Conference PaperPDF Available

Analyzing calendar aging data towards a lifetime prediction model for lithium-ion batteries

Authors:

Abstract

For a reliable integration of batteries into the vehicle, knowledge about battery behavior and especially the lifetime of the battery in the application is indispensible. This work aims at the development of a lifetime prediction approach based on an aging model for lithium-ion batteries. Extended accelerated lifetime tests are performed at different temperatures and states of charge (SOC) to investigate the impact of these conditions on the impedance rise and capacity loss. The results are used to find mathematical expressions describing the impact of storage time, temperature and voltage on aging, to build up a model coupling an impedance-based electric-thermal part with a semi-empirical (physically motivated) aging model. Based on these models different drive cycles, use patterns and management strategies can be analyzed with regard to their impact on the lifetime. This is an important tool for vehicle designers and for the implementation of business models. The strength of this paper is the good data basis and the detailed modeling approach.
EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 1
EVS26
Los Angeles, California, May 6-9, 2012
Analyzing Calendar Aging Data towards a Lifetime
Prediction Model for Lithium-Ion Batteries
M. Ecker1, J. B. Gerschler, J. Vogel, S. Käbitz, F. Hust, P. Dechent, D. U. Sauer
1 Madeleine Ecker (corresponding author) Institute for Power Electronics and Electrical Drives (ISEA), RWTH
Aachen University, Jaegerstrasse 17-19, D-52066 Aachen, Germany, er@isea.rwth-aachen.de;
(batteries@isea.rwth-aachen.de)
Abstract
For a reliable integration of batteries into the vehicle, knowledge about battery behavior and especially the
lifetime of the battery in the application is indispensible. This work aims at the development of a lifetime
prediction approach based on an aging model for lithium-ion batteries. Extended accelerated lifetime tests
are performed at different temperatures and states of charge (SOC) to investigate the impact of these
conditions on the impedance rise and capacity loss. The results are used to find mathematical expressions
describing the impact of storage time, temperature and voltage on aging, to build up a model coupling an
impedance-based electric-thermal part with a semi-empirical (physically motivated) aging model. Based on
these models different drive cycles, use patterns and management strategies can be analyzed with regard to
their impact on the lifetime. This is an important tool for vehicle designers and for the implementation of
business models. The strength of this paper is the good data basis and the detailed modeling approach.
Keywords: Lithium-ion, aging, lifetime prognosis, battery model, HEV
1. Introduction
Lifetime prediction for lithium-ion batteries
under real operation is a key issue for a reliable
integration of the battery into the vehicle and for
warranty issues. As aging tests using real
operation conditions are very time and cost
intensive, accelerated aging tests are discussed to
be a powerful method. To extrapolate data
obtained from accelerated aging test to real life
conditions, aging models are required. So far
simple model approaches for lifetime predictions
have been reported in literature, like e.g.
approaches based on neuronal networks [1].
These approaches usually lack the ability to
make extrapolations to conditions that were not
used in the learning test set. This work aims to a
more physically based approach, able to
extrapolate the data from accelerated aging tests to
get real life condition lifetime predictions.
Aging in lithium-ion batteries leads to increase of
inner resistance, capacity and power loss as well as
to changes in impedance spectra due to
electrochemical and mechanical processes. Aging
strongly depends on temperature, SOC or rather
electrode potential, cycling depth and charge
throughput [2-4]. Few studies are reported in
literature, investigating the calendar and cycle life
of different cells using large test matrixes [4-7].
These studies illuminate the aging characteristics
of lithium-ion batteries. But so far, this knowledge
has not been utilized to develop an aging model
that is able to predict the lifetime cycle of real
application. Aging models based on mathematical
functions obtained from extended aging tests can
be directly linked to impedance-based models,
EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 2
which determine electrical and thermal behavior
of the battery [8, 9]. Coupling of impedance-
based thermo-electrical battery models with
aging models enables investigation of the
dynamical interaction between thermal, electrical
and aging behavior of the battery. A higher
temperature for example causes a faster aging
and therefore a faster increase in the inner
resistance, affecting the electrical performance of
the battery. These relations have been
investigated in [10] but lacking a profound
parameterization of the developed model using
aging test results. This work will focus on the
parameterization of the aging model by
experimental data using extended aging test
results.
2. Experimental
To parameterize impedance-based aging models,
extensive aging tests are necessary. In this work
a lithium-ion high power pouch cell with a
nominal capacity of 6 Ah and a nominal voltage
of 3.6 V was used. The anode consists of hard
carbon, the cathode of LiNi1/3Mn1/3Co1/3O2
(NMC) as active material. Cells with similar
characteristics are typically used in HEV
applications.
Extended accelerated calendar aging tests have
been performed by storing batteries at constant
voltage at different temperatures and different
SOC. The test matrix is shown in Table 1. Three
cells have been tested under the same condition
in order to get statistic relevance. At regular
intervals of 6 weeks capacity tests, measurements
of the inner resistance of the battery and
electrochemical impedance spectroscopy (EIS)
were performed at room temperature. Some cells
were stored at float conditions (constant voltage),
whereas for other cells storage conditions were
applied (open circuits). The cells stored with
open circuits showed self-discharge processes
over time. Therefore, the average voltage during
the 6 weeks of storage is used for evaluation of
the data. In general, aging tests performed at float
conditions are more desirable for the
parameterization of aging models, as they ensure
constant conditions.
The capacity was determined by a 1C discharge
following a standard charge of the cell. For
calculation of the inner resistance a high pulse
power characterization profile as defined by
VDA (German association of the automotive
industry) [11] at different depths of discharge
was used. Therefore a 18s 4 C-rate discharge pulse
followed by a 40 s rest period and a 10s 3 C-rate
charge pulse also followed by a 40 s rest period
was employed. In this work the so called overall
discharge resistance at 20 % DOD calculated by
the ratio of voltage change and current during the
40 s rest period after the 4 C-rate discharge pulse is
used for the aging analysis.
T / SOC 20 %
(3,05 V) 50%
(3,51 V) 80 %
(3,92 V) 100 %
(4,10 V)
25 °C X
35 °C X X X
50 °C X X X X
65 °C X X
Table 1: Test matrix of calendar aging tests
performed on 6Ah high power lithium-ion batteries
with NMC as cathode material.
Impedance spectra were measured at room
temperature at different DOD (0%, 20%, 50%,
80%) in galvanostatic mode using frequency range
from 5 kHz to 10 mHz. All spectra were measured
without superposed DC current at 23°C.
