CN104849675B - The acquisition methods of lithium ion battery battery chemically and thermally coupling model - Google Patents
The acquisition methods of lithium ion battery battery chemically and thermally coupling model Download PDFInfo
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Abstract
The acquisition methods of lithium ion battery battery chemically and thermally coupling model, are related to intelligent grid Large Copacity energy storage field.The present invention is to solve the problems, such as to lack changed with time to battery terminal voltage and the skin temperature electrochemistry emulated and thermal coupling model.It is of the present invention to put lithium ion battery at different temperature, to lithium ion battery input current, according to battery terminal voltage and casing of lithium ion battery temperature response curve, obtain lithium ion battery battery chemically and thermally coupling model parameter.The coupling model can be used for the terminal voltage and skin temperature of emulation lithium ion battery.
Description
Technical field
The present invention relates to electrochemistry-thermal coupling modelling by mechanism and its parameter acquiring method, is electrical engineering, electrochemistry, heat
The multi-disciplinary intersection such as, applied mathematics, belong to intelligent grid Large Copacity energy storage field.
Background technology
The outstanding feature of lithium ion battery is that voltage is high, energy density is big, good cycle, self discharge are small, memoryless effect
Answer, be green, being large scale equipment or the main energy storage device of system.Security, reliability and the economy of battery these three
The performance of aspect constrains the use of its further genralrlization.Say that battery management system is to giving full play to battery from application angle
Performance has vital meaning.
Lithium ion battery mechanism model is capable of the physics of accurate description inside battery complexity, chemical process, has to any
The simulation estimate ability of the lower battery response of load current excitation.But model generally has complicated form, calculate and take, and need
Mechanism model parameter is obtained by electrochemical measuring method or intelligent algorithm, not possess quick, lossless ability getparms.
At present, mechanism model is mainly used in the design and improvement of battery, rarely seen to be used in battery management system.
The content of the invention
The present invention in order to solve it is existing lack to change with time to battery terminal voltage and skin temperature emulate
The problem of electrochemistry and thermal coupling model.The acquisition methods of lithium ion battery battery chemically and thermally coupling model are now provided.
The acquisition methods of lithium ion battery battery chemically and thermally coupling model, it includes herein below：
Lithium ion battery is put at different temperature, to lithium ion battery input current, obtains lithium ion battery end electricity
Press Uapp(t)：
(formula 1)
In formula,It is battery under reference temperature, solid-state diffusion, concentration polarization, reaction polarization and ohmic polarization shadow
Sound is the terminal voltage in the case of zero, ηact-polarization(t) it is reaction polarization overpotential, ηohm-polarization(t) it is ohm
Overvoltage, ηcon-polarization(t) it is concentration polarization overpotential,
With casing of lithium ion battery hygrometric formula：
(formula 2)
In formula, RcondFor inside battery thermal resistance, h is the coefficient of heat transfer, CcanFor the thermal capacitance of shell, TaFor environment temperature, A is to have
Imitate area of dissipation, mcanFor outer cover quality, Tsurf(tk) be the k moment casing of lithium ion battery temperature, Tsurf(tk-1) when being k-1
The casing of lithium ion battery temperature at quarter, tkFor k moment, tk-1For the k-1 moment,
So as to obtain lithium ion battery battery chemically and thermally coupling model.
Beneficial effects of the present invention are：The present invention according to the solid phase potential on positive and negative electrode two borders at collector it
Poor UappAnd casing of lithium ion battery temperature T (t)surf(tk) electrochemistry and thermal coupling model are established, the model can be realized arbitrarily
Under load current and environment temperature, the accurate estimation to battery terminal voltage and skin temperature, realize to inside battery electrochemistry and
Thermal behavior more comprehensively describes.
Fig. 8 to Figure 21 is given at a temperature of continuous constant current charge-discharge and dynamic load electric current and varying environment, battery
Response includes battery terminal voltage and the change curve of skin temperature, and simulation result shows：In the case of continuous discharge and recharge, big
When multiplying power (1.5C) is discharged, battery surface temperature simulation error is larger.During due to big multiplying power discharging, inside battery heating is obvious,
The error that this simplified calculating is brought is just relatively larger.When environment temperature be in room temperature and it is neighbouring when, voltage simulated effect compared with
Accurately；When environment temperature is slightly higher or relatively low, meeting guiding discharge cut-off point estimation is inaccurate, and then have impact on estimation on the whole
Precision.In the case of dynamic load electric current, the position of maximum local temperature appearance, emulation is relatively for actual measurement, and there occurs one
Fixed skew, caused by this is due to the entropy coefficient of battery plus-negative plate material.The simulation calculation of dynamic process voltage is more accurate.
