锂离子电池的产热量测量

Journal of Thermal Analysis and Calorimetry

An International Forum for Thermal Studies

ISSN 1388-6150

J Therm Anal Calorim

DOI 10.1007/s10973-014-3672-z

Comparison and validation of methods for estimating heat generation rate of large-format lithium-ion batteries

Jianbo Zhang, Jun Huang, Zhe Li, Bin Wu, Zhihua Nie, Ying Sun, Fuqiang An & Ningning Wu

all rights are held exclusively by Akadémiai Kiadó, Budapest, Hungary. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication

and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com”.

13

Comparison and validation of methods for estimating heat generation rate of large-format lithium-ion batteries

Jianbo Zhang •Jun Huang •Zhe Li •

Bin Wu •Zhihua Nie •Ying Sun •Fuqiang An •Ningning Wu

Received:14October 2013/Accepted:27January 2014

ÓAkade

´miai Kiado ´,Budapest,Hungary 2014Abstract The heat generation rate of a large-format 25Ah lithium-ion battery is studied through estimating each term of the Bernardi model.The term for the reversible heat is estimated from the entropy coefficient and compared with the result from the calorimetric method.The term for the irreversible heat is estimated from the intermittent current method,the V–I characteristics method and a newly developed energy method.Using the obtained heat generation rates,the average cell temperature rise under 1C charge/discharge is calculated and validated against the results measured in an accelerating rate calo-rimeter (ARC).It is found that the intermittent current method with an appropriate interval and the V–I charac-teristics method using a pouch cell yield close agreement,while the energy method is less accurate.A number of techniques are found to be effective in circumventing the difficulties encountered in estimating the heat generation rate for large-format lithium-ion batteries.A pouch cell,using the same electrode as the 25Ah cell but with much reduced capacity (288mAh),is employed to avoid the significant temperature rise in the V–I characteristics method.The first-order inertial system is utilized to correct the delay in the surface temperature rise relative to the

internal heat generation.Twelve thermocouples are used to account for the temperature distribution.

Keywords Lithium-ion battery ÁHeat generation rate ÁEnergy method ÁV–I characteristics method ÁIntermittent current method

Introduction

The lithium-ion battery is becoming the mainstream power sources for electric vehicles because of its high energy density and long cycle life [1].However,the thermal issues,such as the potential risk of thermal run-away [2–4]and the stringent restriction on both the limits and the variation of the cell operation temperatures,constitute one of the bottlenecks for the widespread use of large-format lithium-ion batteries in electric vehicles.In addition to experimental investigation [1,5,6],thermal simulation is a powerful tool to elucidate the mechanism underlying these thermal issues [7,8].The fundamental governing equation used in the thermal simulation is the heat transfer equation:q C P

o T

o t

¼r Ák r T ðÞþq ð1Þ

where q is density,C p is heat capacity,T is temperature,k denotes thermal conductivity,q is the heat generation rate per unit volume.

It is evident that the accuracy of the thermal simulation depends on the accuracy of the models to predict the heat generation rates for cells at different states and under various operation conditions.These heat generation rate models can be classified into two types.The first type is based on the thermal-electrochemical battery model and

J.Zhang ÁJ.Huang ÁZ.Li (&)ÁB.Wu

Department of Automotive Engineering,State Key Laboratory of Automotive Safety and Energy,Tsinghua University,Beijing 100084,China

e-mail:lizhe1212@gmail.com

J.Huang

e-mail:huangjun12@mails.tsinghua.edu.cn Z.Nie ÁY.Sun ÁF.An ÁN.Wu

CITIC Guo’an MGL Power Technology Co.,Ltd,Beijing 102200,China

123

J Therm Anal Calorim

DOI 10.1007/s10973-014-3672-z

Q¼Q revþQ irrevð2Þ

Q rev¼IT

o U

P

ð3Þ

Q irrev¼I VÀU

ðÞð4Þwhere Q is the total heat generation rate of lithium-ion batteries,Q rev is the reversible heat corresponding to the entropy change of the lithium intercalation/deintercalation reaction,Q irrev is the irreversible heat generated from electrode polarization,V is the terminal voltage,U is the equilibrium potential,and I is the charge/discharge current, assumed to be positive during charge.

Bernardi model is solidly founded on physics and has much less parameters.It is the most widely used model in the thermal simulation of the battery.In practice,the irreversible heat generation rate is usually further simpli-fied through defining an overpotential resistance,R,as:

R¼VÀU

ðÞ=I:ð5ÞThe irreversible heat generation rate equation now becomes:

Q irrev¼I2Rð6ÞBased on Eqs.(2–6),various methods have been developed[12–20]to estimate the reversible/irreversible heat generation for small lithium-ion batteries used in electronic devices.Much fewer works,however,have been found to study and to validate the heat generation rate for large-format lithium-ion batteries.

Regarding the reversible heat term,two methods,the potentiometric method and the calorimetric method,have been proposed and utilized[12–20].The potentiometric method measured the equilibrium potential of the cell adjusted at certain SOC at various temperatures.Taking the derivative of the equilibrium potential with respect to the temperature gave the entropy coefficient,d U/d T.The calorimetric method measured the heatflows during charge and discharge.Assuming that the irreversible heat gener-ation rates during charge and discharge were identical,the entropy coefficient was calculated from the difference of the heatflows.In[15,16],the authors studied the entropy changes associated with the structural and phase changes in negative and positive electrodes.Using half-cell,they further quantified the individual contribution of each electrode[19].Thomas et al.[20]concluded that,with proper correction for self-discharge,the potentiometric method was more accurate than the calorimetric method in calculating the reversible heat.

Regarding the irreversible heat term,Onda et al.[12–14] developed four methods:(1)the V–I characteristics method using voltage–current curves of discharge at a series of constant currents;(2)the OCV-V method using the dif-ference between the open-circuit voltage and the terminal voltage;(3)the intermittent current method using the voltage change after60s of discharge at a constant current;

(4)the AC impedance method.

