant phase element Z CPE :

[0030]

[0031] where α is a dimensionless dispersion index with a value range of 0 - 1; Q is a constant phase element constant that comprehensively reflects electrode characteristics, interfacial behavior, and reaction kinetics; j is the imaginary unit; and ω is the frequency.

[0032] The diffusion impedance Z D :

[0033]

[0034] where R w is defined as the resistance of the active material diffusion process and is the diffusion resistance; T is the time constant for the diffusion of the active material in a medium of finite length.

[0035] Preferably, the S3 is specifically as follows:

[0036] S31. Place the liquid flow battery storage tank in a constant temperature bath and adjust the flow rate and temperature required for the liquid flow battery test;

[0037] S32. Charge and discharge the liquid flow battery to the specified state of charge according to actual requirements;

[0038] S33. Stop charging and discharging, and continue to circulate the electrolyte for 1 minute using a circulation pump to bring the liquid flow battery to steady-state conditions;

[0039] S34. Use an excitation signal voltage with an amplitude of 10 mV and select an electrochemical impedance spectrum in the frequency range of 0.1 Hz to 1000 Hz to measure the impedance spectrum for the specified state of charge; continue charging and discharging to the next specified state of charge;

[0040] S35. Repeat S31 - S34 until all states of charge are measured;

[0041] S36. Export the electrochemical impedance spectrum data for different states of charge for subsequent analysis.

[0042] Preferably, the impedance characteristic parameters are obtained through an electrochemical impedance spectrum model, including the ohmic impedance R ohm , the charge transfer impedance R t , the diffusion resistance R w , the diffusion time constant T, the constant phase element constant Q, and the dispersion coefficient α.

[0043] Preferably, in step S4, fitting analysis is performed from the Nyquist plot using the least squares principle.

[0044] Preferably, in step S5, when the absolute value of the Pearson correlation coefficient R between the state of charge and the impedance characteristic parameter is > 0.9, it is considered that the impedance characteristic parameter is a characteristic parameter with a strong correlation with the state of charge; furthermore, using the selected characteristic parameters, a mapping relationship between the state of charge and the impedance characteristic parameter is established to complete the state of charge estimation.

[0045] Furthermore, the mapping relationship is expressed as:

[0046] SOC = ax + b

[0047] In the formula, SOC is the state of charge; a is the proportionality coefficient in the mapping relationship, representing the influence degree of the change of the impedance characteristic parameter x on SOC; b is the constant offset in the mapping relationship, representing the reference value of SOC when the impedance characteristic parameter x is zero; x is the impedance characteristic parameter.

[0048] Preferably, the flow battery includes a vanadium redox flow battery, a zinc-iron flow battery, and a zinc-bromine flow battery.

[0049] The present invention has the following beneficial effects compared with the prior art:

[0050] 1) The present invention innovatively combines the positive and negative electrode reaction mechanisms of the flow battery to establish a physical-based electrochemical impedance model, which can accurately describe the charge transfer, diffusion process, and double-layer effect inside the battery. Compared with the traditional equivalent circuit model, the proposed model of the present invention has stronger physical significance and can better reflect the actual working state of the battery.

[0051] 2) Through the electrochemical impedance spectroscopy technology, the present invention can obtain the information of the electrochemical reaction and mass transfer process inside the battery in real time and non-destructively. Combining with the electrochemical impedance model of the flow battery, the accuracy and real-time performance of SOC estimation are significantly improved. Compared with the traditional SOC estimation methods relying on voltage, current, and temperature, the present invention can more accurately reflect the actual state of the battery, especially in the case of electrolyte concentration change and complex electrode reactions.

[0052] 3) The method of the present invention is applicable to various flow battery systems, including vanadium redox flow batteries, zinc-based flow batteries, iron-based flow batteries, organic flow batteries, lead-acid flow batteries, etc. By adjusting the model parameters and characteristic parameter extraction methods, it can easily adapt to different battery systems, with wide applicability and scalability. This generality makes the present invention have stronger generality and promotion value in energy storage systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a framework diagram of a method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy provided by an embodiment of the present invention;

[0054] Figure 2 It is a schematic diagram of the electrochemical impedance model of the flow battery in the present invention. Specific Embodiments

[0055] To more clearly elaborate the objectives, technical paths, and their advantages of the present invention, the following will be described in detail in combination with the accompanying drawings and specific embodiments. It should be clear that the description of the embodiments here only covers some application scenarios of the present invention, rather than all embodiments. Therefore, without departing from the spirit and scope of the present invention, other embodiments derived by those skilled in the art without creative efforts shall fall within the protection scope of the present invention.

