Electrochemical Impedance Spectroscopy
2010
Characterization of the Dynamic Performance
of Li-ion Traction Batteries for
Electrical Vehicles
Author: Tomasz Minko
Supervisor: Søren Juhl Andreasen
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Nomenclature list
Symbol
𝑖
𝑖𝑎
𝑖𝑐
𝑖0
𝛼
F
q
R
T
𝜂𝑠
𝜔
t
△
𝜃
r
Z,z
𝑍𝑟 , 𝑧𝑟
𝑍𝑗 , 𝑧𝑗
C
L
R
CPE
𝑄0
𝜎
Cb
D
𝐼𝑟
𝐼𝑗
𝐼
𝑉𝑟
𝑉𝑗
𝑉
f
3
Unit
𝑚𝐴/𝑐𝑚2
𝑚𝐴/𝑐𝑚2
𝑚𝐴/𝑐𝑚2
𝑚𝐴/𝑐𝑚2
.
C/equiv
.
.
K
V
Rad/s
s
.
°
Ω
Ω
Ω
F
H
Ω
F
𝑆𝑠 𝑛
.
.
.
A
A
A
V
V
V
Hz
Description
current density
anodic current density
cathodic current density
exchange current density
symmetry factor
faraday constant F=96.487
number of transferred electrons
universal gas constant
absolute temperature
surface overpotential
angular frequency
time
amplitude
phase angle
impedance magnitude
impedance
real impedance part
imaginary impedance part
capacitance
inductance
resistance
constant phase element
admittance measured at 𝜔 = 1
warburg coefficient
bulk concentration
diffusion coefficient
currents real part
currents imaginary part
currents
voltage real part
voltage imaginary part
voltage
frequency
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List of content
1
Introduction ................................................................................................................................................... 7
2
Insight on the electrochemical battery ........................................................................................................... 8
3
2.1
Battery construction ............................................................................................................................... 8
2.2
Electric double layer .............................................................................................................................. 8
2.3
Equilibrium in electrochemical system................................................................................................ 10
2.4
Polarization in electrochemical systems .............................................................................................. 11
Electrical models ......................................................................................................................................... 12
3.1
4
Impedance-based electrical model ....................................................................................................... 13
3.1.1
The constant phase element ........................................................................................................ 15
3.1.2
Warburg impedance .................................................................................................................... 16
Electrochemical impedance spectroscopy approach. ................................................................................... 18
4.1
5
Hardware and software ........................................................................................................................ 18
Noise effect .................................................................................................................................................. 21
5.1
6
Error structure ...................................................................................................................................... 21
Experimental results .................................................................................................................................... 23
6.1
Kokam lithium polimer battery 53 Ah. ................................................................................................ 24
6.1.1
Kokam lithium polimer battery 25 Ah ....................................................................................... 28
6.2
Lithium ion polymer battery 20Ah (LIPB) .......................................................................................... 31
6.3
Lithium ion polymer battery 14Ah (LIPB) .......................................................................................... 33
7
Summary and conclusions ........................................................................................................................... 34
8
Bibliography ................................................................................................................................................ 35
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Introduction
Subject of this work is focused on electrochemical batteries, which represents a group of chemical electric
current sources, which works on a basis of creating an electrical energy due to chemical reactions that are taking
place in a source. Among chemical electric current sources there are fuel cells (primary cell), which in order to
create electric energy, their chemical reactions use chemical components in an irreversible manner. Second kind
of chemical electric current sources is called secondary cell. The most characteristic attribute of secondary cells
is that they can be reused, the discharged process cad be reversed. Galvanic cell was created by Alessander Volt,
who by referring to Luigi Galvani experiments proved that creating an electric current is connected to a metals
dipped in a electrolyte. For his experiment he used silver and zinc plates dipped in salt water.14 Since this
moment different galvanic cells were founded. In 1877 Georges Leclanche invented a zinc-carbon battery
(picture 16 ), in which zinc cup was both a container and an anode. Inside the cup
electrolyte paste consisting water, ammonium chloride and manganese dioxide cathode was
used.14 Those batteries are not very resistant for long storage and under high load
electrolyte leaking is possible, though their popularity comes from low price.8 In 1950s
Lewis Urry invented alkaline battery (picture 29 ). The name comes from the material used
for an electrolyte, which is potassium hydroxide (KOH). Comparing alkaline and zinccarbon batteries, for the same voltage of 1.5V, alkaline have larger capacitance and can
provide between 3 to 5 times longer operation time than zinc-carbon batteries.8 Because of
used materials, alkaline batteries are more expensive. This work is focused on rechargeable
batteries. The oldest and most commonly used rechargeable battery is lead-acid one (picture 310 ), invented in
1859 by French physicist Gaston Plante nowadays is used in most of the internal combustion motor vehicles.
