CN109033619A - A kind of transient temperature model modelling approach of 18650 type lithium battery discharge cycles - Google Patents

Abstract

The present invention relates to a kind of transient temperature model modelling approach of 18650 type lithium battery discharge cycles, comprising steps of 1) the foundation rule of lithium battery monomer discharge cycles thermal model；2) governing equation of transient state thermal behavior is established；3) boundary condition of transient state thermal behavior is established.The beneficial effects of the present invention are: the present invention is based on the pseudo- two dimensional models of Newman to establish transient temperature model of the lithium battery monomer under different discharge-rate operating conditions, designed, designed constant current charge-discharge experimental provision, acquisition calculates and emulates single battery thermal behavior data, and transient temperature parameter and voltage distribution curves are subjected to interpretation of result, transient temperature model proposed by the present invention has good reliability and validity；New model and new algorithm calculating speed proposed by the present invention is fast simultaneously, and computational solution precision is higher.

Description

A transient temperature model modeling method for 18650 type lithium battery discharge cycle

technical field

The present invention relates to a transient temperature model and a voltage distribution simulation curve of a 18650 lithium battery discharge cycle working condition, more specifically, it relates to the establishment of a lithium battery transient temperature model under a constant current discharge working condition, and The function relationship curve between temperature and discharge voltage.

Background technique

Lithium batteries are favored by the industry due to their advantages such as high energy density, long life, and low self-discharge rate, and currently occupy the main market for power batteries. Lithium batteries also have relatively large limitations, mainly because they need to work at a suitable ambient temperature. Too high or too low a temperature will have a great impact on its performance, cycle life and safety. Many scholars at home and abroad are committed to the research of lithium battery temperature model, and propose different modeling methods, such as artificial neural network, finite element model (FEM) or lumped parameter model (LPM), linear parameter variation (LPV) model or partial differential Equation (PDE) model, CFD model. The model based on electrochemical equations accurately describes the internal physical and chemical processes of the battery, and the electrochemical model is practical and reliable when designing battery cells. However, the calculation time of this model is long and it is not suitable for the highly dynamic lithium battery working environment. Newman and Tie proposed for the first time a method for electrochemical modeling of porous electrodes with dynamic applications in lithium batteries. In porous electrode theory, the electrode is considered as a superposition between the electrolyte solution and the solid matrix. The matrix itself is modeled as microscopic spherical particles in which lithium ions diffuse and react on the surface of the spheres. The method was promoted by Full et al., and the design included two composite models and a temperature model of the separator. This model is suitable for both lithium batteries and MH-Ni batteries.

According to the internal mechanism of lithium battery charge and discharge, the positive electrode, negative electrode and total reaction formula in the electrochemical reaction are:

positive electrode

negative electrode

total formula

Contents of the invention

The purpose of the present invention is to overcome the deficiencies in the prior art, and provide a transient temperature model modeling method of a 18650 type lithium battery discharge cycle.

The transient temperature model modeling method of this 18650 type lithium battery discharge cycle includes the following steps:

Step 1): The rules for establishing the thermal model of the lithium battery cell discharge cycle; the two-dimensional electrochemical model based on physical characteristics is combined with the charge conservation and thermal diffusion equations reflecting the performance of lithium batteries to calculate the temperature distribution value;

Step 2): establish the governing equation of transient thermal behavior; the equation describes the conservation of charge in the solid phase, the conservation of charge in the electrolyte phase, the conservation of lithium ions in the solid phase, and the conservation of lithium ions in the electrolyte phase;

Step 2-1): Establish the solid-phase charge conservation equation as follows:

▽(ρ ^eff ▽φ _s )-i ^Li ＝0 (4)

Another representation is:

And

And

Among them, ρ ^eff is the effective conductivity of the solid phase, ρ ₊ and ρ _- are the effective conductivity of the positive and negative electrodes respectively, φ ₊ and φ _- are the phase potential positive and negative electrodes respectively, l _n is the length of the negative electrode, and l _s is the separator Length, l _p is the length of the positive pole, L=l _n +l _s +l _p is the total length;

Step 2-2): Establish the electrolyte phase charge conservation equation as follows:

And

where κ ^eff is the effective diffusion conductivity, which satisfies β is the Burggeman porosity index; For the effective ionic conductivity, the calculation formula is:

Among them, f _± is the molecular activity system or the electrolyte activity coefficient of the electrolyte, _ξe is the volume fraction of the electrolyte phase in the electrode, R is the universal gas constant, F is the Faraday constant, Is the transfer number of lithium ions, and _Ce is the lithium concentration in the electrolyte;

