CN112083336A - Lithium ion battery pack electrochemical model parameter acquisition method - Google Patents

Abstract

The invention provides a method for obtaining parameters of an electrochemical model of a lithium-ion battery pack, which compares and analyzes the voltage curves of the discharge terminals of different individual batteries under the identified working conditions based on the excitation response analysis, and estimates each single cell under the identified working conditions. The corresponding discharge capacity is extracted and the terminal voltage of the idle terminal in the identification condition is extracted, so as to identify the relevant parameters of the basic working process of the electrochemical model of different single cells, and then implement the acquisition of other parameters, realizing the electrochemical model in the battery pack. At the same time, it provides technical support for the application of simplified electrochemical models in battery management systems, such as state of charge estimation, state of health assessment, etc.

Description

A method for obtaining parameters of electrochemical model of lithium ion battery pack

technical field

The invention relates to the field of electrochemical model parameter identification of lithium ion battery packs, in particular to a method for obtaining electrochemical model parameters of a battery pack.

Background technique

As an excellent energy storage device, lithium-ion battery has received extensive attention in various fields. Accurately obtaining the internal parameters of the battery can more accurately assess its health status, which is important for implementing effective battery health management and improving the reliability and safety of battery use. significant.

Some inventors of the present invention participated in the research and development of the application number: CN201810559026.8 and the name is: a method for obtaining parameters of an electrochemical model of a lithium ion battery. A fast and non-destructive method for electrochemical model parameters of bulk batteries, and simultaneously realizes the simulation analysis of battery terminal voltage and case temperature changes with time. The electrochemical model of lithium-ion battery can accurately describe the complex reaction process inside the battery, and can accurately simulate the internal and external characteristics of the battery, but the model structure is relatively complex, the calculation amount is large, the number of model parameters is large, and it is difficult to obtain battery parameters accurately, especially After the single cells are formed into a battery pack, the consistency problem between the single cells is revealed, resulting in different voltage responses of the single cells under the same current excitation conditions, and then there are problems due to incomplete voltage test data. The problem of inaccurate battery discharge capacity test results in the inability to accurately obtain all single battery model parameters.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the above-mentioned deficiencies of the prior art, and to propose a method for obtaining electrochemical model parameters suitable for a lithium ion battery pack.

The technical solution adopted by the present invention to solve the above-mentioned deficiencies of the prior art is as follows: in order to solve the problem that the discharge voltages of the single cells in the battery pack are not synchronous at the end of the discharge stage of the battery pack, a capacity approximation compensation method is adopted, that is, according to the maximum discharge voltage in the battery pack The fast discharge voltage curve of the single battery is used to compensate the capacity of the remaining undischarged cells to determine their total capacity, and then carry out the model parameter distribution identification.

The specific identification steps are as follows:

Step 1, establishing an electrochemical model of the lithium-ion battery pack; Step 2, applying parameter identification conditions to the lithium-ion battery pack, charging and discharging the lithium-ion battery pack, and obtaining the voltage of each single cell in the lithium-ion battery pack under the condition of charging and discharging data and current data; step 3, obtain the model of each single cell of the lithium ion battery pack according to the electrochemical model of the lithium ion battery pack and the voltage data and current data of the single cell of the lithium ion battery pack under the condition of charging and discharging parameter.

Further, the electrochemical model of the lithium-ion battery cell includes the open-circuit voltage E _ocv (t), the concentration fraction of lithium intercalation on the surface of the positive active particles y _surf (t), the concentration fraction of lithium intercalation on the surface of the negative active particles x _surf (t), the concentration difference Polarization overpotential η _{con-polarization} (t), reaction polarization overpotential η _{act-polarization} (t), ohmic polarization overpotential η _{ohm-polarization} (t) and terminal voltage U _app (t).

Further, obtain the voltage data and current data of the single battery, use the ampere-hour integration method to calculate the discharge capacity Q _all corresponding to the fastest discharging single battery, obtain the battery state of charge SOC sequence according to formula (1), and extract The terminal voltage of the shelving end,

Fit the unknown parameters according to formula (2):

E _ocv = U _p [y ₀ +D _y (1-soc)]-U _n [x ₀ -D _x (1-soc)] (2)

Among them, soc is the state of charge SOC of the battery, I is the external current, and the discharge is positive and the charge is negative; y ₀ and x ₀ are the initial lithium insertion rate of the positive and negative electrodes, and _{Dy and D x are} the positive and negative electrodes. The change range of the rate; the positive and negative open-circuit potential curves U _p and U _n are known functions.

