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Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015) A1849
Parameterization of a Physico-Chemical Model of a Lithium-Ion
Battery
II. Model Validation
Madeleine Ecker,a,b,zStefan K¨
abitz,a,b Izaro Laresgoiti,a,b and Dirk Uwe Sauera,b,c
aChair for Electrochemical Energy Conversion and Storage Systems, Institute for Power Electronics and Electrical
Drives (ISEA), RWTH Aachen University, 52066 Aachen, Germany
bJuelich Aachen Research Alliance, JARA-Energy, Germany
cInstitute for Power Generation and Storage Systems (PGS) @ E.ON ERC, RWTH Aachen University,
52056 Aachen, Germany
Todraw reliable conclusions about the internal state of a lithium-ion battery or about ageing processes using physico-chemical models,
the determination of the correct set of input parameters is crucial. In the first part of this publication, the complete set of material
parameters for model parameterization has been determined by experiments for a 7.5 Ah cell produced by Kokam. In this part of the
publication, the measured set of parameters is incorporated into a physico-chemical model. Model results are compared to validation
test results conducted on the Kokam cell. The influence of current rate and temperature is considered as well as a comparison with
pulse tests is shown. It is discussed to which extent material parameters obtained by experimental investigation of laboratory coin
cells can be transferred to commercial cells of the same material. The validity of physico-chemical models to describe cells is shown.
© The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons
Attribution Non-Commercial No Derivatives 4.0 License (CC BY-NC-ND, http://creativecommons.org/licenses/by-nc-nd/4.0/),
which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is not changed in any
way and is properly cited. For permission for commercial reuse, please email: oa@electrochem.org. [DOI: 10.1149/2.0541509jes]
All rights reserved.
Manuscript submitted January 13, 2015; revised manuscript received May 14, 2015. Published June 29, 2015.
There are different kinds of models to simulate lithium-ion bat-
teries, each addressing different purposes. Electrical models, based
on simple electric circuit diagrams, are usually used for battery man-
agement systems as they are superior due to their high computing
time efficiency.1Impedance-based models2are more complex, but
are able to provide certain measures of extrapolation as they map
physical processes. They can be coupled to thermal models to de-
sign pack configurations and cooling systems.3Theyarealsousedin
semi-empirical ageing models aiming to predict lifetimes of batteries
in real life applications.4Physico-chemical models on the other hand
are even more complex as they simulate both, the physical and chem-
ical processes based on the fundamental physical principles. Usually,
such models describe the migration and diffusion processes as well as
the charge transfer kinetics. They are not only able to reproduce the
voltage/current behavior of a battery and to make extrapolations; they
also display the internal state of a battery as potential or concentration
distributions. They can therefore be used to gain a better understanding
of the processes occurring inside a lithium-ion battery by providing
much more information than just the terminal voltage. As they are pa-
rameterized by material properties, they help to optimize the material
development process and they support purpose-designed cell devel-
opment processes. The impact of changes in material properties on
the system behavior can be simulated with such models. Also, ageing
mechanisms such as lithium-plating,5formation of solid electrolyte
interphase (SEI)6,7or mechanical stresses8can be addressed. Physico-
chemical models are the only way to elaborate the performance of a
battery cell before it even has been manufactured.
Several papers have been published developing physico-chemical
simulation models that are based on the work of Newman and Tiede-
mann 1975,9amongst others.10–14 Further approaches used elec-
tronic networks to simulate the physical and chemical processes in
batteries.15–17 Also extensions of these models including effects in 2D,
for example temperature distributions, are reported in literature.18,19
However, a key part of physico-chemical models is the model pa-
rameterization. Especially if conclusions about the internal state of
the battery or about ageing effects are to be drawn, the most important
thing is to choose the correct set of parameters for the material under
consideration. To the knowledge of the authors no work modelling
zE-mail: batteries@isea.rwth-aachen.de
lithium-ion batteries exists where a simulation model was completely
parameterized by parameters determined for the special material un-
der consideration using samples taken from the test object. In most
published models, a significant amount of parameters was derived
from literature sources or even just roughly estimated. Only few com-
prehensive parameterization efforts were made. Doyle and Newman
199611 validated a model based on measured values, but did not deter-
mine diffusion coefficients and kinetic parameters for their material.
Less et al. 201220 parameterized a half cell, but did not determine the
kinetic parameters. Furthermore some publications deal with param-
eter determination using nonlinear regression.19,21 Such approaches
can be helpful, if a careful analysis of the parameters is performed for
cases where the battery runs into different limitation effects and if the
correlation feedback is taken into account seriously. However, a re-
gression process is not easy to use and requires a profound knowledge
of the battery behavior and the impact of the considered model pa-
rameters. Furthermore, for lithium-ion batteries parameters exist that
are indeterminate using regression processes on full cell experiments.
Shifting parameters against each other can lead to the same electrical
behavior but completely changes the internal state of the battery. This
is especially the case for the reaction kinetics of the two electrodes
and their activation energies as shown by.19
In most papers dealing with physico-chemical models, values from
supplementary literature sources were taken, bearing the risk of dif-
ferent material properties, due to slight changes in the material. Smart
et al. 201122 for example showed that only small changes in the com-
position of the electrolyte can lead to high changes in the exchange
current density of the system. Especially the parameters determining
the cell kinetic are problematic as either no reliable data are avail-
able in literature or the literature values of the parameters differ by
several orders of magnitudes (see e.g. the discussion of the diffusion
coefficient in part I of this publication23).
