Modeling method of electrochemical model under high-rate working condition based on experimental analogy

Abstract

The present invention discloses a method for constructing an electrochemical model under high-rate working conditions based on an experimental analogy method, including the determination of key parameters for modeling under high-rate working conditions, the solution of key parameters for high-rate electrochemistry, the construction of a model with variable parameters and high rates, etc. Beneficial effects: The present invention not only inherits the characteristic of good accuracy of traditional electrochemical models under low rates, but also overcomes the defect of poor accuracy of traditional electrochemical models under high-rate working conditions, and solves the problem of low accuracy of previous electrochemical models under low temperature and high rates from the perspective of electrochemical mechanism. The proposed method for establishing the relationship between key parameters and temperature and concentration based on the experimental analogy method solves the problem that conventional electrochemical model parameters are often obtained through half-cell testing, which makes it difficult to disassemble the battery and the model parameters difficult to obtain quickly.

Description

Technical Field

[0001] The present invention relates to a method for constructing a battery model, and in particular to a method for constructing a high-rate working condition electrochemical model based on an experimental analogy method, and belongs to the technical field of power batteries. Background Art

[0002] In order to ensure the safety of power battery packs, optimize the energy efficiency of power battery packs, and extend the cycle life of power battery packs, power battery packs are often equipped with a battery management system to manage them. The main functions of the Battery Management System (BMS) include battery pack state estimation, charge and discharge control, thermal management, and safety management, among which battery state estimation is one of the core functions of BMS. Model-based battery state estimation has the advantages of high estimation accuracy, closed-loop feedback control, and strong adaptability. How to obtain a high-precision model to achieve accurate estimation of battery state has become a hot topic in industry research. At this stage, battery models mainly consider normal temperature or low-rate operating conditions, but as the charge and discharge rate increases or the ambient temperature decreases, the model accuracy will deteriorate.

[0003] Electrochemical models are based on electrochemical kinetics and mass transfer equations. They simulate the internal microscopic reactions and characteristics of a battery during charge and discharge. The physical meaning of the electrochemical model parameters is clear and can be mapped to the battery's terminal voltage. Full-order electrochemical models consist of highly nonlinear and strongly coupled partial differential equations, involving numerous parameters that are difficult to identify and perform real-time calculations. To address this issue, numerous researchers have devoted significant effort to simplifying electrochemical models. There are two main approaches to simplifying electrochemical models. The first is to simplify the model's physical structure, simplifying certain chemical and physical processes within the battery. Common simplified models include single-particle models and average-value models. The second is to simplify from a mathematical perspective, using mathematical transformations to degrade and reconstruct the partial differential equations.

[0004] The main advantages of the two simplified models mentioned above are their simplicity and low computational complexity, which can meet the requirements of online lithium-ion battery applications. Their main disadvantage is that they are not suitable for conditions such as high discharge rates. Under high-rate conditions, liquid phase diffusion becomes the primary controlling factor, which leads to increased concentration differential polarization. Both simplified models treat the liquid phase lithium ion concentration as a constant and ignore the liquid phase concentration differential overpotential, resulting in poor model accuracy under high-rate conditions. Therefore, many high-rate models have been expanded upon the single-particle model and the average value model to ensure accuracy while minimizing computational costs.

[0005] Researchers have found that by adding the liquid phase concentration difference overpotential to the high-rate model, the accuracy of the model will be improved, but there will be fluctuation points with large errors throughout the discharge process, especially the "voltage rebound phenomenon" in the initial discharge stage and the "overpotential rebound phenomenon" in the later discharge stage of the battery at low temperature and high rate (when the battery is working, the difference between the open circuit voltage and the terminal voltage is the overpotential) cannot be accurately simulated. Some researchers have found that the electrochemical parameters of the model are not constant values. Many electrochemical parameters are affected by temperature or concentration, which in turn affects the battery terminal voltage. Therefore, modeling under high-rate conditions needs to consider not only the concentration difference overpotential, but also the voltage rebound phenomenon in the initial discharge stage of the battery under high-rate conditions and the overpotential rebound phenomenon in the later discharge stage. Summary of the Invention

[0006] Purpose of the invention: To address the deficiencies in the prior art, a method for modeling a high-rate electrochemical model based on experimental analogy is proposed. The present invention analyzes and solves the overpotential mechanism based on a quasi-two-dimensional (P2D) model, exploring the causes of voltage recovery in the early stages of discharge and overpotential rebound in the middle and late stages of discharge. Key aspects of high-rate modeling are identified, and key parameters affected by temperature or concentration under high-rate conditions are screened. Furthermore, the relationship between key parameters and temperature and concentration is established based on experimental analogy, ultimately constructing a high-rate electrochemical model with variable parameters.

[0007] Technical solution: A high-rate electrochemical modeling method based on experimental analogy includes the following steps:

[0008] Step 1: Determine the key parameters for high-rate operating condition modeling, including overpotential mechanism analysis and solution, and battery characteristics analysis at high rates;

[0009] Step 2: Solving the key parameters of high-rate electrochemistry, including model parameter acquisition experiments, solving the initial lithium insertion rate, solving the solid-phase diffusion coefficient, and solving the reaction rate constant;

[0010] Step 3: High-rate electrochemical model construction, including variable parameter high-rate model construction;

[0011] Step 4: Verification of high-rate electrochemical model, including verification of variable-parameter high-rate model under different working conditions.

