Pulse power characterisation for lithium ion cells in automotive

Pulse power characterisation for lithium ion cells in automotive
Pulse power characterisation for lithium
ion cells in automotive applications
Small and large signal cell impedance analysis
Master’s thesis in Electric Power Engineering
SANDEEP NITAL DAVID
Department of Energy and Environment
C HALMERS U NIVERSITY OF T ECHNOLOGY
Gothenburg, Sweden 2016
M ASTER ’ S THESIS R EPORT 2016
Pulse power characterisation for lithium ion cells in
automotive applications
Small and large signal cell impedance analysis
SANDEEP NITAL DAVID
Department of Energy and Environment
Division of Electric Power Engineering
C HALMERS U NIVERSITY OF T ECHNOLOGY
Gothenburg, Sweden 2016
Pulse power characterisation for lithium ion cells in automotive applications
Small and large signal cell impedance analysis
SANDEEP NITAL DAVID
© SANDEEP NITAL DAVID.
Supervisors: Stefan Skoog, Chalmers
Bengt Axelsson, CEVT AB
Examiner: Torbjörn Thiringer, Energy and Environment
Department of Energy and Environment
Division of Electric Power Engineering
Chalmers University of Technology
SE-412 96 Gothenburg
Telephone +46 31 772 1000
Cover: Equivalent circuit model to represent EIS data in time domain
Typeset in LATEX
Chalmers Bibliotek, Reproservice
Gothenburg, Sweden 2016
iv
Pulse power characterisation for lithium ion cells in automotive applications
Small and large signal cell impedance analysis
SANDEEP NITAL DAVID
Department of Energy and Environment
Division of Electric Power Engineering
Chalmers University of Technology
Abstract
The pulse power capability of a Lithium ion cell is an important factor to be considered while dimensioning a traction battery pack. Pulse Power characterization of a Lithium ion cell requires an accurate Equivalent Circuit Model(ECM) in
order to describe its dynamic behaviour. The two widely adopted methods for
parametrising ECMs are the Current Interruption and Electrochemical Impedance
Spectroscopy(EIS) methods. These methods are rarely unified for model development, and therefore this thesis seeks to analyse cells from two different chemistries
using both methods in order to draw vital deductions regarding cell impedance
behaviour under different operating conditions. The parametrised model obtained is validated using a vehicle driving cycle and a deviation of 30 mV in
Root Mean Square Error(RMSE) value between measurement and simulation is
obtained. The cell parameters are further used to derive and quantify the pulse
power capability of a battery pack which consists of the cells used in this study.
Keywords: Lithium ion cell, Electrochemical Impedance Spectroscopy (EIS), Equivalent Circuit Modelling (ECM), Dual Polarisation (DP) model, Current Interruption (CI) method, Pulse power
v
Acknowledgements
First and foremost I would like to express my appreciation to my supervisor at
Chalmers, Stefan Skoog, for his overwhelming technical support and guidance
throughout this thesis. I also want to thank my supervisor at CEVT, Bengt Axelsson for providing the opportunity for this thesis and his constant support during
the work. Furthermore, I would like to express my gratitude to my examiner,
Torbjörn Thiringer, for all the meetings and insightful feedback on my practical
and written work.
Sandeep David, Gothenburg, June 2016
vii
Contents
1
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3
4
Introduction
1.1 Background .
1.2 Aim . . . . . .
1.3 Scope . . . . .
1.4 Contributions
1.5 Thesis outline
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Equivalent circuit modelling: Time domain
2.1 Cell chemistries under consideration . . . . . .
2.2 Cell impedance phenomena to be observed . .
2.2.1 Cell Open Circuit Voltage . . . . . . . .
2.2.2 DC Resistance . . . . . . . . . . . . . . .
2.2.2.1 Ohmic voltage drop . . . . . .
2.2.2.2 Charge transfer polarisation .
2.2.3 Diffusion polarisation . . . . . . . . . .
2.3 Choice of method for cell parametrisation . . .
2.3.1 Overview of common techniques used
2.3.2 Current Interruption technique . . . . .
2.4 Model Selection . . . . . . . . . . . . . . . . . .
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Equivalent circuit modelling: Frequency domain
3.1 EIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Characteristic points on the EIS measurements . . . . .
3.3 Model Selection . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Equivalent circuit with Constant phase elements
3.3.2 Equivalent circuit with RC elements . . . . . . .
3.3.2.1 Comprehensive model:6 RC . . . . . .
3.3.2.2 Approximation based model:2 RC . . .
Experimental setup and Measurements: Large signal
4.1 Test setup . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Cell formatting . . . . . . . . . . . . . . .
4.2 Procedure . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Post-processing . . . . . . . . . . . . . . .
4.3 Measurements . . . . . . . . . . . . . . . . . . . .
4.3.1 OCV curve determination . . . . . . . . .
4.3.2 Impedance behaviour over SOC . . . . .
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ix
Contents
4.3.3
4.3.4
5
Impedance behaviour over temperature range . . . . . . . .
Impedance behaviour with different current magnitudes . .
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7
Model fitting: Small signal
7.1 6 RC model fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 2 RC model fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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8
Comparison of all developed models
8.1 Cell behavioural trends captured by both methods . . . . . . . . .
8.1.1 DC resistance behaviour over SOC and Temperature . . .
8.1.2 Diffusion resistance behaviour over SOC and Temperature
8.1.3 Impedance dependence on Crate . . . . . . . . . . . . . . .
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Validation of models
9.1 Development of simulation model . . . . . . . . . . . . . . . . . . .
9.2 Drive-cycle selection . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Model evaluation by error comparison . . . . . . . . . . . . . . . . .
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10 Derivation of pulse power limits
10.1 Pulse power characterisation . . . . . . . . . . . . . . . . . . . . . .
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47
11 Conclusions
11.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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51
Bibliography
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6
9
x
Experimental setup and Measurements: Small signal
5.1 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Measurements . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 OCV curve determination . . . . . . . . . . . .
5.3.2 Impedance behaviour over SoC range . . . . .
5.3.3 Impedance behaviour over temperature range
21
22
Model fitting: Large signal
6.1 2 RC model fit . . . . . . . . . .
6.1.1 Algorithm . . . . . . . .
6.1.2 Parameter identification
6.2 R10 value based simulation . .
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Contents
List of Symbols and Abbreviations
HEV
EV
CI
EIS
BT
R DC
Ro
CPE
OCV
SOC
ECM
TEM
C-rate
DP
Li
SSE
RMSE
Electric Vehicle
Electric Vehicle
Current Interruption
Electrochemical Impedance Spectroscopy
Battery Tester
Resistance of a cell within few hundred milliseconds
Cell ohmic resistance
Constant Phase Element
Open Circuit Voltage
State of Charge
Equivalent Circuit Model
Thermo Electric Module
Current-rate
Dual Polarization
Lithium ion
Sum of Squared Errors
Root Mean Square Error
xi
Contents
xii
Chapter 1
Introduction
1.1
Background
Dimensioning the traction battery pack for any form of hybrid or pure electric
vehicle needs to encompass several parameters so that the vehicle is capable of
meeting all its necessary performance criteria. When choosing cells for the battery pack, a factor which in general tends to be crucial is the maximum power
extractable from the cells, or in short, the pulse power characteristic of a cell. This
characteristic shows a strong dependency on the cell’s impedance behaviour[1].
Moreover during high current loading, the heat generated from the battery and
its energy efficiency are also primarily determined by the cell’s internal impedance.
Therefore the knowledge of the internal impedance of a lithium ion cell is one of
the most important factors while designing a complete battery system. Investigations described in literature regarding cell impedance characteristics show that it
depends on several factors which include the SOC, temperature, current magnitude and history of usage[1].
Two techniques which are predominantly used for cell impedance study are the
Current pulse method and Electrochemical Impedance Spectroscopy. The former
involves the measurement of the cell voltage response during or after a DC current pulse and concerns a study in the time domain[2], whereas the latter in comparison uses much smaller current signals and is a frequency domain study[3].