3. Calendar Aging Results
In order to develop and parameterize an aging
model, the calendar aging tests were evaluated. In
this section the most important results of the aging
data are discussed and summarized in order to
support the assumptions made for the setup of the
model.
It is widely known from literature, that electrolyte
decomposition and the corresponding formation of
solid electrolyte interphase (SEI), is the dominant
aging process in most graphite-based lithium-ion
batteries during storage leading to capacity decline
(due to loss of active lithium) and impedance rise
(due to increase in film layer thickness) [3, 12-14].
Theoretical derivations of the time dependency of
the SEI growth rate are quite opposing. Broussely
et al. [3] for example describe a formation process
taking place at the SEI/electrolyte interface,
leading to the conclusion, that the electronic
conductivity of SEI is the rate limiting step of
formation. Ploehn et al [12] in contrast state a SEI
formation that takes place at the anode/SEI
interface and is limited by solvent diffusion
process. Nevertheless all theories lead to the
conclusion that the formation process evolves with
a square root of time dependency. A similar trend
can be seen in the aging behavior of capacity loss
EVS26 I
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ity fade dep
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r
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lectric Vehic
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ase transiti
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ity fade and
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u
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ling, the ma
t
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m
inimum of
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t SOC aroun
d
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a
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m
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cell more de
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nd its influe
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ity fade in a
2
over storag
e
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he cell was
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ers tempera
t
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r
esistance in
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c
ies on stora
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re 3a shows
3
c
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te on
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ius law
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cy in
on the
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ated
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EVS26 I
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The imp
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a
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e
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r
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to evaluate
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a)
a
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a
c
e spectra d
u
a
nd 50% SO
C
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e intercept
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o
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s
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ollector and
eding aging.
m
i-circle is e
n
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rease of SEI
a
nce and cha
n
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er capacity.
e
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r
g
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b
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s
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sistance and
o
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e
lement consi
s
t
ant phase el
e
the paramet
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)
Φ
ω
,
i
bes the indu
c
resistance th
e
ZARC-elem
e
y
semi-circle
u
sed to descri
b
c
e spectra of
a
t different st
a
r
a were meas
u
c
tric circuit
n
t
he impedan
c
a
nd Fuel Cell
E
u
ring aging f
o
C
. It can be
w
ith the real
s
tances like
electrolyte i
s
Additionally
n
larging,
resistance,
n
ges in the
To evaluate
r
ic circuit
s
isting of an
two ZARC-
e
impedance
s
ts of a
e
ment in
e
rs R, C and
Φ
(1)
c
tive part of
e
intercept w
i
e
nt accounts
and the seco
n
b
e the
a cell stored
a
a
te of health.
u
red at 23°C
n
etwo
r
k that
c
e spectra.
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lectric Vehic
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at
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c
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u
roo
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u
R
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m
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f
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r
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l
e Symposiu
m
u
re 4a show
s
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edance para
m
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e
parameters
o
n
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e
r time. Ther
e
e
n conducted.
c
omparison t
o
t
SEI formati
o
h
e cell. Simi
l
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lts, the imp
e
t
of time dep
e
m
perature and
a
meters on a
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endency, as
e
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ation. The
o
h
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u
impedance
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r
e parabolic
d
i
ch can be re
l
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a
bolic functi
o
p
endency of
R
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re 4: a) sho
w
a
nd C
1
norm
a
l
s stored at 5
0
m
alized to i
n
f
erent states
o
r
e measured
a
b
)
)
the time ev
o
m
eters R
ser
,
R
e
Impedance
p
o
f the second
n
d the data re
e
fore no furt
h
The parame
t
o
R
ser
leading
o
n is the do
m
l
ar to the lar
g
e
dance para
m
e
ndency ove
r
voltage dep
e
g
ing reveal a
n
e
xpected fro
m
o
nly deviatio
n
u
nd for the v
o
arameter R
se
r
d
ependency
o
l
ated to corro
s
ing the ohm
i
f the electrol
y
o
n is used to
f
R
ser
to the agi
n
w
s the imped
a
lized to initi
a
0
°C and 100
%
n
itial value o
v
o
f health. Th
e
a
t 23°C and
8
o
lution of the
R
1
and C
1
. Th
e
p
arameters
L
ZARC-elem
e
e
veal a large
s
h
er investigat
i
t
er R
1
increa
s
to the concl
u
m
inant aging
p
g
e signal mea
m
eter show a
s
r
lifecycle. A
e
ndency of i
m
n
exponentia
l
m
the theory
o
n
from expo
n
o
ltage depen
d
r
. Figure 4
b
s
h
o
f R
ser
on vol
t
o
sion of curre
n
m
ic resistance
y
te. Therefo
r
fit the voltag
n
g data in th
e
d
ance parame
t
a
l values ove
r
%
SOC. b) s
h
v
er storage v
o
e
impedance
s
8
0% SOC.
4
e
, φ
1
and
e
nt on
s
cattering
i
on has
s
es faster
u
sion,
p
rocess
surement
s
quare
l
so the
m
pedance
l
o
f SEI
n
ential
d
ency of
h
ows a
t
age,
n
t
at low
r
e a
e
e
t
ers R
ser
,
r
time for
h
ows R
ser
o
ltage fo
r
s
pectra
EVS26 I
n
Figure 5
over agi
n
SOC. In
normali
z
the OC
V
capacity
nominal
aging. U
capacity
same. F
o
that it is
n
accordin
g
to simpl
y
order to
a
Figure 5
:
at 50°C
a
states of
normali
z
over DO
D
4. M
a
A
gi
Based
o
section,
empiric
a
shown
i
followin
g
used:
As t
h
far t
h
cycle
a)
b)
n
ternational B
a
shows the e
v
n
g for cells s
t
Figure 5a th
e
z
ed to nomin
a
V
over DOD
n
is shown. U
s
capacity, the
sing the DO
D
in contrast, t
h
o
r the use in
a
not necessar
y
g
to the state
y
use the latt
e
a
djust the O
C
:
OCV curve
s
a
nd 50% SO
C
health. a) sh
o
z
ed to nomin
a
D normalize
d
a
thematic
i
n
g
Beha
v
o
n the cons
i
a lifetime
a
l approach c
a
i
n the exte
n
g
simplificat
i
h
e cycle life
h
e requireme
aging is
n
a
ttery, Hybrid
a
v
olution of th
t
ored at 50°C
e
OCV over
D
a
l capacity a
n
n
ormalized t
o
s
ing the DO
D
OCV curve
c
D
normalize
d
h
e OCV cur
v
a
n aging mod
y
to change t
h
of health of
t
e
r definition
o
C
V.
