CN113109722B - A multi-factor battery charging internal resistance modeling method integrating charging rate - Google Patents

Abstract

The invention discloses a multi-factor battery charging internal resistance modeling method integrating charging multiplying power. In order to realize multi-factor prediction of the battery charging internal resistance and improve the prediction precision, the method mainly comprises the following steps: firstly, establishing battery charging internal resistance models under different charge states and temperatures by adopting a binary polynomial of a least square method; then fusing the charging multiplying powers by adopting a cubic spline interpolation algorithm, and constructing battery charging internal resistances under different charging multiplying powers, states of charge and temperatures for modeling; and finally, estimating the charging internal resistance under different states by adopting the established multi-factor dynamic internal resistance model, so as to accurately predict the charging 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

A multi-factor battery charging internal resistance modeling method integrating charging rate

technical field

The invention belongs to the technical field of battery thermal management, and more specifically relates to a multi-factor battery charging internal resistance modeling method integrating charging rate.

Background technique

As the energy crisis becomes increasingly prominent, lithium-ion batteries, as the main energy storage device for electric vehicles, have become an important part of electric vehicles. However, during the charging process, the battery will release heat. The charging internal resistance is a key parameter for the amount of heat generated by the battery during charging. Accurate modeling of the battery charging internal resistance has a decision-making reference for the safety and thermal management system of electric vehicles. significance.

At present, there are two common methods for obtaining the charging internal resistance of lithium-ion batteries: describing the battery characteristics based on the equivalent circuit model and obtaining the charging internal resistance, or obtaining the charging internal resistance based on the charging pulse current and voltage.

The method of describing the battery characteristics and obtaining the charging internal resistance based on the equivalent circuit model usually has a large amount of calculation and is slow in calculation, and has high requirements on the quantity and quality of the data used. In the case of insufficient data or poor data quality, etc. The estimation accuracy is poor, which is not conducive to online implementation. Obtain charging internal resistance based on charging pulse current and voltage By analyzing the influence of temperature and SOC on battery charging internal resistance, and constructing an internal resistance model of charging internal resistance with respect to temperature and SOC. However, the prediction results obtained by only considering the charging internal resistance affected by temperature and SOC have large errors. In summary, the existing battery charging internal resistance prediction models mainly have large model errors, and do not integrate all charging internal resistance factors for accurate modeling. In view of this situation, building a battery charging internal resistance model and realizing accurate prediction of battery charging internal resistance has become the focus of researchers in the battery field, which is of great significance to the development of the battery industry.

Contents of the invention

The purpose of the present invention is to overcome the defects of the existing battery charging internal resistance modeling method, and propose a multi-factor battery charging internal resistance modeling method integrating charging rate. By testing the charging internal resistance under different charging rates, temperatures and SOC and analyzing its characteristics, and finally taking the above three factors as independent variables and internal resistance as dependent variable, a multi-factor dynamic charging internal resistance model is constructed to realize the High-precision prediction of battery charging internal resistance.

For realizing above-mentioned goal, the technical scheme that this method adopts is:

A multi-factor battery charging internal resistance modeling method integrating charging rate, at least including two parts: construction of battery multi-factor dynamic charging internal resistance model and Multi-rate HPPC method internal resistance test experiment to measure battery charging internal resistance.

The construction of the multi-factor dynamic charging internal resistance model of the battery at least includes the following steps:

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

Step 2: Under different charging rates C=(C ₁ ,C ₂ ,…,C _n ), respectively establish the function fitting of charging internal resistance R with respect to T and SOC: use the binary polynomial function fitting factor of the least square method The n(n≥4) order functional relationship between the variable R and the independent variable T and SOC:

分别是R在不同充电倍率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分别是在不同充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 under different charging rates C ₁ , C ₂ ,...,C _n ; a _ij,1 ,a _ij,2 ,...,a _ij,n are the binary polynomial coefficients at different charging rates;

Step 3: According to the binary polynomial obtained in step 2, extract the binary polynomial function coefficients a _ij,1 ,a _ij,2 ,...,a _{ij, n} , the coefficient group a _ij constituting 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 set of binary polynomial function coefficients of R about T and SOC fitting under all measured charge 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 charging rate C;

Step 4-1: Take the binary polynomial function coefficient group a _ij extracted in step 3 under different charging ratios, and take m+1 nodes on the charging ratio array interval based on the cubic spline interpolation method, so that the charging ratio array interval is [ C ₁ ,C _m+1 ], divide the charge 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 the charging rate data points of each segment of the charging rate array;

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

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

Step 5: Construct a multi-factor dynamic charging internal resistance mathematical model of R with respect to T, SOC and charging rate C: Substituting formula (4) into formula (2) to obtain the charging rate C as an independent variable, R is binary with respect to 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 constructed with internal resistance as the dependent variable and temperature, SOC and charging rate as independent variables.

The described Multi-rateHPPC method internal resistance test experiment measures battery charging internal resistance at least including the following steps:

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

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

Step 3: Multi-rate HPPC charging internal resistance test: First, discharge the battery at a constant current rate of I ₁ C for 10s, then leave it for 40s, then charge it with a constant current of I ₂ C rate for 10s, leave it for 40s, and finally charge it with a constant current of I ₃ C rate Charge for 10s (for short-term recharging of the battery to realize capacity compensation), and put aside 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 current of I ₁ by 0.25C, and repeat the Multi-rateHPPC charging internal resistance test, I ₂ and I ₃ are changed according to a fixed ratio until the maximum charge and discharge rate of the battery is reached .

