heat generation in high power prismatic li-ion battery cell with limnnicoo 2 ...

Heat generation in high power prismatic Li-ion batterycell with LiMnNiCoO2 cathode materialYasir Abdul-Quadir1,*,†, Tomi Laurila1, Juha Karppinen1, Kirsi Jalkanen2, Kai Vuorilehto2,Lasse Skogström1 and Mervi Paulasto-Kröckel1

1Department of Electronics, Aalto University, School of Electrical Engineering, Otakaari 7, 02150 Espoo, Finland2Department of Chemistry, Aalto University, School of Chemical Technology, Kemistintie 1, PO Box 6100, FI-00076 Espoo, Finland

SUMMARY

While in use, battery modules and battery packs generate large amounts of heat, which needs to be accounted for. The mainchallenge in battery thermal management is the correct estimation of heat generation in the battery cell during charging/discharging. In this paper, a method to calculate accurate heat generation in one individual cell is provided. The heatgeneration is calculated by measuring the overpotential resistances with four different methods and entropic heat generationin the cell. The effect and contribution of entropic heat generation towards the total heat generation in the cell are alsocalculated and measured. Finally, calorimeter tests are carried out to compare the calculated and measured heat generation.The results indicate that except for direct current resistance measured by impedance spectroscopy, all the overpotentialresistances are very close to each other. Copyright © 2014 John Wiley & Sons, Ltd.

KEY WORDS

Li-ion battery; heat generation; overpotential resistance; entropy change; calorimeter

Correspondence

*Yasir Abdul-Quadir, Aalto University, School of Electrical Engineering, Department of Electronics, Otakaari 7, 02150 Espoo, Finland.†E-mail: [email protected]

Received 8 May 2012; Revised 16 December 2013; Accepted 18 December 2013

1. INTRODUCTION

The lithium-ion battery (Li-ion battery) is the preferredpower source for hybrid electric vehicles (HEVs) andelectric vehicles (EVs) because of its high specific energy,high voltage and low self-discharge rate. To provideaffordable HEVs and EVs with satisfactory performance,there are still major technical challenges to improve thecharacteristics of Li-ion batteries such as low cost, highpower density, long service life and proven safety. Becausesafety is one of the major challenges for the Li-ion batteryin HEV and EV applications, the thermal management ofLi-ion batteries is especially important. The main concernin the thermal management of Li-ion battery is thesignificant temperature increase that can occur especiallyduring high power extraction in HEV and EV applications,which may cause battery degradation and thermal runaway.Thermal modelling can play a key role in controlling theoperating temperature and temperature uniformity of Li-ionbatteries within a suitable range [1–3].

There have been many previous studies on thermalmodelling of Li-ion batteries [4–17]. Bernardi et al. [4]developed a general energy balance for battery systemsincluding the contributions from electrochemical reactions,

mixing enthalpies and phase changes. Rao and Newman[5] presented a method of calculating the heat generationrate based on the general energy balance and the enthalpypotential method for a Li-ion battery system. Chen andEvans [6–8] developed two-dimensional and three-dimensional models to study the thermal behaviour oflithium polymer batteries (Li-polymer batteries) and Li-ion batteries. They assumed that the heat generation rateis uniform throughout the cell. Pals and Newman presenteda one-dimensional model for predicting the thermalbehaviour of Li-polymer batteries for a single cell [9] anda cell stack [10]. Baker and Verbugge [11] modelled thethree-dimensional current and temperature distributions inLi-polymer battery modules. Botte et al. [12] studied theinfluence of design variables on the thermal behaviour ofLi-ion batteries based on one-dimensional model. Songand Evans [13] developed an electrochemical–thermal modelof Li-polymer batteries by coupling a two-dimensionalthermal model with one-dimensional electrochemicalmodel. Gu and Wang [14] and Srinivasan and Wang [15]developed a two-dimensional thermal and electrochemicalcoupled model to analyse the electrochemical and thermalbehaviour of Li-ion battery cells. Chen et al. [16]developed a three-dimensional model of Li-ion batteries

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. (2014)

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.3156

Copyright © 2014 John Wiley & Sons, Ltd.

considering the location-dependent convection and radia-tion at the boundaries to reflect the different heatdissipation performances on all of the surfaces. Ondaet al. [17,18] proposed a simplified formula for total heatgeneration in a battery cell, which included overpotentialand entropic heat. They went on to measure differentresistances related with overpotential heat. Karimi andLi [19] implemented various cooling strategies to examinethe relationship between battery thermal behaviour andthermal management design system. They reasoned thatthe equivalent internal resistance for the flat type batteriesused in the EV is proprietary and not available in the openliterature. They used the internal resistance, which hasbeen measured for the commercially available small sizeLi-ion batteries, which is structurally very similar to thoseof flat batteries.