Step 2-3): establish the solid-phase lithium ion conservation equation; the mass balance particle of lithium ion in the active solid material is in the spherical coordinate system and the equation is:

Combined with the boundary conditions as follows,

And

Among them, C _s is the concentration of lithium ions in the solid phase, D _s is the mass diffusion coefficient of lithium ions in the electrolyte, r is the radial coordinate along the active material particles, R _s is the radius of the solid active material particles; let a _s is the current distribution coefficient, and lithium ions are expressed as a _s,a and a _s,c during the insertion and deintercalation process, respectively, then the transfer current i ^Li caused by the insertion and deintercalation of lithium ions on the electrode/electrolyte interface is expressed as:

Step 2-4): Establish the electrolyte lithium ion conservation equation:

or expressed as:

where _ξe is the volume fraction/porosity of the electrolyte, is the effective diffusion coefficient, satisfying is the lithium ion transfer rate based on the solvent flow rate;

Step 3): Establish boundary conditions for transient thermal behavior;

Step 3-1): Establish the reaction rate equation; transform it into the governing equation of the coupled charge system:

where the local surface overpotential is expressed as:

η＝φ _s -φ _e -U (19)

The exchange current density is expressed as:

Among them, i ₀ is the exchange current density, α _a and α _c are the transfer coefficients of the anode and cathode, respectively, T is the temperature value, η is the overpotential, U is the thermodynamic OCV, C _s,max is the maximum concentration of solid-phase lithium, C _s,e is the concentration of lithium on the surface of solid particles, φ _s and φ _e are the potentials of the solid phase and the electrolyte phase, respectively;

The model is coupled to introduce temperature-based physical and chemical parameters, such as the electrolyte diffusion coefficient D _s and the lithium ion conductivity parameter k _m , the two parameters are expressed as:

At the same time, the formula for calculating the phase diffusion coefficient of the electrolyte is:

where Ds is the solid-phase diffusion coefficient, _Ds.ref is the reference solid diffusion coefficient, _km.ref is the reference reaction rate coefficient, _De is the diffusion coefficient of the electrolyte phase _{, Ed} is the activation controlling the temperature sensitivity of _Ds energy, E _r is the _activation energy controlling the temperature sensitivity of km, and T _ref is the temperature reference coefficient;

Step 3-2): Establish the energy conservation formula:

or expressed as:

The above formula is further modified as:

Wherein, the calculation formulas of each parameter in formula (26) and formula (27) are as follows:

▽(ρ ₊ ▽ _φ+ )＝-i (28)

▽(ρ _- ▽ _φ - )＝+i (29)

in, is the electrochemical heat, which satisfies formula (31):

Among them, _{ip is the lithium ion transfer current within the range of length l p ,} which satisfies the formula

As preferably: described step 1) comprises the following steps:

Step 1-1): The new model gives the governing equations and boundary conditions, and calculates the material characteristic parameters used for model establishment;

Step 1-2): The features of the new model are as follows: use a two-dimensional model based on physical characteristics to accurately estimate the dynamic behavior of the positive and negative electrodes; consider the material phase transition inside the active electrode particles; use the scanning electron microscope to obtain the particle size distribution inside the electrode .

The beneficial effect of the present invention is: the present invention is based on Newman's pseudo-two-dimensional model (P2D) and establishes the transient temperature model of lithium battery monomer under different discharge rate working conditions, designs constant current charging and discharging experiment device by oneself, collects, calculates and By simulating the thermal behavior data of a single battery, and analyzing the results of the transient temperature parameters and the voltage distribution curve, the transient temperature model proposed by the present invention has good reliability and effectiveness. Simultaneously, the new model and the new algorithm proposed by the invention have fast calculation speed and high calculation result precision.

Description of drawings

Figure 1 is a structural block diagram of the 18650 lithium battery experimental test device;

Figure 2 is a comparison result diagram of the experimental temperature and the simulated temperature at a discharge rate of 1C;

Fig. 3 is the comparison result figure of experimental temperature and simulated temperature under 4C discharge rate;

Fig. 4 is the comparison result diagram of experimental voltage and simulated voltage under 1C discharge rate;

Fig. 5 is a comparison result graph of the experimental voltage and the simulated voltage at a discharge rate of 4C.