In this work, a commercially available cell of unknown design and
material content is considered. In the first part of this publication, the
cell has been opened under argon atmosphere and all material param-
eters relevant to parameterize a physico-chemical model have been
determined by experiment. Parts of the parameters have been deter-
mined building laboratory–made coin cells. In this part of the paper,
a simple electrical model with 1D spatial resolution is introduced and
all parameters measured in the first part are integrated into the model.
A validation of the model including the measured parameters is given.
A1850 Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015)
Subsequently, it is discussed to which extent parameters obtained in
laboratory cells can be transferred to commercial cells of the same
material.
Experimental
For model development, a commercial high energy pouch lithium-
ion battery with 7.5 Ah manufactured by Kokam, labelled SLPB
75106100, was used. The anode consists of graphite, the cathode of
Li(Ni0.4Co0.6 )O2material. A detailed cell description can be found in
the first part of this paper.23
The validation tests for the 7.5 Ah Kokam cell were performed
withacyclingdevicebyDigatron(ECO10A0–6Vormultiple cell
tester 100-06-12 ME, 100 A / 6 V). Temperature was regulated with a
climate chamber (Binder MK53 −40◦Cto+180◦C). The temperature
of the cell was logged using a temperature sensor on the cell surface.
Additionally, the OCV curve for this cell was recorded during a step-
wise charging process, where the OCV was detected after a break of
5 h in each step.
Simulation-Model
In this section, a physico-chemical model is introduced that is able
to simulate the electrical behavior of the lithium-ion battery intro-
duced in Experimental section. In a first step, the complete dynamical
model describing a full cell sandwich is introduced. For validation
purposes, a modification of this model is implemented and discussed
in the following, neglecting all dynamic processes in the battery, only
simulating the open circuit behavior (model for electrode balancing
determination).
Dynamic cell model.— The model relies on the governing physical
and chemical processes in a lithium-ion battery, comprising diffusion
and migration processes in the electrolyte and the solid material as
well as the charge transfer process, and has a 1D spatial resolution. 2D
effects are neglected and an average temperature is assumed for the
simulated cells. The model is able to simulate the externally accessible
voltage Ubatt response of a battery to a given current Ibatt or vice versa
as well as the time evolution of internal parameters of the battery like
local potentials or concentration distribution of lithium ions in the
electrolyte or the active material. It is based on the porous electrode
theory originally derived by Newman and Tiedemann 19759,24 and
applies the equations for a dual lithium-ion insertion cell described by
Fuller et al. 1994.10
The reaction kinetics of the intercalation process is described by
the Butler-Volmer equation. The active material is assumed to consist
of spherical particles. The surface of the particles is used to deter-
mine the reaction surface. The dependency of the exchange current
density of the lithium concentration on the surface of the active ma-
terial particles and in the electrolyte is implemented as described by
Ref. 24. Arrhenius equation is used to model the temperature depen-
dency of the exchange current density. The equations applied in the
model, describing the charge transfer reaction to determine the pore-
wall flux jDbetween electrolyte and active material are summarized
in the appendix. The reaction overpotential ηDis defined as:
ηD=1−2−U−iD·RSEI [1]
1and 2are the potentials in the solid phase and the solution,
respectively.
Urepresents the open circuit potential of the considered electrode
in dependency on the lithium concentration on the surface of the solid
material. The open circuit potential curves have been measured for
the cathode and anode using coin half cell setups.23
The resistance RSEI [] describes the ionic conductivity of the SEI.
This resistance is assumed to be zero for the simulation shown in this
work but can become more important if ageing effects changing the
SEI resistance are considered. In the model considered here, the effect
of the SEI is included directly in the exchange current density (i.e. in
the difference 1–2).
The solid phase potential is determined by Ohm’s law:
j1=−σs·∇1[2]
j1is the current density in the solid phase and σsthe solid phase
conductivity.
The potential in the solution is calculated using:
∇2=j2
σe,eff
+R·T
z·F·1−t+
0·∇ln (ce)[3]
The first term describes the potential drop due to the current density
j2and the ionic conductivity σe,eff, the second term the concentration
overpotential due to concentration gradients in the electrolyte. Ris the
gas constant, Tthe temperature, zthe charge number (for lithium-ion
battery z=1) Fthe Faraday constant, t0+the transport number and
cethe electrolyte concentration. The activity coefficient is assumed to
be constant.
σe,eff reflects the ionic conductivity of the electrolyte inside the
porous structure of the electrodes and is dependent on the lithium
concentration in the electrolyte and on temperature. The concentration
dependency of the ionic conductivity of the bulk electrolyte σehas
been measured in the first part of this publication.23 The resulting
fitting function is given in Table II. However, the effective conductivity
σe,eff in a porous structure differs from the conductivity of the bulk
electrolyte σeand is described using the tortuosity factor κand the
porosity εof the material:
σe,eff =σe·ε
κ
[4]
The temperature dependency of the electrolyte conductivity is
modelled using the Arrhenius equation.
The divergence of current density in the electrolyte j2is related to
the pore wall flux jDby:
a·jD=∇j2[5]
where ais the ratio between the contact area between electrode and
electrolyte and the considered volume.