Battery itself is heavy, have a low cycle life, a quick self discharge, and low
energy densities. Still lead-acid batteries are very attractive in systems where
high voltage and high demands of power densities are not needed. Among
other rechargeable batteries nickel cadmium (NiCd), nickel metal
Picture 1. Zinccarbon battery
hydride(NiMH), lithium ion(Li-ion), and lithium ion polymer(Li-ion polymer). Picture 2. Alkaline battery
Nowadays electrochemical secondary batteries are widely used in many
electrical systems. The ability of converting the chemical energy stored inside them into electrical energy makes
it possible to deliver this energy to the electrical system whenever there is a need for it. They can be used as
energy storage systems for windmills, which sometimes produce more energy than actual demand is. Such
storage system can be also used for balancing the network grid. It could accumulate
the energy at night time and use it during network load peaks. At Bornholm island
tests are made, where such system is investigated witch usage of the electric cars, as
storage system.15 Among other applications, electrochemical batteries are widely used
for portable electronic devices like cell phones, laptops, digital cameras, different
power tools. All those applications became more demanding towards the batteries. Picture 3. Lead-acid battery
Size limitations, efficiency, runtime and the amount of the battery life cycles, all this
made us realize that better understanding of those batteries is needed and developing
new types of batteries is necessary to fulfill the growing expectations.16 This project is focused on last two
mentioned types of secondary batteries, Li-ion and Li-ion polymer. Their built, rules of working are going to be
described in next chapter. Moreover an approach towards creating an impedance model of the battery is going to
be shown. Such model can be helpful in investigating electrochemical phenomena, like corrosion, surface
treatments, battery testing, biological and photoelectric effects.11
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Insight on the electrochemical battery
Preface
The aim of this chapter is to describe some of the reactions and effects that take place inside the battery,
their built and laws being helpful in better understanding how the battery works. Firstly the built of the
secondary lithium ion and lithium ion polymer battery are going to be shown, next short description about what
processes occurs inside the battery. After that the description of the electric double layer will bring us closer to
the how battery works, next the law of equilibrium is going to be explained, moreover polarization behaviors,
kinetic control and mass transfer control.
2.1
Battery construction
The built of lithium batteries chemistry has been developing during the last years. Lithium metal has been
exchanged with lithium compounds. Cathodes consist of a layered crystal (graphite) into which the lithium is
intercalated. Experimental cells have also used lithiated metal oxide such as LiCoO 2, NiNi0.3Co0.7O2, LiNiO2,
LiV2O5, LiV6O13, LiMn4O9, LiMn2O4, LiNiO0.2CoO2. Electrolytes are usually LiPF6, although this has a problem
with aluminum corrosion, and so alternatives are being sought. One such is LiBF 4. The electrolyte in current
production batteries is liquid, and uses an organic solvent, as for an anode carbon compound, graphite is used.8
The lithium ion polymer a battery differs from standard lithium ion battery, the electrolyte is solid. Polymer
is a material widely used in industry and everyday human’s life, it is a typical isolator. Thanks to A.G. Mc
Diarmid, A.J. Heeger and H.Shirikawa who invented the conductive polymer, new applications were found for
this material, also in the batteries. In year 2000 they have got a noble prize in chemistry for their work on
polyacetylenes. There are known three kinds of conductive polymers:17
I.
II.
III.
2.2
Ionic conductive polymers – in which the polymers chain itself do not have any conductive abilities,
dissolved in polymer electrolyte is a conductor.
Polymers based on oxidizing mechanisms and redox reduction. Conductivity works on a basis of
jumping(hopping) of the electrons between redox centers of the polymer
Polymers where for transport of electrons the polymers chain bindings are responsible.
Electric double layer
Electrochemistry is a branch of science which teaches us about relationships between chemical processes
and electric charge flow. The last mentioned part can be divided into ionic and electrode part, ionic part takes
care of the processes that occur in electrolyte, electrode part about heterogenic processes which take place during
the charges flow between the boundaries of the
phases. Mentioned processes take place in
electrochemical systems, which consist of electron
conductors called electrodes(carbon, iron oxides,
iron) and electrolyte, which is a ionic conductor,
usually liquid-salt mixture, though constant
polymer electrolytes are also available. In case
when our system is built from liquid electrolyte
extract and constant electrode, absorption effect
always takes place. It means that our electrolytes
density on the surface of electrode differ from the
density measured in the middle of it. If the surface
density is higher than the middle one, then it is
positive absorption if lower than negative. It was
mentioned that both the electrolyte and electrode
are conductors, because of this and that there is a
Picture 4 Interfacial double layer.
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Electrochemical Impedance Spectroscopy
2010
charge difference between each of those conductors there is always a charge flow in the electrodes, despite the
fact that there might not be any external charge sources. The sign and initial potential is described by material
electrodes and what electrolyte was made. When solid body is placed in a liquid on the surface of the solid object
an electrical double layer occur.17
Picture 422 presents interfacial double layer. The double layer is built from two parallel layers of charge
surrounding the object. The first layer, the surface charge (either positive or negative), constitute of ions
absorbed directly onto the object, in this case the electrode. Second layer constitute of ions dragged and attached
to the surface by the Coulomb force. The earliest model of double layer was presented by German physician
Herman von Helmholtz. He described the double layer as a capacitor, based on physical model in which a single
layer of ions is absorbed at the surface, second layer is neglected. Later an improvement was made by Louis
Gouy and David Chapman. They have proposed a new approach based on diffuse model of electrical double
layer. According to them electric potential decreases exponentially away from the surface of the fluid bulk. It
was pointed out that new model did not describe properly highly charged double layers. Because of it the model
has developed again by adding an internal Stern layer. This models is currently the most common one for
describing the double layer: internal Stern Layer an external diffuse layer.18,19,20,21
Description of the effects that take place in double layer can be shown in steps:
I.
Non-electric similarities of charge-determining ions on the surface creates the electric surface charge
(C/𝑚2 ).
Electrostatic field created by the surface charge affects the liquids (electrolyte) ions. In the result a
counter charge is created in the diffuse layer, which is separate from the surface charge. The
amplitudes of both charges are equal, and with opposite polarity. Complete structure is electrically
neutral.