s
over aging
f
C
are shown
a
o
ws the OC
V
a
l capacity a
n
d
to actual c
a
al Descri
p
v
ior
i
derations o
f
model foll
o
a
n be develo
p
n
ded aging
i
ons and ass
u
of the batte
r
nts of appli
c
n
eglected in
a
nd Fuel Cell
E
e OCV curv
e
and 50%
D
OD
n
d in Figure
5
o
actual
D
normalized
c
hanges ove
r
d
to actual
v
e stays the
el, this mean
s
h
e OCV curv
t
he battery, b
o
f DOD in
f
or cells stor
e
a
t different
V
over DOD
n
d b) the OC
V
ap
acity.
p
tion of
f
the previ
o
o
wing a se
m
p
ed. It has b
e
tests, that
t
u
mptions can
r
ies exceeds
c
ation in H
E
the followi
n
E
lectric Vehic
l
e
5
b
to
r
s,
v
e
b
ut
e
d
V
o
us
m
i-
e
en
t
he
be
by
E
V,
n
g.
L
Ba
s
eq
u
cal
e
[
1
L
L
+
wh
e
inn
e
F(t
)
to
co
m
F
(
c
a
i
ref
e
spe
ele
c
agi
n
A
(
T
pot
e
acc
l
e Symposiu
m
Cycle tests
w
60% and 80
equivalent f
u
end of cap
a
reached.
Different re
s
over aging.
resistance w
a
of the aging
m
The calenda
r
square root
seen in fitt
i
functions to
experimenta
l
The rate o
f
exponentiall
y
Only for t
h
p
arabolic de
p
the aging da
t
The aging b
e
accounted f
o
nominal cap
a
As the sensi
t
L
, R
2
, C
2
, Φ
1
data reveal
n
they are take
n
s
ed on th
e
u
ations can
e
ndaric agin
g
),(
),,(
F
VTA
VTt
L
cal
+
=
e
re LL
cal
is
u
e
r resistance
)
describes t
h
the domi
n
m
bination:
β
tct
a
=)
(
i
s a coeffici
e
e
rence condi
t
cific proce
s
c
trolyte dec
o
n
g process, β
T
,V) describ
e
e
ntial on
ording to:
w
here cells
%
SOC hav
e
u
ll cycles ca
n
a
city life (
C
s
istances ev
o
Therefore,
a
s chosen fo
r
m
odel.
r
aging of th
e
of time dep
e
i
ng results
describe the
l
aging data (
s
calendar d
e
y
with tem
p
h
e voltage
d
p
endency on
a.
e
havior of t
h
o
r, using the
a
city for the
d
t
ivity of the
I
1
and Φ
2
on
a
n
o significant
n
to be const
a
e
se assump
t
be derived
g
data:
]
)(
,(
0
t
F
T
tLL
cal
=
u
sed for the
e
or impeda
n
h
e time dep
e
n
ant aging
.
e
nt describin
g
t
ions T
0
and
s
s. Under
o
mposition
b
ecomes 0.
5
s the impac
the calend
a
were cycle
d
e shown, th
a
n
be obtaine
d
C
act
= 70%
o
lve in a si
m
the total
r
the param
e
e cells evol
v
e
ndency. Th
i
using vario
u
time evolut
i
see Table 1).
e
gradation a
c
p
erature an
d
d
ependency
o
n
voltage is
u
h
e OCV cur
v
actual inste
d
efinition of
D
I
mpedance p
a
ging is sma
correlation
o
ant over tim
e
t
ions the
to fit the
),V
T
,
evolution o
f
n
ce paramet
e
e
ndency and
processes
g
the rate o
f
V
0
dependi
n
the assum
p
being the
5
.
c
t of temper
a
a
r degrada
t
5
d
between
a
t 30 000
d
until the
C
BOL
) is
m
ilar way
discharge
e
terization
v
es with a
i
s can be
u
s fitting
i
on of the
c
celerates
d
voltage.
o
f R
ser
a
u
sed to fit
v
e can be
ad of the
D
OD.
arameters
l
l and the
o
ver time,
e
.
f
ollowing
measured
(2)
capacity,
e
rs either.
is related
or their
(3)
f
aging at
n
g on the
p
tion of
dominant
a
ture and
t
ion rate
EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 6
V
VV
V
T
TT
TccVTA Δ
Δ
= 00
),( (4)
The first factor describes the temperature impact
on the aging rate, the second one the impact of
the potential. cT and cV are fitting parameters,
describing the impact of temperature and voltage
on aging, respectively. T0 and V0 are reference
temperature and voltage and can be chosen
arbitrarily. For the following we chose T = 25°C
and V0 = 3.5V. ΔT was set to 10°C, meaning, that
an increase in temperature by 10°C results in an
increase in aging by a factor cT compared to
reference conditions T0. Similarly ΔV was set to
0.1V. Similar equations have been also used by
Bohlen et al. [8, 9] to describe the aging behavior
of super capacitors.
The only exception has been found in the aging
evolution of the impedance parameter Rser, where
a parabolic dependency on voltage has been
detected (see Figure 4b). Therefore to describe
the aging evolution of Rser eq. (4) was substituted
by:
+
Δ
= Δ
1),(
2
0
0
V
VV
ccUTA V
T
TT
T
(5)
Eq. (2) was used to fit the extended aging data,
leaving the parameters ca, cT and cV free for
regression analysis. Non-linear least square
algorithm was used for regression. The fits
include data of the test matrix, introduced in
section 3, containing about 30 batteries stored at
different temperatures and voltages. For
comparison, beside square root of time
dependencies also combinations of square root of
time and linear time dependencies as well as
combinations of square root of time and
logarithmic time dependencies have been
investigated in fittings. To assess the goodness of
fit an analysis of correlation coefficient was
carried out. Table 1 compares the fit results of
the different approaches for the capacity fade.
Especially considering the linear behavior, it can
be seen, that the linear contribution to the fit is
very small or even zero. Therefore apart from
increasing the number of free parameters the linear
term did not yield significant improvement
compared to eq. (2). The fitting results for the
functions including a logarithmic term show, that
also logarithmic time dependency can be an
approach to describe calendar aging. The
difference to the square root dependency is that the
logarithmic time dependency is steeper in the
beginning and becomes flatter later. Therefore it
overestimates the aging at the beginning, but yields
better results after some time. As the logarithmic
behavior lacks of physical explanation, we will
focus on the square root dependency in the
following. Square root function on time can be
directly derived from theoretical investigation of
SEI formation. The physical process behind the
mathematical expression is the critical issue to
ensure the ability of the model for extrapolations.