The double layer capacity of the battery is neglected in this model
as it only contributes to the voltage on very small time constants (in the
range of ms). Ong et al. 199925 integrated a double layer capacity into
a physico-chemical model. They showed that a double layer capacity
leads to a smoother transition toward the maximum potential at a given
current.
Finally, the lithium concentration on the surface of the solid ma-
terial cs,sur as well as in the electrolyte ce, these concentrations have
to be determined as well. Therefore, a model system is assumed, con-
sisting of spherical active mass particles. The particles are assumed to
have electrical contact but no inter-particle diffusion. Neglecting the
effects of stress and anisotropic diffusion and assuming that the active
material is a good electronic conductor (transport number t−≈1), the
diffusion in the solid material can then be described by Fick’s second
law converted to spherical coordinates:
dcs
dt=1
r2·d
drDs(cs)·r2·dcs
dr[6]
ris the radius and Ds(cs) the concentration-dependent diffusion con-
stant of the solid material. On the surface of the particles the change
in concentration is determined by diffusion as well as by the charge
transfer current density jD, leading to the boundary condition:
dcs
dr
r=R
=− jD
Ds·Fandinthecore: dcs
dr
r=0
=0[7]
Finally, to determine the concentration in the electrolyte the diffu-
sion processes within the electrolyte have to be simulated. To model
the porous electrode it is assumed that the space between the spheri-
cal particles is filled with inactive materials and electrolyte and has a
certain tortuosity factor κand a porosity ε. Therefore, the diffusion in
this porous structure proceeds with an effective diffusion coefficient
Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015) A1851
De,eff (similar to Equation 4) according to26
De,eff =D·ε
κ
[8]
For battery systems, usually concentrated solution theory is applied
deviating from dilute solution theory by incorporating the interaction
between the ions as well. This interaction is described by Stefan-
Maxwell multicomponent diffusion. Applying the continuity equation
of mass and charge, the Stefan-Maxwell diffusion can be used to derive
an expression describing the change in lithium ion concentration with
time in a binary electrolyte:
dce
dt=1
ε
·∇De,eff ·∇ce+1−t+
0
F·ε
·a·jD[9]
with zero flux at the current collectors:
dce
dt
x=0andx=l
=0 [10]
De,eff is the effective value of the chemical diffusion coefficient of
the electrolyte in the porous structure and t0+is the transport number
for Li+in this electrolyte with respect to solvent velocity. It describes
the contribution of the lithium ions to the total migration current. ais
the ratio between the contact area between electrode and electrolyte
and the considered volume. In Equation 9convection is neglected and
t0+is assumed to be constant with concentration. Furthermore, poros-
ity is assumed not to change with time. This is true as long as no ageing
of the system is considered and the porosity change due to the volume
change is neglected. It is additionally assumed that dln(c0)/dln(ce)=0,
where c0is the solvent concentration. Finally, Equation 9resembles
the diffusion equation derived by dilute solution theory. A detailed
derivation of transport equations in dilute and concentrated solution
theory can be found in.27
The balancing of the system is determined by the start concentra-
tion of the anode csn,start and the cathode csp,start in the model. In Figure 1
the active material concentrations of cathode and anode are outlined
for a cell directly after fabrication (upper figure) and in a charged state
after the first formation cycles (lower figure). Prior to the first forma-
tion cycle, the anode consists of pure graphite (without lithium) and
the cathode contains the maximum possible amount of lithium csp,max.
Usually the lithium in Li(Ni0.4Co0.6 )O2- based cathode materials is
only used partly due to the low stability of lithium poor phases.28 In
Figure 1. Scheme of the active material concentration in anode and cathode
directly after fabrication (upper figure) and in the charged state after the first
initialization cycles. For a charged cell, csn,start and csp,start are used as start
concentrations.
the following, the used percentage of lithium in the cathode is called
‘utilization’. During the first charge process, the lithium is deinterca-
lated from the cathode and intercalated partly to the anode, the other
part is irreversibly consumed in SEI formation (CSEI). Therefore, a
cell in charged state has the following concentrations:
csp,start=(1−utili zation)·csp,max [11]
csn,start =(utili zati on −CSEI)·csp,max
·Vp·1−εp·1−inactivepart,p
Vn·(1−εn)·1−inactivepart,n[12]
Vdenotes the volumes of the electrode coatings, εthe porosities and
inactivepart fraction of inactive material in the electrodes. For a cell in
a discharged state one obtains:
csp,start =(1−CSEI)·csp,max [13]
csn,start =0 [14]
The theoretical maximal concentration of an active material parti-
cle cs,max can be calculated by the density ρand the molar mass Mof
the intercalation compound LiC6or Li(Ni0.4Co0.6 )O2:
cs,max =ρ
M[15]
Model for cell balancing determination.— The model for cell bal-
ancing determination is a simplification of the dynamic cell model
described in Dynamic cell model section where all dynamical pro-
cesses are neglected. Hence, the model consists of one active material
particle for each electrode where lithium can accumulate, without
modelling the diffusion or the intercalation process itself. It serves
as a tool to validate the balancing of the electrodes by comparing
the simulated OCV curves with measured ones (see Model-Validation
section). For each electrode, the open circuit voltage in dependency
on the amount of intercalated lithium is provided. A given current
directly changes the lithium content of the anode and cathode particle
and therefore the OCV. The balancing of the two electrodes is deter-
mined by the utilization of the cathode, the amount of formed SEI and
the capacity of the active materials. The latter is calculated from the
geometrical dimensions of the two electrodes, the theoretical capacity
of the active materials, the amount of inactive material in the elec-
trodes and their porosity (see Equations 11 and 12). The parameters
needed for model parameterization are listed in Table I.
