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Citation: Droese, D.; Kowal, J.
Thermal Characterisation of
Automotive-Sized Lithium-Ion
Pouch Cells Using Thermal
Impedance Spectroscopy. Appl. Sci.
2023,13, 2870. https://doi.org/
10.3390/app13052870
Academic Editor: Dong-Won Kim
Received: 2 February 2023
Revised: 16 February 2023
Accepted: 21 February 2023
Published: 23 February 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
applied
sciences
Article
Thermal Characterisation of Automotive-Sized Lithium-Ion
Pouch Cells Using Thermal Impedance Spectroscopy
Dominik Droese * and Julia Kowal
Electrical Energy Storage Technology (EET), Institute of Energy and Automation, Technische Universität Berlin,
Einsteinufer 11, D-10587 Berlin, Germany
*Correspondence: dominik.dr[email protected]
Abstract:
This study used thermal impedance spectroscopy to measure a 46 Ah high-power lithium-
ion pouch cell, introducing a testing setup for automotive-sized cells to extract the relevant thermal
parameters, reducing the time for thermal characterisation in the complete operational range. The
results are validated by measuring the heat capacity using an easy-to-implement calorimetric mea-
surement method. For the investigated cell at 50% state of charge and an ambient temperature of
25
◦
C, values for the specific heat capacity of 1.25 J/(kgK) and the cross-plane thermal conductivity
of 0.47 W/(mK) are obtained. For further understanding, the values were measured at different states
of charge and at different ambient temperatures, showing a notable dependency only on the thermal
conductivity from the temperature of
−
0.37%/K. Also, a comparison of the cell with a similar-sized
60 Ah high-energy cell is investigated, comparing the influence of the cell structure to the thermal
behaviour of commercial cells. This observation shows about 15% higher values in heat capacity and
cross-plane thermal conductivity for the high-energy cell. Consequently, the presented setup is a
straightforward implementation to accurately obtain the required model parameters, which could
be used prospectively for module characterisation and investigating thermal propagation through
the cells.
Keywords:
lithium-ion battery; thermal characterisation; thermal impedance spectroscopy; heat
capacity; thermal conductivity
1. Introduction
Ramping up the usage of lithium-ion batteries (LIBs) on a global scale, mainly in
the automotive context, requires, besides cell ageing, a broad understanding of both the
electrical and the thermal behaviour. Ideal thermal management, especially for large-
scale battery systems, is crucial for the maximum possible power and energy supply the
system can contribute at a particular state. This optimisation must be done to improve the
acceptance of electric vehicles by minimising the required battery cells due to higher power
and energy availability without decreasing the driving range.
Thermal characterisation is divided into two general approaches. The first uses
external excitation to obtain both the heat capacity (e.g., calorimetric tests [
1
–
3
]) and
the thermal conductivity (e.g., one-sided heat pulses using a calefaction plate [
4
–
6
] or
a flashlight [
7
,
8
]). Often these methods require extended auxiliary testing equipment.
The other approach uses internal thermal excitation of heat created by the current in the
cell. These tests require only standard laboratory equipment and are faster and easier to
integrate into battery characterisation procedures.
In this paper, the focus lies on the usage of the latter. Here, the literature introduces and
discusses multiple different approaches. The procedures often follow well-known electrical
characterisation methods, for instance, pulse response triggered by a direct current as in the
hybrid pulse power characterisation [
9
] or using a sinusoidal current as in electrochemical
impedance spectroscopy [10,11].
Appl. Sci. 2023,13, 2870. https://doi.org/10.3390/app13052870 https://www.mdpi.com/journal/applsci
Appl. Sci. 2023,13, 2870 2 of 13
These testing principles are adjusted to observe the thermal response of the cell [
12
,
13
].
Thermal characterisation tests need a longer overall testing time due to the longer time
constants, and obtaining an appropriate temperature response often requires high currents,
which leads to necessary adaptations in the testing schemes. The state of charge (SOC)
plays an essential role in the thermal behaviour of a battery cell. While the parameters
of the cell remain nearly constant, as shown in this paper following the literature [
14
–
16
],
the heating of the battery itself differs due to the so-called reversible heat term. Therefore,
pulsing the excitation current at a relatively high frequency is often required to maintain a
quasi-stationary SOC for obtaining the thermal parameters [
17
–
19
]. This paper uses thermal
impedance spectroscopy (TIS) as an easy-to-implement approach to calculate the battery
cell’s heat capacity and thermal conductivity for large-area cells. TIS was first introduced
by [
12
] using an external heating coil to investigate the temperature response of the cell
and afterwards adapted by other researchers using internal heating [
20
,
21
] to obtain the
cell’s parameters. The investigations mostly correspond to smaller cell formats, for example
cylindrical [
21
,
22
] or small pouch cells [
20
,
23
]. This paper firstly investigates and compares
two same-sized large-area cells with different cell configurations and capacities, as further
described in Section 2.2. Utilising a polystyrene arrangement around the significant cell
surfaces in this paper shows that the TIS can be used for automotive-sized cells accordingly
while also displaying the cell behaviour in the complete operational range. The results can
benefit the implementation of a thermal management system in automotive applications
by showing considerable differences in the system behaviour at usage.
2. Materials and Methods
2.1. Test Definitions
A standard test procedure is introduced to cover the relevant thermal cell behaviour.
Using the procedure from [
20
,
23
], the plan utilises seven measuring points at logarithmi-
cally distributed frequencies from 3 mHz as the first measurement point to 160
µ
Hz as the
last tested frequency. Also, the number of repetitions per point is changed by modifying
the first measuring frequency to 50 repetitions, allowing the cell temperature to reach a
quasi-steady state in the first 40 oscillations. A carrier signal utilising a frequency of 5 Hz is
overlaid to each corresponding measuring frequency to maintain a stationary state. Here,
mainly the testing system defines the carrier frequency.
The frequency band in Table 1defines the limits of the upcoming spectra. The upper
boundary results from the minor measurable temperature response at a particular excitation
current and the corresponding generated heat. In contrast, the lower boundary corresponds
to the compromise of the overall test duration and the benefit of using lower frequencies
to the resulting spectra and fitting. Also, the influence of heating of ambient materials,
for instance, the climate chamber and the air around the tested setup, limits the lower
end of the test [
22
]. The first quarter of the resulting data points per frequency for further
investigation gets cut out. This results in reducing the number of observed oscillations to
seven or three. As described in [
20
], this adjustment helps to minimise inaccuracies due to
a change in the occurring ∆Tper measurement point.
Table 1. Signal configuration per test cycle to acquire the significant spectra.