Bandhauer et al. [20] critically reviewed the availableliterature on major thermal issues for Li-ion batteries. Theyconcluded that majority of the experimental work thatmeasure heat produced by the Li-ion battery has beencarried out on coin cells and at low to moderate charge/discharge rates (<1C). They also commented that entropicheat is nearly the same order of magnitude as theirreversible heat for the 1C discharge rate, thus having anon-negligible impact on the heat generation and perfor-mance of a cell.

Hence, it is a fact that most of the heat generation exper-imental work on Li-ion battery has been performed oncoin cells or cells with lower capacity. This work willconcentrate on the heat generation in a high powerprismatic cell, look at the significance of entropic heatgeneration for large capacity cells and the assumption thatheat generation in a cell is uniform. Calorimeter tests arecarried out to obtain necessary parameters for the heatgeneration calculations and to validate the obtained results.

2. THEORY AND EXPERIMENTS

The most common equation describing heat generation in abattery cell during an electrochemical process (charge ordischarge) is given by [4,19]:

q ¼ I Vo � Vð Þ � ITdVo

dT(1)

where q is the heat generation in the battery cell, VO is theopen circuit voltage, V is the cell voltage, I is the appliedcurrent and T is the temperature of the cell.

The first term in Eqn (1) is the overpotential due toohmic losses in the cell, charge transfer overpotentials atthe interface and mass transfer limitations. The secondterm is the entropic heat, and the potential derivative withrespect to temperature is often referred to as the entropicheat coefficient [19].

When a current flows in a battery, the cell voltage Vdeviates from the open circuit voltage VO because ofelectrochemical polarization. The resulting energy loss is

converted into heat. This heat generation can be expressedas overpotential heat QP:

QP ¼ I Vo � Vð Þ ¼ I2Rη (2)

QP represents heat generation during both charging anddischarging. Expressing the difference between V and VO

by IRη, QP can be related to the overpotential resistance Rη.The entropic heat generation QS caused by the entropy

change ΔS is expressed as follows:

Qs ¼ TΔSI

nF

� �¼ ∂ΔG

∂Tcell¼ nFT

∂Eemf

∂T

� �(3)

where n is the number of moles of electrons exchanged in thereaction, F is the Faraday’s constant (9.648456 ∙ 104C/mol)and Eemf is the cell potential.

In this paper, a Li-ion battery cell is also discharged inan adiabatic calorimeter to validate the overpotential andentropic heat measurements. The following equation hasbeen used to compare the test results:

Ccell þ Cliquid þ Calorimeter Constant� � dTcell

dt¼ q (4)

where q is the same as calculated in Eqn (1). The specificheat capacity of the cell is measured separately as well asthe calorimeter constant. C is heat capacity of the materialin J/K and can be calculated by multiplying specific heat ofthe material with its mass.

In order to obtain the total heat generation in the batterycell, the overpotential resistance and entropic heatgeneration within the cell have to be measured. Once theseparameters are obtained, Eqn (1) can be used to calculatethe total heat generation. This is then validated by chargingor discharging the cell inside a calorimeter and usingEqn (4) to compare the measured heat generation with theone calculated with Eqn (1). Some extra parameters usedin Eqn (4) are also measured here, namely, the specific heatof the battery cell and the calorimeter constant.

The cell tested here is a high capacity commerciallyavailable (Kokam SLPB100216216H [21]) Li-ion cell withrated capacity of 40Ah as shown Figure 2. The specifica-tions of the cell are listed in Table I.

States of charge (SOCs) were set at 100% and 0%,respectively, at the end of the rated charge and dischargecycles. The rated current is defined as the current todischarge the rated capacity of 40Ah in 1 h.

The following heat generation components weremeasured:

2.1. Characterization of battery cell

Charge–discharge and capacity tests were performed onthe cell to make sure that the battery is in good workingcondition. The charging profile was as follows:

• At constant current until the voltage reaches 4.2V.• At constant voltage until the current reaches 2A.

Heat generation in high power prismatic Li-ion battery cellY. Abdul-Quadir et al.

Int. J. Energy Res. (2014) © 2014 John Wiley & Sons, Ltd.DOI: 10.1002/er

The discharge was carried out at constant current untilthe cell reached a voltage of 2.7V.

Figure 1a shows the discharge curve at different rates.Figure 1b shows the charge and discharge curve at 0.5Cwith respect to the rated capacity of the cell.

2.2. Uniformity of heat generation in abattery cell

Equation (1) is based on the assumption that there is auniform heat generation in a Li-ion battery cell. To validate

this assumption, temperature during discharge at differ-ent C-rates were measured on seven different points onthe surface of the cell. This is illustrated in Figure 2.The cell was placed on few plastic threads on one sideso as to mimic the ‘hanging in air condition’. This wasdone to ensure that all the sides were exposed to naturalconvection. Figure 3 shows the result of the temperaturemeasured on battery during 1C, 2C and 4C discharge.The figure clearly shows that temperature on the surfaceof the cell is relatively uniform, with the hottest pointbeing in the middle of the cell, which is position 7 inFigure 2. While the temperature difference increasesbetween the highest and the lowest point of the curveswith increasing C-rate, it is not significant, and for allpractical purposes, the battery could be assumed to beat a uniform temperature. Thus, even with relativelylarge temperature change, the surface temperatureremains essentially evenly distributed. The result implies

Figure 2. Location of thermocouples for heat generationuniformity test.