II.
An electric double layer is a structure which describes the electric potential changes near the surface e.g.
electrodes. The difference between the double layer on an electrode and interfacial one is that electrodes surface
charge can be controlled by feeding it with external electric potential. The picture number 5 represents double
layer on an electrode, where:18,19,20,21,22
l. IHP inner Helmholtz layer
2. OHP outer Helmholtz layer
3. Diffuse layer
4. Solvated ions
5. Peculiar adsorptive ions
6. Solvent molecule.
Picture 5 Electric double layer.
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2.3
Equilibrium in electrochemical system
Lets consider an electrochemical system which is built as shown on the picture 6. R represents the
electrolyte resistance, V voltage between two electrodes. It is also possible to describe it in other way, by
dividing it into phases. Starting the description from the left there is a wire (LW), left electrode(LE),
electrolyte(E), right electrode(RE), wire(RW).3
Picture 6 Electrochemical battery scheme.
Different equilibriums can be pointed out:
Thermal equilibrium demands that adjacent phases have its temperature equal: 𝑇 𝐿𝑊 = 𝑇 𝐿𝐸 = 𝑇 𝐸 =
𝑇 𝑅𝐸 = 𝑇 𝑅𝑊 .
II.
Mechanical equilibrium demands that adjacent phases pressure was equal:
𝑝𝐿𝑊 = 𝑝𝐿𝐸 = 𝑝𝐸 = 𝑝𝑅𝐸 = 𝑝𝑅𝑊 .
III.
Chemical equilibrium demands that, when species are in adjacent phases, then their electric potential must
𝐿𝐸
𝑅𝐸
𝑅𝑊
− = 𝜇𝑒 − ; 𝜇𝑒 − = 𝜇𝑒 −
be equal: 𝜇𝑒𝐿𝑊
I.
In case where electrodes are made of low chemical reactivity materials, like platinum, gold and that the
electrolyte is an extract of 𝑁𝑎2 𝑆𝑂4 in distilled water, current is dependent not only on ohmic resistance but
𝑉
also voltage potential 𝐼 = , which forces the charge-transfer reactions. Without electrochemical reactions
𝑅
the current will not be able to flow. Moreover the system needs to overcome certain critical potential
(standard cell potential) to inaugurate the current flow. In case where materials for electrodes was
characterized with high chemical reactivity and electrolytes material is a good electric conductor the current
would flow more freely.
𝐻2 𝑂 + 𝑒 − ↔
1
𝐻 + 𝑂𝐻 −
2 2
1
𝐻2 𝑂 ↔ 𝑂2 + 2𝐻 + + 2𝑒 −
2
By taking equilibrium condition it is possible to express electrochemical reactions in terms of the
electrochemical potential equality.3
1
𝜇𝐻2 𝑂 = 𝜇𝐻2 + 𝜇𝑂𝐻 −
2
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Electrochemical Impedance Spectroscopy
2.4
Polarization in electrochemical systems
Before taking any impedance measurements it is crucial to make
polarization curves (picture 73 ). According to those curves it is easier to
choose appropriate EIS perturbation amplitude, plus information gained
from those curves can be useful in the battery model advancement.
According to the polarization curve it is possible to distinguish points in
which impedance measurements should be made. Polarization curve
characterizes the batteries voltage as a function of current. The current
itself imitates the load on which the battery is working. Batteries are
known from its very good partial load performance, since the voltage
increases, load decreases. This is a big advantage for electric engines,
internal combustion engines do not show this quality, they work most
Picture 7 Polarization curve
efficiently at full load. Polarization is caused by chemical and
physical factors that are connected with various elements of the
battery. It is possible to distinguish three basic regions (picture 7), which describe the current in the battery:17,3
I.
II.
III.
Zero current
Current controlled by reaction kinetics
Current controlled by mass transfer
The zero current region, which represent the balance between positive current of the anodic reaction and
negative current of cathodic reaction. In the situation where those two currents represents forward and backward
rates of the same reaction, balance of the currents, so called zero current will be achieved, though all conditions
from 3.3 must be fulfilled. If the two currents represent forward and backward rates of different reactions the
equilibrium will not be possible to achieve. As an example copper was chosen.
Forward (anodic) reaction can be written as:
𝐶𝑢 → 𝐶𝑢2+ + 2𝑒 −
Backwards (cathodic) reaction can be written as:
𝐶𝑢2+ + 2𝑒 − → 𝐶𝑢
𝑖 = 𝑖𝑎 + 𝑖𝑐
Where:
𝑖𝑎 -anodic reaction current; 𝑖𝑐 -cathodic reaction current; 𝑖𝑐 < 0; 𝑖𝑎 > 0
When the equilibrium is achieved: 𝑖𝑎 = −𝑖𝑐 , hence 𝑖 = 0. The potential at which current is zero is called
equilibrium potential.
In case when the equilibrium is not achieved, when zero current arises through balancing different reactions, the
net rate for each reaction is not equal to zero.
