CN113189508B - Reverse calculation method and device for internal thermal resistance parameters of lithium ion soft package battery - Google Patents
Reverse calculation method and device for internal thermal resistance parameters of lithium ion soft package battery Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/389—Measuring internal impedance, internal conductance or related variables
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- G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
- G01K7/00—Measuring temperature based on the use of electric or magnetic elements directly sensitive to heat ; Power supply therefor, e.g. using thermoelectric elements
- G01K7/02—Measuring temperature based on the use of electric or magnetic elements directly sensitive to heat ; Power supply therefor, e.g. using thermoelectric elements using thermoelectric elements, e.g. thermocouples
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/378—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator
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Abstract
The invention relates to the technical field of lithium ion battery thermal management, discloses a reverse method and a reverse device for solving internal thermal resistance parameters of a lithium ion soft package battery, and aims to provide an estimation tool for key parameters for accurately calculating the temperature of the lithium ion soft package battery. Firstly, defining internal thermal resistance parameters to be solved, and constructing a thermal resistance parameter reverse solving experimental device to implement a thermal induction experiment; secondly, physical equations such as heat generation, gas generation, heat transfer, expansion and the like are established and fused into a soft package battery temperature evaluation model; and thirdly, constructing a reverse model of the internal thermal resistance parameter of the soft package battery, and solving based on the test data and the physical model to obtain the internal thermal resistance parameter of the battery. Compared with the prior art, the thermal resistance parameter obtained by the method is suitable for the lithium ion soft package battery with the same electrolyte, and the application range is larger; based on experimental data and a physical model, the thermal resistance parameter is calculated by a reverse solving technology, so that the precision is high; clear steps, easy understanding, simple device, clear definition and good engineering practicability.
Description
Technical Field
The invention relates to the technical field of lithium ion battery thermal management, in particular to a method and a device for reversely solving internal thermal resistance parameters of a lithium ion soft package battery.
Background
The lithium ion soft package battery is widely applied to consumer electronic equipment due to the advantages of high energy density, continuous reduction of cost and the like, and is gradually expanded to the fields of energy storage systems and power automobiles. But safety problems due to thermal runaway of the battery are always present. Under the condition of thermal abuse, a chemical exothermic reaction occurs inside the soft package battery; when the heat release rate exceeds the heat release efficiency, the internal temperature rise accelerates the exothermic reaction, resulting in the continuous accumulation of heat and reaction gas inside the battery. Reaching a critical value of temperature or pressure will trigger thermal runaway of the cell, releasing a significant amount of heat and combustible gases.
In order to effectively predict the thermal behavior of the lithium ion soft package battery, a thermal model needs to be constructed to accurately estimate the internal temperature of the lithium ion soft package battery. The accuracy of temperature estimation depends on modeling parameters to a great extent, some modeling parameters are easy to be measured by experiments or obtained by theoretical derivation, while some parameters are difficult to obtain accurate values directly, and internal thermal resistance parameters are one of the parameters. In the soft-package battery, the heat is realized from the battery cell to the soft package through the conduction, and the thermal resistance exists in the gas-liquid mixture of electrolyte and reaction gas in the clearance between the battery cell and the soft package. The most important thermal resistance parameter is the thermal conductivity of the gas-liquid mixture. The prior research shows that the heat conductivity of the gas-liquid mixture is related to both temperature and pressure, and the steady-state heat conductivity is controversial in the aspect of a theoretical calculation method. Under the condition of thermal abuse, a dynamic process of drastic change of temperature and pressure exists in the soft package battery, and the dynamic thermal conductivity of the gas-liquid mixture is more difficult to calculate by adopting a theory. On the other hand, the method is limited by the packaging form and the testing means of the soft package battery, and the dynamic curve of the thermal conductivity of the gas-liquid mixture obtained by the testing method is also challenging.
Therefore, aiming at the difficult problem of estimating the internal thermal resistance parameter of the lithium ion soft package battery, the internal thermal resistance parameter estimation method of the lithium ion soft package battery, which has the advantages of wide applicability, high precision and good usability, is developed, and the internal thermal resistance parameter testing device of the soft package battery, which has a simple structure and is easy to implement, is designed, so that the temperature prediction precision of the lithium ion soft package battery under the condition of thermal abuse can be effectively enhanced, and the method has important engineering significance for improving the reliability and the thermal management level of the lithium ion soft package battery.
Disclosure of Invention
The invention overcomes the defects of the prior art and provides a method and a device for reversely solving the internal thermal resistance parameter of a lithium ion soft package battery. Firstly, defining internal thermal resistance parameters of a lithium ion soft package battery to be solved, and constructing a thermal resistance parameter reverse solving experimental device to implement a thermal induction experiment; secondly, physical equations such as heat generation, gas generation, heat transfer, expansion and the like are established and fused into a soft package battery temperature evaluation model; and thirdly, constructing a reverse model of the internal thermal resistance parameter of the soft package battery, and solving based on the test data and the physical model to obtain the internal thermal resistance parameter of the battery. The invention provides a key parameter estimation tool for accurately calculating the temperature of the lithium ion soft package battery.
In order to achieve the purpose, the invention adopts the following technical scheme:
(1) defining internal thermal resistance parameters of the lithium ion soft package battery to be solved;
(2) constructing a reverse experimental device of thermal resistance parameters;
(3) implementing a soft package battery thermal induction experiment;
(4) establishing a soft package battery temperature evaluation model;
(5) and constructing a reverse model of the internal thermal resistance parameter of the soft package battery and solving to obtain the thermal resistance parameter.
Further, in the step (1), the internal thermal resistance parameter of the lithium-ion soft package battery to be obtained comprises initial thermal conductivity K0Thermal conductivity temperature index n; initial thermal conductivity K0The thermal conductivity of a gas-liquid mixture filled in a gap between a battery cell and a soft package in the soft package battery at the temperature of 273.15K is shown; the expression of the thermal conductivity temperature index n is that n is log (K)w/K0)/log(Tcel/273.15), wherein KwDenotes the temperature T of the gas-liquid mixturecelThermal conductivity of the steel.
