CN112798971B - Soft-package type lithium ion battery coupling electric thermal model - Google Patents

Abstract

The invention relates to a soft package type lithium ion battery coupling electric thermal model, which comprises the following components: step 1, establishing a thermal model of a lithium ion battery; step 2, establishing an electrical model of the lithium ion battery; step 3, establishing a lithium ion battery thermal generation model; step 4, calculating characteristic parameters of the coupling electric thermal model; and 5, experimental verification. The invention has the beneficial effects that: the invention can provide effective temperature information for the lithium battery management system under the condition of not using a temperature sensor, thereby realizing the homogenization of the temperature distribution of the single battery; the provided coupling electric thermal model can be applied to a cylindrical lithium battery monomer to establish a lithium battery full-parameter model; the coupling electric thermal model suitable for the soft package type lithium ion battery considers the non-uniform current distribution characteristics and estimates the influence of current on the surface temperature; the method is applied to the lithium polymer soft package type lithium ion battery, the error of the predicted actual average temperature in the current transient process is less than 2K, and the error in the current stable state is less than 1.5K.

Description

A Coupling Electrical-Thermal Model of a Soft-Packed Li-ion Battery

technical field

The invention belongs to the field of charging and discharging of lithium ion batteries, and in particular relates to a coupled electrical thermal model of a soft pack lithium ion battery; more particularly, to an electrical model, a heat generation model and a thermal Model establishment and testing of electrical model parameters, thermal performance parameters and heat capacity parameters.

Background technique

With the increasing emphasis on environmental protection in the world, new energy electric vehicles have been vigorously promoted by various countries, and soft-pack lithium-ion batteries have become the first choice for power batteries. When a lithium-ion battery is charged and discharged, a complex chemical reaction occurs inside. The chemical reaction generates heat and the ohmic heat generated by the internal resistance when the current flows through the battery, as well as the specific heat capacity and thermal conductivity of the battery. , The research on the working principle and thermal characteristics of the lithium-ion battery cell can provide a theoretical basis for the design of the thermal management system of the battery pack. The internal resistance of the battery is not constant during the discharge process, it varies with the ambient temperature and the depth of discharge (DOD) of the battery itself. Li Zhe et al. conducted experimental research on the temperature characteristics of power batteries. The experiments showed that the ambient temperature has a great influence on the battery capacity. The lower the ambient temperature, the faster the capacity decay. The ohmic internal resistance varies more with temperature than the polarization internal resistance. By analyzing the thermal characteristics of the battery, Ren Baofu found that the heat of reaction is indispensable in the analysis of the heat generation of the battery. The battery exhibits an endothermic reaction during the charging process and an exothermic reaction during the discharging process.

At present, most scholars conduct a series of simplifications on the theoretical model to study the heat generation of the battery in the research on the thermal model of the pouch lithium-ion battery. By analyzing and studying the Bernardi heat generation rate model, different heat generation models can be constructed. According to different dimensions, there are concentrated mass model, one-dimensional model, two-dimensional model, and three-dimensional model. According to the principle of heat generation, it can be divided into electrochemical-thermal coupling model, electrical-thermal coupling model, thermal abuse model, etc. The electrical-thermal coupling model is relatively common in battery research, mainly based on the current density distribution inside the battery or the electrical-thermal coupling model established by the RC circuit impedance model. However, the former needs to obtain the current density distribution inside the battery, which is mostly used in two-dimensional or three-dimensional temperature field analysis. The latter needs to obtain the internal resistance of the battery and its change curve, which can be used for zero-dimensional, one-dimensional, and multi-dimensional analysis.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies in the prior art and provide a coupling electric thermal model of a soft-pack lithium-ion battery.

This pouch-type Li-ion battery coupled electrical thermal model includes the following steps:

Step 1. Establish a lithium-ion battery thermal model: establish an equivalent circuit of the lithium-ion battery thermal model, define the lithium-ion battery thermal model parameters, and calculate the air thermal resistance;

Step 2. Establish an electrical model of the lithium-ion battery: set four longitudinal resistors _Re1 with symmetrical structures and the same value, and set up two lateral resistors _Re2 with symmetrical structures and the same value; one of the lateral resistors _Re2 is connected to both ends After one vertical resistor _Re1 , it is connected in parallel with another horizontal resistor _Re2 ; both ends of the other horizontal resistor _Re2 are also connected to one end of the remaining two vertical resistors _Re1 , and the other ends of the remaining two vertical resistors _Re1 are respectively connected The connection point of the positive and negative electrodes outside the battery; the total input current i of the battery is divided into branch current i ₁ and branch current i ₃ , and the branch current i ₁ continues to be divided into branch current i ₂ and branch current i ₄ ; the heat generated in the upper branch is Q _a , the heat of generation in the lower branch is Q _b ;

