Method for calculating battery differential capacitance

Abstract

The application discloses a kind of battery differential capacitance calculation methods, the method comprises: based on the frequency interval of pre-set electrochemical impedance spectrum test is carried out to battery, obtain the original impedance spectrum data of the battery under the frequency interval, screen out inductance data to obtain test impedance spectrum data in the original impedance spectrum data;Based on the test impedance spectrum data obtains the test capacitive reactance spectrum data under the frequency interval;Based on the regularization method, the theoretical capacitive reactance spectrum data of the battery under different relaxation time is calculated, based on the test capacitive reactance spectrum data, the theoretical capacitive reactance spectrum data and the minimum target method calculates the differential capacitance data of the battery under different relaxation time.The technical scheme provided in the application can solve the technical problems that the differential capacitance data is difficult to be accurately obtained when the battery is in different relaxation time in the prior art electrochemical impedance spectrum test.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of battery, in particular to a method for calculating differential capacitance of battery. BACKGROUND

[0002] Electrochemical impedance spectroscopy (EIS) is an efficient in-situ / non-in situ electrochemical characterization technique, which has been widely used in the field of lithium-ion batteries. At present, the most commonly used EIS data analysis method is the fitting technology based on equivalent circuit. This analysis method needs to make prior assumptions about the model first, but it is difficult to implement. A semicircle in the EIS diagram can be formed by overlapping multiple semicircles, and it is difficult to determine the number of characteristic time constants, resulting in uncertainty in impedance analysis.

[0003] The prior art uses the distribution of relaxation times (DRT) to determine the characteristic time constant. The DRT method does not need to establish an equivalent circuit model, can directly determine the number of time constants and the approximate frequency range and calculate the corresponding impedance values, can greatly reduce the experimental workload and can reduce the uncertainty of analysis. However, when studying lithium-ion batteries, the data obtained by low-frequency testing cannot be analyzed by DRT because the differential capacitance dominates the diffusion process. The low frequency limits the application of the DRT method in lithium-ion batteries. The prior art can only evaluate lithium-ion batteries from the perspective of impedance, and it is difficult to obtain differential capacitance data of lithium-ion batteries at different relaxation times. SUMMARY

[0004] The present application provides a method for calculating the differential capacitance of a battery, which aims to effectively solve the technical problem of accurately obtaining differential capacitance data at different relaxation times when performing electrochemical impedance spectroscopy testing on a battery in the prior art.

[0005] According to one aspect of the present application, the present application provides a method for calculating the differential capacitance of a battery, the method comprising:

[0006] Performing electrochemical impedance spectroscopy testing on the battery based on a predetermined frequency interval, obtaining original impedance spectroscopy data of the battery at the frequency interval, and screening out inductive reactance data in the original impedance spectroscopy data to obtain test impedance spectroscopy data;

[0007] Based on the test impedance spectroscopy data, test capacitive reactance spectroscopy data at the frequency interval is obtained;

[0008] Based on a regularization method, theoretical capacitive reactance spectroscopy data of the battery at different relaxation times is calculated;

[0009] The differential capacitance data of the battery at different relaxation times is calculated based on the test reactance spectrum data, the theoretical reactance spectrum data and a minimization objective method.

[0010] Further, the inductive reactance data in the original impedance spectrum data is screened to obtain the test impedance spectrum data, which comprises:

[0011] The data with an impedance imaginary part value less than a preset value in the original impedance spectrum data is determined as the inductive reactance data.

[0012] The inductive reactance data is deleted in the original impedance spectrum data to obtain the test impedance spectrum data.

[0013] Further, the test reactance spectrum data in the frequency range is obtained based on the test impedance spectrum data, which comprises:

[0014] Impedance real part data and impedance imaginary part data of the test impedance spectrum data at different test frequencies in the frequency range are obtained.

[0015] The test reactance spectrum data is obtained based on the impedance real part data, the impedance imaginary part data and the test frequencies.

[0016] Further, the theoretical reactance spectrum data of the battery at different relaxation times is calculated based on a regularization method, which comprises:

[0017] A radial basis function and a shape factor corresponding to the radial basis function are determined.

[0018] A to-be-determined relaxation time distribution function is obtained based on the radial basis function, the shape factor and a discretization method.