Analysis of the previous literatures leads to the follow-ing observations:

Firstly,all the methods were originally developed for the small lithium-ion battery.Applying these methods to the large-format lithium-ion batteries will encounter a number of difficulties.One problem is the significant rise of temperature and the evolution of temperature variation across the cell even at moderate rates of charge/discharge [6].Rising and non-uniform temperature makes it difficult to define a representative temperature for the measured overpotential resistance,which is strongly dependent on the battery temperature.Another problem is that there exists a considerable delay in the response of the surface temperature relative to the internal heat generation[6].As a result,it is unconvincing to directly use the surface temperature at one point to calculate the heat generation rate and then to use it to validate the estimated values based on the Bernardi model.

Secondly,comparing the various methods can guide the selection of appropriate method to estimate the heat gen-eration rate.Onda et al.[12–14]developed four methods to estimate the irreversible heat term,but they only compared these methods in terms of the overpotential resistance obtained using each method,and then without convincing reasons,they applied the V–I characteristics method alone to simulate the cell temperature rise.In addition,in[17, 18],only the intermittent current method was employed. Onda et al.[12–14]pointed out that the AC method gives much lower overpotential resistance than other three methods,hence it is not considered in this study.Besides, the OCV-V method is essentially the same as the V–I characteristics method when considering the OCV curve as the discharge curve at sufficiently small current,thus,only the V–I characteristics method is included here.The V–I characteristic method has problems in considerable tem-perature rise,while the intermittent current method relies on the selection of the calculation interval,which is somewhat arbitrary in the previous studies.Therefore,the implementation details of these methods need to be closely examined,and the accuracy needs to be compared and validated against measured results.In addition,a new

J.Zhang et al.

123method,developed in our group and named energy method in this study,will also be included in the comparison.

Therefore,the objectives of this paper are to explore techniques to circumvent the above mentioned difficulties so as to extend,compare,and validate the various methods developed for small lithium-ion batteries to estimate the heat generation rate for large-format lithium-ion batteries.A large-format25Ah lithium-ion battery was used and its heat generation rate was studied based on the simplified Bernardi heat generation model.The potentiometric method and the calorimetric method were used to estimate the reversible heat. The intermittent current method,the V–I characteristics method and a newly proposed energy method were used to estimate the irreversible heat.The estimated values were compared and validated against the results measured in an ARC.A number of techniques,including the use of a pouch cell,the compensation of the time delay,and the use of12 thermocouples to get the average cell temperature,were proposed to circumvent the problems encountered in dealing with large-format cells.The structure of this paper is as fol-lows:‘‘Method development’’section introduces the methods employed in this study;‘‘Experimental’’section describes the experimental details;in‘‘Results and discussion’’section,firstly,we report the results of the entropy coefficient and overpotential resistance,secondly,we validate the estimated heat generation rate using the measured date by the ARC,finally,discussion concerning various methods is provided;‘‘Conclusions’’section is the conclusion.

Method development

The reversible heat

The potentiometric method

The term of the reversible heat generation rate was cal-culated by measuring the entropy coefficient d U/d T as shown in Eq.(3).The equilibrium potential of the25Ah cell at a specified initial SOC was measured at a series of temperatures,and the entropy coefficient at this SOC was attained by calculating the slope of thefitted‘temperature-potential’line.Then the SOC of the cell was adjusted with a step length of0.1each time,and the entropy coefficient at each different SOC was obtained.

The calorimetric method

The calorimetric method assumed that the irreversible heat generation rates during charge and discharge were assumed to be identical under the same current amplitude I,and then the entropy coefficient was calculated by Eq.(7)based on Eq.(2):

o U

o T

P

¼

Q chaÀQ dis

2IT

ð7Þ

here,Q cha and Q dis are the total heat generation rate during charge and discharge,respectively,which were measured with the ARC or other calorimetric methods.

The irreversible heat

The V–I characteristics method

A series of constant-current charge or discharge tests at different C-rates are needed to explore the V–I character-istics of the battery[13].Under a specified SOC and temperature,an approximate linear relationship between the terminal voltage and the applied current was found in the constant-current charge or discharge tests.As a result, the slope of the linearlyfitted line gave the overpotential resistance,R VI,of the V–I characteristics method[13].

The intermittent current method

The battery overpotential resistance is widely estimated from the intermittent charge or discharge at a definite SOC and temperature.The most frequently used intermittent current method to obtain the battery DC resistance is introduced in the HPPC test procedures[21].The overpo-tential resistance,R IC,was estimated by Eq.(8):

R IC¼V tÀV0

ðÞ=Ið8Þwhere(V t-V0)is the voltage change after charging/dis-charging at current I(positive during charge)for time t, which is termed as the interval throughout this paper.

Different values of t have been used in the literature.For example,4h was adopted by Yang et al.[18],30s was adopted by Lu et al.[17],and60s was used in[12–14].In the experimental part of this paper,a series of t(10,30,60, 90,110s)was applied and its effect on the accuracy of the estimation results was examined.

The energy method

The irreversible heat was calculated from the overpotential resistance in most of the previous studies[12–19].In addition to these methods,a new method,which was inspired by the concept proposed in the work of Lv et al.

[22],was developed in this study to calculate the irre-versible heat directly.The new method is to be referred to as energy method hereafter.

(1)Energy balance during charge when charging the

battery from SOC1to SOC2,the total consumed energy from the power supply such as a

Comparison and validation of methods for estimating heat generation rate

123comprehensive tester or a charger,E cha,consisted of three parts,the energy stored in the battery,E bat,the energy corresponding to entropy change,E rev,cha,and the energy dissipation by polarization,E irrev,cha,as expressed in Eq.(9):

E cha¼E batþE rev;chaþE irrev;cha:ð9Þ

(2)Energy balance during discharge Similarly,when

discharging the battery from SOC2back to SOC1,the energy consumption,E bat,also consisted of three parts,the electrical work performed by the battery,

E dis,the energy corresponding to entropy change,

E rev,dis,and the energy dissipation by polarization,

E irrev,dis,as shown in Eq.(10):

E bat¼E disþE rev;disþE irrev;dis:ð10Þ

Since the E bat terms in Eqs.(9)and(10)were identical, the irreversible heat could be calculated according to Eq.