𝐹𝑒 → 𝐹𝑒 2+ + 2𝑒 −
Is balanced by
𝑂2 + 2𝐻2 𝑂 + 4𝑒 − → 4𝑂𝐻 −
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In this case the potential at which zero current appears is called mixed potential. Kinetic control region is
characterized by current densities and is exponential function of potential. Butler-Volmer equation describes
influence of potential on current density:
𝑖 = 𝑖0 {𝑒𝑥𝑝 (
(1 − 𝛼)𝑞𝐹
𝛼𝑞𝐹
𝜂𝑠 )} − 𝑒𝑥𝑝 (−
𝜂 )
𝑅𝑇
𝑅𝑇 𝑠
Where:
𝑖0 is an exchange current density; 𝜂𝑠 represents departure from the equilibrium potential if 𝜂𝑠 = 0 then 𝑖 = 0; 𝛼
is the traction of the surface overpotential, it promotes the cathodic reaction, 𝛼 ≈ 0.5, 0 < 𝛼 < 1. Kinetics is
very important when trying to interpret measured impedance curves, it allows to explain the reaction
mechanisms. The rate of the electrochemical reactions may be limited by the finite rate at which the reacting
species may be carried to the electrode surface. Law of mass transfer implements kinetic equations, which are
crucial for modeling the charge transfer resistance, which can be found in electrochemical impedance
spectroscopy.3
3
Electrical models
Preface
The aim of this chapter is to bring the reader closer to the idea of modeling itself, to show that the
expression “model” should be anticipated with a phrase that will precise more accurately what kind of modeling
is being described. Bigger focus was made on an impedance-based modeling which is the subject of this work.
Moreover description of the basic and more advanced elements used for creating a model is going to be given.
Introduction
Researchers from all over the world have been working on developing new models of electrochemical
batteries. Acquired models were varying with the degree of complexity. Depending from the usage purpose like
performance estimation to circuit simulation, different models were created. Mathematical models use empirical
equations or mathematical methods like stochastic approaches to predict battery runtime, efficiency, or capacity.
Those models are too abstract to be able to emerge any practical meaning but they are widely used by system
designers. Disadvantage of this modeling is that any I-V information are not possible to be acquired. According
to Min Chen and Gabriel A. Rincon,16 most of mathematical models result in 5%-20% error. For electrical
engineer electric models are more suitable than mathematical ones, they are more intuitive, useful and easier to
handle. Among all of the so far created electrical models we can distinguish three main groups: Thevenin,
impedance, and runtime-based models.16
The most simple Thevening model consist series resistor (𝑅𝑠𝑒𝑟𝑖𝑒𝑠 ) and RC parallel network
(𝑅𝑇𝑟𝑎𝑛𝑠𝑖𝑒𝑛𝑡 𝑎𝑛𝑑 𝐶𝑇𝑟𝑎𝑛𝑠𝑖𝑒𝑛𝑡 ) to predict battery response to transient load events at particular state of charge
(SOC), by assuming the open-circuit voltage [𝑉𝑂𝐶 (𝑆𝑂𝐶)] is constant. By this assumption it is though impossible
to get the battery steady state voltage variations (dc response) and runtime information. Improved Thevenin
models make it possible to acquire that information but still instead of 𝑉𝑂𝐶 (𝑆𝑂𝐶), which represents the voltage
source they use a regulated capacitor, which occur in 5% runtime error and 0.4 V error voltages for constant
charge/discharge currents. Thevenin models give us an idea about nonlinear relation between the open-circuit
voltage and SOC, but do not give any information about transient behavior. Runtime-based electrical model, use
a complex circuit network to simulate battery runtime and dc voltage response for constant discharge current.
Those models though cannot predict battery runtime or voltage response accurately.16
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Electrochemical Impedance Spectroscopy
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Impedance-based electrical model
Impedance-based models use the electrochemical impedance spectroscopy in order to create an acequivalent impedance model in the frequency domain. According to the shape of the impedance plot it is
possible to describe the elements that should be used in such model. Impedance is dependent from surrounding
temperature and battery state of charge (SOC),16 that is why it is necessary to do not create an model according
to one impedance spectrum, but according to set of impedance spectrums made in different temperatures and
battery state of charges, then it is possible to observe changes and trend that are taking place. Most common
elements used for creating the impedance model of the battery are: resistance R, capacitance C, inductance L,
and their variations.
Investigated
system
1 Resistor
2 Capacitor
3 Inductor
4 Capacitor and
resistor in series
5 Inductor
and
resistor in series
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Equivalent circuit
Impedance plot
Magnitude plot, phase plot
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Electrochemical Impedance Spectroscopy
6 Capacitor
resistor
parallel
and
in
7 Series Resistor
with
parallel
resistor
and
capacitor
Tabel 1. Impedance and Bode representation of different electric elements and their combinations.
