CN113109726A - Method for estimating internal resistance of lithium ion battery based on error compensation multi-factor dynamic internal resistance model - Google Patents

Abstract

The invention discloses a method for estimating the internal resistance of a lithium ion battery based on a multi-factor dynamic internal resistance model based on error compensation. In order to realize the multi-factor prediction of the battery discharge internal resistance and improve the prediction accuracy, the method of the present invention mainly includes the steps of: firstly using the binary polynomial of the least square method to establish the battery discharge internal resistance model under different states of charge and temperatures; The strip interpolation algorithm integrates the discharge rate, and builds the battery discharge internal resistance under different discharge rates, states of charge and temperatures for modeling; secondly, the established multi-factor dynamic internal resistance model is used to estimate the charging internal resistance under different states; Finally, the binary cubic spline interpolation function of the estimation error of the discharge internal resistance in different discharge rate ranges is fitted, and a multi-factor dynamic discharge internal resistance model with an error compensation strategy is constructed to achieve accurate prediction of the battery discharge internal resistance. The invention has the characteristics of easy operation, high model prediction accuracy and the like, and can be applied in a battery thermal management system.

Description

A multi-factor dynamic internal resistance model based on error compensation to estimate the internal resistance of lithium-ion batteries

technical field

The invention belongs to the technical field of battery thermal management, and more particularly relates to a method for estimating the internal resistance of a lithium ion battery based on a multi-factor dynamic internal resistance model based on error compensation.

Background technique

In the context of the increasingly prominent energy crisis, lithium-ion batteries have the characteristics of high specific energy, high power, long life, low self-discharge rate, and environmental friendliness, and have become the preferred power battery for electric vehicles. However, the safety of lithium-ion batteries is one of the most important issues in the development of electric vehicles. When the lithium-ion battery works under high current discharge conditions or works for a long time, overheating will occur. The heat of the lithium-ion battery mainly comes from the irreversible heat generated by the internal resistance of the discharge. Therefore, the discharge internal resistance is a key parameter for the amount of heat generated by the battery during discharge operation. The accurate modeling of the battery discharge internal resistance is of great reference significance for the thermal analysis of the battery and the design of the thermal management system.

At present, the common lithium-ion battery discharge internal resistance modeling methods are mainly divided into two types: a discharge internal resistance model based on one of the three influencing factors of temperature, SOC and discharge rate, or a discharge internal resistance model based on temperature, SOC and discharge rate. Two of the three influencing factors of discharge rate establish a discharge internal resistance model with two influencing factors.

The modeling methods of the discharge internal resistance model with single influence factor and the discharge internal resistance model with dual influence factors usually only build the discharge internal resistance model with respect to temperature and SOC. However, in the actual discharge process of the battery, the discharge rate is also an important factor affecting the discharge internal resistance, and the prediction result obtained by only considering the discharge internal resistance affected by temperature and SOC has a large error. To sum up, the existing battery discharge internal resistance prediction models mainly have large model errors and fail to integrate all the factors affecting the discharge internal resistance for accurate modeling. In view of this situation, building a battery discharge internal resistance model to achieve accurate prediction of battery discharge internal resistance has become the focus of researchers in the battery field, which is of great significance to the development of the battery industry.

SUMMARY OF THE INVENTION

The purpose of the invention is to overcome the defects of the existing battery discharge internal resistance modeling methods, and propose a method for estimating the internal resistance of lithium ion batteries based on a multi-factor dynamic internal resistance model based on error compensation. By testing the discharge internal resistance under different discharge rates, temperatures and SOC and analyzing its characteristics, finally, with the above three factors as independent variables and the internal resistance as the dependent variable, a multi-factor dynamic discharge internal resistance model is constructed to realize the High-precision prediction of battery discharge internal resistance.

In order to achieve the above goals, the technical solution adopted in this method is:

A method for estimating the internal resistance of a lithium-ion battery based on a multi-factor dynamic internal resistance model based on error compensation, at least including the estimation of the multi-factor dynamic internal resistance model based on error compensation and the multi-rate HPPC method internal resistance test experiment to measure the battery discharge internal resistance. part.

