CN113109726B - Error compensation-based method for estimating internal resistance of lithium ion battery by multi-factor dynamic internal resistance model - Google Patents

Error compensation-based method for estimating internal resistance of lithium ion battery by multi-factor dynamic internal resistance model Download PDF

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CN113109726B
CN113109726B CN202110317110.0A CN202110317110A CN113109726B CN 113109726 B CN113109726 B CN 113109726B CN 202110317110 A CN202110317110 A CN 202110317110A CN 113109726 B CN113109726 B CN 113109726B
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陈琳
吴淑孝
丁云辉
潘海鸿
姚起宏
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Guangxi University
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Abstract

The invention discloses a method for estimating the internal resistance of a lithium ion battery by a multi-factor dynamic internal resistance model based on error compensation. In order to realize multi-factor prediction of the discharge internal resistance of the battery and improve the prediction precision, the method mainly comprises the following steps: firstly, establishing battery discharge internal resistance models under different charge states and temperatures by adopting a binary polynomial of a least square method; then fusing discharge multiplying power by adopting a cubic spline interpolation algorithm, constructing battery discharge internal resistances under different discharge multiplying power, charge state and temperature, and modeling; secondly, the method comprises the following steps of; estimating the charging internal resistance under different states by adopting the established multi-factor dynamic internal resistance model; and finally, fitting a binary cubic spline interpolation function of discharge internal resistance estimation errors in different discharge rate intervals, and constructing a multi-factor dynamic discharge internal resistance model with an error compensation strategy to accurately predict the discharge internal resistance of the battery. The method has the characteristics of easy operation, higher model prediction precision and the like, and can be applied to a battery thermal management system.

Description

Error compensation-based method for estimating internal resistance of lithium ion battery by multi-factor dynamic internal resistance model
Technical Field
The invention belongs to the technical field of battery thermal management, and particularly relates to a method for estimating internal resistance of a lithium ion battery based on an error compensation multi-factor dynamic internal resistance model.
Background
Under the condition that the energy crisis problem is increasingly highlighted, the lithium ion battery has the characteristics of high specific energy, high power, long service life, low self-discharge rate, environmental friendliness and the like, and becomes the first choice power battery of the electric automobile. However, the safety of lithium ion batteries is one of the most important problems in the development of electric vehicles. When the lithium ion battery works under the condition of high-current discharge or works for a long time, overheat phenomenon can occur, and the heat of the lithium ion battery mainly comes from irreversible heat generated by discharge internal resistance. Therefore, the discharge internal resistance is a key parameter of the heat generated by the battery during discharge operation, and the accurate modeling of the discharge internal resistance of the battery has great reference significance on the thermal analysis of the battery and the design of a thermal management system.
At present, common lithium ion battery discharge internal resistance modeling methods are mainly divided into two types: and establishing a discharge internal resistance model of a single influence factor based on one of three influence factors of temperature, SOC and discharge multiplying power or establishing a discharge internal resistance model of double influence factors based on two of three influence factors of temperature, SOC and discharge multiplying power.
The modeling method of the discharge internal resistance model of the single influencing factor and the discharge internal resistance model of the double influencing factors generally only builds the discharge internal resistance model of the discharge internal resistance with respect to temperature and SOC. However, in the actual discharging process of the battery, the discharging multiplying power is also an important influencing factor of the discharging internal resistance, and only the temperature and the discharging internal resistance influenced by the SOC are considered, so that the error of the obtained prediction result is larger. In summary, the existing battery discharge internal resistance prediction model mainly has large model errors, and does not integrate all discharge internal resistance influence factors to perform accurate modeling. Aiming at the situation, the construction of a battery discharge internal resistance model to realize the accurate prediction of the battery discharge internal resistance is already the focus of attention of researchers in the battery field, and has important significance for the development of the battery industry.
Disclosure of Invention
The invention aims to overcome the defects of the existing battery discharge internal resistance modeling method and provides a method for estimating the internal resistance of a lithium ion battery by using a multi-factor dynamic internal resistance model based on error compensation. And finally, constructing a multi-factor dynamic discharge internal resistance model by taking the three factors as independent variables and the internal resistance as dependent variables to realize high-precision prediction of the discharge internal resistance of the battery.
In order to achieve the above object, the technical scheme adopted by the method is as follows:
the method for estimating the internal resistance of the lithium ion battery by using the Multi-factor dynamic internal resistance model based on error compensation at least comprises two parts of Multi-factor dynamic internal resistance model estimation based on error compensation and Multi-rate HPPC method internal resistance test experiment measurement of the internal resistance of the battery.