If a voltage is applied across an electrochemical cell a current I forced to flow through this cell, with a
value defined by chemical reactions that are taking place in the cell. This reaction is the formation of new
chemical species as result of the movement of ions through the electrolyte. This movement is caused by applied
voltage difference and is the cause of flowing current. If the applied voltage is a sinusoid (△ 𝐸𝑠𝑖𝑛𝜔𝑡) then the
responsive current will have form of sinusoid with a value (△ 𝐼𝑠𝑖𝑛(𝜔𝑡 + 𝜃). The relationship of the applied
voltage and current is known as the impedance.11 Impedance 𝑧 has magnitude:3
𝑟 = |𝑧| = √𝑧𝑟2 + 𝑧𝑗2
Where: 𝑧𝑟 and 𝑧𝑗 are impedance real and imaginary part respectively and they can be presented as follows:
𝑧𝑟 = 𝑟𝑐𝑜𝑠(𝜃)
𝑧𝑗 = 𝑟𝑠𝑖𝑛(𝜃)
Impedance has also the phase angle
𝑧𝑗
𝜃 = 𝑡𝑎𝑛−1 ( )
𝑧𝑟
Table 1 presents impedance changes, magnitude and phase changes of such elements as resistor,
capacitor, inductor and their different combinations. For simulating those systems following values were taken:
𝐶 = 1.1557 ∙ 𝑒 −2 ; 𝐿 = 1.5 ∙ 10−3 ; 𝑅 = 1.2 ∙ 10−3 . Referring to the example number one in table 1, which
represents the situation where a sinusoidal potential is applied to a resistance R, then the magnitude of
impedance 𝑧 = 𝑅 and phase 𝜃 = 0 in all range of the frequency. Example number two represents the same
situation, but capacitor C is being under investigation. In such case impedance 𝑧 =
1
𝜔𝐶
and 𝜃 = 90°. While the
frequency is increasing the magnitude decreases. A clarification of presented nyquist diagram is crucial at this
point. The impedance changes are presented according to both positive and negative frequencies, lower
semicircle represents positive frequencies while the one above x axis represents negative frequencies. In the
future part of this project mostly, negative frequencies are going to be shown. Third case represents the inductor,
𝑧 = 𝜔𝐿 , 𝜃 = 90° and towards increasing frequency, magnitude increases.
Different combinations are available of those three elements, joining their attributes can give interesting
results. More detailed descriptions of parallel and series combinations will be presented together with
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experimental results where an attempt of creating an impedance-based model of the batteries will be shown. Not
always though those elements are capable of imitating investigated system in appropriate way, not always the
semicircle of impedance is going to look so perfect as in parallel connection of resistor and capacitor. In those
cases an element called constant phase element (CPE) is used.
3.1.1
The constant phase element
Constant phase element (CPE) is very useful, while creating an equivalent battery model. It is possible
to say that CPE is a not perfect brother of capacitance C. As it was shown before parallel combination of resistor
and capacitor results in plotting a depressed semicircle on nyquist plane, in real life though it is almost
impossible to achieve a perfect semicircle, CPE is a solution. It is said that CPE represents the inhomogeneity of
the charge distribution in EIS measurements.12 Mathematically CPE can be expressed as follows:
1
= 𝑄0 (𝑗𝜔)𝑛
|𝑍|
Where: 𝑄0 is an admittance at 𝜔 = 1
𝑟𝑎𝑑
𝑠
. 𝑄0 is described in 𝑆𝑠 𝑛 . It is clear that when the n=1 then 𝑄0
represents admittance of the capacitor.
1
= 𝑗𝜔𝑄0 = 𝑗𝜔𝐶
|𝑍|
Picture 8 CPE and p(CPE,R) dependency graph
Picture 8 present CPE (red line) and series connection of resistor with
paralel connection of resistance and CPE element (black line). CPE is
a line which angle towards x axis depends from n value 𝜑 = 𝑛 ∙ 90°,
the semicircle also depend from n value, more specifically
cemicircles depression can be described with an equation (1 − 𝑛) ∙
90°, so in this case where 𝑛 = 0.5 𝜑 = 45° and semicircle is
depressed with the same angle. Resistor in series 𝑅𝑠 = 1.5 ∙ 10−3
which represents the electrolyte resistance., paralel resistor 𝑅𝑐𝑡 = 4 ∙
10−4 Ω. Data cursor place on paralel connection of resistance and CPE
element plot represents the peak and can be shown as
𝜔𝑚𝑎𝑥 =
15
Picture 9 Magnitude Z changes
1
𝐶𝑑𝑙 𝑅𝑐𝑡
Picture 10 Phase vs frequency
2010
Electrochemical Impedance Spectroscopy
Where
𝑅𝑐𝑡 = 2|𝑍|𝑡𝑎𝑛𝜑𝑚𝑎𝑥
and represent the resistance of charge transfer (activation resistance), 𝐶𝑑𝑙 represents double layer capacitance.
Picture 9 shows the magnitude changes, for low frequencies(𝜔 → 0)
|𝑍| = 𝑅𝑠 + 𝑅𝑐𝑡
for 𝜔 → ∞
|𝑍| = 𝑅𝑠
Picture 10 shows the phase shift changes, the peak value.
1
𝑅𝑐𝑡
𝜔𝜑 𝑚𝑎𝑥 = √(
) ∙ (1 +
)
𝐶𝑑𝑙 𝑅𝑐𝑡
𝑅𝑠
Picture 11 shows the behavior of the system, when the 𝑛 parameter is being changed, starting from 0.5 and
increased by 0.1 The closer value of n to 1 the more perfect, more similar CPE’s semicircle is to capacitor one
Picture 11 Impedance curve shape changes for
different values of n
When registering the impedance curves of investigating battery an identification of its shape is crucial. When
having a 45° line it can be imitated by CPE element or it could be a Warburg element, which represents the
diffusion in the cell.12
3.1.2
Warburg impedance
Picture 12 represents the Bode plot for of Warburg impedance (W) in series with a charge transfer
resistance ( 𝑅𝐶𝑇 ) at the lower frequencies where the impedance of the Warburg dominates, the slope of the |Z|
1
Bode plot is (− ). In this region, the phase angle is 45°. At the higher frequencies, the charge transfer resistance
2
dominates and the phase angle becomes 0°.12
Picture 12 Warburg impedance nyquist plot
16
2010
Electrochemical Impedance Spectroscopy
Picture 13 show the real and imaginary parts of Z, plotted against
1
√𝜔
. The lines should be straight and
parallel: The slope of both lines should be equal to 𝜎, the Warburg constant. The line for the imaginary
component (shown in red) should intersect the Z axis at zero, while the intercept for the real component (shown
𝑧𝑗
in black) is 𝑅𝐶𝑇 .12 The slope of the curves is determined according to the equation 𝜃 = 𝑡𝑎𝑛−1 ( ). For the
𝑧𝑟
simulation 𝑅𝐶𝑇 = 0.0018Ω as shown in the picture if the line was longer it would cross the y axis at 0.0018.
