CN109033619A - A kind of transient temperature model modelling approach of 18650 type lithium battery discharge cycles - Google Patents
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- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 title claims abstract description 42
- 229910052744 lithium Inorganic materials 0.000 title claims abstract description 42
- 230000001052 transient effect Effects 0.000 title claims abstract description 25
- 239000000178 monomer Substances 0.000 claims abstract description 9
- 239000003792 electrolyte Substances 0.000 claims description 46
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 claims description 40
- 229910001416 lithium ion Inorganic materials 0.000 claims description 40
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- 238000004088 simulation Methods 0.000 description 9
- 238000002474 experimental method Methods 0.000 description 4
- 238000007599 discharging Methods 0.000 description 3
- 238000003487 electrochemical reaction Methods 0.000 description 3
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- 229910017704 MH-Ni Inorganic materials 0.000 description 1
- 229910017739 MH—Ni Inorganic materials 0.000 description 1
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- 239000012798 spherical particle Substances 0.000 description 1
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- 238000012360 testing method Methods 0.000 description 1
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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
Technical Field
The invention relates to a transient temperature model and a voltage distribution simulation curve under a 18650 lithium battery discharge cycle working condition, in particular to establishment of the transient temperature model of the lithium battery under a constant-current discharge working condition and a functional relation curve between temperature and discharge voltage.
Background
Lithium batteries are favored by the industry due to the advantages of high energy density, long service life, low self-discharge rate and the like, and currently occupy the main market of power batteries. Lithium batteries also have great limitations, mainly requiring working at a suitable ambient temperature, and having too high or too low temperature will have great influence on their performance, cycle life and safety. Various scholars at home and abroad are dedicated to the research of the lithium battery temperature model, and different modeling methods are proposed, such as an artificial neural network, a Finite Element Model (FEM) or Lumped Parameter Model (LPM), a Linear Parameter Variation (LPV) model or Partial Differential Equation (PDE) model, and a CFD model. The model based on the electrochemical equation accurately describes the physical and chemical processes in the battery, and the electrochemical model is practical and reliable when the battery monomer is designed. However, the calculation time of the model is long, and the model is not suitable for a high-dynamic lithium battery working environment. Newman and Tie first proposed a porous electrode electrochemical modeling method with lithium battery dynamic applications. In porous electrode theory, the electrode is considered to be a superposition between the electrolyte solution and the solid matrix. The matrix itself is modeled as microscopic spherical particles, where lithium ions diffuse and react on the surface of the sphere. Full et al generalize the method to design a temperature model that includes two composite models and a separator, which model is suitable for both lithium and MH-Ni batteries.
According to the internal mechanism of lithium battery charging and discharging, the positive electrode, negative electrode and total reaction formula in electrochemical reaction are as follows:
positive electrode
Negative electrode
General formula
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a 18650 lithium battery discharge cycle transient temperature model modeling method.