The estimation of the multi-factor dynamic internal resistance model based on error compensation at least includes the following steps:

Step 1: Use the Multi-rate HPPC method to test the internal resistance of the battery to obtain the data of the open circuit voltage E, working voltage U and working current I during the discharge process of the battery, and calculate the discharge internal resistance R of the battery at each discharge moment:

Step 2: Under different discharge _rates C=(C ₁ , C ₂ , . The n (n≥4) order functional relationship between variable R and independent variable T and SOC:

分别是R在不同放电倍率C₁,C₂,...,C_n下关于温度和SOC的二元多项式拟合函数；a_ij,1,a_ij,2,...,a_ij,n分别是在不同放电倍率下的二元多项式系数；in,

are the bivariate polynomial fitting functions of R with respect to temperature and SOC at different discharge rates C ₁ , C ₂ ,...,C _n respectively; a _ij,1 ,a _ij,2 ,...,a _ij,n are the binary polynomial coefficients at different discharge rates, respectively;

Step 3: According to the bivariate polynomial obtained in step 2, extract the bivariate polynomial function coefficients a _ij,1 ,a _ij,2 ,...,a _{ij of R with respect to T and SOC fitting under different discharge rates, n} , which constitutes the coefficient group a _ij of the bivariate polynomial coefficients, expressed as formula (3):

a _ij = (a _ij,1 ,a _ij,2 ,…,a _ij,n ) (3)

Among them, a _ij =(a _ij,1 ,a _ij,2 ,...,a _ij,n ) is to extract the coefficient group of R with respect to T and SOC fitting binary polynomial function under all measured discharge rates;

Step 4: Use the cubic spline interpolation method to establish the intrinsic functional relationship between the binary polynomial function coefficient group a _ij fitted in step 3 and the discharge rate C;

Step 4-1: Take the binary polynomial function coefficient group a _ij under different discharge rates extracted in step 3, and select m+1 nodes on the discharge rate array interval based on the cubic spline interpolation method, so that the discharge rate array interval is [ C ₁ ,C _m+1 ], divide the discharge rate array [C ₁ ,C _m+1 ] into m segments: [C ₁ ,C ₂ ],[C ₂ ,C ₃ ],…,[C _m ,C _m+1 ];

Step 4-2: construct a cubic spline interpolation function segmentally between each segment of the discharge rate data points in the discharge rate array;

Step 4-3: Obtain an overall continuous cubic spline interpolation function with the discharge rate C as the independent variable:

Among them, A _ij is the cubic spline fitting function of the discharge rate C about the coefficient group a _ij , F ₁ (C), F ₂ (C),..., F _m (C) are the discharge rates in the corresponding interval [C ₁ , C ₂ ],[C ₂ ,C ₃ ],…,[C _m ,C _m+1 ] about the cubic spline piecewise fitting function of the coefficient group a _ij ;

Step 5: Construct a multi-factor dynamic charging internal resistance mathematical model of R about T, SOC and charging rate C: Substitute formula (4) into formula (2) to obtain the charging rate C as the independent variable, R is binary about T and SOC The coefficient of the polynomial function is the functional relationship of the dependent variable, namely:

Among them, R(T, SOC, C) is a mathematical model of internal resistance to construct discharge resistance with internal resistance as dependent variable, and temperature, SOC and discharge rate as independent variables.

Step 6: Calculate the estimated error R _error of the discharge internal resistance from the experimental value R _test and the estimated value R ₀ of the battery discharge internal resistance, namely:

R _error = R _test -R ₀ (6)

Among them, R _test is the experimental value of the battery discharge internal resistance, and R _error is the estimated error of the discharge internal resistance;

Step 7: Fit the discharge internal resistance error function: use the binary cubic spline interpolation method to calculate the estimated discharge internal resistance R ₀ (T,SOC,C) at low temperature (below 25°C) and low SOC (less than 0.3) ) and the experimental value R _test , the error R _error is the dependent variable, and it is fitted to a binary cubic spline interpolation function with temperature T and SOC as independent variables:

Among them, R _S,0.25C～1C is a binary cubic spline interpolation function constructed with temperature T and SOC as independent variables when the battery discharge rate is in the interval of 0.25C～1C, and R _S,1C～2C is the battery discharge rate in the range of 0.25C～1C. A binary cubic spline interpolation function constructed with temperature T and SOC as independent variables in the range of 1C to 2C, R _{S, 2C to 3C} is the battery discharge rate in the range of 2C to 3C, with temperature T and SOC as the The bivariate cubic spline interpolation function constructed by the independent variable;