Picture 13 Warburg real and imaginary
impedance curves
The equations, which define a Warburg Impedance, are
𝑍𝑤 =
𝜎
1
𝜔2
|𝑍| =
1
𝜔2
√2𝜎
1
𝜔2
and the Warburg coefficient, 𝜎, is given by:
𝜎=
𝜎
−𝑗
𝑅𝑇
𝑛2 𝐹 2 𝐴√2
(
1
1
𝐷𝑂2 𝐶𝑂𝑏
+
1
)
1
2 𝑏
𝐷𝑅 𝐶𝑅
The equation for 𝜎 applies to both reversible and quasi-reversible reactions for which both halves of the
couple are soluble. The subscripts O and R represent the Oxidized and Reduced forms of the species, and Cb
denotes a bulk concentration. D is the diffusion coefficient of the species.
The Warburg coefficient, 𝜎 , can be obtained from the slope of the Warburg plot, or by fitting to an
equivalent circuit model which includes a Warburg impedance. However, most equivalent circuit modeling
1
1
programs return "|𝑍| " rather than . |𝑍| is the magnitude of the admittance at 𝜔=1 rad/s (~0.16 Hz) .12
𝜎=
|𝑍|
√2
Summary
Choosing appropriate model elements is complex, they should be chosen not only according known impedances
but also according to the cells chemical reactions.
17
Electrochemical Impedance Spectroscopy
4
2010
Electrochemical impedance spectroscopy approach.
Preface
This chapter is dedicated to the electrochemical impedance spectroscopy method, the idea of this method is
going to be shown, next the hardware and software used for the experiment are going to be described.
Introduction
For acquiring impedance-based model
usage
of
electrochemical
impedance
spectroscopy method is necessary. This
method makes it possible to obtain an acequivalent impedance model in frequency
domain, next the impedance spectra need to
be evaluated, appropriate model representing
the battery behavior needs to be chosen and
then appropriate values for chosen model
elements needs to be found by fitting the
modeled spectra into original measured ones.
Impedance-based models work only for a
fixed SOC and temperature setting, they
cannot predict dc response or runtime.16
Electrochemical impedance spectroscopy
(EIS) is a tool for investigating the
mechanisms of electrochemical reactions, for
measuring dielectric and transport properties
Picture 14 Block diagram of used equipment
of material, for exploring the properties of
porous electrodes. EIS can be performed
either in a galvanostatic or in a potentiostatic mode. First approach is based on putting through a battery a small
amplitude ac current, then its voltage response is measured. When having ac current and ac voltage responses, it
is possible to acquire impedance. Battery impedance is computed online using discrete Fourier transforms
(DFTs), and superimposed with ac excitation signal. Dc (charge/discharge) current defines the overall working
point of the cell. To get more accurate results impedance is measured at few points. When having the impedance,
which consist the real and imaginary part 𝑍 = 𝑅𝑒 − 𝑗 ∙ 𝐼𝑚 we can create a model which will imitate the battery
behavior.
4.1
Hardware and software
Picture 14 show the set up which was used for EIS measurements consist of 2 computers, which worked in
a real time mode: host and target. Kepco bipolar power supply connected to a battery with supply copper wires
by flat copper plates, such connection gave a wide connection surface, what is important with flat shaped outputs
of the battery. Additionally in order to reduce losses on the cables, connection of the battery with power supply
and NI card by thin copper wires for direct voltage measurements was made. National laboratory measurement
card is used, which is responsible for gathering measured signals and organize the data traffic. Moreover battery
surface temperature measurement is made, information about which is given directly to the computer.
18
Electrochemical Impedance Spectroscopy
2010
Picture 15 Main interface of EIS program
Used program was made using Labview environment. Programs interface is divided vertically into two
main parts, the top part of the interface control running the subprograms, gives overall information if everything
is going well during the test. Round diodes at the top indicates the status of the subprograms, if an error will
occur the diode will turn on, or if the datalogging, which is nothing else than saving the measured data is not
turned on, the diode will let you know. The lower part consist of a few layouts: the Main, EIS Parameters,
Impedance Datalogging, Charge/Discharge Datalogging, Safety Shutdown, Error Handling Program itself give a
possibility to control the charge and discharge of the batteries, by controlling the bipolar power source. Setting
the current to positive values is followed with charge of the battery, with negative values with discharge. The
program gives a possibility for continuous observations of voltage, current and temperature changes while
testing the battery. Besides changing the current in steps, it was possible to use ramp function with different user
defined ramp rates. Picture 15 and 16 represents the interface of the EIS program, its main window. Variables
that can be changed in this window can be called as global ones, in this interface part manual control of the
charge/discharge current is done, current values and limits, can be changed, moreover real time observations are
available. Given real time graphical representations consist of: Lissajou, nyquist, and bode plots.
Picture 16 Main interface of EIS program
19
Electrochemical Impedance Spectroscopy
2010
Picture 17 Block diagram of Labview EIS program
Moreover in here main manual safety control in available. Program communicates with a bipolar power source
and gives possibility to cut off the load by using “Load OFF!” button. As for the EIS measurements itself in this
part of the interface it is possible to set up maximum amplitude of the current used for impedance measurement.