The 18650 lithium battery discharge cycle transient temperature model modeling method comprises 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:
▽(ρeff▽φs)-iLi＝0 (4)
the other expression mode is as follows:
And
And
where ρ iseffIs the effective conductivity of the solid phase, p+And ρ-Effective conductivity, phi, of the positive and negative electrodes, respectively+And phi-Respectively positive and negative of phase potential, |nIs the length of the negative electrode, /)sFor the length of the separator, /)pFor positive electrode length, L ═ Ln+ls+lpThe total length is shown;
step 2-2): the electrolyte phase charge conservation equation was established as follows:
And
wherein, κeffFor 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, ξeIs 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, CeIs 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, CsConcentration of lithium ions in the solid phase, DsIs the mass diffusion coefficient of lithium ions in the electrolyte, R is the radial coordinate along the active material particle, RsRadius of the solid active substance particles; let asFor the current distribution coefficient, lithium ions are denoted as a during insertion and extraction, respectivelys,aAnd as,cTransfer current i caused by insertion and extraction of lithium ions at the electrode/electrolyte interfaceLiExpressed as:
step 2-4): establishing an electrolyte lithium ion conservation equation:
or as:
wherein ξeIs 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＝φs-φe-U (19)
the exchange current density is expressed as:
wherein i0to exchange the current density, αaand alphacthe transmission coefficients of the anode and the cathode are respectively, T is a temperature value, η is an overpotential, U is thermodynamic OCV, Cs,maxIs the maximum concentration of solid-phase lithium, Cs,eIs the concentration of lithium on the surface of the solid particlessAnd phiePotentials 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 DsAnd lithium ion conductivity parameter kmTwo parameters are expressed as:
meanwhile, the electrolyte phase diffusion coefficient calculation formula is as follows:
wherein D issIs the solid phase diffusion coefficient, Ds.refFor reference to the solid diffusion coefficient, km.refFor reference to the reaction rate coefficient, DeIs the diffusion coefficient of the electrolyte phase, EdTo control DsActivation energy of temperature sensitivity, ErTo control kmActivation energy of temperature sensitivity, TrefIs 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:
▽(ρ+▽φ+)＝-i (28)
▽(ρ-▽φ-)＝+i (29)
wherein,satisfies formula (31) for electrochemical heating:
wherein ipIs of length lpThe lithium ion transfer current in the range satisfies the formula
Preferably, the method comprises the following steps: the step 1) comprises the following steps:
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.
The invention has the beneficial effects that: the transient temperature model of the lithium battery monomer under different discharge rate working conditions is established based on a Newman pseudo-two-dimensional model (P2D), a constant-current charge-discharge experimental device is designed automatically, thermal behavior data of the single battery is collected, calculated and simulated, and result analysis is carried out on transient temperature parameters and a voltage distribution curve. Meanwhile, the new model and the new algorithm provided by the invention have high calculation speed and higher calculation result precision.
Drawings
FIG. 1 is a block diagram of an experimental testing device for 18650 lithium batteries;
FIG. 2 is a graph showing the results of comparing the experimental temperature and the simulated temperature at 1C discharge rate;
FIG. 3 is a graph showing the results of comparing the experimental temperature and the simulated temperature at 4C discharge rate;
FIG. 4 is a graph showing the results of comparing the experimental voltage and the simulation voltage at a discharge rate of 1C;
fig. 5 is a graph showing the result of comparing the experimental voltage and the simulation voltage at the 4C discharge rate.
Detailed Description
The present invention will be further described with reference to the following examples. The following examples are set forth merely to aid in the understanding of the invention. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
The 18650 type lithium battery discharge cycle transient temperature model modeling method comprises the following steps:
step 1): and (3) establishing rules of the lithium battery monomer discharge cycle thermal model. And 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 the temperature distribution value.
Step 1-1): the new model gives the control equations and boundary conditions and calculates the material property parameters for the model building.
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 (SEM).
Step 2): and 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): and establishing a solid phase charge conservation equation. The solid phase charge conservation equation is established based on the ohm rule as follows:
▽(ρeff▽φs)-iLi＝0 (4)
the other expression mode is as follows:
And
And
where ρ iseffIs the effective conductivity of the solid phase, p+And ρ-Effective conductivity, phi, of the positive and negative electrodes, respectively+And phi-Respectively positive and negative of phase potential, |nIs the length of the negative electrode, /)sFor the length of the separator, /)pIs the anode length. L ═ Ln+ls+lpIs the total length.
Step 2-2): the electrolyte phase charge conservation equation was established as follows:
And
wherein, κeffFor 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, ξeThe volume fraction of electrolyte phase in the electrode, R is a general gas constant, the value is 8.3143kJ/kg. mol, K and F are Faraday constants, the value is 96485 column/mole,is the number of lithium ion transfers, CeIs the lithium concentration in the electrolyte.