Generally speaking, more than near room temperature or room temperature, model has suitable well for middle low range and dynamic operation condition
The property used.
Brief description of the drawings
Fig. 1 is the principle schematic of the lithium ion battery battery chemically and thermally coupling model described in embodiment one；
Fig. 2 is the curve map for applying load current to lithium ion battery described in embodiment three；
Fig. 3 is attached at different temperatures, to apply Fig. 2 current value battery terminal voltage response curve to lithium ion battery
Icon note 1 represents battery terminal voltage response curve at 25 DEG C, and reference 2 represents battery terminal voltage response curve at 45 DEG C, attached
Icon note 3 represents battery terminal voltage response curve at 35 DEG C；
Fig. 4 is at different ambient temperatures, to apply Fig. 2 current value battery case temperature response curve to lithium ion battery
Figure；
Fig. 5 is the ohmic polarization and reaction polarization process transient period curve map described in embodiment three；
Fig. 6 is that the solid liquid phase described in embodiment four spreads steady-state process curve map；
Fig. 7 be embodiment five described under different multiplying, skin temperature time history plot, accompanying drawing
Under the expression 2C multiplying powers of mark 11, battery case temperature versus time curve；Under the expression 1.5C multiplying powers of reference 12, battery
Skin temperature versus time curve；Reference 13 represents under 1.25C multiplying powers that battery case temperature changes with time song
Line；Under the expression 1C multiplying powers of reference 14, battery case temperature versus time curve；Reference 15 represents 0.75C times
Under rate, battery case temperature versus time curve；Reference 16 represents under 0.5C multiplying powers that battery case temperature is with the time
Change curve；Under the expression 0.4C multiplying powers of reference 17, battery case temperature versus time curve；The table of reference 18
Show under 0.2C multiplying powers, battery case temperature versus time curve；Under the expression 0.1C multiplying powers of reference 19, battery case temperature
Spend versus time curve；
Fig. 8 is environment temperature when being 15 DEG C, and terminal voltage simulation value and the measured value control of continuous constant current charge-discharge battery are bent
Line chart,Simulation value is represented ,-represent measured value；From starting electric discharge to be down to terminal voltage it is 2.75V in battery, discharge-rate is
1.5C；In battery terminal voltage 4.2V, rate of charge 1C are risen to from 3.5V or so；Dropped again from 3.75V or so in battery terminal voltage
To 2.75V, discharge-rate 0.75C；4.2V, rate of charge 0.5C are risen to again from 3.3V or so in battery terminal voltage；
Fig. 9 is environment temperature when being 15 DEG C, skin temperature simulation value and the measured value control of continuous constant current charge-discharge battery
Curve map, terminal voltage decline, and skin temperature rises, and multiplying power is bigger, and skin temperature rises obvious；
Figure 10 is environment temperature when being 25 DEG C, and terminal voltage simulation value and the measured value control of continuous constant current charge-discharge battery are bent
Line chart, from starting electric discharge to be down to terminal voltage it is 2.75V, discharge-rate 1.5C in battery；In battery terminal voltage from 3.5V or so
Rise to 4.2V, rate of charge 1C；2.75V, discharge-rate 0.75C are down to again from 3.75V or so in battery terminal voltage；In electricity
Pond terminal voltage rises to 4.2V, rate of charge 0.5C again from 3.3V or so；
Figure 11 is environment temperature when being 25 DEG C, skin temperature simulation value and the measured value control of continuous constant current charge-discharge battery
Curve map；
Figure 12 is environment temperature when being 35 DEG C, and terminal voltage simulation value and the measured value control of continuous constant current charge-discharge battery are bent
Line chart, from starting electric discharge to be down to terminal voltage it is 2.75V, discharge-rate 1.5C in battery；In battery terminal voltage from 3.5V or so
Rise to 4.2V, rate of charge 1C；2.75V, discharge-rate 0.75C are down to again from 3.75V or so in battery terminal voltage；In electricity
Pond terminal voltage rises to 4.2V, rate of charge 0.5C again from 3.3V or so；