More detailed control of the EIS process is possible in the second part of the interface (picture 17): EIS
parameters. This layout is handling EIS parameterization. User can define the frequency range, divided into
logarithmic scale in which test is going to be run. User can define number of measurements points per decade
and number of periods that are going to be sampled in order to acquire frequency domain data on the output.
User can interfere into RMS Voltage amplitude value, amplitude of sinusoidal current, moreover it gives an
access to control used low pass filters frequency, with cutoff frequency 10 times higher than sampled signal.24
Picture 1824 represents the EIS program ideology.
Next 2 layouts: Impedance Datalogging and Charge/Discharge Datalogging, are responsible for managing the
storage of the data. Taking into account that behavior of testing batteries is not known for the researcher a
LabView program was implemented(Safety Shutdown layout) which automatically cuts off the load after
crossing previously précised safety value, like cut off low and high voltage, max temperature. The high voltage
Picture 18 Interface of the LabView EIS subprogram
limit is additionally controlled by used power source, which decrees the current value when getting close to the
limited voltage. Last crimp, the Error Handling contains information about an error if any occurs. Error case of
each subprogram is shown in this layout, makes it easy to detect and recognize the error.
Summary
Used program was satisfying for this project. It is easy to handle and user friendly. For future EIS tests it
would be useful to create a fitting program, which would compare experimental data with modeled data and find
optimal values.
20
Electrochemical Impedance Spectroscopy
5
2010
Noise effect
Preface
In this chapter a problem with noise that occurred during the tests will be presented and the effects of used
low pass filter.
Introduction
As mentioned before signal for EIS measurements is time based signal (picture 19), which is converted to
frequency domain signal, then according to this conversion result impedance is calculated (picture 20, 21, 22).
While making the EIS measurements signals are influence by different factors that results in an error.
5.1
Error structure
Error structure can be presented as follows
𝑍𝑜𝑏 (𝜔) − 𝑍𝑚𝑜𝑑 (𝜔) = 𝜀𝑓𝑖𝑡 (𝜔) + 𝜀𝑠𝑡𝑜𝑐ℎ (𝜔) + 𝜀𝑏𝑖𝑎𝑠 (𝜔)
Where: 𝑍𝑜𝑏 (𝜔) represents measured (observed)
impedance of the tested battery, 𝑍𝑚𝑜𝑑 (𝜔) is a
impedance of the created battery model. On the
right side of the equation 𝜀𝑓𝑖𝑡 (𝜔) stands for
inaccuracy of the model, 𝜀𝑠𝑡𝑜𝑐ℎ (𝜔) represent
stochastic error and 𝜀𝑏𝑖𝑎𝑠 (𝜔) the bias error. The
problem of interpretation of impedance data is
defined to consist of two parts: first is an
identification of experimental errors, which
includes estimation of consistency with
Kramers-Kronig method, second based on
model identification, examination of residual
error. The stochastic error arises from the fact
that original signal is represented by function of
time, which is affected by the noise coming
from the instrumental source, thermal
Picture 20 Measured Current, Voltage without filter affected by noise
fluctuations of resistivity, thermal fluctuations
of the concentration of the species and the rate of electrochemical reactions.3 Bias error cannot be assigned to the
error occurred because of inaccurate battery model. Bias error represents instrumentation artifacts, parts of
measured system which do not represent battery in any way and shouldn’t be taken under consideration. It also
represents battery nonstationary behavior, which can be seen especially for lower frequencies, when chemical
changes occur in the battery during long measurements time.3 Picture
19 shows the measured current and voltage used for EIS
measurements. Current amplitude is 4A voltages 0.01V. As seen on
the picture noise effect is particularly seen on voltage characteristics,
where even small amplitude noise is being a high percentage of
voltage amplitude and affects it in significant way. Moreover during
the tests high peaks occurred with different amplitudes, sometimes
the real impedance part was changed and imaginary stayed at the
same level on other it was opposite. Sometimes even the frequency at
which the measurement supposed to be made got changed, increased
ten
times or decreased. The cause of this noise was not explained,
Picture 19 Measured data without filter
possible is that some other equipment in
21
2010
Electrochemical Impedance Spectroscopy
Picture 22 Measured data for filter set to 4
Picture 21Measured data for filter set to 2
the laboratory was affecting the measurements. Picture 20, 21 and 22 shows different effects of using low pass
filter on the measured data. First case (picture 20) represents EIS data when no filter was implemented. Two
strong peaks are noticeable. Second case (picture 21) represents EIS data with used low pass filter, whose
frequency was increased 4 times. Comparing the results with no filter situation, it clearly seen that even with this
filter strong peaks are noticeable. Last case (picture 22) represents the situation when strong filter is used, it
works well and no peaks are noticeable, though strong filter might affect result in giving fake results. For done
battery impedance measurements second case option was chosen. Acquired data after conversion from time
domain into frequency domain are a set of points, every one of them described with imaginary and real part of
the impedance and the frequency at which the measurement point was made. Showed curves are the effect of
implementing the interpolation function and then smoothing function in order to acquire important for battery
Picture 24 Impedance curve with noise peaks
Picture 23 Sharpen impedancje curie influence by noise
peaks
Picture 26 Impedance curve without noise peaks
Picture 25 Smothed impedancje curve without noise
peaks
22
Electrochemical Impedance Spectroscopy
2010
According to 𝑂𝑟𝑎𝑧𝑒𝑚 3 some actions can be made to reduce stochastic errors.