[0019] The theoretical reactance spectrum data is obtained based on the to-be-determined relaxation time distribution function and test frequencies.

[0020] Further, the differential capacitance data of the battery at different relaxation times is calculated based on the test reactance spectrum data, the theoretical reactance spectrum data and a minimization objective method, which comprises:

[0021] A weight parameter in the to-be-determined relaxation time distribution function is calculated based on the test reactance spectrum data, the theoretical reactance spectrum data and a penalty term function and a minimization objective method.

[0022] A real relaxation time distribution function is obtained based on the weight parameter and the to-be-determined relaxation time distribution function.

[0023] The differential capacitance data is obtained based on the real relaxation time distribution function and the theoretical reactance spectrum data.

[0024] Further, the obtaining the test capacitive reactance spectrum data based on the impedance real part data, the impedance imaginary part data and the test frequency comprises:

[0025] The test capacitive reactance spectrum data is calculated according to the following formula:

[0026]

[0027] Wherein, C exp represents the test capacitive reactance spectrum data, Z Im represents the impedance imaginary part data, Z Re represents the impedance real part data, and f represents the test frequency, and j is an imaginary unit.

[0028] Further, the obtaining the undetermined relaxation time distribution function based on the radial basis function, the shape factor and the discretization method comprises:

[0029] The undetermined relaxation time distribution function is calculated according to the following formula:

[0030]

[0031] Wherein, γ (lnτ) represents the undetermined relaxation time distribution function, x m represents the mth undetermined weight parameter, represents the radial basis function, μ represents the shape factor, and τ m represents the mth relaxation time constant, represents the cumulative summation operation function, and ln() represents a logarithmic function.

[0032] Further, the obtaining the theoretical capacitive reactance spectrum data based on the undetermined relaxation time distribution function and the test frequency comprises:

[0033] The theoretical capacitive reactance spectrum data is calculated according to the following formula:

[0034]

[0035] Wherein, C model represents the theoretical capacitive reactance spectrum data, γ (lnτ) represents the undetermined relaxation time distribution function, τ represents the relaxation time constant, f represents the test frequency, and j is an imaginary unit.

[0036] Further, the calculating the weight parameter in the undetermined relaxation time distribution function based on the test capacitive reactance spectrum data, the theoretical capacitive reactance spectrum data and the penalty term function and the minimization target method comprises:

[0037] The weight parameter is calculated according to the following formula:

[0038] S (x) = || C model · x - Cexp || 2 + λp(x),

[0039] wherein S(x) represents a minimization objective function, C model represents the theoretical reactance spectrum data, C exp represents the test reactance spectrum data, x represents the weight parameter, λ represents the regularization parameter, p(x) represents the penalty term function, and || || represents the norm function.

[0040] Further, the penalty term function is obtained according to the following formula:

[0041]

[0042] p(x) represents the penalty term function, γ(lnτ) represents the to-be-determined relaxation time distribution function, τ represents the relaxation time constant, d() represents the differential of the logarithmic value, and || || represents the norm function.

[0043] By one or more of the above embodiments in the present application, at least the following technical effects can be achieved:

[0044] In the technical solution disclosed in the present application, the lithium ion battery is subjected to electrochemical impedance testing to obtain test impedance spectrum data, and the theoretical reactance spectrum data is calculated through a regularization method, and finally the differential capacitance data of the battery under different relaxation time constants is obtained. The present solution can quickly and accurately obtain the distribution function of the differential capacitance under different relaxation times, is simple to operate, and the data results are reliable, thereby providing a theoretical basis for analyzing the kinetic characteristics of the charge transfer process and the diffusion process of the lithium ion battery. BRIEF DESCRIPTION OF DRAWINGS

[0045] The technical solution and other beneficial effects of the present application will become apparent through the following detailed description of the specific embodiments of the present application in conjunction with the accompanying drawings.

[0046] Figure 1 A step flowchart of a battery differential capacitance calculation method provided for an embodiment of the present application;

[0047] Figure 2 A raw impedance spectrum data graph provided for an embodiment of the present application;

[0048] Figure 3 A test impedance spectrum data graph provided for an embodiment of the present application;

[0049] Figure 4 A differential capacitance data graph provided for an embodiment of the present application. DETAILED DESCRIPTION

[0050] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative effort should fall within the scope of the present application.