Detailed ways

The present invention will be further described below in conjunction with the examples. The description of the following examples is provided only to aid 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, some improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

The transient temperature model modeling method of described 18650 type lithium battery discharge cycle, comprises the following steps:

Step 1): Establishment rules for the thermal model of the lithium battery cell discharge cycle. A two-dimensional electrochemical model based on physical characteristics is combined with the charge conservation and thermal diffusion equations reflecting the lithium battery performance to calculate the temperature distribution value.

Step 1-1): The new model gives the governing equations and boundary conditions, and calculates the material property parameters for model building.

Step 1-2): The features of the new model are as follows: use a two-dimensional model based on physical characteristics to accurately estimate the dynamic behavior of the positive and negative electrodes; consider the phase transition of the material inside the active electrode particles; use a scanning electron microscope (SEM) to obtain the internal state of the electrode. Particle size distribution.

Step 2): Establish the governing equations for the transient thermal behavior. The equations describe the conservation of charge in the solid phase, the conservation of charge in the electrolyte phase, the conservation of lithium ions in the solid phase, and the conservation of lithium ions in the electrolyte phase.

Step 2-1): Establish solid phase charge conservation equation. Based on Ohm's law, the solid-phase charge conservation equation is established as follows:

▽(ρ ^eff ▽φ _s )-i ^Li ＝0 (4)

Another representation is:

And

And

Among them, ρ ^eff is the effective conductivity of the solid phase, ρ ₊ and ρ _- are the effective conductivity of the positive and negative electrodes respectively, φ ₊ and φ _- are the phase potential positive and negative electrodes respectively, l _n is the length of the negative electrode, and l _s is the separator length, l _p is the length of the positive electrode. L=l _n +l _s +l _p is the total length.

Step 2-2): Establish the electrolyte phase charge conservation equation as follows:

And

where κ ^eff is the effective diffusion conductivity, which satisfies β is the Burggeman porosity index. For the effective ionic conductivity, the calculation formula is:

Among them, f _± is the molecular activity system of the electrolyte or the electrolyte activity coefficient, ξ _e is the volume fraction of the electrolyte phase in the electrode, R is the universal gas constant, the value is 8.3143kJ/kg.mol.K, F is the Faraday constant, The value is 96485Columb/mole, is the transfer number of lithium ions, and _Ce is the lithium concentration in the electrolyte.

Step 2-3): establishing a solid-phase lithium ion conservation equation. According to Fick's second law, the mass balance particles of lithium ions in active solid materials have the following equation in the spherical coordinate system:

Combined with the boundary conditions as follows,

And

Among them, C _s is the concentration of lithium ions in the solid phase, D _s is the mass diffusion coefficient of lithium ions in the electrolyte, r is the radial coordinate along the active material particle, and R _s is the radius of the solid active material particle. Assuming that a _s is the current distribution coefficient, and lithium ions are denoted as a _s,a and a _s,c during the insertion and deintercalation process, respectively, the transfer current i ^Li caused by the insertion and deintercalation of lithium ions on the electrode/electrolyte interface is expressed as :

Step 2-4): Establish the electrolyte lithium ion conservation equation:

or expressed as:

where _ξe is the volume fraction/porosity of the electrolyte, is the effective diffusion coefficient, satisfying is the lithium ion transfer rate based on the solvent flow rate.

Step 3): Establish boundary conditions for transient thermal behavior.

Step 3-1): Establish a reaction rate equation. The electrode surface electrochemical reaction rate is usually described by the Butler Volmer equation, which is transformed into the governing equation of the coupled charge system in the present invention:

where the local surface overpotential is expressed as:

η＝φ _s -φ _e -U (19)

The exchange current density is expressed as:

where _i0 is the exchange current density ( _a function of the lithium concentration in the electrolyte and the solid active material), α and α are the transfer coefficients of the anode and cathode, respectively, T is the temperature value ( _K ), and η is the overpotential (V) , U is the thermodynamic OCV, C _s,max is the maximum concentration of lithium in the solid phase, C _s,e is the concentration of lithium on the surface of solid particles, φ _s and φ _e are the potentials of the solid phase and the electrolyte phase, respectively.