The multi-factor dynamic internal resistance model estimation based on error compensation at least comprises the following steps:
step 1: the data of open circuit voltage E, working voltage U and working current I in the discharging process of the battery are obtained by adopting a Multi-rate HPPC method internal resistance test experiment, and the discharging internal resistance R of each discharging moment of the battery is calculated:
Figure BDA0002991610500000021
step 2: at different discharge rates c= (C 1 ,C 2 ,…,C n ) Then, function fitting of the discharge internal resistance R with respect to T and SOC is respectively established: the binary polynomial function of the least square method is adopted to fit an n (n is more than or equal to 4) order function relation between the dependent variable R, the independent variable T and the SOC:
Figure BDA0002991610500000022
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0002991610500000023
r is respectively at different discharge multiplying powers C 1 ,C 2 ,...,C n A binary polynomial fit function for temperature and SOC; a, a ij,1 ,a ij,2 ,...,a ij,n The coefficients of the binary polynomials under different discharge multiplying powers are respectively;
step 3: extracting the binary polynomial function coefficient a of R fitting with respect to T and SOC under different discharge multiplying powers according to the binary polynomial obtained in the step 2 ij,1 ,a ij,2 ,...,a ij,n Coefficient group a constituting binary polynomial coefficient ij Expression is as shown in formula (3):
a ij =(a ij,1 ,a ij,2 ,…,a ij,n ) (3)
wherein a is ij =(a ij,1 ,a ij,2 ,…,a ij,n ) Extracting R-related T and SOC fitting binary polynomial function coefficient groups under all measured discharge multiplying powers;
step 4: interpolation using cubic splineThe method establishes the binary polynomial function coefficient group a fitted in the step 3 ij An intrinsic functional relationship with the discharge rate C;
step 4-1: combining the binary polynomial function coefficient group a extracted in the step 3 under different discharge multiplying powers ij Taking m+1 nodes on the discharge rate array interval based on a cubic spline interpolation method to enable the discharge rate array interval to be [ C ] 1 ,C m+1 ]Array of discharge multiplying power [ C ] 1 ,C m+1 ]Dividing into m segments: [ C 1 ,C 2 ],[C 2 ,C 3 ],…,[C m ,C m+1 ];
Step 4-2: constructing a cubic spline interpolation function by sectioning each section of discharge rate data points of the discharge rate array;
step 4-3: obtaining a cubic spline interpolation function taking discharge multiplying power C as an independent variable in a whole and continuous way:
Figure BDA0002991610500000024
wherein A is ij Is the discharge rate C with respect to the coefficient group a ij Is a cubic spline fitting function of F 1 (C),F 2 (C),…,F m (C) Is that the discharge multiplying power is in the corresponding interval [ C ] 1 ,C 2 ],[C 2 ,C 3 ],…,[C m ,C m+1 ]With respect to coefficient group a ij Is used for a cubic spline piecewise fitting function;
step 5: constructing a multi-factor dynamic charging internal resistance mathematical model of R with respect to T, SOC and a charging multiplying power C: substituting the formula (4) into the formula (2) to obtain a functional relation with the charging multiplying power C as an independent variable and the coefficient of the binary polynomial function of the T and the SOC as a dependent variable, namely:
Figure BDA0002991610500000031
wherein, R (T, SOC, C) is a mathematical model of the internal resistance of discharge with the internal resistance as a dependent variable and the temperature, SOC and discharge multiplying power as independent variables.
Step 6: experimental value R of internal resistance discharged from battery test And an estimated value R 0 Calculating to obtain an estimated error R of the internal resistance of the discharge error The method comprises the following steps:
R error =R test -R 0 (6)
wherein R is test Is the experimental value of the discharge internal resistance of the battery, R error Is an estimation error of the internal resistance of the discharge;
step 7: fitting a discharge internal resistance error function: adopting a binary cubic spline interpolation method to estimate the internal resistance R under the low-temperature (below 25 ℃) and low-SOC (below 0.3) state 0 (T, SOC, C) and Experimental value R test Error R between error As dependent variables, fitting a binary cubic spline interpolation function taking temperature T and SOC as independent variables:
Figure BDA0002991610500000032
wherein R is S,0.25C~1C Is a binary cubic spline interpolation function constructed by taking temperature T and SOC as independent variables in a range of 0.25-1C of battery discharge multiplying power, R S,1C~2C Is a binary cubic spline interpolation function constructed by taking temperature T and SOC as independent variables in a range of 1-2C of battery discharge multiplying power, R S,2C~3C The method is a binary cubic spline interpolation function constructed by taking the temperature T and the SOC as independent variables in a range of 2-3C of the battery discharge multiplying power;
step 8: introducing a binary cubic spline interpolation function (formula 7) of the discharge internal resistance error into a binary cubic spline interpolation function (formula 5) of T and SOC, and constructing a multi-factor dynamic discharge internal resistance model with an error compensation strategy, namely:
Figure BDA0002991610500000033
wherein R is 0.25C~1C Is a multi-factor dynamic discharge internal resistance model with an error compensation strategy in a discharge multiplying power range of 0.25-1C, R 1C~2C Is a multi-factor dynamic discharge internal resistance model with an error compensation strategy in a discharge multiplying power range of 0.25-1C, R 2C~3C The multi-factor dynamic discharge internal resistance model with the error compensation strategy in the discharge multiplying power range of 0.25-1C.