Therefore these two techniques will from now on be referred to as the Large signal and Small signal methods. These methods are rarely unified for model development and parametrisation, thus providing a niche for a significant research
contribution through this thesis.
1.2
Aim
To quantify and validate the pulse power deliverable from a lithium ion cell
through extensive investigation of its internal impedance at different operating
SOCs, temperatures and current magnitudes. To also establish and validate a
1
1. Introduction
suitable approach for modelling EIS measurements in the time domain.
1.3
Scope
This thesis is aimed at developing an accurate equivalent circuit model for a
lithium ion cell by investigating its impedance characteristic under various operating conditions. The variations under which the cell impedance is studied
includes different SOC points, temperatures and current magnitudes. The parameters for the ECMs are independently obtained through the Large and Small
signal methods. Though presently a clear method for unifying the results from
the two methods doesn’t exist, this work will seek to make a contribution towards
this. The parametrised ECMs obtained through each method will be verified, and
followingly validated using the HPPC dynamic drive cycle. The results obtained
will be further used for determining the pulse power limits of a cell. In order to
further ascertain the results purported from this work, experiments will not be restricted to a single cell, but rather to three cells, covering two different chemistries
which currently finds wide application in the automotive industry[4].
In practice, the pulse power deliverable by a cell also depends on the contribution it would have on the rapid aging of the cell. In other words, the maximum
extractable power must be limited in order to conserve the life time of the cell.
Numerous tests described in research publications show that high current discharge rates results in a much shorter cell life expectancy[5]. Studying the effect
of discharge rates on cell aging requires numerous accelerated cycling tests to
be performed on the cells and due to the limited time available, no such experiments on cell aging will be conducted during this thesis. Since the implications of
higher discharge rates on cell-life span is quite evident, the pulse discharge current ratings explicitly specified by the cell manufacturer will be strictly adhered to
throughout this thesis. Moreover since the temperature and voltage limits could
also have a considerable impact of cell aging[6][7], these too will be adhered due
to during all experiments.
This thesis is solely focused on the pulse discharge characteristics of cells and
therefore studying the pulse charge characteristics is outside the scope. Moreover when considering cell performance modelling, any phenomena showing up
at battery pack level which may include cell voltage imbalance, the BMS, cable
inductance, HV connector resistance, fuse non-linearity, cell tab interconnection
losses, etc. will not be taken into account.
2
1. Introduction
1.4
Contributions
The highlight of this thesis is the possible unification of the Large and Small signal
methods, and in doing so, being able to draw vital deductions from the data obtained from both backgrounds. This could lead to the developments of more comprehensive lithium ion cell models. Several researchers have used either method
for measurements independently, but very few have used both simultaneously
to enhance model development. Whilst trying to replicate EIS measurements
in the frequency domain with their ECM models, researchers generally tend to
use Constant Phase Elements(CPE)[5][8][9]. However, there is no accurate representation of CPEs in the time domain and therefore most researchers using the
EIS technique find it hard to interpret their results, especially at lower frequencies(typically < 0.5 Hz). However understanding the cell behaviour from EIS
measurement at lower frequencies is extremely important, especially while simulating automotive drive cycles[10].
In [11] Buller states that CPEs can be represented as an approximation in the
time domain. The authors of [3] have made a suitable approximation for the
CPEs in the time domain which gave satisfactory results but use as many as 3 RC
networks which can be considered as fairly complex in terms of computational
power required for its real-time implementation. Hereby this work will focus
on trying to further simplify the complexity of the ECMs required to approximate the EIS data from the frequency domain to the time domain. During this
work several ECMs ranging from being highly accurate yet complex, to less accurate and simple models will be devised to represent EIS data for different cells
at different SOCs and temperatures in the time domain. The results obtained
from these ECMs will be both verified and validated appropriately. They will
then be used to derive the cell’s pulse power limits at various conditions. During the course of this work, some characteristic trends observed in terms of cell
behaviour with respect to type of cell chemistry or operating conditions will be
mentioned, and further substantiated with previously published research work.
1.5
Thesis outline
Following a brief introduction for the thesis covered in this chapter, a comprehensive collection of used theory with respect to equivalent circuit modelling in
the time and frequency domain is presented in the chapters to follow. Consequently the test setups for all the experiments conducted are described together
with visualisations for some of the important measurements obtained. Model fitting of the practical data in both time and frequency domain are comprehensively
analysed, followed by their verification and validation explained in independent
chapters. In conclusion, pulse power limits for the cells are derived and then the
thesis is concluded with some inferences obtained together with comments on
future work which could be done.
3
1. Introduction
4
Chapter 2
Equivalent circuit modelling: Time
domain
2.1
Cell chemistries under consideration
Two different cell chemistries are used for experiments during this work. This
section provides a brief summary for each chemistry used, in addition to highlighting its intrinsic characteristics.
Lithium Nickel Manganese Cobalt Oxide (NMC): This cell type combines a
nickel cathode which has high specific energy, together with a manganese structure which gives it a very low internal resistance. It is commonly used together
with a graphite anode. These cells typically have a nominal cell voltage of around
3.65 V and a maximum voltage of 4.2 V. NMC type cells have potentially long
cycle lives and good characteristics with respect to safety. These cells can be
customized by the manufacturer to have high specific energy or high specific
power[12].
Lithium Iron Phosphate (LFP): When LFP is used as a the cathode material, it
has becomes very safe, has good thermal stability, high tolerance to abuse, high
power density and long cycle life. It is commonly used together with a graphite
anode. However its energy density is relatively lower than other mixed metal
oxides. This can be mainly attributed to the fact that it has a lower nominal cell
voltage of 3.3V and maximum of 3.6V. Notably LFP has a higher self-discharge
than other Li-ion batteries[12].
2.2
Cell impedance phenomena to be observed
Cell impedance can be described in terms of the voltage drop over a cell when a
load current is applied as shown in Figure 2.1. In the first moment after applying
the current pulse, the voltage drops immediately over its pure ohmic resistance,
followed by the charge transfer resistance within a few hundred milliseconds.
5
2. Equivalent circuit modelling: Time domain
The gradual voltage decrease measured further on in time is mainly due to the
slow diffusion processes taking place within the cell. Likewise when the current
stops flowing, the ohmic voltage drop immediately disappears followed quickly
by the disappearance of the voltage drop due to the charge transfer resistance.
The slow rise observed thereafter in the voltage curve is again due to slow diffusion processes taking place.
Figure 2.1: Voltage drop over cell upon discharge current pulse
2.2.1
Cell Open Circuit Voltage
The difference between the two electrodes of a cell at zero current density is called
the open circuit voltage of the cell at a given state-of-charge. According to the
work in [13], the OCV predominantly varies with SOC and is typically found to
be fairly independent of temperature between the range of -10 to 50◦ C.
2.2.2
DC Resistance
The term DC Resistance R DC is used to refer to the voltage drop which occurs
across the cell from the instant of applying a current pulse till the first few hundreds of milliseconds. Therefore it comprises of not only the ohmic voltage drop
but also the voltage drop due to charge transfer polarisation.
2.2.2.1
Ohmic voltage drop
This voltage drop is a combination of the resistances arising from the active material of the anode and the cathode, the separator and the electrolyte[14].
6
2. Equivalent circuit modelling: Time domain
2.2.2.2
Charge transfer polarisation
This time-dependent resistance is attributed to the double layer capacitance which
occurs between the electrolyte and the ions traveling through the electrolyte towards the anode or cathode. The charge transfer resistance reflects the chargetransfer process during the reactions taking place on the electrode–electrolyte interfaces.
2.2.3
Diffusion polarisation
This is the main factor contributing to the sluggish voltage response of the cell
both during and after a current pulse. The Li ions need to be transported from
the surface to the centre of the active material, and this process is termed as solid
state diffusion. The concentration difference between the Li concentration at the
surface, and the equilibrium concentration causes the diffusion polarisation[15].