[0051] In the description of the present application, it should be noted that, unless otherwise explicitly specified and limited, the term "and / or" in the present application is only to describe the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B can mean that there are three cases of A alone, A and B together, and B alone. In addition, the character " / " in the present application generally represents an "or" relationship between the front and rear associated objects without special explanation.

[0052] According to an aspect of the present application, the present application provides a battery differential capacitance calculation method, Figure 1 The step flow chart of the battery differential capacitance calculation method provided by the embodiment of the present application is shown, and the method comprises:

[0053] Step 101: Based on the preset frequency interval, the electrochemical impedance spectrum of the battery is tested, the original impedance spectrum data of the battery under the frequency interval is obtained, and the inductive reactance data in the original impedance spectrum data is screened out to obtain the test impedance spectrum data;

[0054] Step 102: Based on the test impedance spectrum data, the test capacitive reactance spectrum data under the frequency interval is obtained;

[0055] Step 103: Based on the regularization method, the theoretical capacitive reactance spectrum data of the battery under different relaxation time is calculated;

[0056] Step 104: Based on the test capacitive reactance spectrum data, the theoretical capacitive reactance spectrum data and the minimization target method, the differential capacitance data of the battery under different relaxation time is calculated.

[0057] When the lithium ion battery is tested by electrochemical impedance spectrum to obtain data, low frequency test will cause differential capacity, which cannot be decomposed by DRT. The present application introduces differential capacitance distribution function (DDC) to analyze the low frequency capacitance tail data in impedance spectrum. The DDC analysis technology analogizes the electrochemical system as a system composed of infinite differential capacitance elements in parallel, and the analysis method is basically the same as the principle of DRT analysis technology. Because the characteristic time constants corresponding to different differential capacitances are different, the characteristic time distribution function can be extracted to study the characteristics of the electrochemical system. Through DDC analysis, the differential capacitance characteristic time constant distribution function can be obtained, so as to analyze the kinetic characteristics of charge transfer / diffusion process.

[0058] The following is a detailed description of steps 101 to 104 above.

[0059] In step 101, the battery is subjected to electrochemical impedance spectroscopy test based on a preset frequency range to obtain the original impedance spectrum data of the battery in the frequency range, and the inductive impedance data in the original impedance spectrum data is screened out to obtain the test impedance spectrum data.

[0060] For example, the lithium-ion battery sample used for electrochemical impedance spectroscopy (EIS) testing can be any type of lithium-ion battery, such as a coin cell or a pouch cell, like a lithium iron phosphate pouch cell. First, the battery's charge needs to be adjusted to a specified state of charge (SOC) value before the EIS test is performed; for example, the SOC of the lithium iron phosphate battery might be adjusted to 50% before testing.

[0061] The imaginary part of the AC impedance of lithium iron phosphate pouch batteries at different frequencies within the frequency range was collected, and AC complex impedance spectrum data at different frequencies were constructed. The AC complex impedance spectrum data is the original impedance spectrum data. Specifically, assuming the frequency range is 100kHz to 2mHz, the original impedance spectrum data is the imaginary part of the impedance of the sample lithium-ion battery under frequency excitation of 100kHz to 2mHz, which can be written in the corresponding complex number form. Figure 2 This invention provides a raw impedance spectrum data diagram as an embodiment of the invention. Figure 2 The original impedance spectrum data does not include frequency data. According to the convention of AC impedance spectroscopy, the frequency decreases from left to right. The complex form of the original impedance spectrum data can be expressed by the following formula:

[0062] Z(ω)=Z Re +Z Im ·j,

[0063] Where Z(ω) represents the original impedance spectrum data, Z Re Z represents the real part of the impedance. Im This represents the imaginary part of the impedance, where j is the imaginary unit.

[0064] After obtaining the raw impedance spectrum data, the inductive reactance data is deleted, and the remaining data is the test impedance spectrum data. Figure 3 An impedance spectrum data diagram provided in an embodiment of the present invention. Figure 3 The data is Figure 2 Data deletion in -Z Im The test impedance spectrum data obtained after the data acquisition point corresponding to ≤0.

[0065] In step 102, the test capacitive reactance spectrum data in the frequency range is obtained based on the test impedance spectrum data.