(11),which was the result of adding Eqs.(9)and(10)using the following two assumptions:first,the sum of the heat due to entropy change during charge and discharge process equaled zero,that is,E rev;disþE rev;cha¼0:Second,the irreversible heat generation during charge and discharge at any temperature and SOC were identical,that is,

E irrev;dis¼E irrev;cha¼E iirev:

E irrev¼ðE chaÀE disÞ=2ð11Þ

According to the energy method,an overpotential resistance,R EM,was defined as in Eq.(12)to facilitate the comparison with other methods which estimate the irre-versible heat through the overpotential resistance:

R EM¼E chaÀE dis

2I D t

;ð12Þ

where I is the current and D t is the duration of charge or discharge.

Direct measurement of the heat generation rate

by the ARC

The ARC was used to provide an adiabatic environment for the cell placed in its chamber under the temperature feedback-and-chasing mode.When the cell underwent a charge or discharge process,its heat generation rate was calculated as in Eq.(13):

Q¼mC P d T

d t

;ð13Þ

where m is the cell mass,C p is the thermal capacity,d T/ d t is the temperature rising rate,which was measured by the attached feedback thermocouples on the surface of the cell.The positions of the feedback thermocouples were strategically chosen to reflect the average temperature of the surface.

Experimental

A25Ah cell and a pouch cell were used in this study, which had the same cathode composited of LiMn x Co y-Ni z O2and LiMn2O4,and the same graphite anode;the only differences were the size and capacity.The specifications of the two cells are shown in Table1.Each fresh cell was cycled forfive times before it was used in the heat mea-surement tests to ensure it had entered a stage of stable performance.During each cycle,the cell wasfirst charged in a constant current-constant voltage(CC–CV)pattern with1/3C as the constant current charging rate,and then discharged at the same rate.

Four tests were conducted in this study to explore all the methods introduced in‘‘Method development’’section:(1) Test1:the measurement of the entropy coefficient to estimate the reversible heat;(2)Test2:the intermittent charge/discharge tests of the25Ah cell,which were used to calculate the overpotential resistance both by the inter-mittent current method and the energy method;(3)Test3: the constant current charge/discharge tests of the pouch cell to measure the overpotential resistance by the V–I char-acteristics method and the energy method;(4)Test4:the direct measurement of heat generation rate with the ARC. The detailed experimental design and parameter settings of these four tests are presented below.

Measurement of the entropy coefficient

An environment chamber GDJW-225(Yashilin,China) and a six and half voltage monitor34972A(Agilent,USA) were used in this test.The voltage in the equilibrium state Table1The specifications of the two cells

Cell specification Value

25Ah cell Pouch cell

Capacity of1/3C at25°C25Ah288mAh Size16920cm210cm2 Number of active electrode pairs332

Cathode material LiMn x Co y Ni z O2and LiMn2O4 Anode material Graphite

Nominal voltage 3.8V

Recommended charging method CC-CV

EODV/end of discharge voltage3V

EOCV/end of charge voltage 4.2V

J.Zhang et al.

123

was recorded at four temperatures(5,15,25,35°C)as well as eleven SOCs(from1.0to0,in a step length of0.1),and a threshold value of voltage changing rate(voltage changing in a rate less than0.1mV/30min)was preset to control the timing of equilibrium potential measurement. Intermittent charge/discharge tests of the25Ah cell

Only pulse charge and discharge were conducted on the 25Ah cell since continuous charge or discharge would lead to both significant temperature rise and variation, making it difficult to define a representative temperature for the estimated irreversible heat generation rate.During the intermittent charge/discharge tests,the25Ah cell regulated to a definite SOC was charged at0.1C for 2min(except at SOC=1.0where the25Ah cell was dischargedfirst)and then discharged with the same cur-rent back to the original state after8min of rest.The above experiment was repeated at11SOCs(from1.0to0, step=0.1),four temperatures(5,15,25,35°C)andfive charging/discharging C-rates(0.1,0.3,0.5,0.7,0.9C).

Constant current charge/discharge tests of the pouch

cell

The constant current charge/discharge tests of the pouch cell at0.3,0.5,0.7,0.9,1.1,1.3,1.5C were performed at cell temperatures of5,15,25,and35°C,respec-tively.In order to verify the effectiveness of the pouch cell to suppress the temperature rise during battery cycling,one thermocouple was attached on the surface of the cell.

Direct measurement of the heat generation rate

with the ARC

The basics about how the ARC works was introduced elsewhere[23].Li et al.[6]observed significant spatial temperature variations in a25-Ah cell of the same type using thermocouples embedded at12locations inside the cell and another12thermocouples attached at the cor-responding locations on the surface.After analyzing the temperature data of these12locations inside and outside battery in[6],we selected two locations that closely represented the cell average temperature during charge/ discharge to place the feedback thermocouples on the surface of the25-Ah cell.Another12thermocouples were attached on the surface of the25Ah cell as shown in Fig.1.The cell was connected to a battery cycler made by Arbin(USA)and was charged and then dis-charged at1C.The initial temperature of the environ-ment chamber was set as30°C.The threshold temperature rising rate in the feedback-and-chasing mode of the ARC was set as0.02K min-1.

Results and discussion

The entropy coefficient(d U/d t)

The equilibrium potential of the25Ah cell was found to be almost linear with respect to the temperature,and the slope of thisfitted‘‘potential-temperature’’line gave the entropy coefficient,d U/d t.It should be noted that when the SOC was above0.8and the ambient temperature was above25°C,the self-discharge of the cell was significant.Therefore,under this circumstance,only the equilibrium potentials at lower temperatures were used in the linearfitting to diminish the influence of self-discharge.The entropy coefficient is plot-ted in Fig.2as a function of SOC.The results of the three cells showed good consistency,therefore,only the result of one cell is shown here for concise.