Frequency [mHz] 3 1.8 1.1 0.7 0.43 0.26 0.16
Repetitions [-] 40 + 10 10 10 4 4 4 4
The paper investigates the cell’s thermal behaviour according to the SOC and ambient
temperature. Therefore, a test matrix considering the SOC at 20%, 35%, 50%, 65% and
80% and T
amb
of 10
◦
C, 15
◦
C, 25
◦
C, 35
◦
C and 45
◦
C is spread out. The SOC starts at
50% in 15% steps in both directions. The limits at 20% and 80% rely on the safety limits of
the cell to maintain the cell’s voltage range. The temperature values cover a broad range
in which a battery is typically used. Here, the datasheet defines the lower limit at 10
◦
C.
Appl. Sci. 2023,13, 2870 3 of 13
It is the minimum ambient temperature at which a high charging current, as utilised in
the test, lies within the safety limits. The upper temperature at 45
◦
C, again, is a value
which lies within the boundaries of the cell datasheet and represents a temperature in a
real-world application. A consistent current amplitude is specified at I= 92 A, representing
a maximum current of a 2C-rate. The modulated current signal is shown in Figure 1.
Appl.Sci.2023,13,xFORPEERREVIEW3of14
Thepaperinvestigatesthecell’sthermalbehaviouraccordingtotheSOCandambi‐
enttemperature.Therefore,atestmatrixconsideringtheSOCat20%,35%,50%,65%and
80%andT
amb
of10°C,15°C,25°C,35°Cand45°Cisspreadout.TheSOCstartsat50%
in15%stepsinbothdirections.Thelimitsat20%and80%relyonthesafetylimitsofthe
celltomaintainthecell’svoltagerange.Thetemperaturevaluescoverabroadrangein
whichabatteryistypicallyused.Here,thedatasheetdefinesthelowerlimitat10°C.Itis
theminimumambienttemperatureatwhichahighchargingcurrent,asutilisedinthe
test,lieswithinthesafetylimits.Theuppertemperatureat45°C,again,isavaluewhich
lieswithintheboundariesofthecelldatasheetandrepresentsatemperatureinareal‐
worldapplication.AconsistentcurrentamplitudeisspecifiedatI=92A,representinga
maximumcurrentofa2C‐rate.ThemodulatedcurrentsignalisshowninFigure1.
Figure1.Sectionofmodulatedcurrentsignalfor160μHzdatapoint.(a)Generalbehaviour,show‐
ingtheamplitudeandtheoffset;(b)zoomeddatatoshowthe5Hzcarriersignaloverlaidtothe
testedfrequency.
Thethermalresponseofthebatterycellandtheminimumsensorexcitationdefine
thecurrentratesincetheinfluenceofthenoiseonthetemperaturesignalatthemeasure‐
mentpointsonthecell’ssurfacegetsmoresignificantatthehigherfrequenciescausedby
lessoverallgeneratedheat.Adirectcurrentoffsetusingathirdoftheamplitude(I
off
=
30.66A)isoverlaidtominimiseextensivecoolingofthecellduringphasesnearthezero
crossingofthesignal[22].TheinfluencecanbeseeninFigure2a,astheminimumheat
generationis0.6W.
Figure2.Sectionofrealmeasureddatafor160μHzdatapoint.(a)Dissipatedheatbyirreversible
heat;(b)measuredthermalresponseonthecentreofthecell’ssurfacecausedbythecorresponding
heatingin(a).
Figure 1.
Section of modulated current signal for 160
µ
Hz data point. (
a
) General behaviour, showing
the amplitude and the offset; (
b
) zoomed data to show the 5 Hz carrier signal overlaid to the tested
frequency.
The thermal response of the battery cell and the minimum sensor excitation define the
current rate since the influence of the noise on the temperature signal at the measurement
points on the cell’s surface gets more significant at the higher frequencies caused by less
overall generated heat. A direct current offset using a third of the amplitude (I
off
= 30.66 A)
is overlaid to minimise extensive cooling of the cell during phases near the zero crossing of
the signal [
22
]. The influence can be seen in Figure 2a, as the minimum heat generation is
0.6 W.
Appl.Sci.2023,13,xFORPEERREVIEW3of14
Thepaperinvestigatesthecell’sthermalbehaviouraccordingtotheSOCandambi‐
enttemperature.Therefore,atestmatrixconsideringtheSOCat20%,35%,50%,65%and
80%andT
amb
of10°C,15°C,25°C,35°Cand45°Cisspreadout.TheSOCstartsat50%
in15%stepsinbothdirections.Thelimitsat20%and80%relyonthesafetylimitsofthe
celltomaintainthecell’svoltagerange.Thetemperaturevaluescoverabroadrangein
whichabatteryistypicallyused.Here,thedatasheetdefinesthelowerlimitat10°C.Itis
theminimumambienttemperatureatwhichahighchargingcurrent,asutilisedinthe
test,lieswithinthesafetylimits.Theuppertemperatureat45°C,again,isavaluewhich
lieswithintheboundariesofthecelldatasheetandrepresentsatemperatureinareal‐
worldapplication.AconsistentcurrentamplitudeisspecifiedatI=92A,representinga
maximumcurrentofa2C‐rate.ThemodulatedcurrentsignalisshowninFigure1.
Figure1.Sectionofmodulatedcurrentsignalfor160μHzdatapoint.(a)Generalbehaviour,show‐
ingtheamplitudeandtheoffset;(b)zoomeddatatoshowthe5Hzcarriersignaloverlaidtothe
testedfrequency.
Thethermalresponseofthebatterycellandtheminimumsensorexcitationdefine
thecurrentratesincetheinfluenceofthenoiseonthetemperaturesignalatthemeasure‐
mentpointsonthecell’ssurfacegetsmoresignificantatthehigherfrequenciescausedby
lessoverallgeneratedheat.Adirectcurrentoffsetusingathirdoftheamplitude(I
off
=
30.66A)isoverlaidtominimiseextensivecoolingofthecellduringphasesnearthezero
crossingofthesignal[22].TheinfluencecanbeseeninFigure2a,astheminimumheat
generationis0.6W.
Figure2.Sectionofrealmeasureddatafor160μHzdatapoint.(a)Dissipatedheatbyirreversible
heat;(b)measuredthermalresponseonthecentreofthecell’ssurfacecausedbythecorresponding
heatingin(a).
Figure 2.
Section of real measured data for 160
µ
Hz data point. (
a
) Dissipated heat by irreversible
heat; (
b
) measured thermal response on the centre of the cell’s surface caused by the corresponding
heating in (a).
The following Equation (1) usually defines the generated heat
.