Step 3. Establish a heat generation model for the lithium-ion battery, decompose the total calorific value Q _total into an irreversible thermal component Q _ir and a reversible thermal component Q _r , and calculate the total calorific value Q _total :

In the above formula, Q _ir is the irreversible thermal component, Q _r is the reversible thermal component, R _b is the ohmic internal resistance of the lithium-ion battery, i is the total battery input current, T _s is the surface temperature of the lithium-ion battery, and E is the total lithium-ion battery. energy;

According to the electrical model of the lithium-ion battery established in step 2, the parameters of the heat generation model are calculated, and the calculation formulas of the generation heats Q _a and Q _b are:

In the above formula, Q _a and Q _b are generated heat, R _e1 is the vertical resistance, R _e2 is the lateral resistance, i ₁ , i ₂ , i ₃ , i ₄ are the branch currents, and T ₁₃ is the difference between T ₁ and T ₃ Mathematical average value, T1 and T3 are the temperatures of temperature measurement point ₁ and temperature measurement point ₃ in the equivalent circuit of the thermal model of the lithium _- ion battery respectively _{; T24} is the mathematical average value of T2 and T4, _T2 and _T4 are the temperature of temperature measurement point 2 and temperature measurement point 4 in the equivalent circuit of the thermal model of the lithium-ion battery, respectively; in the electrical model of the lithium-ion battery, the lateral resistance _Re2 is equally distributed between the left and right branches;

Step 4. Calculate the characteristic parameters of the coupled electrical thermal model, where the characteristic parameters of the coupled electrical thermal model include thermal resistance, thermal capacity and electrical model parameters;

Step 5. Experimental verification: cyclic charge and discharge experiments are performed on the soft pack battery, the same current distribution is input into the electrical thermal model, and simulation calculations are performed.

Preferably, step 1 specifically includes the following steps:

Step 1-1. Establish an equivalent circuit of the thermal model of the lithium ion battery. There are five RC parallel circuits in the thermal model equivalent circuit, and four connecting resistors R _t1 connect the center of the lithium ion battery to the outside, and the connecting resistor R _t1 The two groups are connected in series and then divided into two groups. The two groups of connection resistances R _t1 are located on both sides of the lithium-ion battery and are symmetrical with respect to the lithium-ion battery. Each group of connection resistances R _t1 is connected to both ends of an air thermal resistance R _ta ; the thermal resistance After R _t2 is connected in parallel with the capacitor C _t2 , the two ends are respectively connected between the two series connection resistors R _t1 in the two groups of connection resistors R _t1 ; the two capacitors C _t1 are connected in series to form a group of capacitors, and the two capacitor groups are The two sides of the lithium-ion battery are symmetrical, and the two ends of the two capacitor groups are connected in parallel; after the thermal resistance R _t2 is connected in parallel with the capacitor C _t2 , the two ends are also connected between two series-connected capacitors C _t1 ;

Step 1-2: Define the thermal model parameters of the lithium-ion battery: R _t1 is the thermal resistance, which is used to connect the center of the lithium-ion battery with the outside; R _ta is the air thermal resistance, and the thermal resistances R _t1 and The air thermal resistance R _ta is symmetrical and has the same resistance value; C _t1 is a capacitor, and the four equivalent capacitors C _t1 represent vertical thermal capacitors; R _t2 is a thermal resistance, C _t2 is a capacitor, and two thermal resistance R _t2 and capacitor C _t2 are connected vertical branch;

Step 1-3. Calculate the air thermal resistance R _ta according to the air thermal coefficient h (h=30W/m ² K) and the surface area of 1/2 lithium ion battery:

In the above formula, W is the width of the single lithium-ion battery, L is the length of the single lithium-ion battery, h is the air thermal coefficient, and R _ta is the air thermal resistance.

Preferably, step 4 specifically includes the following steps:

Step 4-1. Establish a thermal resistance model, test and calculate the thermal resistance through the test circuit: using N battery patches as a heat source (2≤N≤5), the calculation formula for the heat generated by each battery patch is:

In the above formula, Q is the heat generated by each battery patch, α is the Seebeck coefficient of the semiconductor material, T _c is the measured temperature of the battery patch, and T _c corresponds to the temperature measurement point 3 in the equivalent circuit of the thermal model of the lithium-ion battery. Temperature T ₃ and temperature T 4 of temperature measuring point ₄ ; T _d is the side temperature of the battery, T _d corresponds to the temperature of the radiator; R _p is the battery chip resistance, θ is the battery chip thermal resistance, and i _p is the battery chip internal current;

其中Q_pa和Q_pb为电池贴片的生成热；根据式(4)计算电池贴片的生成热Q_pa和Q_pb，然后计算热电阻R_t1：Use N battery patches at the same time to meet the