Step 2-3): and establishing a solid-phase lithium ion conservation equation. According to Fick's second law, the equation for a material balance particle of lithium ions in an active solid material in a spherical coordinate system is:
the binding boundary conditions are as follows,
And
wherein, CsConcentration of lithium ions in the solid phase, DsIs the mass diffusion coefficient of lithium ions in the electrolyte, R is the radial coordinate along the active material particle, RsThe radius of the solid active substance particles. Suppose asFor the current distribution coefficient, lithium ions are denoted as a during insertion and extraction, respectivelys,aAnd as,cTransfer current i caused by insertion and extraction of lithium ions at the electrode/electrolyte interfaceLiExpressed as:
step 2-4): establishing an electrolyte lithium ion conservation equation:
or as:
wherein ξeIs the volume fraction/porosity of the electrolyte,is an effective diffusion coefficient, satisfies The lithium ion transfer rate is based on the solvent flow rate.
Step 3): boundary conditions for transient thermal behavior are established.
Step 3-1): a reaction rate equation is established. The electrochemical reaction rate of the electrode surface is generally described by a Butler Volmer equation, and the invention converts the electrochemical reaction rate into a control equation of a coupled charge system:
wherein the local surface overpotential is represented as:
η＝φs-φe-U (19)
the exchange current density is expressed as:
wherein i0alpha is the exchange current density (function of lithium concentration in the electrolyte and solid active material)aand alphacthe transmission coefficients of the anode and the cathode are respectively, T is a temperature value (K), η is an overpotential (V), U is thermodynamic OCV, and Cs,maxIs the maximum concentration of solid-phase lithium, Cs,eIs the concentration of lithium on the surface of the solid particlessAnd phieThe potentials of the solid and electrolyte phases, respectively.
Coupling the model to introduce a temperature-based physicochemical parameter, such as the electrolyte diffusion coefficient DsAnd lithium ion conductivity parameter km(K) Two parameters are expressed according to the Arrhenius equation as:
meanwhile, the electrolyte phase diffusion coefficient is calculated by the following formula,
wherein D issIs the solid phase diffusion coefficient, Ds.refFor reference to the solid diffusion coefficient, km.refFor reference to the reaction rate coefficient, DeIs the diffusion coefficient of the electrolyte phase, EdTo control DsActivation energy of temperature sensitivity, ErTo control kmActivation energy of temperature sensitivity, TrefThe value of the temperature reference coefficient is 298K.
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:
▽(ρ+▽φ+)＝-i (28)
▽(ρ-▽φ-)＝+i (29)
wherein,satisfies formula (31) for electrochemical heating:
wherein ipIs of length lpThe lithium ion transfer current in the range satisfies the formula
Effect of the Algorithm
The invention provides a transient temperature model and a voltage distribution simulation curve under a 18650 type lithium battery monomer discharge cycle working condition. Under two conditions of 1C (low current) and 4C (high current) discharge rates, simulation and experimental research are carried out on the temperature distribution and the voltage distribution of the single battery, and the following algorithm effects are obtained:
(1) along with the increase of the discharge rate, the temperature distribution value of the surface of the single battery is increased, and the thermocouple measured value close to the electrode is larger than that of the central line thermocouple;
(2) the internal heat generation phenomenon of the lithium battery monomer causes the change of temperature and discharge time;
(3) the simulated temperature value obtained by the new model simulation is higher than the experimental value, particularly under the high-rate discharge working condition, and the simulated value under the low-rate discharge working condition is closer to the experimental value;
(4) the simulated temperature value of the 4C discharge rate is 46.86 ℃, and the simulated value of the 1C discharge rate is 29.6 ℃;
(5) the experiment and simulation results of the transient temperature model and the voltage distribution model established by the invention realize the design and thermal optimization process of the lithium battery and provide an important physical and chemical model basis.