[0066] Exemplarily, the test impedance spectrum data is converted into the alternating current complex reactance spectrum data at different frequencies, i.e., the test reactance spectrum data. In the data conversion process, the test reactance spectrum data is obtained through multiple data processing, and the data is the actual data obtained through the experiment,

[0067] In step 103, the theoretical reactance spectrum data of the battery at different relaxation times is calculated based on a regularization method.

[0068] Exemplarily, the theoretical reactance spectrum data is obtained through the radial basis function and the discretization method.

[0069] In step 104, the differential capacitance data of the battery at different relaxation times is calculated based on the test reactance spectrum data, the theoretical reactance spectrum data, and a minimization target method.

[0070] Exemplarily, the weight parameter in the relaxation time distribution function needs to be calculated in the process. After the weight parameter is calculated, the weight parameter is brought into the relaxation time distribution function, and the final theoretical reactance spectrum data is calculated, i.e., the differential capacitance data of the battery at different relaxation time constants.

[0071] Further, the inductive reactance data in the original impedance spectrum data is screened out to obtain the test impedance spectrum data, including:

[0072] The data with an impedance imaginary part less than a preset value in the original impedance spectrum data is determined as the inductive reactance data.

[0073] The inductive reactance data is deleted in the original impedance spectrum data to obtain the test impedance spectrum data.

[0074] Exemplarily, the inductive reactance data is determined in the original impedance spectrum data, for example Figure 2 The alternating current impedance imaginary part data of the lithium iron phosphate soft package battery at 100 kHz-2 mHz is shown in the figure, the inductive reactance data is-Z Im ≤0 corresponding data acquisition point, the inductive reactance data in the alternating current impedance spectrum data is removed, and the processed electrochemical impedance spectrum is the test impedance spectrum data. The specific data graph is shown in Figure 3 .

[0075] Further, the test reactance spectrum data in the frequency interval is obtained based on the test impedance spectrum data, including:

[0076] The impedance real part data and the impedance imaginary part data of the test impedance spectrum data at different test frequencies in the frequency interval are obtained.

[0077] The test reactance spectrum data is obtained based on the impedance real part data, the impedance imaginary part data, and the test frequency.

[0078] Exemplarily, the test impedance spectrum data is converted into test capacitive reactance spectrum data at different frequencies. In the data conversion process, the test capacitive reactance spectrum data is finally obtained through multiple data processing. Specifically, first, the capacitive reactance spectrum data can be obtained according to the relevant data during the electrochemical impedance spectrum test, and the capacitive reactance spectrum data is obtained according to the battery charge at different test frequencies and the test applied voltage; second, the battery charge at different test frequencies can be obtained according to the test applied current and the angular frequency; third, the test applied voltage and current can obtain the resistance value; then, the angular frequency and the resistance value can be represented by the impedance real part data, the impedance imaginary part data and the test frequency, and finally the test capacitive reactance spectrum data is obtained.

[0079] Further, the calculating the theoretical capacitive reactance spectrum data of the battery at different relaxation times based on the regularization method comprises:

[0080] determining a radial basis function and a shape factor corresponding to the radial basis function;

[0081] obtaining a to-be-determined relaxation time distribution function based on the radial basis function, the shape factor and a discretization method;

[0082] obtaining the theoretical capacitive reactance spectrum data based on the to-be-determined relaxation time distribution function and the test frequency.

[0083] Exemplarily, according to the alternating current capacitive reactance spectrum data of the sample lithium ion battery at different frequencies, the differential capacitance distribution function of the corresponding sample lithium ion battery at different relaxation times is calculated based on the Tikhonov regularization method.

[0084] The radial basis function is a real-valued function whose value depends only on the distance from the origin, and the discretization method is a method of using a finite number of parameters to approximate the physical quantities in continuous medium mechanics. This process mainly uses mathematical methods to process data to obtain a to-be-determined relaxation time distribution function. In the to-be-determined relaxation time distribution function, there is a weight parameter that is currently unknown. Based on the to-be-determined relaxation time distribution function and the test frequency, the theoretical capacitive reactance spectrum data is obtained. Since the weight parameter is unknown, the theoretical capacitive reactance spectrum data is also to-be-determined data under the current state.

