A lithium battery modeling and parameter identification method based on electrochemical impedance spectroscopy

Abstract

The application discloses a lithium battery modeling and parameter identification method based on electrochemical impedance spectroscopy, which is based on lithium battery EIS test data, and is used for effectively and rapidly decomposing the digital method of EIS spectrum, decoupling the kinetic process inside the battery, and introducing an improved relaxation time distribution method to establish a multi-order composite equivalent circuit model of the lithium battery system. The model parameter identification method is achieved by dividing the battery into a low-frequency area and a high-frequency area. The impedance spectrum in the high-frequency area is considered to be related to the ohmic impedance of the battery, and the low-frequency area is considered to be capable of reflecting the semi-diffusion effect of the lithium battery, so that a plurality of constant phase elements CPE are used to characterize, thereby effectively avoiding the error problem caused by the DRT analysis of the non-polarization reaction structure part in the actual battery, and finally, the DRT distribution function gamma(ln tau) is fitted through a regularization method to complete modeling. The equivalent circuit model with high physical significance established by the method can be effectively applied to battery life prediction, battery classification and screening, battery step utilization and the like.

Description

Technical Field

[0001] This invention relates to a method for lithium battery modeling and parameter identification based on electrochemical impedance spectroscopy. Background Technology

[0002] Lithium-ion batteries, due to their high energy density, strong power capability, long cycle life, and relatively light weight, are considered one of the most promising onboard energy sources for electric vehicles (EVs). The pursuit of safer, more reliable, more efficient, and longer-lasting electrochemical energy storage and conversion technologies relies heavily on the support of electrochemical characterization techniques. Existing lithium battery modeling methods mainly include cyclic voltammetry, chronoamperometry (CFC), special performance testing conditions, and electrochemical impedance spectroscopy (EIS).

[0003] Electrochemical impedance spectroscopy (EIS) primarily involves applying multiple sinusoidal signals of different frequencies to the battery and analyzing the collected data to predict its current performance. Compared to other methods, it offers numerous advantages, including shorter processing time, higher accuracy, wider bandwidth, simpler operation, and non-destructive testing. Furthermore, in EIS diagnostic analysis, EIS test data is often fitted to a given equivalent circuit to extract circuit model parameters, thereby analyzing the characteristics of the physicochemical system, such as diffusion coefficients, chemical reaction rates, and microstructural features. It exhibits excellent sensitivity to both external and internal parameters of the electrochemical system and has therefore been widely applied in fields such as new energy, electrocatalysis, and battery modeling and parameter identification.

[0004] Currently, mainstream EIS modeling methods include digital modeling (such as deep learning networks) and mechanistic modeling. Digital modeling methods require large amounts of data input and learning, and do not focus solely on the relationship between battery impedance spectrum and resulting state parameters, resulting in a weaker explanation of battery mechanisms. Mechanistic modeling, on the other hand, can employ electrochemical models, thermodynamic models, coupled models, and equivalent circuit models. The equivalent circuit model has the advantage of not requiring in-depth analysis of the battery's internal electrochemical reactions; it describes the battery's open-circuit voltage, DC internal resistance, and polarization internal resistance through a circuit, thus characterizing the battery's external properties.

[0005] However, existing equivalent circuit model methods still have many shortcomings and deficiencies, such as the need for prior assumptions. For example, the combined effect of internal and external parameters of a lithium battery system will appear on a limited bandwidth, causing its characteristic peaks to overlap or its characteristic time constants to be similar and difficult to separate, thus leading to ambiguity and uncertainty in EIS diagnostic analysis results. On the other hand, because the characteristic time constants of physicochemical processes are relatively close, the impedance spectrum arcs obtained from the tests overlap significantly, making the corresponding impedance spectrum analysis difficult. Summary of the Invention

[0006] To overcome the shortcomings of the existing technology, this invention provides a lithium battery modeling and parameter identification method based on electrochemical impedance spectroscopy, aiming to achieve DRT analysis and parameter identification of lithium battery electrochemical impedance spectra, thereby enabling efficient and high-precision modeling of lithium battery systems.