The model is coupled and temperature-based physicochemical parameters are introduced, such as the electrolyte diffusion coefficient D _s and the lithium ion conductivity parameter k _m (K). According to the Arrhenius equation, the two parameters are expressed as:

At the same time, the formula for calculating the phase diffusion coefficient of the electrolyte is,

where Ds is the solid-phase diffusion coefficient, _Ds.ref is the reference solid diffusion coefficient, _km.ref is the reference reaction rate coefficient, _De is the diffusion coefficient of the electrolyte phase _{, Ed} is the activation controlling the temperature sensitivity of _Ds Energy, E _r is the activation energy to control the temperature sensitivity of km, T _ref is the temperature reference coefficient, the value is _298K .

Step 3-2): Establish the energy conservation formula:

or expressed as:

The above formula is further modified as:

Wherein, the calculation formulas of each parameter in formula (26) and formula (27) are as follows:

▽(ρ ₊ ▽ _φ+ )＝-i (28)

▽(ρ _- ▽ _φ - )＝+i (29)

in, is the electrochemical heat, which satisfies formula (31):

Among them, _{ip is the lithium ion transfer current within the range of length l p ,} which satisfies the formula

algorithm effect

The invention proposes a transient temperature model and a voltage distribution simulation curve under the single discharge cycle working condition of a 18650 type lithium battery. Under the two conditions of 1C (small current) and 4C (high current) discharge rate, the temperature distribution and voltage distribution of the battery cell are simulated and experimentally studied, and the following algorithm effects are obtained:

(1) As the discharge rate increases, the temperature distribution on the surface of the single battery increases, and the measured value of the thermocouple near the electrode is larger than the measured value of the centerline thermocouple;

(2) The internal heat generation phenomenon of lithium battery cells, resulting in changes in temperature and discharge time;

(3) The simulated temperature value obtained by the simulation of the new model is higher than the experimental value, especially the high-rate discharge condition, and the simulated value of the low-rate discharge condition is closer to the experimental value;

(4) The simulated temperature value of 4C discharge rate is 46.86°C, and the simulated value of 1C discharge rate is 29.6°C;

(5) The experimental and simulation results of the transient temperature model and the voltage distribution model established by the present invention realize the design and thermal optimization process of the lithium battery, and provide an important physical and chemical model basis.

As shown in Figure 1, the 18650 lithium battery is selected to measure the charging and discharging voltage, current and temperature parameters of the single battery. Table 1 lists the discharge rate and the charging and discharging current value of the single battery charging and discharging experiment. The device mainly consists of five parts: Arbin battery tester, National Instruments (NI) temperature measuring device, lithium battery unit with thermocouple, computer interface PC-1 and PC-2. The Arbin battery tester (BITRODE) has a maximum voltage of 20V and a maximum current of 1200A. Through the Visual C software, PC-1 controls the charging and discharging process of the single battery cycle, and records the charging and discharging voltage and current data, and PC-2 controls the thermal data collection.

Table 1 Constant current discharge experiment parameter settings

Discharge rate Constant current value 1C 1.5A 2C 3.0A 3C 4.5A 4C 6.0A

As shown in Figure 2 and Figure 3, it is the comparison result between the experimental temperature and the simulated temperature distribution under the discharge rate conditions of 1C and 4C. The initial temperature of the discharge experiment was set at 22 °C.

(1) Under the discharge rate conditions of 1C and 4C, the average surface temperature rises to 29.25°C and 42.16°C;

(2) The simulated temperature value obtained by the new algorithm simulation is higher than the experimental value, especially in the high-rate discharge condition. The simulated temperature value of the 4C discharge rate is 46.86°C, and the simulated value of the 1C discharge rate is 29.6°C, which is closer to the experimental value;

(3) The higher the discharge rate, the faster the surface temperature increases, and the change of temperature and discharge time may be caused by internal heat generation. It can be seen that the advantages of the new model and new algorithm proposed by the present invention are fast calculation speed and high calculation result accuracy.

As shown in Figure 4 and Figure 5, it is the comparison result between the experimental voltage and the simulated voltage distribution curve under the discharge rate conditions of 1C and 4C.

(1) The charge and discharge experiment is a constant current, and the discharge cycle is set to charge at 1C, rest for 2 hours, discharge at 1C, and rest for 2 hours;

(2) The upper and lower limits of the voltage value are set between 2.0V and 3.6V;

(3) There is good agreement between the simulated and experimental values of the voltage distribution model.