[0012] Preferably, the overpotential mechanism analysis and solution in step 1 includes decomposition of the total overpotential and determination of overpotential influencing parameters of each part;

[0013] Total overpotential decomposition,

[0014] First, solve the open circuit voltage in the electrochemical model. Subtract the terminal voltage from the battery open circuit voltage to obtain the descriptive equation of the total overpotential:

[0015]

[0016] -(η act,p (L,t)-η act,n (0,t)) ②

[0017] -(φ e (L,t)-φ e (0,t)) ③

[0018] +I(t)R SEI ④

[0019] +I(t)R ohm-connect ⑤

[0020] Where, is the open circuit voltage, U t is the terminal voltage, U p and U n are the equilibrium potentials of the positive and negative electrodes, respectively. and are the average lithium insertion rates of the positive and negative electrodes, and are the surface lithium insertion rates of the positive and negative electrodes, η act,p and η act,n Represent the electrochemical reaction overpotential of the positive and negative electrodes, φ e represents the liquid phase potential, L represents the total thickness of the positive electrode, negative electrode and separator, I represents the current, t represents the time, R SEI is the SEI film resistance, R ohm-connect is the connection resistor;

[0021] As can be seen from the above formula, the total overpotential includes: ① solid phase diffusion overpotential, ② electrochemical reaction overpotential, ③ liquid phase overpotential, ④ negative electrode SEI film impedance overpotential, ⑤ connection resistance overpotential;

[0022] Among them, the liquid phase overpotential can be further decomposed into liquid phase ohmic overpotential, solid phase ohmic overpotential and liquid phase concentration difference overpotential:

[0023] φ e (L,t)-φ e (0,t)=η liquid-con (t)+η solid-ohm (t)+η liquid-ohm (t)

[0024] Where η liquid-con (t) is the liquid phase concentration difference overpotential, η solid-ohm (t) is the solid phase ohmic overpotential, ηliquid-ohm (t) is the liquid phase ohmic overpotential;

[0025] Therefore, the total overpotential includes seven overpotentials: solid phase diffusion overpotential, electrochemical reaction overpotential, liquid phase ohmic overpotential, liquid phase concentration difference overpotential, solid phase ohmic overpotential, negative electrode SEI film impedance overpotential, and connection resistance overpotential.

[0026] Preferably, the determination of the overpotential influence parameters of each part includes the determination of the concentration difference overpotential influence parameters, the determination of the electrochemical reaction overpotential influence parameters and the determination of the ohmic overpotential influence parameters;

[0027] Determination of the parameters affecting concentration difference overpotential,

[0028] This includes constructing a description equation for solid-phase diffusion and liquid-phase concentration difference overpotential based on the quasi-two-dimensional P2D (Pseudo-two-Dimensional, P2D) model, and further analyzing the electrochemical parameters that affect the solid-phase diffusion overpotential and the liquid-phase concentration difference overpotential based on the overpotential equation mechanism; the electrochemical parameter that affects the solid-phase diffusion overpotential is the solid-phase diffusion coefficient D s and the radius R of the solid spherical particle s ; The electrochemical parameter that affects the liquid phase concentration difference overpotential is the lithium ion liquid phase transfer coefficient Liquid lithium ion concentration c at the positive and negative electrode current collectors e , effective diffusion coefficient of lithium ions in liquid phase Liquid volume fraction ε e ;

[0029] Determination of parameters affecting electrochemical reaction overpotential,

[0030] First, the electrochemical reaction overpotential describing the electrode is constructed, and then the electrochemical parameters affecting the electrochemical reaction overpotential are analyzed based on the overpotential equation mechanism, including the exchange current density i0, the reaction rate constant k s , initial concentration of solid particles c s,0 , solid phase diffusion coefficient D s and the radius R of the solid spherical particle s ;

[0031] Ohmic overpotential affects parameter determination,

[0032] Based on the quasi-two-dimensional model, the description equation of the ohmic overpotential is constructed, and the electrochemical parameters affecting the ohmic overpotential are obtained based on the overpotential mechanism analysis, including the connection impedance R ohm-connect , liquid conductivity κ eff and SEI film resistance R SEI .

[0033] In summary, the parameters that are most affected by temperature or concentration and play a key role in overpotential under high rate conditions are: (1) solid phase effective diffusion coefficient D s,p 、D s,n , liquid phase effective diffusion coefficient These three parameters control the diffusion rate of lithium ions; (2) the reaction rate constant k p 、k n , these two parameters control the rate of electrochemical reaction; (3) liquid conductivity and These three parameters represent the ionic conductivity.

[0034] Preferably, the battery characteristic analysis at high rate in step 1 includes battery characteristic experiments, analysis of initial voltage rise phenomenon at high rate, analysis of overpotential rebound phenomenon in the middle and late stages at high rate, and determination of key parameters for high rate modeling;

[0035] Battery characteristics experiment,

[0036] Including full-battery constant current operating conditions experiments at different temperatures and different rates, full-battery hybrid power pulse (Hybrid Pulse Power Characteristic, HPPC) experiments at different temperatures, and low-rate experiments at different temperatures, to obtain the relationship curves between fast impedance (fast impedance includes electrochemical reaction impedance and ohmic impedance) and state of charge (State of Charge, SOC) at different temperatures, and full-battery capacity increment (Incremental Capacity, IC) curves at different temperatures;

[0037] Analysis of the initial voltage recovery phenomenon at high rate,

[0038] Based on the relationship curve between fast impedance and SOC at different temperatures and the battery surface temperature characteristic curve at different rates, the reasons for the phenomenon that the terminal voltage first decreases, then increases, and then decreases again at the initial stage of constant current discharge when the ambient temperature is 5°C and the rate is greater than or equal to 3C are analyzed; the analysis shows that there are two reasons, one is caused by fast impedance; the other reason is that the battery itself has a rapid temperature rise, which leads to a decrease in battery polarization.

[0039] Analysis of overpotential rebound phenomenon in the middle and late stages at high rates,

[0040] Based on the relationship curves between overpotential and capacity at different temperatures and different rates and the full-battery IC curve, the reasons for the phenomenon that the overpotential first decreases and then increases in the middle and late stages of discharge when the ambient temperature is 5°C and the rate is below 4C are analyzed; the analysis shows that the increase in the total overpotential in the middle and late stages is mainly caused by the increase in solid-phase diffusion overpotential.

[0041] Determination of key parameters for modeling at high magnification,

[0042] The key parameters affected by temperature and concentration that affect the concentration gradient overpotential, ohmic overpotential, electrochemical overpotential, and the initial voltage recovery and mid-to-late overpotential rebound at high rates were screened. These parameters include the reaction rate constant affecting the electrochemical reaction overpotential, the solid-phase diffusion coefficient and liquid-phase diffusion coefficient affecting concentration gradient polarization, and the liquid-phase conductivity affecting the liquid-phase ohmic overpotential. The key parameters affected by temperature or concentration in each overpotential are shown in Table 1. The key parameters that also affect the initial voltage recovery and mid-to-late overpotential rebound at high rates include the reaction rate constant, the initial solid-phase lithium ion concentration of the positive and negative electrodes, and the solid-phase diffusion coefficient.