The Multi-rate HPPC method internal resistance test experiment for measuring the discharge internal resistance of the battery at least comprises the following steps:
step 1: the battery was charged at standard constant voltage-constant current (CC-CV) until the battery was fully charged, at which time the state of charge soc=100%, and left to stand for 1h.
Step 2: the battery is placed in a high-low temperature alternating test box, a first temperature measuring point is set to be 5 ℃, the battery is discharged to the state of charge (SOC) at a constant current of 1C, the SOC is reduced by 10%, and the battery is kept stand for 1h.
Step 3: multi-rate HPPC discharge internal resistance experimental test: the battery is firstly subjected to I 1 C multiplying power constant current discharge for 10s, rest for 40s, then use I 2 C multiplying power constant current charging for 10s, placing for 40s, finally taking I as 3 C multiplying power constant current charging for 10s (for realizing capacity compensation for short recharging of the battery), and standing for 40s; wherein I is 1 Initial value of 0.25C, I 1 、I 2 And I 3 The fixed proportion relation among the three is as follows: i 2 =0.75I 1 ,I 3 =0.75I 1 The method comprises the steps of carrying out a first treatment on the surface of the Will I 1 The current was increased by 0.25C and the Multi-rate HPPC discharge internal resistance test, I, was repeated 2 And I 3 And changing according to the fixed proportion until the maximum discharge multiplying power of the battery is reached.
Step 4: internal resistance test under nine SOC states: and (3) respectively adjusting the SOC of the battery to 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2 and 0.1, repeating the steps 2-3, and measuring and recording the response voltage and response current data of the battery under the nine SOC conditions.
Step 5: internal resistance test at four temperature points: the temperature measurement points in the step 2 are sequentially adjusted as follows: and repeating the steps 1 to 4 at 15 ℃, 25 ℃, 35 ℃ and 45 ℃ to respectively measure the response voltage and the response current data of the battery under the four temperature conditions.
Step 6: calculating the internal resistance of discharge: and (3) according to the steps 1 to 5, response voltage data of the battery at different temperatures, different percentages of SOC and different discharge multiplying powers are obtained, and the multi-multiplying power discharge internal resistance of the battery at different temperatures and different percentages of SOC is calculated.
The invention has the beneficial effects that:
(1) The internal resistance estimated value and the experimental value keep good consistency under the change of different discharge multiplying powers and SOC; (2) The experimental verification result shows that the established dynamic internal resistance model can accurately estimate the discharge internal resistance of the battery under various multiplying powers and temperatures.
Drawings
Fig. 1 is a flowchart of a method for estimating the internal resistance of a lithium ion battery based on an error compensation multi-factor dynamic internal resistance model.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in figure 1, in order to overcome the defect of low prediction precision of a battery discharge internal resistance model in the prior art, the invention provides a method for estimating the internal resistance of a lithium ion battery by using a multi-factor dynamic internal resistance model based on error compensation, which specifically comprises the following steps:
step 1: the data of open circuit voltage E, working voltage U and working current I in the discharging process of the battery are obtained by adopting a Multi-rate HPPC method internal resistance test experiment, and the discharging internal resistance R of each discharging moment of the battery is calculated:
Figure BDA0002991610500000041
a Multi-rateHPPC method discharge internal resistance experiment test platform is built in a laboratory and consists of a battery charge-discharge system, a high-low temperature alternating test box and a lithium ion battery, wherein the charge-discharge system mainly comprises a direct current power supply, an electronic load instrument, an upper computer and the like.
And pre-acquiring battery discharge data such as battery discharge current, battery discharge voltage and the like from a discharge internal resistance experiment test platform.
