isie

ch86, Mt, W

Article history:Received 13 March 2014Accepted 24 June 2014

Keywords:Commercial Li-ion batteriesFirst-principle modelingParametersSensitivity analysis

In this work, a methodology based on rigorous model tting and sensitivity analysis is presented to deter-

etry). These features signicantly affect the performance of thebattery including its average potential, reversible specic capacityand volumetric energy density. In addition to this, the life-span,aging mechanisms and safety of the batteries are major concernsto extend their durability. Intensive research is ongoing to develop

1/3 1/3 1/3 2 4

ture of the mate-preparatioex analysisamount o

utilized to evaluate their actual conditions, e.g. aging phen[14,15]. Different models have been reported in the litdescribing Li-ion batteries subjected to different conditions andchemistries [1,1633]. Although the basis to develop these modelsis similar, e.g. electric and mass balances, porous electrode andconcentrated solution theories [1], a different chemistry of the sys-tem alters the main contributions affecting the response of the bat-tery. For instance, it is well-known that LiFePO4 cathode materialspresent the formation of two phases in the electrode unlike other

Corresponding author. Tel.: +52 555 804 4600x2686.E-mail addresses: jgva@xanum.uam.mx, jorge_gva@hotmail.com

(J. Vazquez-Arenas).

Energy Conversion and Management 87 (2014) 472482

Contents lists availab

Energy Conversion

seLi-ion batteries. Their selection for a determined applicationdepends mainly on the chemistry of the cathode and other struc-tural factors involved in the fabrication of the cells (e.g. densityof the material, porosity, particle size in the electrodes, cell geom-

tics of these cathodes strongly depend on the narial and are affected by their method ofModeling provides the tools to perform a complperformance of Li-ion batteries and reduces thehttp://dx.doi.org/10.1016/j.enconman.2014.06.0760196-8904/ 2014 Elsevier Ltd. All rights reserved.n [7].of thef timeomenaerature1. Introduction

Li-ion batteries are a promising technology in electric vehiclesand other electronic devices; however, their future relies upontheir ability to meet the performance demands and low-costrequired in commercial applications. Many endeavors have beenundertaken to commercialize different types and chemistries of

more precise methods to determine and analyze these characteris-tics to extend the durability of the battery and reduce the costs ofits fabrication.

To date, various chemistries have been considered for the fabri-cation of cathode materials for Li-ion batteries, with some of theprincipal cathode materials being LiMn2O4 [14], LiCoO2 [2,4,5],LiNi Mn Co O (NMC) [69], LiFePO [1013]. The characteris-mine the parameters describing the physicochemical behavior of commercial pouch Li-ion batteries ofhigh-capacity (16 A h), utilized in electric vehicles. It is intended for a rapid estimation of the kineticand transport parameters, state of charge and health of a Li-ion battery when chemical information isnot available, or for a brand new system. A pseudo 2-D model comprised of different contributionsreported in the literature is utilized to describe the mass, charge and thermal balances of the cell and por-ous electrodes; and adapted to the battery chemistry under study. The sensitivity analysis of key modelparameters is conducted to determine condence intervals, using Analysis of Variance (ANOVA) for non-linear models. Also individual multi-parametric sensitivity analysis is conducted to assess the impact ofthe model parameters on battery voltage. The battery is comprised of multiple cells in parallel containingcarbon anodes and LiNi1/3Co1/3Mn1/3O2 (NMC) cathodes with maximum and cut-off voltages of 4.2 and2.7 V, respectively. Mass and charge transfer limitations during the discharge/charge of the battery arediscussed as a function of State of Charge (SOC). A thermal analysis is also conducted to estimate the tem-perature rise on the surface of the battery. This modeling methodology can be extended to the analysis ofother chemistry types of Li-ion batteries, as well as the evaluation of other material phenomena includingcapacity fade.

2014 Elsevier Ltd. All rights reserved.a r t i c l e i n f o a b s t r a c tA rapid estimation and sensitivity analysthe behavior of commercial Li-ion batter

Jorge Vazquez-Arenas a,, Leonardo E. Gimenez b, MiaDepartamento de Qumica, Universidad Autnoma Metropolitana, San Rafael Atlixco 1bChemical Engineering Department, University of Waterloo, 200 University Avenue WescGeneral Motors Company R&D Center, 30500 Mound Rd, Warren, MI 48090, USA

journal homepage: www.elof parameters describings including thermal analysis

ael Fowler b, Taeyoung Han c, Shih-ken Chen c

xico, DF 09340, Mexicoaterloo, ON N2L 3G1, Canada

le at ScienceDirect

and Management

vier .com/locate /enconman

aging [47].In some of the aforementioned studies [42,44] there is often no

sionLi-ion battery chemistries [16]. Additionally, the variation of thechemistry of the material composites involves a modication ofthe crystallographic, chemical and electrical properties which leadto different parameters describing the phenomena occurringacross the battery, e.g. conductivities, diffusivities, densities, kinet-ics. Consequently, the sum of all these contributions produceschanges in the overall performance of the battery. The identica-tion of these contributions and their quantication (e.g. kineticsparameters) are decisive to analyze the mechanisms operating inthe battery and detect major problems deteriorating the life ofthe battery. However, these factors are not easy to perceive sincethe battery is a complex system where different contributionsinteract, and sometimes, chemical properties cannot be estimatedwhatsoever.

The determination of kinetic parameters through tting meth-ods and corresponding sensitivity analyses are powerful tools todescribe the complex behavior of a Li-ion battery. In addition,these tools allow a quick analysis of the mechanisms operatingwithin the battery and can be used to simulate non-accessibleexperimental conditions. The rst one involves the determinationof the parameters and constants through the minimization of theerror in the potential of the battery at different experimental C-ratetests, whereas the sensitivity analysis determines the importanceof the parameters or contributions under the experimental condi-tions of the analysis.

Although a considerable amount of models have been reportedto describe the behavior of Li-ion batteries [1,1620], most of themhave mainly focused in the analysis of button cells, which couldpresent a slightly different behavior compared to actual commer-cial batteries (due to vast differences in cell geometry, thermalconditions, and macroscopic mass transfer regimes). Just a fewstudies have undertaken the physicochemical modeling of com-mercial cells or batteries [16,34,35].

Many modern publications dealing with physicochemical mod-eling, battery SOC and performance estimation provide lumpedparameter or reduced order models [3641] for faster computa-tion, based on existing physicochemical models. These studiesoften report model parameters that are either taken from previousliterature, estimated-through tting experimental data or other-wise, and/or determined experimentally; battery manufacturersare not always willing to provide parameters that may compro-mise proprietary technology or information.