[0007] The present invention adopts the following technical solution to solve the technical problem:

[0008] The present invention provides a lithium battery modeling and parameter identification method based on electrochemical impedance spectroscopy, characterized by the following steps:

[0009] Step S1: Charge the lithium battery under test to a state of charge (SOC) of 100% and let it stand for a period of time.

[0010] Step S2: After the lithium battery has been left to stand, connect it to the voltage and current sensors and perform electrochemical impedance spectroscopy to obtain impedance data at each frequency point, including the frequency distribution {f1, f2, ..., f...}. m ,…,f M}、Real part of impedance {Z′1,Z′2,…,Z′ m ,…,Z′ M The result of inverting the imaginary part of the impedance is {Z″1, Z″2, ..., Z″}. m ,…,Z″ M}; where f m Z′ represents the m-th frequency. m f represents the m-th frequency m The real part of the impedance, Z″ m f represents the m-th frequency m Invert the imaginary part of the impedance;

[0011] Step S3: Construct the DRT model of the lithium battery under test, consisting of a high-frequency inductor L, an ohmic resistor R0, a DRT distribution function γ(lnτ), and a constant-phase element {Q}. CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K} are connected in series; where Q CPE_k This represents the k-th constant-phase element;

[0012] Step S4: Process the high-frequency and low-frequency impedance data in the DRT model of the lithium battery under test to complete parameter identification.

[0013] Step S4.1: According to {f1,f2,…,f m ,…,f M}, from {Z′1,Z′2,…,Z′ m ,…,Z′ MThe s highest frequency real parts of impedance are selected to identify the ohmic resistor R0, and the identified resistance value of the ohmic resistor R0 is obtained; at the same time, the s highest frequency imaginary parts of impedance are selected to identify the high-frequency inductor L, and the identified inductance value of the high-frequency inductor L is obtained.

[0014] Step S4.2: According to {f1,f2,…,f m ,…,f M}, from {Z′1,Z′2,…,Z′ m ,…,Z′ M} Select the v real parts of the impedance with the lowest frequency and subtract the identification resistance value of the ohmic resistor R0 and the identification inductance value of the high-frequency inductor L respectively to obtain the corrected v real parts of the impedance.

[0015] From {Z′1,Z′2,…,Z′ m ,…,Z′ M} Select the v imaginary parts of impedance with the lowest frequency and subtract the identification resistance value of the ohmic resistor R0 and the identification inductance value of the high-frequency inductor L respectively to obtain the corrected v imaginary parts of impedance.

[0016] By fitting the real and imaginary parts of the corrected v impedances using the least squares method or nonlinear regression, the constant-phase elements Q are obtained. CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K The resistance value;

[0017] Step S4.3: Set the m-th frequency f m The real part of the impedance Z′ m Subtract the identification resistance of the ohmic resistor R0 and the constant phase element Q respectively CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K After obtaining the real part of the impedance, the m-th frequency f is obtained. m The real part of the DRT impedance Thus, the real part of the DRT impedance at each frequency point is obtained.

[0018] The m-th frequency f m Inverting the imaginary part of the impedance Z″ m Subtract the identification inductance value of the high-frequency inductor L and the constant-phase element Q respectively. CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K After obtaining the imaginary part of the impedance, the m-th frequency f is obtained. m Inverting the imaginary part of the DRT impedance Thus, the imaginary part of the DRT impedance at each frequency point is obtained.

[0019] Step S5: Utilize the frequency distribution {f1, f2, ..., f m ,...,f M} and its corresponding real part of the DRT impedance and the imaginary part of the DRT impedance The DRT model of the lithium battery under test is solved to obtain the fitted DRT distribution function γ(lnτ), thereby realizing the parameter identification of the DRT model of the lithium battery under test.

[0020] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the lithium battery modeling and parameter identification method, and the processor is configured to execute the program stored in the memory.