Claims (2)

1. A18650 type lithium battery discharge cycle transient temperature model modeling method is characterized by comprising the following steps:

step 1): establishing rules of a lithium battery monomer discharge cycle thermal model; combining a two-dimensional electrochemical model based on physical characteristics with a charge conservation and thermal diffusion equation reflecting the performance of the lithium battery, thereby calculating a temperature distribution value;

step 2): establishing a control equation of the transient thermal behavior; the equation describes the conservation of solid phase charge, the conservation of electrolyte phase charge, the conservation of solid phase lithium ions and the conservation of electrolyte phase lithium ions;

step 2-1): the solid phase charge conservation equation is established as follows:

▽(ρ^eff▽φ_s)-i^Li＝0 (4)

the other expression mode is as follows:

And

And

where ρ is^effIs the effective conductivity of the solid phase, p₊And p-is the effective conductivity, phi, of the positive and negative electrodes, respectively₊And phi-are positive and negative poles of phase potential, respectively, l_nIs the length of the negative electrode, /)_sFor the length of the separator, /)_pFor positive electrode length, L ═ L_n+l_s+l_pThe total length is shown;

step 2-2): the electrolyte phase charge conservation equation was established as follows:

And

wherein, κ^effFor effective diffusion of conductivity, satisfyβ is the Burrgeman porosity index;for effective ionic conductivity, the calculation formula is:

wherein f is_±is the molecular activity system of the electrolyte or the activity coefficient of the electrolyte, ξ_eIs the volume fraction of the electrolyte phase in the electrode, R is the universal gas constant, F is the Faraday constant,is the number of lithium ion transfers, C_eIs the lithium concentration in the electrolyte;

step 2-3): establishing a solid-phase lithium ion conservation equation; the equation of the material balance particle of lithium ion in the active solid material under a spherical coordinate system is as follows:

the binding boundary conditions are as follows,

And

wherein, C_sConcentration of lithium ions in the solid phase, D_sIs the mass diffusion coefficient of lithium ions in the electrolyte, R is the radial coordinate along the active material particle, R_sRadius of the solid active substance particles; let a_sFor the current distribution coefficient, lithium ions are denoted as a during insertion and extraction, respectively_s,aAnd a_s,cTransfer current i caused by insertion and extraction of lithium ions at the electrode/electrolyte interface^LiExpressed as:

step 2-4): establishing an electrolyte lithium ion conservation equation:

or as:

wherein ξ_eIs the volume fraction/porosity of the electrolyte,is an effective diffusion coefficient, satisfies Is the lithium ion transfer rate based on the solvent flow rate;

step 3): establishing boundary conditions of transient thermal behavior;

step 3-1): establishing a reaction rate equation; converting the charge into a control equation of a coupled charge system:

wherein the local surface overpotential is represented as:

η＝φ_s-φ_e-U (19)

the exchange current density is expressed as:

wherein i₀to exchange the current density, α_aand alpha_cthe transmission coefficients of the anode and the cathode are respectively, T is a temperature value, η is an overpotential, U is thermodynamic OCV, C_s,maxIs the maximum concentration of solid-phase lithium, C_s,eIs the concentration of lithium on the surface of the solid particles_sAnd phi_ePotentials of the solid phase and the electrolyte phase, respectively;

coupling the model to introduce a temperature-based physicochemical parameter, such as the electrolyte diffusion coefficient D_sAnd lithium ion conductivity parameter k_mTwo parameters are expressed as:

meanwhile, the electrolyte phase diffusion coefficient calculation formula is as follows:

wherein D is_sIs the solid phase diffusion coefficient, D_s.refFor reference to the solid diffusion coefficient, k_m.refFor reference to the reaction rate coefficient, D_eIs the diffusion coefficient of the electrolyte phase, E_dTo control D_sActivation energy of temperature sensitivity, E_rTo control k_mActivation energy of temperature sensitivity, T_refIs a temperature reference coefficient;

step 3-2): establishing an energy conservation formula:

or as:

the above formula is further modified as:

wherein, the calculation formula of each parameter in the formula (26) and the formula (27) is as follows:

wherein,satisfies formula (31) for electrochemical heating:

wherein i_pIs of length l_pThe lithium ion transfer current in the range satisfies the formulaAnd i ═ ai_p。

2. The modeling method for the transient temperature model of 18650 lithium battery discharge cycle of claim 1, wherein step 1) comprises the steps of:

step 1-1): giving a control equation and boundary conditions by the new model, and calculating material characteristic parameters for establishing the model;

step 1-2): the new model features are as follows: accurately estimating the dynamic behaviors of the anode and the cathode by using a two-dimensional model based on physical characteristics; considering the phase change condition of the material inside the active electrode particles; the particle size distribution inside the electrode was obtained using a scanning electron microscope.