[0043] Table 1 Important parameters affected by temperature or concentration in the overpotential of each part

[0044]

[0045] Preferably, the model parameter acquisition experiment in step 2 includes an HPPC experiment of a full cell at different temperatures and a Galvanostatic Intermittent Titration Technique (GITT) experiment of a half cell to obtain the open circuit voltage curve of the full cell at different temperatures, the positive and negative electrode equilibrium potentials of the half cell, and the relationship curve between the solid phase diffusion coefficient and the concentration.

[0046] Preferably, the solution of the initial lithium insertion rate in the step 2 includes calculating the actual open circuit voltage of the full battery based on the positive and negative electrode equilibrium potentials of the half-cell, and adjusting the model parameters within a reasonable range so that the simulated open circuit voltage of the full battery is well consistent with the measured open circuit voltage in combination with the theoretical working range of the positive and negative electrode equilibrium potentials, thereby obtaining the actual working range of the positive and negative electrode equilibrium potentials, and further determining the initial lithium ion insertion rate of the positive and negative electrodes, that is, the initial solid-phase lithium ion concentration of the positive and negative electrodes.

[0047] Preferably, the solution of the solid-phase diffusion coefficient in step 2 includes obtaining the positive and negative electrode solid-phase diffusion coefficients at room temperature (25°C) based on a half-cell GITT experiment and establishing the relationship between the positive and negative electrode solid-phase diffusion coefficients and temperature based on a full-cell HPPC experiment analogy;

[0048] The relationship between the positive and negative electrode solid phase diffusion coefficients and SOC at room temperature (25°C) is obtained by the half-cell GITT experiment and the following formula;

[0049]

[0050] Where D s is the diffusion coefficient, n Mand V M are the molar mass and volume of the active material, S is the area of ​​the battery electrode / electrolyte interface, τ is the duration of the pulse, and ΔE s Indicates the voltage change in steady state, ΔE t represents the change in voltage during the pulse;

[0051] Based on the full-battery HPPC experimental analogy method, the relationship between the positive and negative electrode solid phase diffusion coefficients and temperature is established, and the solution is:

[0052] S1: Transform the above formula,

[0053]

[0054] make A trend coefficient used to express the solid phase diffusion coefficient;

[0055] S2: D at different temperatures obtained based on full-cell HPPC experiments ref The relationship curve between and SOC;

[0056] S3: D of full battery HPPC ref The relationship curve with SOC is compared with the solid phase diffusion coefficient curve in the actual working range of the positive and negative electrodes, and the trend coefficient D of the solid phase diffusion coefficient of the positive and negative electrodes in the actual working range and the solid phase diffusion coefficient of the whole battery is obtained. ref interpersonal relationships;

[0057] S4: Establish the relationship between the solid-phase diffusion coefficients of the positive and negative electrodes and temperature based on the analogy of the full-battery HPPC experiment.

[0058] Preferably, the reaction rate constant in step 2 is solved by solving the fast impedance at different temperatures based on the full-cell HPPC experiment, solving the electrochemical reaction impedance that is greatly affected by temperature, and establishing the relationship between the electrochemical reaction impedance and temperature; considering that there is a certain relationship between the electrochemical impedance and the reaction rate constant, as shown in the following formula, a curve of the relationship between the reaction rate constant and temperature is established based on the analogy of the full-cell HPPC experiment;

[0059] Within a certain range, the inverse of the electrochemical reaction impedance is proportional to the reaction rate constant, which can be expressed as:

[0060]

[0061] Where R act Represents the electrochemical reaction impedance.

[0062] Preferably, the construction of the variable parameter high-rate model in step three refers to adding the liquid phase concentration difference overpotential to the electrochemical average value model, establishing the relationship between the key parameter reaction rate constant and temperature, and establishing the relationship between the solid phase diffusion coefficient and temperature and concentration, thereby establishing a variable parameter high-rate model that adapts to different temperatures.

[0063] Preferably, the model verification under different working conditions and different magnifications in step 4 includes the following steps:

[0064] ST1: Construct model accuracy evaluation indicators, including,

[0065] Mean Absolute Error (MAE),

[0066]

[0067] Root Mean Square error (RMSE),

[0068]

[0069] Maximum Error (ME),

[0070]

[0071] Where, Indicates the measured value, V k It is expressed as an estimated value, and n is n sets of measured and estimated voltage values;

[0072] ST2: Establish a constant parameter model, treat the reaction rate constant and solid-phase diffusion coefficient as constants, and compare them with the high-rate model with variable parameters;

[0073] ST3: Compare the model simulation results with the experimental results at different temperatures and different magnifications.

[0074] Beneficial effects: The present invention analyzes and solves the parameters that are greatly affected by temperature or concentration and play a key role in overpotential under high-rate conditions from the perspective of overpotential mechanism; then, the causes of the voltage recovery phenomenon in the initial discharge and the overpotential rebound phenomenon in the middle and late discharge under high rate are analyzed, and the key links and key parameters for modeling high-rate conditions are determined; further, it is proposed to establish the relationship between key parameters and temperature and concentration through experimental analogy; finally, a high-rate model with variable parameters adapted to high-rate conditions is built. The present invention not only inherits the characteristics of traditional electrochemical models with good accuracy at low rates, but also overcomes the defect of traditional electrochemical models with poor model accuracy under high-rate conditions, and solves the problem of low accuracy of previous electrochemical models at low temperatures and high rates from the perspective of electrochemical mechanism. In addition, the proposed method of establishing the relationship between key parameters and temperature and concentration based on experimental analogy solves the problem that conventional electrochemical model parameters are often obtained through half-cell testing, which makes it difficult to disassemble the battery and the model parameters difficult to obtain quickly. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0076] Figure 1 This is a graph showing the relationship between fast impedance and SOC at different temperatures.

[0077] Figure 2 This is a graph of battery surface temperature at different rates at 5°C.