With the current rate of advancement of battery materials andtechnology it may be inappropriate to use parameters found in lit-erature, particularly because the materials used in the literatureand those in the battery application may possess slight variationssignicantly affecting the properties in question. Experimentaldetermination methods are time consuming, may require expen-sive equipment and may involve cell disassembly or handlingwhich may change the properties of the otherwise intact batterymaterials. In addition, there are some battery parameters, such aseffective electrode porosity, which are difcult to measure experi-mentally. Hence, estimating all or most of the kinetic parametersthrough tting appropriate physicochemical models remains themost viable option- it is relatively fast, inexpensive, and onlyrequires a few cycles (unless parameters related to aging are beingdetermined). This method is becoming faster and more technolog-ically feasible in recent years thanks to modern computationaladvances. There are few publications which estimate kineticparameters for full physicochemical models through tting meth-ods with experimental validation [4244].

Whenever tting or estimation methods are used for determin-ing parameters in physicochemical models, the sensitivity and

J. Vazquez-Arenas et al. / Energy Converaccuracy of the model parameters is rarely considered, so long asthe model succeeds in providing estimation of operating voltage,capacity, and temperature. Thus, it is unclear which parametersindication to the tting method or estimation technique used inparameter determination, simply an indication that the parameterwas somehow estimated. The goal of this study is to provide amethod of kinetic parameter estimation given a previously devel-oped physicochemical model [17], as well as experimental valida-tion and sensitivity analyses on the parameters in order toidentify critical model parameters. A previous work conducted byour research group proposed a model to account comprehensivelyfor the behavior of a LixC6LiyMn2O4 cell to understand their perfor-mance at both beginning of life (BOL) and end of life (EOL) [17].Comparisons between baseline and complex models were system-atically utilized to analyze different thermal and capacity fadeeffects (e.g. heat generation, SEI formation, dissolution of LiyMn2O4particles) during typical cycle-life tests. However, the previousstudy did not include any experimental work to validate the contri-butions of the model. To the authors knowledge, the determinationof kinetic parameters and sensitivity analysis for commercialGraphite/LiNi1/3Co1/3Mn1/3O2 batteries have not been conductedeither. Their importance is crucial to identify the mechanisms con-trolling the behavior of this type of batteries, design, optimization,quantication of their rates allowing the prompt detection of prob-lems to extend their life and reduce the costs of their fabrication.Thus, the present study focuses on the analysis of the kinetic param-eters andmechanisms controlling the behavior of a Li-ion battery atBOL, utilizing real data collected from commercial 16 A h Kokambatteries [48] at different C-rate tests. Rather than reporting anew physicochemical model, particular focus is placed onmore rig-orous least-square tting to obtain the systemparameters and a sta-tistical analysis of the t of the model to the experimental data toestimate the condence intervals of the parameters. A systematicanalysis is also proposed,where individual interactions are incorpo-rated to a baseline model and subsequently evaluated based on itssignicance.

A thermal analysis is also conducted to account for the temper-ature rise on the surface of the battery. There are a wide variety ofmodels that accurately describe the thermal prole of many bat-teries during cycling [20,22,36,42,4952]. Further studies will beaimed to corroborate the magnitude of the parameters using addi-tional chemical and electrochemical measurements, as well asevaluating aging mechanisms and more comprehensive thermaldistributions for these commercial batteries.

2. Materials and methods

2.1. Modeling

Table 1 shows the thermalmodel utilized in this study to accountfor the response of the batteries under different C-rates. It describesthe diffusion (e.g. porous electrode theory) and conduction of Li+

ions with conservation of charge (e.g. Ohms law) in the solid andelectrolyte phases across the cell, e.g. anode, separator and cathode.are critical for successful model predictions (and from the manu-facturers perspective, for optimizing battery performance) andwhich can vary within a certain range without signicant impacton model (or battery) performance. Examples of this model basedoptimization from a manufacturers perspective is the comparisonof critical design parameters for a cathode through model basedsensitivity analysis [45], the maximization of electrode energydensity through many parameter simultaneous optimization [46],and effects of manufacturing variations on cell performance and

and Management 87 (2014) 472482 473Further details of the derivation of thematerial and charge balanceshave been described in Refs. [1,17,19,35,53]. The isothermal studiesdo not consider the energy equations shown in Table 1.

mo

anF

T @U@T

n@ ln@x

0je

sionTable 1Domain equations, initial and boundary conditions involved in the lithium-ion battery

Region of thecell

Balance Governing equations

Anode Material, solidphase

@cs;n@t Ds;n 1r2 @@r r2

@cs;n@r

Charge, solid phase reff;n@2U1;n@x2 anFjn

Charge, liquid phase @@x jeff ;n@U2;n@x

2RT1t0F

@@x jeff ;n @ ln c@x

Material, liquidphase

ee;n @c@t @@x Deff ;n @c@x 1 t0anjn

Energy qnCp @T@t @@x kn @T@x U1;n U2;n Un reff ;n@U1;n@x

2 jeff ;n@U2;n@x 2 2RT1t0F jeff ;

Separator Charge, liquid phase jeff;s @U2;s@x 2RT1t0

F jeff ;s@ ln c@x 0

Material, liquidphase

e @c@t @@x Deff;s @c@x

Energy qsCp @T@t @@x ks @T@x jeff;s@U2;s@x

2 2RT1tFCathode Material, solid

phase

@cs;p@t Ds;p 1r2 @@r r2

@cs;p@r

Charge, solid phase reff;p@2U1;p@x2 apFjp

474 J. Vazquez-Arenas et al. / Energy ConverThe model was t to the experimental data of cell potential(Ecell, refer to Fig. 5) recorded for the different C-rate plots to obtainparameter estimates by minimization of the sum-of-squares errorbetween the model predictions (Table 1) and data. This involvedthe use of the tness function below in conjunction with a trust-region-reective algorithm provided by the Matlab R2011b tool-box [54]:

Fitness function Xm1

Xn1

Emodelcell Eexperimentalcell 2 1

where Emodelcell and Eexperimentalcell are the model-predicted and experi-

mental cell voltages in the discharge plots (i.e. Fig. 5), respectively;n is the number of points recorded per C-rate, and m the corre-sponding C-rate plot (e.g. 1C, C/2, C/5 and C/25). Charge and mate-rial balances in the solid-phase and liquid-phase as well as thekinetic contributions were considered one at a time to t the modelparameters associated with them to the four different dischargeplots, and then their importance was determined through a sensi-tivity analysis shown in Fig. 4 (see details below). The individual t-ting of the charge balance in the solid phase, charge balance in theliquid phase, material balance in the solid phase, material balancein the liquid phase and kinetics involved 2, 1, 4, 2 and 9 parametersrespectively. The tting stage was completed by performing a glo-bal t involving sensitive and non-sensitive parameters, including18 parameters from all balances and kinetics. This procedure wascarried out with the intention of observing the variability of non-sensitive parameters when sensitive parameters of other balancesare subjected to variations. The parameters determined from thislast stage and non-tted parameters are reported in Table 2. The

Charge, liquid phase @@x jeff ;p@U2;p@x

2RT1t0F

@@x jeff ;p @ ln c@x apF

Material, liquidphase

ee;p @c@t @@x Deff;p @c@x 1 t0apjp

Energy qpCp @T@t @@x kp @T@x U1;p U2;p Up T @Up@Treff;p@U1;p@x

2 jeff ;p@U2;p@x 2 2RT1t0F jeff;p @ ln@xdel.