Step 2: at different positionsElectric multiplying power c= (C 1 ,C 2 ,…,C n ) Then, function fitting of the discharge internal resistance R with respect to T and SOC is respectively established: the binary polynomial function of the least square method is adopted to fit an n (n is more than or equal to 4) order function relation between the dependent variable R, the independent variable T and the SOC:
Figure BDA0002991610500000051
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0002991610500000052
r is respectively at different discharge multiplying powers C 1 ,C 2 ,...,C n A binary polynomial fit function for temperature and SOC; a, a ij,1 ,a ij,2 ,...,a ij,n The coefficients of the binary polynomials under different discharge multiplying powers are respectively;
step 3: extracting the binary polynomial function coefficient a of R fitting with respect to T and SOC under different discharge multiplying powers according to the binary polynomial obtained in the step 2 ij,1 ,a ij,2 ,...,a ij,n Coefficient group a constituting binary polynomial coefficient ij Expression is as shown in formula (3):
a ij =(a ij,1 ,a ij,2 ,…,a ij,n ) (3)
wherein a is ij =(a ij,1 ,a ij,2 ,…,a ij,n ) Extracting R-related T and SOC fitting binary polynomial function coefficient groups under all measured discharge multiplying powers;
step 4: establishing the binary polynomial function coefficient group a fitted in the step 3 by adopting a cubic spline interpolation method ij An intrinsic functional relationship with the discharge rate C;
step 4-1: combining the binary polynomial function coefficient group a extracted in the step 3 under different discharge multiplying powers ij Taking m+1 nodes on the discharge rate array interval based on a cubic spline interpolation method to enable the discharge rate array interval to be [ C ] 1 ,C m+1 ]Array of discharge multiplying power [ C ] 1 ,C m+1 ]Dividing into m segments: [ C 1 ,C 2 ],[C 2 ,C 3 ],…,[C m ,C m+1 ];
Step 4-2: constructing a cubic spline interpolation function by sectioning each section of discharge rate data points of the discharge rate array;
step 4-3: obtaining a cubic spline interpolation function taking discharge multiplying power C as an independent variable in a whole and continuous way:
Figure BDA0002991610500000053
wherein A is ij Is the discharge rate C with respect to the coefficient group a ij Is a cubic spline fitting function of F 1 (C),F 2 (C),…,F m (C) Is that the discharge multiplying power is in the corresponding interval [ C ] 1 ,C 2 ],[C 2 ,C 3 ],…,[C m ,C m+1 ]With respect to coefficient group a ij Is used for a cubic spline piecewise fitting function;
step 5: constructing a multi-factor dynamic discharge internal resistance mathematical model of R with respect to T, SOC and discharge multiplying power C: substituting the formula (4) into the formula (2) to obtain a functional relation with the discharge multiplying power C as an independent variable and the coefficient of the R with respect to the T and SOC binary polynomial function as a dependent variable, namely:
Figure BDA0002991610500000061
wherein, R (T, SOC, C) is a structural charge internal resistance mathematical model taking internal resistance as a dependent variable and taking temperature, SOC and discharge multiplying power as independent variables.
While the above examples describe specific embodiments of the present invention to facilitate understanding of the present invention by those skilled in the art, it should be noted that the examples are merely representative examples of the present invention. It will be evident that the invention is not limited to the particular embodiments disclosed above, but is capable of numerous modifications, variations and modifications. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. Any simple modification, equivalent variation and modification of the above embodiments according to the technical substance of the present invention should be considered to be within the scope of the present invention.