[0078] Figure 3 This is a graph of discharge voltage at different temperatures and different rates.

[0079] Figure 4 This is the total overpotential diagram at different temperatures and different rates.

[0080] Figure 5 The figure below shows the discharge curve and IC diagram of the battery at 25°C.

[0081] Figure 6 It is the positive and negative electrode equilibrium potential diagram.

[0082] Figure 7 This is a graph of the open circuit voltage of the full battery at 5°C, 25°C, and 55°C.

[0083] Figure 8 This is the open circuit voltage diagram calculated by the least squares method at different temperatures.

[0084] Figure 9It is a working range diagram of the positive and negative electrode equilibrium potential at different temperatures.

[0085] Figure 10 It is the working range diagram of the positive and negative electrode solid phase diffusion coefficients.

[0086] Figure 11 It is a graph of the diffusion coefficient trend at different temperatures.

[0087] Figure 12 It is the solid phase diffusion coefficient diagram of positive and negative electrodes in the working range.

[0088] Figure 13 This is the relationship between the positive and negative solid phase diffusion coefficients and temperature.

[0089] Figure 14 It is the inverse electrochemical impedance diagram at different temperatures.

[0090] Figure 15 This is the fitting diagram of the inverse of electrochemical impedance and temperature.

[0091] Figure 16 This is a comparison chart between the model simulation results and the experimental results at different temperatures and different magnifications.

[0092] Figure 17 This is the overall flow chart of the method for constructing an electrochemical model for high-rate working conditions based on the experimental analogy method. DETAILED DESCRIPTION

[0093] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only 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 are within the scope of protection of the present invention.

[0094] like Figure 17 As shown, a high-rate electrochemical modeling method based on experimental analogy method includes the following steps:

[0095] Step 1: Determine the key parameters for high-rate operating condition modeling, including overpotential mechanism analysis and solution, and battery characteristics analysis at high rates.

[0096] The overpotential mechanism analysis and solution in step 1 include the decomposition of the total overpotential and the determination of the overpotential influencing parameters of each part.

[0097] Total overpotential decomposition,

[0098] First, solve the open circuit voltage in the electrochemical model. Subtract the terminal voltage from the battery open circuit voltage to obtain the descriptive equation of the total overpotential:

[0099]

[0100] -(η act,p (L,t)-η act,n (0,t)) ②

[0101] -(φ e (L,t)-φ e (0,t)) ③

[0102] +I(t)R SEI ④

[0103] +I(t)R ohm-connect ⑤

[0104] Where, is the open circuit voltage, U t is the terminal voltage, U p and U n are the equilibrium potentials of the positive and negative electrodes, respectively. and are the average lithium insertion rates of the positive and negative electrodes, and are the surface lithium insertion rates of the positive and negative electrodes, η act,p and η act,n Represent the electrochemical reaction overpotential of the positive and negative electrodes, φ e represents the liquid phase potential, L represents the total thickness of the positive electrode, negative electrode and separator, I represents the current, t represents the time, R SEI is the SEI film resistance, R ohm-connect For connecting resistors.

[0105] As can be seen from the above formula, the total overpotential includes: ① solid phase diffusion overpotential, ② electrochemical reaction overpotential, ③ liquid phase overpotential, ④ negative electrode SEI film impedance overpotential, and ⑤ connection resistance overpotential.

[0106] Among them, the liquid phase overpotential can be further decomposed into liquid phase ohmic overpotential, solid phase ohmic overpotential and liquid phase concentration difference overpotential:

[0107] φ e (L,t)-φ e (0,t)=η liquid-con (t)+η solid-ohm (t)+η liquid-ohm (t)

[0108] Where η liquid-con (t) is the liquid phase concentration difference overpotential, η solid-ohm (t) is the solid phase ohmic overpotential, η liquid-ohm (t) is the liquid phase ohmic overpotential.

[0109] Therefore, the total overpotential includes seven overpotentials: solid phase diffusion overpotential, electrochemical reaction overpotential, liquid phase ohmic overpotential, liquid phase concentration difference overpotential, solid phase ohmic overpotential, negative electrode SEI film impedance overpotential, and connection resistance overpotential.

[0110] The determination of the overpotential influence parameters of each part includes the determination of the concentration difference overpotential influence parameters, the determination of the electrochemical reaction overpotential influence parameters and the determination of the ohmic overpotential influence parameters.

[0111] Determination of the parameters affecting concentration difference overpotential,

[0112] This includes constructing a description equation for solid-phase diffusion and liquid-phase concentration difference overpotential based on the quasi-two-dimensional P2D (Pseudo-two-Dimensional, P2D) model, and further analyzing the electrochemical parameters that affect the solid-phase diffusion overpotential and the liquid-phase concentration difference overpotential based on the overpotential equation mechanism; the electrochemical parameter that affects the solid-phase diffusion overpotential is the solid-phase diffusion coefficient D s and the radius R of the solid spherical particle s ; The electrochemical parameter that affects the liquid phase concentration difference overpotential is the lithium ion liquid phase transfer coefficient Liquid lithium ion concentration c at the positive and negative electrode current collectors e , effective diffusion coefficient of lithium ions in liquid phase Liquid volume fraction ε e .

[0113] Determination of parameters affecting electrochemical reaction overpotential,

[0114] First, the electrochemical reaction overpotential describing the electrode is constructed, and then the electrochemical parameters affecting the electrochemical reaction overpotential are analyzed based on the overpotential equation mechanism, including the exchange current density i0, the reaction rate constant k s , initial concentration of solid particles c s,0 , solid phase diffusion coefficient D s and the radius R of the solid spherical particle s .

[0115] Ohmic overpotential affects parameter determination,

[0116] Based on the quasi-two-dimensional model, the description equation of the ohmic overpotential is constructed, and the electrochemical parameters affecting the ohmic overpotential are obtained based on the overpotential mechanism analysis, including the connection impedance R ohm-connect , liquid conductivity κ eff and SEI film resistance R SEI .