Among them, Q _pa and Q _pb are the heat of generation of the battery patch; calculate the heat of generation Q _pa and Q _pb of the battery patch according to formula (4), and then calculate the thermal resistance R _t1 :

In the above formula, T ₁ and T ₃ are the temperatures of temperature measurement point 1 and temperature measurement point 3 in the equivalent circuit of the thermal model of the lithium-ion battery, respectively; T ₂ and T ₄ are the temperature measurement points in the equivalent circuit of the thermal model of the lithium-ion battery, respectively. The temperature of point 2 and temperature measurement point 4; Q _pa and Q _pb are the heat generated by the battery patch;

Step 4-2. Thermal capacity test and calculation: establish a simplified thermal model circuit: connect the thermal resistance R _t1 and the air thermal resistance R _ta in series, calculate the equivalent resistance R _t after the two branches are connected in parallel, R _t = (R _t1 + R _ta )/2, establish the state matrix formula of the heat capacity calculation formula:

The eigenvalues λ ₁ and λ ₂ in the state matrix formula (6) are calculated as follows:

In the above formula (6) and the above formula (7), C _t1 is a capacitor, C _t is a parallel capacitor of two C _t1 , C _t =2C _t1 ; C _t2 is a capacitor; T _m1 and T _m2 are simplified thermal model circuits The temperature value of the vertical midpoint of the left and right branches; R _t is the equivalent resistance after the two branches are connected in parallel, Q _a and Q _b are the heat generated by the electrical model of the lithium-ion battery, λ ₁ and λ ₂ are the formula ( 6) eigenvalues;

Using the sliding window filter, the average zero-phase temperature second-order exponential function is fitted, and the eigenvalues in equation (7) are obtained:

In the above formula, a, b and c are fitting coefficients, which depend on the initial conditions and temperature input values; λ ₁ and λ ₂ are the eigenvalues of formula (6); the calculation formulas of heat capacity C _t1 and C _t2 are:

其中E为电池总能量，T_s为锂离子电池表面温度；假设R_e1＝R_e2＝R_e，则电池等效内阻R_o与R_e之间的关系表示为：Step 4-3, test and calculate the electrical model parameters: find the equivalent internal resistance R _o and entropy coefficient of the battery

Among them, E is the total energy of the battery, and T _s is the surface temperature of the lithium-ion battery. Assuming that _Re1 = _Re2 = _Re , the relationship between the battery equivalent internal resistance _Ro and _Re is expressed as:

Since the equivalent internal resistance value R _o of the battery is related to temperature, the internal resistance value R _o (T) related to temperature is calculated by the following exponential function interpolation:

温度值空间分布模型中，锂离子电池单个内阻R_e与T_m1、T_m2具有相关性，T_m3为T_m1和T_m2的数学平均值；T_m1为温度值空间分布模型中上支路的温度值，T_m2为温度值空间分布模型中下支路的温度值；In the above formula, k ₁ , k ₂ , and k ₃ are interpolation coefficients; a spatial distribution model of temperature values is established to calculate the entropy coefficient

In the temperature value spatial distribution model, the single internal resistance _Re of the lithium-ion battery has a correlation with T _m1 and T _m2 , and T _m3 is the mathematical average of T _m1 and T _m2 ; T _m1 is the upper branch in the temperature value spatial distribution model. The temperature value of , T _m2 is the temperature value of the lower branch in the temperature value spatial distribution model;

The entropy coefficient as a function of SOC, the entropy coefficient is expressed as:

In the above formula, parameters k ₄ and k ₅ are temperature calibration values, and the SOC value is between 0 and 1.

Preferably, the lithium ion battery described in steps 1 to 5 is a polymer soft pack lithium ion battery.

Preferably, in step 5, Matlab/Simulink is used for simulation calculation.

The beneficial effects of the present invention are:

(1) The present invention proposes a coupled electrical thermal model suitable for a soft-pack lithium-ion battery. Based on the current value of the lithium battery and the environmental conditions of heat exchange, the temperature values at different points on the battery surface and inside the battery are calculated.

(2) The coupled electrical-thermal model suitable for pouch-type lithium-ion batteries considers the non-uniform current distribution characteristics and estimates the effect of current on the surface temperature.

(3) The present invention applies the coupled electrical thermal model of the pouch type lithium ion battery to the lithium polymer pouch type lithium ion battery. The experimental test and simulation results show that the error of predicting the actual average temperature in the current transient process is less than 2K, The error is less than 1.5K under the current steady state.

(4) The coupled electrical thermal model of the soft-pack lithium-ion battery can provide effective temperature information for the lithium battery management system without using a temperature sensor, and realize the uniform temperature distribution of the single battery.