In Table 2 the values of the resulting fitting
parameters for capacity fade, resistance increase
and impedance parameters using eq. (2) and the
corresponding correlation coefficients R² are
shown. The parameters describing the capacity
evolution indicate an acceleration of aging by a
factor of cT = 1.55 caused by a temperature
increase of ΔT= 10°C compared to T0. For
potential dependency of the capacity, fitting
reveals an acceleration factor of cV = 1.15 for an
increase of ΔV = 0.1 V. This differs from the rule
of thumb, predicting that aging rate doubles by
increasing the temperature by 10°C or the voltage
by 0.1 V. The aging rate at reference conditions T0
and U0 becomes ca = 0.0064. Similar results are
received for the inner resistance and the impedance
parameters Rser, R1, C1, differing slightly as they
are impacted by different aging effects. Thus this
approach convinces due to its simplicity and its
physical correspondent.
EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 7
Equation
Parameter
Parameter value
R²
Number of free
parameter
tccc
C
tC T
TT
T
V
VV
Va
init
+= Δ
Δ
00
1
)( ca -0,0064 0,9341
3
cV 1,1484
cT 1,5479
[]
tctccc
C
tC
aa
T
TT
T
V
VV
V
init
++= Δ
Δ
21
00
1
)( ca1 -0,0064 0,9341
4
ca2 0
cV 1,1484
cT 1,5479
tccctccc
C
tC T
TT
T
V
VV
Va
T
TT
T
V
VV
Va
init
++= Δ
Δ
Δ
Δ
0000
222111
1
)( ca1 -0,0053 0,9447 6
cV1 1,1392
cT1 1,6389
ca2 -0,00005
cV2 1,87333
cT2 0,59485
tccc
C
tC T
TT
T
V
VV
Va
init
log1
)( 00 += Δ
Δ
ca -0,010392 0,9365
3
cV 1,15069
cT 1,554253
[]
tctccc
C
tC
aa
T
TT
T
V
VV
V
init
log1
)(
21
00 ++= Δ
Δ
ca1 -0,00291 0,9433 4
ca2 -0,00565
cV 1,14959
cT 1,55187
tccctccc
C
tC T
TT
T
V
VV
Va
T
TT
T
V
VV
Va
init
log1
)( 0000
222111 ++= Δ
Δ
Δ
Δ
ca1 -0,00094 0,9604 6
cV1 1,055624
cT1 2,255951
ca2 -0,008921
cV2 1,225323
cT2 1,284523
Table 1: Fit results for different mathematical functionalities for the capacity fade are shown.
ca cV cT R²
Capacity -0.0064 1.1484 1.5479 0.934
Resistance 0.0484 1.0670 1.5665 0.96
Rser 0.0206 0.0471 1.7586 0. 85
R1 0.0766 1.0618 2.1437 0.89
C1 -0.0457 1.0258 1.2248 0.79
Table 2: Fitting parameters for capacity fade,
resistance increase and impedance parameters
Rser, R1 and C1 using eq. (2) and the
corresponding correlation coefficients R²
Fitting results for the evolution of capacity and
overall resistance during storage at 50% SOC at
different temperatures are shown exemplarily in
Figure 6. The fittings for these values yield good
results, with a R² of 0.934 and 0.96, respectively. It
has to be kept in mind that data of about 30 cells at
a variety of storage conditions have been fitted
using one set of parameters. This of course yields
deviations of the fit from the data at certain
conditions. Nevertheless the overall fitting result is
unquestionable.
EVS26 I
n
Figure
6
(actual
c
and b)
normalis
eq. (2) i
s
different
measure
d
fittings.
Equatio
n
descripti
o
paramet
e
depende
n
the data
scatterin
g
resistanc
0.79 an
d
in the d
a
determi
n
electric
c
results
f
paramet
e
SOC at
Figure 7
.
a)
b)
n
ternational B
a
6
: Fitting
r
e
c
apacity nor
m
resistance
i
ed to initial
s
shown for
temperatu
r
d
data result
s
n
(2) also
y
o
n of the
f
e
rs. For
R
n
cy was take
n
concerning
g
more co
m
e data, corr
e
d
0.89 could
a
ta is due to
t
n
e impedan
c
c
ircuit diagr
a
f
or the ev
o
e
rs R
ser
, R
1
a
n
different t
e
.
a
ttery, Hybrid
a
e
sults for a)
m
alised to i
n
i
ncrease (ac
t
resistance)
o
cells stored
a
r
es. The d
o
s
for the cel
l
y
ields good
f
ittings of
t
R
ser
a par
a
n
into accou
n
impedance
m
pared to th
e
e
lation coeff
i
be obtained.
t
he addition
a
c
e pa
r
amet
e
a
m in Figure
o
lution of
t
n
d C
1
for cell
e
mperatures
a
nd Fuel Cell
E
capacity f
a
n
itial capaci
t
t
ual resista
n
o
ver time us
i
a
t 50% SOC
o
ts mark
t
l
s, the lines
t
r
esults for
t
t
he Impeda
n
a
bolic volt
a
n
t. Even tho
u
parameters
a
e
capacity
a
i
cients betw
e
The scatter
i
a
l fitting step
e
rs using
t
3
b
. The fitt
i
t
he impeda
n
s
stored at 5
0
are shown
E
lectric Vehic
l
a
de
t
y)
n
ce
i
ng
at
t
he
t
he
t
he
n
ce
a
ge
u
gh
a
re
a
nd
e
en
i
ng
to
t
he
i
ng
n
ce
0
%
in
Fig
u
im
p
eq.
te
m
nor
m
me
a
fitt
i
5.
Th
e
use
dif
f
im
p
ma
t
res
u
life
t
par
a
a
)
b)
c
)
l
e Symposiu
m
u
re 7: Fittin
g
p
edance para
m
(2) for cells
s
m
peratures ar
e
m
alized to t
h
a
sured data r
e
i
ngs.