[0117] In summary, the parameters that are most affected by temperature or concentration and play a key role in overpotential under high rate conditions are: (1) solid phase effective diffusion coefficient D s,p 、D s,n, liquid phase effective diffusion coefficient These three parameters control the diffusion rate of lithium ions; (2) the reaction rate constant k p 、k n , these two parameters control the rate of electrochemical reaction; (3) liquid conductivity and These three parameters represent the ionic conductivity.

[0118] The battery characteristic analysis at high rate in step 1 includes battery characteristic experiments, analysis of initial voltage recovery phenomenon at high rate, analysis of overpotential rebound phenomenon in the middle and late stages at high rate, and determination of key parameters for high rate modeling.

[0119] Battery characteristics experiment,

[0120] It includes full-battery constant current operating conditions experiments at different temperatures and different rates, full-battery hybrid power pulse (Hybrid Pulse Power Characteristic, HPPC) experiments at different temperatures, and low-rate experiments at different temperatures. The relationship curves between fast impedance (fast impedance includes electrochemical reaction impedance and ohmic impedance) and state of charge (SOC) at different temperatures and the full-battery capacity increment (IC) curve at different temperatures are obtained.

[0121] The basic battery parameters for the battery characterization experiments are shown in Table 2. The constant current operating condition experiment specifically involved discharging the full battery at current rates of 0.5C, 1C, 2C, 3C, 4C, and 6C at 5°C, 25°C, and 55°C. The HPPC experiment was conducted over a temperature range of 5°C to 65°C, with an HPPC experiment performed every 5°C and a 2C pulse current. The low-rate experiment specifically involved discharging the battery at a current rate of 1 / 25C at 5°C, 25°C, and 55°C, with upper and lower cutoff voltages of 4.2V and 2.5V, respectively.

[0122] Table 2 Basic characteristics of ternary lithium-ion batteries

[0123]

[0124] Analysis of the initial voltage recovery phenomenon at high rate,

[0125] Based on the relationship curve between fast impedance and SOC at different temperatures, such as Figure 1 As shown in the figure, the battery surface temperature characteristic curves at different rates are as follows: Figure 2 As shown in the figure, when the ambient temperature is 5℃ and the rate is greater than or equal to 3C, the terminal voltage first decreases, then increases, and then decreases again in the initial stage of constant current discharge. Figure 3 As shown. Combined Figure 1-3 Analysis shows that there are two possible reasons for the initial rise in terminal voltage: ① At the beginning and end of discharge, the impedance across the battery is large, and this phenomenon is more pronounced at low temperatures. At the beginning, the current density and impedance are both large, causing the battery's terminal voltage to drop rapidly. As discharge continues, the impedance begins to decrease rapidly, while the current density remains constant. At this point, the instantaneous overpotential decreases, causing the battery's terminal voltage to rebound. ② At high rates, the battery's temperature rises rapidly. As the battery temperature rises, the battery polarization effect decreases, causing the overpotential to decrease, which also causes the battery's terminal voltage to rebound.

[0126] Analysis of overpotential rebound phenomenon in the middle and late stages at high rates,

[0127] Based on the relationship curve between overpotential and capacity at different temperatures and different rates, such as Figure 4 As shown in the figure, the reason why the overpotential first decreases and then increases when the ambient temperature is 5°C and the rate is below 4°C is analyzed. Figure 5 The reason for the overpotential rebound phenomenon in the middle and late stages is obtained from the analysis of the full battery IC curve: at 5°C, with the increase of the rate, Figure 4 The total overpotential from point A to point B decreases, which is mainly related to temperature, while the overpotential from point B to point C (<4°C) increases, with concentration becoming the main factor affecting the increase in overpotential. In other words, the increase in the total overpotential in the middle and late stages is mainly caused by the increase in solid-phase diffusion overpotential.

[0128] Determination of key parameters for modeling at high magnification,

[0129] The key parameters affected by temperature and concentration that affect the concentration difference overpotential, ohmic overpotential, electrochemical overpotential, and the initial voltage recovery and mid-to-late overpotential rebound phenomena at high rates were screened. These parameters are the reaction rate constant that affects the electrochemical reaction overpotential, the solid-phase diffusion coefficient and liquid-phase diffusion coefficient that affect concentration difference polarization, and the liquid-phase conductivity that affects the liquid-phase ohmic overpotential. The important parameters affected by temperature or concentration in each part of the overpotential are shown in Table 3. The key parameters that also affect the initial voltage recovery phenomenon at high rates and the mid-to-late overpotential rebound phenomenon at high rates include the reaction rate constant, the initial solid-phase lithium ion concentration of the positive and negative electrodes, and the solid-phase diffusion coefficient.

[0130] Table 3 Important parameters affected by temperature or concentration in the overpotential of each part

[0131]

[0132] Step 2: Solve the key parameters of high-rate electrochemistry, including model parameter acquisition experiments, solution of initial lithium insertion rate, solution of solid-phase diffusion coefficient and solution of reaction rate constant.

[0133] The model parameter acquisition experiment in the second step includes the HPPC experiment of the full cell at different temperatures and the Galvanostatic Intermittent Titration Technique (GITT) experiment of the half cell to obtain the equilibrium potential of the half cell, as Figure 6 shown, and the open circuit voltage curve of the full cell at different temperatures, as Figure 7 shown.

[0134] The solution of the initial lithium intercalation rate in the second step refers to using the least squares method to subtract the negative electrode equilibrium potential from the positive electrode equilibrium potential of the half cell, that is, the calculated open circuit voltage of the full cell, so that the sum of the squares of the deviations from the measured open circuit voltage of the full cell is minimized, as Figure 8 shown. Statistically analyze the actual working ranges of the positive and negative electrode equilibrium potentials at different temperatures, as Figure 9 shown. It is statistically obtained that the main working range of the positive electrode is 0.177 < x < 1, and the main working range of the negative electrode is around 0.092 < x < 0.925. Combining the working ranges of the positive and negative electrode equilibrium potentials, by adjusting the model parameters within a reasonable range, the simulated voltage has a good agreement with the experimental voltages at different temperatures and different rates, and the initial lithium ion intercalation rates of the positive and negative electrodes are determined to be 0.345 and 0.95 respectively.