(5) The coupled electrical thermal model proposed by the present invention can be applied to a cylindrical lithium battery cell to establish a full parameter model of the lithium battery.

Description of drawings

Figure 1 is a thermal model diagram of a soft-pack lithium-ion battery;

Figure 2 is a front view of the electrical model;

Figure 3 is a thermal resistance model diagram;

Figure 4 is a diagram of the R _t2 test model;

Fig. 5 is the battery temperature distribution trend diagram in the heat capacity estimation experiment;

Figure 6 is a simplified thermal model circuit diagram;

Figure 7 is a spatial distribution diagram of temperature values;

Figure 8(a) is the temperature value curve of the electrical thermal model at point T1, Figure ₈ (b) is the temperature value curve of the electrical thermal model at point T2, and Figure ₈ ( _c ) is the temperature value curve of the electrical thermal model at point T3 Temperature value curve, Figure 8( _d ) is the temperature value curve of the electrical thermal model at point T4;

Fig. 9(a) is the temperature average error curve of experimental test and simulation calculation under 50A charge and discharge current, Fig. 9(b) is the temperature average error curve of experimental test and simulation calculation under 40A charge and discharge current, Fig. 9(c) ) is the temperature average error curve of experimental test and simulation calculation under 20A charge-discharge current.

Detailed ways

The present invention will be further described below in conjunction with the embodiments. The following examples are illustrative only to aid in the understanding of the present invention. It should be pointed out that for those skilled in the art, without departing from the principle of the present invention, the present invention can also be modified several times, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

The invention provides a coupled electrical-thermal model suitable for a soft-pack type lithium ion battery, and identifies the surface temperature and the internal temperature of the lithium ion battery according to the ambient temperature.

As an embodiment, a working method for coupling an electrical thermal model of a pouch-type lithium-ion battery includes the following steps: Step 1: Establish a thermal model of a pouch-type lithium-ion battery; the lithium-ion battery sample is a polymer pouch-type lithium-ion battery Battery.

Step 1-1. The equivalent circuit of the thermal model of the lithium-ion battery is shown in Figure 1. H represents the height of the single battery, L represents the length of the single battery, Q _a and Q _b represent the heat generation value based on the input current, and T _a is Ambient temperature; different from the existing thermal model, the thermal model equivalent circuit established in this embodiment can calculate the internal intermediate temperature and the temperature values (T ₁ , T ₂ , T ₃ , T ₄ ) at different points on the upper and lower surfaces, while maintaining Lower computational complexity.

Step 1-2: Define the thermal model parameters of the soft-pack lithium-ion battery: The thermal model is divided into five RC parallel circuits, which can better represent the transient thermal behavior; the specific parameters are defined as follows: R _t1 is the connection resistance, used to connect The center of the pouch-type lithium-ion battery is connected to the outside; R _ta is the air thermal resistance, the air thermal resistance R _ta on both sides of the pouch-type lithium-ion battery is symmetrical and has the same resistance value, and the air on both sides of the pouch-type lithium-ion battery The thermal resistance R _ta is related to the thermal conductivity of the pouch type lithium-ion battery in the vertical direction; C _t1 is the capacitance, and the four equivalent capacitances C _t1 represent the vertical thermal capacitance; R _t2 is the connection resistance, C _t2 is the capacitance, connected The resistor R _t2 and the capacitor C _t2 connect the two vertical branches and are related to the thermal conductivity and thermal capacitance in the horizontal direction;

Step 1-3. Calculate the air thermal resistance R _ta according to the air thermal coefficient h (h=30W/m ² K) and the surface area of the 1/2 soft-pack lithium-ion battery:

In the above formula, W is the width of the soft-pack single-cell lithium-ion battery, L is the length of the soft-pack single-cell lithium-ion battery, h is the air thermal coefficient, and R _ta is the air thermal resistance;

Step 2. Establish the electrical model of the pouch type lithium-ion battery: Figure 2 is a front view of the electrical model of the pouch type lithium ion battery. Four longitudinal resistors R _e1 with symmetrical structures and the same value are set, and two structures are symmetrical and take the same value. Lateral resistors _Re2 with the same value; two ends of one of the lateral resistors _Re2 are connected with a vertical resistor _Re1 , and then connected in parallel with the other lateral resistor _Re2 ; the two ends of the other lateral resistor _Re2 are also connected to the remaining two vertical resistors One end of _Re1 and the other ends of the remaining two longitudinal resistors _Re1 are respectively connected to the external positive and negative terminals of the battery; the longitudinal resistance _Re1 and the lateral resistance _Re2 are related to the heat generated by the Joule effect and the polarization effect. The Joule effect and The heat generated by the polarization effect corresponds to the irreversible heat value inside the battery; the total input current i of the battery is divided into branch current i ₁ and branch current i ₃ , and the branch current i ₁ continues to be divided into branch current i ₂ and branch current i ₄ ; The generated heat of the channel is Q _a , and the generated heat of the lower branch is Q _b ;