Develop
m
e
fitting resul
t
d to develop
f
erent opera
t
p
edance-
b
ase
d
t
hematical e
x
u
lts. Such a
s
t
ime predict
i
a
meterizatio
n
)
)
)
g
results for t
h
m
eters a) R
ser
s
tored at 50
%
e
shown. The
h
e initial valu
e
e
sults for the
m
ent of
L
t
s of the cale
n
a model to
p
t
ion conditi
o
d
electro-th
e
x
pressions o
b
s
emi-empiric
a
i
ons has the
n
based on
h
e evolution
o
r
, b) R
1
and c
)
%
SOC at dif
f
values are
e. The dots
m
cells, the lin
e
L
ifetime
M
n
dar aging d
a
p
redict lifeti
m
o
ns by com
b
e
rmal model
b
tained fro
m
al model ap
p
advantage o
accelerated
8
o
f the
)
C
1
using
f
erent
m
ark the
e
s the
M
odel
a
ta can be
m
es under
b
ining an
with the
m
the test
p
roach for
f an easy
calendar
EVS26 I
n
lifetime
t
Moreov
e
different
tempera
t
derived
i
processe
such a
m
models
u
are restr
i
used as
l
goal of
t
set of e
m
mathem
a
main de
g
The ele
c
impedan
c
diagram
capacity
different
resulting
model a
s
and vo
l
depende
n
current
obtained
The elec
to calcu
l
current
p
simple t
h
producti
o
and the
r
space t
environ
m
found i
n
model f
o
The the
r
b
ehavio
r
approac
h
As agin
g
voltage,
and volt
a
electrica
l
infinites
i
predomi
n
voltage,
applicati
o
tempera
t
Therefo
r
increme
n
equation
n
ternational B
a
t
ests and an
e
r the approa
c
operation
t
ure, as th
e
i
n section 4
a
s in the batt
e
m
odel appr
o
u
sing neuro
n
i
cted to the
c
l
earning set.
t
he semi-em
p
m
pirical equ
a
tical expres
s
g
radation me
c
c
trical mode
l
c
e-
b
ased mo
d
in Figure 3
C
d
to descri
b
temperat
u
g
impedance
p
s
lookup tabl
e
l
tages. To
n
cy of the
i
dependency
from pulse
trical netwo
r
l
ate the volt
a
p
ulse. The t
h
h
ermal netw
o
o
n as a one
p
r
mal conduc
t
o simulate
m
ent. More
d
n
[18], wher
e
o
r the cell us
e
r
mal, as wel
l
r
can be sim
u
h
was also us
e
g
depends s
t
the aging
m
a
ge evolutio
n
l
model.
I
i
mal aging
n
ating condi
is calcul
a
o
n and on
t
t
ure and
v
r
e it is n
e
n
tal loss of l
i
(2):
a
ttery, Hybrid
a
acceptable c
c
h enables e
x
conditions,
e
mathemat
a
re based on
e
ry. This is
a
o
ach in com
p
n
al network
a
c
onditions o
f
It is therefo
r
p
irical appro
a
ations for t
h
s
ions that a
r
c
hanisms.
l
used in t
h
d
el, using th
e
b
with an a
b
e the impe
d
u
res and
v
p
arameters
a
e
s for differe
n
parameteriz
e
i
mpedance
p
of the i
n
power pro
f
r
k is then us
e
a
ge response
h
ermal mode
l
o
rk includin
g
p
oint source,
t
ivity in ea
c
heat tran
s
d
etails on th
e
e
also the v
a
e
d in this wo
r
l
as the dy
n
u
lated accur
a
e
d in [16, 19
]
t
rongly on t
e
m
odel recei
v
n
calculated
I
n each ti
m
of the ce
l
tions, i.e. t
e
a
ted. Depe
n
t
he applied
c
v
oltage var
y
e
cessary to
i
fe time in t
h
a
nd Fuel Cell
E
o
mputing ti
m
x
trapolations
e.g. to lo
w
ic
a
l equati
o
physical ag
i
a
n advantage
p
arison to
e
a
pproaches t
h
f
the aging d
a
r
e an import
a
a
ch to deriv
e
h
e aging, us
i
r
e close to
t
h
is work is
e
electric circ
u
d
ditional se
r
d
ance spectra
v
oltages.
T
a
re given to
t
n
t temperatu
r
e
the curr
e
p
arameters,
t
n
ner resista
n
f
iles was us
e
e
d in the mo
d
of the cell t
o
l
is based o
n
g
an ohmic h
e
a heat capac
c
h direction
s
fer with
t
e
model can
a
lidation of
t
k
can be fou
n
n
amic electri
c
a
tely. A simi
]
e
mperature
a
es temperat
u
b
y the ther
m
m
e step,
t
l due to
t
e
mperature
a
n
ding on
t
c
urrent prof
i
y
over ti
m
add up
t
h
e model us
i
E
lectric Vehic
l
m
e.
to
w
er
o
ns
i
ng
of
e
.g.
h
at
a
ta
a
nt
e
a
i
ng
t
he
an
uit
r
ial
a
at
T
he
t
he
r
es
e
nt
t
he
n
ce
e
d.
d
el
o
a
n
a
e
at
ity
in
t
he
be
t
he
n
d.
c
al
lar
a
nd
u
re
m
o-
t
he
t
he
a
nd
t
he
i
le,
m
e.
t
he
i
ng
N
i
L
L
=1
Fin
ca
p
par
a
sta
t
It i
s
de
g
do
m
gro
w
thi
c
dir
e
thi
c
thi
c
var
y
su
b
eq.
sch
Fig
u
agi
n
6.
Fo
r
pro
cy
c
rea
l
ha
v
spe
the
80
%
l
e Symposiu
m
c
cal
cal
LLdLL
V
tTt
L
(
),(,(
ally all para
m
acity, inn
e
a
meters are
t
e of health
fo
s
important
t
g
radation, e.g
m
inated by
S
w
th is m
a
c
kness, capa
c
e
ctly propo
r
c
kness. Since
c
kness is the
y
ing temper
a
stituted by t
h
(6), represe
n
ematically t
h
u
re 8: Work
i
n
g model.
Simulat
i
r
the simula
t
file for HE
V
le the batter
y
l
istic operat
i
v
e been a
d
cifications.