Q
. It covers the main
heating aspects [
24
,
25
]. The first term on the right side describes the irreversible or joule
heating using the current
I
and the ohmic resistance
Ri
. The second term represents the
reversible heat by entropic changes during the change of the SOC. Here, the temperature
T
and the open circuit voltage UOCV are further introduced:
.
Q=I2∗Ri−I∗T∗dUOCV
dT (1)
Appl. Sci. 2023,13, 2870 4 of 13
As mentioned above, reversible heat is excluded as a quasi-stationary SOC is main-
tained. That leads to heat generation independent of the current direction, shown in
Equation (2): .
Q=I2∗Ri(2)
The resulting heat generation is shown for the 160
µ
Hz frequency in Figure 2a and the
corresponding temperature response in Figure 2b. The timeframe on both x-axes represents
the actual test time while measuring this frequency point. The data are then preprocessed
utilising the envelope function and a second-order sinus fit created by the quadratic current
to acquire the maximum value for both the heat generation and the temperature response
and the phase shift between both. The values lead to the thermal impedance calculated by
Equation (3), using
∆ϕ
as the phase shift between the generated heat
.
Q
and the temperature
response ∆Tat a particular frequency:
Zth(f)=ˆ
∆T(f)
ˆ
.
Q(f)
=ˆ
∆T
ˆ
.
Q
∗ej∆ϕ(3)
2.2. Cell Setup
This paper investigates a 46 Ah LIB pouch cell of the manufacturer Kokam. The
cell consists of a nickel–manganese–cobalt cathode and is built in a high-power (HP)
configuration using wider current collectors and thinner layers of active material. This
composition must be considered when comparing results to other test results. The cell
measures 226
×
225
×
12 mm. Excluding the weld results in a width of w = 210 mm and
a height of h = 190 mm. Figure 3schematically shows the arrangement of seven used
PT100 temperature sensors on the cell surface. The locations are shown in relative values
due to better reproducibility using cells in different shapes. In the middle of the cell, a
sensor is attached to both sides of the battery cell. This arrangement covers the validation
for equal heat distribution in both directions perpendicular to the layers. The same test
procedure was replicated as a reference using an equal-sized 60 Ah cell in a high-energy
(HE) arrangement.
Appl.Sci.2023,13,xFORPEERREVIEW5of14
Figure3.Locationsoftemperaturemeasurementpoints.
Figure4showstheoverallsetup.Here,twoplatesofpolystyrenewithathicknessof
30mmeachcoverthetwowidersidesofthecell.Toholdtheseplatesinplaceandto
applyanequalpressurealloverthecell’ssurface,twoidenticalpolyvinylchlorideplates
ofathicknessof10mmareattachedandmoderatelycompressedbysixequallydistrib‐
utedsprings.ThetestswereconductedusingaBasyTecMRScellcyclerandaMemmert
ICP110climatechambertoobtainaconstantambientconditionatparticulartempera‐
tures.
Figure4.Depictionoftestsetup.
2.3.ModelApproach
Thesimplestmodeltodescribethethermalbehaviourofthebatterycellisafirst‐
orderCauermodel.ThiskindofmodelcorrespondswithanRCelementinsystemtheory.
Oftenthescopeofthatmodelisenoughtofeedbackonthesystemresponsetoaspecific
currentsignalofanelectricmodel.Here,themodelisadjustedforthesysteminFigure5.
Theapproachrequiresassumptions.Forinstance,heatgeneration𝑄󰇗andtheheatcapac‐
ity’sC
p
locationoccurinthecell’svolumetriccentre.Also,theheattransferinbothcross‐
planedirections,meaningtowardsthelarge‐areasurfaces,isequallydistributed.This
simplifiestheoverallmodelsetup,likedividingtheinternalthermalresistance𝑅into
twosimilarparts.Polystyreneplatescovertheouterboundariesofthebattery,asshown
inFigure4.Inthemodel,thesealsosimplifyassingleresistances,𝑅,excludingthe
heatcapacityoftheplatesassumingtheimpactisnegligible.Thevalue𝑅canbecal‐
culatedsinceallmaterialconstantsanddimensionsareknown.ConsideringFigure4,the
Figure 3. Locations of temperature measurement points.
Figure 4shows the overall setup. Here, two plates of polystyrene with a thickness of
30 mm each cover the two wider sides of the cell. To hold these plates in place and to apply
an equal pressure all over the cell’s surface, two identical polyvinyl chloride plates of a
thickness of 10 mm are attached and moderately compressed by six equally distributed
Appl. Sci. 2023,13, 2870 5 of 13
springs. The tests were conducted using a BasyTec MRS cell cycler and a Memmert ICP110
climate chamber to obtain a constant ambient condition at particular temperatures.
Appl.Sci.2023,13,xFORPEERREVIEW5of14
Figure3.Locationsoftemperaturemeasurementpoints.
Figure4showstheoverallsetup.Here,twoplatesofpolystyrenewithathicknessof
30mmeachcoverthetwowidersidesofthecell.Toholdtheseplatesinplaceandto
applyanequalpressurealloverthecell’ssurface,twoidenticalpolyvinylchlorideplates
ofathicknessof10mmareattachedandmoderatelycompressedbysixequallydistrib‐
utedsprings.ThetestswereconductedusingaBasyTecMRScellcyclerandaMemmert
ICP110climatechambertoobtainaconstantambientconditionatparticulartempera‐
tures.
Figure4.Depictionoftestsetup.
2.3.ModelApproach
Thesimplestmodeltodescribethethermalbehaviourofthebatterycellisafirst‐
orderCauermodel.ThiskindofmodelcorrespondswithanRCelementinsystemtheory.
Oftenthescopeofthatmodelisenoughtofeedbackonthesystemresponsetoaspecific
currentsignalofanelectricmodel.Here,themodelisadjustedforthesysteminFigure5.
Theapproachrequiresassumptions.Forinstance,heatgeneration𝑄󰇗andtheheatcapac‐
ity’sC
p
locationoccurinthecell’svolumetriccentre.Also,theheattransferinbothcross‐
planedirections,meaningtowardsthelarge‐areasurfaces,isequallydistributed.This
simplifiestheoverallmodelsetup,likedividingtheinternalthermalresistance𝑅into
twosimilarparts.Polystyreneplatescovertheouterboundariesofthebattery,asshown
inFigure4.Inthemodel,thesealsosimplifyassingleresistances,𝑅,excludingthe
heatcapacityoftheplatesassumingtheimpactisnegligible.Thevalue𝑅canbecal‐
culatedsinceallmaterialconstantsanddimensionsareknown.ConsideringFigure4,the
Figure 4. Depiction of test setup.