Model-Parameterization: Summary of the Measured Parameters
In this section, the measured model parameters are summa-
rized. The parameters have been measured in the first part of
this publication23 by post-mortem analysis of Kokam cells (SLPB
75106100). Hg-porosimetry as well as conductivity measurements
have been conducted. Electrochemical measurements have been per-
formed on laboratory-made coin cells in order to determine open
circuit voltage curves, diffusion coefficients and the charge transfer
kinetics of the active materials as well as the balancing of the system.
For all measurements, an electrolyte produced by BASF (LP50) has
been employed. This electrolyte has been assumed to be most similar
to the one of the original system, even though the exact composi-
tion of this system is unknown. In Table I, the measured parameters
determining the balancing of the system are given. In some cases a
deviation from the measured parameter is identified in order to obtain
an agreement between experimental and simulation results. Therefore
also the parameter values finally used for the simulation of the Kokam
cell are listed. If no model value is given, the parameters are used
as measured originally. Deviations of the model parameter from the
measured value are discussed in Model-validation section. In Table II,
the parameters determining the dynamic behavior of the system are
A1852 Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015)
Table I. Model parameter for the model for cell balancing determination. The measured values as well as the values finally used in the Kokam cell
simulation are listed. If no model value is given, the parameters are used as measured originally. All parameters were measured at a temperature
of 23◦C.
Abbreviation Description Unit Measured value Final model value
wcell,p width of cathode of Kokam cell μm85·103
wcell,n width of anode of Kokam cell μm87·10385 ·103
hcell,p length of cathode of Kokam cell μm 101 ·103
hcell,n length of anode of Kokam cell μm 103 ·103101 ·103
Dxpthickness of cathode μm 54.5±0.5
Dxnthickness of anode μm 73.7±1
Dxsthickness of separator μm19
εpporosity of cathode % 29.6±0.7
εnporosity of anode % 32.9±0.5
εsporosity of separator % 50.8±2
inactivepart,p inactive part of cathode % 39.17 42
inactivepart,n inactive part of anode % 40.37 44.5
csn,max calculated maximal possible lithium concentration in an anode particle mol/dm331.92
csp,max calculated maximal possible lithium concentration in a cathode particle mol/dm348.58
CSEI capacity loss due to initial SEI % 14 6.8
utilization degree of utilization of cathode material % 74
OCVpOCV vs. ×of cathode V See Figures 3–6in Ref. 23
OCVnOCV vs. ×of anode V See Figures 3–5in Ref. 23
Vmax maximal voltage V 4.2
Vmin minimal voltage V 2.7
given. Furthermore, the measured values as well as the values fi-
nally used in the simulation are listed and deviations are discussed in
Model-Validation section.
Model-Validation
In this chapter, all parameters are incorporated into the models
described in Simulation-model section to simulate the commercially
available 7.5 Ah Kokam cell. It is investigated whether parameters
obtained from coin cell setups23 can be transferred to the original
system. The simulations are compared with validation experiments
performed at different temperatures. The temperature on the surface
of the cell, measured by a sensor, is given to the model to include cell
heating in the simulation.
First, an OCV curve at 25◦C is used to validate the balancing of
the cell. Measurement results are compared with results obtained by
Table II. Model parameters for the dynamic model. The measured values as well as the values finally used in the Kokam cell simulation are listed.
If no model value is given, the parameters are used as measured originally. All parameters were measured at a temperature of 23◦C.