In Fig.2,the entropy coefficient is negative and shows a sharp increase for SOC\\0.2.When the SOC increases from 0.3to0.5,the entropy coefficient turns to be positive and reaches its peak value at SOC=0.5.After this peak,the entropy coefficient tends to decrease till SOC=0.7.The minimum value of the entropy coefficient around SOC=0

Pos Neg.

A1A5

T1T2

A9

A10

A11

A7

A3

A4A8A12

A2A6

Fig.1A schematic plot of the locations of thermocouplesis ascribed to the graphite anode(refer to Fig.4in[23]). Meanwhile,both the peak at SOC=0.5and the valley at SOC=0.7are possibly related to the cathode material of LiMn2O4(refer to Fig.1in[25]).The features shown in Fig.2are similar to those in literatures(refer to Fig.7in[24] and Fig.1in[25]).However,since the composition of electrode materials in this study is not identical with that in the literatures,no further attempt is made to compare these results quantitatively.Measurement of the overpotential resistance

The overpotential resistance of the25Ah cell by the energy method

According to Eq.(12),the overpotential resistance of the 25Ah cell by the energy method was calculated from the data of the intermittent charge/discharge tests.As shown in Fig.3a,the R EM is a nonlinear function of temperature,

SOC and C-rate.In addition,as shown in Fig.3b,the R EM follows a negative correlation with the C-rate.Similar phenomenon has also been observed by Lu and Prakash [17].There are several possible reasons.First,the charge transfer resistance is smaller at higher C-rates according to Butler–Volmer equation[26].Second,even though the ambient temperature is controlled by the thermostat,more heat is actually generated inside the cell during charge/ discharge at higher C-rates.This results in a transient higher internal temperature of the cell and leads to a decrease of the R EM.Furthermore,it indicates that the C-rate dependency of the R EM is more significant at lower temperatures and smaller SOCs,because the C-rate dependency is weakened when the SOC approaches1.0, and is negligible when the temperature is35°C.

It should be noted that the energy method is based on the assumption that the irreversible heat generation rate during charge is the same as that during discharge.Therefore,the R EM of charge and discharge are not distinguished in this section.

The overpotential resistance of the25Ah cell

by the intermittent current method

The overpotential resistance of the25Ah cell by the intermittent current method,R IC,was calculated by applying the Eq.(12)to the data of intermittent charge/ discharge tests with a specific t,which equals60s in Fig.4.Figure4shows that the R IC decreases with the increase of temperature,SOC or C-rate,which is quite similar with that of the R EM in‘‘The overpotential resis-tance of the pouch cell by the V–I characteristics method’’section.However,unlike that of R EM,the R IC during charge and discharge can be calculated,respectively.It is shown in Fig.4c that the R IC during discharge is larger than that during charge at lower SOC ranges,while the R IC during charge is larger at some higher SOCs.This phenomenon is confirmed by other methods in this study(‘‘The overpo-tential resistance of the pouch cell by the V–I characteris-tics method’’section)and the mechanism is to be explained later in‘‘The overpotential resistance of the pouch cell by the V–I characteristics method’’section.

The overpotential resistance of the pouch cell

by the V–I characteristics method

A thermocouple was attached to the surface of the pouch cell to verify the effectiveness of using the pouch cell to avoid the significant temperature rise.Due to the small capacity and large heat dissipation surface of the pouch cell,the temperature rise during charge and discharge at1C was found to be less than1°C.

A linear relationship between the terminal voltage and the constant current is detected at most SOCs except when SOC equals0.0during charge and0.1during discharge. The slope of the V–I curve gave the overpotential resis-tance of charge and discharge by the V–I characteristics method,R VI.Figure5indicates that the R VI of discharge is larger than that of charge when the SOC is smaller than0.4. When the SOC increases further,the R VI of charge exceeds

that of discharge.The underlying reasons were studied in [27]using both the current-interrupt technique in the time-domain and the dynamic electrochemical impedance spectroscopy (DEIS)in the frequency-domain.It was found that the charge transfer resistance and the diffusion resistance during charge are larger than those during dis-charge under high SOCs,while the situation is opposite at low SOCs.Furthermore,using a half-cell,the charge transfer resistances during charge and discharge of one electrode were compared using the DEIS [28].It was contended that due to the dependency of the exchange current on the surface concentration and due to the surface concentration variation during intermittent charge/dis-charge,the charge transfer resistances,which are related to the exchange current,are different between charge and discharge,and specifically,that of discharge is usually larger than that of charge [28].

The overpotential resistance of the pouch cell by the energy method

When the pouch cell is charged or discharged at constant currents,Eq.(11)could be written as:R EM ¼

V cha ÀV dis

2I

ð14Þ

where V cha and V dis are the terminal voltage of the pouch cell under charging and discharging with the current I at a specified SOC.Equation (14)was applied to process the data of the constant-current charge/discharge tests,and the calculated overpotential resistance of the pouch cell by the energy method,denoted as R EM,P or ‘‘R EM of pouch cell’’,is shown in Fig.5as a function of SOC and temperature.Figure 5shows that the R EM,P is inversely correlated with the charge/discharge C-rate,which is similar to the R EM in ‘‘The overpotential resistance of the 25Ah cell by the energy method ’’section,and generally larger than the R VI .Two considerations are presented as follows.First,the explanation concerning why the R EM is inversely correlated

with the C-rate is also feasible in the case of the R EM,P .Second,a possible explanation for the relationship between the value of the R EM,P and that of the R VI is shown in Fig.6.In the V–I characteristics method,when extending the V –I line to zero-current,the zero-current voltage is possibly larger (smaller)than the equilibrium potential U during charge (discharge).Therefore,the slope of the solid V –I line in Fig.6,which gives the R VI ,is smaller than the slope of the dotted line connecting the two points (I i ,V i )and (0,U ),which corresponds to the R EM,P .In addition,when the applied current I i is larger,the slope of the dotted line becomes smaller.Therefore,it is another approach to show that the R EM,P tends to decrease when the applied current C-rate is increased.