[0021] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program is executed by a processor to perform the steps of the lithium battery modeling and parameter identification method.

[0022] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0023] 1. Compared with existing methods such as cyclic voltammetry and chronoamperometry, the method of the present invention uses EIS testing technology, which has advantages such as high accuracy, wide bandwidth (theoretically covering all physical electrochemical processes), simple operation and non-destructive nature. In addition, EIS is also sensitive to both external and internal parameters of the electrochemical system.

[0024] 2. The method of the present invention addresses the problem that prior assumptions are often required when using equivalent circuit models, i.e., it is necessary to know or pre-assume that there are several characteristic time constants in the impedance spectrum, but this is often difficult to determine. The DRT method can more accurately fit different types of lithium batteries without trial and error, and the training model has high fitting accuracy and good convergence.

[0025] 3. The method of this invention only uses the improved DRT method to fit the polarized part of the lithium battery, and at the same time decouples the non-polarized and non-convergent ohmic internal resistance and constant phase part, thereby improving the DRT test accuracy. Combined with a special DRT function identification algorithm, it realizes rapid modeling.

[0026] 4. The method of this invention makes full use of EIS data across the entire frequency band for partitioning processing, obtains component parameters with strong physical significance, and combines linear fitting to identify them. The model and parameter identification results established by the method of this invention provide a reliable solution for applications in scenarios such as SOC / SOH / RUL / consistency assessment.

[0027] 5. This invention introduces the DRT method to effectively distinguish different internal electrochemical processes, which not only retains the advantages of EIS testing and analysis models, but also overcomes the defects of ambiguity and uncertainty in diagnostic analysis results and difficulty in analysis due to severe overlap of impedance spectrum arcs. Attached Figure Description

[0028] Figure 1 The Nyquist plot of the measured EIS impedance spectrum of the lithium battery in this invention;

[0029] Figure 2a This is a circuit model based on typical DRT analysis techniques;

[0030] Figure 2b This is the circuit model under the DRT analysis technique in this invention;

[0031] Figure 3 This is a diagram showing the current flow direction of the circuit model as the AC impedance frequency changes in this invention.

[0032] Figure 4a This is a graph showing the change in EIS impedance data after improved DRT analysis in this invention.

[0033] Figure 4b This is a schematic diagram of the relaxation time distribution function γ(lnτ) fitted in this invention. Detailed Implementation

[0034] In this embodiment, a lithium battery modeling and parameter identification method based on electrochemical impedance spectroscopy (EIS) is proposed. This method introduces the concept of relaxation time distribution (DRT) function to extend the equivalent circuit model of the lithium battery polarization reaction. The sampling frequency is divided into low-frequency and high-frequency regions for parameter identification, which is then combined with the other regions. The specific steps include:

[0035] Step S1: Charge the lithium battery under test to a state of charge (SOC) of 100% and let it stand for a period of time.

[0036] Step S2: After the lithium battery has been left to stand, connect it to the voltage and current sensors and perform electrochemical impedance spectroscopy (EIS) testing. Based on the obtained EIS data, plot the data from high frequency to low frequency, from left to right. Obtain the impedance data at each frequency point through Fourier transform. To ensure the accuracy of the impedance data, the EIS test should be repeated multiple times, and the reliability of the three sets of test data should be verified according to the KK transformation relationship. Select the set with the smallest average relative error as the final EIS data, including the frequency distribution {f1, f2, ..., f...}. m ,...,f MThe real part of the impedance is {Z′1, Z′2, ..., Z′}. m ,...,Z′ M The result of inverting the imaginary part of the impedance is {Z″1,Z″2,...,Z″}. m ,…,Z″ M}; where f m Z′ represents the m-th frequency. m f represents the m-th frequency m The real part of the impedance, Z″ m f represents the m-th frequency m The imaginary part of the impedance is inverted. At this point, the Nyquist plot of the lithium battery EIS test impedance spectrum can be plotted, as shown below. Figure 1 As shown, this step is mainly to obtain the raw EIS impedance data;