Boundary or initial condition

cs,n|t=0 = cn,ini

Ds;n @cs;n@rr0

0 Ds;n @cs;n@rrRp;n

jnU1;n

xA 0 reff ;n

@U1;n@x

xA=S

0

jn jeff ;n @U2;n@xxA

0

jeff ;n @U2;n@xxA=S

jeff ;s @U2;s@xxA=S

cjt0 c0

Deff ;n @c@xxA 0 Deff ;n @c@x

xA=S Deff ;s @c@x

xA=S

nanFjnc @U2;n

@x

Tnjt0 Tenvkn @T@xxA hT Tenv kn @T@x

xA=S ks @T@x

xA=S

jeff ;n @U2;n@xxA=S

jeff ;s @U2;s@xxA=S

jeff ;s @U2;s@xxS=C

jeff ;p @U2;p@xxS=C

cjt0 c0

Deff ;n @c@xxA=S Deff ;s @c@x

xA=S

Deff ;s @c@xxS=C Deff ;p @c@x

xS=C

ff ;s@ ln c@x

@U2;s@x

Tsjt0 Tenvkn @T@xxA=S ks @T@x

xA=Sks @T@x

xS=C kp @T@x

xS=C

cs;pt0 cp;ini Ds;p

@cs;p@r

r0

0 Ds;p @cs;p@rrRp;p

jp

reff;p @U1;p@xxS=C

0 reff ;p @U1;p@xxC

IapU1;p jxC Ecell

and Management 87 (2014) 472482condence intervals of these parameters were rigorously calculatedusing the statistical analysis reported in Ref. [55] for non-linearmodels. This procedure involved the calculations of the covariancematrix and the analysis of variance (ANOVA) through the residualsvector and the Jacobian matrix yielded from the output of the trust-region-reective algorithm from Matlab [54]. Condence intervalsfor insensitive parameters to the model were not determined sincethey were very large (specied in Table 2), and represent non-accu-rate estimations within the experimental conditions of analysis ofthe batteries. However, they are considered in the model to accountfor steps which are not rate-controlling. As shown in the propertiesand parameters utilized in the lithium-ion battery model (Table 1),the model is able to describe the material and charge transport inthe liquid and solid phases of the battery. These mechanisms andtheir interactions are well-known to occur during the operation ofa Li-ion battery [56,57]. However, this does not imply that all ofthem are rate controlling during the discharge/charge of the bat-tery, but they are necessary to construct the physics of the battery.The rate controlling steps can vary with temperature, materialchemistry, discharge/charge rates and state of charge. Their signi-cance is statistically estimated in this study. The model parametersdetermined by the global t were independently studied using aMulti-Parametric Sensitivity Analysis (MPSA) in order to determinetheir relative importance in the model, and corroborate the calcula-tions established by the condence intervals. This test was con-ducted according to the owchart described in Fig. 4. MPSAmeasures the variation of the model prediction with respect tothe experiment when the parameters are modied via a normal dis-tribution with a variation range of 10%, situated according to val-ues determined by the tting. The coefcients (ddev) determined

jp jeff ;p @U2;p@xxC

0 jeff;s @U2;s@xxS=C

jeff ;p @U2;p@xxS=C

cjt0 c0 Deff;p @c@xxC 0 Deff ;s @c@x

xS=C Deff ;p @c@x

xS=C

apFjpc @U2;p

@x

Tpt0 Tenvks @T@x

xS=C kp @T@x

xS=C

kp @T@xxC hTenv T

oughugh

0

10

0.494 14 S

Effective ionic conductivity jeff,s = jeee,n

a

sionLi transference number

Intercalation/deintercalation rate constant kn = 3.67 106 m2.5 mol0.5 s1ddev = low

Anodic transfer coefcient for lithiation a_Aneg = 0.5a

ddev = lowTable 2Properties and parameters utilized in the lithium-ion battery model determined thrintermediate and high) of sensitivity of the parameter to the model, determined thro

Description Anode

Initial electrolyte salt concentration

Maximum concentration in intercalation materialctn = 26,390 mol m3 [1]

Initial state of charge SOCn;ini 0:66Solid phase Li-diffusivity in the particles Ds;n 3:9 1014 m2 s1 [1]

Volume fraction of electrolyte phase ee,n = 0.303a

ddev = lowVolume fraction of solid active material phase es;n 1 ee;n ep;n ef ;n = 0.200

ddev = highSeparator porositySpecic surface area an 3es;nrp;n = 8.153 10

5 m2

Salt diffusivity in the electrolyte De 104:4354

T2295x103 c0:22x103cx

Effective salt diffusivity in the electrolyte Deff De;ne1:5e m2 s1Electronic conductivity of the solid phase r0,n = 100 S m1 [1]Effective conductivity of the solid phase reff ;n r0;ne1:5s;nIonic conductivity of the electrolyte je = (10.5c + 0.668 103c2 +

0.074cT 1.78 105c2T 8.86105cT2 + 2.80 108c2T2)2 10

J. Vazquez-Arenas et al. / Energy Converfrom the sensitivity analysis are also included in Table 2, and denotethe degree (low, intermediate and high) of sensitivity of the param-eter to the model. Further details of the MPSA can be consulted inRef. [55].