Figure 13 is environment temperature when being 35 DEG C, skin temperature simulation value and the measured value control of continuous constant current charge-discharge battery
Curve map；
Figure 14 is environment temperature when being 45 DEG C, and terminal voltage simulation value and the measured value control of continuous constant current charge-discharge battery are bent
Line chart, from starting electric discharge to be down to terminal voltage it is 2.75V, discharge-rate 1.5C in battery；In battery terminal voltage from 3.5V or so
Rise to 4.2V, rate of charge 1C；2.75V, discharge-rate 0.75C are down to again from 3.75V or so in battery terminal voltage；In electricity
Pond terminal voltage rises to 4.2V, rate of charge 0.5C again from 3.3V or so；
Figure 15 is environment temperature when being 45 DEG C, and continuous constant current charge-discharge battery case temperature simulation value and measured value control are bent
Line chart；
Figure 16 is environment temperature when being 15 DEG C, dynamic load galvanic cell terminal voltage simulation value and measured value control curve
Figure, from starting electric discharge to be down to terminal voltage it is 2.75V, discharge-rate 1.5C in battery；Risen in battery terminal voltage from 3.5V or so
To 4.2V, rate of charge 1C；2.75V, discharge-rate 0.75C are down to again from 3.75V or so in battery terminal voltage；In battery
Terminal voltage rises to 4.2V, rate of charge 0.5C again from 3.3V or so；
Figure 17 is environment temperature when being 15 DEG C, dynamic load galvanic cell skin temperature simulation value and measured value control curve
Figure；
Figure 18 is environment temperature when being 30 DEG C, dynamic load galvanic cell terminal voltage simulation value and measured value control curve
Figure, from starting electric discharge to be down to terminal voltage it is 2.75V, discharge-rate 1.5C in battery；Risen in battery terminal voltage from 3.5V or so
To 4.2V, rate of charge 1C；2.75V, discharge-rate 0.75C are down to again from 3.75V or so in battery terminal voltage；In battery
Terminal voltage rises to 4.2V, rate of charge 0.5C again from 3.3V or so；
Figure 19 is environment temperature when being 30 DEG C, dynamic load galvanic cell skin temperature simulation value and measured value control curve
Figure；
Figure 20 is environment temperature when being 45 DEG C, dynamic load galvanic cell terminal voltage simulation value and measured value control curve
Figure, from starting electric discharge to be down to terminal voltage it is 2.75V, discharge-rate 1.5C in battery；Risen in battery terminal voltage from 3.5V or so
To 4.2V, rate of charge 1C；2.75V, discharge-rate 0.75C are down to again from 3.75V or so in battery terminal voltage；In battery
Terminal voltage rises to 4.2V, rate of charge 0.5C again from 3.3V or so；
Figure 21 is environment temperature when being 45 DEG C, dynamic load galvanic cell skin temperature simulation value and measured value control curve
Figure.
Embodiment
Embodiment one：Reference picture 1 illustrates present embodiment, the lithium ion battery battery described in present embodiment
The chemically and thermally acquisition methods of coupling model, it includes herein below：
Lithium ion battery is put at different temperature, to lithium ion battery input current, obtains lithium ion battery end electricity
Press Uapp(t)：
(formula 1)
In formula,It is battery under reference temperature, solid-state diffusion, concentration polarization, reaction polarization and ohmic polarization shadow
Sound is the terminal voltage in the case of zero, ηact-polarization(t) it is reaction polarization overpotential, ηohm-polarization(t) it is ohm
Overvoltage, ηcon-polarization(t) it is concentration polarization overpotential,
With casing of lithium ion battery hygrometric formula：
(formula 2)
In formula, RcondFor inside battery thermal resistance, h is the coefficient of heat transfer, CcanFor the thermal capacitance of shell, TaFor environment temperature, A is to have
Imitate area of dissipation, mcanFor outer cover quality, Tsurf(tk) be the k moment casing of lithium ion battery temperature, Tsurf(tk-1) when being k-1
The casing of lithium ion battery temperature at quarter, tkFor k moment, tk-1For the k-1 moment, T is internal mean temperature,
So as to obtain lithium ion battery battery chemically and thermally coupling model.
In present embodiment, analyzed battery as a system, the system there are two input variables：Discharge and recharge electricity
Stream and environment temperature；Two can survey output variable：Battery terminal voltage and casing surface temperature.