[0085] Further, the calculating the differential capacitance data of the battery at different relaxation times based on the test capacitive reactance spectrum data, the theoretical capacitive reactance spectrum data and the minimization target method comprises:

[0086] calculating the weight parameter in the to-be-determined relaxation time distribution function based on the test capacitive reactance spectrum data, the theoretical capacitive reactance spectrum data and a penalty term function and a minimization target method;

[0087] obtaining a real relaxation time distribution function based on the weight parameter and the to-be-determined relaxation time distribution function;

[0088] The differential capacitance data is obtained based on the real relaxation time distribution function and the theoretical reactance spectrum data.

[0089] Exemplarily, first, the specific value of the weight parameter is calculated according to the test reactance spectrum data and the theoretical reactance spectrum data, and the method used is the minimization objective method. The test reactance spectrum data, the theoretical reactance spectrum data and the penalty function are used to generate the minimization objective function, and the value corresponding to the weight parameter when the minimization objective function is minimized is obtained. The penalty function is a way to deal with constraint problems. When dealing with constraint problems, the penalty function is usually added to the objective function, so that the constraint problem becomes an unconstrained problem. For example, when the fitness value is small and not within the constraint condition, the penalty function is added to increase the fitness value, so as to eliminate unsuitable data.

[0090] After the value of the weight parameter is determined, the weight parameter is brought into the to-be-determined relaxation time distribution function, and the real relaxation time distribution function can be obtained. Further, the real relaxation time distribution function is brought into the theoretical reactance spectrum data, and the function finally obtained is the differential capacitance data.

[0091] Further, the test reactance spectrum data is obtained based on the impedance real part data, the impedance imaginary part data and the test frequency, and the test reactance spectrum data comprises:

[0092] The test reactance spectrum data is calculated according to the following formula:

[0093]

[0094] Wherein, C exp represents the test reactance spectrum data, Z Im represents the impedance imaginary part data, Z Re represents the impedance real part data, and f represents the test frequency. j is the imaginary unit.

[0095] Exemplarily, first, the relevant data during electrochemical impedance spectrum test is obtained, including the electric quantity of the battery under different test frequencies and the applied voltage during test. The reactance spectrum data is obtained according to the electric quantity and the voltage, and the reactance spectrum data is shown in the following formula:

[0096]

[0097] Wherein, C(ω) represents the reactance spectrum data, Q(ω) represents the electric quantity of the battery under different test frequencies, and U(ω) represents the applied voltage during test.

[0098] The electric quantity of the battery under different test frequencies can be obtained according to the test applied current and the angular frequency. Further, the reactance spectrum data is shown in the following formula:

[0099] The electric quantity of the battery under different test frequencies can be obtained according to the test applied current and the angular frequency. Further, the reactance spectrum data is shown in the following formula:

[0100] where C(ω) represents the capacitive reactance spectrum data, I(ω) represents the test applied current, ω represents the angular frequency, j is the imaginary unit, and U(ω) represents the test applied voltage;

[0101] In the above formula, U(ω) represents the test applied voltage, and I(ω) represents the test applied current, both of which can obtain the resistance value of the data, and further, the capacitive reactance spectrum data is as follows:

[0102]

[0103] where C(ω) represents the capacitive reactance spectrum data, Z(ω) represents the resistance value, and ω represents the angular frequency, j is the imaginary unit;

[0104] In the above formula, the angular frequency and the resistance value can be represented by the impedance real part data, the impedance imaginary part data, and the test frequency, and further, the capacitive reactance spectrum data is as follows:

[0105]

[0106] where C(ω) represents the capacitive reactance spectrum data, Z Im represents the impedance imaginary part data, Z Re represents the impedance real part data, f represents the test frequency, and j is the imaginary unit;

[0107] Data arrangement is performed on the above formula, and further, the capacitive reactance spectrum data is as follows:

[0108]

[0109] C(ω) represents the capacitive reactance spectrum data, Z Im represents the impedance imaginary part data, Z Re represents the impedance real part data, f represents the test frequency, and j is the imaginary unit.

[0110] The test capacitive reactance spectrum data can be obtained according to the impedance real part data, the impedance imaginary part data, and the test frequency, the impedance real part data and the impedance imaginary part data are consistent with the capacitive reactance spectrum data in the above formula, and therefore, the test capacitive reactance spectrum data is as follows:

[0111]

[0112] where C exp represents the test capacitive reactance spectrum data, Z Im represents the impedance imaginary part data, Z Re represents the impedance real part data, f represents the test frequency, and j is the imaginary unit.