Calculate the total discharge capacity of the incompletely discharged battery: For the battery cells whose discharge voltage has not dropped to the cut-off voltage, by comparing the cut-off voltage of the incompletely discharged single cell and the fully discharged single cell, a bisection iterative calculation method based on model simulation is adopted. Determine the amount of electricity ΔQ that the incompletely discharged single battery can still release when the whole group stops discharging, and the total capacity of the incompletely discharged single battery is equal to the sum of the undischarged electricity ΔQ and Q _all , which is determined by the bisection iterative calculation method The specific implementation process of ΔQ is as follows:

(1) First, obtain the voltage of the i-th single cell that is not fully discharged when the entire battery is discharged, denoted as U _i , the discharge performance of this single cell is theoretically consistent with the performance of the fastest discharging single cell, from In the battery data of the fastest discharging single battery, the priori discharge capacity compensation value corresponding to the cut-off voltage from U _i to 2.75V is intercepted, and denoted as ΔQ _i ;

(2) Add ΔQ _i and Q _all to obtain the prior total discharge capacity of the incompletely discharged single cell, denoted as Q _{all_i} ;

(3) Substitute the priori total discharge capacity Q _{all_i} into formula (1), use the ampere-hour integration method to obtain the SOC at different times, and then use the LSF fitting method to obtain the basic working process parameters of the battery _{y 0} , x ₀ , Dy , D _x , calculate the positive and negative electrode capacities Q _p and Q _n according to formula (3);

(4) In the case of a given current I, use the formula (2) to simulate the terminal voltage of the single battery, intercept the time corresponding to the battery discharge from the fully charged voltage to the cut-off voltage, and then use the ampere-hour integration method to obtain the simulation total discharge capacity Q _{all_i} ';

(5) Compare the a priori total discharge capacity Q _{all_i} with the simulated total discharge capacity Q _{all_i} ′, if the difference between the two is greater than the given value of 0.01A·s, take the average value of the two, and then assign it to Q _{all_i} , set The optimized Q _{all_i is} substituted into formula (1), and steps (3) to (5) are repeated until the difference between the priori total discharge capacity Q _{all_i} and the simulated total discharge capacity Q _{all_i} ' is less than a given value.

The beneficial effects of the present invention are: considering the inconsistent discharge behavior of the single cells in the battery pack, based on the existing electrochemical model of the single cell, a parameter acquisition method suitable for the battery pack is proposed. The method can realize accurate, non-destructive and fast acquisition of the model parameters of the battery pack and its internal battery cells, so as to meet the simulation accuracy requirements of the terminal voltage of the battery pack.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only It is an embodiment of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to the provided drawings without creative work.

Figure 1 shows the current excitation for parameter identification conditions;

Figure 2 is the external characteristic response curve of the battery pack;

Fig. 3 shows the secondary optimization estimation method of the capacity parameter of the incompletely discharged single battery;

Fig. 4 is the voltage data of the standstill end of the single battery;

Figures 5-10 are the simulation results of batteries 1-6 under the condition of 0.25C constant current discharge;

Figure 11 shows the simulation results of the battery pack under the 0.25C constant current discharge condition;

Figures 12-17 are the simulation results of No. 1-6 batteries under the condition of 0.5C constant current discharge;

Figure 18 shows the simulation results of the battery pack under the 0.5C constant current discharge condition;

Figures 19-24 are the simulation results of No. 1-6 batteries under the 1C constant current discharge condition;

Figure 25 shows the simulation results of the battery pack under the 1C constant current discharge condition;

Figure 26 shows the voltage simulation results under the complete operating condition of the battery pack.

Detailed ways

In order to make the above objects, features and advantages of the present invention more clearly understood, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

In order to solve the consistency problem of the single cells in the battery pack, the current excitation conditions in Figure 1 are used, but when the battery cut-off condition is set, the battery pack voltage is updated: different from the single cells, when the battery is constant at 1C. When the current is discharged to 18V, the battery is put on hold for 10min, and then the battery is discharged at a constant current of 0.02C to the cut-off voltage of the whole group of 17V. The external characteristic response curve of the battery pack is shown in Figure 2.