Further, in the step (2), the thermal resistance parameter reverse-solving experimental device comprises a soft package battery, a clamping module, a temperature change test box, a temperature measuring instrument and a coordinate system; appearance size X of soft package batterycel×Ycel×ZcelInitial volume is V0The battery consists of a battery cell, a soft package and electrolyte; the soft package is of thickness dpThe aluminum-plastic film of (1); the clamping module comprises a first clamping plate, a second clamping plate, a first bolt, a second bolt, a first nut and a second nut; the first clamping plate and the second clamping plate are completely consistent in structure, the epoxy glass cloth laminated plate is selected as a material, and the overall dimension X isb×Yb×ZbIs Xb＝0.15·Xcel，Yb＝Ycel+0.3·Xcel，Zb＝0.1·YcelAt XbD in a direction away from the first endb＝0.07·XcelAt a position of D from the second endbAre respectively provided with a diameter DbA first circular hole and a second circular hole; the first bolt and the second bolt are inner hexagonal flat round head screws with the standard number of GB/T70.2-2015, and the pitch diameter d of the threadsb＝int(Db) Length of thread hb＝int(Zcel+2·Zb+1.5·Db) Where int (·) denotes an integer arithmetic; the first nut and the second nut are butterfly nuts with standard numbers of GB62-88, and the pitch diameter of the threads is db. The temperature change test chamber is a general test device which can provide a rapid temperature change environment and a constant temperature environment; the temperature measuring instrument is a general thermocouple type temperature measuring instrument with at least two temperature measuring channels and comprises a first thermocouple, a second thermocouple, a signal wire and a host.
Further, in the step (2), the assembling steps of the thermal resistance parameter reverse experiment device are as follows:
(2.1) aligning and sequentially stacking the centers of the first clamping plate, the thermocouple, the soft package battery and the second clamping plate;
(2.2) passing the first bolt through the first round holes of the first clamping plate and the second clamping plate, and fastening the first bolt with the first nut;
(2.3) passing the second bolt through the second round holes of the first clamping plate and the second clamping plate, and fastening the second bolt with the second nut;
(2.4) controlling the distance between the first splint and the second splint to be Zbb＝0.95·Zcel；
(2.5) sticking the second thermocouple on the upper surface of the soft package battery;
(2.6) suspending the assembled soft package battery, the clamping module and the temperature measuring instrument at the central position inside the temperature change test box;
(2.7) placing the host of the temperature measuring instrument at a position which is convenient to observe outside the temperature change test box.
Further, in the step (3), the heat induction experiment of the soft package battery is implemented as follows:
(3.1) based on the thermal resistance parameter reverse experiment device, setting the temperature change process in the temperature change test box as follows: the initial temperature is 298K, the temperature is kept for 20min, the temperature is increased to 398K at the speed of 5K/min, and the temperature is kept for 20 min.
(3.2) reading the measured temperature T 'of the battery core measured by the first thermocouple and the second thermocouple in the experimental process'celAnd an actually measured temperature T 'of the soft bag'surReading the temperature T of the air in the box output by the temperature change test boxairRecording T 'of the current time T every 1 minute'cel，T’sur，Tair(ii) a A series of T'cel， T’sur，TairCan be written as vectors:
T’cel＝(T’cel,1,T’cel,2,...,T’cel,t,...,T’cel,T)
T’sur＝(T’sur,1,T’sur,2,...,T’sur,t,...,T’sur,T)
Tair＝(Tair,1,Tair,2,...,Tair,t,...,Tair,T)
where T denotes the time of the last recording.
Further, in the step (4), the step of establishing the soft package battery temperature evaluation model is as follows:
(4.1) establish the heat generation equation E1: q. q ofcel＝mrea·sum(Δhj·Rj) J is 1, 2; wherein sum (·) represents a summation operation; q. q.scelDenotes the heat generation rate, mgasDenotes the mass of the liberated gas, R1,R2Respectively represents the reaction rates of SEI decomposition and reconstruction, delta h1,Δh2Respectively representing reaction enthalpy changes of SEI decomposition and reconstruction;
further, in step (4.1), the reaction rate R of the SEI film was calculated using the lithium ion battery thermal model proposed by Hatchard and DahnjDifferential equation of (a): rj＝-dt(xj)＝fj·xj·exp(-Ej/(Ru·Tcel) ); where dt (-) represents the derivative operation over time t, i.e., the rate of change; exp (. cndot.) denotes an exponential operation, x1,x2Respectively represent the amount of lithium ions contained and inserted in the SEI film; f. of1,f2Frequency factors representing SEI decomposition and reconstruction reactions, respectively, E1,E2Respectively representing activation energy of SEI decomposition and reconstruction reaction; ruIs the universal gas constant; t iscelRepresenting a temperature of the cell; solving for the reaction rate RjThe differential equation of (c) yields:
Rj＝fj·xj 0·exp{-Ej/(Ru·Tcel)-fj·t·exp[-Ej/(Ru·Tcel)]}
wherein t is the current moment; x is the number of1 0,x2 0Respectively indicate the initial amount of lithium ions contained in and inserted into the SEI film.
(4.2) establishing the gas production equation E2: dt (m)gas)＝cgas·qcel(ii) a Wherein m isgasDenotes the mass of the released gas, cgasIndicating the proportionality coefficient between the gas generation rate and the heat generation rate.
(4.3) based on the theory of heat transfer, the heat transfer equation E3 is established:
qcel＝Ccel·dt(Tcel)+(Tcel-Tsur)/Rcel
wherein, CcelRepresents the heat capacity of the cell, RcelRepresents the equivalent thermal conduction resistance, T, from the cell to the soft bagsurIndicating the temperature of the soft pack.
(4.4) based on the thermal convection theory, the thermal convection equation E4 is established:
(Tcel-Tsur)/Rcel＝(Tsur-Tair)/Rair
wherein R isairRepresenting the convective thermal resistance from the outer surface of the soft pack to the air inside the temperature change test chamber.