Step 3. Establish a heat generation model of the pouch type lithium-ion battery, decompose the total calorific value Q _total into an irreversible thermal component Q _ir and a reversible thermal component Q _r , both of which are related to the amount of electricity; calculate the total calorific value Q _total :

In the above formula, Q _ir is the irreversible thermal component, Q _r is the reversible thermal component, R _b is the ohmic internal resistance of the pouch type lithium ion battery, i is the total input current of the battery, T _s is the surface temperature of the pouch type lithium ion battery, E is the total energy of the soft-pack lithium-ion battery;

The irreversible thermal component Q _ir is related to the Joule effect and polarization effect. According to the electrical model of the pouch lithium-ion battery established in step 2 (see Figure 2), the parameters of the heat generation model are calculated. The calculation formulas of the generated heats Q _a and Q _b are: :

In the above formula, Q _a and Q _b are generated heat, R _e1 is the vertical resistance, R _e2 is the lateral resistance, i ₁ , i ₂ , i ₃ , i ₄ are the branch currents, and T ₁₃ is the difference between T ₁ and T ₃ Mathematical average value, T1 and T3 are the temperatures of temperature measurement point ₁ and temperature measurement point ₃ in the equivalent circuit of the thermal model of the lithium _- ion battery respectively _{; T24} is the mathematical average value of T2 and T4, _T2 and _T4 are the temperature of temperature measurement point 2 and temperature measurement point 4 in the equivalent circuit of the thermal model of the lithium-ion battery, respectively; in the electrical model of the soft-pack lithium-ion battery, the lateral resistance R _e2 is evenly distributed between the left and right branches; the above formula (3) shows that the reversible thermal component Q _r related to the total current i is equally divided between Q _a and Q _b ;

Step 4. Calculate the characteristic parameters of the coupled electrical thermal model, where the characteristic parameters of the coupled electrical thermal model include thermal resistance, thermal capacity and electrical model parameters;

Step 4-1. Establish the thermal resistance model shown in Figure 3, and test and calculate the thermal resistance through the test circuit shown in Figure 4: In order to characterize the thermal resistance characteristics of the battery, use N battery patches as the heat source (2≤N≤5 ), the calculation formula for the heat generated by each battery patch is:

In the above formula, Q is the heat generated by each battery patch, α is the Seebeck coefficient of the semiconductor material, T _c is the measured temperature of the Peltier battery patch, and T _c corresponds to the temperature measurement point 3 in the equivalent circuit of the thermal model of the lithium-ion battery. The temperature T ₃ and the temperature T 4 of the temperature measuring point ₄ ; T _d is the battery side temperature, T _d corresponds to the radiator temperature; R _p is the battery chip resistance, θ is the battery chip thermal resistance, and i _p is the battery chip On-chip current;

其中Q_pa和Q_pb为Peltier电池贴片的生成热；根据式(4)计算Peltier电池贴片的生成热Q_pa和Q_pb，然后计算热电阻R_t1：In the experimental process of the present invention, N battery patches are used at the same time, and the thermal resistance model is shown in FIG.

Among them, Q _pa and Q _pb are the generated heat of the Peltier battery patch; calculate the generated heat Q _pa and Q _pb of the Peltier battery patch according to formula (4), and then calculate the thermal resistance R _t1 :

In the above formula, T ₁ and T ₃ are the temperatures of temperature measurement point 1 and temperature measurement point 3 in the equivalent circuit of the thermal model of the lithium-ion battery, respectively; T ₂ and T ₄ are the temperature measurement points in the equivalent circuit of the thermal model of the lithium-ion battery, respectively. The temperature of point 2 and temperature measurement point 4; Q _pa and Q _pb are the generated heat of the battery patch; Figure 4 is the R _t2 test circuit, using the actual measured temperature to calculate the R _t2 resistance value.