[0056] As Figure 1 shown, it is a method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy provided by the present invention. The estimation method mainly includes the following steps:

[0057] Step S1: Establish a mechanism model of the flow battery considering the electrochemical reaction process.

[0058] As a relatively preferred embodiment of the present invention, in this step, the mechanism model of the flow battery includes the Faraday impedance Z F , the charge transfer impedance R t , the diffusion impedance Z D , the double-layer impedance Z c , and the ohmic impedance R ohm . Specifically as follows:

[0059] During the charge and discharge process of the flow battery, considering the Faraday current and the charging current caused by the double layer at the electrode interface. Among them, the Faraday impedance Z F caused by the Faraday current is expressed as:

[0060]

[0061] In the formula, f is a function of the interfacial potential V and the concentration c of the active substance, V is the interfacial potential, c is the concentration of the active substance, j is an imaginary number, ω is the frequency, and g is a function of the interfacial potential V and the concentration c of the active substance.

[0062] The charge transfer impedance R t is expressed as:

[0063]

[0064] The diffusion impedance Z D is expressed as:

[0065]

[0066] The double-layer impedance Z caused by the charging current c , which is expressed as:

[0067]

[0068] In the formula, C dl is the interfacial capacitance, j is the imaginary number, and ω is the frequency.

[0069] In addition, the ohmic impedance R caused by the proton transfer resistance in the membrane, the electrolyte solution resistance, the current collector resistance, and the contact resistance between different battery components ohm .

[0070] Step S2: Based on step S1, establish an electrochemical impedance spectrum model of the flow battery.

[0071] As a preferred embodiment of the present invention, in this step, the electrochemical impedance spectrum model of the flow battery includes the ohmic impedance R ohm , the charge transfer impedance R t , the constant phase element Z CPE and the diffusion impedance Z D . Specifically as follows:

[0072] The ohmic impedance R that is independent of frequency and has a constant real part and a zero imaginary part ohm and the charge transfer impedance R t ;

[0073] Considering that the porous electrode surface is affected by factors such as roughness, zinc deposition, and uneven current distribution, there is a dispersion effect and the double-layer impedance Z needs to be corrected c , so the introduced constant phase element Z CPE , which is expressed as:

[0074]

[0075] where α is a dimensionless dispersion index with a value range of 0-1; Q is a constant phase element constant that comprehensively reflects the electrode characteristics, interfacial behavior, and reaction kinetics.

[0076] The diffusion impedance Z D According to the boundary layer conditions of the flow battery, it can be described by the finite-length Warburg impedance of the transmission boundary, which is expressed as:

[0077]

[0078] where R w is defined as the resistance of the active substance diffusion process and is the diffusion resistance; T is the time constant of the active substance diffusion in the finite-length medium.

[0079] Finally, impedance characteristic parameters are obtained through the established electrochemical impedance spectroscopy model. The impedance characteristic parameters include ohmic impedance R ohm , charge transfer impedance R t , diffusion resistance R w , diffusion time constant T, constant phase element constant Q, dispersion coefficient α, etc.

[0080] Step S3: Measure the electrochemical impedance spectroscopy of the flow battery under different SOCs.

[0081] As a preferred embodiment of the present invention, this step is specifically as follows:

[0082] S31: Place the storage tank of the flow battery in a constant temperature bath and adjust the flow rate and temperature required for battery testing;

[0083] S32: Charge and discharge the flow battery to the specified SOC according to actual needs;

[0084] S33: Stop charging and discharging, and continue to circulate the electrolyte for 1 minute using a circulation pump to make the battery reach steady-state conditions;

[0085] S34: Use an excitation signal voltage with an amplitude of 10 mV and select an EIS with a frequency range of 0.1 Hz to 1000 Hz to measure the impedance spectroscopy of the specified SOC;

[0086] S35: Continue to charge and discharge to the next specified SOC, and repeat the above steps until all SOCs are measured;

[0087] S36: Export the EIS impedance spectroscopy data under different SOCs for subsequent analysis.

[0088] Step S4: Perform fitting analysis on the impedance spectroscopy data measured in step S3 using the electrochemical impedance spectroscopy model mentioned in step S2, and extract impedance characteristic parameters.

[0089] As a preferred embodiment of the present invention, this step is specifically as follows:

[0090] Perform fitting analysis from the Nyquist diagram using the least squares principle, and extract impedance characteristic parameters including ohmic impedance R ohm , charge transfer impedance R t , diffusion resistance R w , diffusion time constant T, constant phase element constant Q, dispersion coefficient α, etc.