U
b
atteries w
e
%
, 45%-65%
i
ii
c
al
ca
dt
tTt
LLt
V
=
1
(),(
))(
m
eters of the
e
r resistan
c
updated acc
o
fo
llowing eq.
o note that
w
.
capacity fa
d
S
EI growth.
a
inly deter
m
ity fade and
r
r
tional to t
h
not the ong
o
only contin
u
a
ture and volt
a
h
e actual ca
p
n
ting SEI thic
e working pr
i
ng principle
on Resul
t
ion of the
c
V
according
y
and to inve
s
on conditio
n
d
justed acc
o
U
sing the pro
f
e
re cycled a
t
and 30%-50
%
i
i
a
l
t
tV
V
tTt
Δ
00
))(),
),(,(
e
electrical
m
c
e and i
m
o
rding to th
e
(6) in each
t
w
e assumed
t
d
e and resist
a
As the rat
e
m
ined by t
resistance in
c
h
e change
o
ing time, bu
t
u
ous parame
t
t
age, the tim
e
p
acity or res
i
c
kness. Figur
e
r
inciple of th
e
of the semi
-
t
s
c
ell a realist
i
to VDA wa
s
tigate the a
g
n
s. The cur
r
o
rding to
file shown i
n
t
40°C betw
e
%
SOC.
9
t
V
+
0
))(
(6)
m
odel, like
m
pedance
e
ir actual
t
ime step.
t
he actual
a
nce to be
e
of SEI
h
e layer
c
rease are
in layer
t
the layer
t
er during
has to be
i
stance in
e
8 shows
e
model.
-
empirical
i
c current
s
used to
g
ing under
r
ent rates
the cell
n
Figure 9
e
en 60%-
EVS26 I
n
Figure
simulati
o
Figure 1
0
increase
profile.
initial c
a
years w
h
80% S
O
obtained
b
etween
charge l
e
b
e seen
resistanc
compare
d
Figure 1
0
(actual
c
and b)
normalis
shown,
f
profile b
e
a)
b)
n
ternational B
a
9: HEV
o
ns.
0
shows the
c
during cycli
n
Wheras end
a
pacity) is al
r
h
ile cycling
O
C, even 6
, when th
e
30%-50%
S
e
ads to a fa
s
that the e
n
e doubles)
d
to end of c
a
0
: Simulatio
n
c
apacity nor
m
resistance
i
ed to initia
l
f
or the cell c
y
e
tween diffe
r
a
ttery, Hybrid
a
profile ap
p
c
apacity fad
e
n
g of the cel
l
of capacit
y
r
eady reache
the battery
years of li
e
battery i
s
S
OC. The
h
s
ter degradat
i
n
d of resisti
is reache
d
a
pacity life.
n
results for
a
m
alised to i
n
i
ncrease (ac
t
l
resistance)
y
cled at 40 °
C
r
ent SOC.
a
nd Fuel Cell
E
p
lied for
t
e
and resista
n
l
with the H
E
y
life (80%
d after abou
t
between 60
%
fetime can
s
cycled o
n
h
igher state
i
on. It can a
l
ve life (ini
t
much fas
t
a
) capacity f
a
n
itial capaci
t
t
ual resista
n
over time
C
with the H
E
E
lectric Vehic
l
t
he
n
ce
E
V
of
t
2
%
-
be
n
ly
of
l
so
t
ial
ter
a
de
t
y)
n
ce
is
E
V
7.
In
t
pre
d
rea
l
co
u
mo
d
for
of
t
obt
a
wh
i
the
ap
p
cal
e
ap
p
b
at
t
ap
p
of
t
we
l
vol
t
O
C
ins
t
of
par
a
an
d
fun
obt
a
b
e
h
ma
k
im
p
Ba
s
pat
t
an
a
Ex
e
on
t
dif
f
on
t
are
Po
w
Th
i
res
e
Fe
d
fun
co
n
l
e Symposiu
m
Conclus
i
t
his work a
s
d
ict lifetim
e
l
istic operati
o
u
ples an i
m
d
el to a semi
the impact
o
t
he battery.
T
a
ined from
i
ch were use
d
aging test r
e
p
roach could
e
ndar aging
t
p
roximation
o
t
eries excee
d
p
lication. Tes
t
t
ime depend
e
l
l as an e
x
t
age and tem
p
V curve wa
t
ead of the
n
DOD. Th
e
a
meters L, R
2
d
was the
r
ctions, base
d
a
ined from t
h
h
avior and to
k
e extrapo
p
lemented i
n
s
ed on the
m
t
erns and
a
lyzed with
r
e
mplarily th
e
t
he aging of
a
f
erent operat
i
t
he results as
presented in
w
er Sources.
Acknow
l
i
s work has
b
e
arch initiati
v
d
eral Minist
r
ding numbe
r
n
tent of this p
u
i
ons
s
imulation m
o
of a lithi
u
o
n condition
.
m
pedance b
a
-
empirical a
g
f aging on t
h
T
he aging mo
d
extended ac
c
d
to paramet
e
e
sults simpli
fi
be derived.
t
est results c
o
f lifetime,
d
s by far
t
results sho
w
e
ncy can be
a
p
onential b
e
p
erature. Th
e
s accounted
n
ominal capa
c
sensitivity
2
, C
2
, Φ
1
an
d
r
efore negl
d
on physic
a
h
e test result
s
ensure the
a
l
ations. T
h
n
a semi-e
m
m
odel differ
e
m
anagement
r
egard to the
i
impact of a
a
high power
i
on ranges.
M
well as a ve
r
a paper sub
m
l
ed
g
ment
b
een done in
v
e “KVN” f
u
r
y for Edu
c
r
13N9973.
R
u
blication li
e
m
odel was pr
e
um
-ion batt
e
.
The model
ased electr
i
g
ing model, t
h
e dynamica
l
del is based
o
celerated ag
e
rize the mo
d
f
ications for
t
It was obs
e
c
an be used
f
as cycle li
f
the require
m
w
ed, that a s
q
a
pplied to th
e
havior of
a
e
aging beha
v
for, using
t
a
city for the
of the I
m
d
Φ
2
on agin
g
l
ected. Mat
h
a
l aging eff
e
s
to describe
a
bility of the
h
e functio
n
m
pirical agin
r
ent drive c
y
t
strategies
ir impact o
n
a
realistic H
E
cell was si
m
M
ore detaile
d
r
ification of
t
m
itted to the
J
t
the framew
o
fu
nded by th
e
c
ation and
R
R
esponsibili
t
e
s with the a
u
10
e
sented to
e
ry under
approach
c-thermal
o
account
l
behavior
o
n results
ing tests,
d
el. From
t
he model
e
rved that
f
or a first
f
e of the
m
ents of
q
uare root
e
data, as
a
ging on
v
ior of the
t
he actual
d
efinition
m
pedance
g
is small
h
ematical
e
cts, were
the aging
model to
n
s were
g model.
y
cles, use
can be
n
lifetime.
E
V profile
u
lated for
d
accounts
t
he model
J
ournal of
o
rk of the
e
German
R
esearch,
t
y for the
u
thor.
EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 11
References
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B.Y.Liaw, A. Urbina, T. L Paez, D. H Doughty
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[2] J. Vetter, P. Novák, R. M. Wagner, C. Veit, K.-
C. Möller, J. O. Besenhard, M. Winter,
M. Wohlfahrt-Mehrens, C. Vogler,
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[3] M. Broussely, S. Herreyre, P. Biensan,
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[4] M. Broussely, P. Biensan, F. Bonhomme,
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[5] R.B Wright, C.G Motloch, J.R Belt, J.P
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Battaglia, G. L. Henriksen, C. G. Motloch, R.
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[8] O. Bohlen, J. Kowal, D. U. Sauer, Ageing
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capacitors Part I. Experimental study and
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[9] O. Bohlen, J. Kowal, D. U. Sauer, Ageing
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for dynamic application, Journal of Power
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[10] J. B. Gerschler, H. Witzenhausen, F. Hust, D.
U. Sauer, Three-Dimensional Performance and
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Spatially-Resolved Models are Required for
Accurate Simulation of Large-Sized Cells,
Electric Vehicle Symposium (EVS-25)
Shenzhen, China, Nov. 5-9, 2010
[11] Test Specification for Li-Ion Battery Systems
for Hybrid Electric Vehicles, Association of
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Release 1.0, 2007
[12] H. J. Ploehn, P. Ramadass, R. E. White,
Solvent Diffusion Model for Aging of Lithium-
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[16] S. Buller, M. Thele, K. Kahlen, R. W. De
Doncker, Impedance-based simulation models of
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electrochemical impedance spectroscopy. II:
Modelling, J. Power Sources, 196 (2011) 5349-
5356
EVS26 I
n
Au
t
Email:
e
URL:
w
Madelein
e
Universit
y
joined IS
2010 she
field of
m
as well a
s
b
atteries
w
Jochen
B
degree f
r
2005. He
July 2005
he left IS
E
in the fi
interest a
and NiM
H
resolved
m
Jan Voge
l
Aachen
U
about agi
n
Stefan K
ä
RWTH
A
joined IS
E
he is tea
m
n
ternational B
a
t
hors
Dipl.-P
h
Institute
Electric
a
Aachen
Jaegerst
r
Tel:
Fax:
e
r@isea.rwth-
a
w
ww.isea.rwt
h
e
Ecker receiv
y
of Heidelb
e
EA as a rese
is team lead
e
m
odeling. Her
s physico-che
m
w
ith a special
f
Dipl.-
I
Gersc
h
Institu
t
Electri
c
Aache
n
ge@is
e
B
ernhard Ge
r
r
om Technica
l
worked at IS
E
5
till March 20
E
A he was te
a
eld of lithiu
m
a
re modeling
a
H
batteries w
i
m
odeling and
c
BSc. Ja
n
Institut
e
Electric
a
Aachen
jan.vog
e
l
studies Elect
r
U
niversity. He
n
g mechanism
Dipl.-
I
Instit
u
Electr
i
Aach
e
kb@i
s
ä
bitz received
A
achen Univer
s
E
A as resear
c
m
leader for I
S
a
ttery, Hybrid
a
hy
s. Madelein
e
for Power
a
l Drives (
r
asse 17 – 19,
D
+49-241-809
+49-241-809
a
achen.de
h
-aachen.de
ed his diplom
a
e
rg in 2009. I
n
arch associat
e
e
r for ISEA’s
areas of inter
m
ical modeli
n
f
ocus on cell
a
I
n
g
. Joch
e
h
ler
t
e for Power
c
al Drives
(
n
Univer
s
e
a.rwth-aache
n
r
schler receiv
e
l
University
o
E
A as a resear
c
11. Since Sept
a
m leader for
I
m
-ion batteri
e
a
nd character
i
i
th a special f
o
c
ell aging.
n
Vo
g
el
e
for Power
a
l Drives
(
Univer
s
e
l@rwth-aach
e
r
ical Engineer
i
did his bachel
o
s in lithiu
m
-io
n
I
n
g
. Stefan
K
u
te for Powe
r
i
cal Drives
e
n Univ
e
s
ea.rwth-aach
e
his diploma
s
ity in 2010. I
n
c
h associate.
S
S
EA´s activiti
e
a
nd Fuel Cell
E
e
Ecker
Electronics
a
I
SEA), RW
T
Univer
s
D
-52066 Aac
h
6977
2
203
a
in Physics fr
o
n
July 2009
s
e
. Since Octo
b
activities in
t
e
st are empiri
n
g of lithiu
m
-
i
geing.
e
n Bernh
a
Electronics
a
(
ISEA), RW
T
s
ity, Em
a
n
.de
e
d his diplo
m
o
f Dortmund
c
h associate fr
o
e
mber 2009 u
n
I
SEA’s activi
t
e
s. His areas
i
zation of Li-
I
o
cus on spati
a
Electronics
a
ISEA), RW
T
s
ity, Em
a
e
n.de
i
ng at the RW
T
o
r thesis at IS
E
n
batteries.
äbitz
r
Electronics
(ISEA), R
W
e
rsity, E
m
n.de
degree from
t
n
March 2010
S
ince April 2
0
e
s in the field
E
lectric Vehic
l
a
nd
T
H
s
ity
h
en
o
m
s
he
b
er
t
he
cal
i
on
a
rd
a
nd
T
H
a
il:
m
a
in
o
m
n
til
t
ies
of
I
on
a
lly
a
nd
T
H
a
il:
T
H
E
A
and
W
TH
m
ail:
t
he
he
0
11
of
lith
i
im
p
for
l
Fri
e
maj
Aa
c
a st
u
Dip
Phi
l
R
W
wo
r
to f
i
Dir
k
Uni
wo
r
200
Aft
e
200
b
at
t
em
p
for
Sys
t
l
e Symposiu
m
i
u
m
-ion batt
e
p
edance-
b
ased
l
ithiu
m
-ion ba
t
Ca
n
Ins
t
El
e
Un
i
fri
e
e
drich Hust s
t
or in Electri
c
c
hen Universit
y
u
dent assistan
t
l.Wirt.-Ing de
g
Ca
n
Ins
t
Ele
c
Un
i
phi
l
l
ipp Dechen
s
W
TH Aachen
U
r
king as a stu
d
i
nish his bach
e
U
n
S
a
I
n
E
l
A
a
E
m
k
Uwe Sauer
versity of Da
r
r
ked at Fraun
h
0 – 2003 as
t
e
r receiving
h
3, topic: "O
eries in phot
o
p
hasis on batt
e
Electrochemi
c
t
ems.