2.3. Model Approach
The simplest model to describe the thermal behaviour of the battery cell is a first-order
Cauer model. This kind of model corresponds with an RC element in system theory. Often
the scope of that model is enough to feedback on the system response to a specific current
signal of an electric model. Here, the model is adjusted for the system in Figure 5. The
approach requires assumptions. For instance, heat generation
.
Q
and the heat capacity’s C
p
location occur in the cell’s volumetric centre. Also, the heat transfer in both cross-plane
directions, meaning towards the large-area surfaces, is equally distributed. This simplifies
the overall model setup, like dividing the internal thermal resistance
Rin
into two similar
parts. Polystyrene plates cover the outer boundaries of the battery, as shown in Figure 4.
In the model, these also simplify as single resistances,
Rpoly
, excluding the heat capacity
of the plates assuming the impact is negligible. The value
Rpoly
can be calculated since
all material constants and dimensions are known. Considering Figure 4, the temperature
measurement points lie between the cell surface and the individual polystyrene plates. In
Figure 5, these points are marked as T
sur,up
and T
sur,down
, respectively. The conditions inside
the climate chamber are assumed to be homogeneous in the whole chamber. Therefore, the
ambient temperature Tamb on all sides of the setup is set to be equal.
1
Figure 5. Representation of utilised model configuration.
The measured spectra need to be fitted to extract the cell’s heat capacity and thermal
conductivity in a cross-plane direction. This approach implements a least-squares fitting
algorithm utilising an RC element as the model equation. Therefore, two unknown values,
the time constant
τ
and the resistance value
R
, are fitted. When neglecting the impact of
additional heat capacities, like the polystyrene plates and the effect of the temperature
sensors, as discussed later, the cell’s heat capacity is calculated by
C
=
τ
/
R
. Dividing the
resulting value by the cell mass gives the specific heat capacity cp=C/mcell.
The fitted value
R
, representing the overall thermal resistance, is adapted to obtain the
cross-plane thermal conductivity
λ⊥
. As described above, the system assumes an equal
heat distribution at the top and the bottom. This postulation is required to simplify the
Appl. Sci. 2023,13, 2870 6 of 13
model’s calculation to only one dimension by two resistive elements (
Rin
and
Rpoly
). At the
measurement point Tsur, both Rin and Rpoly are connected in parallel:
Rin =R
1−R
Rpoly (4)
Therefore, as shown in Equation (4), it is necessary to calculate
Rin
from the fitted
R
by subtracting the known thermal resistance of the polystyrene plate. Afterwards, the
resulting
Rin
is divided by two, assuming an equal heat dissipation in both cross-plane
directions of the cell. Finally, converting the final thermal resistance by the dimensions
results in the cell’s cross-plane heat conductivity
λ⊥
using
l
as the cell thickness and
A
as
the cell area in the following Equation (5):
λ⊥=l
Rin
2∗A(5)
2.4. Calorimetric Reference Test
The characterisation method described by [26] using a pseudo-calorimetric reference
test was conducted to get reference values for the specific heat capacity of the tested cells.
The testing scheme requires a reference material with known thermal properties. In this
case, an aluminium plate with dimensions similar to the battery cell surface was used.
The test utilises an insulation setup, as shown in Figure 6a, using a polystyrene casing
with a cut-off in the object’s size to minimise convection and radiation. In the first step,
the setup is heated in the climate chamber to a steady-state temperature of T
amb
= 50
◦
C
with the aluminium plate inserted. After temperature sensors on the object surface inside
the polystyrene casing show the same steady-state temperature, the chamber switches off.
The resulting temperature decrease is recorded inside the insulation (T
s
) and in ambient
conditions inside the climate chamber (T
amb
). Afterwards, the battery cell is inserted,
conducting the same test procedure. This test does not need prior information on the
heat flow. The calculation of the resulting heat capacity is described in [
26
], fitting the
logarithmic temperature difference ∆T=Ts−Tamb as shown in Figure 6b.
Appl.Sci.2023,13,xFORPEERREVIEW7of14
resultingtemperaturedecreaseisrecordedinsidetheinsulation(T
s
)andinambientcon‐
ditionsinsidetheclimatechamber(T
amb
).Afterwards,thebatterycellisinserted,conduct‐
ingthesametestprocedure.Thistestdoesnotneedpriorinformationontheheatflow.
Thecalculationoftheresultingheatcapacityisdescribedin[26],fittingthelogarithmic
temperaturedifference∆𝑇=T
s
−T
amb
asshowninFigure6b.
(a)(b)
Figure6.Referencetestingscheme.(a)Depictionoftheusedsetup;(b)resultingtemperaturedif‐
ferenceofthecellonalogarithmicscale,showingbothmeasuredandfitteddata.
3.Results
Inthefirststep,multiplepre‐testscharacterisingthecell’sbehaviourunderdifferent
ambientconditionsareconductedbeforesamplingthetestmatrix.Themainadaptions
arepresentedandcomparedusingtheconcludingspectra.Duetobettervisualisation,all
upcomingspectraareshownwithlinearinterpolatedgraphsinaNyquistplot.Ifnotmen‐
tionedfurther,thegivenspectrumshowstheresultsfortheuppermeasurementpointin
thecell’scentre.
3.1.Pre‐Tests
Thesetup’ssymmetrymustbeconfirmedtoutilisethemodelgeneralisationde‐
scribedinSection2.ThespectrashowninFigure7representthemeasurementpoints
above(red)andunderneath(green)thecell.Thebehaviourofbothpositionsexhibitsa
similarresult.Thedifferencesinthespecificheatcapacityandthecross‐planethermal
conductivitystayinarangeoflessthan2%forallperformedtests.Forfurtherevaluation,
bothcorrespondingvaluesfromaboveandbelowthecellareaveraged.
Figure7.Symmetryofthetestsetuponthetopandbottomtypesatthesameconditions(T
amb
=25
°C,SOC=50%andI≙2C).
Figure 6.
Reference testing scheme. (
a
) Depiction of the used setup; (
b
) resulting temperature
difference of the cell on a logarithmic scale, showing both measured and fitted data.
3. Results
In the first step, multiple pre-tests characterising the cell’s behaviour under different
ambient conditions are conducted before sampling the test matrix. The main adaptions
are presented and compared using the concluding spectra. Due to better visualisation,
all upcoming spectra are shown with linear interpolated graphs in a Nyquist plot. If not
Appl. Sci. 2023,13, 2870 7 of 13
mentioned further, the given spectrum shows the results for the upper measurement point
in the cell’s centre.
3.1. Pre-Tests
The setup’s symmetry must be confirmed to utilise the model generalisation described
in Section 2. The spectra shown in Figure 7represent the measurement points above (red)
and underneath (green) the cell. The behaviour of both positions exhibits a similar result.
