A battery model considering nonlinear behavior of battery based on electrochemical impedance spectroscopy and its construction method

Abstract

This invention provides a battery model and construction method based on electrochemical impedance spectroscopy that considers the nonlinear behavior of batteries. These methods belong to the field of battery state monitoring technology. The model adopts the topological structure of the Thevenin model, improves and simplifies the solid-phase diffusion equation, and rederives the Buter-Volmer equation to describe the nonlinear behavior of batteries at low states of charge and high current rates, respectively. The embodiments of the invention provide a battery model suitable for low states of charge and high current rates. This solves the problem of significant loss of accuracy of traditional equivalent circuit models at low states of charge and high current rates, provides a scientific basis for the application of batteries under such extreme conditions, and improves the accuracy of the battery model.

Description

Technical Field

[0001] The present invention relates to the technical field of battery status monitoring, and in particular to the technical field of lithium battery modeling, and specifically to a battery model and a construction method thereof that considers the nonlinear behavior of the battery based on electrochemical impedance spectroscopy. Background Art

[0002] Lithium batteries are the primary energy source for electric vehicles due to their high energy density, long cycle life, and low self-discharge rate. In recent years, demand for larger-capacity lithium batteries has increased to alleviate the range concerns of electric vehicles. However, as capacity increases, safety concerns about large-capacity lithium batteries have become increasingly prominent. Therefore, to minimize serious safety incidents such as thermal runaway in large-capacity lithium batteries and maximize the range of electric vehicles, it is necessary to design a model that can accurately characterize and monitor the battery's status.

[0003] Currently, the main modeling approaches can be categorized into three categories: electrochemical models, equivalent circuit models, and data-driven models. Electrochemical models are based on differential equations that describe the electrochemical reactions within batteries. While these models accurately characterize the internal electrochemical reactions and describe changes in battery composition and structure, they are computationally expensive. Therefore, electrochemical models are typically used to guide battery structure and electrode design, but are difficult to deploy in electric vehicle battery management systems (EV BMSs) with limited computing resources. Data-driven models, such as neural networks and Gaussian process regression, use historical data to estimate the battery state without understanding the internal electrochemical reactions. However, to ensure accurate estimation, they require extensive training data. Furthermore, inappropriate data can lead to model non-convergence, poor generalization, and increased cost. Equivalent circuit models, due to their simple structure and high reliability, are often integrated into BMSs for EV lithium-ion battery state estimation.

[0004] Currently, equivalent circuit models primarily use integer-order components such as resistors and capacitors to describe the battery's voltage response, and battery voltage data is used to identify the resistor and capacitor parameters in the equivalent circuit model. However, existing equivalent circuit models still suffer from insufficient accuracy under various operating conditions. First, due to electrode diffusion effects, integer-order components are insufficient to accurately reflect the battery's voltage response. Furthermore, using low-sampling-rate voltage data for model parameter identification makes it difficult for the equivalent circuit model to describe fast electrochemical reactions within the battery with small time constants, such as charge transfer. Second, the equivalent circuit model is composed of linear components, which cannot accurately represent the battery's nonlinear behavior, especially at high current rates and low states of charge, leading to more severe errors. Electric vehicles often face these application scenarios, necessitating a new mathematical model to improve the accuracy of battery terminal voltage estimation under low states of charge and high current rates.

[0005] Considering that the electrochemical impedance spectroscopy of the battery can accurately capture various electrochemical reactions inside the battery within a wide frequency range, and that the electrochemical principles of the battery can explain and model the nonlinear behavior of the battery, proposing a battery model based on the electrochemical impedance spectroscopy that considers the nonlinear behavior of the battery and its construction method are of great significance for achieving accurate modeling of electric vehicle batteries. Summary of the Invention

[0006] To solve the above problems, the purpose of the present invention is to provide a battery model and a construction method thereof that considers the nonlinear behavior of the battery based on electrochemical impedance spectroscopy, so as to achieve accurate estimation of the terminal voltage of the lithium battery, especially when the battery is at a current rate exceeding 1C and when the battery is below 20% SOC, the nonlinear behavior of the battery is exacerbated.