The electrochemical model of the single lithium ion battery based on the method for obtaining the parameters of the electrochemical model of the lithium ion battery pack of the present invention is:

Among them, U _app is the terminal voltage of the lithium-ion battery, that is, the difference between the solid-phase potentials of the two boundaries where the positive and negative electrodes of the lithium-ion battery are close to the current collector;

U _p and U _n are positive and negative open circuit potentials;

t is time, t ₊ is cation migration number;

y _surf and x _surf are the lithium ion concentration on the solid phase surface of the positive and negative electrodes;

R is the ideal gas constant;

F is Faraday's constant;

T is the working temperature of the lithium-ion battery, which is a constant value of 25°C without considering the influence of temperature on the battery behavior;

c ₀ is the initial lithium ion concentration in the electrolyte;

m _p and m _n are intermediate variables with no specific physical meaning;

Δc ₁ and Δc ₂ are the changes of the lithium ion concentration at the positive and negative current collectors relative to the initial lithium ion concentration c ₀ in the electrolyte;

R _ohm is the equivalent ohmic internal resistance of a lithium-ion battery;

I is the external current, which specifies that discharge is positive and charging is negative.

Since the battery pack is connected in series, the total voltage U _{app_pack} of the battery pack is equal to the sum of the voltages of the single cells in series. The calculation formula of the terminal voltage of the battery pack is as follows:

Among them, i is the number of single cells of the battery pack connected in series, and U _{app_cell_i} is the terminal voltage of the ith battery.

In order to simulate the terminal voltage behavior of the battery pack, it is necessary to obtain the parameters in the single cell model, and then add the simulated voltages of each single cell to obtain the terminal voltage behavior of the group.

A lithium-ion battery pack is formed by connecting each battery cell in series, so the voltage of the battery pack is the sum of the voltages of all the cells in it. Here, the lithium-ion battery cell is analyzed as a system, and the input variables and output variables of the system are: charge and discharge current and battery terminal voltage respectively. The behavior description of the lithium-ion battery is to give the size of its terminal voltage under different external currents. Its essence can be described as: the physical and chemical processes inside the lithium-ion battery are comprehensively carried out. The difference between the solid-phase potentials of the two boundaries at the collector, that is, the value of the terminal voltage U _app .

A calculation method that the terminal voltage U _app of the lithium ion battery cell is equivalent to formula (4) is as follows:

U _app (t)=E _ocv (t)-n _{con-polarization} (t)-n _{act-polarization} (t)-n _{ohm-polarization} (t) (6)

The terminal voltage can be decomposed into ideal electromotive force and three parts overpotential: concentration polarization overpotential, reaction polarization overpotential and ohmic polarization overpotential.

1. Basic working process and parameter identification steps

1.1 Due to the differences in the single cells in the battery pack, when the battery pack reaches the specified discharge cut-off voltage, the voltages of each cell are inconsistent, but there must be a certain battery that first reaches the discharge cut-off voltage of 2.75V or below. According to the parameters developed in the past During the identification process, the battery voltage data of this section is sufficient for all the data required for parameter identification. For other batteries whose discharge voltage has not dropped to 2.75V, the voltage test data is not enough to complete the data required for the identification of the four basic parameters, so it is necessary to perform capacity accounting for the battery cells that are not fully discharged.

By default, this scheme has completed the battery screening during the battery grouping process, and the performance of each single cell in the battery pack is basically similar. Therefore, it can be assumed that the discharge characteristics of different single cells at the discharge end are exactly the same. The cut-off voltage of the discharged and fully discharged cells can determine the battery cells that are not fully discharged and the amount of electricity ΔQ that can still be released when the entire group stops discharging. Calculate the discharge capacity corresponding to a fully discharged single battery according to the ampere-hour integration method, and denote it as Q _{all_0} . For an incompletely discharged battery, the undischarged power ΔQ obtained in the first step needs to be added as the i-th battery The total capacity Q _{all_i} .