[0091] Step S5: By calculating the Pearson correlation coefficient R between SOC and each impedance characteristic parameter, screen out the characteristic parameters with strong correlation with SOC, establish the mapping relationship between SOC and impedance characteristic parameters, SOC = ax + b, and complete SOC estimation.

[0092] As a preferred embodiment of the present invention, in this step, when the absolute value of the Pearson correlation coefficient R between the SOC and each impedance characteristic parameter > 0.9, it is considered that the impedance characteristic parameter is a characteristic parameter with strong correlation with the SOC, and the mapping relationship between the SOC and the impedance characteristic parameter can be established, that is, SOC = ax + b, and then the SOC estimation is completed.

[0093] The method of the present invention is applicable to various flow battery systems, including all-vanadium flow batteries, zinc-based flow batteries, iron-based flow batteries, organic flow batteries, lead-acid flow batteries, etc.

[0094] Next, the method and effect of the present invention will be further described through examples.

[0095] Example

[0096] As Figure 1 shown, a method for estimating the SOC of a flow battery based on electrochemical impedance spectroscopy provided in this embodiment. In this embodiment, an alkaline zinc-iron flow battery with 0.2 mol / L Na4Fe(CN)6 and 0.1 mol / L Zn(OH)2 as the positive and negative electrode electrolytes respectively is used as the test sample for SOC estimation. The method includes the following steps:

[0097] S1. Establish a mechanism model of the flow battery considering the electrochemical reaction process. The specific process is as follows:

[0098] The positive electrode reaction equation of the zinc-iron flow battery is as follows

[0099]

[0100] The Faraday current density can be expressed as

[0101]

[0102] Perform Taylor expansion on i F and retain the first-order term

[0103]

[0104] Among them, the complex form is

[0105]

[0106] The Faraday impedance is

[0107]

[0108] Among them, the charge transfer resistance R t is

[0109]

[0110] The concentration of the positive electrode active material can be described by Fick's second law.

[0111]

[0112] Substitute After

[0113]

[0114] Similarly, Solving the second-order linear homogeneous ordinary differential equation gives the general solution as

[0115]

[0116] where the boundary conditions are:

[0117] At the electrode surface

[0118] x = 0

[0119]

[0120] At the boundary layer

[0121] y = δ N

[0122]

[0123] Solving gives

[0124]

[0125] Substituting into the Faraday impedance gives

[0126]

[0127] Therefore, the Faraday impedance can be expressed as

[0128]

[0129] The diffusion impedance is

[0130]

[0131] The negative electrode reaction equation of the zinc-iron flow battery is as follows

[0132]

[0133] The Faraday current density of the negative electrode reaction can be expressed as

[0134]

[0135] Performing Taylor expansion on it and retaining the first-order term, the Faraday current density can be obtained as

[0136]

[0137] where the current perturbation value is

[0138]

[0139] The Faraday impedance is

[0140]

[0141] where the charge transfer impedance

[0142]

[0143] The negative electrode diffusion impedance is derived using Fick's second law. The process is the same as that of the positive electrode diffusion impedance. The Faraday impedance of the negative electrode can be obtained as

[0144]

[0145] The diffusion impedance is

[0146]

[0147] S2. Based on step S1, an electrochemical impedance spectroscopy model of the flow battery is established. The specific process is as follows:

[0148] The Ohmic impedance R ohm and the charge transfer impedance R t are independent of frequency. Their real parts are constants and their imaginary parts are zero. On the impedance complex plane, they can be represented by a point on the real axis.

[0149] Considering the constant phase angle element Z CPE introduced by the dispersion effect due to factors such as roughness, zinc deposition, and uneven current distribution on the surface of the porous electrode, it is expressed as:

[0150]

[0151] where α is a dimensionless dispersion index with a value range of 0 - 1; Q is a constant phase angle element constant that comprehensively reflects electrode characteristics, interfacial behavior, and reaction kinetics.

[0152] The diffusion impedance Z D According to the boundary layer conditions of the flow battery, it can be described by the finite-length Warburg impedance of the transmission boundary, expressed as:

[0153]

[0154] Among them, R w is defined as the resistance of the active material diffusion process, which is the diffusion resistance; T is the time constant of the active material diffusion in the finite-length medium.

[0155] The impedance characteristic parameters include the ohmic impedance R ohm , the charge transfer impedance R t , the diffusion resistance R w , the diffusion time constant T, the constant phase angle element constant Q, the dispersion coefficient α, etc.

[0156] Figure 2 This is the schematic diagram of the electrochemical impedance spectrum model of the flow battery in this embodiment.