(4.5) establishing an equivalent thermal resistance equation E5 based on the parallel thermal circuit theory.
(4.6) establishing a soft package deformation equation E6 based on finite element analysis;
(4.7) establishing an equivalent clearance equation E7: delta is 0.5. V0·Ce(Pgas)/(Xcel·Ycel)。
(4.8) equations E1-E7 are combined to obtain a soft package battery temperature evaluation model M1:
further, in step (4.5), the step of establishing the equivalent thermal resistance equation E5 is as follows:
(4.5.1) establishing a parallel thermal resistance equation: r iscel＝1/sum(Kw·Ai/δi) 1,2, 6; wherein A isiDenotes the ith heat transfer surface, and the soft package battery has 6 heat transfer surfaces in 3 directions such as X, Y, Z, deltaiRepresenting the clearance, K, from the cell to the soft pack for the ith heat transfer surfacewIn relation to the cell temperature, write: kw＝K0·(Tcel/273.15)n；
(4.5.2) introducing an equivalent gap δ mean (δ)i) Mean (-) denotes the averaging operation;
(4.5.3) writing the parallel thermal resistance equation to equivalent thermal resistance equation E5 based on the equivalent gap δ: rcel＝δ·Asur -1·K0 -1·(0.0127·Tcel)-n(ii) a Wherein A issur＝sum(Ai) The surface area of the soft package battery is shown.
Further, in step (4.6), the step of establishing the soft package deformation equation E6 is as follows:
(4.6.1) establishing a reaction gas equation of state according to the ideal gas law: pcel·Vgas＝mgas·Rgas·Tcel(ii) a Wherein, PcelPresentation instrumentInternal air pressure, V, of the soft package batterygasDenotes the volume of gas, RgasRepresents a gas constant of the reaction gas;
(4.6.2) based on the thermal resistance parameter reverse experiment device, establishing 1/4 type finite element structures including a second soft package through the existing commercial finite element analysis software;
(4.6.3) cell arrangement, the cells of the second soft pack being arranged to have a thickness dpThe housing unit of (a);
(4.6.4) setting material properties including: elastic modulus 4106MP, Poisson ratio 0.33, stress and plastic strain table;
(4.6.5) setting boundary conditions including: setting an X-direction symmetric boundary for the first area, a Y-direction symmetric boundary for the second area, a Z-direction symmetric boundary for the third area, and a clamped boundary for simulating the clamping module for the fourth area;
(4.6.6) setting m different pressure loads P to a fifth region of the second soft packcel,jEstablishing a corresponding solving condition when j is 1, 2.. multidot.m;
(4.6.7) calling a general static solver of the commercial finite element analysis software, solving the solving conditions one by one to obtain a gas volume response Vgas,jJ 1, 2.. m, calculating the relative expansion coefficient Ce,j＝Vgas,j/V0；
(4.6.8) based on the m sets of pressure loads Pcel,jAnd said gas volume response Vgas,jFitting to obtain the relationship between the pressure load and the gas volume as follows: vgas＝Vgas(Pcel) Substituting into the relation P between the pressure load and the internal air pressurecel＝Pgas-P0Obtaining a pressure-volume equation: vgas＝Vgas(Pgas) In which P is0Represents standard atmospheric pressure;
(4.6.9) substituting the gas pressure-volume equation into the gas equation of state to arrive at the soft pack deformation equation E6: pcel·Vgas(Pgas)＝mgas·Rgas·Tcel。
Further, in the step (5), a reverse model of the internal thermal resistance parameter of the soft package battery is constructed, and the thermal resistance parameter is obtained by solving the model as follows:
(5.1) establishing a cell temperature function and a soft package temperature function, wherein the method comprises the following steps: at the initial thermal conductivity K0And the thermal conductivity temperature index n is used as an input variable, a solver of the conventional commercial numerical analysis software is called to solve the temperature evaluation model, the cell temperature and the soft package temperature at all moments are obtained and used as output variables, and the output variables are written into vectors
Tcel＝(Tcel,1,Tcel,2,...,Tcel,t,...,Tcel,T)
Tsur＝(Tsur,1,Tsur,2,...,Tsur,t,...,Tsur,T)
Wherein T iscel,t＝Tcel(K0N, T) is the cell temperature function, Tsur,t＝Tsur(K0And n, t) is a function of the soft package temperature.
(5.2) establishing a reverse optimization objective function, and writing into: fobj(K0,n)＝||Tcel-T’cel||+||Tsur-T’surAnd | l, wherein | · | | represents vector modulo arithmetic.
(5.3) establishing a reverse model M2 of the internal thermal resistance parameter of the soft package battery, and writing the model into a standard optimized model form:
minFobj(K0,n)
s.t.K0>0,n>0
where min represents the minimization and s.t. represents the constraint.
(5.4) calling a solver of the commercial numerical analysis software to solve the thermal resistance parameter inverse model to obtain the optimal initial thermal conductivity K0 *And an optimum thermal conductivity temperature index n*Namely, the solution of the thermal resistance parameter to be solved.
Compared with the prior art, the invention has the advantages that:
firstly, in the aspect of applicability, the thermal resistance parameter obtained by the method is suitable for estimating the internal temperature of the lithium ion soft package battery with the same electrolyte, and has a larger application range. In the aspect of precision, the method is based on experimental data, combines physical models of heat generation, gas generation, heat transfer, expansion and the like, has theoretical guarantee and experimental basis on the precision of thermal resistance parameters obtained by a reverse calculation technology, and has more advantages compared with solutions of theoretical derivation methods or empirical estimation methods. Thirdly, the method does not relate to complicated and tedious coupled simulation of multiple physical fields and algorithm programming processes, has clear steps, is beneficial to understanding, and has excellent usability for general engineering technicians. Finally, the device for reversely solving the thermal resistance parameter in the lithium ion soft package battery has the advantages of simple structure, clear definition, no need of manufacturing complex tools and high-end instruments, and good engineering practicability.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention.