2.3
2.3.1
Choice of method for cell parametrisation
Overview of common techniques used
The authors in [16] have discussed several methods for determining the internal
impedance of a cell. Two general methods discussed either involved using current steps to study the voltage response or measuring the heat loss from the cell.
Interestingly, both types of methods yielded same results. However, the current
step method is used in this work as it more prevalent among researchers and also
convenient since the accurate measurement of heat loss requires sophisticated
equipment. While considering the current step method, one can either chose the
current injection technique or the current interruption technique. Procedures involving both these methods were adopted in [2] and it is concluded that they give
similar results provided that sufficient relaxation time is allowed while using the
current interruption method. This is mainly to allow sufficient time for diffusion
polarization to take place.
2.3.2
Current Interruption technique
The current interruption technique is utilised in this work for large signal based
impedance analysis. This is mainly due to the fact that when current injection is
performed, the SOC of the cell is no longer constant and therefore the extracted
parameters cannot be associated with a specific SOC point. However, in accordance with[2], when using current interruption, sufficient time is allowed to account for diffusion polarisation. All experiments are done using discharge current pulses, thereby only determining the cell’s discharge resistance, and not its
charge resistance. Several researchers[17][18] have experimentally proven that
charge and discharge resistances are certainly within comparable range, but typically show differing trends over the SOC range. Therefore it is evident that assuming identical values for charge and discharge resistance at the same operating
7
2. Equivalent circuit modelling: Time domain
conditions would not lead to large inaccuracies in the models developed using
them.
2.4
Model Selection
In order to predict the performance of a cell at different operating conditions and
loading, simulations based on an ECMs are widely used[19][20][21]. ECMs which
are used to represent battery dynamics are computationally more efficient than
complex physical battery models and therefore well suited to applications in the
BMS for EVs and HEVs. They are commonly used for two purposes: to predict
battery performance and for accurate SOC prediction.
Figure 2.2: Rint model
The simplest ECM described in [22] is the Rint model shown in Figure 2.2. This
model uses only two elements, representing the cell’s OCV and its internal resistance respectively. The OCV is generally expressed as a function of SOC and
resistance as function of SOC and temperature. However it is fairly obvious that
this model will not be able to replicate the transient voltage behaviour which is
typically exhibited by a Li-ion cell. Therefore one ought to incorporate a certain
number of RC branches into this model in order to improve its modelling accuracy.
8
2. Equivalent circuit modelling: Time domain
Figure 2.3: Dual Polarisation Model
The work in [20] shows that 3 RC branches are required in order to accurately
capture both the quick and slow aspects of the transient behaviour of an LFP cell.
However the issue with using 3 RC branches is the increased computational complexity involved and therefore a slightly simpler option is sought for. The authors
of[19] and [22]have compared simpler models which include the Dual Polarisation(DP),Single Polarisation(SP) model and the Rint model. These models have
two, one and no RC branches respectively. Results from these works show that
the DP model shown in Figure 2.3 achieves a good compromise between model
accuracy and complexity, wherein one RC branch represents the quick transient
while the other represents the relatively slower transient.
Based on these mentioned findings, the DP model is chosen as the candidate to
analyse cell impedance behaviour under various operating conditions. Since the
DP ECM will be used to replicate the cell’s voltage rise after the current pulse has
been removed,
Vt = V0 + V1 e
− R tC
1 1
+ V2 e
− R tC
2 2
(2.1)
can be mathematically used to represent this type of behaviour. In fact, this equation forms the basis for the curve fitting tool which is to be used for parameter
extraction.
9
2. Equivalent circuit modelling: Time domain
10
Chapter 3
Equivalent circuit modelling:
Frequency domain
3.1
EIS
EIS is a widely used technique to investigate electrochemical systems. It is especially valuable when used as a tool to calculate and observe various phenomena
occurring within a cell. The advantage of EIS is that it is non-destructive to the
investigated system. It basically involves imposing a small sinusoidal current
signal at a given frequency on the cell. The voltage response measured at the
cell is approximately a sinusoidal signal, and this procedure is repeated across a
wide range of frequencies. Finally, the impedance Z of the system is calculated
and expressed in terms of its real and imaginary magnitudes in milli-ohms as a
function of the frequency. The phenomena arising at different regions in the frequency spectrum are thus obtained and some characteristic points can be used to
describe the dynamic behavior of the cell, thereby allowing the creation of models.
Since the excitation signal used is sinusoidal, a significant consequence is that
the cell being tested remains at the same SOC point throughout the entire EIS
measurement. Also, unlike in the Large signal method, the impedance measured
is neither the charge nor discharge impedance but rather the average of these two
quantities.
11
3. Equivalent circuit modelling: Frequency domain
3.2
Characteristic points on the EIS measurements
Figure 3.1: Typical EIS measurement at a specific SOC and Temperature
Upon analysing Figure 3.1, it can be inferred that at very high frequencies the
spectrum shows inductive behaviour caused by metallic elements in the cell and
cables. The curve’s intersection with the real axis, approximately represents the
ohmic resistance Ro which is the sum of the resistances of current collectors, active
material, electrolyte and separator [5]. The semicircle-like shape which follows is
typically associated with the double layer capacity and charge transfer resistance
Rct at the electrodes. According to [5], the real part of the impedance at the local
minima approximately represents the sum of Ro and Rct . In older cells, a second
semi circle might also be present, representing the SEI layer which is formed during cycling on the surface of the anode. The final, low frequency part of the curve
is attributed to the diffusion processes taking place in the active material of the
electrodes[21]. This low frequency diffusion gives rise to what is known as the
Warburg impedance. At the initial part of the spectrum, i.e. at the high frequencies, the Warburg impedance isn’t very significant since diffusing reactants don’t
have to move very far. However at low frequencies, the reactants have to diffuse
farther, thus increasing the Warburg-impedance[23].
12
3. Equivalent circuit modelling: Frequency domain
3.3
3.3.1
Model Selection
Equivalent circuit with Constant phase elements
Figure 3.2: CPE based ECM representation of EIS data
Despite the fact that EIS can be used for comprehensively determining the cell
impedance by distinguishing its individual components such as ohmic, charge
transfer and mass transfer polarizations from a single experiment, it often faces
the issue of being too complex, especially in terms of interpretation of the data.
Using the data obtained from EIS measurements,appropriate ECMs are parametrised through fitting procedures in the frequency domain in order to be able to interpret the EIS results in the time domain.
The most common ECMs used for modelling EIS data comprise of constant phase
elements, which are needed in order to obtain a satisfactory fit with the EIS
measurements. Typical EIS measurements can be fitted by equivalent circuits
as shown in Figure 3.2 which were used in [5][3][8]. In these types of ECMs,
L represents the inductive behaviour at high frequencies, Ro is ohmic resistance
comprising of the electrolyte, separator, and electrode resistance. Rct and Cdl are
charge-transfer resistance and its related double-layer the mid-frequency range.
The Warburg impedance which is related to the diffusion of the lithium ions in
the active material, is represented by a straight sloping line at the low frequency.
13
3. Equivalent circuit modelling: Frequency domain
0.5
alpha=1
0.45
alpha=0.8
alpha=0.5
0.4
0.35
-ImZ
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ReZ
Figure 3.3: Impact of alpha value on CPE behaviour in frequency domain
In the mid-frequency range of the EIS measurement shown in Figure 3.1, it can be
seen that the shape of the spectrum doesn’t represent an ordinary semicircle, but
rather a depressed semicircle. Using an ordinary capacitor to represent this kind
of behaviour in the frequency domain is not successful since it is incapable of
producing the depressed-circles. Capacitors show up at perfect half cycles when
modelled in the frequency domain. Therefore, a CPE is necessary in order for the
ECM to reproduce a depressed-circular shape in the frequency domain and is the
reason why there are commonly used in ECMs to represent EIS data.