Step 8: Bring the binary cubic spline interpolation function (formula 7) of the discharge internal resistance error into the binary cubic spline interpolation function (formula 5) about T and SOC to construct a multi-factor dynamic with an error compensation strategy Discharge internal resistance model, namely:

Among them, R _0.25C～1C is a multi-factor dynamic discharge internal resistance model with an error compensation strategy in the range of 0.25C～1C, and R _1C～2C is an error compensation strategy in the range of 0.25C～1C. The multi-factor dynamic discharge internal resistance model of R _{2C ~ 3C} is a multi-factor dynamic discharge internal resistance model with an error compensation strategy in the range of 0.25C ~ 1C discharge rate.

The Multi-rate HPPC method internal resistance test experiment to measure the battery discharge internal resistance at least includes the following steps:

Step 1: Charge the battery with standard constant voltage-constant current (CC-CV) until the battery is fully charged, and the state of charge at this time is SOC=100%, and let it stand for 1 hour.

Step 2: Put the battery in a high and low temperature alternating test box, set the first temperature measurement point to 5°C, discharge the battery at a constant current of 1C until the SOC is reduced by 10%, and let it stand for 1h.

Step 3: Multi-rate HPPC discharge internal resistance experimental test: firstly discharge the battery with I ₁ C rate constant current for 10s, put it on hold for 40s, then charge it with I ₂ C rate constant current for 10s, put it on hold for 40s, and finally discharge it with I ₃ C rate constant current Flow charging for 10s (for short-term recharging of the battery to make up for capacity loss), shelving for 40s; the initial value of I ₁ is 0.25C, and the fixed proportional relationship among I ₁ , I ₂ and I ₃ is: I ₂ =0.75I ₁ , I ₃ =0.75I ₁ ; increase the I ₁ current by 0.25C, and repeat the Multi-rate HPPC discharge internal resistance test, I ₂ and I ₃ are changed according to a fixed ratio until the maximum discharge of the battery is reached magnification.

Step 4: Internal resistance test under nine SOC states: adjust the battery SOC to 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, repeat the above steps 2 to 3, measure and record the battery Response voltage and response current data for nine SOC conditions.

Step 5: Internal resistance test at four temperature points: Adjust the temperature measurement points in step 2 to: 15°C, 25°C, 35°C, and 45°C, repeat steps 1 to 4, and measure the temperature of the battery at this point. Response voltage and response current data for four temperature conditions.

Step 6: Calculate the discharge internal resistance: According to steps 1 to 5, the response voltage data of the battery at different temperatures, different percentages of SOC and different discharge rates are obtained, and the multi-rate discharge internal resistance of the battery at different temperatures and different percentages of SOC is calculated. resistance.

The beneficial effects of the present invention are:

(1) There is a good consistency between the estimated internal resistance and the experimental value under different discharge rates and SOC changes; (2) The experimental verification results show that the established dynamic internal resistance model can be used at various rates and temperatures. Realize accurate estimation of battery discharge internal resistance.

Description of drawings

FIG. 1 is a flowchart of a method for estimating the internal resistance of a lithium-ion battery based on a multi-factor dynamic internal resistance model based on error compensation of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

As shown in FIG. 1, in order to overcome the defect of low prediction accuracy of the battery discharge internal resistance model in the prior art, the present invention proposes a method for estimating the internal resistance of a lithium-ion battery based on a multi-factor dynamic internal resistance model based on error compensation. Include the following steps:

Step 1: Use the Multi-rate HPPC method to test the internal resistance of the battery to obtain the data of the open circuit voltage E, working voltage U and working current I during the discharge process of the battery, and calculate the discharge internal resistance R of the battery at each discharge moment:

A multi-rate HPPC method discharge internal resistance experimental test platform is built in the laboratory. The experimental test platform consists of three parts: battery charging and discharging system, high and low temperature alternating test chamber and lithium ion battery. The charging and discharging system mainly includes DC power supply, electronic load instrument and host computer, etc.

The battery discharge data such as battery discharge current and battery discharge voltage are obtained in advance from the discharge internal resistance experimental test platform.