Embodiment two：Present embodiment be to the lithium ion battery battery described in embodiment one chemically and thermally
The acquisition methods of coupling model are described further, and in present embodiment, calculate battery ideal electromotive forceProcess：
Under the small multiplying powers of 0.02C, using lithium ion battery discharge voltage as battery ideal electromotive force, it is known that both positive and negative polarity is opened a way
Potential Up, and Un, use the initial embedding lithium rate y of Least Square Method both positive and negative polarity0And x0, and both positive and negative polarity excursion DyAnd Dx, root
According to formula：
(formula 3)
Obtain both positive and negative polarity capacity QpAnd Qn, embedding lithium rate skew yofs；
In formula, QallFor the total capacity of small multiplying power discharging,
Bring formula 3 into battery ideal electromotive forceIn：
(formula 4)
Obtain battery ideal electromotive force
In formula, yavgAnd xavgRepresent average lithium concentration, y inside both positive and negative polarity active particleavg=y0+It/Qp, xavg=
(1-yofs-yavg)Qp/Qn, I is load current, it is specified that electric discharge is that just, t is the time.
Embodiment three：Reference picture 2 illustrates present embodiment to Fig. 5, and present embodiment is to specific implementation
The acquisition methods of lithium ion battery battery described in mode one chemically and thermally coupling model are described further, in present embodiment,
Calculate reaction polarization overpotential ηact-polarizationWith ohmic polarization overpotential ηohm-polarizationProcess：
Battery is placed at a temperature of varying environment after a period of time, applies the excitation of 1kHz sinusoidal voltages, using least square
Approximating method is fitted to different temperatures, obtains ohmic internal resistance RohmWith the varying type of internal temperature of battery：
Rohm=β1T3+β2T2+β3T1+β4, (formula 5)
In formula, βiTo treat fitting parameter, i=1,2,3,4,
According to formula：
ηohm-polarization(t)=RohmI (t), (formula 6)
Obtain ohmic polarization overpotential ηohm-polarization,
Under different multiplying, environment temperature controls at 25 DEG C, 35 DEG C, 45 DEG C respectively, 7 points each to battery constant current charging-discharging
Clock, then battery is shelved 10 minutes, each 7 minutes of cycle charge-discharge, and to battery shelve the mistake of 10 minutes successively successively
Journey, electric current change to a certain fixed value in a flash from 0, and voltage has saltus step Δ U, and voltage jump Δ U includes reaction polarization mistake
Potential and ohmic polarization overpotential,
Voltage jump Δ U subtracts ohmic polarization overpotential ηohm-polarization, reaction polarization overpotential can be obtained
ηact-polarization：
(formula 7)
In formula,
R is ideal gas constant, and F is Faraday constant, c0
For concentration of electrolyte,Using least square method, pole is reacted at a temperature of Fitted reference
Change coefficientWith activation energy coefficient lambda.
In present embodiment, the time constant of each physical and chemical process of inside battery is different, and frequency response is also different.Ohm
The response of polarization electronic conduction process is most fast, the time very of short duration after current excitation is applied of pressure drop caused by Ohmic resistance
It can produce.By comparison, the frequency response of lithium ion mass transfer motion process is more slowly.Ohmic internal resistance also by environment temperature with
And the influence of internal temperature.Therefore, the ohmic internal resistance of battery is measured using the high band of electrochemical impedance spectroscopy, specific practice is
Battery is placed at a temperature of varying environment after a period of time, applies the excitation of 1kHz sines small voltage, measures the current-responsive of battery,
Calculate ohmic internal resistance.State is shelved because battery is in, internal temperature and environment temperature are approximately the same.
In the initial time of discharge and recharge, battery is in poised state, and solid phase lithium concentration is uniformly distributed.In load current
The moment of application, solid phase surface and internal average lithium concentration will not be mutated, and after one section of transit time, it is established that
Stable concentration difference.Liquid phase diffusion is similar with solid-state diffusion, and liquid concentration distribution is also required to a period of time just can be into stabilization
State.Reaction polarization is compared with diffusion process, and the speed of foundation is very fast.