Measurement of the heat generation rate of the 25Ah cell with the ARC

Figure 7shows the average temperature rising rates of the 25Ah cell during charge and discharge at 1C in an adiabatic environment provided by the ARC.Since there exists a response delay of the surface temperature rise to the internal

Charge current/A

V o l t a g e /V

k 0 = R VI

k i = R EM,i

U 0

I i ,V i

Fig.6A schematic plot of the explanation why the R EM,P holds an inverse proportion to the charge/discharge C-rate and is generally larger than the R VI

As shown in Fig.7,at the very beginning of charge,the temperature rising rate is negative.It turns positive and increases sharply,leading to thefirst exothermic peak around SOC=0.1.When the SOC further increases to0.2, a shallow valley of the temperature rising rate is observed. Then a large exothermic plateau shows up in the SOC range of0.3–0.6.At SOC[0.7,the temperature rising rate increases again,and then decreases sharply after SOC=0.9due to the decreasing charge current during the CV stage in the charge pattern.The temperature rising rate for the discharge exhibits an essentially symmetric profile to that for the charge.

Based on the measured heat generation rate in the ARC, the entropy coefficient was calculated from Eq.(7)and the result was compared with that from the potentiometric method in‘‘The entropy coefficient(d U/d t)’’section.As shown in Fig.2,a good qualitative agreement is found between these two results.However,at SOC\\0.2and SOC[0.6,the difference between the d U/d T obtained by the potentiometric method and that by the calorimetric method is more significant than other SOCs.The causes are analyzed as follow.

As shown in Fig.5,the difference between the over-potential resistance during charge and discharge was also more remarkable at SOC\\0.2and SOC[0.6.This means that at these SOCs,the irreversible heat generation rates are not identical during charge and discharge. Therefore,the fundamental assumption in the calorimetric method becomes questionable and the accuracy of the calorimetric method to calculate the entropy coefficient could hardly be satisfactory.

Despite its relatively low accuracy,the calorimetric method is more time efficient to estimate the entropy coefficient.The potentiometric method took almost 1month to get the entropy coefficient point by point in this study.Relatively,the calorimetric method only cost a few hours to obtain the entropy coefficient of the total SOC range at a time.

Validation of the calculated cell temperature rising rate and the cell temperature

The rising rate of the average cell temperature of the25Ah cell in an adiabatic environment can be calculated according to Eq.(15),which is obtained after combining Eq.(2–4)and Eq.(13):

d T

d t

¼

1

mC p

I2RþITÁ

o U

o T

P

!

:ð15Þ

The major terms in Eq.(15)and their determination methods are summarized in Table2.In addition,the fol-lowing three issues need to be addressed to enable the calculation as well as a meaningful validation:

(1)The conversion of the overpotential resistance from the

pouch cell to the25Ah cell.The area specific overpo-tential resistance of the pouch cell and that of the25Ah cell are expected to be equivalent.Therefore,the overpotential resistance of the25Ah cell was converted from that of the pouch cell according to the following equation:

R25AhÁA25Ah¼R sÁA sð16Þwhere R s is the overpotential resistance of the pouch cell and R25Ah is the corresponding overpotential resistance of the25Ah cell.A s and A25Ah are the

active electrode area of the pouch cell and 25Ah cell,respectively.

(2)The interpolation of the overpotential resistance and

the entropy coefficient.The overpotential resistance and the entropy coefficient are estimated at a number of discrete temperature and SOC points.To calculate the overpotential resistance at other SOCs and temperatures during charge/discharge,a 2D look-up table was created and a linear interpo-lation was utilized in Matlab/Simulink.Similarly,the d U /d T over the full range of SOC was linearly interpolated from the available values at discrete SOCs.

(3)The compensation of the time delay.As stated above,a

time delay exists between the rise of the surface temperature and the internal heat generation.Such time delay needs to be compensated to achieve a reliable comparison between the calculated and the measured temperature rising rate of the 25Ah cell.In this study,a first-order inertial system,as introduced in [6],was assumed as follows:T surf s ðÞT cal s ðÞ¼

1

1þs s

ð17Þhere T cal is the calculated temperature using Eq.(15),and T surf is the corresponding surface temperature.The time constant s was set as 250s,which is based on our previous study of the spatial and temporal temperature variation using the same type of the 25Ah cell [6].Figure 8compares the temperature rising rates calculated from Eq.(15)with that measured in ARC of the 25Ah cell during discharge at 1C.The plot (a)shows the comparison results before the compensation for the time delay,and plot (b)shows the results after the compensation.It is found that a better agreement was achieved after the compensation,especially at the beginning of discharge.The temperature rising rates during charge are compared in Fig.9.It should be noted that the same reversible heat generation rate was used in calculating each curve in Figs.8and 9,while for the irre-versible heat generation rate,different overpotential resis-tances,as shown in Table 2,were used.

The calculated and measured cell temperature curves are displayed in Fig.10.It should be mentioned that the measured cell temperature was actually the average of 12thermocouples on the cell surface.As shown in Fig.10,the slope of tem-perature curve is relatively steep both at the beginning and the end of discharge,while it is relatively moderate across the middle stage of discharge.In contrast,relatively steep tem-perature rise occurs in the middle stage of charge at SOC around 0.6.In addition,the average cell temperature increases by 12°C after discharge at 1C,while it increases by 10°C,2°C smaller,after charge at the same C-rate.