2.2. Experimental set-up

Four different discharge plots (C/25, C/5, C/2 and 1C) were col-lected utilizing commercial Kokam batteries (Model SLPB75106205) with a rated capacity of 16 A h. Note that the maxi-mum continuous discharge rate allowed for the operation of thesebatteries is 1C (16 A). The maximum pulse discharge rate is 5C(80 A), but it can be sustained only during a 10 s pulse. Presum-ably, the rate limitation for these batteries is associated with thepolymer-gel electrolyte since the application of high C-rates leadsto a signicant temperature rise producing the eventual degrada-tion and capacity fade of the batteries. The cells of these batteriesare comprised of a certain number of mesocarbon microbeads(MCMB) anodes, separators and NMC cathodes. Other cell geome-try details are not revealed in brevity to maintain manufacturecondentiality. Cell specications of these batteries can be seenin reference [58]. The discharge proles were collected using aMaccor battery cycler utilizing the following protocol: (a) Thebattery was rested for at least ve hours, (b) then the batterywas charged at a constant current of 16 A followed by a constantvoltage charging stage at 4.2 V until a cut-off current of 0.8 A, (c) arest period was applied to attain a constant open circuit voltage,(d) followed by the constant current discharge of the battery at16 A until a cut-off voltage of 2.7 V, (e) the battery was newly

Cathodic transfer coefcient for lithiation a_Cneg = 0.5a

ddev = lowIntercalation/deintercalation current density jint=deinn knctn cs;n

rRp;n

a Anegcs;nca Anegexp0:5FRT gn exp 0:5RT

Resistance of SEI formation RSEI = 0.035Xm2a

ddev = low

a The condence interval was not determined since the parameter had a low sensitivtting or from the literature. ddev is the coefcient representing the degree (low,a Multi-Parametric Sensitivity Analysis.

Separator Cathode

c0 = 2000 mol m3

[1]ctp 53,284 mol m3SOCp;ini 0:07Ds;p 1.64 1014 m2 s1addev = lowee;p 0:127addev = low

.001 es;p 1 ee;p ep;p ef ;p 0.338 0.005ddev = high

e = 1 [1]

ap 3es;prp;p = 1.236 105 m2

4 m2 s1 [63]

r0,p = 0.023 S m1 [64]reff ;p r0;pe1:5s;p

106c3 +010c3T 6.96 m1 [63]

jeff,s = jees jeff,p = jeee,pt0 0:57addev = low

kp = 1.30 106 m2.5 mol0.5 s1ddev = lowa_Apos = 0.36 0.035ddev = intermediate

and Management 87 (2014) 472482 475rested until constant voltage, (f) proceeding the charge of the bat-tery at the C-rate of interest to 4.2 V, then constant voltage charg-ing at 4.2 V until a cut-off current of 0.8 A (g) rest until constantvoltage, (h) discharge of the battery at C-rate of interest to cut-off voltage of 2.7 V. Stages (a) to (e) correspond to a pre-testchargedischarge cycle in order to attain the same state of charge(SOC) in the batteries before running the C-rate tests and to verifythat the performance of the battery is consistent with previouscycles in terms of capacity at 1 C.

During the tests, the batteries were placed in a Cincinnati Sub-Zero MicroClimate thermal chamber with the temperature con-trolled by forced air convection at 25 0.2 C. Within thechamber, the batteries were fastened in a jig that consists of twoseparate aluminum plates, each one encased in a larger acrylicplate which can be fastened to the other with screws (see Fig. 1).The jig was built in order to prevent convective cooling of the bat-tery faces within the chamber; the aluminum plates aid in the heatdistribution and compression of the batteries (representative ofpack conditions) and allow the measurement of heat ux throughthe jig. Eight T-type thermocouples were taped in different loca-tions on the jig, four were placed approximately 1 cm below eachof the two tabs on both faces (at these locations, the highest surfacebattery temperature was observed), and four directly across theenclosing aluminum plate on each outer side (to estimate one-dimensional heat ux). Fig. 1 indicates the placement of four ofthese thermocouples (the other four are symmetrically placed onthe reverse side of the battery). The temperature of all 8 thermo-couples was read every second by using a FieldPoint System fromNational Instruments controlled using LabVIEW software.

a_Cpos = 0.46 0.048ddev = intermediate

rRp;na Cneg

F gnjint=deinp kpctp cs;p

rRp;p

a Aposcs;nrRp;p

a Cpos

ca Apos exp 0:5FRT gp

exp 0:5FRT gp

ity to the model.

3. Results

3.1. Isothermal studies

Equations describing the OCV in each electrode are difcult toderive due to the dependence of this value upon SOC. Thus, inthe present work these expressions were empirically estimatedfor each electrode by tting their cell voltage as a function ofSOC, from discharge plots conducted at C/25 (not shown). Theexpression for the cathode material (NMC) was estimated to be:

Up;ref 0:48 3:44 106 tanh1:29 1016

4:63 1016 SOCp 1:67 1014

1:12 106 13:04 106 SOCp

0:56

!

1:70 106 exp0:036 SOC0:0096p 1:03 103

exp1:03 104 10:57 SOCp 2

Fig. 1. Position of the thermocouples. (a) On the aluminum plate once the jig is closed, (b) on the battery face.

476 J. Vazquez-Arenas et al. / Energy Conversion and Management 87 (2014) 472482The rst simulations were conducted utilizing the parametersreported in reference [1] for a LixC6LiyMn2O4 cell (e.g. previousto the application of tting methods), with the intention to presentthe original deviations between the model and the four experimen-tal C-rate tests. Fig. 2 shows these results where the poor quality ofthe cell voltage (Ecell) prediction is clearly evidenced. This is notsurprising, given the variation existing between the battery com-ponents (e.g. cathode material) and the magnitude of the phenom-ena operating within it. The next step involved the determinationof the kinetic parameters, which was sequentially carried out fol-lowing the stages described in the owchart shown in Fig. 3.Fig. 5 shows the experimental and modeling cell voltage as a func-tion of the depleted capacity at four different C-rates: C/25, C/5, C/2and 1C. As observed in this plot, the quality of the ts is better thanthe one shown in Fig. 2. This indicates that even when the modeldescribes properly the physicochemical contributions of the sys-tem, parameters and constants must be appropriately selectedand tted to describe the magnitude of these phenomena in themodel.

In order to reduce the uncertainty of some of the constants andparameters utilized by our model described in the plots shown inFig. 5, the research program has tried to measure them throughdata contained in the literature or by using our own experimentalmeasurements whenever possible. One of these variables is theopen circuit voltage (OCV) of electrode reaction depending onthe local state of charge (h) at a reference temperature (Uj,ref).

4.52

2.5

3

3.5

4

0 5 10 15

E cel

l/ V

Capacity/ A h

1C

C/5

C/2

C/25

Fig. 2. Computed and experimental cell voltages as a function of capacity forKokam batteries characterized at four different discharge rates. Symbols describethe experiments and continuous lines represent the simulations calculated usingthe parameters reported in reference [1].Charge balance in the solid-phase

Least-square fit todetermine parameters

Baseline model

Are the parameters

YES NO

Incorporation of theparameters to the

Charge balance in the liquid-phase

sensitive?