[0007] In order to achieve the above object, the technical solution provided by the present invention is as follows:

[0008] The present invention provides a battery model based on electrochemical impedance spectroscopy and considering battery nonlinearity, comprising: using a fractional-order Thevenin equivalent circuit model as the topology of the battery model, wherein the Thevenin equivalent circuit model includes a controlled voltage source connected in series, a second resistor, and a parallel network consisting of a first resistor and a first fractional-order constant phase element; the controlled voltage source represents the state of charge (SOC) of the battery surface. surf ) is determined by an open circuit voltage OCV, the second resistor represents the ohmic internal resistance of the battery, the first resistor represents the charge transfer resistance of the battery, and the first fractional-order constant phase element represents the double-layer capacitance of the battery with a diffusion effect; an improved and simplified solid-phase diffusion equation is used to describe the effect of a low state of charge on the controlled voltage source; and a re-derived Buter-Volmer equation is used to describe the effect of a large current rate on the charge transfer resistance;

[0009] The improved and simplified solid phase diffusion equation is expressed as follows:

[0010]

[0011] in, is the surface stoichiometry of the i-pole, i=p indicates the surface solid phase stoichiometry of the positive electrode; i=n indicates the surface solid phase stoichiometry of the negative electrode; It is the difference between the surface solid phase stoichiometry and the average solid phase stoichiometry. When i=p, it means the difference between the surface solid phase stoichiometry of the positive electrode and the average solid phase stoichiometry of the positive electrode; when i=n, ​​it means the difference between the surface solid phase stoichiometry of the negative electrode and the average solid phase stoichiometry of the negative electrode; C s,i is the electrode capacity; τ s,i is the electrode solid phase diffusion time constant; t is time, I is current; is the average stoichiometric coefficient, which is expressed as follows:

[0012]

[0013] in, It is the solid phase stoichiometric number of the i-th electrode when the battery state of charge is 1. When i=p, it indicates that it is the solid phase stoichiometric number of the positive electrode; when i=n, ​​it indicates that it is the solid phase stoichiometric number of the negative electrode; It is the solid-phase stoichiometric number of the i-pole when the battery state of charge is 0. When i=p, it indicates that it is the solid-phase stoichiometric number of the positive electrode; when i=n, ​​it indicates that it is the solid-phase stoichiometric number of the negative electrode. SOC is the battery state of charge obtained by the ampere-hour integration method.

[0014] Based on the calculated surface stoichiometric number of the positive electrode The surface state of charge SOC can be obtained surf :

[0015]

[0016] The expression of the controlled voltage source is:

[0017] Uocv=a1(SOC surf ) 5 +a2(SOC surf ) 4 +a3(SOC surf ) 3 +a4(SOC surf ) 2 +a5(SOC surf ) 1 +a6 (5)

[0018] Where Uocv represents the controlled voltage source; a1, a2, a3, a4, a5, a6 represent the polynomial coefficients; SOC surf Indicates the surface state of charge of the battery.

[0019] When the battery is in a balanced state, the re-derived Butler-Volmer equation is expressed as:

[0020]

[0021] in It represents the charge transfer resistance of the i-pole when the battery is in equilibrium. When i=p, it represents the charge transfer resistance of the positive electrode; when i=n, ​​it represents the charge transfer resistance of the negative electrode; F is the Faraday constant; R is the gas constant; T is the absolute temperature; c i are the coefficients derived from the Butler-Volmer equation; I represents the current.

[0022] When the battery is balanced, the first resistance is expressed as

[0023]

[0024] When the battery is in working state, the re-derived Butler-Volmer equation expression is:

[0025]

[0026] where R ct,i It indicates the charge transfer resistance of the i-pole when the battery is in working state. When i=p, it indicates the charge transfer resistance of the positive electrode; when i=n, ​​it indicates the charge transfer resistance of the negative electrode.

[0027] When the battery is in operation, the first resistance is expressed as

[0028] R1=R ct,p +R ct,n (14)

[0029] A method for constructing a battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery, including constructing the above-mentioned model and the following steps of respectively obtaining the values ​​of the controlled voltage source, the second resistor, the first resistor and the first fractional-order constant phase element under preset typical conditions through preset parameter identification experiments (including pulse discharge test and electrochemical impedance spectroscopy experiment). The pulse discharge test is used to obtain the value of the controlled voltage source under preset typical conditions. The electrochemical impedance spectroscopy experiment is used to obtain the values ​​of the second resistor, the first resistor and the first fractional-order constant phase element under preset typical conditions. Based on the value of the first resistor under preset typical conditions obtained by the electrochemical impedance spectroscopy experiment, the parameters of the Buter-Volmer equation are re-derived when the battery is in equilibrium: the coefficient c i , When the battery state of charge is 1, the solid phase stoichiometric number of the positive or negative electrode and the solid phase stoichiometric number of the positive or negative electrode when the battery state of charge is 0