Embodiment four：Reference picture 6 illustrates present embodiment, and present embodiment is to embodiment one
The acquisition methods of described lithium ion battery battery chemically and thermally coupling model are described further, and in present embodiment, are calculated dense
Poor overvoltage ηcon-polarizationProcess：
Under different multiplying, environment temperature controls at 25 DEG C, 35 DEG C, 45 DEG C respectively, 7 points each to battery constant current charging-discharging
Clock, then battery is shelved 10 minutes, each 7 minutes of cycle charge-discharge, and to battery shelve the mistake of 10 minutes successively successively
Journey, the diffusion process of lithium ion battery needs one section of transit time, just into new steady s tate, in liquid phase diffusion and solid phase
After diffusion enters steady-state process, the poor Δ y of positive electrode surface and average embedding lithium concentrationstable, negative terminal surface and average embedding lithium concentration
Poor Δ xstableWith the concentration difference Δ c of collector boundarystableIt is definite value, expression formula is as follows：
(formula 8)
In formula, liquid phase diffusion ratio FACTOR Pcon=aTb+ c, a, b and c are unknown parameter to be fitted,
23 cut offs of constant current charge-discharge are selected, at cut off, solid-state diffusion and liquid phase diffusion process all have been enter into
Steady-state process, the terminal voltage of cut off meet formula：
(formula 9)
In formula,Concentration polarization overpotential during stable state is represented,
Formula 9 is deformed into：
(formula 10)
Using least square fitting, the time constant of the positive pole solid-state diffusion at a temperature of varying environment is obtainedConsolidate with negative pole
The mutually time constant of diffusionAnd liquid phase diffusion ratio FACTOR PconIn a, b and c,
Calculate the concentration polarization overpotential under continuous dynamic constant current charge-discharge operating mode：
(formula 11)
By ηohm-polarizationReversely solve the variable quantity of battery afflux liquid boundary liquid phase lithium concentration under the operating mode
Δc(t)：
(formula 12)
In formula, t+Load transfer number is represented,
According to the variation delta c (t) of liquid phase lithium concentration and liquid phase diffusion ratio FACTOR Pcon, calculate τe：
(formula 13)
According to formula：
(formula 14)
Obtain concentration polarization overpotential ηcon-polarization,
In formula, the variation delta c (t) of liquid phase lithium concentration iteration form is
In present embodiment, diffusion process needs one section of transit time, just into new steady s tate.In order to keep away as far as possible
Exempt from temperature and influence is brought on parameter Estimation, the time control of excitation every section of constant current charge-discharge of operating mode is 7 minutes.
Embodiment five：Reference picture 7 illustrates present embodiment, and present embodiment is to embodiment one
The acquisition methods of described lithium ion battery battery chemically and thermally coupling model are described further, and in present embodiment, calculating is changed
The process of hot coefficient h：
According to formula：
Gexchange(t)=(Tsurf(t)-Ta(t))/Ramb, (formula 15)
Obtain the heat transfer rate G of battery and environmentexchange,
Wherein, RambThermal resistance is exchanged with ambient heat for battery case, its expression formula is Ramb=1/hA0, TaFor environment temperature,
A0For the effective area of dissipation of battery, h is the coefficient of heat transfer, and when load current is zero, battery heat production is zero, inside and outside temperature phase
Deng by outside batteries hygrometric formula：
(formula 16)
It is deformed into：
(formula 17)
When battery surface temperature and internal temperature are equal, during t=0, T (0)=T0；As t=∞, T (∞)=Ta, arrange
Formula 17, is obtained：
Tsurf(t)=Ta(t)+(T0-Ta)exp(-hA0t/(Cpmroll)), (formula 18)
Wherein, Tsurf(t) it is the battery case temperature of t, timeconstantτheat=Cpmroll/(hA0), CpFor battery electricity
Pole winding body thermal capacitance, mrollWeight, T are wound for electrode0For initial cells internal temperature,
Battery is placed in insulating box and tested, thermometric is carried out in battery case attachment temperature sensor, at different times
Under rate, battery case temperature changes with time, and after battery stops electric discharge, makes battery return to the temperature of setting in insulating box
Skin temperature in different time, is fitted, obtains each timeconstantτ by degree using formula 18heat, each time is normal
Number τheatAverage is taken, and then obtains coefficient of heat transfer h.
In present embodiment, for low capacity coiled battery, due to every layer of very thin thickness, heat production in the radial direction
Difference and unobvious, internal temperature of battery situation of change can be characterized with a mean temperature, the description of its temperature includes two
Individual part, i.e., with T and TsurfTo describe internal temperature and surface temperature.