FIG. 2 is a schematic diagram of a reverse experimental apparatus for thermal resistance parameters in an embodiment of the present invention.
Fig. 3 is a schematic diagram of expansion finite element analysis of a pouch battery in an embodiment of the present invention.
Reference numerals: 20. a thermal resistance parameter reverse experiment device; 21. a pouch cell; 22. a clamping module; 23. a temperature change test chamber; 24. a temperature measuring instrument; 211. an electric core; 212. soft packing; 213. an electrolyte; 221. a first splint; 222. a second splint; 223. a first bolt; 224. a second bolt; 225. a first nut; 226. a second nut; 241. a first thermocouple; 242. a second thermocouple; 243. a signal line; 244. a host; 2211. a first end; 2212. a second end; 2213. a first circular hole; 2214. a second circular hole; 30. a finite element structure; 31. a second soft package; 32. a first region; 33. a second region; 34. a third region; 35. a fourth region; 36. and a fifth region.
Detailed Description
The invention will now be further described with reference to the following examples, which are not to be construed as limiting the invention in any way, and any limited number of modifications which can be made within the scope of the claims of the invention are still within the scope of the claims of the invention.
As shown in fig. 1-3, the invention provides a reverse method and device for obtaining internal thermal resistance parameters of a lithium ion soft package battery, wherein the method comprises the following processing steps:
step S1: and defining the internal thermal resistance parameter of the lithium ion soft package battery to be solved. The soft package battery consists of an electric core, a soft package and Electrolyte, wherein a Solid Electrolyte Interface (SEI) on the surface of an anode of the electric core generates decomposition-reconstruction reaction under a certain temperature condition, and heat and gas are released. The reaction gas and the electrolyte form a gas-liquid mixture which is filled in the gap between the battery cell and the soft package. The heat of reaction has to be conducted through the gap to the soft pack and finally released to the environment. Thermal conductivity of gas-liquid mixture and initial thermal conductivity K at 273.15K0And the thermal conductivity temperature index n and the like. Therefore, the internal thermal resistance parameter of the lithium ion soft package battery to be obtained is defined as: initial thermal conductivity K0And a thermal conductivity temperature index n.
Step S2: and constructing a reverse experimental device of thermal resistance parameters. As shown in fig. 2, in the embodiment, the thermal resistance parameter inverse experiment apparatus 20 includes a pouch cell 21, a clamping module 22, a temperature change test box 23, a temperature measuring instrument 24, and a coordinate system 25. External dimension X of soft package battery 21cel×Ycel×Zcel82mm by 63mm by 4.3mm, initial volume V0＝22214mm3The weight is 20g, the capacity is 3940mAh, and the battery comprises a battery cell 211, a soft package 212 and electrolyte 213. The anode material of the battery core 211 is graphite, and the cathode material is lithium cobaltate; the soft bag 212 is an aluminum plastic film (thickness d)p0.088 mm); the electrolyte 213 is prepared by dissolving lithium hexafluorophosphate in a solvent of ethylene carbonate and diethyl carbonate with a mass ratio of 1:1, wherein the mole fraction of lithium hexafluorophosphate is 1.0 mol/L. The clamping module 22 includes a first clamping plate 221, a second clamping plate 222, a first bolt 223, a second bolt 224, a first nut 225, and a second nut 226. The first clamping plate 221 and the second clamping plate 222 have the same structure, and are made of epoxy glass cloth laminated plates with the overall dimension Xb×Yb×ZbIs Xb＝0.15·Xcel，Yb＝Ycel+0.3·Xcel， Zb＝0.1·YcelAt XbD oriented at a distance from the first end 2211b＝0.07·XcelPosition of, D from the second end 2212bAre respectively provided with a diameter DbFirst circular aperture 2213, second circular aperture 2214. The first bolt 223 and the second bolt 224 are inner hexagonal flat round head screws with standard numbers GB/T70.2-2015 and the pitch diameter d of the threadsb＝int(Db) Length of thread hb＝int(Zcel+2·Zb+1.5·Db) Where int (·) denotes an integer arithmetic. The first nut 225 and the second nut 226 are wing nuts with standard number GB62-88, and the pitch diameter of the threads is db. The thermometer 24 is a thermocouple type thermometer, and includes a first thermocouple 241, a second thermocouple 242, a signal line 243, and a host computer 244. The assembly process of the thermal resistance parameter reverse experiment device 20 is as follows: the first clamping plate 221, the thermocouple 241, the soft package battery 21 and the second clamping plate 222 are aligned in center and are stacked in sequence; secondly, the first bolt 223 passes through the first circular hole 2213 of the first clamping plate 221 and the second clamping plate 222 to be coupled and fastened with the first nut 225, the second bolt 224 passes through the second circular hole 2214 of the first clamping plate 221 and the second clamping plate 222 to be coupled and fastened with the second nut 226, and the distance between the first clamping plate 221 and the second clamping plate 222 is controlled to be Zbb＝ 0.95·Zcel(ii) a Sticking a second thermocouple on the upper surface of the soft package battery 21; thirdly, the assembled soft package battery 21, the clamping module 22 and the temperature measuring instrument 24 are suspended in the center inside the temperature change test box 23, and the host 243 of the temperature measuring instrument 24 is placed outside the temperature change test box 23 to facilitate observation.
Step S3: a pouch cell heat induction experiment was performed. The experimental procedure was as follows:
(3.1) reversely solving the experimental device 20 based on the thermal resistance parameters, and setting the temperature change process in the temperature change test box as follows: the initial temperature is 298K, the temperature is kept for 20min, the temperature is increased to 398K at the speed of 5K/min, and the temperature is kept for 20 min.