The differences in the specific heat capacity and the cross-plane thermal conductivity stay in
a range of less than 2% for all performed tests. For further evaluation, both corresponding
values from above and below the cell are averaged.
Appl.Sci.2023,13,xFORPEERREVIEW7of14
resultingtemperaturedecreaseisrecordedinsidetheinsulation(T
s
)andinambientcon‐
ditionsinsidetheclimatechamber(T
amb
).Afterwards,thebatterycellisinserted,conduct‐
ingthesametestprocedure.Thistestdoesnotneedpriorinformationontheheatflow.
Thecalculationoftheresultingheatcapacityisdescribedin[26],fittingthelogarithmic
temperaturedifference∆𝑇=T
s
−T
amb
asshowninFigure6b.
(a)(b)
Figure6.Referencetestingscheme.(a)Depictionoftheusedsetup;(b)resultingtemperaturedif‐
ferenceofthecellonalogarithmicscale,showingbothmeasuredandfitteddata.
3.Results
Inthefirststep,multiplepre‐testscharacterisingthecell’sbehaviourunderdifferent
ambientconditionsareconductedbeforesamplingthetestmatrix.Themainadaptions
arepresentedandcomparedusingtheconcludingspectra.Duetobettervisualisation,all
upcomingspectraareshownwithlinearinterpolatedgraphsinaNyquistplot.Ifnotmen‐
tionedfurther,thegivenspectrumshowstheresultsfortheuppermeasurementpointin
thecell’scentre.
3.1.Pre‐Tests
Thesetup’ssymmetrymustbeconfirmedtoutilisethemodelgeneralisationde‐
scribedinSection2.ThespectrashowninFigure7representthemeasurementpoints
above(red)andunderneath(green)thecell.Thebehaviourofbothpositionsexhibitsa
similarresult.Thedifferencesinthespecificheatcapacityandthecross‐planethermal
conductivitystayinarangeoflessthan2%forallperformedtests.Forfurtherevaluation,
bothcorrespondingvaluesfromaboveandbelowthecellareaveraged.
Figure7.Symmetryofthetestsetuponthetopandbottomtypesatthesameconditions(T
amb
=25
°C,SOC=50%andI≙2C).
Figure 7.
Symmetry of the test setup on the top and bottom types at the same conditions (T
amb
=
25 ◦C, SOC = 50% and Iˆ=2C).
The frequency band is mainly defined by comparing two tests using different lower
boundaries. Adding two additional frequencies at 100
µ
Hz and 50
µ
Hz, as described in
Table 1, results in the red-coloured spectrum in Figure 8. Comparing the extended spectrum
to a standard test using the Nyquist plot in Figure 8a and the Bode plot in Figure 8b also
shows good test repeatability.
Figure 8.
Comparison of two tests using a different lower boundary frequency. (
a
) Nyquist plot; (
b
)
corresponding Bode plot; top: amplitude; bottom: phase.
Both tests show practically similar values; especially the specific heat capacity is
roughly the same. When averaging both central measurement points above and underneath
the cell, the difference between both tests stays lower than 1%. The difference between the
cross-plane thermal conductivities shows a higher deviation of approximately 7%. The
thermal influence of the surroundings causes these variations as the heating phases become
longer. Therefore, a higher overall temperature increase results in a smaller general thermal
Appl. Sci. 2023,13, 2870 8 of 13
resistance
Rth
and a higher corresponding thermal conductivity
λ⊥
while testing lower
frequencies.
3.2. Comparision to Reference Test and Other Cell Configurations
The calorimetric test procedure defined in the materials section validates the results
given by the TIS schedule. Also, a comparison to an HE cell using the same geometrical
format as the observed cell is investigated.
In Figure 9, the resulting impedance spectra of both cells are shown. Here, the higher
the temperature response per generated heat is, the larger the resulting semi-circle becomes.
That mainly results from a smaller heat capacity of the cell, causing a more elevated
temperature increase. As expected, the HE cell also shows a smaller cross-plane heat
conductivity resulting from the different layer thicknesses. Especially the thinner current
collectors of HE cells made of proper thermal conductive materials (aluminium and copper)
and thicker active materials decrease the overall cross-plane heat conductivity.
Appl.Sci.2023,13,xFORPEERREVIEW9of14
Figure9.ComparisonoftheNyquistplotfordifferentcelltypesatthesameconditions(T
amb
=25
°C,SOC=50%andI≙2C).
ComparingtheresultsofbothcellsinTable2showstheexpectedbehaviour,usinga
standardambientconfigurationofT
amb
=25°CandaSOCof50%each.Thespecificheat
capacityshowsadifferenceofnearly13%,whilethecross‐planeheatconductivitydiffers
byapproximately16%.Forbothvalues,theHPcelldeliversthesurplus.Whencomparing
bothcelltypesusingthecalorimetrictestsetup,thedifferencebetweenthecellsisre‐
duced,showingadifferenceofonly3%.Apossiblereasonisthesetupused,whichis
highlydependentonthepolystyrenecasing.Moreover,theinfluenceofthesurrounding
airintheclimatechamberismoreprominenthere.Also,adeviationoflessthan2%for
thefurtherinvestigatedHPcellbetweentheTISandthecalorimetrictestcanbeobserved.
ConsideringtheHEcell,thedifferenceisalmost9%.
Table2.Resultingdataforthe46Ahandthe60AhcellatT
amb
=25°CandSOC=50%.
46AhHPCell60AhHECell
Timeconstantτ[s]20922312
Thermalconductivity
λ
[W/(m∙K)]0.470.40
Specificheatcapacityc
p
[J/(kg∙K)]1.251.09
Specificheatcapacityreferencetestc
p
[J/(kg∙K)]1.231.19
3.3.AnalysisofCellBehaviour
Afterfinishingthepre‐testsandthereferenceschedulesusingasimilar‐sizedcelland
acalorimetrictestalternative,thedecisivetestmatrixcoveringtheSOCandtemperature
dependencywascarriedout.Thisinvolvedrepeatingthestandardtestprocedureatthe
differentcellstates,investingfiveSOCs,startingataminimumvalueof20%andincreas‐
ingin15%steps.Also,thetestmatrixstretchedfurther,coveringfivetemperaturemeas‐
urementpointsfrom10°Cto45°CperSOC.
InFigure10,theparameteradaptationiscompared.Ontheleft‐handside,inFigure
10a,theSOCdiffersatastandardtemperatureof25°C,whileintherightplot(Figure
10b),thetemperaturevariesatfixedSOCof50%.Here,thetemperatureimpactappears
tobemoreinfluentialtothebatterycell.Incontrast,theSOCshowsnearlynoparticular
significance,whiletheimpedancespectrumbecomeslargerwhenincreasingtheambient
temperature.Thatimpactresultsfromthesmallertotalheatgeneratedduetoadecreasing
ohmicresistanceofthecellwhenincreasingthetemperature.