Abbreviation Description Unit Original values
Final model
values
rpparticle radius of cathode μm6.49±0.1
rnparticle radius of anode μm8.7±0.9 13.7
κptortuosity factor of cathode 1.94±0.006
κstortuosity factor of separator 1.67±0.02
κntortuosity factor of anode 2.03±0.006
Ds,p diffusion coefficient of cathode cm2/s see Figures 3–9in Ref. 23
Ds,n diffusion coefficient of anode cm2/s see Figures 3–9in Ref. 23
j0,p exchange current density of cathode at 50% SOC A/cm22.23 ·10−4
j0,n exchange current density of anode at 50% SOC A/cm27.05 ·10−55.39 ·10−4
αptransfer coefficient of cathode 0.527
αntransfer coefficient of anode 0.489
σs,p electronic conductivity of cathode S/cm 0.681±0.44
σs,n electronic conductivity of anode S/cm 0.14±0.03
Dediffusion coefficient of electrolyte cm2/s 2.4 ·10−6
t0+transport number of electrolyte literature value30:0.26
σeionic conductivity of electrolyte S/cm σe=2.667 ·c3
e−12.983 ·c2
e+17.919 ·ce+1.726
if 0.5≤x≤1.5
σeis the electrolyte conductivity in [mS/cm] and cethe salt
concentration in [mol/l]
Ea,Dsp activation energy of diffusion coefficient of cathode J/mol 80.6 ·103
Ea,Dsn activation energy of diffusion coefficient of anode J/mol 40.8 ·10330.3 ·103
Ea,De activation energy of diffusion coefficient of
electrolyte
J/mol 17.1 ·103
Ea,j0p activation energy of exchange current density of
cathode
J/mol 43.6 ·103
Ea,j0n activation energy of exchange current density of
anode
J/mol 53.4 ·103
Ea,σeactivation energy of ionic conductivity of electrolyte J/mol 17.1 ·103
Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015) A1853
0 2 4 6 8
2.5
3
3.5
4
4.5
Voltage [V]
Discharge Capacity [Ah]
(a)
-1
0
1
2
3
Error [%]
Simulation
Measurement
Error
0 2 4 6 8
2.5
3
3.5
4
4.5
Voltage [V]
Discharge Capacity [Ah]
(b)
-1
0
1
2
3
Error [%]
Simulation
Measurement
Error
Figure 2. Comparison of a simulated and measured OCV curve of a 7.5 Ah Kokam cell at 25◦C. The simulation error is displayed on the right axis. (a): Simulation
performed with the measured set of model parameters, (b): Simulation performed with an adapted set of model parameters determining the balancing (see Table
II). The inactive parts of anode and cathode are increased from 39.17% to 42% and from 40.37% to 44.5%, respectively, the oversize of the anode is neglectedand
the capacity loss due to SEI is decreased from 14% to 6.8%.
the model for cell balancing determination introduced in Model for
cell balancing determination section. Figure 2a displays a comparison
of the model results using the measured parameter set (see Table I)
with measurement results. The graph shows that the capacity of the
cell is not reproduced accurately by the model. To match simulation
and experiment, the inactive part of the anode and cathode material
determined in23 is adapted from 39.19% to 42% and from 40.37% to
44.5% for the cathode and the anode, respectively. The inactive part
of the material is an arguable parameter that has high uncertainty in its
determination (see Ref. 23). Therefore, it seems to be justified to make
these small changes. A second set of parameters that has to be adapted
in order to reproduce the OCV curve are the geometrical dimensions
of the anode. To prevent lithium plating, the anode is designed to be
larger compared to the cathode (2 mm in width and 2 mm in length).
Therefore, the anode is not completely covered by a cathode in the
cell. It is feasible that the part of the anode that is not covered by a
cathode is not completely used in the system. Therefore, the anode
is assumed to have the same size as the cathode. Furthermore, the
capacity loss due to SEI has been measured in a coin cell setup. It is
therefore likely that during cell disassembling, removal of the coating
and reassembling in a coin cell, the SEI of the anode material gets
destroyed in some way and reforms during the first cycles in the coin
cell to a SEI with a potentially different structure. The formation of a
new structure is probable as it is not clear whether the same electrolyte
has been used for parameterization measurement as the one employed
in the original system. The results of the first two formation cycles
of coin full cells show that for these cells indeed about 6% of the
capacity go into a side reaction during the first two formation cycles.
This leads to the fact that in a coin cell additional lithium is lost for the
system, which is reflected in a higher value for CSEI (capacity loss due
to SEI). Thus, the measured value of CSEI is lowered in the following.
Figure 2b shows the simulation result obtained using the discussed
adaptation of the parameters which is summarized in Table I.Withthe
change in the inactive part of the material, the geometrical dimensions
of the anode and the amount of lithium lost in SEI formation, the
measured OCV curve can be reproduced perfectly. In the following
simulations, these parameters are used and addressed to as the final
set of parameters determining the balancing.
In a second step, all measured dynamic parameters of the Kokam
cell listed in Table II are implemented into the dynamical cell model
where the current is scaled according to the number of active material
layers. Figure 3a shows simulation results obtained with the measured
set of dynamical model parameters. The parameters determining the
balancing are adjusted according to the discussion above. The simula-
tion is compared to a measured discharge curve with 1 C at 25◦C. The
model reproduces the experimental results well, but an offset is visible
at begin of discharge. This offset seems to be due to a deviation in the
charge transfer, which has been determined in a coin cell setup. As
discussed before, it is likely that during cell disassembling, removal of
the coating and reassembling in a coin cell, the SEI of the anode ma-
terial gets destroyed and reforms during the first cycles in the coin cell
to a SEI with a potentially different structure, especially if a different
electrolyte is used in the setup compared to the original system. With
a different structure the SEI resistance changes as well. As SEI is cou-
pled to the charge transfer resistance in the model, a changed exchange
current density of the anode due to changed SEI resistance is likely.
