-
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: [email protected], [email protected]
(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
2040
2080
2120
c| x=
cc/A
/ mol
m-3
Capacity/ A h
1960
2000
2040
0 5 10 15 20
c| x=
C/cc
/ mol
m-3
(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.
References
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Electrochem Soc1996;143:1890.
[2] Winter M, Besenhard JO, Spahr ME, Novak P. Adv Mater
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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