These phenomena can be explained by the following two considerations.First,the reversible heat generation rates during charge and discharge share the identical absolute value but have opposite signs.Therefore,the total reversible heat generation was endothermic during charge and exothermic during discharge,which contributed to a higher cell temper-ature rise occurred during discharge.Second,with regard to the different temperature rise profiles during charge and dis-charge,the opposite signs of the reversible heat generation rates accounted for the major differences.In addition,the time delay also made a contribution,for instance,a peak of internal heat generation rate at a specific SOC could stimulate a delayed temperature response at a smaller SOC during dis-charge and a larger SOC during charge.

Table 2The terms in Eq.(15)and their determination methods Terms Meaning Determination method Source or corresponding section C p/

J g -1K -1The thermal capacity Calculating from the applied heat and temperature rise in ARC [29]

m/g Mass Weighing

None

o U ÀÁP =V K

À1

The entropy coefficient The potentiometric method See ‘‘The entropy coefficient (d U /d t )’’section

R /X

The overpotential resistance

25Ah cell

The energy method See ‘‘The overpotential resistance of the 25Ah cell by the energy method ’’section

The intermittent current method

See ‘‘The overpotential resistance of the 25Ah cell by the intermittent current method ’’section

Pouch cell

The V–I characteristics method

See ‘‘The overpotential resistance of the pouch cell by the V–I characteristics method ’’section

The energy method

See ‘‘The overpotential resistance of the pouch cell by the energy method ’’section

In order to quantitatively compare the four methods esti-mating the overpotential resistance,the average sum-square error(ASSE)of each method was defined as follows:

ASSE¼1

N

X N

k¼1

^V

k

ÀV k

ÀÁ2

ð18Þ

where^V k is the simulated value(cell temperature or its

rising rate),V k is the corresponding measured value,N is

the number of data points.

The ASSE values of the four methods are shown in

Table3.The intermittent current method using the25Ah cell

yielded the best agreement for the cell temperature rising rate,

followed by V–I characteristics method using the pouch cell, and then the energy methods using the25Ah cell.With respect to the cell temperature,the best agreement was obtained with the V–I characteristics method using the pouch cell,followed by the intermittent current method using the 25Ah cell.Part of the inaccuracies comes from the influence of reversible heat generation on the overpotential resistance when operating the cells.Further discussion is to be made in the following section.

Discussion of the methods to estimate the irreversible heat

The energy method

As shown in Figs.8and9,the energy method of the25Ah cell underestimated the irreversible heat generation rate for both charge and discharge,while the energy method of the pouch cell gave a better agreement.The differences exist in the fact that R EM of the25Ah cell comes from the120s intermittent charge/discharge test,while the R EM of the pouch cell results from the continuous charge/discharge test.These two tests differ in the test duration,which affects the corresponding R EM.To elucidate the effect of test duration on the energy method and to analyze the under-estimation of R EM of the25Ah cell,we take the intermittent charge/discharge test for further analysis. Equation(19)could be deduced from Eq.(12):

R EM¼

P t d

t¼0

V chaÀV discha

ðÞ

2IN V

ð19Þ

where t d is the test duration and is120s in the intermittent charge/discharge test,N V is the number of the voltage sampling points during the2min pulse intermittent charge/ discharge,which equals120in our tests.Equation(19) indicates clearly that the R EM depends on the test duration, furthermore,it would be greater when the test duration is longer.Since V chaÀV discha is a convex function with respect to time,Eq.(20)holds:

R EM\

V chaÀV discha

ðÞj t¼N

V

=2

2I

¼

1

2

R IC;chaþR IC;dis

ÀÁ

:ð20Þ

This equation shows that the overpotential resistance calculated by the energy method is smaller than the aver-aged overpotential resistance of charge and discharge cal-culated with the intermittent current method in this study.This explains why the energy method yields under-esti-mation.However,it is noted that Eq.(20)does not always hold when t \\N v /2.

In addition,the overpotential resistance results imply that the irreversible heat generation rates are not identical during charge and discharge.In this case,the most important assumption in the energy method becomes questionable and the accuracy of the energy method to calculate the heat generation could hardly be satisfactory.Despite all this,the energy method is still a valuable method in that it does not require extra tests,instead,it can be directly applied to the test data of the V–I characteristic method and the intermittent current method.The intermittent current method

A good agreement was obtained when the intermittent current method with an interval of 60s was used to esti-mate the irreversible heat generation rate.However,the accuracy of the intermittent current method depends strongly on the interval.Figure 11plots the calculated cell temperature rising rate at various intervals and the corre-sponding ASSEs.It is clear that the ASSE decreases sharply when the interval increases from 10to 60s.Afterwards,the ASSE exhibits a relatively flat trend and its minimum value is achieved at the interval of 90s.

The irreversible heat is composed of the heat generated by the activation (interfacial kinetics),the concentration (diffusion process),and the ohmic losses.The ohmic loss is essentially instantaneous,and the characteristic frequency associated with the interfacial reaction is normally much higher than 1Hz in ambient temperature.The character-istic time of the diffusion process is expressed as:

t d %L 2 D ð21Þwhere L is the characteristic length of the diffusion process and D is the diffusion coefficient.From Eq.(21),it is clear that t d differs for different battery systems and is affected by temperature due to the strong temperature dependency of the diffusion coefficient.Order of magnitude analysis shows that the t d is about 102–103s in this study.

As the interval used in this study is much larger than 1s,but smaller than the t d ,we believe that the estimated rate of irreversible heat generation is attributed to the ohmic loss,the charge transfer loss,and part of the diffusion loss.A different interval determines a different percentage of the total diffusion loss included in the calculation,which could result in a different overpotential resistance and affect the

T a b l e 3C o m p a r i s o n o f t h r e e m e t h o d s t o e s t i m a t e t h e i r r e v e r s i b l e h e a t g e n e r a t i o n r a t e f o r l a r g e -f o r m a t l i t h i u m -i o n b a t t e r i e s

I t e m

C a p a b l e o f d i s t i n g u i s h i n g c h a r g e a n d d i s c h a r g e

D e p e n d e n t o n c u r r e n t

A S S E o f t e m p e r a t u r e r i s i n g r a t e p r e d i c t i o n

A S S E o f c e l l t e m p e r a t u r e p r e d i c t i o n

R e m a r k

D i s .