[0113] Further, the obtaining the undetermined relaxation time distribution function based on the radial basis function, the shape factor and a discretization method comprises:

[0114] The undetermined relaxation time distribution function is calculated according to the following formula:

[0115]

[0116] Wherein, γ (lnτ) represents the undetermined relaxation time distribution function, x m represents the mth undetermined weight parameter, represents the radial basis function, μ represents the shape factor, τ m represents the mth relaxation time constant, represents the cumulative summation operation function, ln() represents the logarithmic function.

[0117] Exemplarily, the Gaussian function can be selected as the radial basis function, wherein the shape factor μ can be determined as 0.5, and in actual application, the shape factor is determined according to requirements, and the present application is not limited, and the radial basis function is represented by the following formula:

[0118]

[0119] Wherein, represents the radial basis function, μ represents the shape factor.

[0120] Further, the obtaining the theoretical reactance spectrum data based on the undetermined relaxation time distribution function and the test frequency comprises:

[0121] The theoretical reactance spectrum data is calculated according to the following formula:

[0122]

[0123] Wherein, C model represents the theoretical reactance spectrum data, γ (lnτ) represents the undetermined relaxation time distribution function, τ represents the relaxation time constant, f represents the test frequency, and j is the imaginary unit.

[0124] Further, the calculating the weight parameter in the undetermined relaxation time distribution function based on the test reactance spectrum data, the theoretical reactance spectrum data, a penalty term function and a minimization target method comprises:

[0125] The weight parameter is calculated according to the following formula:

[0126] S (x) = || C model · x - C exp || 2 + λp (x),

[0127] wherein S(x) represents a minimized objective function, C model represents the theoretical reactance spectrum data, C exp represents the test reactance spectrum data, x represents the weight parameter, λ represents a regularization parameter, p(x) represents the penalty term function, and || || represents a norm function.

[0128] Exemplarily, in the formula, when S(x) is a minimum value, the value of the corresponding weight parameter is the finally determined weight parameter value.

[0129] Further, the penalty term function is obtained according to the following formula:

[0130]

[0131] p(x) represents the penalty term function, γ(lnτ) represents the to-be-determined relaxation time distribution function, τ represents a relaxation time constant, d() represents a differential value of a logarithmic value, and || || represents a norm function.

[0132] Exemplarily, λ is a regularization parameter, and the value can be determined as 10 -3 In actual application, the value can be determined according to requirements, and the present application does not limit this.

[0133] After the value of the weight parameter is determined, the weight parameter is brought into the to-be-determined relaxation time distribution function, and the real relaxation time distribution function can be obtained, and further, the real relaxation time distribution function is brought into the theoretical reactance spectrum data, and the finally obtained function is the differential capacitance data. That is, through the obtained weight parameter, the relaxation time distribution function γ(lnτ) of the differential capacitance is calculated, Figure 4 Fig. 1 is a differential capacitance data graph provided by an embodiment of the present application, specifically a differential capacitance distribution graph of a 50% SOC lithium iron phosphate battery at different relaxation times.

[0134] Through one of the above embodiments or multiple embodiments in the present application, at least the following technical effects can be achieved:

[0135] In the disclosed technical solution, the lithium ion battery is subjected to electrochemical impedance spectroscopy to obtain test impedance spectrum data, and the theoretical reactance spectrum data is calculated through a regularization method, and finally the differential capacitance data of the battery at different relaxation times is obtained. The present solution can quickly and accurately obtain the distribution function of the differential capacitance at different relaxation times, is simple to operate, and the data result is reliable, thereby providing a theoretical basis for analyzing the kinetic characteristics of the charge transfer process and the diffusion process of the lithium ion battery.

[0136] In summary, although the present application has been disclosed with preferred embodiments as above, the preferred embodiments are not intended to limit the present application, and those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application, and therefore the protection scope of the present application is defined by the scope of the claims.