A CPE is a non-intuitive circuit element that is invented while looking at the
response of real-world systems. The depressed semicircle which it exhibits in the
frequency domain has been explained to be due to the fact that some property of
the system is not homogeneous or that there is some distribution or dispersion of
the value of some physical property of the system. A CPE can be mathematically
represented as
ZCPE =
1
( jω )α C
(3.1)
where C is its capacitive impedance, ω is the frequency and α represents the ratio
of the extent of its behaviour between a capacitor and resistor. The value of α
controls the level of depression of the semicircles as is seen in Figure 3.3.
Similar to how the CPE is used to model Cdl , it is also used to represent the Warburg impedance. Since the Warburg impedance appears as a straight line with a
slope at roughly 45◦ , it basically has almost equal real and imaginary impedances
at the lower frequencies. Therefore it can be modelled as a CPE with a with α=45◦ .
Once again the issue with using CPEs in the ECMs is that they have no physical
representation and therefore it makes it hard to interpret the results obtained from
these ECMs.
14
3. Equivalent circuit modelling: Frequency domain
3.3.2
Equivalent circuit with RC elements
3.3.2.1
Comprehensive model:6 RC
0.5
alpha=0.8
0.45
3RC
1RC
0.4
0.35
-ImZ
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ReZ
Figure 3.4: Approximate representation of CPE using RC elements
Buller in his work [11] found that it is possible to find approximations for a CPE
using only R and C elements. He suggested both 5 RC and 3 RC based networks
whose values when chosen suitably become equivalent to a CPE. The 5 RC model
is more accurate but the 3 RC model is more computationally efficient since it involved lesser number of parameters. Buller also validated both models in his
work and suggested that the 3 RC network is recommended as the general simulation tool and the fit it gives to replicate the behaviour of a CPE is shown in
Figure 3.4.
Figure 3.5: Comprehensive RC network based representation
Adopting the findings of Buller, the 3 RC nework is used to replace the 2 CPEs
in the ECM depicted in Figure 3.2. Therefore a total of six RC elements were
15
3. Equivalent circuit modelling: Frequency domain
required in the new ECM in Figure 3.5. Since the values of α are different for each
of the two CPEs, they need to be represented independently with 3 RC networks.
While performing the model fitting using numerical optimisation algorithms, a
fit similar to that shown in Figure 3.4 can be expected.
3.3.2.2
Approximation based model:2 RC
As discussed in the previous section, the 6 RC model is able to comprehensively
replicate the EIS measurements without any CPEs. However a 6 RC ECM is very
complex and requires a lot of computational power. It is therefore not a practically viable option. In order to further simplify the 6 RC based ECM without
sacrificing too much accuracy, a new 2 RC based model is proposed, wherein a
fixed Resistance R DC and 2 RC networks represent the EIS data. This ECM is
depicted in Figure 3.6. It is evident that this ECM isn’t capable of replicating the
complete spectrum, but it can be made to replicate a certain aspect of the spectrum.
Figure 3.6: Approximate 2 RC network based representation
Considering the fact that this ECM is to be applied in an automotive application,
where drive cycle frequencies are typically lower than 2 Hz, this model can be
tuned to only focus on capturing the low frequency behaviour of the cell. The
low frequency behaviour of the cell is basically governed by its diffusion processes, and therefore it is generally the Warburg impedance which needs to be
captured by these two RC networks. According to this approach, RCT is coupled
with Ro and represented together as R DC and so this model closely represents
the DP model described in the previous chapter2.4. Even though this ECM fails
to capture the time dynamic caused by Cdl , the typical values of Cdl found in
other related works[8][24] and my work, are in the range of nearly 100F. This Cdl
value when multiplied with RCT , gives a maximum time constant of upto a couple hundreds of milliseconds. Since such high frequencies are not very relevant
while running automotive drive cycle, its exclusion can be justified.
16
Chapter 4
Experimental setup and
Measurements: Large signal
4.1
Test setup
Since this large signal test method utilises large current pulse magnitudes, it is
necessary that all electrical connections are made appropriately in order to avoid
unnecessary voltage drop which could lead to measurement inaccuracies. In order to achieve a good connection between the cables of the test equipment and
the cell tabs, copper bars are used to provide a high clamping force. Additionally
it is necessary to include sufficient insulation between the cell tabs in order to
avoid the possibility of external short circuiting of the cell.
Table 4.1 shows a list of cells which are used during this work. Individual cells
are been assigned unique tag names which are used to refer to them from here
onwards.
Table 4.1: List of cells to be investigated
Cell tag
Cell name
Type
Cell A
Cell 25Ah
NMC
Cell B
Cell 30Ah
NMC
Cell C A123 19.5Ah LFP
4.1.1
Package
Pouch
Pouch
Pouch
Cell formatting
Before performing any kind of experiments on new or unused cells, they must be
undergo "formatting" or "formation cycling" which is the process by which a cell
is cycled multiple times consecutively using a moderately low current (typically
1C). The test protocols for formation cycling are similar to capacity tests which
are designed to measure the maximum capacity that a cell can supply between
two predefined voltage limits. The reason for performing the formation cycles is
to gradually build up the film that forms on the surface of the electrodes known
17
4. Experimental setup and Measurements: Large signal
as the solid-electrolyte inter-phase layer. This layer facilitates the flow of Li ions
and prevents internal shorting, which could be otherwise caused by dendrite formation. Since Li-ions are consumed in this layer formation, it leads to initial irreversible capacity loss[5]. Constructing a stable and efficient SEI is among the most
effective strategies to inhibit the dendrite growth and to thus achieve a superior
cycling performance[25]. An ideal SEI is one which possesses minimum electrical conductivity and maximum Li + conductivity [25]. After formation, cells can
undergo characterization tests and then the measurements obtained would be a
better representation of the cell’s long term behaviour.
4.2
Procedure
The general procedure for tests using the Digatron Battery Testing equipment
involved studying how the cells behaviour over different SOCs at a particular
temperature. The temperature is then changed and then the same procedure is
repeated, according to the parameters stated in Table 4.2. Since the cells being
tested are highly sensitive to temperature, it is necessary that the temperature is
maintained constant throughout the test and for this a single NTC temperature
sensor is used to monitor cell temperature. In order to maintain consistency in the
procedure among all the tests on the different cells, a current magnitude of 2C is
chosen as it is both high and within the limits of the equipment. For further clarification, when considering a 25 Ah cell, 2C would numerically mean a current
of is 50 Amperes. A relaxation time of 60 minutes is allowed after every current
pulse which is applied on the cell. The flowchart in Figure 4.1 briefly summarises
the procedure followed during tests using the Digatron BT.
Table 4.2: List of parameter variations on Digatron tests
18
Parameter of interest
Test range
Other variables
State of Charge(SoC)
0 to 100 %
constant T, I=2C
Temperature
12 to 36 ◦ C
0 to 100 %, I=2C
Current Magnitude
0.5C to 5C
T=24 ◦ C, 0 to 100 % SOC
4. Experimental setup and Measurements: Large signal
Figure 4.1: Digatron overall procedure
4.2.1
Post-processing
Upon completion of the current pulse tests, the measurement data from the tests
is imported to Matlab in order to use it for cell parameter extraction. The postprocessing therefore involved extraction of the cell’s voltage response at every
SOC point and subsequent CM parameter identification from it. The methods
used for it will be explained more in detail in Chapter 6.