C h a .

D i s .

C h a .

V –I c h a r a c t e r i s t i c m e t h o d

Y e s

N o 0.0027

0.0026

0.1035

0.8085

T h e V –I c h a r a c t e r i s t i c m e t h o d s h o u l d b e a p p l i e d i n c o n j u n c t i o n w i t h a p o u c h c e l l t o a v o i d s i g n i fic a n t t e m p e r a t u r e r i s e .F a b r i c a t i n g a p o u c h c e l l w i t h t h e s i m i l a r c o m p o s i t i o n m a y n o t b e c o n v e n i e n t i n p r a c t i c e .

E n e r g y m e t h o d

P o u c h c e l l

N o

Y e s

0.0018

0.0053

1.116

5.0708

T h e e n e r g y m e t h o d d o e s n o t r e q u i r e s e p a r a t e s e t o f t e s t s t o b e c o n d u c t e d .I t i s v e r s a t i l e i n t h a t i t c a n b e u s e d t o p r o c e s s t h e d a t a o f t h e V –I c h a r a c t e r i s t i c m e t h o d a n d i n t e r m i t t e n t c u r r e n t m e t h o d ,a s w e l l a s t h e r e s u l t s o f o t h e r t e s t s .H o w e v e r ,i t c a n n o t d i s t i n g u i s h d i f f e r e n c e s b e t w e e n c h a r g e a n d d i s c h a r g e a n d i s t h e l e a s t a c c u r a t e o n e i n t h e t h r e e m e t h o d s .

25A h c e l l

0.00700.00274.37512.4657I n t e r m i t t e n t c u r r e n t m e t h o d

Y e s

Y e s 0.00110.0021

0.58

0.0284

T h e i n t e r m i t t e n t c u r r e n t m e t h o d i s v e r y c o n v e n i e n t t o u s e a n d g i v e s g o o d a c c u r a c y i f t h e c h a r a c t e r i s t i c t i m e i s r e a s o n a b l e s e l e c t e d .

The V–I characteristic method

The V–I characteristic method was applied to a pouch cell instead of the25Ah large-format cell to avoid the signif-icant temperature rise during continuous charge/discharge of large cells.From Table3,it is found that the V–I characteristic method using the pouch cells is an effective method to estimate the irreversible heat generated by the large-format cells.However,due to the necessity of fab-ricating pouch cells,this method is not as convenient as other methods in practice.

With respect to the V–I characteristic method,an over-estimation of heat generation rates at low SOC range between0and0.2was detected,especially during discharge, as shown in Figs.8and9.The underlying reason can be ascribed to the nonlinear current dependency of terminal voltage at low SOC ranges.To be specific,the nonlinear current dependency of terminal voltage at SOC=0.1during discharge magnified the overpotential resistance,and then the estimated heat generation rate was enlarged.

The features of these three methods,i.e.,the V–I charac-teristic method(using the pouch cell),the energy method (using both the pouch cell and25Ah cell),the intermittent current method(using the25Ah cell)are summarized in Table3.

Conclusions

The heat generation rate of a large-format25-Ah lithium-ion battery was studied based on the simplified Bernardi heat generation model.The heat generation rate was divi-ded into the reversible and irreversible heat terms,with each term being estimated with different methods and subsequently validated against measured temperature rise.

The methods developed for small lithium-ion batteries were extended to the large-format25Ah lithium-ion bat-tery with the following techniques employed:

(1)A pouch cell,using the same electrodes as the25Ah

cell but with a simple structure as well as a much smaller capacity,was employed in the V–I character-istics method to avoid the significant temperature rise of large cells during charge and discharge.The overpotential resistance of the pouch cell was converted to that of the25Ah cell based on the concept of equivalent area-specific resistances. (2)Twelve thermocouples were used for calculating the

average cell temperature to accommodate the tem-perature variations across the cell.

(3)Thefirst-order inertial system was assumed to correct

the delay in the response of the surface temperature to the internal heat generation,and the time constant of the system was set as250s in this study.

Then,the accuracy of different methods was compared and the main features of these methods were elucidated and summarized as follows:

(1)In calculating the reversible heat,the entropy coef-

ficient measured with the potentiometric method was believed to be more accurate,while the calorimetric method was more efficient.The less accuracy of the latter method partly comes from its assumption that the irreversible heat generation rates of charge and discharge are identical.

(2)The irreversible heat was estimated by calculating the

overpotential resistance of the cell.Among the three methods to measure the overpotential resistance,the intermittent current method is both easy-to-imple-ment and accurate if the interval is appropriately

chosen.For the25Ah cell in this study,it is found that the error of the intermittent current method remained small when the interval was in the range of 60to120s.With the help of a pouch cell,the V–I characteristic method was proven to achieve compa-rable accuracy.However,the necessity of fabricating

a pouch cell incurs some inconvenience for this

method.The newly developed energy method does not require extra tests,instead,it can be directly applied to the test data of the V–I characteristic method and the intermittent current method.How-ever,it cannot distinguish between charge and discharge and it is the least accurate among these three methods.

Acknowledgements This study was supported by the National Natural Science Foundation of China under the grant number of 51207080,the Independent Research Programs of Tsinghua Univer-sity under the subject number of2011Z01004,and the China Post-doctoral Science Foundation under the Grant number of 2012M510436.

References

1.Yang K,An JJ,Chen S.Temperature characterization analysis of

LiFePO4/C power battery during charging and discharging.

J Therm Anal Calorim.2010;99:515–21.

2.Jhu CY,Wang YW,Wen CY,Chiang CC,Shu CM.Self-reactive

rating of thermal runaway hazards on18650lithium-ion batteries.