[0135] The solution of the solid phase diffusion coefficient in the second step includes obtaining the solid phase diffusion coefficients of the positive and negative electrodes at room temperature (25 °C) based on the half cell GITT experiment and establishing the relationship between the solid phase diffusion coefficients of the positive and negative electrodes and temperature by analogy based on the full cell HPPC experiment.

[0136] The solution of the solid phase diffusion coefficients of the positive and negative electrodes at room temperature (25 °C) based on the half cell GITT experiment is to solve the relationship curve between the solid phase diffusion coefficients of the positive and negative electrodes and SOC at room temperature through the half cell GITT experiment and the following formula, as Figure 10 shown.

[0137]

[0138] In the formula, D s is the diffusion coefficient, n M and V M are the molar mass and volume of the active material respectively, S is the area of the battery electrode / electrolyte interface, τ is the duration of the pulse, ΔE s represents the voltage change at steady state, and ΔE t represents the voltage change during the pulse.

[0139] The method for establishing the relationship between the solid phase diffusion coefficients of the positive and negative electrodes and temperature by analogy based on the full cell HPPC experiment is as follows:

[0140] S1: Transform the above formula,

[0141]

[0142] make A trend coefficient used to express the solid-phase diffusion coefficient.

[0143] S2: D at different temperatures obtained based on full-cell HPPC experiments ref The relationship curve between and SOC, such as Figure 11 shown.

[0144] S3: Convert the SOC of the actual working range of the positive and negative electrode solid phase diffusion coefficients to 0 to 1, such as Figure 12 As shown, the SOC range of the positive and negative electrode solid phase diffusion coefficients is ref The SOC range of the full battery HPPC is ref The relationship curve with SOC is compared with the solid phase diffusion coefficient curve in the positive and negative electrode working range to analyze Figure 11 and 12 Solve for D ref The diffusion characteristics displayed externally are the diffusion characteristics of the entire battery. In the early stage of discharge, the positive electrode solid-phase diffusion characteristics are displayed externally, and in the middle and late stages of discharge, the negative electrode solid-phase diffusion characteristics are displayed externally.

[0145] S4: Based on the full battery HPPC experiment analogy, the relationship between the positive and negative electrode solid phase diffusion coefficients and temperature is established. Figure 11 The relationship between the first low peak and temperature is taken as the relationship between the positive electrode solid phase diffusion coefficient and temperature, and the relationship between the second high peak and temperature is taken as the relationship between the negative electrode solid phase diffusion coefficient and temperature. The Arrhenius equation is used to fit the relationship between the temperature coefficient of the positive and negative electrode diffusion and temperature. The temperature coefficient of the positive and negative electrode diffusion and temperature are converted into a linear relationship by conversion. The fitting curve is as follows Figure 13 As shown, Figure 13 (a) is the positive electrode diffusion coefficient D s,T,p The relationship curve with temperature, Figure 13 (b) is the cathode diffusion coefficient D s,T,n The relationship curve between temperature and Arrhenius equation is shown in formula (10):

[0146]

[0147] Where D s,T is the temperature coefficient of diffusion coefficient, a s and b s is the temperature fitting coefficient of the diffusion coefficient, and T represents the temperature.

[0148] The reaction rate constant in step 2 is solved based on the fast impedance at different temperatures obtained from the full-cell HPPC experiment, the electrochemical reaction impedance that is greatly affected by temperature is solved, and the relationship between the electrochemical reaction impedance and temperature is established; considering that there is a certain relationship between the electrochemical impedance and the reaction rate constant, as shown in the following formula, a curve of the relationship between the reaction rate constant and temperature is established based on the analogy of the full-cell HPPC experiment;

[0149] The relationship between the reaction rate constant and temperature was established by analogy with the full-cell HPPC experiment, which is:

[0150] First, the relationship between electrochemical reaction impedance and temperature is established. Based on the full-cell HPPC experiment, the fast impedance at different temperatures is obtained, such as Figure 1 As shown in , the fast impedance mainly includes electrochemical reaction impedance and ohmic impedance, among which the relationship between electrochemical impedance and temperature conforms to the Arrhenius equation. Figure 1 It can be seen that after the temperature exceeds 55℃, the fast impedance is small and does not change much. From 55℃ to 65℃, the fast impedance drops by less than 1mΩ, which means that the temperature change at this time has little effect on the battery fast impedance. Therefore, taking the fast impedance at 65℃ as the benchmark, the electrochemical reaction impedance that is greatly affected by temperature can be obtained. The relationship between electrochemical reaction impedance and temperature is obtained when SOC=50%. Figure 14 In order to establish the inverse electrochemical impedance at different temperatures, the inverse electrochemical impedance and temperature are converted into a linear relationship by conversion, and the fitting curve is as follows Figure 15 shown.

[0151] Next, the relationship between electrochemical impedance and reaction rate is established. Within a certain range, the inverse of the electrochemical reaction impedance is proportional to the reaction rate constant, which can be expressed as:

[0152]

[0153] Where R act Represents the electrochemical reaction impedance.

[0154] Finally, through the relationship between electrochemical reaction impedance and temperature, a curve of the relationship between reaction rate constant and temperature was established based on the analogy of the full-cell HPPC experiment.

[0155] Step 3: High-rate electrochemical model construction, including variable parameter high-rate model construction;

[0156] The construction of the variable parameter high-rate model in step three refers to adding the liquid phase concentration difference overpotential to the electrochemical average value model, establishing the relationship between the key parameter reaction rate constant and temperature, and establishing the relationship between the solid phase diffusion coefficient and temperature and concentration, thereby establishing a variable parameter high-rate model that adapts to different temperatures.

[0157] Step 4: Verification of high-rate electrochemical model, including verification of variable-parameter high-rate model under different working conditions.

[0158] The model verification under different working conditions and different magnifications in step 4 includes the following steps:

[0159] ST1: Construct model accuracy evaluation indicators, including,

[0160] Mean Absolute Error (MAE),

[0161]

[0162] Root Mean Square error (RMSE),

[0163]

[0164] Maximum Error (ME),

[0165]

[0166] Where, Indicates the measured value, V k It is expressed as an estimated value, and n is n sets of measured and estimated voltage values;

[0167] ST2: Establish a constant parameter model, treat the reaction rate constant and solid-phase diffusion coefficient as constants, and compare them with the high-rate model with variable parameters;

[0168] ST3: Compare the model simulation results with the experimental results at different temperatures and different magnifications.