Embodiment six：Present embodiment be to the lithium ion battery battery described in embodiment one chemically and thermally
The acquisition methods of coupling model are described further, and in present embodiment, calculate inside battery thermal resistance RcondProcess：
Due to reaction polarization overpotential ηact-polarization, ohmic polarization overpotential ηohm-polarizationWith concentration polarization
Potential ηcon-polarizationAll related to internal temperature, if overpotential, which calculates, relatively large deviation occurs, hot result of calculation will appear from
Larger error, then can not backheatingHeat production such as following formula：
(formula 19)
Then heat production rate expression formula is：
(formula 20)
In formula,For the entropy coefficient of positive electrode,For the entropy coefficient of negative material, TrefFor reference
Temperature,
By battery case temperatureWrite as the form of iteration, obtained
The calculating formula of battery case temperature：
(formula 21)
By internal temperature of batteryWrite as the form of iteration, obtain calculating formula：
T(tk)=T (tk-1)+(tk-tk-1)(G(tk-1)-(T(tk-1)-Tsurf(tk-1))/Rcond)/(mrollCp), (formula 22)
Simultaneous formula 20 and formula 21, obtain inside battery thermal resistance Rcond,
In formula, G (tk-1) be the k-1 moment heat production rate.
Embodiment seven：Present embodiment be to the lithium ion battery battery described in embodiment six chemically and thermally
The acquisition methods of coupling model are described further, in present embodiment, to battery ideal electromotive forceThe mistake being modified
Journey：
Battery itself heat production rate is G, including can not backheatingWith can backheatingTwo parts, expression formula difference are as follows：
(formula 23)
(formula 24)
Wherein,It is battery material build-in attribute for the entropy coefficient of positive and negative electrode material,
According to formula 22 and 21, to current inside temperature T and reference temperature TrefUnder battery open circuit potentialCarry out
It is modified to：
(formula 25)
Wherein, Eocv(t) battery open circuit potential is represented.
In present embodiment, revised battery open circuit potential is obtainedThen by revised battery open circuit electricity
GestureBring intoIn, obtain
Obtain lithium ion battery terminal voltage Uapp(t)。
Embodiment：
The numbering that Tianjin Li Shen companies produce is used to carry out parameter Estimation and emulation for LS.LR1865BC cobalt acid lithium battery
Checking.The collection of battery terminal voltage, electric current, watchcase temperature is realized by battery test system.
Parametric estimation step is as follows：
A) battery is placed in insulating box in the environment of 25 DEG C first, by measuring small multiplying power 0.02C discharge voltage profiles,
Estimate battery groundwork four parameters of process；
B) measurement of ohmic internal resistance is realized by internal resistance test device, is surveyed after varying environment temperature shelves a period of time
Amount, and be fitted with cubic polynomial to obtain its functional relation varied with temperature；
C) least square fitting is carried out according to formula 5 to formula 7, estimates reaction polarization parameterAnd λ；
D) least square fitting is carried out according to formula 10, estimates solid-state diffusion time constantLiquid phase spreads ratio
FACTOR Pcon, by the P under different temperaturesconIt is fitted, obtains its functional relation varied with temperature.Calculated according to formula 13
τe；
E) coefficient of heat transfer h is relevant with the heat dissipation environment residing for battery, need to only estimate once；
F) at different ambient temperatures, obtained R is estimatedcondIt is basically unchanged, takes its average as final result.