Are the parameters

YES NO

sensitive?

Material balance in the solid-phaseAre the parameters

YES NO

sensitive?modelMaterial balance in the liquid-phaseAre the parameters

YES NO

sensitive?

KineticsAre the parameters

YES NO

sensitive?

Set of Kinetic Parameters

Overall Fitting

Fig. 3. Flowchart used to determine the parameters of the model accounting for thebehavior of the Kokam batteries.

Fig. 4. Flowchart of the Multi-Parametric Sensitivity Analysis (MPSA) used toestimate the sensitivity of the parameters (Table 2) to the model.

1C

C/5

C/2

C/25

2

2.5

3

3.5

4

4.5

0 5 10 15

E cel

l/ V

Capacity/ A h

Fig. 5. Computed and experimental cell voltages as a function of capacity forKokam batteries characterized at four different discharge rates. Symbols describethe experiments and continuous lines represent the simulations calculated usingthe parameters reported in Table 2.

J. Vazquez-Arenas et al. / Energy Conversionwhile the OCV of the anode material (graphite) is described by thefollowing expression determined from our battery:

Un;ref 0:0286:33exp3:52SOCn9:67103 exp0:87SOCn9:64103

exp1:03103 SOCn0:001exp0:001SOCn 3The local states of charge are respectively dened for the cath-

ode and anode materials as:

SOCn cs;nctn4

SOCp cs;pctp5

These values are difcult to measure accurately at fully chargedstate since there is a loss of cyclable lithium during the manufac-ture of the batteries to form the solid electrolyte interface (SEI)[18]. Therefore, they were determined from tting initial experi-mental discharge curves to yield the values shown in Table 2.These values are close to those reported by other researchers forLixC6LiyMn2O4 cells (0.53 and 0.17). The maximum concentrationin the electrodes was determined using the density and the molec-ular weight of the material. Values of 26,390 and 30,555 mol m3

Li+ have been reported by Doyle et al. [1] and Ning et al. [18],respectively for the anode material. These values are similar tosome extent for most of the batteries since most of the Li-ion cellscontain mesophase microbeads of carbon (LixC6). Values of53284 mol m3 were estimated for the maximum concentrationin the cathode utilizing the density of the NMC material(4.77 106 g m3) [59] and its molecular weight (89.52 g mol1).A solid state diffusion coefcient of 3.9 1014 m2 s1 (Ds,n) hasbeen reported by Doyle et al. for carbon electrodes [1], whereas avalue of 1.64 1014 m2 s1 (Ds,p) was found for the cathodethrough tting. Ds,p differs by almost one order of magnitude(Ds;LiyMn2O4 = 1 1013 m2 s1) for LiyMn2O4 [1], while diffusioninside LiFePO4 particles has been shown to be even slower thanin NMC cathodes, e.g. 1.18 1018 m2 s1 [16]. These differencesare a clear evidence of the modication in the transport of Li+ ionsinside the electrode particles due to changes in the crystal struc-ture of the cathode. It is known that Ds,p relies on different proper-ties of the cathode including electrode composition, porosity,morphology, etc. Likewise, it is a strong function of the techniquesutilized to fabricate the cathode and used to determine its value(e.g. different time domain conditions). Ds,p values in the order of1014 m2 s1 have been reported for LiNi1/3Mn1/3Co1/3O2 electrodesfabricated by wet chemical methods and characterized using elec-trochemical impedance spectroscopy (EIS) [60], 10141015 m2 s1

for similar electrodes synthesized at high temperature viaprecursor methods and characterized using CV [61], 1015,1014 m2 s1 and 1015 m2 s1 for LiNi0.36Mn0.29Co0.35O2 electrodesfabricated using co-precipitation methods and characterizedthrough CV, GITT and PITT, respectively [62]. However, despitethis variation Ds,p is averagely found within the range of1014 m2 s1 as the value determined by our tting (Table 2), and3.3 1014 m2 s1 via potentiostatic intermittent titration tech-nique (PITT) (details not shown) as part of a related study. Thelow sensitivity calculated for this parameter denotes its poor inu-ence in the model. Although, this effect is evaluated for the overallbehavior of the battery voltage, a signicant behavior will beobserved at certain SOC values (i.e. depending on capacity) forthe diffusive processes occurring in the battery (e.g. inside the par-ticle electrodes). This effect is further discussed below.

and Management 87 (2014) 472482 477The volume fractions for the electrolyte phase, the current con-ductive llers and the polymer phase (e.g. NMC contains a polymerelectrolyte) for the cathode and anode materials are also reported

in Table 2. The volume fractions of the polymer phase and the con-ductive llers for NMC electrodes were not revealed by the manu-facturer. In this work, all the terms were incorporated into oneterm (e.g. volume fraction of solid active material, es) in order tosimplify this parameter in the model. Sensitivity analyses con-ducted for the volume fractions reveal that the solid phases presenta considerably higher sensitivity compared to the electrolytephases, which are insensitive in the range of experimental condi-tions evaluated. Apparently, this behavior is observed since themechanisms controlling the behavior of the battery are associatedwith the solid phase (i.e. electronic conduction) and not with theelectrolyte inputs (i.e. mass-transfer in the liquid phase). More-over, this high sensitivity could also be connected with the impor-tance of the active surface area and the particle size of thematerials. The particle radii of the electrodes were found in therange of 106 m, which are within the typical range of particles uti-lized for the fabrication of Li-ion batteries. These parameters werefound to be non-sensitive in the model. As aforementioned, this is

transfer coefcients in the cathode vary from the typical values(0.5) reported for other positive electrodes (values shown inTable 2), suggesting kinetic changes for the intercalation of Li+ ionsfor NMC materials. This nding is corroborated by the sensitivityanalysis revealing that the transfer coefcients in the cathode aresensitive in the model. This conrms that the behavior of the bat-tery can be also controlled by the insertion process in one of theelectrodes, and not only by electrical conduction or mass-transferphenomena. A different situation occurs for the transfer coef-cients of the negative electrode, which are insensitive in the model.Although, it could be suggested that this occurs due to the fact thatone cannot assess the signicance of these values in the anodeindependently during the discharge of the battery. More experi-mental evidence is required to analyze this effect, particularlythe engagement of charge proles which will be evaluated furtherin this paper. Note that the transfer coefcients are more sensitivein the model than the rate constants. A similar nding wasreported above, and it has been particularly reported for other

478 J. Vazquez-Arenas et al. / Energy Conversion and Management 87 (2014) 472482most likely due to a statistical correlation between the volumefraction of the solid phase and the active surface area of the elec-trodes (which is sensitive within the model), i.e. ai = 3es,i/rp,i.