Smart et al. 201122 also showed that changes in electrolyte composi-
tion lead to high changes in exchange current density of the anode due
to differences in SEI formation, whereas the exchange current density
of the cathode is found to be only marginally affected by a change
in electrolyte. In Figure 3b simulation results obtained by changing
the exchange current density of the anode from 7.05 ·10−5A/cm2to
5.39 ·10−4A/cm2are shown. All other parameters are fixed as be-
fore. The beginning of the 1 C discharge curve at 25◦C can now be
reproduced well by the model. This is important for the short-term
behavior of the cell, which is of great concern in applications like elec-
tric vehicles. Therefore, the new exchange current density is used for
the following simulations. However, there still seems to be a problem
with the limitation of the cell at the end of the discharge. According
to Arora et al. 200012 limitations during dynamic discharge are due
to diffusion effects. For high rate discharge they found the solution-
phase limitation being the major limiting factor. But also solid state
diffusion can limit the capacity of the cell. Ender 201529 showed that
solid state diffusion limitations can decrease the simulated capacity
of a cell, when taking the distribution of particle size into account
instead of using an average particle size. In the case of the Kokam
cell considered in this work, the Hg-porosimetry conducted in23 re-
vealed a distribution including two particle sizes for the anode as well
as for the cathode. Especially for the anode a considerable amount
of volume is represented by particles of a radius around 40 μm. To
account for the stronger limitation due to this distribution, the anode
particle radius is increased from 8.7 μm to 13.7 μm in the follow-
ing. The final parameter that is adjusted in order to obtain a good
agreement between simulation and experiment is the activation en-
ergy of solid state diffusion. As discussed in,23 uncertainties occurred
in the determination of the activation energy of solid state diffusion
depending on the method (i.e. EIS and GITT). Starting with the val-
ues obtained from EIS measurement, the activation energy of solid
state diffusion of the anode is adapted to achieve the best agreement
between measurement data and simulation results. Considering dis-
charge curves with different current rates at different temperatures,
the best results are obtained using the value of Ea,Dn =30.3 kJ/mol
for graphite. The activation energy of the Li(Ni0.4Co0.6)O2mate-
rial is kept as obtained by the EIS measurement. The measured
A1854 Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015)
00.5 11.5
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
Voltage [V]
Time [h]
0
1
2
Error [%]
Simulat ion
Measurement
Error
(a)
original dynamic
parameters
1C, 25°C
00.5 11.5
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
Voltage [V]
Time [h ]
0
1
2
Error [%]
Simulat ion
Measurement
Error
(b)
j
0,n
=5.39*10
-4
A/cm²
1C, 25°C
00.5 11.5
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
Voltage [V]
Time [h]
0
1
2
Error [%]
Simulat ion
Measurement
Error
(c)
final parameter set
1C, 25°C
Figure 3. Comparison of a simulated and measured discharge curve of a 7.5 Ah Kokam cell with 1 C at 25◦C. The simulation error is displayed on the right axis.
(a): Simulation performed with the measured set of model parameters, (b): Simulation performed with an increased exchange current density of the anode from
7.05 ·10−5A/cm2to 5.39 ·10−4A/cm2(see Table II). (c): Simulation performed with an increased exchange current density of the anode from 7.05 ·10−5A/cm2
to 5.39 ·10−4A/cm2, an increased particle radius of the anode from 8.7 μm to 13.7 μm and a decreased activation energy of the solid state diffusion of the anode
from 40.8 kJ/mol to 30.3 kJ/mol (see Table II). In all cases the parameters determining the balancing are adjusted according to the discussion above.
Table III. Activation energies for solid state diffusion coefficients
obtained by different measurement techniques, literature and
model fitting.
GITT EIS Literature
Best fitting
value
Graphite 48.9
kJ/mol
40.8
kJ/mol
35
kJ/mol 31
30.3
kJ/mol
Li(Ni0.4Co0.6 )O231.7
kJ/mol
80.6
kJ/mol
- 80.6
kJ/mol
activation energies as well as literature values and the values obtained
by model fitting are summarized in Table III. The final set of dynami-
cal parameters for the 7.5 Ah Kokam cell is listed in Table II. Figure 3c
shows simulation results for the 1 C discharge at 25◦C obtained with
this final set of dynamical model parameters. The model reveals a
good agreement with the measured data, with a maximum error below
0.9%.
The final set of parameters is further used to simulate discharge
curves at different C rates, charge and discharge curves as well as
pulse profiles. In Figure 4a, simulation results of discharge curves
with different current rates at 25◦C are compared with experimental
results of a 7.5 Ah Kokam cell. The model shows a good agreement
with the measured data. Likewise, the 1 C charge-discharge curve
(constant current charge, followed by a constant voltage phase, a 1 h
break and a constant current discharge), shown in Figure 4b, can be
reproduced by the model. Figure 5shows the comparison between
model and experimental results during a 1 C discharge to 50% SOC
followed by a pulse profile using pulses with different currents and of
0 2 4 6 8
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
Discharge Capacity [Ah]
Voltage [V]
5C simulation
5C measurement
3C simulation
3C measurement
1C simulation
1C measurement
0.25C simulation
0.25C measurement
(a)
25°C
0 1 2 3 4
2.5
3
3.5
4
4.5
Time [h]
Voltage [V]
Simulation
Measurement
(b)
25°C, 1C
Figure 4. (a): Comparison of simulated and measured discharge curves of the 7.5 Ah Kokam cell at 25◦C and different C rates. (b): Comparison of a simulated
and measured charge-discharge curves at 25◦C and 1 C. The charging process consists of a constant current, followed by a constant voltage phase. A break of 1 h
is made before discharge. All simulations are performed with the final set of parameters listed in Table Iand Table II.
Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015) A1855
0 2 4 6 8
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
Time [h]
Voltage [V]
Simulation
Measurement
(a)
25°C
44.5 55.5
3.7
3.75
3.8
3.85
Time [h]
Voltage [V]
Simulation
Measurement
(b)
Figure 5. Comparison of a simulated and measured pulse profile after a 1 C discharge to 50% SOC of the 7.5 Ah Kokam cell at 25◦C. Pulses with different
current rates (0.25 C, 0.5 C, 1 C and 1.3 C) and different durations (10 s and 100 s) are compared. (b) shows a zoom of (a) to display the pulses in more detail.