[0157] S3. Measure the electrochemical impedance spectra of the flow battery at different SOCs. The specific process is as follows:

[0158] Place the zinc-iron flow battery storage tank in a constant-temperature bath, and adjust the flow rate required for battery testing to 100 ml / min and the temperature to 30 °C;

[0159] According to actual requirements, charge the zinc-iron flow battery to a specified SOC of 20% with a current density of 60 mA / cm 2 ;

[0160] Stop charging, and continue to circulate the electrolyte for 1 minute using a circulation pump to make the battery reach the steady-state condition;

[0161] Use an EIS with an excitation signal of voltage, an amplitude of 10 mV, and a frequency range of 0.1 Hz to 1000 Hz to measure the impedance spectrum at 20% SOC;

[0162] Continue charging and discharging to the next specified SOC, and repeat the above steps until all SOCs (20%, 30%, 40%, 50%, 60%, 70%, 80%) are measured;

[0163] Export the EIS impedance spectrum data at different SOCs for subsequent analysis.

[0164] S4. Use the electrochemical impedance spectrum model mentioned in step S2 to perform fitting analysis on the impedance spectrum data measured in step S3, and extract the impedance characteristic parameters. The impedance characteristic parameters include the ohmic impedance R ohm , the charge transfer impedance R t , the diffusion resistance R w , the diffusion time constant T, the constant phase angle element constant Q, the dispersion coefficient α, etc. The specific values are shown in Table 1.

[0165] Table 1 Values of impedance characteristic parameters of zinc-iron flow battery at 20%-80% SOC

[0166] SOC <![CDATA[R ohm (Ω)]]> Q α <![CDATA[R t (Ohm)]]> <![CDATA[R w (Ω)]]> T 20％ 0.13115 1.655 0.52374 0.057515 0.0082044 0.54837 30％ 0.13297 1.514 0.51584 0.053503 0.01037 0.5608 40％ 0.13417 1.632 0.5084 0.043779 0.011877 0.56826 50％ 0.13659 1.751 0.5043 0.030061 0.013284 0.57075 60％ 0.13929 2.13 0.4988 0.022916 0.014161 0.57357 70％ 0.14152 2.547 0.49471 0.018482 0.015462 0.64484 80％ 0.145 4.438 0.4904 0.01501 0.01647 0.69293

[0167] S5. By calculating the Pearson correlation coefficient R between the SOC and each impedance characteristic parameter, the characteristic parameters with strong correlation with the SOC are screened out, and the mapping relationship between the SOC and the impedance characteristic parameters is established as SOC = ax + b to complete the SOC estimation. Table 2 shows the specific values of the Pearson correlation coefficient R between the SOC and each impedance characteristic parameter.

[0168] Table 2 Specific values of the Pearson correlation coefficient R between the SOC and each impedance characteristic parameter

[0169]

[0170]

[0171] Ohmic impedance R ohm The absolute value of the Pearson correlation coefficient R between it and the SOC is 0.991, which is greater than 0.9, and its mapping relationship with the SOC is SOC = 0.02277R ohm + 0.12585, which can be used to complete the SOC estimation.

[0172] The absolute value of the Pearson correlation coefficient R between the dispersion coefficient α and the SOC is 0.992, which is greater than 0.9, and its mapping relationship with the SOC is SOC = -0.05424α + 0.53229, which can be used to complete the SOC estimation.

[0173] Charge transfer impedance R t The absolute value of the Pearson correlation coefficient R between it and the SOC is 0.982, which is greater than 0.9, and its mapping relationship with the SOC is SOC = -0.07801R t + 0.07347, which can be used to complete the SOC estimation.

[0174] Diffusion resistance R w The absolute value of the Pearson correlation coefficient R between it and the SOC is 0.991, which is greater than 0.9, and its mapping relationship with the SOC is SOC = 0.01331R w + 0.00618, which can be used to complete the SOC estimation.

[0175] The present invention establishes a mechanism model and an electrochemical impedance spectroscopy model of a flow battery considering the electrochemical reaction process, measures the electrochemical impedance spectroscopy at different SOCs, and uses the models to perform fitting analysis on the impedance spectroscopy data to extract impedance characteristic parameters such as ohmic impedance, charge transfer impedance, diffusion resistance, diffusion time constant, constant phase angle element constant, and dispersion coefficient. By calculating the Pearson correlation coefficient between the SOC and each impedance characteristic parameter, the characteristic parameters with strong correlation with the SOC are screened out, and the mapping relationship between the SOC and the impedance characteristic parameters is established to achieve accurate estimation of the SOC of the flow battery. The present invention combines the physical models of the internal electrochemical process of the battery, has the advantages of strong physical meaning, high real-time performance, wide applicability, etc., improves the accuracy and reliability of the SOC estimation, and is applicable to the flow battery system under different working conditions.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the specific technical solutions of the present invention, rather than limiting the present invention. Although the present invention has been described in detail through the above embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features therein. These modifications or replacements will not change the essence of the technical solutions of the present invention and all fall within the protection scope of the present invention.