The expressions describing the salt diffusivity (De) and the ionicconductivity of the electrolyte (je) as a function of the Li+ concen-tration and temperature across the cell were taken from the workreported by Valoen and Reimers [63]. These values were obtainedfor LiPF6 in a propylene carbonate/ethylene carbonate/dimethyl/carbonate mixture, and were estimated as a function of tempera-ture and LiPF6 concentration. The electronic conductivity of thecarbon has been typically reported to be 100 S m1 (r0,n), whereasfor NMC materials the conductivity was found for each of the fol-lowing compositions: LiNi0.475Co0.05Mn0.47O2 (0.023 S m1) [64]and LiNi0.4Co0.4Mn0.2O2 (0.0140.068 S m1 from 21 to 100 C)[65]. These values should be close to the electronic conductivityof the LiNi1/3Mn1/3Co1/3O2 electrode used in the batteries testedin this work. Likewise, it is known that r0,p is lower than the LiCoO2material (10 S m1) but higher than the LiFePO4 material(0.005 S m1) [19].

The Li transference number in LiPF6 for our batteries was esti-mated to be 0.57 from the tting of the parameter. This value isclose to that one (0.363) reported for a concentration of 1.2 M LiPF6in lithium polymer cells [66] and was found to be non-sensitive inthe model. On the other hand, the intercalation/deintercalationrate constants were found to be in the order of 106 m2.5 mol0.5

s1. These values are similar to those reported for other chemis-tries, LiMn2O4 [1], LiCoO2 [18]. In this regard, the values of the

1CC/5C/2 C/25

2

2.5

3

3.5

4

4.5

0 5 10 15

E cel

l/ V

Capacity/ A h

Fig. 6. Computed and experimental cell voltages as a function of capacity for

Kokam batteries characterized at four different charge rates. Symbols describe theexperiments and continuous lines represent the simulations calculated using theparameters reported in Table 2.electrochemical systems. This situation can be explained in termsof the correlation existing between the transfer coefcients andthe rate constants, given the exponential form of the ButlerVol-mer equation [67,68].

The resistance due to the SEI formation at the anode side wascalculated to be 0.035Xm2, which is found within the range forcarbon electrodes [1,18]. In the present study, it is assumed thatthe commercial Kokam batteries utilized in the experimentalcharacterization were initially cycled to form a pseudo steady-state SEI during their manufacture with the intention to avoidthe loss of Li+ ions from the electrolyte during subsequent opera-tion. This agrees with reports in literature where the SEI formationis considered within the rst one or two charge/discharge cycles[69,70]. It is also known that for some particular anodes, this lmcontinues growing but its effects of the additional growth can beconsidered negligible [71], unless it undergoes major damage orlong-term degradation which requires a signicant loss of Li+ ions.As observed in Table 2, RSEI was found to be non-sensitive in themodel, perhaps because its effects are known to occur over long-term cycling or at the end of life of the battery [17,18] and not inthe range of testing life undertaken in this work.

The capabilities of a model describing the physics of a Li-ionbattery can be evaluated considering discharge and charge prolesat different C-rates. To date, only discharge proles have been con-sidered in this work. In order to assess the capabilities of predictionof the model and the magnitudes of the parameters and constants(refer to Table 2) determined through tting the discharge plots,

1920

1960

2000

2040

2080

2120

0 1 2 3

c / m

ol m

-3

x / dimensionless

0.111.563.114.676.227.789.3310.8912.441415.5515.96 A h

Anode Separator Cathode

C/CCCC/AFig. 7. Concentration of Li+ in the electrolyte (c) across the battery plotted atdifferent capacity values. CC/A and C/CC represent the interfaces located in thecurrent collectors between the anode and the cathode, respectively. 1C test.

compared to the insertion in the cathode or heating in the interiorelectrodes. As observed, in Fig. 8b, after the pseudo-steady regimeof concentration in the cathode, the concentration remains aroundthe value obtained for this previous stage, which suggests that it isnot consumed fast enough as it arrives to the surface of the cathodeparticles, where it builds up in this section of the battery. Note inTable 2 that the maximum concentration in intercalation materialis higher for the cathode than the anode, thus, there are no limita-tions regarding the number of active sites available for lithiation.This phenomenon conrms the nding reported in the sensitivityanalysis, where the kinetics of the cathode controlled the lithiationprocess. Thus, more Li+ ions cannot be transferred from the anodeto the cathode since they are inserted more slowly, whereby ionsare accumulated in the electrolyte as observed in 8a for the rangeof depleted state of charge located between 9.33 and 12.44. At theend of discharge, a drop in Li+ concentration is observed (Fig. 8a) atthe current collector/anode interface as a result of the concentra-tion gradient created inside the anode particles and the movingfront of the Li+ insertion in the cathode. Likewise, these effects pro-duce an increase in the ohmic drop, reected in the potential dropin the electrolyte (/2) at the end of discharge (not shown).

To date, this work has only analyzed the phenomena occurringin the electrolyte phase across the cell. Valuable information canalso be collected from the analysis of the solid-phase in the elec-trodes since this permits to determine the phenomena governingthe behavior inside the particles, as well as nding out the most

+

19200 5 10 15 20

Capacity/ A h

Fig. 8. Concentration of Li+ in the electrolyte as a function of the capacity. (a)Current collector/Anode interface and (b) Cathode/Current collector interface. 1Ctest.

sioncharge proles were simulated at four different C-rates: C/25, C/5,C/2 and 1C, maintaining all the parameters described in Table 2constant, only the initial concentration in negative and positiveelectrodes were varied to estimate SOCn,ini and SOCp,ini. The poten-tial of the cell as a function of depleted capacity is shown in Fig. 6for the charge proles conducted at different C-rates. As observed,the quality of the simulation is good considering that the kineticparameters determined from the tting to the discharge proleswere used for this purpose. Only small deviations are observed atthe beginning of the charging period for the simulation carriedout at 1C. This may be due, at least in part, to the heat generatedby the battery at 1C (which is more signicant than at lower C-rates), as well as a higher polarization at faster rates. As previouslymentioned in the discussion of the discharge proles, the transfercoefcients of the negative electrode were insensitive during thesensitivity analysis conducted for the discharge proles. A similarsituation occurs in the case of the charge proles shown in Fig. 6,where it was found that they were not sensitive either, whereasthe transfer coefcients of the positive electrode are sensitive. Thisoccurs even if the transfer coefcients are allowed to vary duringthe tting. This nding suggests that there is a kinetic control inthe positive electrode at determined moment of the dischargeand charge of the battery. In order to get further insights of themechanisms controlling the operation of the commercial batteries,some variables associated with the parameters were calculated.