[0037] Step S3: Construct the DRT model of the lithium battery under test, such as... Figure 2b As shown, the model mainly consists of a high-frequency inductor L, an ohmic resistor R0, a DRT distribution function γ(lnτ), and a constant-phase element {Q}. CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K} are connected in series; where Q CPE_k This represents the k-th constant-phase element. It is compared with a commonly used typical DRT model, such as... Figure 2a As shown, the lithium battery DRT model proposed in this invention is more accurate and comprehensive, better reflecting the complex chemical reaction process inside the lithium battery system, and also providing a better fit to EIS impedance data. The DRT distribution function γ(lnτ) represents an infinite number of interconnected RC loops, with the relaxation time constant uniformly distributed within (0, +∞), used to describe the unknown number and intensity of polarization processes inside the battery. At this point, the impedances of each part can be calculated.

[0038] High-frequency inductors and resistors:

[0039] Z RL =R0+j2πfL (1)

[0040] The impedance generated by infinitely many N polarized RC circuits is:

[0041]

[0042] Here, γ(lnτ) = τg(τ);

[0043] The impedance generated by k constant-phase elements, decomposed according to Euler's formula, is:

[0044]

[0045] Step S4: Process the high-frequency and low-frequency impedance data in the DRT model of the lithium battery under test to complete parameter identification.

[0046] Step S4.1: According to {f1,f2,…,f m ,…,f M}, from {Z′1,Z′2,…,Z′ m ,…,Z′ M The s highest frequency real parts of impedance are selected to identify the ohmic resistor R0, and the identified resistance value of the ohmic resistor R0 is obtained; at the same time, the s highest frequency imaginary parts of impedance are selected to identify the high-frequency inductor L, and the identified inductance value of the high-frequency inductor L is obtained.

[0047] like Figure 3 As shown in the figure, a simple analysis at this point yields... Z CPEk Approximately equal to 0, it is assumed that the input impedance can be approximated as only Z. RL The function is to start from the highest test frequency, for example, select 5 consecutive impedance points {Z1, Z2, Z3, Z4, Z5} to perform least squares fitting on the high-frequency inductor L and ohmic resistor R0.

[0048]

[0049] Step S4.2: According to {f1,f2,…,f m ,…,f M}, from {Z′1,Z′2,…,Z′ m ,…,Z′ M} Select the v real parts of the impedance with the lowest frequency and subtract the identification resistance value of the ohmic resistor R0 and the identification inductance value of the high-frequency inductor L respectively to obtain the corrected v real parts of the impedance.

[0050] From {Z′1,Z′2,…,Z′ m ,…,Z′ M} Select the v imaginary parts of impedance with the lowest frequency and subtract the identification resistance value of the ohmic resistor R0 and the identification inductance value of the high-frequency inductor L respectively to obtain the corrected v imaginary parts of impedance.

[0051] By fitting the real and imaginary parts of the corrected v impedances using the least squares method or nonlinear regression, the constant-phase elements Q are obtained. CPE_1 Q CPE_2 ,...,Q CPE_k ,…,Q CPE_K The resistance value;

[0052] like Figure 3 The formula for the direction of current flow and impedance can be simply analyzed as follows: With ZCPEk It is a purely resistive element and at this time:

[0053]

[0054] For example, assuming K=5, it is assumed that the imaginary part of the impedance is entirely composed of the imaginary parts of constant-phase elements, and that the imaginary part of the impedance is mainly composed of constant-phase elements. Furthermore, once the n of the constant-phase element (positively correlated with the impedance angle) is determined, and at least six consecutive frequency points are taken as known variable parameters based on low-frequency EIS data, the impedance can be obtained using the least squares method or other optimal solution methods. The actual values ​​of the parameters of the constant-phase elements {Q1, Q2, Q3, Q4, Q5} are used to construct the parameter values ​​of the constant-phase elements in the equivalent circuit.