Step 2: Under different discharge _rates C=(C ₁ , C ₂ , . The n (n≥4) order functional relationship between variable R and independent variable T and SOC:

分别是R在不同放电倍率C₁,C₂,...,C_n下关于温度和SOC的二元多项式拟合函数；a_ij,1,a_ij,2,...,a_ij,n分别是在不同放电倍率下的二元多项式系数；in,

are the bivariate polynomial fitting functions of R with respect to temperature and SOC at different discharge rates C ₁ , C ₂ ,...,C _n respectively; a _ij,1 ,a _ij,2 ,...,a _ij,n are the binary polynomial coefficients at different discharge rates, respectively;

Step 3: According to the bivariate polynomial obtained in step 2, extract the bivariate polynomial function coefficients a _ij,1 ,a _ij,2 ,...,a _{ij of R with respect to T and SOC fitting under different discharge rates, n} , which constitutes the coefficient group a _ij of the bivariate polynomial coefficients, expressed as formula (3):

a _ij = (a _ij,1 ,a _ij,2 ,…,a _ij,n ) (3)

Among them, a _ij =(a _ij,1 ,a _ij,2 ,...,a _ij,n ) is to extract the coefficient group of R with respect to T and SOC fitting binary polynomial function under all measured discharge rates;

Step 4: Use the cubic spline interpolation method to establish the intrinsic functional relationship between the binary polynomial function coefficient group a _ij fitted in step 3 and the discharge rate C;

Step 4-1: Take the binary polynomial function coefficient group a _ij under different discharge rates extracted in step 3, and select m+1 nodes on the discharge rate array interval based on the cubic spline interpolation method, so that the discharge rate array interval is [ C ₁ ,C _m+1 ], divide the discharge rate array [C ₁ ,C _m+1 ] into m segments: [C ₁ ,C ₂ ],[C ₂ ,C ₃ ],…,[C _m ,C _m+1 ];

Step 4-2: construct a cubic spline interpolation function segmentally between each segment of the discharge rate data points in the discharge rate array;

Step 4-3: Obtain an overall continuous cubic spline interpolation function with the discharge rate C as the independent variable:

Among them, A _ij is the cubic spline fitting function of the discharge rate C about the coefficient group a _ij , F ₁ (C), F ₂ (C),..., F _m (C) are the discharge rates in the corresponding interval [C ₁ , C ₂ ],[C ₂ ,C ₃ ],…,[C _m ,C _m+1 ] about the cubic spline piecewise fitting function of the coefficient group a _ij ;

Step 5: Construct the multi-factor dynamic discharge internal resistance mathematical model of R with respect to T, SOC and discharge rate C: Substitute formula (4) into formula (2) to obtain the discharge rate C as the independent variable, R is binary about T and SOC The coefficient of the polynomial function is the functional relationship of the dependent variable, namely:

Among them, R(T, SOC, C) is a mathematical model of charging internal resistance with internal resistance as the dependent variable and temperature, SOC and discharge rate as independent variables.

Although the above embodiments describe specific embodiments of the present invention so as to facilitate those skilled in the art to understand the present invention, it should be noted that the embodiments are only representative examples of the present invention. Obviously, the present invention is not limited to the above-mentioned specific embodiments, and various modifications, transformations and deformations can also be made. Accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense. Any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention shall be considered to belong to the protection scope of the present invention.

Claims (2)

1. A method for estimating the internal resistance of a lithium-ion battery based on a multi-factor dynamic internal resistance model of error compensation, is characterized in that, utilizing the multi-factor dynamic internal resistance model to fuse temperature T, state of charge (State of Charge, abbreviated as SOC) and The discharge rate C affects the discharge internal resistance R to estimate R. The method includes the following steps: Step 1: Use the internal resistance test experiment to obtain the data of the open circuit voltage E, working voltage U and working current I during charging, and calculate the discharge internal resistance R:

Step 2: Under different charging _rates C=(C ₁ , C ₂ , . The n (n≥4) order functional relationship between variable R and independent variable T and SOC:

are the bivariate polynomial fitting functions of R with respect to temperature and SOC at different discharge rates C ₁ , C ₂ ,...,C _n respectively; a _ij,1 ,a _ij,2 ,...,a _ij,n are the binary polynomial coefficients at different discharge rates, respectively; Step 3: According to the bivariate polynomial obtained in step 2, extract the bivariate polynomial function coefficients a _ij,1 ,a _ij,2 ,...,a _{ij of R with respect to T and SOC fitting under different discharge rates, n} , which constitutes the coefficient group a _ij of the bivariate polynomial coefficients, expressed as formula (3): a _ij = (a _ij,1 ,a _ij,2 ,…,a _ij,n ) (3) Among them, a _ij =(a _ij,1 ,a _ij,2 ,...,a _ij,n ) is to extract the coefficient group of R with respect to T and SOC fitting binary polynomial function under all measured discharge rates; Step 4: establish the intrinsic function relationship between the coefficient group a _ij and the discharge rate; Step 4-1: Take the binary polynomial function coefficient group a _ij under different discharge rates extracted in step 3, and select m+1 nodes in the magnification array interval based on the cubic spline interpolation method, and divide the magnification array into m segments; Step 4-2: Build a cubic spline interpolation function segmentally between each segment of the magnification data points in the magnification array; Step 4-3: Obtain an overall continuous cubic spline interpolation function with the discharge rate C as the independent variable:

Among them, A _ij is the cubic spline fitting function of the discharge rate C about the coefficient group a _ij , F ₁ (C), F ₂ (C),..., F _m (C) are the different discharge rates in their corresponding intervals [C ₁ ,C ₂ ],[C ₂ ,C ₃ ],…,[C _m ,C _m+1 ] the cubic spline piecewise fitting function about the coefficient group a _ij ; Step 5: Construct the multi-factor dynamic discharge internal resistance mathematical model of discharge internal resistance R with respect to T, SOC and discharge rate C: Substitute formula (4) into formula (2) to obtain the discharge rate C as the independent variable, R is related to T and The coefficient of the SOC bivariate polynomial function is the functional relationship of the dependent variable, namely:

Among them, R ₀ (T, SOC, C) is a mathematical model of the internal resistance of the discharge with internal resistance as the dependent variable, and temperature, SOC and discharge rate as the independent variables. Step 6: Calculate the estimated error R _error of the discharge internal resistance from the experimental value R _test and the estimated value R ₀ of the battery discharge internal resistance, namely: R _error = R _test -R ₀ (6) Among them, R _test is the experimental value of the battery discharge internal resistance, and R _error is the estimated error of the discharge internal resistance; Step 7: Fit the internal resistance error function: use the binary cubic spline interpolation method to calculate the estimated value of the discharge internal resistance R ₀ (T,SOC,C) at low temperature (below 25°C) and low SOC (less than 0.3) The error R _error between the experimental value R _test is the dependent variable, and it is fitted to a bivariate cubic spline interpolation function with temperature T and SOC as independent variables:

Among them, R _S,0.25C～1C is a binary cubic spline interpolation function constructed with temperature T and SOC as independent variables when the battery discharge rate is in the interval of 0.25C～1C, and R _S,1C～2C is the battery discharge rate in the range of 0.25C～1C. A binary cubic spline interpolation function constructed with temperature T and SOC as independent variables in the range of 1C to 2C, R _{S, 2C to 3C} is the battery discharge rate in the range of 2C to 3C, with temperature T and SOC as the The bivariate cubic spline interpolation function constructed by the independent variable; Step 8: Bring the binary cubic spline interpolation function (formula 7) of the internal resistance error into the binary cubic spline interpolation function (formula 5) about T and SOC to construct a multi-factor dynamic discharge with an error compensation strategy Internal resistance model, namely:

Among them, R _0.25C～1C is a multi-factor dynamic discharge internal resistance model with an error compensation strategy in the range of 0.25C～1C, and R _1C～2C is an error compensation strategy in the range of 0.25C～1C. The multi-factor dynamic discharge internal resistance model of R _{2C ~ 3C} is a multi-factor dynamic discharge internal resistance model with an error compensation strategy in the range of 0.25C ~ 1C discharge rate. 2. A multi-factor battery discharge internal resistance modeling method incorporating discharge rates according to claim 1, wherein in the step 2, the discharge internal resistance R under different discharge rates varies with T and SOC. Variety.

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