(3.2) during the experiment, the measured temperature T 'of the battery cell 211 measured by the first thermocouple 241 and the second thermocouple 242 is read'celAnd the measured temperature T 'of the soft bag 212'surReading the temperature T of the air in the box output by the temperature change test box 23airRecord the current every 1 minuteT 'at time T'cel，T’sur，Tair. A series of T'cel，T’sur， TairCan be written as vectors:
T’cel＝(T’cel，1，T’cel，2，...，T’cel，t，...，T’cel，T)
T’sur＝(T’sur，1，T’sur，2，...，T’sur，t，...，T’sur，T)
Tair＝(Tair，1，Tair，2，...，Tair，t，...，Tair，T)
where T denotes the time of the last recording. Some of the test data are listed in table 1.
TABLE 1
| t(min) | T’cel(K) | T’sur(K) | Tair(K) |
| 1，2，...，20 | 298.0 | 298.0 | 298.0 |
| 21 | 298.5 | 298.5 | 302.2 |
| 22 | 299.7 | 299.7 | 306.3 |
| ... | ... | ... | ... |
| 38 | 372.6 | 374.3 | 389.7 |
| 39 | 377.2 | 379.1 | 393.8 |
| ... | ... | ... | ... |
| 59 | 409.2 | 398.3 | 398.0 |
| 60 | 409.4 | 399.3 | 398.0 |
Step S4: and establishing a soft package battery temperature evaluation model M1. The modeling steps are as follows:
(4.1) establish the heat generation equation E1: q. q.scel＝mrea·sum(Δhj·Rj)，j＝1，2
Wherein sum (·) represents a summation operation; q. q.scelDenotes the heat generation rate, mgasDenotes the mass of the liberated gas, R1,R2Respectively represents the reaction rates of SEI decomposition and reconstruction, delta h1,Δh2Respectively show the reaction enthalpy changes of SEI decomposition and reconstruction. Calculating the reaction rate R of SEI film by using the thermal model of lithium ion battery proposed by Hatchard and Dahnj：
Rj＝-dt(xj)＝fj·xj·exp(-Ej/(Ru·Tcel))
Where dt (-) denotes the derivation operation over time t, exp (-) denotes the exponential operation, x1,x2Respectively represent the amount of lithium ions contained and inserted in the SEI film; f. of1,f2Respectively representing frequency factors of SEI decomposition and reconstruction reactions, E1, E2Respectively representing activation energy of SEI decomposition and reconstruction reaction; ruIs the universal gas constant; t iscelIndicating the temperature of the cell 211. The above equation is a differential equation, which is solved to obtain:
Rj＝fj·xj 0·exp{-Ej/(Ru·Tcel)-fj·t·exp[-Ej/(Ru·Tcel)]}
wherein t is the current moment; x is a radical of a fluorine atom1 0,x2 0Respectively indicate the initial amount of lithium ions contained in and inserted into the SEI film.
(4.2) establishing the gas production equation E2: dt (m)gas)＝cgas·qcel
Wherein m isgasDenotes the mass of the liberated gas, dt (m)gas) Indicating the rate of gas production, cgasIndicating the proportionality coefficient between the gas generation rate and the heat generation rate.
(4.3) based on the theory of heat transfer, the heat transfer equation E3 is established:
qcel＝Ccel·dt(Tcel)+(Tcel-Tsur)/Rcel
wherein, CcelDenotes the heat capacity, R, of the cell 211celRepresents the equivalent thermal conduction resistance, T, from the battery cell 211 to the soft package 212surIndicating the temperature of the soft pack 212.
(4.4) based on the thermal convection theory, the thermal convection equation E4 is established:
(Tcel-Tsur)/Rcel＝(Tsur-Tair)/Rair
wherein R isairRepresenting the convective resistance from the outside surface of the soft pack 212 to the air inside the temperature-varying test chamber 23.
(4.5) establishing an equivalent thermal resistance equation E5 based on the parallel thermal circuit theory, and the steps are as follows.
(4.5.1) establishing a parallel thermal resistance equation:
Rcel＝1/sum(Kw·Ai/δi),i＝1,2,...,6
wherein, AiShowing the ith heat transfer surface, the pouch cell 21 has 6 heat transfer surfaces in 3 directions such as X, Y, Z, δiDenotes the clearance, K, from the cell 211 to the soft pack 212 for the ith heat transfer surfacewIn relation to the cell 211 temperature, write: kw＝K0·(Tcel/273.15)n；
(4.5.2) introducing an equivalent gap δ mean (δ)i) Mean (-) indicates the averaging operation.
(4.5.3) based on the equivalent gap δ, the parallel thermal resistance equation is rewritten as an equivalent thermal resistance equation E5:
Rcel＝δ·Asur -1·K0 -1·(0.0127·Tcel)-n
wherein A issur＝sum(Ai) Representing the surface area of pouch cell 21.
(4.6) based on finite element analysis, the soft pack deformation equation E6 is established, as follows.
(4.6.1) establishing a reaction gas equation of state according to the ideal gas law:
Pcel·Vgas＝mgas·Rgas·Tcel
wherein, PcelIndicates the internal air pressure, V, of the pouch cell 21gasDenotes the volume of gas, RgasRepresents a gas constant of the reaction gas;
(4.6.2) based on the thermal resistance parameter back-solving experiment device 20, establishing 1/4 type finite element structure 30 in the finite element analysis software ABAQUS, wherein the finite element structure comprises a second soft package 31;
(4.6.3) setting the cells of the second soft pack 31 to have a thickness wpThe shell element of (a), corresponding to the soft pack 212 in fig. 2;
(4.6.4) setting material properties including: modulus of elasticity 4106MP, poisson's ratio 0.33, stress and plastic strain table (as in table 2);
TABLE 2
| Stress (MPa) | 24.4 | 27.6 | 30.2 | 34.8 | 40.3 | 50.1 |
| Strain (x 10)-3) | 0 | 0.76 | 1.08 | 3.38 | 7.35 | 1.78 |
(4.6.5) setting boundary conditions including: setting an X-direction symmetric boundary for the first region 32, a Y-direction symmetric boundary for the second region 33, a Z-direction symmetric boundary for the third region 34, and a clamped boundary for simulating the clamping module 22 shown in FIG. 2 for the fourth region 35;
(4.6.6) applying m-6 different pressure loads P to the fifth region 36 of the second soft pack 31cel，jEstablishing a corresponding solving condition, wherein j is 1,2,. and m;
(4.6.7) calling a general static solver of ABAQUS to respectively solve each solution condition to obtain a gas volume response Vgas，j，j ═ 1, 2.., m, the calculations are given in table 3;
TABLE 3
| Pcel，j(kPa) | 0.4 | 0.8 | 1.2 | 1.6 | 2.0 | 2.4 |
| Vgas | 0.26·V0 | 0.53·V0 | 0.79·V0 | 1.05·V0 | 1.32·V0 | 1.58·V0 |
(4.6.8) based on m sets of pressure loads Pcel，jAnd gas volume response Vgas，jFitting to obtain the relationship between the pressure load and the gas volume as follows: vgas＝0.658·V0·PcelSubstituting into the relation P between the pressure load and the internal air pressurecel＝Pgas-P0Obtaining a pressure-volume equation: vgas＝0.658·V0·(Pgas-P0)，P0Indicating standard atmospheric pressure.