Claims (2)
1. the acquisition methods of lithium ion battery battery chemically and thermally coupling model, it is characterised in that it includes herein below：
Lithium ion battery is put at different temperature, to lithium ion battery input current, obtains lithium ion battery terminal voltage Uapp
(t)：
In formula,Be battery under reference temperature, solid-state diffusion, concentration polarization, reaction polarization and ohmic polarization influence be
Terminal voltage in the case of zero, ηact-polarization(t) it is reaction polarization overpotential, ηohm-polarization(t) it is ohmic polarization
Potential, ηcon-polarization(t) it is concentration polarization overpotential,
With casing of lithium ion battery hygrometric formula：
In formula, RcondFor inside battery thermal resistance, h is the coefficient of heat transfer, CcanFor the thermal capacitance of shell, TaFor environment temperature, A is effectively scattered
Hot area, mcanFor outer cover quality, Tsurf(tk) be the k moment casing of lithium ion battery temperature, Tsurf(tk-1) it is the k-1 moment
Casing of lithium ion battery temperature, tkFor k moment, tk-1For the k-1 moment, T is internal mean temperature,
So as to obtain lithium ion battery battery chemically and thermally coupling model；
Battery is calculated under reference temperature, solid-state diffusion, concentration polarization, reaction polarization and ohmic polarization influence are zero situation
Under terminal voltageProcess：
Under 0.02C multiplying powers, using lithium ion battery discharge voltage as battery under reference temperature, solid-state diffusion, concentration polarization,
Reaction polarization and ohmic polarization influence are the terminal voltage in the case of zeroKnown both positive and negative polarity open circuit potential UpAnd Un, use
The initial embedding lithium rate y of Least Square Method both positive and negative polarity0And x0, and both positive and negative polarity excursion DyAnd Dx, according to formula：
Obtain both positive and negative polarity capacity QpAnd Qn, embedding lithium rate skew yofs；
In formula, QallFor the total capacity of small multiplying power discharging,
Formula 3 is brought into battery under reference temperature, solid-state diffusion, concentration polarization, reaction polarization and ohmic polarization influence are
Terminal voltage in the case of zeroIn：
Battery is obtained under reference temperature, solid-state diffusion, concentration polarization, reaction polarization and ohmic polarization influence are zero situation
Under terminal voltage
In formula, yavgAnd xavgRepresent average lithium concentration, y inside both positive and negative polarity active particleavg=y0+It/Qp, xavg=(1-
yofs-yavg)Qp/Qn, I is load current, it is specified that electric discharge is that just, t is the time；
Calculate reaction polarization overpotential ηact-polarizationWith ohmic polarization overpotential ηohm-polarizationProcess：
Battery is placed at a temperature of varying environment after a period of time, applies the excitation of 1kHz sinusoidal voltages, using least square fitting
Method is fitted to different temperatures, obtains ohmic internal resistance RohmWith the varying type of internal temperature of battery：
Rohm=β1T3+β2T2+β3T1+β4, (formula 5)
In formula, βiTo treat fitting parameter, i=1,2,3,4,
According to formula：
ηohm-polarization(t)=RohmI (t), (formula 6)
Obtain ohmic polarization overpotential ηohm-polarization,
Under different multiplying, environment temperature controls at 25 DEG C, 35 DEG C, 45 DEG C respectively, 7 minutes each to battery constant current charging-discharging,
Then battery is shelved 10 minutes, each 7 minutes of cycle charge-discharge, and to battery shelve the process of 10 minutes successively successively,
Electric current changes to a certain fixed value in a flash from 0, and voltage, which has saltus step △ U, voltage jump △ U, includes reaction polarization overpotential
With ohmic polarization overpotential,
Voltage jump △ U subtract ohmic polarization overpotential ηohm-polarization, reaction polarization overpotential can be obtained
ηact-polarization：
In formula,
R is ideal gas constant, and F is Faraday constant, c0For electrolysis
Liquid concentration,Using least square method, reaction polarization coefficient at a temperature of Fitted referenceWith activation energy coefficient lambda, PactFor reaction polarization coefficient, TrefFor reference temperature；
Calculate concentration polarization overpotential ηcon-polarizationProcess：
Under different multiplying, environment temperature controls at 25 DEG C, 35 DEG C, 45 DEG C respectively, 7 minutes each to battery constant current charging-discharging,
Then battery is shelved 10 minutes, each 7 minutes of cycle charge-discharge, and to battery shelve the process of 10 minutes successively successively,
The diffusion process of lithium ion battery needs one section of transit time, just into new steady s tate, in liquid phase diffusion and solid-state diffusion
After entering steady-state process, the poor △ y of positive electrode surface and average embedding lithium concentrationstable, negative terminal surface and average embedding lithium concentration difference
△xstableWith the concentration difference △ c of collector boundarystableIt is definite value, expression formula is as follows：