The present invention adopts the bipartite iterative calculation method based on model simulation to carry out the quadratic optimization of the estimated Q _{all_i} to ensure the accuracy of the capacity compensation strategy, and uses the voltage test results in FIG. 3 to identify five parameters Q _all , y ₀ , x ₀ , Q _p and Q _n , the identification steps are as follows:

(1) First, obtain the voltage of the i-th single cell that is not fully discharged when the entire battery is discharged, denoted as U _i , the discharge performance of this single cell is theoretically consistent with the performance of the fastest discharging single cell, from In the battery data of the fastest discharging single battery, the priori discharge capacity compensation value corresponding to the cut-off voltage from U _i to 2.75V is intercepted, and denoted as ΔQ _i ;

(2) Add ΔQ _i and Q _all to obtain the prior total discharge capacity of the incompletely discharged single cell, denoted as Q _{all_i} ;

(3) Substitute the priori total discharge capacity Q _{all_i} into formula (1), use the ampere-hour integration method to obtain the SOC at different times, and then use the LSF fitting method to obtain the basic working process parameters of the battery _{y 0} , x ₀ , Dy , D _x , calculate the positive and negative electrode capacities Q _p and Q _n according to formula (3);

(4) In the case of a given current I, use the formula (2) to simulate the terminal voltage of the single battery, intercept the time corresponding to the battery discharge from the fully charged voltage to the cut-off voltage, and then use the ampere-hour integration method to obtain the simulation total discharge capacity Q _{all_i} ';

(5) Compare the a priori total discharge capacity Q _{all_i} with the simulated total discharge capacity Q _{all_i} ′, if the difference between the two is greater than the given value of 0.01A·s, take the average value of the two, and then assign it to Q _{all_i} , set The optimized Q _{all_i is} substituted into formula (1), and steps (3) to (5) are repeated until the difference between the priori total discharge capacity Q _{all_i} and the simulated total discharge capacity Q _{all_i} ' is less than a given value.

Next, extract the terminal voltage of each single battery in the identification condition, and use the LSF method to fit the parameters _{y 0} , x ₀ , D _x , and Dy in Equation 5, and obtain Q _p and Q _n according to Equation 3 . The voltage data required to fit the above single cell parameters are marked with red dots in Figure 4.

Among them, the positive and negative open-circuit potential curves U _p and U _n are known functions, and the function forms are as follows:

1.2 Extract the change value ΔU of the battery terminal voltage when the current excitation is applied, calculate the reaction polarization overpotential η _{act-polarization} using the directly assigned ohmic internal resistance R _ohm and the external current I, and use the LSF method to fit the reaction pole according to the following formula. The transformation coefficient P _act :

where R is the ideal gas constant, F is the Faraday constant, c ₀ is the initial lithium ion concentration in the electrolyte, T is the operating temperature of the lithium ion battery, m _p and m _n are intermediate variables with no specific physical meaning, c ₀ is the initial lithium ion concentration in the electrolyte, and _Pact is the reaction polarization coefficient.

1.3 In order to ensure that the model has better simulation accuracy, the parameter values R _ohm , τ _e , c ₀ , τ _p , τ _n , P _{con_a} , and P _{con_b} are set as constants based on existing experience, and the above models of different single cells The parameters have the same values, 0.03Ω, 100s, 1000mol/m ³ , 10s, 10s, 950mol/(A·m ³ ), and 500mol/(A·m ³ ), respectively.

2. Experimental steps

The battery test equipment used in the present invention is a 60V-20A battery charge and discharge tester produced by Shenzhen Newwell Electronics Co., Ltd., and its voltage accuracy and current accuracy are one thousandth.

2.1 The steps to obtain battery pack model parameters are as follows:

a) The design identification working condition is shown in Figure 1, and the discharge voltage curve of the battery pack under this working condition is obtained, as shown in Figure 2.

b) Using the time-ampere integration method, combined with the battery capacity compensation, the total capacity Q _all of each single cell of the battery pack is obtained, and the four parameters y ₀ , x ₀ , Q of the basic working process of each single cell are estimated by the least square method _p and Q _n ;

c) Extract the change value of the terminal voltage of each single cell when the current excitation is applied, and use the directly assigned ohmic internal resistance R _ohm and external current I to calculate the reaction polarization overpotential η _{act-polarizationt} , according to formulas (8), ( 9) Carry out least squares fitting to estimate the reaction polarization parameter P _act of each single cell;

d) Since the parameters R _ohm , τ _e , c ₀ , τ _p , τ _n , P _{con_a} , and P _{con_b} do not change much for different battery cells, they are directly assigned based on a large number of experiments.