(4.6.9) substituting the pressure-volume equation into the gas equation of state to obtain the soft pack deformation equation E6:
0.658·Pcel·V0·(Pgas-P0)＝mgas·Rgas·Tcel
(4.7) establishing an equivalent clearance equation E7: delta 0.5. Vgas/(Xcel·Ycel)。
(4.8) equations E1-E7 are combined to obtain a soft package battery temperature evaluation model M1:
in this example, the parameters of the temperature evaluation model M1 are shown in table 4.
TABLE 4
| Parameter(s) | Unit of | Numerical value | Data source |
| mrea | g | 16.2 | Battery specification |
| Δh1 | J/g | 275 | Battery specification |
| Δh2 | J/g | 1714 | Battery specification |
| f1 | 1/s | 1.67E+15 | Battery specification |
| f2 | 1/s | 2.50E+13 | Battery specification |
| x1 0 | Dimensionless | 0.15 | Battery specification |
| x2 0 | Dimensionless | 0.75 | Battery specification |
| E1 | J/mol | 1.35E+5 | Battery specification |
| E2 | J/mol | 1.35E+5 | Battery specification |
| Ru | J/(mol·K) | 8.314 | Engineering constant |
| cgas | g/W | 6.2E-4 | Battery specification |
| Ccel | J/K | 49.88 | Battery specification |
| Rair | K/W | 4.88 | Determination of the experiment |
| Asur | mm2 | 11579 | Battery specification |
| V0 | mm3 | 22214 | Battery specification |
| P0 | KPa | 101.3 | Engineering constant |
| Rgas | J/(kg·K) | 1833 | Ingredient testing |
| Xcel | mm | 82 | Battery specification |
| Ycel | mm | 43 | Battery specification |
Step S5: constructing a reverse model M2 of the internal thermal resistance parameter of the soft package battery and solving to obtain the thermal resistance parameter, wherein the modeling steps are as follows:
and (5.1) establishing a cell temperature function and a soft package temperature function. At an initial thermal conductivity K0And the thermal conductivity temperature index n is used as an input variable, an ODE solver in commercial numerical analysis software MATLAB is called to solve the temperature evaluation model M1, the cell temperature and the soft package temperature at all the moments are obtained and used as output variables, and a vector T is writtencel＝(Tcel,1,Tcel,2,...,Tcel,t,...,Tcel,T) And Tsur＝(Tsur,1,Tsur,2,...,Tsur,t,...,Tsur,T) (ii) a Wherein T iscel,t＝Tcel(K0N, T) is a functional function of the cell temperature, Tsur,t＝Tsur(K0And n, t) is a function of the temperature of the soft package.
(5.2) establishing a reverse optimization objective function, and writing into: fobj(K0,n)＝||Tcel-T’cel||+||Tsur-T’surI, where i | ·irepresents a vector modulo operation.
(5.3) establishing a reverse model M2 of the internal thermal resistance parameter of the soft package battery, and writing the model into a standard optimized model form:
min Fobj(K0,n)
s.t.K0>0,n>0
where min represents the minimization and s.t. represents the constraint.
(5.4) calling an optimization problem solver 'fmincon' of MATLAB to solve the model M2 to obtain the optimal initial thermal conductivity K0 *0.055W/(m.K) and an optimum thermal conductivity temperature index n*1.84, the solution of the thermal resistance parameter to be found.
The embodiment shows that the method and the device for reversely solving the internal thermal resistance parameter of the lithium ion soft package battery have the following advantages. Firstly, in the aspect of applicability, the thermal resistance parameter obtained by the method is suitable for estimating the internal temperature of the lithium ion soft package battery with the same electrolyte, and has a larger application range. For example, the sample electrolyte adopted in the embodiment is widely applied to the lithium ion soft package battery, and the obtained thermal resistance parameter is suitable for a series of similar battery products, so that the development cost of a battery manufacturer can be greatly saved, and the product development iteration cycle can be shortened. In the aspect of precision, the method is based on experimental data, combines physical models such as heat generation, gas generation, heat transfer, expansion and the like (such as a soft-package battery temperature evaluation model M1 in step 4.8), has theoretical guarantee and experimental basis on the precision of thermal resistance parameters obtained by a reverse solving technology, and has more advantages compared with solutions of theoretical derivation methods or empirical estimation methods. Thirdly, the method does not relate to complicated and tedious coupled multi-physical field simulation and algorithm programming processes (for example, models M1 and M2 can be solved by MATLAB), and the steps are clear, easy to understand and easy to use for general engineering technicians. Finally, the reverse thermal resistance parameter solving device in the lithium ion soft package battery provided by the invention is simple in structure and clear in definition, does not need to manufacture complex tools, does not need high-end instruments (such as adiabatic acceleration calorimeter/ARC), and has good engineering practicability.