Table I. Specifications of the Li-ion battery cell used.

Size 220×215×10.7mmAnode material GraphiteCathode material Lithium cobalt manganese

nickel oxide (LiMnNiCoO2)Electrolyte Solution of lithium

hexafluorophosphate (LiPF6)Nominal voltage 3.7 VCut-off voltage 2.7 VOperating temperature Charge: 0 °C to +40 °C

Discharge: �20 °C to +60 °CCapacity 40AhMaximum charge current 80A (2C)Maximum discharge current 400A (10C)

Figure 1. (a) Discharge curves at different C-rates and (b) capacityof the cell at 1C charge and discharge.

Figure 3. Temperature change on cell surface for 1C, 2C and4C discharge.

Heat generation in high power prismatic Li-ion battery cell Y. Abdul-Quadir et al.


that for thermal simulation, a uniform heat source couldbe applied to the battery model.

The core temperature of the battery cell is very diffi-cult to measure, especially for a commercial batterycell. Lee et al. [22] manufactured a voltage andtemperature sensor by microelectromechanical systemsprocess to monitor the temperature of the core. Theyalso monitored the temperature of the battery cellsurface using a thermocouple. They showed that whilethe core temperature of the battery is higher than thesurface temperature, they both follow the same patternduring charge or discharge. Similar result was shownby Lin et al. [23]. Taheri and Bahrami [24] alsoobtained similar temperature curves for a prismatic cellfor 10A (0.5C), 20A (1C), 40 A (2C), 60A (3C) and100A (5C) discharge.

Overpotential resistance of the cell was measured withfour different techniques as follows.

2.3. Resistance by V� I characteristics

Charging (from 0.5C to 2C) and discharging (0.3C to 2C)tests were carried out at room temperature for variousC-rates. The obtained data (cell voltage and charge–discharge current) from constant current charge–dischargetests were plotted as V� I characteristic as function ofSOC. The V� I characteristics for charging and dischargingat ambient temperature are shown in Figure 4. The V� Icharacteristics are generally linear. The overpotentialresistance is calculated from the slope of the V� I curve.The slope of the curves is determined by the least squaresapproximation assuming that the V� I characteristic is, onthe whole, a straight line. The R2 values for the fit were onaverage 0.98.

2.4. Resistance by open circuit voltage (VO)and cell voltage (V)

Cell voltage (V) during charge–discharge cycle is differ-ent to open circuit voltage (VO). Overpotential resis-tance can be measured by dividing the differencebetween V and VO by the charging or dischargingcurrent. In our study, the cell was charged ordischarged to the desired SOC level with 1C current.Once the desired SOC level was achieved, the cellwas left to stabilize. The stabilization time was chosenon the basis of the moment when the battery reachesa constant open circuit voltage and has started to self-discharge. This period is necessary for active materialdiffusion to enable the open circuit potential to bereached (or at least approached). The cell voltage afterthe chosen stabilization period was taken as open circuitvoltage (VO). The experiments showed that this stabili-zation time increases as SOC decreases, with the celltaking as long as 21 h to stabilize at 20% SOC, whereasit took only 4 h to stabilize at 80% SOC.

2.5. Resistance by intermittent discharge

The overpotential cell resistance can also be measured by in-termittent discharge. In this method, the cell is discharged(with a known C-rate) to a known SOC and then kept at thatSOC for 10min. This cycle is repeated until the cell voltagelimit is reached (2.7V, 0% SOC). The drop in voltage in60 s, after the commencement of discharge, is then dividedby the current to calculate the overpotential resistance corre-sponding to the particular SOC.

2.6. Resistance obtained by alternatingcurrent impedance method

Alternating current (AC) impedance measurements of thecell at several SOC values were carried out by an electro-chemical impedance analyzer (Autolab potentiostat(PGSTAT302N), Frequency Response Analyzer (version4.9)). The cell was charged to 100% SOC (4.15V) atwhich the first electrical impedance spectroscopy (EIS)measurements were carried out. It was then incrementallydischarged by 10% SOC until the voltage reached 2.7V(0% SOC). Discharge current was 20A, and AC imped-ance was measured at each of 10% SOC increments.Impedance measurements were done in the frequencyrange of 0.15–4000Hz using galvanostatic mode and 0.5perturbation amplitude.

Figure 4. Voltage–current characteristics during chargingand discharging.