Calculations of variables such as the concentration of the Li+

across the battery and inside the electrodes, and the electric poten-tial offer further evidence of the phenomena controlling the behav-ior of the battery. From time to time, some of these phenomenacannot be measured experimentally and therefore, numerical eval-uations need to be performed. Additionally, numerical estimationscan provide the evolution of these variables as a function of time orbattery capacity, which allows determining critical points of thecycling of the battery. Simulations for different variables were con-ducted at 1 C-discharging at different locations of the cell. Fig. 7shows the Li+ concentration in the electrolyte (c) across the cellat different depleted capacities (refer to Fig. 5 for cell voltage val-ues). Similar proles have been reported by Doyle et al. for cellscontaining LiMn2O4 cathodes [1]. As observed, the concentrationproles always drop in the direction of the cathode, since this isthe ow of the Li+ concentration during the discharge. Note thatduring the rst 25 s (Q = 0.11 A h), the concentration has the larg-est increase among the other proles shown in the Figure. Thiseffect occurs as a result of the kinetic control that operates in thebattery during the rst seconds of discharging. This phenomenonis more clear to observe if the Li+ concentration is plotted as a func-tion of time in the interfaces located between the current collector/anode (Fig. 8a) and cathode/current collector (Fig. 8b). Fig. 8ashows that there is a rise in c (i.e. concentration of Li+ in the elec-trolyte) produced by the deinsertion of Li+ ions from the anode andtheir transference to the electrolyte. Note that the concentrationplotted in Fig. 8 is the concentration of Li+ in the electrolyte andnot in the solid phase, which presents a different behavior. Onthe other hand, the initial decay observed in Fig. 8b results fromthe concentration available to be inserted into the cathode. Theconcentration is higher at the beginning of the test since thereare no mass-transfer limitations in the electrolyte, but once thisoccurs the concentration drops to a steady-state value. The samebehavior is observed for the concentrations shown in Figs. 7 and8a. Apparently, this pseudo-steady state prole is a consequenceof the time constant domain for the diffusion in the battery, whichis long enough to attain this steady state condition [1]. After thisstage, the Li+ concentration proles shown in Fig. 7, particularly

J. Vazquez-Arenas et al. / Energy Converin the anode, show again a rise around 2100 s (Q = 9.93 A h). Ingeneral, this rise is not presented for low-capacity cells or batteriesand could be associated with a faster deinsertion in the anode1960

2000

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c| x=

cc/A

/ mol

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Capacity/ A h

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c| x=

C/cc

/ mol

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(a)

(b)

and Management 87 (2014) 472482 479reactive zones of the electrodes. Fig. 9 shows the Li concentrationat the surface of particles as a function of the length of the anode(Fig. 9a) and the cathode (Fig. 9b). As observed in Fig. 9a at low

depleted capacities (i.e. low depth of discharge (DOD)), most of theconcentration drop occurs in the region close to the separator(Length = 1) as a result of the utilization of the anode mainly at thiszone of the electrode [1]. At intermediate depleted capacity values,other portions of the electrode are utilized as gradients of concen-tration are also generated in the electrolyte. At the end of dis-charge, the concentration proles in the anode present a steady-state behavior as a result of the diffusion control dictating themass-transfer across the particles. On the other hand, Fig. 9b showsthat the concentration proles in the surface of the cathode parti-cle do not develop any drop as a function of the length of the elec-trode. This again conrms the kinetic limitations present in thecathode particles to insert Li+ ions.

3.2. Thermal analysis

The role of temperature is critical on the performance andsafety of the batteries. Particularly for automotive applications,information concerning the thermal distribution across the cell isnecessary to identify local spots that cause thermal overheating,and may lead to battery failure or permanent material degradation.More importantly, the performance and aging of the battery aresignicantly affected by temperature. In order to provide maxi-mum range for as long as possible the battery should be cycledclose to room temperature. Accordingly, one of the motivationsof this work is to explore through experiments and model

development, the temperature rise produced on the surface ofthe battery during a typical discharge of the battery at 1 C. Thisanalysis will not only allow the determination of the individualthermal contributions generated by one battery, but also to inves-tigate the phenomena generating this input. The thermal model ispresented in Table 1, including the energy balances for each sec-tion of the battery (cathode, separator and anode). For the energybalances of the cathode and anode sections, the term on the leftside describes the heat accumulation, the rst term on the rightside corresponds to the heat conduction, the second term repre-sents the heat effect due to electrode reactions, while the thirdto fth terms account for the Joule heating in the solid active mate-rial and electrolyte phases, respectively.

Fig. 10 shows the experimental and modeled temperature pro-les as a function of depleted capacity during a typical discharge ofthe battery at 1 C. As described in the experimental section, fourthermocouples were placed below the tabs on the surface of thebattery (see Fig. 1). The prole shown in Fig. 10 describes the max-imum surface temperature rise. This also agrees with the 1-D

12000

16000

200000.11 1.56 3.11 4.676.22 7.78 9.33 10.8912.44 14 15.55 15.96 A h

24000

mol

m-3

(a)

480 J. Vazquez-Arenas et al. / Energy Conversion and Management 87 (2014) 4724820

8000

16000

1.5 2 2.5

c s / m

ol m

-3

Length of Cathode / dimensionlessS/C C/CC

Fig. 9. Concentration of Li+ inside the particles (cs) across the lengths of the: (a)0

4000

8000

0 0.5 1Length of Anode / dimensionless A/SCC/A

32000

c s /

0.11 1.56 3.11 4.676.22 7.78 9.33 10.8912.44 14 15.55 15.96 A h

(b)anode and (b) cathode at different capacity values. CC/A, A/S, S/C, C/CC represent theinterfaces Current collector/Anode, Anode/Separator, Separator/Cathode and Cath-ode/Current collector, respectively. 1C test.model (e.g. cross-section of the battery) used in this work to modelthe behavior of the Li-ion battery. The thermal properties utilizedin the model are reported in Table 3, and they were determinedthrough tting the model to the experimental data. The parametersdescribing the thermal properties were found to be insensitive tothe model, and as such the condence intervals could not be eval-uated. The parameters reported in Table 2 associated with themass and charge balances in the liquid and solid phase of the bat-tery were maintained xed during the tting of temperature. How-ever, their contributions were allowed to vary with temperature,e.g. De, je. Additionally, some of the parameters (e.g. k, Ds,i) wereconverted in terms of the form described by Arrhenius equation[20]. As observed in Fig. 10, a temperature rise of 4.5 K is producedfor the battery at the end of discharge. Although, this increase isnot signicant for one battery, this situation can become crucialwhen the heat generated for each battery is integrated for theentire battery pack and the batteries are found under quasi-adia-batic conditions.