[0055] Step S4.3: Set the m-th frequency f m The real part of the impedance Z′ m Subtract the identification resistance of the ohmic resistor R0 and the constant phase element Q respectively CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K After obtaining the real part of the impedance, the m-th frequency f is obtained. m The real part of the DRT impedance Thus, the real part of the DRT impedance at each frequency point is obtained.

[0056] The m-th frequency f m Inverting the imaginary part of the impedance Z″ m Subtract the identification inductance value of the high-frequency inductor L and the constant-phase element Q respectively. CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K After obtaining the imaginary part of the impedance, the m-th frequency f is obtained. m Inverting the imaginary part of the DRT impedance Thus, the imaginary part of the DRT impedance at each frequency point is obtained.

[0057] Depend on Figure 3 The circuit model proposed in this invention consists of three parts. At this point, specific parameters are obtained by fitting the battery's high-frequency inductor L, ohmic resistor R0, and constant-phase elements {Q1, Q2, Q3, Q4, Q5} in the first two steps. Because DRT analytical technology processes data from an ideal multi-series parallel RC network, data preprocessing is required for non-convergent components and purely resistive resistors to further improve function reliability. Therefore, after circuit correction, the impedance composition of the multi-series parallel RC network under pure DRT characterization can be obtained:

[0058]

[0059] The corrected impedance spectrum was obtained, and thus the DRT function was derived, as follows: Figure 4a Corrected EIS impedance spectroscopy used for DRT analysis.

[0060] Step S5: Utilize the frequency distribution {f1, f2, ..., f m ,…,f M} and its corresponding real part of the DRT impedance and the imaginary part of the DRT impedance The DRT model of the lithium battery under test is solved to obtain the fitted DRT distribution function γ(lnτ), thereby realizing the parameter identification of the DRT model of the lithium battery under test.

[0061] The DRT function is the distribution function of polarization resistance in the time constant domain. The process of obtaining the DRT function is a problem of solving a large number of unknowns with a small amount of known information. It is a very typical ill-posed problem in mathematics. Commonly used numerical integration methods cannot obtain stable solutions to this type of problem. It is possible to consider using methods including Fourier transform and regularization. In this embodiment of the invention, the regularization method is used to obtain the DRT analytical function.

[0062] The method primarily involves minimizing the following sum of squares:

[0063]

[0064] Finally, based on the DRT analysis results, the distribution of polarization resistance inside the battery can be briefly analyzed, and its advantages in various applications can be discussed. For example... Figure 4b The DRT distribution function plotted after DRT analysis is presented in this invention. It can be seen that the distribution has several characteristic peaks that characterize the clustering distribution of polarization resistance, effectively reflecting the polarization reaction distribution inside the battery. At this point, the complete lithium battery model based on electrochemical impedance spectroscopy described in this invention is obtained, and the parameters of the model and the proposed DRT analytical function are identified.

[0065] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0066] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0067] In summary, the lithium battery modeling and parameter identification estimation method based on electrochemical impedance spectroscopy (EIS) of this invention is based on lithium battery EIS test data. To effectively and rapidly decompose the EIS spectrum using digital methods and decouple the internal dynamic processes of the battery, an improved relaxation time distribution method is introduced to establish a multi-order composite equivalent circuit model of the lithium battery system. A low-to-high frequency partitioning method is used to identify model parameters. The high-frequency region impedance spectrum is often considered to be related to the battery's ohmic impedance, while the low-frequency region is considered to reflect the semi-diffusion effect of the lithium battery. Multiple constant-phase elements (CPEs) are used for characterization, effectively avoiding the error problem introduced by the DRT analysis caused by the non-polarized reaction structure in actual batteries. Finally, the DRT distribution function γ(lnτ) is fitted using a regularization method to complete the modeling. This method provides methodological guidance for battery mechanism research and mathematical and physical modeling. The established equivalent circuit model with high physical significance can be effectively applied to battery life prediction, battery classification and screening, and battery cascade utilization.