19
4. Experimental setup and Measurements: Large signal
4.3
Measurements
4.3.1
OCV curve determination
3.6
4.2
3.4
3.8
OCV [V]
OCV [V]
4
3.6
3.2
3
3.4
3.2
2.8
3
10
20
30
40
50
60
70
80
90
100
0
10
State of charge [%]
(a) OCV
vs SOC for Cell A
20
30
40
50
60
70
80
State of charge [%]
(b) OCV
vs SOC for Cell C
Figure 4.2: OCV curves for two different cell chemistries at 24 ◦ C
Since cell parameters tend to show strong dependency on its operating SOC
point, it is of utmost importance to experimentally determine the OCV characteristics for every cell which is under study using this large signal method. The
principle used to determine the OCV at different points of the cell’s SOC window
involved measuring the cell’s relaxed voltage after a current pulse has been applied. In other words, once a current pulse had been applied and the cell moved
to a new SOC point, it is allowed to relax so that all the diffusion process had time
to settle down and reach equilibrium. Ideally the cell should be relaxed for several hours for it to reach equilibrium. However in this procedure, only an hour is
allowed for relaxation. Once this time had surpassed, and before the application
of the next current pulse, the cell voltage is measured and recorded as its OCV
at that particular SOC point. Since the cell isn’t allowed to rest for a very long
period of time, which is necessary for it to reach steady state, the OCV measured
may be slightly inaccurate. To compensate for this, when the cell parameters are
extracted and the ECM is developed, it is run with a similar current pulse and
then its voltage response at nearly infinite time(or steady state) is considered as
the OCV.
Figure 4.2 shows the plots for OCV vs SOC for cells A and C. It is evident that
Cell A has a much sharper gradient in its OCV between its SOC limits, where Cell
C has a much flatter voltage profile. This behaviour is due to the difference in the
cell chemistries, and more specifically due to the phase transitions that take place
within the cell. According to [26], the LFP cell chemistry inherently possesses
a two-phase transition which results in a producing constant lithium concentrations within the phase regions and so shows only a minor change in OCV. On
the contrary, cell A which is of NMC type chemistry has an OCV which drops by
0.6 V nearly linearly between its SOC limits due to the absence of the two phase
transition effect.
20
90
100
4. Experimental setup and Measurements: Large signal
4.3.2
Impedance behaviour over SOC
In order to comprehensively study the cell impedance behaviour over the operating SOC window of the cell, it is decided to use roughly 13-14 equally spaced
SOC points. The intention is to maintain other factors which affect cell impedance
constant, and to only focus the analysis on the impedance behaviour with respect
to SOC. This experiment is done at room temperature and using current pulses
of 2C. Relaxation time of up-to an hour is allowed so that the cell is almost completely rested by the time its voltage response is studied at the next SOC point.
Typical measurements obtained from such a test as described above is shown in
Figure 4.3
(a)
(b)
Figure 4.3: Digatron voltage and current measurements for entire test 4.3a and
magnified view for two pulses 4.3b
4.3.3
Impedance behaviour over temperature range
In order to study the effects of temperature on the cell impedance behaviour, this
experiment is aimed at carrying out the exact procedure as is previously done
to study the impedance behaviour over SOC. The difference in this case is that
the cell is tested at different temperatures. The additional challenge in this experiment is trying to maintain the cell temperature at a constant value without
using a climate chamber. This is accomplished by the use of Thermo Electric
Modules(TEMs) which when suitably controlled are able to produce a heating
or cooling effect on the cell being tested. However the temperature range under
which the experiment could be conducted is limited by the capability of the TEMs
to between 12 to 36 ◦ C. Six modules are used to bring about the heating/cooling
effect on the cell on one side of it. Since the system did not heat or cool both sides
of the cell, it is necessary to use an additional temperature sensor to measure the
temperature of the other side of the cell. It can be stated that an accuracy of ±1◦ C
is achieved in temperature measurement in this method.
21
4. Experimental setup and Measurements: Large signal
4.3.4
Impedance behaviour with different current magnitudes
Since some parts of the cell’s impedance seem to show strong dependency on
the magnitude of current as suggested by the authors in [1], in addition to performing tests at different SOCs and temperatures, current pulses with different
amplitudes are also applied for full characterisation of the cell impedance. Since
applying high current magnitudes would result in extra cell heating, it is important to make sure that the cell’s temperature is maintained constant under
all loading conditions. The primary objective of this experiment is to isolate the
effects of temperature on the cell’s impedance, and to only obtain effect of the
variation over C-rates. The climate chamber is used to conduct this test and suitable temperature measurements are in place. Additionally the cell being tested is
sandwiched between two large metal bars in order to increase its thermal mass,
and thereby reducing the opportunity for a rise in cell temperature during loading. C-rates used for this test ranged from 0.5C to 5C, while the temperature of
the climate chamber is at 24 ◦ C.
22
Chapter 5
Experimental setup and
Measurements: Small signal
5.1
Test setup
EIS measurements on the selected cells were performed using a very sensitive
scientific instrument, namely the GAMRY Reference 3000. The sine wave generator on this equipment allows its use for impedance measurements at a wide
range of frequencies. It must be connected to a computer during its operation,
and requires initial calibration before use to avoid effects of noise from the external environment. The Gamry is a four probe instrument and the functions of each
of the probes required during the test is briefly described in the table below.
Table 5.1: Four wire connection for EIS measurement
Electrode name
Colour
Function
Working electrode
Green
Current-carrying from positive terminal
Counter
Red
Completes current path at negative electrode
Working sense
Blue
Voltage measurement at positive terminal
Reference
White
Voltage measurement at negative terminal
The instrument has three modes of operation. The Potentiostatic mode involves
measuring the impedance by applying a sinusoidal voltage to the sample and
measuring the current. The Galvanostatic EIS involves the application of an AC
current and measurement of the potential. A galvanostatic EIS measurement provides higher accuracy and precision than potentiostatic EIS on low impedance
samples such as batteries and fuel cells. This is because the potential can be measured with higher accuracy than it can be controlled. The Hybrid EIS mode is in
essence a blend of potentiostatic and galvanostatic modes. It can be described as
23
5. Experimental setup and Measurements: Small signal
a modified form of Galvanostatic EIS in which the applied AC current is continually adjusted to optimize the value of the measured potential[27].
The Hybrid EIS mode is found suitable to be used in the experiments throughout
this work. Whilst setting up a Hybrid EIS measurement, the user specifies the
desired AC Voltage, the estimated impedance of the sample and the frequency
range. In the case, the magnitude of the voltage signal is chosen as 2mV and the
frequency range is between 10 mHz to 100 Hz. The frequency range is selected on
the basis of it being significant when considering an automotive drive cycle [10].
Based on these values, the EIS300 Software then calculates and applies an AC
current followed by measuring the AC voltage. As the impedance varies over
frequency, the amplitude of the AC current is continually regulated so that the
AC voltage does not extend beyond the linear, non-destructive range of the cell.
5.2
Procedure
The general procedure involved during the tests using the Gamry equipment
involved studying how the cells behaviour over different SOCs at a particular
temperature. The temperature is then changed and then the same procedure is
repeated, according to the parameters stated in Table 5.2. Since the cells being
tested were highly sensitive to temperature, it is necessary that the temperature
is maintained constant throughout the test. In order to accommodate for this,
all tests were performed inside a Climate Chamber and additionally four NTC
temperature sensors were used to monitor cell temperature at its tabs and on
its body. The flowchart in Figure 5.1 briefly summarises the procedure followed
during EIS measurements.
Table 5.2: List of parameter variations on EIS tests
24
Parameter of interest
Test range
Other variables
State of Charge(SoC)
0 to 100 %
constant T, I=0.5 mA
Temperature
-10 to 48 ◦ C
0 to 100 % SOC, I=0.5 mA
5. Experimental setup and Measurements: Small signal
Figure 5.1: EIS overall test procedure
5.3
5.3.1
Measurements
OCV curve determination
4.2
4
49 degC
Open Circuit Voltage [V]
6 degC
3.8
3.6
3.4
3.2
3
2.8
0
10
20
30
40
50
60
70
80
90
100
SOC (%)
Figure 5.2: OCV vs SOC at two extreme temperatures for cell A
Since cell parameters tend to show strong dependency on its operating SOC
point, it is of utmost importance to experimentally determine the OCV characteristics for every cell which is analysed using this small signal method. In order
25
5. Experimental setup and Measurements: Small signal
to accomplish this, the approach suggested by the author of [13] is followed. This
procedure involves charging and discharging the cell at a constant current and
temperature, until and even a little beyond the operating voltage limits of the
cell. During discharging, the cell terminal voltage can be represented as
y1 = OCV (SOC ) − Rdischarge i
(5.1)
and correspondingly during charging it can be represented as
y2 = OCV (SOC ) + Rcharge i.