In formula, liquid phase diffusion ratio FACTOR Pcon=aTb+ c, a, b and c are unknown parameter to be fitted,For positive pole solid-state diffusion
Time constant,For the time constant of negative pole solid-state diffusion,
23 cut offs of constant current charge-discharge are selected, at cut off, solid-state diffusion and liquid phase diffusion process all have been enter into stable state
Stage, the terminal voltage of cut off meet formula：
In formula,Concentration polarization overpotential during stable state is represented,
Formula 9 is deformed into：
Using least square fitting, the time constant of the positive pole solid-state diffusion at a temperature of varying environment is obtainedExpand with negative pole solid phase
Scattered time constantAnd liquid phase diffusion ratio FACTOR PconIn a, b and c, UpFor positive pole open circuit potential function, UnFor negative pole
Open circuit potential function,
Calculate the concentration polarization overpotential under continuous dynamic constant current charge-discharge operating mode：
By ηohm-polarizationReversely solve the variable quantity △ c (t) of battery afflux liquid boundary liquid phase lithium concentration under the operating mode：
In formula, t+Load transfer number is represented,
According to the variable quantity △ c (t) of liquid phase lithium concentration and liquid phase diffusion ratio FACTOR Pcon, calculate the liquid phase expansion at k+1 moment
Dissipate timeconstantτe：
According to formula：
Obtain concentration polarization overpotential ηcon-polarization,
In formula, the variable quantity △ c (t) of liquid phase lithium concentration iteration form is
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Calculate coefficient of heat transfer h process：
According to formula：
Gexchange(t)=(Tsurf(t)-Ta(t))/Ramb, (formula 15)
Obtain the heat transfer rate G of battery and environmentexchange,
Wherein, RambThermal resistance is exchanged with ambient heat for battery case, its expression formula is Ramb=1/hA0, TaFor environment temperature, A0For
The effective area of dissipation of battery, h are the coefficient of heat transfer, and when load current is zero, battery heat production is zero, and inside and outside temperature is equal, will
Outside batteries hygrometric formula：
It is deformed into：
When battery surface temperature and internal temperature are equal, during t=0, T (0)=T0；As t=∞, T (∞)=Ta, arrange formula
17, obtain：
Tsurf(t)=Ta(t)+(T0-Ta)exp(-hA0t/(Cpmroll)), (formula 18)
Wherein, Tsurf(t) it is the battery case temperature of t, timeconstantτheat=Cpmroll/(hA0), CpTwined for battery electrode
Hold around body heat, mrollWeight, T are wound for electrode0For initial cells internal temperature,
Battery is placed in insulating box and tested, thermometric is carried out in battery case attachment temperature sensor, under different multiplying,
Battery case temperature changes with time, and after battery stops electric discharge, makes battery return to the temperature of setting in insulating box, adopts
The skin temperature in different time is fitted with formula 18, obtains each timeconstantτheat, by each timeconstantτheat
Average is taken, and then obtains coefficient of heat transfer h；
Calculate inside battery thermal resistance RcondProcess：
Due to reaction polarization overpotential ηact-polarization, ohmic polarization overpotential ηohm-polarizationWith concentration polarization overpotential
ηcon-polarizationAll related to internal temperature, if overpotential, which calculates, relatively large deviation occurs, hot result of calculation will appear from larger
Error, then can not backheatingHeat production such as following formula：
Then heat production rate expression formula is：
In formula,For the entropy coefficient of positive electrode,For the entropy coefficient of negative material, TrefFor reference temperature,
Eocv(t) it is battery open circuit potential,
By battery case temperatureWrite as the form of iteration, obtain battery
The calculating formula of skin temperature：
By internal temperature of batteryWrite as the form of iteration, obtain calculating formula：
T(tk)=T (tk-1)+(tk-tk-1)(G(tk-1)-(T(tk-1)-Tsurf(tk-1))/Rcond)/(mrollCp), (formula 22)
Simultaneous formula 20 and formula 21, obtain inside battery thermal resistance Rcond,
In formula, G (tk-1) be the k-1 moment heat production rate.
2. the acquisition methods of lithium ion battery battery according to claim 1 chemically and thermally coupling model, it is characterised in that right
For battery under reference temperature, solid-state diffusion, concentration polarization, reaction polarization and ohmic polarization influence are the end electricity in the case of zero
PressureThe process being modified：
Battery itself heat production rate is G, including can not backheatingWith can backheatingTwo parts, expression formula difference are as follows：
Wherein,It is battery material build-in attribute for the entropy coefficient of positive and negative electrode material,
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According to formula 22 and 21, to current inside temperature T and reference temperature TrefUnder battery under reference temperature, solid-state diffusion,
Concentration polarization, reaction polarization and ohmic polarization influence are the terminal voltage in the case of zeroBe modified for：
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