[0169] Model verification under different working conditions refers to verification under low-rate and high-rate working conditions at different temperatures (5℃, 25℃, 55℃), such as Figure 16 As shown in the figure, discharge conditions with a discharge rate of 2C or less are referred to as low-rate conditions, while discharge conditions with a discharge rate greater than 2C are referred to as high-rate conditions. Furthermore, a constant parameter model is established, treating the reaction rate constant and solid-phase diffusion coefficient as constants, and compared with a high-rate model with variable parameters. Finally, the model simulation results are compared with experimental results at different temperatures and discharge rates.

[0170] The results show that under low-rate conditions, the accuracy of the two models is close, with the maximum error within 35mV. Under high-rate conditions (≤6C), the variable-parameter high-rate model can better simulate the voltage rise in the initial stage and the overpotential rebound phenomenon in the middle and late stages. The maximum error under 4C conditions is within 40mV, as shown in Table 4-6 below:

[0171] Table 4 Simulation error statistics of lower terminal voltage at different rates at 55°C

[0172]

[0173] Table 5 Statistics of simulation errors of lower terminal voltage at different magnifications at 25℃

[0174]

[0175] Table 6 Statistics of simulation error of lower-end voltage at different magnifications at 5℃

[0176]

[0177] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A high-rate electrochemical modeling method based on experimental analogy, characterized by: The following steps are involved: Step 1: Determine the key parameters for high-rate operating condition modeling, including overpotential mechanism analysis and solution, and battery characteristics analysis at high rates; The overpotential mechanism analysis and solution in step 1 includes decomposition of the total overpotential and determination of overpotential influencing parameters of each part; Total overpotential decomposition, First, solve the open circuit voltage in the electrochemical model. Subtract the terminal voltage from the battery open circuit voltage to obtain the descriptive equation of the total overpotential: Where, is the open circuit voltage, U t is the terminal voltage, U p and U n are the equilibrium potentials of the positive and negative electrodes, respectively. and are the average lithium insertion rates of the positive and negative electrodes, and are the surface lithium insertion rates of the positive and negative electrodes, η act,p and η act,n Represent the electrochemical reaction overpotential of the positive and negative electrodes, φ e represents the liquid phase potential, L represents the total thickness of the positive electrode, negative electrode and separator, I represents the current, t represents the time, R SEI is the SEI film resistance, R ohm-connect is the connection resistor; From the above formula, the total overpotential includes: ① solid phase diffusion overpotential, ② electrochemical reaction overpotential, ③ liquid phase overpotential, ④ negative electrode SEI film impedance overpotential, ⑤ connection resistance overpotential; Among them, the liquid phase overpotential is further decomposed into liquid phase ohmic overpotential, solid phase ohmic overpotential and liquid phase concentration difference overpotential: f e (L,t)-φ e (0,t)=η liquid-con (t)+η solid-ohm (t)+η liquid-ohm (t) Where η liquid-con (t) is the liquid phase concentration difference overpotential, η solid-ohm (t) is the solid phase ohmic overpotential, η liquid-ohm (t) is the liquid phase ohmic overpotential; Therefore, the total overpotential includes seven overpotentials: solid phase diffusion overpotential, electrochemical reaction overpotential, liquid phase ohmic overpotential, liquid phase concentration difference overpotential, solid phase ohmic overpotential, negative electrode SEI film impedance overpotential, and connection resistance overpotential. Step 2: Solving the key parameters of high-rate electrochemistry, including model parameter acquisition experiments, solving the initial lithium insertion rate, solving the solid-phase diffusion coefficient, and solving the reaction rate constant; Step 3: High-rate electrochemical model construction, including variable parameter high-rate model construction; The variable parameter high rate model construction in step 3 refers to adding the liquid phase concentration difference overpotential to the electrochemical average value model, establishing the relationship between the key parameter reaction rate constant and temperature, and establishing the relationship between the solid phase diffusion coefficient and temperature and concentration, thereby establishing a variable parameter high rate model that adapts to different temperatures; Step 4: Verification of high-rate electrochemical model, including verification of variable-parameter high-rate model under different working conditions.

2. The high-rate electrochemical modeling method based on the experimental analogy method according to claim 1 is characterized in that: The determination of the overpotential influence parameters of each part includes the determination of the concentration difference overpotential influence parameter, the determination of the electrochemical reaction overpotential influence parameter and the determination of the ohmic overpotential influence parameter; Determination of the parameters affecting concentration difference overpotential, This includes constructing a description equation for solid-phase diffusion and liquid-phase concentration difference overpotential based on a quasi-two-dimensional P2D model, and further analyzing the electrochemical parameters that affect the solid-phase diffusion overpotential and liquid-phase concentration difference overpotential based on the overpotential equation mechanism; the electrochemical parameter that affects the solid-phase diffusion overpotential is the solid-phase diffusion coefficient D s and the radius R of the solid spherical particle s ; The electrochemical parameter that affects the liquid phase concentration difference overpotential is the lithium ion liquid phase transfer coefficient Liquid lithium ion concentration c at the positive and negative electrode current collectors e , effective diffusion coefficient of lithium ions in liquid phase Liquid volume fraction ε e ; Determination of parameters affecting electrochemical reaction overpotential, First, the electrochemical reaction overpotential describing the electrode is constructed, and then the electrochemical parameters affecting the electrochemical reaction overpotential are analyzed based on the overpotential equation mechanism, including the exchange current density i0, the reaction rate constant k s , initial concentration of solid particles c s,0 , solid phase diffusion coefficient D s and the radius R of the solid spherical particle s ; Ohmic overpotential affects parameter determination, Based on the quasi-two-dimensional model, the description equation of the ohmic overpotential is constructed, and the electrochemical parameters affecting the ohmic overpotential are obtained based on the overpotential mechanism analysis, including the connection impedance R ohm-connect , liquid conductivity κ eff and SEI film resistance R SEI .