(5.2)
From this, it is evident that the OCV can be determined as a function of SOC by
adding (5.1) and (5.2) and taking their average. This would of course be assuming
that the charging and discharging resistance to be the same. This point is earlier
discussed in Section 2.3.2 and so it can be concluded that the inaccuracy involved
here is quite small. Figure 5.2 shows a typical result obtained from this test and
depicts the fact that even though OCV shows varies with SOC, it doesn’t show
too much variation at different temperatures within this range.
5.3.2
Impedance behaviour over SoC range
Figure 5.3 shows the EIS spectrum over the operating SOC window of cells A and
C. It can be seen that both cells exhibit a similar EIS spectrum, which only differs
in magnitude of impedance. It is evident that even though Ro is constant over
all SOC points, Rct varies greatly, and drastically increases at the end of the SOC
window. Similar results were observed and reported in [1]. This phenomenon
can be attributed to that fact that the graphite anode shrinks in size at low SOCs,
thus making de-intercalation much harder[15].
26
5. Experimental setup and Measurements: Small signal
1
20%
0.8
40%
60%
0.6
80%
90%
0.4
-ImZ
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.3
1.4
1.5
1.6
1.7
ReZ
(a) Cell
A
1
20%
0.8
40%
60%
0.6
80%
92.5%
0.4
-ImZ
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.7
0.8
0.9
1
1.1
1.2
1.7
ReZ
(b) Cell
C
Figure 5.3: Impedance measurements at different points over the SOC window
for Cell A and Cell C at 24 ◦ C
5.3.3
Impedance behaviour over temperature range
Figure 5.4 shows that the EIS spectrum is quite similar even at different temperatures even though the magnitudes of the impedances differ greatly. It is evident
that the ohmic resistance Ro of all three decreases with increase in temperature
and this result agrees with similar work done in [1] and [21]. The value of the
charge transfer resistance Rct is also seen to significantly decrease with increase
in temperature. The authors of [1] attribute this behaviour to have an exponential
dependence on temperature according to the Arrhenius equation. Notably it can
be seen that even though cell A and B belong to the same chemistry family and
have very close values of Rct at 24 ◦ C, these values differ significantly at lower
temperatures and this may be due to the presence of additives in the electrodes
of either of the cells. It can be stated that an accuracy of ±0.5◦ C is achieved in
temperature measurement in this method.
27
5. Experimental setup and Measurements: Small signal
1
0.8
0.6
0.4
-ImZ
0.2
0
-0.2
80%; 8°C
40%; 8°C
80%; 24°C
-0.4
40%; 24°C
80%; 40°C
-0.6
40%; 40°C
-0.8
-1
0.5
1
1.5
2
2.5
3
ReZ
(a) Cell
A
2.5
2
1.5
-Im Z
1
0.5
80%; 8°C
40%; 8°C
0
80%; 24°C
40%; 24°C
80%; 40°C
-0.5
40%; 40°C
-1
-1.5
0
1
2
3
4
5
6
7
8
9
ReZ
(b) Cell
C
Figure 5.4: Measurements showing the behaviour of cells A and C at two specific
SOC points and three operating temperatures
28
5. Experimental setup and Measurements: Small signal
1.3
Cell A
Cell B
Cell C
1.2
1.1
1
0.9
0.8
0.7
0.6
-10
0
10
20
30
40
50
Temperature [°C]
Figure 5.5: Behaviour of the ohmic resistance of cell A,B and C over temperature
The points in Figure 5.5 were plotted by extracting the point at which the EIS
measurements of all the cells at several temperatures intersect the real axis. This
point was found to be always independent of SOC. It can be used to study the
behaviour of the Ro over a wide range of temperatures.
29
5. Experimental setup and Measurements: Small signal
30
Chapter 6
Model fitting: Large signal
6.1
6.1.1
2 RC model fit
Algorithm
As described in Section 4.2.1, the voltage responses from the cell at each selected
SOC point now needs to be processed in order to extract the cell’s ECM parameters from it. In order to perform this task, the Fit tool available in Matlab is
used.
y f it = a0 + a1 eb1 x + a2 eb2 x
(6.1)
is the expression which is fed into Fit function along with the cell voltage and
time data. This expression was obtained in according with (2.1). Here a0 ,a1 and
a2 represent the respective steady state voltage drops over the resistances R0 ,R1
and R2 respectively, while b1 and b2 represent the negative reciprocal of the quick
and slow time constants. Since the Fit tool works using numerical optimisation
methods, it is necessary to set initial values for the expected time constants, along
with suitable upper and lower boundaries for them. This can be done by tuning
the values of the variables b1 and b2 .
31
6. Model fitting: Large signal
Parameter identification
25
500
20
400
Tau2 [seconds]
Tau1 [seconds]
6.1.2
15
10
300
200
100
5
0
0
0
10
20
30
40
50
60
70
80
90
0
100
10
20
30
40
(a) Time
50
60
70
80
90
100
80
90
100
SOC [%]
SOC [%]
constant of R1 C1 :-1/b1
(b) Time
constant of R2 C2 :-1/b2
0.5
4
0.4
a1 [V]
V 0 [V]
3
2
1
0.3
0.2
0.1
0
0
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
SOC [%]
(c) Open
50
60
70
SOC [%]
circuit voltage:a0
(d) Voltage
drop over R1 :a1
0.025
a2 [V]
0.02
0.015
0.01
0.005
0
0
10
20
30
40
50
60
70
80
90
100
SOC [%]
(e) Voltage
drop over R2 :a2
Figure 6.1: Typical time constant and voltage drop values obtained from curve
fitting measurement done at 24 ◦ C with 2C pulses
Figure 6.1 shows a typical graphical result which is obtained after application of
the curve fitting tool. Each parameter required to solve (6.1) is represented as
a function of SOC. However this is only an intermediate step in the process for
ECM parameter identification. By utilising the values of the variables from the
curve fit, the parameters of the DP model are calculated.
32
6. Model fitting: Large signal
(a) Verification
at two SOC points using measured cell
relaxation and the simulated response
(b) Verification
at two SOC points using measured cell
voltage and the simulated response during complete
current pulse
Figure 6.2: Output from Curve fitting
The values for the parameters shown in Figure 6.1, together with other values
which were measured during the tests such as current pulse magnitude and pulse
duration are then used to determine the values of R0 ,R1 ,R2 ,C1 and C2 as functions
of SOC. The values for the parameters obtained are then used as functions of SOC
to populate a look-up table based Simulink/Simscape model of the cell. In order
to verify that the parameter identification was executed properly, the simulation
model is run with the same current pulse and with the cell at the same SOC point,
and its voltage response is obtained. It is then visually compared with output obtained from the actual measurement as shown in Figure 6.2a. As another step
for verification, the result of the entire voltage response including current injection and interruption of the simulation model is compared with that of the actual
measurements as shown in Figure 6.2b.
6.2
R10 value based simulation
The R10 value of a cell is quite popularly used by battery users for simple cell
modelling. Since the resistance of a Li ion cell varies as a function of time, this
33
6. Model fitting: Large signal
value typically represents the cell resistance at time t=10 seconds. This however
assumes that the cell was completely at rest at time t=0. When used instead of Ro
in a Rint model as in Figure 2.2, it would yield more accurate results. Once a DP
model has been developed, this value can be simply estimated by calculating the
ECM’s resistance at 10 seconds.