[0030] Furthermore, the values ​​of the first fractional-order constant phase element, the first resistor, and the second resistor under preset typical conditions are respectively obtained through a preset parameter identification experiment, including:

[0031] By performing electrochemical impedance spectroscopy testing at a preset SOC interval, the values ​​of the first fractional-order constant phase element, the first resistor, and the second resistor at each typical SOC point are obtained:

[0032]

[0033] Among them, Z meas (ω i ) represents the electrochemical impedance spectroscopy at angular frequency ω i Impedance of point measurement; represents the impedance of the equivalent circuit model selected to fit the electrochemical impedance spectroscopy, and its expression is shown in Equation (16); ω i Represents the angular frequency; Ψ1 represents the parameter vector including is the estimated value of the parameter vector Ψ1; R0 is the resistance value of the second resistor; C1 and n1 are the parameters of the fractional-order constant phase element.

[0034]

[0035] Here, j is a complex unit.

[0036] According to the values ​​of the second resistor and the first fractional-order constant phase element at each typical SOC, the values ​​of the second resistor and the first fractional-order constant phase element in the entire SOC range are obtained by polynomial fitting.

[0037] Furthermore, according to the first resistor The values ​​at each typical SOC point are combined with formula (10) to obtain the coefficient c in the re-derived Butler-Volmer equation expression when the battery is in a balanced state through least square fitting. i , solid phase stoichiometry of the electrode and Its objective function is as follows:

[0038]

[0039] in, represents the value of the first resistor at each of the typical SOC points; It represents the charge transfer resistance of the positive electrode when the battery is in equilibrium, calculated by formula (10); represents the charge transfer resistance of the negative electrode when the battery is in equilibrium, calculated by formula (10); Ψ2 represents the parameter vector including is the estimated value of the parameter vector Ψ2; N EIS Indicates the number of frequency points contained in an electrochemical impedance spectrum.

[0040] Furthermore, pulse discharge tests are performed with preset SOC intervals and fixed discharge rates to obtain the values ​​of the controlled voltage source at each typical SOC point. Since the battery is in a balanced state after a certain period of rest (e.g., two hours) after the pulse discharge, the surface state of charge SOC surf Equal to the battery state of charge SOC, the value of the controlled voltage source under each typical SOC is fitted using formula (5) to obtain polynomial coefficients.

[0041] Beneficial effects:

[0042] The present invention provides a battery model and a construction method thereof that considers the nonlinear behavior of the battery based on electrochemical impedance spectroscopy. By combining two electrochemical equations with an equivalent circuit model, the electrochemical equations are used to describe the parameters of the equivalent circuit at a low state of charge and a high current rate. Ultimately, a battery model suitable for low states of charge and high current rates is obtained. This solves the problem that the traditional equivalent circuit model has a significant decrease in model accuracy at low states of charge and high current rates.

[0043] This paper re-derives the Butler-Volmer equation, deriving an expression for the charge-transfer resistance and state of charge of a battery when it is in equilibrium. This provides a parameterized method for identifying Butler-Volmer equation parameters based on electrochemical impedance spectroscopy. Because electrochemical impedance spectroscopy can capture the charge-transfer reaction of a battery at a high sampling rate, this identification method improves the accuracy of battery models at high current rates. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments.

[0045] Figure 1 is a flow chart of constructing a battery model in one embodiment of the present invention;

[0046] Figure 2 is a structural diagram of a battery model in one embodiment of the present invention;

[0047] Figure 3 1 is a schematic diagram of polynomial fitting between the second resistor R0 and SOC in a battery model according to an embodiment of the present invention;

[0048] Figure 4 1 is a schematic diagram of polynomial fitting between the capacitance C1 and the SOC in the first fractional-order constant phase element in the battery model according to one embodiment of the present invention;

[0049] Figure 5 1 is a schematic diagram of polynomial fitting between n1 and SOC in the first fractional-order constant phase element in the battery model of one embodiment of the present invention;

[0050] Figure 6 is a schematic diagram of fitting the relationship between the second resistance and the SOC using the improved Buter-Volmer equation when the battery is in equilibrium in one embodiment of the present invention;