2.7. Measurement of entropy change

The following method was used to measure the entropychange of the cell for 1C discharge.

a. Cell kept at open circuit voltage for about 21–23 h atroom temperature.

b. Temperature was changed by 10 ºC after every 2.5 h.c. VOwas measured at temperatures 25, 35, 45 and 55 ºC.d. The steps were repeated for different SOCs. The cell

was discharged to a desired SOC level at 1C.

Figure 5a shows the test procedure as explained in theaforementioned steps for the cell at 100% SOC.

It can be seen from Figure 5a that once the cell isfully charged, there is a steep decrease in the voltage(for about 2 h), which is later followed by self-dischargeof the cell. After the cell has been stabilized for about20 h, temperature is changed from 25 to 35 °C. Thisresults in a sharp decline in the voltage, which laterstabilizes (as the self-discharge takes over). This sharp

decline is only observed for about 30min, and theopen circuit voltage stabilizes with the temperature.The graph also shows that the decline of open circuitvoltage (both due to change of temperature and self-discharge) is higher at higher temperature. Bandhaueret al. [19] mentioned that self-discharge can be animportant factor while determining an accurate valueof open circuit voltage at higher SOC and that manyresearchers have had problems maintaining stablevoltages. Same phenomenon is observed in this study.While it was difficult to maintain a stable open circuitvoltage at 100% SOC, shown in Figure 5a, it wasmuch easier at 60% SOC, which is shown in Figure 5b(the stabilization time has been omitted from the graphto show the effect of temperature on open circuitvoltage).

The self-discharge was accounted for in the calcula-tions. The self-discharge of the battery at respectivetemperatures was measured for 5 d. From these data, therate of self-discharge was calculated and accordingly usedin calculating dVO/dT.

Figure 5. (a) dVo/dT measurement steps at 100% state of charge, including the stabilization time and (b) dVo/dT at 60% stateof charge.



2.8. Measurement of specific heat capacityof the battery

To calculate the heat generation of the cell using Eqn (4),specific heat of the cell is required. To obtain thisinformation, the following experiments were carried out.The first step in this procedure was to heat up a knownmaterial (in our case, an aluminium plate, which has sameconfiguration as the cell) to a certain temperature (50 °C inour case) and then cool it down at ambient temperature.We measure the temperature decrease of this block in freeconvection condition to ambient temperature. Blocktemperature T with a known capacity can be given by thefollowing heat balance equation:

dT

dt¼ �Ah

CT � T roomð Þ ¼ � Ah

ρcpvT � T roomð Þ (5)

where C is the heat capacity of the block (calculated fromits density ρ, specific heat capacity cp and volume v) and Aand T are the surface area and the temperature,respectively. The specific heat used here for the Al blockis 900 J/kgK.

Similarly, we measure the temperature decrease of thecell.

2.9. Calorimeter test to measure the totalheat generation in the battery cell

To measure the total heat generation of the battery cellduring discharge, an adiabatic calorimeter was built usingStyrofoam material. The test section was constructedusing insulation foam material [25]. Table II provides theproperties of insulation foam used. Figure 6 shows aschematic of the calorimeter and the actual calorimeterused in this work. The corners and the terminals of the cellare carefully sealed to avoid any penetration of the waterthrough the cell. The water level in the calorimeter is upto the current collectors and not touching the cablesattached to them. The stirrer on the top of the calorimeterlid is motorized and any openings mainly due to the battery

cell cables and thermocouples are carefully sealed to avoidany heat transfer to the ambient. Seven thermocoupleswere attached inside the test area of the calorimeter. Sixthermocouples measured the water temperature, and onethermocouple (TC7) was attached to the centre of thebattery cell. As shown in previous section, the hottestpart in the cell is right in the middle, where the thermocoupleis attached.

The stirrer mechanism used in the current calorimeter,as shown in Figure 6, uses an electric motor. The voltageapplied to the motor can be controlled to obtain anoptimum speed for the stirrers. The speed of the stirrerswas optimized to make sure that the stirring mechanismin itself did not heat up the liquid.

Before determining the actual heat generation of thecell, we had to calculate the heat capacity of the calorime-ter (including the cell holder, cables and thermocouples).This was achieved by cooling a known metal block (insidethe calorimeter) after heating it up to a certain temperature.The following heat balance equation was used to calculatethe heat capacity of the calorimeter (calorimeter constant):

mmetalcpsdT ¼ mliquidcpl þ calorimeter constant� �

dT (6)

where mmetal is the mass of the metal block, cps is thespecific heat capacity of the metal block (aluminium) anddT in the left hand of Eqn (6) is the temperature drop inthe metal block. Similarly, mliquid is the mass of the waterused in the calorimeter (which can be calculated fromdensity and volume), and dT on the right-hand side ofEqn (6) is the increase in water temperature. On the basisof Eqn (6), the calorimeter constant was calculated to beapproximately 1000 J/K (calculation for this process isshown in Appendix A).