34
Chapter 7
Model fitting: Small signal
7.1
6 RC model fit
The RC network based models described in Section 3.3.2 are parametrised in the
frequency domain in accordance with the corresponding EIS measurements obtained at different SOC points and temperatures. In order to obtain a suitable fit
between the simulated and measurement data, numeric optimisation was used.
The method of approach involved using the Fminsearch function in Matlab to
minimise the error between the measured EIS data and the output generated by a
transfer function based model. The transfer function was developed on the basis
of the model described in Section 3.3.2 and is mathematically represented as
H = R0 + Ls +
R2
R3
R4
R5
R6
R1
+
+
+
+
+
R1 C1 s + 1 R2 C2 s + 1 R3 C3 s + 1 R4 C4 s + 1 R5 C5 s + 1 R6 C6 s + 1
(7.1)
.
The Fminsearch algorithm basically requires an initial value for the parameters
which are to be optimised, and after which it optimises the parameters of (7.1)
in order to minimise the difference towards the measured data at a particular
frequency. The initial values are carefully chosen so that 3 RC networks are used
to represent each part of the EIS spectrum which would otherwise have been
represented by a CPE. In order to quantify the fit obtained, the parameter Square
of Sum of Errors(SSE) was used. Figure 7.1 shows the performance of this model
over a wide range of SOC and temperatures.
35
7. Model fitting: Small signal
1
1.5
80%; 0°C-actual
80%; 0°C-fitted
40%; 0°C-actual
40%; 0°C-fitted
80%; 8°C-actual
80%; 8°C-fitted
40%; 8°C-actual
40%; 8°C-fitted
1
0.5
0.5
0
0
-0.5
-1
1
1.5
(a) Model
2
2.5
3
3.5
4
4.5
5
-0.5
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
fit for measurements at 0 ◦ C (b) Model fit for measurements at 8 ◦ C
0.8
0.8
80%; 24°C-actual
80%; 24°C-fitted
40%; 24°C-actual
40%; 24°C-fitted
0.6
80%; 32°C-fitted
80%; 32°C-actual
40%; 32°C-fitted
40%; 32°C-actual
0.6
0.4
0.4
0.2
0.2
0
-0.2
0
-0.4
-0.2
-0.6
-0.4
-0.8
-1
0.7
0.8
(c) Model
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
fit for measurements at 24 ◦ C
-0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
(d) Model fit for measurements at 32 ◦ C
Figure 7.1: 6-RC based Model fit at two specific SOC points for different operating
temperatures for cell A
7.2
2 RC model fit
A similar procedure to what was described above was followed here, with the
exception that since much lesser number of elements were used, the initial values given to these two RC networks had to be so that they would try to replicate
the diffusion part, which is commonly represented by a Warburg circuit element,
thereby neglecting the higher frequencies. In order to make the optimisation algorithm focus more on the lower frequency part where the cell’s impedance is
higher, the error function is squared, so that algorithm now has not to minimise
simply the error, but rather the square of it. Since EIS tests are performed only
down to a frequency of 10 mHz, it is not possible to fit RC networks with too
large time constants. For this model, a fast RC link with a time constant of a couple of seconds, and a slow RC link having a time constant of around 40 seconds
is deemed suitable. Figure 7.2 shows the performance of this model over a wide
36
7. Model fitting: Small signal
range of SOC and temperatures.
1
0.8
0.6
0.4
80%; 8°C-fitted
80%; 8°C-actual
40%; 8°C-fitted
40%; 8°C-actual
80%; 24°C-fitted
80%; 24°C-actual
40%; 24°C-fitted
40%; 24°C-actual
80% 48°C-fitted
80%; 48°C-actual
40%; 48°C-fitted
40%; 48°C-actual
0.2
0
-0.2
-0.4
0.5
1
1.5
2
2.5
3
Figure 7.2: 2-RC based Model fit at two specific SOC points for different temperatures for cell A
37
7. Model fitting: Small signal
38
Chapter 8
Comparison of all developed models
8.1
Cell behavioural trends captured by both methods
This chapter deals with the tests performed on cell B using both large and small
signal methods. The results obtained from each method independently using
the DP or 2RC link based model is compared with the other, in order to understand if both methods yield similar results. This is not a numerical comparison
with respect to accuracy, but rather a comparison for the sake of getting a better understanding of how both models behave. The aspects regarding numerical
accuracy of the models will be dealt with in the next chapter.
8.1.1
DC resistance behaviour over SOC and Temperature
Even though the tests following the two methods were performed at slightly different temperatures, it is evident that both methods are able to capture the characteristic trends exhibited by the cell. The only test which was performed at exactly
the same temperature i.e. at 24 ◦ C shows that the resistance magnitudes estimated through both methods are quite comparable. Notably, Rct which is one of
the two components of R DC shows strong dependency on SOC as shown by other
researchers[1][2]. Similarly, the decrease in R DC at higher temperatures is due to
the fact that both Ro and Rct independently decrease with higher temperature.
39
8. Comparison of all developed models
4.5
4.5
Rdc:12 degC
4
8 degC
Rdc:18 degC
16 degC
4
24 degC
Rdc:24 degC
32 degC
Rdc:36 degC
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
10
20
30
40
50
60
70
80
90
0.5
10
100
20
30
40
(a) Large
50
60
70
80
90
100
SOC(%)
SOC(%)
signal method
(b) Small
signal method
Figure 8.1: DC Resistance of Cell B compared from both methods
8.1.2
Diffusion resistance behaviour over SOC and Temperature
The parameterisation of the R and C variables which represent the cell’s diffusion
behaviour is shown in the following collection of figures. The four other parameters required for the DP model are identified, but using the two different methods.
Upon inspection of the Figures 8.2 and 8.3 which show the variations of the ECM
parameters R1 ,R2 ,τ1 and τ2 , it is evident that even though the results from the
two methods may not be identical, the general trends captured are quite similar.
Another reason for the non-identical results is since the time constants associated
with the diffusion resistances are different for the two methods. Apparently, at
higher temperatures, the resistance associated with diffusion is smaller and the
reaction rates are faster. It is noteworthy that the phenomenon of the phase transition taking place at 70 % has also been captured by both methods.
0.32
4
8 degC
12 degC
0.3
18 degC
3.5
16 degC
24 degC
24 degC
36 degC
32 degC
0.28
3
0.26
2.5
0.24
0.22
2
0.2
1.5
0.18
1
0.16
0.5
0
10
0.14
20
30
40
50
60
70
80
90
100
0.12
10
20
(a) Large
signal method
30
40
50
60
70
80
SOC(%)
SOC(%)
(b) Small
signal method
Figure 8.2: Diffusion Resistance R1 for Cell B compared from both methods
40
90
8. Comparison of all developed models
5
6
12 degC
18 degC
24 degC
36 degC
5
8 degC
16 degC
24 degC
32 degC
4.5
4
4
3.5
3
3
2.5
2
2
1
1.5
0
10
20
30
40
50
60
70
80
90
1
10
100
20
30
40
50
(a) Large
60
70
80
90
SOC(%)
SOC(%)
signal method
(b) Small
signal method
Figure 8.3: Diffusion Resistance R2 for Cell B compared from both methods
Impedance dependence on Crate
8.1.3
Since the Gamry EIS equipment is restricted in terms of its current loading capability, impedance characterisation with respect to different C-rates could only
be done using the large signal method. The tests were performed on cells A and
C, and it is evident that the impedance of the cell behaves differently depending
upon the magnitude of current drawn from it.