Step 4-2, heat capacity test and calculation: Figure 5 shows the battery temperature distribution trend in the heat capacity test experiment. It can be seen from the figure: (1) In the steady state of the current, due to the existence of the reversible heat component, the battery temperature changes frequency and current change The frequency is the same; (2) In the charging stage, the chemical reaction in the battery is an endothermic reaction, and in the discharging stage, an exothermic reaction occurs, causing the temperature value to oscillate. A simplified thermal model circuit is established as shown in Figure 6: connect the thermal resistance R _t1 and the air thermal resistance R _ta in series, and calculate the equivalent resistance R _t after the two branches are connected in parallel, R _t =(R _t1 +R _ta )/2 , establish the state matrix formula of the heat capacity calculation formula:

The eigenvalues λ ₁ and λ ₂ in the state matrix formula (6) are calculated as follows:

In the above formula (6) and the above formula (7), C _t1 is a capacitor, C _t is a parallel capacitor of two C _t1 , C _t =2C _t1 ; C _t2 is a capacitor; T _m1 and T _m2 are simplified thermal model circuits The temperature value of the vertical midpoint of the left and right branches; R _t is the equivalent resistance of the two branches in parallel, Q _a and Q _b are the heat generated by the electrical model of the pouch lithium-ion battery, λ ₁ and λ ₂ is the eigenvalue of formula (6);

According to the temperature change waveform shown in Figure 5, the sliding window filter is used to fit the average zero-phase temperature second-order exponential function, and the eigenvalues in equation (7) are obtained:

In the above formula, a, b and c are fitting coefficients, which depend on the initial conditions and temperature input values; λ ₁ and λ ₂ are the eigenvalues of formula (6); the calculation formulas of heat capacity C _t1 and C _t2 are:

其中E为电池总能量，T_s为软包式锂离子电池表面温度；假设R_e1＝R_e2＝R_e，则电池等效内阻R_o与R_e之间的关系表示为：Step 4-3, test and calculate the electrical model parameters: in order to characterize the electrical model parameters, the equivalent internal resistance R _o and entropy coefficient of the battery must be obtained

Among them, E is the total energy of the battery, and T _s is the surface temperature of the soft-pack lithium-ion battery. Assuming _Re1 = _Re2 = _Re , the relationship between the battery equivalent internal resistance _Ro and _Re is expressed as:

Since the equivalent internal resistance value R _o of the battery is related to temperature, the internal resistance value R _o (T) related to temperature is calculated by the following exponential function interpolation:

温度值空间分布模型中，软包式锂离子电池单个内阻R_e与T_m1、T_m2具有相关性，T_m3为T_m1和T_m2的数学平均值；T_m1为温度值空间分布模型中上支路的温度值，T_m2为温度值空间分布模型中下支路的温度值；In the above formula, k ₁ , k ₂ , and k ₃ are interpolation coefficients; establish the spatial distribution model of temperature values as shown in Figure 7 to calculate the entropy coefficient

In the temperature value spatial distribution model, the single internal resistance _Re of the soft-pack lithium-ion battery has a correlation with T _m1 and T _m2 , and T _m3 is the mathematical average of T _m1 and T _m2 ; T _m1 is the temperature value in the spatial distribution model. The temperature value of the upper branch, T _m2 is the temperature value of the lower branch in the temperature value spatial distribution model;

According to the temperature change trend shown in Figure 5, the entropy coefficient is used as a function of SOC, and the entropy coefficient is expressed as:

In the above formula, parameters k ₄ and k ₅ are temperature calibration values, which are used to calibrate the temperature value fluctuation in Figure 5, and the SOC value is between 0 and 1;

Step 5. Experimental verification: In order to verify the feasibility and effectiveness of the coupled electrical thermal model, in this example, a cyclic charge-discharge experiment was performed on the pouch type battery, the current values were 50A, 40A and 20A, and the same current distribution was input to the electrical In the thermal model, and use Matlab/Simulink for simulation calculation.

Experimental result 1:

FIG. 8 shows the measured value (bold solid curve) and the simulation calculation value (regular solid curve) of the electrical thermal model temperature value of the charge and discharge current value of 20A. Among them, the solid line represents the raw data of measured and simulated values, and the dashed line represents the filtered average data. It can be seen from Fig. 8 that: (1) the unfiltered experimental value and the simulated value have oscillation phenomenon, which is related to the reversible thermal component; ( ₂ ) the error between the experimental test value and the simulated calculated value of T3 is the smallest, and the two solid lines are in good agreement; (3) _The temperature value of T1 is the largest, reaching about 316K, and in the time range of 4000s-5000s, the peak temperature value is generated; (4) The experimental results obtained from the 4 temperature test points are all larger than the simulation calculation values; ( 5) The average value of the filter is related to the irreversible thermal component and is controlled within the range of 300K-308K.

Experimental result 2:

Fig. 9 shows the error value between the average temperature obtained by experimental measurement and simulation calculation, and the charge and discharge currents are 50A, 40A and 20A respectively. The experimental results show that: (1) the maximum error in the transient process is about 2K, and the maximum error in the steady state process is about 1.5K; (2) according to the results of Figure 8 and Figure 9, the integrated electrical thermal mode can The management system provides information without the need to install temperature sensors for all cells in the battery pack; (3) the pouch type battery pack design is realized under the condition that the temperature distribution between the battery packs is more uniform; (4) the new model can be based on the battery pack The temperature of the different batteries in the middle to distribute the current, so as to optimize the working efficiency of the battery pack and prolong the service life of the single battery.