3. RESULTS

3.1. Overpotential resistance measurement

Figure 7 shows the overpotential resistances fordischarging obtained by the R(V� I), R(VO�V) and R(60s) methods. The graph shows a steady increase in resis-tance after about 50% SOC and steep increase after 10%SOC. All the resistances are in very good agreement witheach other.

Results obtained by Onda et al. [18] show that for ahigher capacity cell, resistance by intermittent dischargewas around half of R(V� I) and R(VO�V). This could bedue to only 60 s of waiting time before each discharge intheir work, while in our case, the waiting time is 10min.

3.2. Electrical impedance spectroscopyresults

Figure 8 shows the Nyquist plot for the cell impedance atdifferent SOCs. As described elsewhere [26], the Nyquistplot of a Li-ion cell is mainly comprised of an inductive tail

Table II. Properties of insulation foam.

Properties

Cell structure Over 90% sealed cellsThermal conductivity 0.023W/mKDensity 32–38 kg/m3

Water absorption ≤1.5 vol. �%Water vapour permeability 0.1–1.2 10�12 kg/msPaCompression strength ≥100 kPaTensile strength ≥230 kPaCoefficient ofthermal expansion

5–8 · 10�5/ ºC

Heat resistance �40 to +100 ºC, momentary+250 ºC

Normal products Over +400 °C, flame approx.+300 ºCFlashpoint



(which has been neglected here) at high frequencyfollowed by two semicircles at the medium and low

frequencies. Our data only showed one semi-circle. Similarresults were also obtained by Onda et al. [18].

Figure 6. Schematic of the calorimeter used in this work.

Figure 7. Overpotential resistance measured using voltage–current characteristic curve.



Rodrigues et al. [26] evaluated the impedance parametersof a Li-ion cell at different SOCs using an equivalent circuitshown in Figure 9a. L is the inductance taken in parallel to aresistance RL corresponding to the high frequency inductivetail in impedance spectra; RΩ represents the ohmic resistanceof the battery;Q1 and Q2 are constant phase elements, whichare taken in parallel to the respective resistances, R1 and R2,corresponding to the medium and low frequency semicircles,respectively. In this work, as can be observed from Figure 8,R1 is not present, and L and RL have been shown to be justfitting parameters. Thus, the circuit in Figure 9a can be

simplified to the Randles circuit shown in Figure 9b. In thiscircuit, RΩ represents the ohmic resistance of the battery,Rct is charge transfer resistance, W is Warburg element andCdl is double layer capacitance. By adding the ohmicresistance and the charge transfer resistance, one should beable to obtain the DC resistance of the cell. Table III showsthe value of the fitting parameters for the circuit shown inFigure 9b. The DC resistance in Table III is obtained byadding RΩ and Rct.

Figure 7 shows the overpotential resistance measuredby the four different methods. The graph clearly shows that

Figure 8. Nyquist plot at different states of charge.

Figure 9. (a) Circuit used by other researchers [22,23] and (b) Randles circuit.

Table III. Impedance parameters obtained in this work.

SOC (%) R(Ω)/mΩ C(dl)/F R(ct)/mΩ W/104 DC resistance/mΩ

0 0.6 34.13 0.6 0.12 1.210 0.5 30.65 0.4 0.45 0.920 0.5 30.95 0.3 0.69 0.930 0.5 38.62 0.3 0.96 0.840 0.5 43.48 0.3 0.99 0.850 0.5 47.53 0.2 0.99 0.860 0.6 62.57 0.2 0.90 0.870 0.6 65.87 0.2 0.63 0.780 0.6 70.22 0.2 0.77 0.790 0.6 73.33 0.2 0.89 0.7100 0.6 83.69 0.2 1.02 0.8

SOC, state of charge.



the overpotential resistance measured by AC impedancemethod is less than half of the resistances measured byother three methods. Similar results were obtained byOnda et al. [18]. It is most likely that this is because theimpedance measurements are carried out at a very lowcurrent (0.5A in this study, which is equivalent to0.0125C), while the three other resistance measurementmethods use much higher currents (12–80A). The generaltrend shown in all four resistances is similar, with theresistance increasing with decreasing SOC. This isexpected as during discharge Li-ions are transferredfrom anode to cathode and associated concentrationgradients increase in magnitude. At the end of dischargecycle, Li-ions get depleted from anode, and more energyis needed to transfer the Li-ions from anode to cathode.

3.3. Entropy change measurement

Table IV shows the values of entropic coefficient dVo/dTfor various SOCs at 1C discharge.

The values are generally small except at 0% SOC. Theincreasing trend of dVO/dT values at higher temperaturesis also evident.