Claims

1. A method for lithium battery modeling and parameter identification based on electrochemical impedance spectroscopy, characterized in that, Includes the following steps: Step S1: Charge the lithium battery under test to a state of charge (SOC) of 100% and let it stand for a period of time. Step S2: After the lithium battery has been left to stand, connect it to the voltage and current sensors and perform electrochemical impedance spectroscopy to obtain impedance data at each frequency point, including the frequency distribution {f1, f2, ..., f...}. m ,…,f M }、Real part of impedance {Z′1,Z′2,…,Z′ m ,…,Z′ M The result of inverting the imaginary part of the impedance is {Z″1, Z″2, ..., Z″}. m ,…,Z″ M }; where f m Z′ represents the m-th frequency. m f represents the m-th frequency m The real part of the impedance, Z″ m f represents the m-th frequency m Invert the imaginary part of the impedance; Step S3: Construct the DRT model of the lithium battery under test, consisting of a high-frequency inductor L, an ohmic resistor R0, a DRT distribution function γ(lnτ), and a constant-phase element {Q}. CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K } are connected in series; where Q CPE_k This represents the k-th constant-phase element; Step S4: Process the high-frequency and low-frequency impedance data in the DRT model of the lithium battery under test to complete parameter identification. Step S4.1: According to {f1,f2,…,f m ,…,f M }, from {Z′1,Z′2,…,Z′ z ,...,Z′ M The s highest frequency real parts of impedance are selected to identify the ohmic resistor R0, and the identified resistance value of the ohmic resistor R0 is obtained; at the same time, the s highest frequency imaginary parts of impedance are selected to identify the high-frequency inductor L, and the identified inductance value of the high-frequency inductor L is obtained. Step S4.2: According to {f1,f2,…,f m ,…,f M }, from {Z′1,Z′2,…,Z′ m ,...,Z′ M } Select the v real parts of the impedance with the lowest frequency and subtract the identification resistance value of the ohmic resistor R0 and the identification inductance value of the high-frequency inductor L respectively to obtain the corrected v real parts of the impedance. From {Z′1,Z′2,...,Z′ m ,…,Z′ M } Select the v imaginary parts of impedance with the lowest frequency and subtract the identification resistance value of the ohmic resistor R0 and the identification inductance value of the high-frequency inductor L respectively to obtain the corrected v imaginary parts of impedance. By fitting the real and imaginary parts of the corrected v impedances using the least squares method or nonlinear regression, the constant-phase elements Q are obtained. CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K The resistance value; Step S4.3: Set the m-th frequency f m The real part of the impedance Z′ m Subtract the identification resistance of the ohmic resistor R0 and the constant phase element Q respectively CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K After obtaining the real part of the impedance, the m-th frequency f is obtained. m The real part of the DRT impedance Thus, the real part of the DRT impedance at each frequency point is obtained. The m-th frequency f m Inverting the imaginary part of the impedance Z″ m Subtract the identification inductance value of the high-frequency inductor L and the constant-phase element Q respectively. CPE_1 Q CPE_2 ,…,Q CPE_k ,…,Q CPE_K After obtaining the imaginary part of the impedance, the m-th frequency f is obtained. m Inverting the imaginary part of the DRT impedance Thus, the imaginary part of the DRT impedance at each frequency point is obtained. Step S5: Utilize the frequency distribution {f1, f2, ..., f m ,…,f M } and its corresponding real part of the DRT impedance and the imaginary part of the DRT impedance The DRT model of the lithium battery under test is solved to obtain the fitted DRT distribution function γ(lnτ), thereby realizing the parameter identification of the DRT model of the lithium battery under test.

2. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store programs that support the processor in executing the lithium battery modeling and parameter identification method of claim 1, and the processor is configured to execute the programs stored in the memory.

3. A computer-readable storage medium storing a computer program, characterized in that, The computer program, when run by the processor, executes the steps of the lithium battery modeling and parameter identification method of claim 1.

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