Step 4: Internal resistance test in 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 under 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 in turn, repeat steps 1 to 4, and measure the temperature of the battery at these points respectively. Response voltage and response current data under four temperature conditions.

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

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 charging rates and SOC changes; (2) The experimental verification results show that the established dynamic internal resistance model can be used under various rates and temperatures. Accurate estimation of battery charging internal resistance is achieved.

Description of drawings

Fig. 1 is a flow chart of a multi-factor battery charging internal resistance modeling method integrating charging rate according to the present invention.

Detailed ways

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

As shown in Figure 1, in order to overcome the defect of low prediction accuracy of the battery charging internal resistance model in the prior art, the present invention proposes a multi-factor battery charging internal resistance modeling method integrating charging rate, which specifically includes the following steps:

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

Build a multi-rate HPPC method charging internal resistance experimental test platform in the laboratory. The experimental test platform is composed of three parts: battery charging and discharging system, high and low temperature alternating test box and lithium ion battery. The charging and discharging system mainly includes DC power supply, electronic load instrument and PC, etc.

Acquire battery charging data such as battery charging current and battery charging voltage in advance from the charging internal resistance experimental test platform.

Step 2: Under different charging rates C=(C ₁ ,C ₂ ,…,C _n ), respectively establish the function fitting of charging internal resistance R with respect to T and SOC: use the binary polynomial function fitting factor of the least square method The n(n≥4) order functional relationship between the variable R and the independent variable T and SOC:

分别是R在不同充电倍率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分别是在不同充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 under different charge rates C ₁ , C ₂ ,...,C _n ; a _ij,1 ,a _ij ,2,...,a _ij,n are the binary polynomial coefficients at different charging rates;

Step 3: According to the binary polynomial obtained in step 2, extract the binary polynomial function coefficients a _ij,1 ,a _ij,2 ,...,a _{ij, n} , the coefficient group a _ij constituting 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 set of binary polynomial function coefficients of R about T and SOC fitting under all measured charge 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 charging rate C;

Step 4-1: Take the binary polynomial function coefficient group a _ij extracted in step 3 under different charging ratios, and take m+1 nodes on the charging ratio array interval based on the cubic spline interpolation method, so that the charging ratio array interval is [ C ₁ ,C _m+1 ], divide the charge 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 the charging rate data points of each segment of the charging rate array;

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

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

Step 5: Construct a multi-factor dynamic charging internal resistance mathematical model of R with respect to T, SOC and charging rate C: Substituting formula (4) into formula (2) to obtain the charging rate C as an independent variable, R is binary with respect to 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 constructed with internal resistance as the dependent variable and temperature, SOC and charging rate as independent variables.

Although the above embodiment describes the specific implementation of the present invention, so that those skilled in the art can understand the present invention, it should be pointed out that this embodiment is only a representative example of the present invention. It is obvious that the present invention is not limited to the above specific embodiments, and various modifications, changes and variations can be made. Accordingly, the specification and drawings are to be regarded as illustrative rather than restrictive. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention shall be deemed to belong to the protection scope of the present invention.

Claims (2)

1. A multi-factor battery charging internal resistance modeling method integrating charging rate, characterized in that the establishment of the charging internal resistance model takes into account temperature T, state of charge (State of Charge, abbreviated as SOC) and charging rate The influence of C on charging internal resistance 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, operating voltage U and operating current I during charging, and calculate its charging internal resistance R:

Step 2: Under different charging rates C=(C ₁ ,C ₂ ,…,C _n ), respectively establish the function fitting of charging internal resistance R with respect to T and SOC: use the binary polynomial function fitting factor of the least square method The n(n≥4) order functional relationship between the variable R and the independent variable T and SOC:

R _C1 (T,SOC), R _C2 (T,SOC),…,R _Cn (T,SOC) are the temperature and SOC of R at different charging rates C ₁ ,C ₂ ,…,C _n Binary polynomial fitting function; a _ij,1 ,a _ij,2 ,...,a _ij,n are binary polynomial coefficients at different charging rates; Step 3: According to the binary polynomial obtained in step 2, extract the binary polynomial function coefficients a _ij,1 ,a _ij,2 ,...,a _{ij, n} , the coefficient group a _ij constituting 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 set of binary polynomial function coefficients of R about T and SOC fitting under all measured charge rates; Step 4: Establish the intrinsic functional relationship between the coefficient group a _ij and the charging rate; Step 4-1: Based on the binary polynomial function coefficient group a _ij extracted in step 3 under different charging magnifications, m+1 nodes are selected on the magnification array interval based on the cubic spline interpolation method, and the magnification array is divided into m segments; Step 4-2: Construct a cubic spline interpolation function segmentally between each magnification data point of the magnification array; Step 4-3: Obtain an overall continuous cubic spline interpolation function with the charging rate C as the independent variable:

Among them, A _ij is the cubic spline fitting function of the charging rate C with respect to the coefficient group a _ij , F ₁ (C), F ₂ (C),..., F _m (C) is the charging rate in the corresponding interval [C ₁ , C ₂ ],[C ₂ ,C ₃ ],…,[C _m ,C _m+1 ] Cubic spline piecewise fitting function about the coefficient group a _ij ; Step 5: Construct a multi-factor dynamic charging internal resistance mathematical model of R with respect to T, SOC and charging rate C: Substituting formula (4) into formula (2) to obtain the charging rate C as an independent variable, R is binary with respect to 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 constructed with internal resistance as the dependent variable and temperature, SOC and charging rate as independent variables. 2. According to claim 1, a multi-factor battery charging internal resistance modeling method fused with charge rate is characterized in that, in the step 2, the charging internal resistance R under different charge rates varies with T and SOC Variety.

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