Hallaj et al. [27] provided values of dVO/dT between�0.43 and �0.72mVK�1 for Panasonic (CGR 18650H)and the A&T (18 650) cells. The cathode in the cellsthey studied was made of LiCoO2 material. Chen andEvans [6] reported dVO/dT values of �0.414mVK�1,averaged over a range of SOCs. In this work, the valuesfor dVO/dT are shown to be comparatively smaller(except for at 0% SOC) than the aforementioned valuesreported by other researchers. Lu et al. [28] performeddVO/dT tests for Li1+x[Ni1/3Co1/3Mn1/3]1� xO2 half cells.They calculated the values for dVO/dT to be between�0.06 and �0.12mVK�1. According to them, smallentropy coefficient values mean that the particular cathodematerial is thermally more stable than other Ni-based layeroxides, LiNiO2, LiNi1� xCoxO2 and LiNi1� xCoyAlO2. Inthe current work, while we do see the entropy coefficientturning positive at around 70% SOC, the values are verysmall.

Figure 10a shows the entropy change, ΔS calculatedfrom Eqn (3), at different SOCs for 1C discharge fortemperature difference of 25 to 35 °C.

The graph shows that QS (entropic heat) is exothermicuntil 80% SOC during discharge and endothermic between

60–40% SOC, becoming exothermic again at 20% SOCand below. It is to be noted that the curve in Figure 10ais the result of phenomena taking place both at the anodeand at the cathode.

The negative to positive change in entropy indicates astage structure change in the graphite anode or phasetransition in the cathode. When the change in the configu-rational entropy is negative, ordering of the structuretypically takes place, whereas the opposite is true for thepositive change. It is to be noted that this is somewhat ofan oversimplification as the entropy is in fact composedof a configurational part (arrangement of species in thesystem) and a thermal part (energy distribution over theenergy states in the system).

Saito et al. [29] reported that cells using a Li–Ni–Cocomplex oxide cathode or a LiMn2O4 cathode have aspecial feature in which the dVO/dT is positive or nearlyzero in the half range of high SOCs and negative in the halfrange of low SOCs. They also mentioned that entropychange in cells with the aforementioned cathode is verysmall. Similar results are obtained in the current work.Hallaj et al. [27] also reported that change in dVO/dT fromnegative to positive occurs because of a phase change inthe cathode and a structural change in the anode material.

Thomas and Newman [30] reported entropy change inLiNi0.8Co0.2O2 cathode material. Their investigationsuggests that there is no phase change in the cathodeduring deintercalation of Li. To investigate the possibilityof structural changes with the present cathode material,the open circuit voltage with respect to Li concentration(y) in LiyMnNiCoO2 was plotted. As can be seen fromFigure 10b, no plateaus corresponding to two-phaseequilibrium are observed. This suggests that no phasechange (first order transformation) should occur in thecathode material of the cell under investigation.

Hallaj et al. [31] reported that the dVO/dT changes fromnegative to positive for a coin cell with graphite anode andLiCoO2 cathode at 77% SOC. The same phenomenon isobserved in the current work as illustrated in Figure 10a.Hallaj [31] suggested that endothermic heat effectsnoted for the Panasonic cell during discharge near 4.0V(77% SOC) are in part due to the endothermic heat effectof Li deintercalation from the graphite anode, in conjunc-tion with the endothermic heat effect of the simultaneousorder/disorder phase transition (from hexagonal tomonoclinic) that takes place in the cathode during that

Table IV. dVo/dT values obtained for three different temperature changes.

SOC

Temperature change/°C 100% 80% 60% 40% 20% 0%

dVo/dT (mVK�1)

25–35 �0.13 �0.03 0.06 0.02 �0.07 �0.4435–45 �0.20 �0.05 0.15 0.14 �0.08 �0.4745–55 �0.38 �0.08 0.14 0.15 �0.09 �0.48

SOC, state of charge.



period only. They concluded that the cell discharge causesstructural transformations in the graphite anode, as Li isdeintercalated from graphite. These transformations,characterized by an entropy increase and an endothermicreversible heat effect, reinforce the endothermic spike dueto the monoclinic to hexagonal phase change followingthe initial exothermic spike due to the hexagonal tomonoclinic phase change during discharge, as the SOCapproaches 77%. The dVO/dT values provided by Hallajet al. [31] are much higher at lower SOCs (around �0.5mVK�1) than in the current work, which implies structuralchanges in cathode taking place during discharge. Oursituation is somewhat different in comparison with that ofHallaj et al. [31], as there is no evidence of structuraltransformation at the cathode side, as evidenced by verylow values of dVO/dT (Figure (10a) and Table IV).