Claims

1. A method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy, characterized in that, The details are as follows: S1. Establish a mechanism model of a flow battery considering the electrochemical reaction process; S2. Based on the results of S1, establish an electrochemical impedance spectroscopy model of the flow battery; S3. Measure the electrochemical impedance spectroscopy of the flow battery under different state of charge; S4. For the electrochemical impedance spectroscopy measured in S3, use the electrochemical impedance spectroscopy model described in S2 for fitting analysis to extract impedance characteristic parameters; S5. Based on the results of S4, by calculating the Pearson correlation coefficient between the state of charge and each impedance characteristic parameter, screen out the characteristic parameters with strong correlation with the state of charge, establish the mapping relationship between the state of charge and the impedance characteristic parameters, and complete the state of charge estimation.

2. The method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy according to claim 1, wherein In S1, the mechanism model of the flow battery includes: Faraday impedance Z caused by Faraday current F : where f and g are both functions of the interfacial potential V and the active substance concentration c, j is the imaginary unit, and ω is the frequency; Charge transfer resistance R t : Diffusion impedance Z D : The double-layer impedance Zc caused by the charging current: where C dl is the interface capacitance; The ohmic impedance R caused by the proton transfer resistance in the membrane, the electrolyte solution resistance, the current collector resistance, and the contact resistance between different battery components ohm .

3. A method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy according to claim 1, wherein In S2, the electrochemical impedance spectroscopy model includes: An Ohmic impedance R that is independent of frequency, with a constant real part and a zero imaginary part ohm and a charge transfer impedance R t ; Constant phase angle element Z CPE : where α is a dimensionless dispersion index with a value range of 0 - 1; Q is a constant phase angle element constant comprehensively reflecting electrode characteristics, interfacial behavior, and reaction kinetics; j is the imaginary unit; ω is the frequency. Diffusion impedance Z D : Among them, R w is defined as the resistance of the active substance diffusion process, which is the diffusion resistance; T is the time constant of the active substance diffusion in the finite-length medium.

4. A method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy according to claim 1, characterized in that, The specific steps of S3 are as follows: S31. Place the storage tank of the flow battery in a thermostatic bath and adjust the flow rate and temperature required for the flow battery test; S32. Charge and discharge the flow battery to the specified state of charge according to actual needs; S33. Stop charging and discharging, and continue to circulate the electrolyte for 1 minute using a circulation pump to make the flow battery reach steady-state conditions; S34. Use an excitation signal voltage with an amplitude of 10 mV and an electrochemical impedance spectroscopy with a frequency range of 0.1 Hz - 1000 Hz to measure the impedance spectroscopy of the specified state of charge; continue charging and discharging to the next specified state of charge; S35. Repeat S31 - S34 until all states of charge are measured; S36. Export the electrochemical impedance spectroscopy data under different states of charge for subsequent analysis.

5. The method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy according to claim 1, wherein The impedance characteristic parameters are obtained through an electrochemical impedance spectroscopy model and include ohmic impedance R ohm , charge transfer impedance R t , diffusion resistance R w , diffusion time constant T, constant phase angle element constant Q, and dispersion coefficient α.

6. The method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy according to claim 1, wherein In S4, fitting analysis is performed from the Nyquist plot using the least squares principle.

7. A method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy according to claim 1, wherein In S5, if the absolute value of the Pearson correlation coefficient R between the state of charge and the impedance characteristic parameter is > 0.9, it is considered that the impedance characteristic parameter has a strong correlation with the state of charge; then, using the screened characteristic parameters, establish the mapping relationship between the state of charge and the impedance characteristic parameters to complete the state of charge estimation.

8. A method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy according to claim 7, characterized in that, The mapping relationship is expressed as: SOC = ax + b where SOC is the state of charge; a is the proportionality coefficient in the mapping relationship, indicating the influence degree of the change in the impedance characteristic parameter x on SOC; b is the constant offset in the mapping relationship, indicating the reference value of SOC when the impedance characteristic parameter x is zero; x is the impedance characteristic parameter.

9. A method for estimating the state of charge of a flow battery based on electrochemical impedance spectroscopy according to claim 1, characterized in that, The flow battery includes a all-vanadium flow battery, a zinc-based flow battery, an iron-based flow battery, an organic flow battery, and a lead-acid flow battery.

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