Claims (4)

1. a working method of a soft pack type lithium ion battery coupling electrical thermal model, is characterized in that, comprises the following steps: Step 1. Establish a lithium-ion battery thermal model: establish an equivalent circuit of the lithium-ion battery thermal model, define the lithium-ion battery thermal model parameters, and calculate the air thermal resistance; Step 1-1. Establish an equivalent circuit of the thermal model of the lithium ion battery. There are five RC parallel circuits in the thermal model equivalent circuit, and four connecting resistors R _t1 connect the center of the lithium ion battery to the outside, and the connecting resistor R _t1 The two groups are connected in series and then divided into two groups. The two groups of connection resistances R _t1 are located on both sides of the lithium-ion battery and are symmetrical with respect to the lithium-ion battery. Each group of connection resistances R _t1 is connected to both ends of an air thermal resistance R _ta ; the thermal resistance After R _t2 is connected in parallel with the capacitor C _t2 , the two ends are respectively connected between the two series connection resistors R _t1 in the two groups of connection resistors R _t1 ; the two capacitors C _t1 are connected in series to form a group of capacitors, and the two capacitor groups are The two sides of the lithium-ion battery are symmetrical, and the two ends of the two capacitor groups are connected in parallel; after the thermal resistance R _t2 is connected in parallel with the capacitor C _t2 , the two ends are also connected between two series-connected capacitors C _t1 ; Step 1-2: Define the thermal model parameters of the lithium-ion battery: R _t1 is the thermal resistance, which is used to connect the center of the lithium-ion battery with the outside; R _ta is the air thermal resistance, and the thermal resistances R _t1 and The air thermal resistance R _ta is symmetrical and has the same resistance value; C _t1 is a capacitor, and the four equivalent capacitors C _t1 represent vertical thermal capacitors; R _t2 is a thermal resistance, C _t2 is a capacitor, and two thermal resistance R _t2 and capacitor C _t2 are connected vertical branch; Step 1-3. Calculate the air thermal resistance R _ta according to the air thermal coefficient h (h=30W/m ² K) and the surface area of 1/2 lithium ion battery:

In the above formula, W is the width of the single lithium-ion battery, L is the length of the single lithium-ion battery, h is the air thermal coefficient, and R _ta is the air thermal resistance; Step 2. Establish an electrical model of the lithium-ion battery: set four longitudinal resistors _Re1 with symmetrical structures and the same value, and set up two lateral resistors _Re2 with symmetrical structures and the same value; one of the lateral resistors _Re2 is connected to both ends After one vertical resistor _Re1 , it is connected in parallel with another horizontal resistor _Re2 ; both ends of the other horizontal resistor _Re2 are also connected to one end of the remaining two vertical resistors _Re1 , and the other ends of the remaining two vertical resistors _Re1 are respectively connected The connection point of the positive and negative electrodes outside the battery; the total input current i of the battery is divided into branch current i ₁ and branch current i ₃ , and the branch current i ₁ continues to be divided into branch current i ₂ and branch current i ₄ ; the heat generated in the upper branch is Q _a , the heat of generation in the lower branch is Q _b ; Step 3. Establish a heat generation model for the lithium-ion battery, decompose the total calorific value Q _total into an irreversible thermal component Q _ir and a reversible thermal component Q _r , and calculate the total calorific value Q _total :

In the above formula, Q _ir is the irreversible thermal component, Q _r is the reversible thermal component, R _b is the ohmic internal resistance of the lithium-ion battery, i is the total battery input current, T _s is the surface temperature of the lithium-ion battery, and E is the total lithium-ion battery. energy; According to the electrical model of the lithium-ion battery established in step 2, the parameters of the heat generation model are calculated, and the calculation formulas of the generation heats Q _a and Q _b are:

In the above formula, Q _a and Q _b are generated heat, R _e1 is the vertical resistance, R _e2 is the lateral resistance, i ₁ , i ₂ , i ₃ , i ₄ are the branch currents, and T ₁₃ is the difference between T ₁ and T ₃ Mathematical average value, T1 and T3 are the temperatures of temperature measurement point ₁ and temperature measurement point ₃ in the equivalent circuit of the thermal model of the lithium _- ion battery respectively _{; T24} is the mathematical average value of T2 and T4, _T2 and _T4 are the temperature of temperature measurement point 2 and temperature measurement point 4 in the equivalent circuit of the thermal model of the lithium-ion battery, respectively; in the electrical model of the lithium-ion battery, the lateral resistance _Re2 is equally distributed between the left and right branches; Step 4. Calculate the characteristic parameters of the coupled electrical thermal model, where the characteristic parameters of the coupled electrical thermal model include thermal resistance, thermal capacity and electrical model parameters; Step 5. Experimental verification: cyclic charge and discharge experiments are performed on the soft pack battery, the same current distribution is input into the electrical thermal model, and simulation calculations are performed. 2. according to the working method of the described soft pack type lithium ion battery coupling electric thermal model, it is characterized in that: step 4 specifically comprises the following steps: Step 4-1. Establish a thermal resistance model, test and calculate the thermal resistance through the test circuit: using N battery patches as a heat source (2≤N≤5), the calculation formula for the heat generated by each battery patch is:

In the above formula, Q is the heat generated by each battery patch, α is the Seebeck coefficient of the semiconductor material, T _c is the measured temperature of the battery patch, and T _c corresponds to the temperature measurement point 3 in the equivalent circuit of the thermal model of the lithium-ion battery. Temperature T ₃ and temperature T 4 of temperature measuring point ₄ ; T _d is the side temperature of the battery, T _d corresponds to the temperature of the radiator; R _p is the battery chip resistance, θ is the battery chip thermal resistance, and i _p is the battery chip internal current; Use N battery patches at the same time to meet the

Among them, Q _pa and Q _pb are the heat of generation of the battery patch; calculate the heat of generation Q _pa and Q _pb of the battery patch according to formula (4), and then calculate the thermal resistance R _t1 :

In the above formula, T ₁ and T ₃ are the temperatures of temperature measurement point 1 and temperature measurement point 3 in the equivalent circuit of the thermal model of the lithium-ion battery, respectively; T ₂ and T ₄ are the temperature measurement points in the equivalent circuit of the thermal model of the lithium-ion battery, respectively. The temperature of point 2 and temperature measurement point 4; Q _pa and Q _pb are the heat generated by the battery patch; Step 4-2. Thermal capacity test and calculation: establish a simplified thermal model circuit: connect the thermal resistance R _t1 and the air thermal resistance R _ta in series, calculate the equivalent resistance R _t after the two branches are connected in parallel, R _t = (R _t1 + R _ta )/2, establish the state matrix formula of the heat capacity calculation formula:

The eigenvalues λ ₁ and λ ₂ in the state matrix formula (6) are calculated as follows:

In the above formula (6) and the above formula (7), C _t1 is a capacitor, C _t is a parallel capacitor of two C _t1 , C _t =2C _t1 ; C _t2 is a capacitor; T _m1 and T _m2 are simplified thermal model circuits The temperature value of the vertical midpoint of the left and right branches; R _t is the equivalent resistance after the two branches are connected in parallel, Q _a and Q _b are the heat generated by the electrical model of the lithium-ion battery, λ ₁ and λ ₂ are the formula ( 6) eigenvalues; Using the sliding window filter, the average zero-phase temperature second-order exponential function is fitted, and the eigenvalues in equation (7) are obtained:

In the above formula, a, b and c are fitting coefficients, which depend on the initial conditions and temperature input values; λ ₁ and λ ₂ are the eigenvalues of formula (6); the calculation formulas of heat capacity C _t1 and C _t2 are:

Step 4-3, test and calculate the electrical model parameters: find the equivalent internal resistance R _o and entropy coefficient of the battery

Among them, E is the total energy of the battery, and T _s is the surface temperature of the lithium-ion battery. Assuming that _Re1 = _Re2 = _Re , the relationship between the battery equivalent internal resistance _Ro and _Re is expressed as:

Since the equivalent internal resistance value R _o of the battery is related to temperature, the internal resistance value R _o (T) related to temperature is calculated by the following exponential function interpolation:

In the above formula, k ₁ , k ₂ , and k ₃ are interpolation coefficients; a spatial distribution model of temperature values is established to calculate the entropy coefficient

In the temperature value spatial distribution model, the single internal resistance _Re of the lithium-ion battery has a correlation with T _m1 and T _m2 , and T _m3 is the mathematical average of T _m1 and T _m2 ; T _m1 is the upper branch in the temperature value spatial distribution model. The temperature value of , T _m2 is the temperature value of the lower branch in the temperature value spatial distribution model; The entropy coefficient as a function of SOC, the entropy coefficient is expressed as:

In the above formula, parameters k ₄ and k ₅ are temperature calibration values, and the SOC value is between 0 and 1. 3 . The working method for coupling an electrical thermal model of a pouch type lithium ion battery according to claim 1 , wherein the lithium ion battery in steps 1 to 5 is a polymer pouch type lithium ion battery. 4 . 4. The working method of the coupling electrical thermal model of the soft-pack type lithium ion battery according to claim 1, characterized in that: in step 5, Matlab/Simulink is used to carry out simulation calculation.

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