As shown in fig. 1, 18650 type lithium battery was selected for measuring the charge and discharge voltage, current and temperature parameters of the single battery, and table 1 lists the discharge rate and charge and discharge current values of the charge and discharge experiments of the single battery. The device mainly comprises five parts: the battery tester comprises an Arbin battery tester, a National Instrument (NI) temperature measuring device, a lithium battery unit with a thermocouple, and computer interfaces PC-1 and PC-2. The maximum voltage of the Arbin battery tester (bipolar) was 20V and the maximum current was 1200A. Through Visual C software, PC-1 controls the charging and discharging process of the single battery, and records the charging and discharging voltage and current data, and PC-2 controls the thermal data acquisition.
TABLE 1 constant Current discharge Experimental parameter settings
| Discharge rate | Constant current value |
| 1C | 1.5A |
| 2C | 3.0A |
| 3C | 4.5A |
| 4C | 6.0A |
As shown in fig. 2 and 3, the results of comparing the experimental temperature and the simulated temperature distribution under the discharge rate conditions of 1C and 4C are shown. The initial temperature for the discharge experiment was set at 22 ℃.
(1) Under the working conditions of 1C and 4C discharge rate, the average surface temperature is increased to 29.25 ℃ and 42.16 ℃;
(2) the simulated temperature value obtained by the new algorithm simulation is higher than the experimental value, particularly under the high-rate discharge working condition, the simulated temperature value of the 4C discharge rate is 46.86 ℃, the simulated value of the 1C discharge rate is 29.6 ℃, and the simulated temperature value is closer to the experimental value;
(3) the higher the discharge rate, the faster the surface temperature increases, and the temperature and discharge time changes may be due to internal heat generation. Therefore, the new model and the new algorithm provided by the invention have the advantages of high calculation speed and high calculation result precision.
As shown in fig. 4 and 5, the comparison result between the experimental voltage and the simulated voltage distribution curve under the discharge rate conditions of 1C and 4C is shown.
(1) The charge and discharge experiment is constant current, and the discharge cycle is set to 1C charge, 2 hours of standing, 1C discharge and 2 hours of standing;
(2) the upper and lower limits of the voltage value are set between 2.0V and 3.6V;
(3) the simulation value and the experimental value of the voltage distribution model have better consistency.
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:
▽(ρeff▽φs)-iLi＝0 (4)
the other expression mode is as follows:
And
And
where ρ iseffIs 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, lnIs the length of the negative electrode, /)sFor the length of the separator, /)pFor positive electrode length, L ═ Ln+ls+lpThe total length is shown;
step 2-2): the electrolyte phase charge conservation equation was established as follows:
And
wherein, κeffFor 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, ξeIs 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, CeIs 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, CsConcentration of lithium ions in the solid phase, DsIs the mass diffusion coefficient of lithium ions in the electrolyte, R is the radial coordinate along the active material particle, RsRadius of the solid active substance particles; let asFor the current distribution coefficient, lithium ions are denoted as a during insertion and extraction, respectivelys,aAnd as,cTransfer current i caused by insertion and extraction of lithium ions at the electrode/electrolyte interfaceLiExpressed as:
step 2-4): establishing an electrolyte lithium ion conservation equation:
or as:
wherein ξeIs 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＝φs-φe-U (19)
the exchange current density is expressed as:
wherein i0to exchange the current density, αaand alphacthe transmission coefficients of the anode and the cathode are respectively, T is a temperature value, η is an overpotential, U is thermodynamic OCV, Cs,maxIs the maximum concentration of solid-phase lithium, Cs,eIs the concentration of lithium on the surface of the solid particlessAnd phiePotentials 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 DsAnd lithium ion conductivity parameter kmTwo parameters are expressed as:
meanwhile, the electrolyte phase diffusion coefficient calculation formula is as follows:
wherein D issIs the solid phase diffusion coefficient, Ds.refFor reference to the solid diffusion coefficient, km.refFor reference to the reaction rate coefficient, DeIs the diffusion coefficient of the electrolyte phase, EdTo control DsActivation energy of temperature sensitivity, ErTo control kmActivation energy of temperature sensitivity, TrefIs 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 ipIs of length lpThe lithium ion transfer current in the range satisfies the formulaAnd i ═ aip。
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.
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