[0051] Figure 7 2 is a schematic diagram showing comparison results between the model predicted voltage and the measured voltage under NEDC operating conditions with current rates of 3C, 2C, and 1C in a battery model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0053] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0054] Figure 1 This is a flow chart of a method for constructing a battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery, provided by one embodiment of the present invention. Figure 1 As shown, the method includes:

[0055] Step 101: Use the traditional integer-order Thevenin equivalent circuit model as the topology of the battery model, but use fractional-order constant-phase elements to replace integer-order capacitors; where, Figure 2 As shown, Figure 2 The present invention provides a structural diagram of a battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery, wherein the battery model includes a controlled voltage source, a second resistor, a first resistor and a parallel element consisting of a first fractional-order constant phase element connected in series; the controlled voltage source is a battery surface state of charge SOC surf It is determined that the second resistor represents the ohmic resistance of the battery, the first resistor represents the charge transfer resistance of the battery, and the first fractional-order constant phase element represents the double-layer capacitance of the battery. Step 102, using the improved and simplified solid-phase diffusion equation to calculate the surface solid-phase stoichiometric coefficients of the positive and negative electrodes. The surface state of charge is solved by using the positive electrode solid-phase stoichiometric coefficient, and then the battery open circuit voltage is calculated based on the surface state of charge. The obtained surface solid-phase stoichiometric coefficients of the positive and negative electrodes and the re-derived Buter-Volmer equation are used to describe the effect of the current rate on the charge transfer resistance. The improved and simplified solid-phase diffusion equation is used to describe the effect of solid-phase diffusion on the controlled voltage source when the battery is at a low state of charge, and the re-derived Buter-Volmer equation is used to describe the effect of the current rate on the charge transfer resistance.

[0056] The present invention combines an improved and simplified solid-phase diffusion and a re-derived Butler-Volmer equation with an equivalent circuit model, using electrochemical equations to describe the equivalent circuit model parameters at different current rates and low states of charge. Ultimately, a battery model suitable for high current rates and low states of charge is obtained. This solves the problem that the traditional equivalent circuit model has difficulty describing the nonlinear behavior of the battery at high current rates and low states of charge, resulting in a significant decrease in model accuracy. Furthermore, since the Butler-Volmer equation is re-derived to obtain an expression for the battery charge transfer resistance and state of charge when the battery is in equilibrium, a parameterization method for identifying Butler-Volmer equation parameters based on electrochemical impedance spectroscopy is provided.

[0057] Based on the fractional-order Thevenin equivalent circuit model, the present invention introduces an improved and simplified solid-phase diffusion equation and a re-derived Buter-Volmer equation, which are used to describe the influence of solid-phase diffusion on Uocv and the influence of current rate on R1 at low charge state, respectively.

[0058] The solid-phase diffusion equation is introduced to describe the effect of solid-phase diffusion on Uocv. Its prototype is Fick's second law, and its expression is:

[0059]

[0060] This expression describes the distribution of lithium ions within the electrode. In fact, solving the open circuit voltage of the battery only focuses on the lithium ion concentration on the electrode surface, that is, the surface solid phase stoichiometry. Therefore, it can be simplified to solve only the surface solid phase stoichiometry of the electrode expression:

[0061]

[0062] Among them, the relationship between the average solid phase stoichiometric coefficient and the battery state of charge is as follows:

[0063]

[0064] Surface solid phase stoichiometry and surface state of charge SOC surf The relationship can be solved by the following expression:

[0065]

[0066] Surface state of charge SOC surf Describe the effect of solid phase diffusion on the open circuit voltage of the battery:

[0067] Uocv=a1(SOC surf ) 5 +a2(SOC surf ) 4+a3(SOC surf ) 3 +a4(SOC surf ) 2 +a5(SOC surf ) 1 +a6 (5)

[0068] The Butler-Volmer equation is introduced to describe the effect of rate on charge transfer resistance R1. The Butler-Volmer equation is written as:

[0069]

[0070] Taking the current I as the variable and taking the derivative of equation (6), we can get the expression of the charge transfer resistance R1 of the electrode:

[0071]

[0072] Formula (7) describes the relationship between the charge transfer resistance R1 and the current when the battery is in working state. When the battery is in equilibrium state, the charge transfer resistance expression of the electrode can be obtained as:

[0073]

[0074] Among them, iavg 0,i can be expressed by the solid phase stoichiometric number, and its expression is:

[0075]

[0076] Substituting equation (9) into equation (8), that is, when the battery is in equilibrium, the charge transfer resistance expression is rewritten as:

[0077]

[0078] When the battery is in balance, the first resistance of the battery is expressed as

[0079]

[0080] When the battery is in operation, isurf0,i is expressed as:

[0081]

[0082] When the battery is operating, the charge transfer resistance of the electrode is rewritten as:

[0083]

[0084] When the battery is in operation, the first resistance is expressed as

[0085] R1=R ct,p +Rct,n (14)

[0086] The meaning of the parameters in the formula in Table 1:

[0087]

[0088] The solid phase diffusion equation described by the present invention greatly simplifies the calculation compared with the original equation, and the surface solid phase electrostoichiometric coefficient is used to solve the battery surface charge state SOC surf Improve the accuracy of the battery model at low states of charge. The Butler-Volmer equation was re-derived to derive expressions for the battery's charge transfer resistance when the battery is in equilibrium and operating. Equation (11) for the charge transfer resistance at equilibrium was used in conjunction with electrochemical impedance spectroscopy to determine parameters. Equation (14) for the charge transfer resistance during operation was used to describe the effect of different current rates on the battery's charge transfer resistance, improving model accuracy at high current rates.

[0089] In the embodiment of the present invention, the positive electrode time diffusion time constant is preset to a fixed value.

[0090] Since the negative electrode time constant has little effect on the model accuracy and is difficult to identify, the solid phase diffusion time constants of the positive and negative electrodes are set to be equal. In the embodiment of the present invention, the positive electrode solid phase diffusion time constant τ is set to be equal to the positive electrode solid phase diffusion time constant τ. s,p Take 120s. This time constant can be deduced through experiments and may have different values ​​for different batteries.

[0091] In the present invention, a preset parameter identification experiment is used to obtain the values ​​of the controlled voltage source, the second resistor, and the parallel element composed of the first resistor and the first fractional-order constant phase element under preset typical conditions; a pulse discharge experiment is used to obtain the values ​​of the controlled voltage source at each typical SOC; and an electrochemical impedance spectroscopy measurement experiment is used to obtain the values ​​of the second resistor, the first resistor, and the first fractional-order constant phase element at each typical SOC.

[0092] The step of obtaining the value of the controlled voltage source through a preset parameter identification experiment includes:

[0093] Obtaining the value of the controlled voltage source at each typical SOC point by performing a discharge pulse test at a preset fixed rate and a preset SOC interval;

[0094] The values ​​of the first fractional-order constant phase element, the first resistor, and the second resistor under preset typical conditions are respectively obtained through a preset parameter identification experiment, including:

[0095] By performing an electrochemical impedance spectroscopy test at a preset SOC interval, the electrochemical impedance spectrum obtained at the current SOC is fitted using a fractional-order Thevenin model to obtain the values ​​of the first resistor, the second resistor, and the first fractional-order constant phase element at the current SOC:

[0096]

[0097] Among them, Z meas Represents the impedance measured at each frequency point in the electrochemical impedance spectroscopy; represents the impedance expression of the Thevenin model, which is shown in formula (16); ω represents the angular frequency; Ψ1 represents the parameter vector including [R0, Requ 1, C1, n1]; R0 is the second resistor; C1 and n1 are the values ​​of the first fractional-order constant phase element; Requ 1 is the value of the first resistor when the battery is balanced.

[0098]

[0099] According to the first resistor The values ​​at each typical SOC point are combined with equations (10) and (11) to obtain the re-derived Butler-Volmer equation expression when the battery is in equilibrium by least square fitting, and its coefficient c is obtained. i , solid phase stoichiometry of the electrode and Its objective function is as follows:

[0100]

[0101] in, represents the value of the first resistor at each of the typical SOC points; It represents the charge transfer resistance of the positive electrode when the battery is in equilibrium, calculated by formula (10); represents the charge transfer resistance of the negative electrode when the battery is in equilibrium, calculated by formula (10); Ψ2 represents the parameter vector including N EIS Indicates the number of frequency points contained in an electrochemical impedance spectrum.

[0102] The value of the controlled voltage source at each typical SOC point is obtained by performing a discharge pulse test at a preset fixed rate and a preset SOC interval. Since the battery is in a balanced state when the controlled voltage source value is obtained, the battery state of charge SOC and the battery surface state of charge SOC surfEqual, combined with equation (5), the expression of the controlled voltage source can be obtained by fitting, thereby obtaining the value of the controlled voltage source in the entire SOC range. The typical SOC point can be determined according to the preset SOC interval. For example, with 5% SOC as the interval, the controlled voltage source values ​​when the SOC is 0%, 5%, 10%, ..., 95%, and 100% can be obtained.