All simulations are performed with the final set of parameters listed in Table Iand Table II.
0 5 10 15 20 25
3
3.5
4
4.5
Time [h]
Voltage [V]
Simulation
Measurement
(a)
25°C
6 7 8 9 10 11
3.7
3.75
3.8
3.85
3.9
3.95
Time [h]
Voltage [V]
Simulation
Measurement
(b)
Figure 6. Comparison of a simulated and measured pulse profile of the 7.5 Ah Kokam cell at 25◦C. Pulses at different SOC, with different current rates (0.25 C,
0.5 C, 1 C and 1.3 C) and different durations (10 s and 100 s) are compared. (b) shows a zoom of (a) to display the pulses in more detail. All simulations are
performed with the final set of parameters listed in Table Iand Table II.
different durations. The relaxation after the discharge is reproduced
well by the model. The short-term behavior of the cell during the pulses
can also be reproduced by the model. The maximum error occurring
between simulation and measurement is 2.1%. Finally, the simulation
results of pulses at different SOC are compared with experimental
data as well. The results are shown in Figure 6. Here, the model is
also able to simulate the long term discharge curves as well as the
short term pulses of the cell, which a maximal error of 2.4%.
To validate the Arrhenius approach and the activation energies,
simulation results at different temperatures are also compared with
experimental data. Figure 7a shows measured and simulated discharge
curves conducted with 1 C at different temperatures. The temperature
dependency of the exchange current density seems to be reproduced
accurately. No severe offset occurs at begin or during discharge. The
solid state diffusion of the anode limits the capacity obtained at end
of discharge. The new value of the activation energy seems to be
00.5 11.5
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
Time [h]
Voltage [V]
40 °C simulation
40 °C measurement
25 °C simulation
25 °C measurement
0 °C simulation
0 °C measurement
-10 °C simulation
-10 °C measurement
(a)
1C
0 2 4 6 8
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
Discharge Capacity [Ah]
Voltage [V]
1.3C simulation
1.3C measurement
0.5C simulation
0.5C measurement
0.25C simulation
0.25C measurement
(b)
-10°C
Figure 7. (a): Comparison of simulated and measured discharge curves of the 7.5 Ah Kokam cell with 1 C at different temperatures. (b): Comparison of simulated
and measured discharge curves of the 7.5 Ah Kokam cell at −10◦C and different C rates. All simulations are performed with the final set of parameters listed in
Tab l e Iand Table II.
A1856 Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015)
0 2 4 6 8
3.2
3.4
3.6
3.8
4
4.2
Time [h]
Voltage [V]
Simulation
Measuremen t
(a)
-10°C
44.5 55.5
3.2
3.4
3.6
3.8
4
4.2
Time [h]
Voltage [V]
Simulation
Measurement
(a)
Figure 8. Comparison of a simulated and measured pulse profile after a 1 C discharge to 50% SOC of the 7.5 Ah Kokam cell at −10◦C. Pulses with different
current rates (0.25 C, 0.5 C, 1 C and 1.3 C) and different durations (10 s and 100 s) are compared. (b) shows a zoom of (a) to display the pulses in more detail.
All simulations are performed with the final set of parameters listed in Table Iand Table II.
00.2 0.4 0.6 0.8 1
0
5
10
15
20
25
30
Concentration for Different Particle Radii of Anode
Time [h]
Lithium Concentration [mol/dm³]
(a)
Increasing
Particle Radius
-10°C, 1C,
discharge
00.2 0.4 0.6 0.8 1
10
20
30
40
50
Concentration for Different Particle Radii of Cathode
Time [h]
Lithium Concentration [mol/dm³]
Increasing
Particle Radius
(b)
-10°C, 1C,
discharge
Figure 9. Simulated lithium concentration within the active material on the separator during a 1 C discharge at −10◦C spatially resolved over the particle radius.
(a) Anode. (b) Cathode.
reasonable as the capacities are predicted quite well at different tem-
peratures. The solid state diffusion of the cathode only models the
shape of the discharge curve. The activation energy obtained by EIS
seems to be the proper value as also the shapes of the curves are re-
produced well for different temperatures. Overall, the model is able
to simulate the temperature dependency of the battery.
In the following, the low temperature behavior is investigated in
more detail. Figure 7b displays measured and simulated discharge
curves at −10◦C with different current rates. The dependency on
current rate at low temperature is reproduced well by the model.
050 100 150
0.6
0.8
1
1.2
Electrolyte Concentration
Length [µm]
Lithium Concentration [mol/dm³]
1min
3min
20min
EOD (58min)
-10°C, 1C
discharge
Anode
Separator
Cathode
Figure 10. Simulated lithium concentration within the electrolyte during a
1 C discharge at −10◦C spatially resolved over the cell stack.
Figure 8investigates the relaxation and short-term behavior of the cell
at −10◦C. Again, a simulation of a 1 C discharge to 50% SOC followed
by a pulse profile using pulses with different currents and of different
durations is compared to experimental results. For low temperatures,
the model is also able to reproduce the relaxation after the discharge
as well as the short term behavior of the cell during the pulses.