2.2 Voltage simulation of single battery

After obtaining the parameters of the single battery, firstly carry out the voltage simulation of the single battery. The simulation calculation steps are as follows: a) Using the identified four basic parameters y ₀ , x ₀ , Q _p and Q _n , calculate the positive and negative electrode solids. The phase average lithium ion concentration is calculated as follows:

y _avg (t)=y ₀ +I(t)t/Q _p , x _avg (t)=x ₀ -I(t)t/Q _n (11)

Among them, t is the time, y _avg and x _avg are the average lithium ion concentration in the solid phase of the positive and negative electrodes. In order to calculate the open circuit voltage E _ocv of the lithium ion battery, it is necessary to calculate the lithium ion concentrations y _surf and x _surf on the solid phase surface of the positive and negative electrodes. The differences between them and the average lithium ion concentrations y _avg and x _avg are recorded as Δy and Δx, respectively. The relationship between them is as follows:

y _surf (t)=y _avg (t)+Δy(t) (12)

_xsurf (t)= _xavg (t)-Δx(t) (13)

The formulas for calculating Δy and Δx are as follows:

Among them, τ _p and τ _n are the positive and negative solid phase diffusion time constants, △y' and △x' are intermediate variables, their initial values are 0, and the iterative calculation form is as follows:

According to the following formulas, the open-circuit potentials U _p and U _n of the positive and negative electrodes are calculated.

Then the open circuit voltage E _ocv is obtained according to the following formula

E _ocv (t)=U _p (y _surf (t))-U _n (x _surf (t)) (19)

b) According to Ohm's law, calculate the ohmic polarization overpotential η _{ohm-polarization} in combination with the set ohmic internal resistance R _ohm , and the calculation formula is as follows:

η _{ohm-polarization} (t)=R _ohm I(t) (20)

c) Calculate the changes Δc ₁ and Δc ₂ of the lithium ion concentration at the positive and negative electrode current collectors relative to the initial lithium ion concentration c ₀ in the electrolyte according to the set parameters P _{con_a} and P _{con_b} . The calculation process is as follows:

Among them, the initial values of Δc ₁ and Δc ₂ are 0. After calculating Δc ₁ and Δc ₂ , the calculation formula of concentration polarization overpotential η _{con-polarization} can be obtained as:

d) According to the parameter P _act obtained by identification, and Δc ₁ and Δc ₂ obtained in the previous step, use the following formula to calculate the reaction polarization overpotential η _{act-polarization} .

Among them, R is the ideal gas constant, F is the Faraday constant, c ₀ is the initial lithium ion concentration in the electrolyte, T is the operating temperature of the lithium ion battery, m _p and m _n are intermediate variables with no specific physical meaning, Δc ₁ and Δc ₂ are the changes of the lithium ion concentration at the positive and negative current collectors relative to the initial lithium ion concentration c ₀ in the electrolyte; P _act is the reaction polarization coefficient;

Based on the above steps, the terminal voltage U _{app_cell_i} of the lithium-ion battery cell can be calculated with reference to formula 3. After calculating the voltages of the individual cells separately, they are accumulated to obtain the simulation results of the entire group of voltages U _{app_pack} .

3 Experimental verification

The invention carries out simulation verification for the battery of the lithium iron phosphate positive electrode material, the battery pack adopts a configuration mode of 6 cells in a string, and the numbers of the 6 cells are 1-6 respectively. Comparing the voltage obtained by model simulation and the voltage obtained by experimental measurement under the conditions of 0.25C, 0.5C and 1C constant current discharge, as shown in Figures 5-26.

Aiming at the problem that the existing electrochemical model cannot be accurately simulated in the battery pack, the present invention proposes a corresponding solution, that is, a set of battery pack model parameter acquisition methods based on excitation response analysis are proposed, and different individual batteries are identified in the identification process. Compare and analyze the voltage curves at the discharge end under different conditions, estimate the discharge capacity corresponding to the identified working condition, and extract the terminal voltage at the end of the standstill, so as to identify the relevant parameters of the basic working process of the electrochemical model of different single cells, and then implement other parameters. The acquisition of the electrochemical model realizes the application of the electrochemical model to the battery pack, and provides technical support for the application of the simplified electrochemical model in the battery management system, such as state of charge estimation and state of health assessment.