1.8
2
0.5C
1C
2C
3C
4C
5C
1.7
4
0.5C
1C
2C
3C
4C
5C
1.8
1.6
1.6
0.5C
1C
2C
3C
4C
5C
3.5
3
1.4
1.5
2.5
1.2
1.4
1
2
1.3
0.8
1.5
1.2
0.6
1
1.1
1
10
0.4
20
30
40
50
60
SOC(%)
(a) Resistance
R0
70
80
90
100
0.2
10
20
30
40
50
60
70
80
90
100
0.5
10
20
30
40
50
SOC(%)
(b) Resistance
R1
60
70
80
90
SOC(%)
(c) Resistance
R2
Figure 8.4: Crate dependence of Cell A at constant temperature of 24 degrees C
41
100
8. Comparison of all developed models
4.5
2.3
0.5C
1C
2C
3C
4C
5C
2.2
2.1
5
0.5C
1C
2C
3C
4C
5C
4
0.5C
1C
2C
3C
4C
5C
4.5
4
3.5
2
3.5
3
1.9
3
2.5
1.8
2.5
2
1.7
2
1.5
1.6
1.5
1.5
1.4
10
1
20
30
40
50
60
SOC (%)
(a) Resistance
R0
70
80
90
100
0.5
10
1
20
30
40
50
60
SOC(%)
(b) Resistance
R1
70
80
90
100
0.5
10
20
30
40
50
60
70
80
SOC(%)
(c) Resistance
R2
Figure 8.5: Crate dependence of Cell C at constant temperature of 24 degrees C
42
90
100
43
9. Validation of models
Chapter 9
Validation of models
9.1
Development of simulation model
(a) Cell
model
(b) Implementation
of the Dual Polarisation ECM
Figure 9.1: Simulation model implemented in MATLAB Simulink/Simscape
44
9. Validation of models
MATLAB Simulnk/Simscape was chosen as a suitable environment to implement
all the ECMs developed through the course of this work. The parameterised
ECMs are fed into the cell simulation model shown in Figure 9.1, in the form of
look-up tables which could have up to three dimensions. For instance, a parameter such as the R DC requires a 2D LUT since it depends on SOC and temperature
where as the OCV needs a 1D LUT. The Simulink environment allows easy application of simple current pulses as well as the use of complicated drive cycle
inputs. Therefore, this model is quite robust and flexible to use.
9.2
Drive-cycle selection
In order to validate the models proposed, the Charge-Depleting Cycle Life Test
Profile for the Minimum PHEV Battery will be used [10]. This dynamic drive
cycle will be applied to two cells A and C which are of different chemistries and
also at two temperatures, 24 and 10 ◦ C respectively. Charge-Depleting Cycle life
testing is performed using one of the Charge-Depleting Cycle Life Test Profiles
wherein each cycle runs for 360 seconds. Cycle life testing is performed by repeating the test profile(s) until the Target Energy for the Charge-Depleting mode
is reached. From then onwards the Charge-Sustaining mode is implemented implementing a test profile whose entire cycle keeps the battery SOC neutral.
9.3
Model evaluation by error comparison
Due to practical issues faced while applying the drive cycle on the cells, data pertaining to the Charge depletion mode alone is used for analysis and validation.
Tables 9.1 and 9.2 show the Root Mean Square Error(RMSE) value for the validation test performed on the two cells A and C at 24◦ C. It can be seen that the
comprehensive 6 RC performs poorly in comparison to the 2 RC models. Even
though the performance of the 2RC models obtained from the large and small
signal methods are different, they are produce satisfactory results. The difference
between the parameters obtained from the two different methods could be due
to the effect that the C-rate has on the cell impedance value as was shown previous in Section 8.1.3 and by the authors of [1]. It is seen that the performance of a
model which simply uses the R10 value, which is estimated by choosing the real
part of the impedance measured through EIS at a frequency of 0.1 Hz, is quite
poor. It is noteworthy that the maximum error corresponding to such a model is
also very high and is thereby unsuitable for dynamic cell modelling.
45
9. Validation of models
Table 9.1: Validation setup and results at 24 ◦ C for cell A
ECM
Method of parametrisation MSE [mV]
6 RC
Small signal
29
2 RC
Small signal
20
2 RC
Large signal
12
R10
Small signal
55
Table 9.2: Validation setup and results at 24 ◦ C for cell C
ECM
46
Method of parametrisation MSE [mV]
6 RC
Small signal
34
2 RC
Small signal
30
2 RC
Large signal
34
R10
Small signal
60
Chapter 10
Derivation of pulse power limits
10.1
Pulse power characterisation
The availability of a comprehensive ECM of a Li ion cell such as the DP model facilitates the accurate estimation of the pulse power capability of a cell under various operating conditions. If a comprehensive ECM such as the DP model was not
developed for the cells under this study, the results found in this chapter would
not have been possible. As mentioned previously , the value of maximum current chosen for pulse power characterisation is restricted to the maximum value
permitted by the cell manufacturer. In order to characterise the pulse power that
a cell can deliver for certain time intervals, an accurate estimate of its impedance
behaviour is required. This is achieved using the DP ECM, by which accurate
estimate of the cell’s terminal voltage can be accomplished.
The pulse power limits depicted by Figures 10.1 and 10.2 were results obtained
through the Simulation model which was earlier described in Section 9.1. The
model consists of a battery comprising of 90 cells of type Cell B in series. A constant current load which draws a current equal to the maximum current capability of the cell was used in the model for the respective time interval of the pulse.
The product of the battery terminal voltage and current was thus calculated as
the power delivered by the battery.
47
10. Derivation of pulse power limits
84
Estimated 10s Power
82
Estimated 5s Power
Estimated 2s Power
80
Electric Power [kW]
78
76
74
72
70
68
66
10
20
30
40
50
60
70
80
90
100
SOC(%)
Figure 10.1: Pulse power capability with different pulse durations for battery
containing cell B at 24 ◦ C
Since the resistance of a cell is a function of time, the power capability shown in
Figure can be expected. As discussed in Section 8.1.2, since diffusion effects take
longer time to act, the resistance of a cell which has been at rest, is initially small,
and then gradually increases. This enables the cell to deliver a higher magnitude
of power for very short bursts of time.
85
Estimated 10s Power: 36degC
Estimated 10s Power: 24degC
Estimated 10s Power: 18degC
80
Estimated 10s Power: 12degC
Electric Power [kW]
75
70
65
60
55
10
20
30
40
50
60
70
80
90
100
SOC(%)
Figure 10.2: Pulse power capability over temperature for battery containing cell
B
The trend in Figure 10.2 can again be explained as in Section 8.1, being due the
reduction in the cell’s DC resistance and also subsequent decrease of the diffusion
resistance. Therefore it can be inferred that the pulse power capability of a cell in48
10. Derivation of pulse power limits
creases at higher temperatures. On the other hand, it also significantly decreases
at lower temperatures due to the increase in the resistance.
49
10. Derivation of pulse power limits
50
Chapter 11
Conclusions
This work was aimed at quantifying the pulse power capability of a Li-ion cell
under various operating conditions. In order to achieve this, it was necessary
to develop a dynamic ECM with sufficient number of RC links to represent the
behaviour of a Li-ion cell. In order to parameterise the developed model, the
two methods, namely Current Interruption and EIS were unified and used in an
unique manner. The results obtained through both methods were replicated using the Dual Polarisation ECM. Even though the two methods were significantly
different, this work was able to unify the results of the two methods through the
suitable application of the DP model. Further, the effectiveness of this model in
terms of its accuracy was validated through testing it with a vehicle drive cycle.
Upon comparing the results of the validation cycle, a RMSE value of close 30 mV
was found when comparing actual measurement and simulation results. By the
application of the parametrised ECM, the pulse power capability of a cell was
characterised and quantified.
11.1
Future work
The pulse power available from a cell under different operating conditions was
quantified in this thesis. Further work needs to be done in order to implement
an algorithm in a vehicle by which the pulse power limits of a battery can be
dynamically varied. Moreover, the scope of this thesis was limited to new cycles
which were at their Beginning of Life and so it would be important to perform
similar experiments on cells at various stages of aging, and analyse the decrease
in pulse power capability of the cell. EIS was found to be a very suitable method
for analysing the cell impedance behaviour, and its application could be further
extended into using it for online impedance diagnostics so that pulse power limits
of a cell can be adjusted over its lifetime in a vehicle.
51
11. Conclusions
52
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54
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