It is important at this point to highlight two experimentalobservations: (a) that, as previously mentioned, the temperatureincrease reported was the maximum recorded surface battery tem-perature which always occurs near the current collectors (i.e. high-est current) and that other regions of the battery (those locatedaway from current collectors) may experience half or less of thisrise in temperature (further studies will present more detailed

298

299

300

301

302

303

304

0 5 10 15 20

Tem

pera

ture

/ K

Capacity/ A h

Fig. 10. Computed and experimental temperature proles as a function of capacityfor Kokam batteries characterized at a 1-C rate. Symbols describe the experiment

and the continuous line represent the simulations calculated maintaining theparameters reported in Table 2 xed, and tting the temperature properties shownin Table 3.

rou

1

ad a

sionthermal proles for the battery); and (b) that, while the connec-tions to the battery themselves may be a heat source or vectorfor removal of heat from the batteries, the temperature at variouspoints during the charge/discharge periods was probed with aFluke Infra-red thermometer gun and it was consistently foundthat the current-delivering wires were only slightly (0.5 to1 K) colder than the surface of the battery underneath the tabs,but the surface of the battery away from the tabs was at an evenlower temperature (23 K) than the wires. At this point it is knownthat there is a region within the batteries close to the current col-lector tabs which experiences the highest current density and thisregion is therefore the main source of heat (due to high Joule heat-ing). This is due to the contact resistance between the wire and thetab and is the reason why companies are looking for various meth-ods to reduce the amount of heat generated. Further studies willcorroborate this and investigate other possible mechanisms of heatgeneration/propagation, as well as extend the model to a 3Dsimulation.

Note that at the end of discharge, there is an abrupt rise of tem-perature that is not well-predicted by the current model. There areseveral possible reasons why this effect might be observed; it isimportant to highlight that power discrepancies between modeland experiment is not a valid reason as the thermal model predictsvoltage response to a reasonable degree of accuracy and the cur-rent is input into the simulation exactly as it happened on theexperiment. The variation of reaction rates with SOC has alsoalready been accounted for in the model and is therefore unlikelyto be a cause of this effect. Upon analysis of the model parametersit was found that the internal resistance of the battery does notvary according to expectations. Typically, the internal resistancedecreases in the region between 30% and 70% depth of discharge(DOD), increasing slightly toward 0% DOD and signicantly toward100% DOD [72,73]; this being the main reason why companies tendto operate their batteries within the 2080% DOD range.

In the model, the T slope in the entropy term was found to be asignicant factor in determining the behavior of the internal resis-tance with respect to SOC, and it is believed that this term isresponsible for the unexpected variation observed. Due to conver-gence issues, a more accurate T term that matches both the tem-

Table 3Temperature properties in the lithium-ion battery model determined th

Description Anode

Density of the material qn = 3420 kg m3

Heat capacity at constant pressureThermal conductivity kn = 2.51 Wm1 KHeat transfer coefcient

The condence intervals were not determined since the parameters h

J. Vazquez-Arenas et al. / Energy Converperature and voltage proles could not be found; however, it isbelieved that the T term should, in theory, be replaced with a Tay-lor series expansion [53] in this model.

Another observation is that charging and discharging processes(at the same C-rate) exhibit signicant hysteresis in terms of heatgeneration. This contribution is somewhat lower during chargingat the same C-rate (not shown). This gives an insight into theimportance of heat generation terms due to electrode reactions:if the majority of the heat were simply due to a Joule heating effectthen the temperature proles would be expected to be similar(with the slightly higher temperature rise occurring during thecharging step as slightly more energy is delivered to the batteryin this step). Thus it can be concluded from this that during thecharging process there is some endothermic reactions while duringdischarge these reactions are exothermic. It is possible that thisobservation is due to the similar magnitude of endothermic reac-tions in comparison to Joule heating effects and exothermic reac-tions at (a maximum of) 1 C, i.e. relatively low C-rate. It isexpected that this will be less observable at high C-rates (5 C), asthe relative magnitude of the Joule heating will overshadow endo-thermic reactions. A more detailed thermal analysis will be themotivation of a forthcoming study.

4. Conclusions

This study presented a methodology to rapidly determine theparameters of physicochemical models utilized to account for thebehavior of commercial high capacity (16 A h) pouch Li-ion batter-ies (Kokam), such as the pattern of cells (e.g. SOC, State of Health)that would be used in the automotive industry, when chemicalinformation is not available, or for a brand new system. A pseudo2-D model comprised of different contributions reported in the lit-erature was utilized to describe the mass, charge and thermal bal-ances of the cell and porous electrodes; and adapted to the batterychemistry under study. The methodology was based on combinedtting, calculation of condence intervals using the Analysis ofVariance for non-linear models and individual multi-parametricsensitivity analysis as an efcient method to estimate the phenom-ena governing the battery voltage. The model was validated with abattery comprised of carbon anodes and LiNi1/3Co1/3Mn1/3O2(NMC) cathodes. It was found that the kinetics of Li+ insertion inthe cathode controls mostly the battery voltage despite mass andcharge transfer affect the performance of the batteries. A thermalanalysis was also conducted to account for the temperature riseon the surface of the battery. This methodology will be useful foranalysis and understanding of changes in materials in a commer-cial cell, and it can be extended to the analysis of other types ofLi-ion batteries, as well as the evaluation of other phenomenaincluding capacity fade.

Forthcoming studies will be oriented to measure the possiblekinetic parameters of the pouch Kokam batteries through chem-ical and electrochemical measurements, with the intention to eval-uate the accuracy of the values obtained by the present model.

gh tting.

Separator Cathode

qs = 1930 kg m3 qp = 1760 kg m3

Cp,s = 980 J kg1 K1

ks = 1.23 Wm1 K1 kp = 5.63 Wm1 K1

h = 0.025Wm2 K1

low sensitivity to the model.

and Management 87 (2014) 472482 481Acknowledgments

The authors are indebted to the CONACYT (Grant No. 2012-183230) and NSERC Automotive Partnership Canada for theirnancial support to carry out this work.

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A rapid estimation and sensitivity analysis of parameters describing the behavior of commercial Li-ion batteries including thermal analysis1 Introduction2 Materials and methods2.1 Modeling2.2 Experimental set-up

3 Results3.1 Isothermal studies3.2 Thermal analysis

4 ConclusionsAcknowledgmentsReferences