If one considers just the configurational part of theentropy, concentrates solely on the anode side and takesa look at Figure(10a), the negative entropy change athigh SOC values could be taken to represent thegrowing Li-Li repulsion in the LixC as the Li molefraction in graphite increases. The positive valueobserved in the midrange of SOCs in Figure 10a cancorrespond to the start of the population of a new emptygraphene-graphene layer (intercalation) or layers during

charging as well as deintercalation during discharging.In that case, the change in mixing entropy (configura-tional part) should be relatively high. It is to be notedthat there is in fact a balance between three types ofinteractions in the intercalated graphite. As the graphiteplanes are held together by van der Waals (vdW) typeinteractions, from this point of view, the planes should bekept free of Li in order to maximize the attractive vdWforces between the adjacent layers. On the other hand, thereis also an attractive Li-C interaction that tends to promoteintercalation of Li. Finally, as discussed earlier, there are alsothe repulsive Li-Li interactions, which try to keep Lications as far away from each other as possible. Theaccessibility of a ‘new’ graphene-graphene layer duringcharging, for instance, depends on the delicate balancebetween these different interactions.

The cathode also plays a role in the entropy change, andits effect must be considered as to be superimposed on theanode side as discussed earlier. When one takes a look atFigure 10b, it is noted that there are no sharp discontinuouschanges in the entropy, thus ruling out the possibility offirst order transitions in our system. The smooth variationin entropy is a characteristic of a second order transition,thus heavily indicating that we are dealing here with or-der/disorder transitions, both at the cathode and at the an-ode side. This is also supported by the relatively smallvalues associated with the entropy changes. Lu et al. [28]mentioned that the phase transition in the nickel-based lay-ered oxide is suppressed because of the stabilizing effect ofCo and Al doping.

The entropy change (ΔS) from Figure 10a indicates thatfor this particular chemistry, its magnitude is small.However, the heat generated by entropy change can besignificant (in comparison with overpotential heat) andshould not be neglected while calculating the total heatgeneration in the cell. The effect of entropic heat can beclearly seen in Figure 3, where the temperature of the cellat 1C discharge is measured. There exists a plateau in themiddle part of Figure 3. This plateau roughly correspondsto the same SOC values where the entropy change ispositive. When a chemical reaction is endothermic, itrequires inflow of heat to the system to drive the reaction(positive enthalpy and entropy changes). Within thisregion, the temperature, despite the continuous discharge,remains almost constant, until it starts to rise again(entropy becomes exothermic).

3.4. Specific heat of the battery cell

The method to calculate specific heat of the battery cell hasbeen explained earlier, where the cell and the Al block arecooled down after heating them to a certain temperature.Cooling of the Al block and the cell (Figure 11) iscompared and fitted using Eqn (5). The same is alsosimulated using the computational fluid dynamics method(Flotherm software [32]).

The fitting procedure using Eqn (5) provides a specificheat value of 670 J/kgK for the battery cell.

Figure 10. (a) Entropy change at different states of charge(SOCs) when the temperature changes from 25 °C to 35 °Cand (b) dVo/dT versus state of charge. Graph shows the change

of entropy becoming endothermic at 60% and 40% SOC.



3.5. Calorimeter tests to validate heatgeneration in a battery cell

The cell was next discharged at 2C (80A) and 3C (120A)inside the calorimeter. Figure 12 shows the increase in celltemperature and the average water temperature during thedischarge process. The graph shows that for 3C discharge,the rise in water temperature is about 3 °C, while for 2Cdischarge it is only 2 °C. While the rise in water tempera-ture is almost equal to the rise in cell temperature, at theend of the discharge period (for both 2C and 3C), the risein cell temperature is too fast for the water to catch up. Thisis due to a sudden increase in internal resistance of the cellas it approaches 0% SOC (see EIS results for explanation).This is also shown in our resistance measurements. Theresults indicate that almost all of the heat released bythe cell is taken by the water and that the design of thecalorimeter is good.

The reason that we only see a small increase in thetemperature of water is mainly due to the high thermalmass of the calorimeter. Because of the size of the cell, itwas not possible to build a calorimeter with a lower

thermal mass. While a higher discharge rate could havebeen used to measure a higher change in temperature, thetime of discharge would have been very small. This timewould not have been enough for the water temperature tostabilize. We see a similar trend at the end of the dischargefor both 2C and 3C, where the cell temperature rise ishigher compared with the water temperature.

The temperature rise shown in Figure 12 is calculatedusing Eqn (4) for 2C and 3C discharge. A sample calcula-tion for the rise in temperature of the cell (or water) whenthe cell is discharged from 100% SOC to 80% SOC isshown in Appendix A. Figure 12 also compares the experi-mental rise in temperature with the calculated rise in temper-ature using R(V� I) and R(60s) overpotential resistances.

We can now compare the overpotential and entopic heatfor 1C and 2C discharge by using Eqn (1). Figure 13shows the total heat generated during 1C and 2C discharge,along with the overpotential and entropic heat. The graphclearly shows that the overpotential heat is much higherthan the entropic heat, especially between 100% and 20%SOC. However, after 20% SOC, the entropic heat becomesa higher percentage of the total heat. At 0% SOC (at the

Figure 11. Cooling of battery cell to calculate its heat capacity.