e
ries. His
a
as well as p
h
t
teries with a
s
n
d. Wirt.-In
g.
t
itute for P
o
ctrical Drives
i
versity,
e
drich.hust@is
e
u
dies industri
al Power En
g
y
. Since 2008
t
at the ISEA.
g
ree in 2012.
n
d. B. Sc. Phi
l
itute for P
o
c
trical Drives
versity,
l
ipp.dechent@
i
s
tudies Electr
i
U
niversity. S
i
d
ent assistant
a
e
lor degree in
2
n
iv.-Prof. Dr.
a
uer
stitute for
P
ectrical Dri
v
a
chen Univers
i
m
ail: sr@ise
r
eceived his
d
r
ms
t
adt in 19
9
h
ofer ISE as a
t
eam leader
f
h
is PhD fro
m
p
timisation t
h
o
voltaic-hybri
d
r
y aging", he j
c
al Energy
C
a
reas of in
t
hysico-chemi
c
s
pecial focus o
. Friedrich H
u
ower Electr
o
(ISEA), RW
T
ea.rwth-aache
n
i
al engineerin
g
g
ineering at t
h
he has been
w
He expects t
o
l
ipp Dechent
o
wer Electr
o
(ISEA), RW
T
isea.rwth-aac
h
ical Engineer
i
i
nce 2010 he
a
t the ISEA.
H
2
012.
rer. nat. Dir
k
P
ower Electr
o
v
es (ISEA)
,
ity
e
a.rwth-aache
n
d
iploma in Ph
y
9
4. From 199
4
a
research scie
n
for “Storage
m
University
o
h
e usage of
d systems w
i
j
oined ISEA a
s
C
onversion a
n
12
t
erest are
c
al models
n
EIS.
u
st
o
nics and
T
H Aachen
Email:
n
.de
g
with his
h
e RWTH
w
orking as
o
finish his
o
nics and
T
H Aachen
Email:
h
en.de
i
ng at the
has been
H
e expects
k
Uwe
o
nics and
RWTH
n
.de
y
sics from
4
-2003 he
n
tist, fro
m
Systems”.
o
f Ulm in
lea
d
-acid
i
th special
s
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n
d Storage
... In Eq. 1, k denotes the speed of a chemical reaction that is dependent on a constant pre-factor k 0 , the storage temperature T, the general gas constant R, and E A as activation energy for the underlying chemical reaction [16], [17], [7], [12], [15]. The unknown variables in the Arrhenius dependency, k 0 and E A , can be determined using an Arrhenius graph, as shown in Fig. 1 in underlying aging mechanisms, according to [5]. ...
... Similar observations are made by Ecker at al. [17] and Waldmann et al. [5]. They notice deviations from Arrhenius dependency at storage temperatures above 60 • C. Waldmann et al. [5], investigating a 18650 cell with NMC chemistry, mention that this observation can be related to changing aging mechanisms. ...
Conference Paper
Cell selection is a mandatory first step for the design of automotive battery systems. Thereby, aging characterization enables quantification of aging-related effects at an early stage. For aging characterization in industrial applications, an accelerated implementation is required. Applied methods for acceleration must not alter the composition of aging, and therefore must not initiate different aging mechanisms in comparison to the nonaccelerated reference case. With regard to temperature dependence of calendar aging, this requirement of mechanism consistency corresponds to the validity of the Arrhenius dependency. This paper presents the results of a test series on calendar aging at temperatures ranging from 25 °C to 80 °C. Mechanism consistency is investigated using Differential Voltage Analysis (DVA), proving additional aging mechanisms beyond 60 °C. In conclusion, the limitations of Arrhenius dependency for the investigated cells are discussed.
... In [8], [17] und [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] Die Modelle wurden bis auf wenige Ausnahmen für Temperaturen zwischen 20 und 60°C erstellt. Entladungsgrad und -tiefe unterschieden sich deutlich in den verschiedenen Untersuchungen, ebenso die C-Rate. ...
... There are several issues of practicality and accuracy in in this model which need to be modified to be applicable in DREMUS. The first issue is that the time dependency differs from most observations of the capacity loss of Li-Ion cells, which generally resemble a square-root dependency ( [26,[45][46][47][48][49]) until the EOL capacity is reached. This model indicates a steadily increasing capacity fade. ...
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This paper presents a modelling approach to support the techno-economic analysis of Li-Ion battery energy storage systems (BESS) for third party organisations considering the purchase or use of BESS but lacking the detailed knowledge of battery operation and degradation. It takes into account the severe data-limitations and provides the best possible approximation for its long-term electrical, thermal and ageing performance. This is achieved by constructing flexible and scalable ageing models from experimental data based on manufacturer's datasheets, warranties and manuals as key inputs. The precision of the individual models has been determined using experimental data and has been found with <8 % normalised root-mean-square deviation (NRMSD) in all cases to be sufficiently accurate. Through linearization methods, this model is able to compare the long-term performance of BESS and quantify the degradative impact of specific charge/discharge mission profiles, which improves the tangibility of BESS as value generating asset.
... The power fade during the cycle life is studied at two different working temperatures, relating this parameter to the state of health (Wright et al., 2002). In Wang et al. (2011), accelerated lifetime tests are performed at different working temperatures and different levels of state-of-charge (SOC) to establish a mathematical relationship between the storage time, temperature and voltage to battery ageing (Ecker et al., 2012). In another study on lithium-ion phosphate-based batteries, it is observed that the capacity fade increases with the increase of storage temperature (Kassem et al., 2012). ...
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With coordinated charging and discharging, electric vehicles (EVs) in smart car parks can be used as energy storage systems and a reserve against unexpected outrage. In this work, a modeling and control framework for EVs in a smart car park has been built up, which includes key factors such as the charging and discharging costs, the battery degradation cost, the driving probability, the feed-in tariff (FIT), and the vehicle-to-grid (V2G) rebates. Each EVs' charging and discharging activities are scheduled through an optimization route with the purpose to minimize the car park electricity cost. Results from comprehensive simulation studies demonstrate the potential benefits of V2G for car park systems with multiple EVs subject to vehicle and battery characteristics, FIT and policy support.
... The proposed HBSs prolong the lifetime of their LFP batteries by [38], and others applying degradation models based on the results of numerous experiments [39][40][41][42]. In this study, we adopted the semi-empirical battery degradation model proposed in [40] to calculate battery capacity loss based on the difference between the capacity loss during charging and discharging. ...
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