Figure 9.
Comparison of the Nyquist plot for different cell types at the same conditions (T
amb
= 25
◦
C,
SOC = 50% and Iˆ=2C).
Comparing the results of both cells in Table 2shows the expected behaviour, using
a standard ambient configuration of T
amb
= 25
◦
C and a SOC of 50% each. The specific
heat capacity shows a difference of nearly 13%, while the cross-plane heat conductivity
differs by approximately 16%. For both values, the HP cell delivers the surplus. When
comparing both cell types using the calorimetric test setup, the difference between the cells
is reduced, showing a difference of only 3%. A possible reason is the setup used, which is
highly dependent on the polystyrene casing. Moreover, the influence of the surrounding
air in the climate chamber is more prominent here. Also, a deviation of less than 2% for
the further investigated HP cell between the TIS and the calorimetric test can be observed.
Considering the HE cell, the difference is almost 9%.
Table 2. Resulting data for the 46 Ah and the 60 Ah cell at Tamb = 25 ◦C and SOC = 50%.
46 Ah HP Cell 60 Ah HE Cell
Time constant τ[s] 2092 2312
Thermal conductivity λ⊥[W/(m·K)] 0.47 0.40
Specific heat capacity cp[J/(kg·K)] 1.25 1.09
Specific heat capacity reference test cp[J/(kg·K)] 1.23 1.19
3.3. Analysis of Cell Behaviour
After finishing the pre-tests and the reference schedules using a similar-sized cell and
a calorimetric test alternative, the decisive test matrix covering the SOC and temperature
dependency was carried out. This involved repeating the standard test procedure at the
different cell states, investing five SOCs, starting at a minimum value of 20% and increasing
Appl. Sci. 2023,13, 2870 9 of 13
in 15% steps. Also, the test matrix stretched further, covering five temperature measurement
points from 10 ◦C to 45 ◦C per SOC.
In Figure 10, the parameter adaptation is compared. On the left-hand side, in
Figure 10a, the SOC differs at a standard temperature of 25
◦
C, while in the right plot
(Figure 10b), the temperature varies at fixed SOC of 50%. Here, the temperature impact
appears to be more influential to the battery cell. In contrast, the SOC shows nearly no
particular significance, while the impedance spectrum becomes larger when increasing the
ambient temperature. That impact results from the smaller total heat generated due to a
decreasing ohmic resistance of the cell when increasing the temperature.
Appl.Sci.2023,13,xFORPEERREVIEW10of14
Figure10.ComparisonoftheNyquistplotwhenchangingatestparameter:(a)adaptingSOCvalue
using25°C;(b)adaptingtemperatureusingSOCat50%.
Theresultsshowthatneitherthespecificheatcapacitynorthermalconductivityin‐
dicateasignificantdependencyontheSOC[12,18,27,28].ThemodelapproachinFigure5
issimplifiedtoextracttheparameterfromthecalculatedspectra.Inthispaper,therele‐
vantvaluesfortheheatcapacityandthermalresistancearefittedusingafirst‐orderCauer
model,representingasingleRCelement,asshownintheuppergraphicinFigure11b.
Thethermalresistanceisthenconvertedtothecross‐planethermalconductivity,further
describedinSection2.3.Figure11acomparesafirst‐ andsecond‐orderfittothedata
points.Thefitshowsgoodoverallaccordancewiththedata.Furthermore,itshowsonly
insignificantchangesintheresultingvaluescomparingafirst‐ordermodel(Figure11b,
top)toasecond‐ordermodel(Figure11b,bottom).Here,thesecond‐ordermodelsimu‐
latesthetimedelaycausedbythetemperaturesensorandothersurroundings.Giventhe
minorinfluenceofthatadditionaltimeconstant,thefittingalgorithmisnotadaptedto
thatbehaviour.

(a)(b)
Figure11.Comparisonofcalculateddatapointsandtheresultingmodelfit.(a)Nyquistplot.(b)
Representationoffirst‐orderCauermodel(top)andsecond‐orderCauermodel(bottom).
Figure12presentsbothvaluesasafunctionofSOCforalltemperaturemeasurement
points.ThethermalconductivityinFigure12bshowsnearlyconstantvalues,whilethe
specificheatcapacityinFigure12ashowsslightlydifferentbehaviourforthehighertwo
temperatures.ThespecificheatcapacityscarcelyincreaseswithSOCathighertempera‐
tures.ThiscanbecausedbytherisingnegativerealpartoftheNyquistdiagram(Figure
10b),whichisnotapartofthegeneralRCfitinthiswork.Here,theinfluenceofthesensor
anddifferentsurroundingsaremoresignificant.
Figure 10.
Comparison of the Nyquist plot when changing a test parameter: (
a
) adapting SOC value
using 25 ◦C; (b) adapting temperature using SOC at 50%.
The results show that neither the specific heat capacity nor thermal conductivity
indicate a significant dependency on the SOC [
12
,
18
,
27
,
28
]. The model approach in Figure 5
is simplified to extract the parameter from the calculated spectra. In this paper, the relevant
values for the heat capacity and thermal resistance are fitted using a first-order Cauer
model, representing a single RC element, as shown in the upper graphic in Figure 11b.
The thermal resistance is then converted to the cross-plane thermal conductivity, further
described in Section 2.3. Figure 11a compares a first- and second-order fit to the data
points. The fit shows good overall accordance with the data. Furthermore, it shows only
insignificant changes in the resulting values comparing a first-order model (Figure 11b,
top) to a second-order model (Figure 11b, bottom). Here, the second-order model simulates
the time delay caused by the temperature sensor and other surroundings. Given the minor
influence of that additional time constant, the fitting algorithm is not adapted to that
behaviour.
Figure 12 presents both values as a function of SOC for all temperature measurement
points. The thermal conductivity in Figure 12b shows nearly constant values, while the
specific heat capacity in Figure 12a shows slightly different behaviour for the higher two
temperatures. The specific heat capacity scarcely increases with SOC at higher temperatures.
This can be caused by the rising negative real part of the Nyquist diagram (Figure 10b),
which is not a part of the general RC fit in this work. Here, the influence of the sensor and
different surroundings are more significant.
Overall, the average specific heat capacity values differ from 1.22 J kg
−1
K
−1
(SOC =
50% and T = 25
◦
C) to 1.35 J kg
−1
K
−1
(SOC = 80% and T = 35
◦
C), showing a maximum
spread of approximately 10%. The average value inside the test matrix is
1.27 J kg−1K−1
.