Figure 12. Temperature change during calorimeter tests compared with calculated using two different overpotential resistances for2C and 3C discharge.



end of discharge), the entropic heat is almost equal to theoverpotential heat for 1C discharge, which implies that itcannot be neglected. This effect is not seen in thecalorimeter results mainly because of high heat transferrate between the water surface and the cell and alsobecause of relatively small entropy effect between 20%and 100% SOC levels.

4. CONCLUSIONS

A large capacity, commercially available Li-ion cell, isused to quantify the heat generation in the cell. The totalheat generation is divided into two parts: overpotential heatand entropic heat. Overpotential heat is calculated bymeasuring four different resistances: resistance by V� Icharacteristics during charge and discharge, resistance bydifference between open circuit voltage and cell voltage,

resistance by intermittent discharge and by the ACimpedance measurement. The first three resistances arevery close to each other, implying that any of the threemethods can be used to calculate the overpotential heatgenerated in a battery cell. However, the resistancemeasured by AC impedance method is much smallercompared with other resistances.

Heat generation due to the entropy change is mea-sured by measuring dVO/dT (entropy coefficient) atdifferent SOCs and temperatures. Although small inmagnitude, the entropy effect cannot be neglected intotal heat dissipation, which was shown in temperatureprofile of the cell at 1C discharge. The entropy coeffi-cient is also shown to change from exothermic toendothermic, which is mainly due to ordering changesat the anode. The results obtained here are mainly consis-tent with the information available about small lowpower Li-ion batteries.

Figure 13. Total heat during 2C and 1C discharge compared with overpotential and entropic heat.

Table V. Summary of measurements done in this work.

Parameter obtained Explanation

1 Uniformity of heat distribution in a battery cell Measured the battery surfacetemperature at 1C discharge.

2 Overpotential resistance R(V� I) Obtained the resistance value byV� I characteristics at different C-rates.

3 Overpotential resistance R(VO�V) Obtained the resistance value by measuringthe open circuit voltage at different SOCs.

4 Overpotential resistance R(60s) Measured the resistance value by intermittentdischarge (with holding time of 10min)

5 Entropy coefficient (dVO/dT) Obtained the value by measuring the opencircuit voltage at different temperatures.

6 Specific heat capacity of the battery Measured by fitting the parameters in Eqn (5).7 Total heat generation of battery cell using calorimeter Measured by discharging the battery at

2C and 3C and obtaining the temperatureincrease of the calorimeter.

SOCs, states of charge.



Table V summarizes the measurements carried out inthis work.

NOMENCLATURE

A = area (m2)C = heat capacity (J/K)Cdl = double layer capacitance (F)cp = specific heat (J/kgK)Eemf = cell potential (V)F = Faraday’s constant (9.648456 ∙ 104C/mol)G = Gibbs free energy (J)h = heat transfer coefficient (W/m2K)I = charge or discharge current (A)m = mass (kg)n = number of moles of electrons exchanged in

the reactionq = total heat generated in battery cell (W)QP = overpotential heat (W)QS = entropic heat (W)Rct = charge transfer resistance (Ω)Rη = overpotential resistance (Ω)RΩ = ohmic resistance (Ω)S = entropy (J/K)SOC = state of charget = time (s)T = temperature (K)v = volume (m3)V = cell voltage (V)Vo = open circuit voltage (V)W = Warburg element

Greek symbols

Δ = change in variable∂ = partial derivative operatorρ = density (kg/m3)

APPENDIX : SAMPLECALCULATIONS

a. For measuring heat capacity of the calorimeterconstant using the following equation:

mmetalcpdT ¼ mliquidcp þ Calorimeter constant� �

dT

The following table shows the values of different param-eters of the equation:

Specific heat of water (J/kgK) 4180Specific heat of Al (J/kgK) 900Volume of water (dm3) 3.63Initial temperature of water (°C) 18.3Initial temperature of Al block (°C) 51Final temperature of the system (°C) 19.2

Calorimeter constant = 1005 J/K

b. Calculating temperature rise of the calorimeter systemduring 2C discharge

A sample calculation for the rise in temperature of thebattery cell (or water) when the cell is discharged from100% SOC to 80% SOC is shown in Appendix A.Figure 12 compares the experimental rise in temperaturewith the calculated rise in water temperature using R(V� I)and R(60s) overpotential resistance.

Specific heat capacity of the cell = 670 J/kgKMass of the cell = 0.99 kgVolume of the water = 3.43 dm3

Heat capacity of water = 4180 J/kgKDensity of water = 1000 kg/m3

Heat capacity of calorimeter = 1000 J/KTime to discharge from 100% SOC to 80% SOC at2C= approx. 180 sCurrent = 80AQp= 80 ∙ 80 ∙ 0.0019 = 12.16W (based on R(V� I)resistance at 80% SOC)Qs= [(80 ∙ 300 ∙ (�0.03)]/1000 =�0.7WTotal heat =Qp�Qs = 12.86W

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