Claims

1. A method of calculating a battery differential capacitance, the method comprising: The method comprises: performing an electrochemical impedance spectroscopy test on the battery based on a preset frequency interval, obtaining original impedance spectroscopy data of the battery under the frequency interval, and screening inductive reactance data in the original impedance spectroscopy data to obtain test impedance spectroscopy data; obtaining test capacitive reactance spectroscopy data of the battery under the frequency interval based on the test impedance spectroscopy data; calculating theoretical capacitive reactance spectroscopy data of the battery under different relaxation times based on a regularization method, comprising: determining a radial basis function and a shape factor corresponding to the radial basis function; obtaining a to-be-determined relaxation time distribution function based on the radial basis function, the shape factor, and a discretization method; obtaining the theoretical capacitive reactance spectroscopy data based on the to-be-determined relaxation time distribution function and a test frequency; calculating difference capacitance data of the battery under different relaxation times based on the test capacitive reactance spectroscopy data, the theoretical capacitive reactance spectroscopy data, and a minimization target method, comprising: calculating a weight parameter in the to-be-determined relaxation time distribution function based on the test capacitive reactance spectroscopy data, the theoretical capacitive reactance spectroscopy data, and a penalty term function, and the minimization target method; obtaining a real relaxation time distribution function based on the weight parameter and the to-be-determined relaxation time distribution function; obtaining the difference capacitance data based on the real relaxation time distribution function and the theoretical capacitive reactance spectroscopy data.

2. The method of claim 1, wherein, The screening of the inductive reactance data in the original impedance spectroscopy data to obtain the test impedance spectroscopy data comprises: determining data with an impedance imaginary part less than a preset value in the original impedance spectroscopy data as the inductive reactance data; deleting the inductive reactance data in the original impedance spectroscopy data to obtain the test impedance spectroscopy data.

3. The method of claim 1, wherein, The obtaining of the test capacitive reactance spectroscopy data based on the test impedance spectroscopy data under the frequency interval comprises: obtaining impedance real part data and impedance imaginary part data of the test impedance spectroscopy data under different test frequencies in the frequency interval; obtaining the test capacitive reactance spectroscopy data based on the impedance real part data, the impedance imaginary part data, and the test frequency.

4. The method of claim 3, wherein, The obtaining of the test capacitive reactance spectroscopy data based on the impedance real part data, the impedance imaginary part data, and the test frequency comprises: calculating the test capacitive reactance spectroscopy data according to the following formula: where C exp represents the test impedance data, Z Im represents the imaginary impedance data, Z Re represents the real impedance data, f represents the test frequency, and j is the imaginary unit.

5. The method of claim 4, wherein, The obtaining of the to-be-determined relaxation time distribution function based on the radial basis function and the shape factor and the discretization method comprises: calculating the to-be-determined relaxation time distribution function according to the following formula: where γ(lnτ) denotes the pending relaxation time distribution function, x m denotes the mth pending weight parameter, denotes the radial basis function, μ denotes the shape factor, τ m denotes the mth relaxation time constant, denotes the cumulative summation operation function, ln() denotes the logarithm function.

6. The method of claim 5, wherein, The obtaining of the theoretical capacitive reactance spectroscopy data based on the to-be-determined relaxation time distribution function and the test frequency comprises: calculating the theoretical capacitive reactance spectroscopy data according to the following formula: where C model represents the theoretical reactance spectrum data, γ(lnτ) represents the to-be-determined relaxation time distribution function, τ represents a relaxation time constant, f represents a test frequency, and j is an imaginary unit.

7. The method of claim 6, wherein, The calculation of the weight parameter in the to-be-determined relaxation time distribution function based on the test capacitive reactance spectroscopy data, the theoretical capacitive reactance spectroscopy data, and the penalty term function and the minimization target method comprises: calculating the weight parameter according to the following formula: S(x) = ||C model · x - C exp || 2 + λp(x), where S(x) represents a minimization objective function, C model represents the theoretical reactance spectrum data, C exp represents the test reactance spectrum data, x represents the weight parameter, λ represents a regularization parameter, p(x) represents the penalty term function, and || || represents a norm function.

8. The method of claim 7, wherein, obtaining the penalty term function according to the following formula: p(x) represents the penalty term function, γ(lnτ) represents the to-be-determined relaxation time distribution function, τ represents a relaxation time constant, d() represents differentiation of a logarithmic value, and |||| represents a norm function.

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