Regarding the cross-plane thermal conductivity, the values vary by nearly 28% from
0.38 W m
−1
K
−1
(SOC = 65% and T = 45
◦
C) to 0.53 W m
−1
K
−1
(SOC = 35% and T = 10
◦
C),
with an average value of 0.47 W m−1K−1.
Appl. Sci. 2023,13, 2870 10 of 13
Appl.Sci.2023,13,xFORPEERREVIEW10of14
Figure10.ComparisonoftheNyquistplotwhenchangingatestparameter:(a)adaptingSOCvalue
using25°C;(b)adaptingtemperatureusingSOCat50%.
Theresultsshowthatneitherthespecificheatcapacitynorthermalconductivityin‐
dicateasignificantdependencyontheSOC[12,18,27,28].ThemodelapproachinFigure5
issimplifiedtoextracttheparameterfromthecalculatedspectra.Inthispaper,therele‐
vantvaluesfortheheatcapacityandthermalresistancearefittedusingafirst‐orderCauer
model,representingasingleRCelement,asshownintheuppergraphicinFigure11b.
Thethermalresistanceisthenconvertedtothecross‐planethermalconductivity,further
describedinSection2.3.Figure11acomparesafirst‐ andsecond‐orderfittothedata
points.Thefitshowsgoodoverallaccordancewiththedata.Furthermore,itshowsonly
insignificantchangesintheresultingvaluescomparingafirst‐ordermodel(Figure11b,
top)toasecond‐ordermodel(Figure11b,bottom).Here,thesecond‐ordermodelsimu‐
latesthetimedelaycausedbythetemperaturesensorandothersurroundings.Giventhe
minorinfluenceofthatadditionaltimeconstant,thefittingalgorithmisnotadaptedto
thatbehaviour.

(a)(b)
Figure11.Comparisonofcalculateddatapointsandtheresultingmodelfit.(a)Nyquistplot.(b)
Representationoffirst‐orderCauermodel(top)andsecond‐orderCauermodel(bottom).
Figure12presentsbothvaluesasafunctionofSOCforalltemperaturemeasurement
points.ThethermalconductivityinFigure12bshowsnearlyconstantvalues,whilethe
specificheatcapacityinFigure12ashowsslightlydifferentbehaviourforthehighertwo
temperatures.ThespecificheatcapacityscarcelyincreaseswithSOCathighertempera‐
tures.ThiscanbecausedbytherisingnegativerealpartoftheNyquistdiagram(Figure
10b),whichisnotapartofthegeneralRCfitinthiswork.Here,theinfluenceofthesensor
anddifferentsurroundingsaremoresignificant.
Figure 11.
Comparison of calculated data points and the resulting model fit. (
a
) Nyquist plot. (
b
)
Representation of first-order Cauer model (top) and second-order Cauer model (bottom).
Appl.Sci.2023,13,xFORPEERREVIEW11of14
Figure12.ChangingofthermalparametersoverSOCrangeforallcoveredtemperatures.(a)Specific
heatcapacityc
p
.(b)Cross‐planethermalconductivityλ
⊥
.
Overall,theaveragespecificheatcapacityvaluesdifferfrom1.22Jkg
−1
K
−1
(SOC=50%
andT=25°C)to1.35Jkg
−1
K
−1
(SOC=80%andT=35°C),showingamaximumspreadof
approximately10%.Theaveragevalueinsidethetestmatrixis1.27Jkg
−1
K
−1
.Regarding
thecross‐planethermalconductivity,thevaluesvarybynearly28%from0.38Wm
−1
K
−1
(SOC=65%andT=45°C)to0.53Wm
−1
K
−1
(SOC=35%andT=10°C),withanaverage
valueof0.47Wm
−1
K
−1
.
Whilethespecificheatcapacityremainsnearlyunchangedatthedifferentused
states,thecross‐planethermalconductivitynegativelycorrelateswithtemperature,as
showninFigure13a.Thatcorrelationwasalsoobservedin[5,8,18,29].InFigure13b,the
averageovereachSOCpertemperaturepointwasusedtoobtainthefunctiongainbya
linearfit.Here,thecorrelationis−0.37%/Kforλ⊥.
Figure13.Developmentofcross‐planethermalconductivityλ
⊥
overtemperatureforallcovered
SOC.(a)Measurementpointsandtheaverageateverydatapoint.(b)Averageateverydatapoint
andcorrespondinglinearfit.
4.Discussion
Theresultingvaluesforthespecificheatcapacityandthecross‐planethermalcon‐
ductivityindicateahighercorrelationofthethermalmodelparameterstotheambient
temperaturethantotheSOC.Also,thespecificheatcapacityshowsamoreconsistent
behaviour[26,30–32].Theaveragedc
p
concerningtheSOCdiffersby2.2%foralltests,
showingslightlyhigherresultsforhigherSOCs.Thedifferentaveragedvaluesbythe
temperatureshowadeviationof6.5%,peakingat35°CasshowninFigure12a.Further‐
more,theinformationinFigure12bshowstherisinginfluenceofhigherT
amb
onthetest
results.ThisleadsbacktotheTIStestingscheduleandtheresultingtemperatureresponse
duetolessheatgeneratedbyadecreasedohmicresistanceathighertemperatures.
Figure 12.
Changing of thermal parameters over SOC range for all covered temperatures. (
a
) Specific
heat capacity cp. (b) Cross-plane thermal conductivity λ⊥.
While the specific heat capacity remains nearly unchanged at the different used states,
the cross-plane thermal conductivity negatively correlates with temperature, as shown in
Figure 13a. That correlation was also observed in [
5
,
8
,
18
,
29
]. In Figure 13b, the average
over each SOC per temperature point was used to obtain the function gain by a linear fit.
Here, the correlation is −0.37%/K for λ⊥.
Appl.Sci.2023,13,xFORPEERREVIEW11of14
Figure12.ChangingofthermalparametersoverSOCrangeforallcoveredtemperatures.(a)Specific
heatcapacityc
p
.(b)Cross‐planethermalconductivityλ
⊥
.
Overall,theaveragespecificheatcapacityvaluesdifferfrom1.22Jkg
−1
K
−1
(SOC=50%
andT=25°C)to1.35Jkg
−1
K
−1
(SOC=80%andT=35°C),showingamaximumspreadof
approximately10%.Theaveragevalueinsidethetestmatrixis1.27Jkg
−1
K
−1
.Regarding
thecross‐planethermalconductivity,thevaluesvarybynearly28%from0.38Wm
−1
K
−1
(SOC=65%andT=45°C)to0.53Wm
−1
K
−1
(SOC=35%andT=10°C),withanaverage
valueof0.47Wm
−1
K
−1
.