Claims (2)

1. The method for estimating the internal resistance of the lithium ion battery by utilizing the multi-factor dynamic internal resistance model based on error compensation is characterized in that the influence of a temperature T, a State of Charge (SOC) and a discharge multiplying power C on a discharge internal resistance R is utilized to estimate the R, and the method comprises the following steps:
step 1: obtaining data of open circuit voltage E, working voltage U and working current I during charging by adopting an internal resistance test experiment, and calculating discharge internal resistance R:
Figure FDA0004223545800000011
step 2: at different charging rates c= (C 1 ,C 2 ,…,C n ) Then, function fitting of the discharge internal resistance R with respect to T and SOC is respectively established: the binary polynomial function of the least square method is adopted to fit an n (n is more than or equal to 4) order function relation between the dependent variable R, the independent variable T and the SOC:
Figure FDA0004223545800000012
Figure FDA0004223545800000013
r is respectively at different discharge multiplying powers C 1 ,C 2 ,...,C n A binary polynomial fit function for temperature and SOC; a, a ij,1 ,a ij,2 ,...,a ij,n The coefficients of the binary polynomials under different discharge multiplying powers are respectively;
step 3: extracting the binary polynomial function coefficient a of R fitting with respect to T and SOC under different discharge multiplying powers according to the binary polynomial obtained in the step 2 ij,1 ,a ij,2 ,...,a ij,n Coefficient group a constituting binary polynomial coefficient ij The expression is shown as formula (3):
a ij =(a ij,1 ,a ij,2 ,…,a ij,n ) (3)
Wherein a is ij =(a ij,1 ,a ij,2 ,…,a ij,n ) Extracting R-related T and SOC fitting binary polynomial function coefficient groups under all measured discharge multiplying powers;
step 4: establishing coefficient set a ij An intrinsic functional relationship with the discharge rate;
step 4-1: combining the binary polynomial function coefficient group a extracted in the step 3 under different discharge multiplying powers ij Taking m+1 nodes on a multiplying power array interval based on a cubic spline interpolation method, and dividing the multiplying power array into m sections;
step 4-2: constructing a cubic spline interpolation function by sectioning each section of multiplying power data points of the multiplying power array;
step 4-3: obtaining a wholly continuous cubic spline interpolation function taking discharge multiplying power C as an independent variable:
Figure FDA0004223545800000014
wherein A is ij Is the discharge rate C with respect to the coefficient group a ij Is a cubic spline fitting function of F 1 (C),F 2 (C),…,F m (C) Is different in discharge rate in its corresponding interval [ C ] 1 ,C 2 ],[C 2 ,C 3 ],…,[C m ,C m+1 ]Inner relation coefficient set a ij Is used for a cubic spline piecewise fitting function;
step 5: constructing a multi-factor dynamic discharge internal resistance mathematical model of the discharge internal resistance R with respect to T, SOC and the discharge multiplying power C: substituting the formula (4) into the formula (2) to obtain a functional relation with the discharge multiplying power C as an independent variable and the coefficient of the R with respect to the T and SOC binary polynomial function as a dependent variable, namely:
Figure FDA0004223545800000021
wherein R is 0 (T, SOC, C) is a mathematical model of internal resistance of discharge constructed by taking internal resistance as a dependent variable and taking temperature, SOC and discharge multiplying power as independent variables;
step 6: experimental value R of internal resistance discharged from battery test And an estimated value R 0 Calculating to obtain an estimated error R of the internal resistance of the discharge error The method comprises the following steps:
R error =R test -R 0 (6)
wherein R is test Is the experimental value of the discharge internal resistance of the battery, R error Is an estimation error of the internal resistance of the discharge;
step 7: fitting an internal resistance error function: adopting a binary cubic spline interpolation method to estimate the internal resistance R under the low-temperature (below 25 ℃) and low-SOC (below 0.3) state 0 (T, SOC, C) and Experimental value R test Error R between error As dependent variables, fitting a binary cubic spline interpolation function taking temperature T and SOC as independent variables:
Figure FDA0004223545800000022
wherein R is S,0.25C~1C Is a binary cubic spline interpolation function constructed by taking temperature T and SOC as independent variables in a range of 0.25-1C of battery discharge multiplying power, R S,1C~2C Is a binary cubic spline interpolation function constructed by taking temperature T and SOC as independent variables in a range of 1-2C of battery discharge multiplying power, R S,2C~3C The method is a binary cubic spline interpolation function constructed by taking the temperature T and the SOC as independent variables in a range of 2-3C of the battery discharge multiplying power;
step 8: introducing the binary cubic spline interpolation function (formula 7) of the internal resistance error into the binary cubic spline interpolation function (formula 5) of the T and the SOC, and constructing a multi-factor dynamic discharge internal resistance model with an error compensation strategy, namely:
Figure FDA0004223545800000023
wherein R is 0.25C~1C Is a multi-factor dynamic discharge internal resistance model with an error compensation strategy in a discharge multiplying power range of 0.25-1C, R 1C~2C Is a multi-factor dynamic discharge internal resistance model with an error compensation strategy in a discharge multiplying power range of 0.25-1C, R 2C~3C The multi-factor dynamic discharge internal resistance model with the error compensation strategy in the discharge multiplying power range of 0.25-1C.
2. The method for estimating internal resistance of a lithium ion battery based on an error-compensated multi-factor dynamic internal resistance model according to claim 1, wherein the internal resistance R of the discharge in step 2 varies with the variation of T and SOC.
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