Claims (1)
1. The method for reversely calculating the internal thermal resistance parameter of the lithium ion soft package battery is characterized by comprising the following processing steps of:
(1) defining internal thermal resistance parameters of the lithium ion soft package battery to be solved;
(2) constructing a reverse experimental device of thermal resistance parameters;
(3) implementing a soft package battery thermal induction experiment;
(4) establishing a soft package battery temperature evaluation model;
(5) constructing a reverse model of the internal thermal resistance parameters of the soft package battery and solving to obtain thermal resistance parameters;
in the step (1), the internal thermal resistance parameter of the lithium ion soft package battery to be solved comprises the following steps: initial thermal conductivity K0The temperature index n of the thermal conductivity, the initial thermal conductivity K0The thermal conductivity of a gas-liquid mixture filled in a soft package battery between a battery core and a soft package gap at a temperature of 273.15K is shown, and the expression of the thermal conductivity temperature index n is log (K)w/K0)/log(Tcel/273.15), wherein KwDenotes the temperature T of the gas-liquid mixturecelThermal conductivity of the polymer;
in the step (2), the thermal resistance parameter reverse experiment device comprises: the device comprises a soft package battery, a clamping module, a temperature change test box, a temperature measuring instrument and a coordinate system; appearance size X of soft package batterycel×Ycel×ZcelInitial volume is V0The battery consists of a battery cell, a soft package and electrolyte; the soft package is of thickness dpThe aluminum-plastic film of (1); the clamping module comprises a first clamping plate, a second clamping plate, a first bolt, a second bolt, a first nut and a second nut; the first clamping plate and the second clamping plate are completely consistent in structure, the epoxy glass cloth laminated plate is selected as a material, and the overall dimension X isb×Yb×ZbIs Xb＝0.15·Xcel，Yb＝Ycel+0.3·Xcel，Zb＝0.1·Ycel(ii) a At the position XbD in a direction away from the first endb＝0.07·XcelAt a position of D from the second endbAre respectively provided with a diameter DbA first circular hole and a second circular hole; the first bolt and the second bolt are inner hexagonal flat round head screws with the standard number of GB/T70.2-2015, and the pitch diameter d of the threadsb＝int(Db) Length of thread hb＝int(Zcel+2·Zb+1.5·Db) Where int (·) denotes an integer arithmetic; the first nut and the second nut are butterfly nuts with standard numbers of GB62-88, and the pitch diameter of the threads is db(ii) a The temperature change test chamber is a general test device which can provide a rapid temperature change environment and a constant temperature environment; the temperature measuring instrument is a general thermocouple type temperature measuring instrument with at least two temperature measuring channels and comprises a first thermocouple, a second thermocouple, a signal wire and a host;
the assembly steps of the thermal resistance parameter reverse experiment device are as follows:
(2.1) aligning and sequentially stacking the centers of the first clamping plate, the thermocouple, the soft package battery and the second clamping plate;
(2.2) passing the first bolt through the first round holes of the first clamping plate and the second clamping plate, and fastening the first bolt with the first nut;
(2.3) passing the second bolt through the second round holes of the first clamping plate and the second clamping plate, and fastening the second bolt with the second nut;
(2.4) controlling the distance between the first splint and the second splint to be Zbb＝0.95·Zcel；
(2.5) adhering the second thermocouple to the upper surface of the soft package battery;
(2.6) suspending the assembled soft package battery, the clamping module and the temperature measuring instrument at the central position inside the temperature change test box;
(2.7) placing the host of the temperature measuring instrument at a position which is convenient to observe outside the temperature change test box;
in the step (3), the step of implementing the soft-package battery thermal induction experiment is as follows:
(3.1) based on the thermal resistance parameter reverse experiment device, setting the temperature change process of the temperature change test box as follows: keeping the temperature for 20min at an initial temperature of 298K, heating to 398K at a speed of 5K/min, and keeping the temperature for 20 min;
(3.2) reading the measured temperature T 'of the battery core measured by the first thermocouple and the second thermocouple in the experimental process'celAnd an actually measured temperature T 'of the soft bag'surReading the temperature T of the air in the box output by the temperature change test boxairRecording T 'of the current time T every 1 minute'cel，T’sur，Tair(ii) a A series of T'cel，T’sur，TairCan be written as vectors:
T’cel＝(T’cel,1,T’cel,2,...,T’cel,t,...,T’cel,T)
T’sur＝(T’sur,1,T’sur,2,...,T’sur,t,...,T’sur,T)
Tair＝(Tair,1,Tair,2,...,Tair,t,...,Tair,T)
wherein T represents the time of the last recording;
in the step (4), the step of establishing the soft package battery temperature evaluation model is as follows:
(4.1) establish the heat generation equation E1: q. q.scel＝mrea·sum(Δhj·Rj) J is 1, 2; wherein j-1 represents an SEI decomposition reaction, and j-2 represents an SEI reconstruction reaction; sum (·) denotes a summation operation; q. q.scelDenotes the heat generation rate, mgasDenotes the mass of the liberated gas, RjRespectively represents the reaction rates of SEI decomposition and reconstruction, delta hjIndicating the reaction enthalpy change of SEI decomposition and reconstruction;
in step (4.1), the thermal model of the lithium ion battery proposed by Hatchard and Dahn is used to calculate the SEI decomposition and reconstruction reaction rate: rj＝-dt(xj)＝fj·xj·exp(-Ej/(Ru·Tcel) ); where dt (-) represents the derivative operation over time t, i.e., the rate of change; exp (. cndot.) denotes an exponential operation, x1,x2Respectively represent the amount of lithium ions contained and inserted in the SEI film; f. of1,f2Respectively representing frequency factors of SEI decomposition and reconstruction reactions, E1,E2Respectively representing activation energy of SEI decomposition and reconstruction reaction; ruIs the universal gas constant; t iscelRepresenting a temperature of the cell; solving the reaction rate of SEI decomposition and reconstruction to obtain:
Rj＝fj·xj 0·exp{-Ej/(Ru·Tcel)-fj·t·exp[-Ej/(Ru·Tcel)]}
wherein t is the current moment; at xj 0Wherein j ═ 1 denotes an initial amount of lithium ions contained in the SEI film, and j ═ 2 denotes an initial amount of lithium ions inserted in the SEI film;
(4.2) establishing the gas production equation E2: dt (m)gas)＝cgas·qcel(ii) a Wherein m isgasDenotes the mass of the released gas, cgasExpressing a proportionality coefficient between a gas production rate and a heat generation rate;
(4.3) based on the theory of heat transfer, the heat transfer equation E3 is established:
qcel＝Ccel·dt(Tcel)+(Tcel-Tsur)/Rcel
wherein, CcelRepresents the heat capacity of the cell, RcelRepresents the equivalent thermal conduction resistance, T, from the cell to the soft bagsurRepresenting the temperature of the soft pack;
(4.4) based on the thermal convection theory, the thermal convection equation E4 is established:
(Tcel-Tsur)/Rcel＝(Tsur-Tair)/Rair
wherein R isairRepresenting the convective heat resistance from the outer surface of the soft bag to the air inside the temperature change test chamber;
(4.5) establishing an equivalent thermal resistance equation E5 based on a parallel thermal circuit theory;
in step (4.5), the step of establishing the equivalent thermal resistance equation E5 is as follows:
(4.5.1) establishing a parallel thermal resistance equation: rcel＝1/sum(Kw·Ai/δi) 1,2, ·, 6; wherein A isiDenotes the ith heat transfer surface, and the pouch cell has 6 heat transfer surfaces in X, Y, Z3 directions, deltaiRepresenting the clearance, K, from the cell to the soft pack for the ith heat transfer surfacewIn relation to the cell temperature, write: kw＝K0·(Tcel/273.15)n；
(4.5.2) introducing an equivalent gap δ mean (δ)i) Mean (-) denotes the averaging operation;
(4.5.3) writing the parallel thermal resistance equation to equivalent thermal resistance equation E5 based on the equivalent gap δ: r iscel＝δ·Asur -1·K0 -1·(0.0127·Tcel)-n(ii) a Wherein A issur＝sum(Ai) Representing the surface area of the soft package battery;
(4.6) establishing a soft package deformation equation E6 based on finite element analysis;
in step (4.6), the step of establishing the soft package deformation equation E6 is as follows:
(4.6.1) establishing a reaction gas equation of state according to the ideal gas law: pcel·Vgas＝mgas·Rgas·Tcel(ii) a Wherein, PcelRepresents the internal air pressure, V, of the pouch cellgasDenotes the volume of gas, RgasRepresents a gas constant of the reaction gas;
(4.6.2) based on the thermal resistance parameter reverse experiment device, establishing 1/4 type finite element structures including a second soft package through the existing commercial finite element analysis software;
(4.6.3) cell arrangement, the cells of the second soft pack being arranged to have a thickness dpThe housing unit of (a);
(4.6.4) setting material properties including: elastic modulus 4106MP, Poisson's ratio 0.33, stress and plastic strain table;
(4.6.5) setting boundary conditions including: setting an X-direction symmetric boundary for the first area, a Y-direction symmetric boundary for the second area, a Z-direction symmetric boundary for the third area, and a clamped boundary for simulating the clamping module for the fourth area;
(4.6.6) setting m different pressure loads P to a fifth region of the second soft packcel,jEstablishing a corresponding solving condition when j is 1, 2.. multidot.m;
(4.6.7) calling a general static solver of the commercial finite element analysis software, solving the solving conditions one by one to obtain a gas volume response Vgas,jJ 1, 2.. m, calculating the relative expansion coefficient Ce,j＝Vgas,j/V0；
(4.6.8) based on the m different pressure loads Pcel,jAnd said gas volume response Vgas,jFitting to obtain the relationship between the pressure load and the gas volume as follows: vgas＝Vgas(Pcel) Substituting into the relation P between pressure load and internal air pressurecel＝Pgas-P0Obtaining a pressure-volume equation: vgas＝Vgas(Pgas) In which P is0Represents standard atmospheric pressure;
(4.6.9) subjecting the pressure-volumeSubstituting the equation into the gas state equation to obtain the soft package deformation equation E6: pcel·Vgas(Pgas)＝mgas·Rgas·Tcel；
(4.7) establishing an equivalent clearance equation E7: delta 0.5. Ce(Pgas)/(Xcel·Ycel)；
(4.8) equations E1-E7 are combined to obtain a soft package battery temperature evaluation model M1:
in the step (5), the steps of constructing a reverse model of the internal thermal resistance parameter of the soft package battery and solving to obtain the thermal resistance parameter are as follows:
(5.1) establishing a cell temperature function and a soft package temperature function, wherein the method comprises the following steps: at the initial thermal conductivity K0And the thermal conductivity temperature index n is used as an input variable, a solver of the conventional commercial numerical analysis software is called to solve the temperature evaluation model, the cell temperature and the soft package temperature at all moments are obtained and used as output variables, and the output variables are written into vectors
Tcel＝(Tcel,1,Tcel,2,...,Tcel,t,...,Tcel,T)
Tsur＝(Tsur,1,Tsur,2,...,Tsur,t,...,Tsur,T)
Wherein T iscel,t＝Tcel(K0N, T) is the cell temperature function, Tsur,t＝Tsur(K0N, t) is the soft package temperature function;
(5.2) establishing a reverse optimization objective function, and writing into: fobj(K0,n)＝||Tcel-T’cel||+||Tsur-T’sur| |, where | · | | | represents vector modulo arithmetic;
(5.3) establishing a reverse model M2 of the internal thermal resistance parameter of the soft package battery, and writing the model into a standard optimized model form:
minFobj(K0,n)
s.t.K0>0,n>0
where min represents the minimization and s.t. represents the constraint;
(5.4) calling a solver of the conventional commercial numerical analysis software to solve the thermal resistance parameter inverse model to obtain the optimal initial thermal conductivity K0 *And an optimum thermal conductivity temperature index n*Namely, the solution of the thermal resistance parameter to be solved.
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