[0103] The SOC intervals used in the electrochemical impedance spectroscopy test are consistent with those used in the discharge pulse test. At each typical SOC point, a high-order polynomial is used to fit the values ​​of the second resistor R0 and the first fractional-order constant phase elements C1 and n1, determining their values ​​across the entire SOC range.

[0104] The present invention combines the solid-phase diffusion equation and the Butler-Volmer equation with the equivalent circuit model, and uses these two equations to describe the parameters of the equivalent circuit model at low state of charge and high current rate. Ultimately, a battery model at low state of charge and high current rate is obtained, solving the problem of significant reduction in accuracy of traditional equivalent circuit models at low state of charge and high current rate. In addition, by re-deriving the Butler-Volmer equation to obtain an expression for the battery charge transfer resistance and state of charge when the battery is in equilibrium, a parameterization method for identifying the Butler-Volmer equation parameters based on electrochemical impedance spectroscopy is provided. Since the electrochemical impedance spectroscopy can capture the charge transfer reaction of the battery at a high sampling rate, this identification method makes the battery model more accurate at high current rate.

[0105] Figure 3 This is a schematic diagram of polynomial fitting of the second resistor R0 and SOC in the battery model based on electrochemical impedance spectroscopy and considering the nonlinear behavior of the battery provided in the above embodiment; Figure 4 This is a schematic diagram of polynomial fitting between the capacitance C1 and SOC in the first fractional-order constant phase element of the battery model based on electrochemical impedance spectroscopy and considering the nonlinear behavior of the battery provided in the above embodiment; Figure 5 This is a schematic diagram of polynomial fitting between n1 and SOC in the first fractional-order constant phase element of the battery model based on electrochemical impedance spectroscopy and considering the nonlinear behavior of the battery provided in the above embodiment; Figure 6 This is a schematic diagram of fitting the relationship between the second resistance Requ1 and the SOC using the re-derived Buter-Volmer equation in the battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery provided in the above embodiment when the battery is in equilibrium; Figure 7 It is a schematic diagram of the comparison results of the model predicted voltage and the measured voltage under NEDC conditions of 3C, 2C and 1C in the battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery provided in the above embodiment.

[0106] This example verifies the proposed battery model in detail. To verify the accuracy of the model at low state of charge and high current rate, the battery is discharged from 100% SOC to 5% SOC in NEDC dynamic operating conditions at 3C, 2C and 1C rates. Figure 7 It can be seen that the model proposed in the embodiment of the present invention can achieve high accuracy in low state of charge and high rate current dynamic conditions. In the low state of charge area (10%-5% SOC), the voltage error is close to 0 and remains stable without significant increase. Among them, the root mean square error of the voltage error in the low state of charge area of ​​the traditional first-order RC model under 3C, 2C, and 1C NEDC conditions is 85.3mV, 70.2mV and 67.1mV respectively. The proposed model is 41.0mV, 45.1mV, and 51.0mV respectively. As the current rate increases, the proposed battery model still maintains a stable error distribution without significant increase. Compared with the traditional first-order RC model, the error of the present invention is smaller, especially in the low state of charge area.