Finally, the internal state of the cell during a 1 C dischargeat −10◦C
is analyzed in Figure 9and Figure 10. Figure 9displays the simulated
lithium concentration within an active material particle close to the
separator. Sever gradients can be observed over the particle radius for
the anode as well as for the cathode due to diffusion limitations at these
conditions. The concentration gradients provoke the observed drop of
the voltage and limit the cell capacity compared to the static case.
Concentration gradients also evolve within the electrolyte as shown
in Figure 10. Within the first 3 min of discharge a maximum gradient
is established over the cell stack. However, during further discharge
the cell heats up and the gradient decreases again. The concentration
gradient within the electrolyte contributed to the voltage drop as well.
Conclusions
In the first part of this publication,23 all parameters necessary to
fully parameterize a physico-chemical model have been determined
experimentally for a 7.5 Ah pouch cell produced by Kokam. The
measured values are summarized in Table Iand Table II. The model
parameters have been used for a model validation in this work.
The measured parameters have been integrated in a simple physico-
chemical model to reproduce the dynamical behavior of the 7.5 Ah
Journal of The Electrochemical Society,162 (9) A1849-A1857 (2015) A1857
cell. The model results have been compared with discharge curves at
different current rates and temperatures as well as pulse profiles. The
activation energy of the solid state diffusion has been identified to be
a critical parameter as different measurement techniques reveal val-
ues deviating strongly from each other. Fitting model to experimental
results suggests that activation energies obtained by electrochemical
impedance spectroscopy are more suitable for model parameteriza-
tion. However, future research on adequate measurement technics to
determine activation energies of the solid state diffusion for battery
materials is necessary. The comparison of model and validation test
results also reveals that additional SEI has been formed in the coin cell,
probably due to SEI destruction during the disassembling/assembling
process. Therefore, the amount of lithium irreversibly lost in the SEI
as well as the exchange current density (also dependent on the SEI)
measured by coin cells have to be adjusted to simulate the 7.5 Ah
cell. Furthermore, an increase in the measured average particle size of
the anode material is necessary to reproduce the capacity limitations
during higher discharge rates. This adjustment accounts for the sim-
plification of the model that neglects the particle distribution inside
the active material. With these adjustments, the model is able to repro-
duce the current dependency as well as the temperature dependency
of the cell during usage.
The results show that a physico-chemical model of a commercially
available cell can be parameterized using coin cell measurements
making some physically motivated adjustments. With the derived set
of parameters, the model is able to make quantitative predictions about
the internal state of the battery during cycling. Furthermore, it can also
be used to draw conclusions about ageing processes occurring in the
cell, and it can be used to predict the performance of batteries made
from the characterized materials in arbitrary cell designs.
Acknowledgment
This work has been performed in the framework of the research
initiatives “Modellierung von Lithium-Plating”, “HGF Energie Al-
lianz” and “KVN”. “Modellierung von Lithium-Plating” with the IGF-
number LN 15 was a project of the Research Association FKM, Lyon
Straße 18, 60528 Frankfurt am Main and was financed via the AiF
within a program to promote industrial research (IGF) by the Federal
Ministry of Economic Affairs and Energy based on a decision by the
German Bundestag. “HGF Energie Allianz” was funded by Impuls-
und Vernetzungsfond der Helmholtz-Gemeinschaft e.V. “KVN” was
funded by the German Federal Ministry for Education and Research,
funding number 13N9973. Responsibility for the content of this pub-
lication lies with the authors.
Appendix
Charge transfer.— The reaction kinetics of the intercalation process is calculated
by applying the Butler-Volmer equation which describes the relation between reaction
overpotential ηDand the current going into the reaction iD:
jD=iD
S=j0·exp α·z·F
R·T·ηD+(exp −(1−α)·z·F
R·T·ηD [A1]
j0is the exchange current density, αthe transfer coefficient, zthe charge number (for
lithium-ion battery z=1), Tthe temperature, Rthe gas constant and Fthe Faraday
constant. Sis the reaction surface. For an porous intercalation electrode Scorresponds
to the contact area between electrode and electrolyte is calculated by the total electrode
volume Velectrode, the porosity ε, the inactive part of the material, the volume of a single
active material particle (assumed to be spherical) V1particle and the particle radius rparticle,
following:
S=Velectrode ·(1−ε)·1−inactivepart
V1particle
·4·π·r2
particle [A2]
For a lithium metal electrode the reaction surface is given by the pure geometrical
area of the electrode. For a porous intercalation electrode the dependency of the exchange
current density on the lithium concentration on the surface of the solid cs,sur and the
lithium concentration in the electrolyte ceis described by:24
j0=F·k0·cs,max −cs,sur(1−α)·cα
s,sur ·cα
e[A3]
(cs,max-cs,sur ) is the concentration of unoccupied sites in the intercalation lattice and k0a
proportionality factor.
The temperature dependency of the exchange current density is modeled using Ar-
rhenius equation:
j0(T)=j0(T=296.15 [K])·e
Ea,j0
R·1
296.15[K]−1
T[A4]
Ea,j0 is the activation energy of the charge transfer reaction and 296.15 K is the reference
temperature the parameterization measurements were conducted at Ref. 23.
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