J Therm Anal Calorim.2011;106:159–63.

3.Jhu CY,Wang YW,Wen CY,Chiang CC,Shu CM.Thermal

runaway features of18650lithium-ion batteries for LiFePO4 cathode material by DSC and VSP2.J Therm Anal Calorim.

2011;106:159–63.

4.Lu TY,Chiang CC,Wu SH,Chen KC,Lin SJ,Wen CY,Shu

CM.Thermal hazard evaluations of18650lithium-ion batteries by an adiabatic calorimeter.J Therm Anal Calorim.2013.doi:10.

1007/s10973-013-3137-9.

5.Yang K,Li DH,Chen S,Wu F.Thermal behavior of nickel/metal

hydride battery during charging and discharging.J Therm Anal Calorim.2009;95:455–9.

6.Li Z,Zhang J,Wu B,Huang J,et al.Examining temporal and

spatial variations of internal temperature in large-format lami-nated battery with embedded thermocouples.J Power Sources.

2013;241:536–53.

7.Yang K,An JJ,Chen S.Influence of additives on the thermal

behavior of nickel/metal hydride battery.J Therm Anal Calorim.

2010;102:953–9.

8.Hallaj SA,Maleki H,Hong JS,Selman JR.Thermal modeling

and design considerations of lithium-ion batteries.J Power Sources.1999;83:1–8.

9.Billy W,Vladimir Y,Monica M,Gregory JO,Ricardo FM,Nigel

PB.Coupled thermal-electrochemical modelling of uneven heat generation in lithium-ion battery packs.J Power Sources.

2013;243:544–54.

10.Gu WB,Wang CY.Thermal-electrochemical modeling of battery

systems.J Electrochem Soc.2000;147:2910–22.

11.Bernardi D,Pawlikowski E,Newman J.A general energy balance

for battery systems.J Electrochem Soc.1985;132(1):5–12.12.Onda K,Kameyama H,Hanamoto T,Ito K.Experimental study

on heat generation behavior of small lithium-ion secondary bat-teries.J Electrochem Soc.2003;150:A285–91.

13.Onda K,Ohshima T,Nakayama M,Fukuda K,Araki T.Thermal

behavior of small lithium-ion secondary battery during rapid charge and discharge cycles.J Power Sources.2006;158:535–42.

14.Ohshima T,Nakayama M,Fukuda K,Araki T,Onda K.Thermal

behavior of small lithium-ion battery during rapid charge and discharge cycles.Electr Eng Jpn.2006;157:1521–8.

15.Hallaj SA,Venkatachalapathy R,Prakash J,Selman JR.Entropy

changes due to structural transformation in the graphite anode and phase change of the LiCoO2cathode.J Electrochem Soc.

2000;147:2432–6.

16.Hallaj SA,Prakash J,Selman JR.Characterization of commercial

Li-ion batteries using electrochemical-calorimetric measure-ments.J Power Sources.2000;87:186–94.

17.Lu W,Prakash J.In situ measurements of heat generation in a Li/

mesocarbon microbead half-cell.J Electrochem Soc.

2003;150:A262–6.

18.Yang H,Prakash J.Determination of the reversible and irre-

versible heats of a LiNi0.8Co0.15Al0.05O2/natural graphite cell using electrochemical-calorimetric technique.J Electrochem Soc.

2004;151:A1222–9.

19.Bang H,Yang H,Sun YK,Parakash J.In situ studies of Li x Mn2O4

and Li x Al0.17Mn1.83O3.97S0.03cathode by IMC.J Electrochem Soc.

2005;151:A421–8.

20.Thomas KE,Bogatu C,Newman J.Measurements of the entropy of

the reaction as a function of sate of charge in doped and undoped lithium manganese oxide.J Electrochem Soc.2001;148:A570–5.

21.FreedomCAR Battery Test Manual for Power-Assist Hybrid

Electric Vehicles,DOE/ID-11069,Idaho National Engineering and Environmental Laboratory,Draft,April2003

22.Lv Z,Guo X,Qiu X.New Li-ion battery evaluation research

based on thermal property and heat generation behavior of bat-tery.Chin J Chem Phys.2012;25:725–32.

23.Ishikawa H,Mendoza O,Sone Y,Umeda M.Study of thermal

deterioration of lithium-ion secondary cell using an accelerated rate calorimeter(ARC)and AC impedance method.J Power Sources.2012;198:236–42.

24.Williford RE,Viswanathan VV,Zhang J.Effects of entropy

changes in anodes and cathodes on the thermal behavior of lithium-ion batteries.J Power Sources.2009;1:101–7.

25.Viswanathan VV,Choi D,Wang D,Xu W,Towne S,Williford

RE,Zhang J,Liu J,Yang Z.Effect of entropy change of lithium intercalation in cathodes and anodes on Li-ion battery thermal management.J Power Sources.2010;195:3720–9.

26.Moss PL,Au G,Plichta EJ,Zheng JP.An electrical circuit for

modeling the dynamic response of Li-ion polymer batteries.

J Electrochem Soc.2008;155:A986–94.

27.Zhang J,Huang J,Li Z,Song S,Song W,Wu N.The study of

resistance variation between charging and discharging process by current-interrupt technique and dynamic electrochemical imped-ance spectroscopy(DEIS).2013IEEE vehicle power and pro-pulsion conference(VPPC),Beijing,China,15–18Oct2013. 28.Huang J,Li Z,Zhang J,Song S,Wu N.Exploring differences

between charging and discharging of Li x Mn2O4/Li half-cell with dynamic electrochemical impedance spectroscopy(DEIS).The 9th international symposium on electrochemical impedance spectroscopy,Okinawa,Japan,17–21June2013.

29.Zhang J,Wu B,Zhe L,Huang J.Simultaneous estimation of

multiple thermal parameters of large-format laminated lithium-ion batteries.2013IEEE vehicle power and propulsion confer-ence(VPPC),Beijing,China,15–18Oct2013.