3. The high-rate electrochemical modeling method based on the experimental analogy method according to claim 1 is characterized in that: The battery characteristic analysis at high rate in step 1 includes battery characteristic experiments, analysis of the initial voltage rise phenomenon at high rate, analysis of the overpotential rebound phenomenon in the middle and late stages at high rate, and determination of key parameters for high rate modeling; Battery characteristics experiment, Including full-battery constant current operating conditions experiments at different temperatures and different rates, full-battery mixed power pulse experiments at different temperatures, and small rate experiments at different temperatures, to obtain the relationship curves between fast impedance and state of charge at different temperatures, and full-battery capacity increment curves at different temperatures; Analysis of the initial voltage recovery phenomenon at high rate, Based on the relationship curves between fast impedance and SOC at different temperatures and the battery surface temperature characteristic curves at different rates, we analyze the reasons why the terminal voltage first decreases, then increases, and then decreases again at the beginning of constant current discharge when the ambient temperature is 5°C and the rate is greater than or equal to 3°C; Analysis of overpotential rebound phenomenon in the middle and late stages at high rates, Based on the relationship curves between overpotential and capacity at different temperatures and rates, as well as the full-battery IC curve, we analyze the reasons why the overpotential first decreases and then increases in the middle and late stages of discharge when the ambient temperature is 5°C and the rate is below 4°C. Determination of key parameters for modeling at high magnification, The key parameters affected by temperature and concentration that affect the concentration difference overpotential, ohmic overpotential, electrochemical overpotential, initial voltage recovery at high rate and overpotential rebound in the middle and late stages of discharge are screened, which are the reaction rate constant affecting the electrochemical reaction overpotential, the solid-phase diffusion coefficient and liquid-phase diffusion coefficient affecting the concentration difference polarization, and the liquid-phase conductivity affecting the liquid-phase ohmic overpotential; at the same time, the key parameters that affect the initial voltage recovery phenomenon at high rate and the overpotential rebound phenomenon in the middle and late stages of discharge include the reaction rate constant, the initial concentration of solid-phase lithium ions in the positive and negative electrodes, and the solid-phase diffusion coefficient.

4. The high-rate electrochemical modeling method based on the experimental analogy method according to claim 1 is characterized in that: The model parameter acquisition experiment in step 2 includes an HPPC experiment of the full cell at different temperatures and a constant current intermittent titration technology experiment of the half cell, to obtain the open circuit voltage curve of the full cell at different temperatures, the positive and negative electrode equilibrium potentials of the half cell, and the relationship curve between the solid phase diffusion coefficient and the concentration.

5. The high-rate electrochemical modeling method based on the experimental analogy method according to claim 1 is characterized in that: The solution to the initial lithium insertion rate in step 2 includes calculating the actual open circuit voltage of the full battery based on the positive and negative electrode equilibrium potentials of the half-battery, and adjusting the model parameters within a reasonable range to make the simulated open circuit voltage of the full battery consistent with the measured open circuit voltage in combination with the theoretical working range of the positive and negative electrode equilibrium potentials, thereby obtaining the actual working range of the positive and negative electrode equilibrium potentials, and further determining the initial lithium ion insertion rate of the positive and negative electrodes, that is, the initial solid-phase lithium ion concentration of the positive and negative electrodes.

6. The high-rate electrochemical modeling method based on experimental analogy according to claim 1 is characterized in that: The solution of the solid phase diffusion coefficient in step 2 includes obtaining the positive and negative electrode solid phase diffusion coefficients at room temperature based on the half-cell GITT experiment and establishing the relationship between the positive and negative electrode solid phase diffusion coefficients and temperature based on the full-cell HPPC experiment analogy; The relationship between the solid-phase diffusion coefficients of the positive and negative electrodes at room temperature and SOC is obtained by using the half-cell GITT experiment and the following formula; Where D s is the diffusion coefficient, n M and V M are the molar mass and volume of the active material, S is the area of ​​the battery electrode / electrolyte interface, τ is the duration of the pulse, and ΔE s Indicates the voltage change in steady state, ΔE t represents the change in voltage during the pulse; Based on the full-battery HPPC experimental analogy method, the relationship between the positive and negative electrode solid phase diffusion coefficients and temperature is established, and the solution is: S1: Transform the above formula, make A trend coefficient used to express the solid phase diffusion coefficient; S2: D at different temperatures obtained based on full-cell HPPC experiments ref The relationship curve between and SOC; S3: D of full battery HPPC ref The relationship curve with SOC is compared with the solid phase diffusion coefficient curve in the actual working range of the positive and negative electrodes, and the trend coefficient D of the solid phase diffusion coefficient of the positive and negative electrodes in the actual working range and the solid phase diffusion coefficient of the whole battery is obtained. ref interpersonal relationships; S4: Establish the relationship between the solid-phase diffusion coefficients of the positive and negative electrodes and temperature based on the analogy of the full-battery HPPC experiment.

7. The high-rate electrochemical modeling method based on experimental analogy according to claim 1 is characterized in that: The reaction rate constant in step 2 is solved based on the fast impedance at different temperatures obtained from the full-cell HPPC experiment, the electrochemical reaction impedance affected by temperature is solved, and the relationship between the electrochemical reaction impedance and temperature is established; considering the relationship between the electrochemical impedance and the reaction rate constant, as shown in the following formula, a curve of the relationship between the reaction rate constant and temperature is established based on the analogy of the full-cell HPPC experiment; The inverse of the electrochemical reaction impedance is proportional to the reaction rate constant, which can be expressed as: Where R act Represents the electrochemical reaction impedance.

8. The high-rate electrochemical modeling method based on experimental analogy according to claim 1 is characterized in that: The model verification under different working conditions and different magnifications in step 4 includes the following steps: ST1: Construct model accuracy evaluation indicators, including, Mean absolute error MAE, Root mean square error RMSE, Maximum error ME, Where, Indicates the measured value, V k It is expressed as an estimated value, and n is n sets of measured and estimated voltage values; ST2: Establish a constant parameter model, treat the reaction rate constant and solid-phase diffusion coefficient as constants, and compare them with the high-rate model with variable parameters; ST3: Compare the model simulation results with the experimental results at different temperatures and different magnifications.

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