Whilethespecificheatcapacityremainsnearlyunchangedatthedifferentused
states,thecross‐planethermalconductivitynegativelycorrelateswithtemperature,as
showninFigure13a.Thatcorrelationwasalsoobservedin[5,8,18,29].InFigure13b,the
averageovereachSOCpertemperaturepointwasusedtoobtainthefunctiongainbya
linearfit.Here,thecorrelationis−0.37%/Kforλ⊥.
Figure13.Developmentofcross‐planethermalconductivityλ
⊥
overtemperatureforallcovered
SOC.(a)Measurementpointsandtheaverageateverydatapoint.(b)Averageateverydatapoint
andcorrespondinglinearfit.
4.Discussion
Theresultingvaluesforthespecificheatcapacityandthecross‐planethermalcon‐
ductivityindicateahighercorrelationofthethermalmodelparameterstotheambient
temperaturethantotheSOC.Also,thespecificheatcapacityshowsamoreconsistent
behaviour[26,30–32].Theaveragedc
p
concerningtheSOCdiffersby2.2%foralltests,
showingslightlyhigherresultsforhigherSOCs.Thedifferentaveragedvaluesbythe
temperatureshowadeviationof6.5%,peakingat35°CasshowninFigure12a.Further‐
more,theinformationinFigure12bshowstherisinginfluenceofhigherT
amb
onthetest
results.ThisleadsbacktotheTIStestingscheduleandtheresultingtemperatureresponse
duetolessheatgeneratedbyadecreasedohmicresistanceathighertemperatures.
Figure 13.
Development of cross-plane thermal conductivity
λ⊥
over temperature for all covered
SOC. (
a
) Measurement points and the average at every data point. (
b
) Average at every data point
and corresponding linear fit.
Appl. Sci. 2023,13, 2870 11 of 13
4. Discussion
The resulting values for the specific heat capacity and the cross-plane thermal con-
ductivity indicate a higher correlation of the thermal model parameters to the ambient
temperature than to the SOC. Also, the specific heat capacity shows a more consistent
behaviour [
26
,
30
–
32
]. The averaged c
p
concerning the SOC differs by 2.2% for all tests,
showing slightly higher results for higher SOCs. The different averaged values by the tem-
perature show a deviation of 6.5%, peaking at 35
◦
C as shown in Figure 12a. Furthermore,
the information in Figure 12b shows the rising influence of higher T
amb
on the test results.
This leads back to the TIS testing schedule and the resulting temperature response due to
less heat generated by a decreased ohmic resistance at higher temperatures.
Examining the cross-plane thermal conductivity showed a more significant reliance
on external conditions. While averaging the results per SOC, a minor deviation of 2.3%
emerges, compared to the crucial impact of T
amb
. Here, the difference of 21.1% between
the averaged values at 10
◦
C and 45
◦
C shows a linear dependency [
33
,
34
] decreasing
by
−
0.37%/K. Steinhardt et al. [
18
] also detected a similar behaviour using different
measurement methods. A possible reason is the thermal contact resistance, as discussed
in [
5
,
18
]. In contrast, [
3
] did not observe such changes using lithium–iron–phosphate cells,
leading to the assumption that the changes are highly dependent on cell chemistry. Thus,
further investigations, not in the scope of this work, need to be conducted, especially
considering these matters.
Some considerations towards the applicability of the TIS have to be made, especially
regarding the negative real part in the Nyquist plot. This behaviour represents at least a
second heat capacity in the setup, further illustrated in the phase response of Figure 7b,
showing a phase angle of less than
−
90
◦
. An additional phase shift is caused by the impact
of temperature measurements using physically contacted sensors [
22
], like the PT100 in
this work. Also, the surroundings have to be considered in this context since every material
has a heat capacity, which influences the resulting spectra.
In this paper, the used model relies on a single RC element using only the heat capacity
of the battery, which gives the primary response to the heat generated. In the electrical
domain, models are usually described by the Foster model, utilising components connected
in series. Here, every element can be more precisely distinguished. The thermal behaviour
needs to be modelled differently to maintain the physical representation by the Cauer
model, as shown in Figure 11b. The difference lies in the arrangement of the components,
which are nested here. This concludes with the given thermal response and the caused
spectra showing the aforementioned negative real part, representing a phase shift of more
than −90◦.
To summarise, the negative part cannot be represented using the fitting function.
However, this is neglected here since the influence (supposedly from the sensor) only
changes the result insignificantly, as recorded in the literature [
20
,
21
,
23
]. Since a quasi-
stationary state is reached at the beginning of the test schedule by increasing the length
of the first measurement point, the cell’s behaviour does not depend on the test schedule
beforehand. That is important for further usage of TIS as an addition to standard battery
check-up tests, using only slight adaptions to the test setup and increasing the testing time
by approximately one day. The test is easily reproducible, showing only minor derivation
over the conducted tests, for instance, while comparing the frequency bands in Figure 8.
The test results mainly differ when changing the test setup or using another overall test
setup, which causes changes in the thermal resistance,
Rpoly
, which covers the heat transfer
to the surroundings.
Investigating the different measured data points, shown in Figure 3, leads to the
expected cell conditions. This concludes in decreasing specific heat capacity and increasing
cross-plane thermal conductivity the closer the measurement point comes to the tabs and
vice versa. The leading cause is the current distribution inside the cell, which is higher at
the tabs and lower at the distal ends of the battery cell [
35
–
38
], causing faster and more
Appl. Sci. 2023,13, 2870 12 of 13
significant heating at higher current rate locations. That aspect also needs to be considered
regarding upcoming thermal management systems.
5. Conclusions
Overall, the technique presented in this paper shows the possibility of using the TIS to
characterise even large-format LIBs besides decreasing the overall testing time for more
direct implementation in battery characterisation methods. A follow-up to the described
approach can include investigating battery modules to identify the heat propagation from
one cell to the next and the temperature gradients going along with it. Moreover, the
influence of the cell sizing and the impact of the cell configuration as HE or HP need to be
regarded in more detail in upcoming work.
Author Contributions:
Conceptualization, D.D.; methodology, D.D.; software, D.D.; validation, D.D.;
formal analysis, D.D.; investigation, D.D.; resources, D.D.; data curation, D.D.; writing—original
draft preparation, D.D. and J.K.; writing—review and editing, D.D. and J.K.; visualization, D.D.;
supervision, J.K.; project administration, D.D. and J.K.; funding acquisition, J.K. All authors have
read and agreed to the published version of the manuscript.
Funding:
This research was funded by Federal Ministry for Economic Affairs and Energy (BMWE),
grant number 03ETE033B.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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