Claims

1. A battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery, characterized in that: include: The fractional-order Thevenin equivalent circuit model is used as the topology of the battery model, wherein the Thevenin equivalent circuit model includes a controlled voltage source connected in series, a second resistor, and a parallel network consisting of a first resistor and a first fractional-order constant phase element; the controlled voltage source represents the battery surface state of charge SOC surf The open circuit voltage OCV is determined, the second resistor represents the ohmic internal resistance of the battery, the first resistor represents the charge transfer resistance of the battery, and the first fractional-order constant phase element represents the double-layer capacitance of the battery with a diffusion effect; a simplified solid-phase diffusion equation is used to describe the effect of a low state of charge on the controlled voltage source; and an improved Butler-Volmer equation is used to describe the effect of a high current rate on the charge transfer resistance; The simplified solid phase diffusion equation is expressed as: in, Where, is the surface stoichiometry of the i-pole, i∈(n,p), n represents the positive electrode, and p represents the negative electrode; is the difference between the surface solid phase stoichiometry and the average solid phase stoichiometry; C s,i is the electrode capacity; τ s,i is the electrode solid phase diffusion time constant; t is time, I is current; is the average stoichiometric coefficient, is the solid phase stoichiometry of the i-pole when the battery state of charge is 1; It is the solid phase stoichiometric number of the i-pole when the battery state of charge is 0; SOC is the battery state of charge obtained by the ampere-hour integration method; The expression of the controlled voltage source is: Uocv=a1(SOC surf ) 5 +a2(SOC surf ) 4 +a3(SOC surf ) 3 +a4(SOC surf ) 2 +a5(SOC surf ) 1 +a6(5) in, Where, Uocv represents the controlled voltage source; a1, a2, a3, a4, a5, a6 represent the polynomial coefficients; SOC surf Indicates the surface charge state of the battery; When the battery is in equilibrium, the improved Buter-Volmer equation is expressed as follows: in It represents the charge transfer resistance of the i-pole when the battery is in equilibrium; F is the Faraday constant; R is the gas constant; T is the absolute temperature; c i are the coefficients of the re-derived Butler-Volmer equation; When the battery is balanced, the first resistance is expressed as: When the battery is in working state, the improved Butler-Volmer equation expression is: where R ct,i It represents the charge transfer resistance of the i-pole when the battery is in working state. When the battery is in operation, the first resistor is represented by R1=R ct,p +R ct,n (14).

2. A method for constructing a battery model based on electrochemical impedance spectroscopy taking into account the nonlinear behavior of the battery, characterized in that: The method comprises constructing the battery model according to claim 1 and the following steps: The values ​​of the controlled voltage source, the second resistor, the first resistor and the first fractional-order constant phase element under preset typical conditions are respectively obtained through a preset parameter identification experiment; the parameter identification experiment includes a pulse discharge test and an electrochemical impedance spectroscopy experiment; the pulse discharge test is used to obtain the value of the controlled voltage source under preset typical conditions; the electrochemical impedance spectroscopy experiment is used to obtain the values ​​of the second resistor, the first resistor and the first fractional-order constant phase element under preset typical conditions; based on the value of the first resistor under preset typical conditions obtained by the electrochemical impedance spectroscopy experiment, the parameters of the Buter-Volmer equation when the battery is in equilibrium are fitted: the coefficient c i , When the battery state of charge is 1, the solid phase stoichiometric number of the positive or negative electrode and the solid phase stoichiometric number of the positive or negative electrode when the battery state of charge is 0 3. The method for constructing a battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery according to claim 2, characterized in that: The values ​​of the first fractional-order constant phase element, the first resistor, and the second resistor under preset typical conditions are respectively obtained through a preset parameter identification experiment, including: obtaining the values ​​of the first fractional-order constant phase element, the first resistor, and the second resistor at each typical SOC point by performing an electrochemical impedance spectroscopy test at a preset SOC interval; and fitting the values ​​of the second resistor and the first fractional-order constant phase element over the entire SOC range based on the values ​​of the second resistor and the first fractional-order constant phase element at each typical SOC.

4. The method for constructing a battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery according to claim 3, characterized in that: According to the value of the first resistor at each typical SOC point, combined with the improved Butler-Volmer equation when the battery is in a balanced state, the coefficient c in the improved Butler-Volmer equation expression when the battery is in a balanced state is obtained by least squares fitting. i , solid phase stoichiometry of the electrode and Its objective function is as follows: in, represents the value of the first resistor at each of the typical SOC points; It represents the charge transfer resistance of the positive electrode when the battery is in equilibrium; represents the charge transfer resistance of the negative electrode when the battery is in equilibrium; Ψ2 represents the parameter vector; is the estimated value of the parameter vector Ψ2; N EIS Indicates the number of frequency points contained in an electrochemical impedance spectrum.

5. The method for constructing a battery model based on electrochemical impedance spectroscopy considering the nonlinear behavior of the battery according to claim 2, characterized in that: The value of the controlled voltage source under preset typical conditions is obtained by a preset parameter identification experiment, including: obtaining the value of the controlled voltage source at each typical SOC point by performing a discharge pulse test at a preset fixed rate and a preset SOC interval; after the battery pulse discharge is completed and the battery rests for a certain period of time, it is in a balanced state, and the surface state of charge SOC surf Equal to the battery state of charge SOC, the value of the controlled voltage source under each typical SOC is fitted using formula (5) to obtain polynomial coefficients.

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