The above description of the disclosed embodiments enables any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (4)

1. A lithium ion battery pack electrochemical model parameter acquisition method is characterized by comprising the following steps:

step one, establishing an electrochemical model of a lithium ion battery pack;

applying a parameter identification working condition to the lithium ion battery pack to charge and discharge the lithium ion battery, and obtaining voltage data and current data of each single battery in the lithium ion battery pack under the charging and discharging conditions;

thirdly, calculating the discharge capacity Q corresponding to the monomer battery with the fastest discharge by adopting an ampere-hour integration method according to the electrochemical model of the lithium ion battery pack and the voltage data and the current data of each monomer battery of the lithium ion battery pack under the charging and discharging conditions_allAnd further acquiring the total electric capacity of the single batteries which are not completely discharged by a binary iterative calculation method, thereby acquiring the model parameters of each single battery of the lithium ion battery pack.

2. The method for obtaining parameters of an electrochemical model of a lithium ion battery pack according to claim 1, wherein the electrochemical model of the lithium ion battery cells established in the first step comprises an open circuit voltage E_ocv(t) positive electrode active particle surface intercalation lithium concentration fraction y_surf(t) negative electrode active particle surface lithium intercalation concentration fraction x_surf(t) concentration polarization overpotential η_{con-polarization}(t) reaction polarization overpotential η_{act-polarization}(t), ohmic polarization overpotential η_{ohm-polarization}(t) and terminal voltage U_app(t)。

3. The method for obtaining parameters of an electrochemical model of a lithium ion battery pack according to claim 2, wherein in the second step, voltage data and current data of the single battery under the charging and discharging conditions are obtained, and an ampere-hour integration method is adopted to calculate the discharging capacity Q corresponding to the single battery with the fastest discharging speed_allObtaining a battery state of charge (SOC) sequence according to the formula (1), anda terminal voltage of the resting end is extracted,

fitting the unknown parameters according to equation (2):

E_ocv＝U_p[y₀+D_y(1-soc)]-U_n[x₀-D_x(1-soc)] (2)

wherein SOC is the state of charge SOC of the battery, I is the external current, the discharging is specified to be positive, and the charging is specified to be negative; y is₀And x₀Initial rate of lithium intercalation for positive and negative electrodes, D_yAnd D_xThe variation range of the initial lithium intercalation rate of the anode and the cathode; positive and negative open circuit potential curve U_p、U_nIs a known function;

for the battery cell of which the discharge voltage does not drop to the cut-off voltage, calculating the electric quantity delta Q which can still be discharged when the whole group stops discharging by comparing the cut-off voltages of the incompletely discharged battery cell and the completely discharged battery cell, wherein the total capacity of the incompletely discharged battery cell is equal to the electric quantity delta Q which is not discharged and the electric quantity Q which is discharged_allAnd (4) adding.

4. The method for obtaining parameters of an electrochemical model of a lithium ion battery pack according to claim 3, wherein the Δ Q is calculated by a binary iteration method, and the implementation process is as follows:

(1) firstly, the voltage of the ith single battery which is not completely discharged when the discharge of the whole battery pack is cut off is obtained and is marked as U_iThe discharge performance of the single battery is theoretically consistent with that of the single battery with the fastest discharge, and the slave U is intercepted from the battery data of the single battery with the fastest discharge_iThe prior discharge capacity compensation value corresponding to the cut-off voltage of 2.75V is recorded as delta Q_i；

(2) Will be delta Q_iAnd Q_allAdding to obtain the total prior discharge capacity of the incompletely discharged single battery, and recording as Q_{all_i}；

(3) Will be a prioriTotal discharge capacity Q_{all_i}Substituting the equation (1), obtaining SOC at different moments by using an ampere-hour integral method, and further obtaining a basic working process parameter y of the battery by using an LSF fitting method₀、x₀、D_y、D_xCalculating the positive and negative electrode capacities Q according to the formula (3)_pAnd Q_n；

(4) Under the condition of a given current I, performing voltage simulation on the single battery by using a formula (2), intercepting the time corresponding to the voltage discharge of the battery from full charge to cut-off voltage, and then acquiring the total simulated discharge capacity Q by using an ampere-hour integration method_{all_i}’；

(5) Comparing the prior total discharge capacity Q_{all_i}And total capacity Q of simulated discharge_{all_i}' if the difference between the two is greater than a given value of 0.01A · s, the mean of the two is taken and then assigned to Q_{all_i}Assigning the optimized Q_{all_i}Substituting the formula (1), and repeating the steps (3) to (5) until the total prior discharge capacity Q_{all_i}And total capacity Q of simulated discharge_{all_i}' the difference is less than a given value.

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