1.
2.
3.
4.
Increasing the amplitude of modulated signal. Made tests prove it, taken EIS measurements
were more accurate when the current amplitude was increased, especially important with
higher capacity batteries, where higher noise was noticed.
Avoid harmonics. Filter should be used in order to get rid of the harmonics.
Increase the amount of sampled periods. For high frequencies big amount of periods should be
sampled, for low 3-4 is enough.
Faraday cage should be considered to be built in order to try to decrease effect of external
sources of electric fields.
In order to reduce bias error is to reduce time for measurements. It can be done by reducing the range of
frequency or number of points per decade, though it will reflect in worse representation of the impedance curve
shape, less measurement points, less data to work on.
Summary
As shown noise effect takes significant matter when using EIS method. It shows big sensitivity towards any
noise. A question occurs, what is counted to actually be an error. Behaviors of tested batteries are unknown so by
peaking randomly data for deleting or not taking into account inconvenient measurement points is not a very
scientific approach. Kramers-Kronig algorithm should be implemented for investigating the systems stability and
linearity.3 Due to time boundaries of this project error calculations and further examination of the noise problem
are going to be left for future projects dedicated to this subject.
6
Experimental results
In this chapter experimental results of tested batteries are going to be shown. This chapter is divided into
subchapters in which each particular tested battery is going to be presented. Charging and discharging behavior,
moreover impedance measurements are going to be made according to which precise information about battery
internal resistance, capacitance changes during battery changes of the state of charge will be shown. Additionally
the phase shift and magnitude will be presented. After presenting each battery behavior, conclusion will be made
and an approach towards creating an equivalent battery impedance-based model. Problems occurred while using
the Zfit program for fitting the battery impedance curves in order to retrieve the model parameters, though only
manual basic fit is going to be made.
The following batteries are going to be tested in the project:
I.
II.
III.
IV.
V.
VI.
KOKAM Lithium Ion Polymer Battery, 23 Ah , Type: NMC
KOKAM Lithium Ion Polymer Battery, model: SLPB 85255255 (53 Ah) , Type: NMC
Amita technologies battery Model Name: AI-33 L (33Ah) Type: LMO
EIG, ltd. Lithium Ion Polymer Battery, model : ePLB C020B. (20Ah) Type: NMC
EiG, ltd. Lithium Ion Polymer Battery, model : ePLB F014 (14Ah)Type: LFP
Thundersky LiFePO4 160 Ah battery. Type: rare earth doped LFP
Where:
NMC- nickel manganese cobalt; LMO- lithium manganese oxide; LFP- lithium iron phosphate. All these cells
have a carbon based anode.
23
2010
Electrochemical Impedance Spectroscopy
6.1
Kokam lithium polimer battery 53 Ah.
Typical Capacity1
Nominal Voltage
Charge conditions
53.0 Ah
3.7 V
53.0 A
4.2±0.03 V
Max. Current
Voltage
Discharge conditions
Continuous Current
Peak Current
Cut-off Voltage
Cycle life [@ 80% DOD]2
Operating Temperature
Charge
Discharge
Dimension
Thickness(mm)
Width(mm)
Length(mm)
Weight
1)
106.0 A (2C)
265 A
2.7 V
>1,500 Cycles
0~40℃
-20~60℃
8.5±0.2
255±2.0
255+5.0/-0.5
1.18±0.04
Typical Capacity: 0.5C, 4.2 ~2.7V at 25℃
2) Voltage range: 4.15V~3.40V
Tabel 2 Kokam 53 Ah battery specification
Tested battery already used before for tests, though its
state is going to be counted as almost new, before making any
measurements it was a few times charged and discharged with 1C
current, in order to get to know the software little bit better. First
thing that occurred was batteries recovery ability from low
voltages. Kokam 53 Ah battery was discharged with 26 A current
(0.5 C) While discharge, after crossing level of 3.4 voltage and
cutting off the discharging load, battery tends to stabilize the
voltage on 3.4 voltage level. Picture 28 clearly shows this
behavior. voltage on 3.4 voltage level. Picture 28 clearly shows
this behavior. This ability made it difficult to take EIS
Picture 28 Polarizaton and temperature changes
measurements below 3.4 V especially because the EIS program
curve (0.5C discharge)
works only in voltage mode, so constant voltage state was
difficult to obtain. It is not recommended to cross lower limit
voltage 2.7, for purpose of taking the temperature characteristic an
exception was made and the battery was discharged till 2.6 V.
Picture 28 shows constant polarization curve (blue line) and
temperature changes during the discharge cycle. Temperature
curve has hyperbolic function sinh(𝑥) =
−𝑥
Picture 27 Temperature In the function of voltage
(discharge) 0.5C
24
𝑥
𝑒 𝑥 −𝑒 −𝑥
2
shape with the
noticeable change from𝑒 into 𝑒 at 3.5V point. It is more vivid
on picture 27, which demonstrate temperature changes towards
voltage changes. Noticeable is that the temperature rise takes place
in two steps. Moreover after crossing the batteries lower voltage
range of 3.4 V battery voltage drops drastically, what results in
lower efficiency of the battery. During this last discharge period
battery surface temperature has significantly increased and in CV
(constant voltage) phase, dropped noticeably. Picture 29 represents
2010
Electrochemical Impedance Spectroscopy
charge characteristic with 0.5 C and the temperature curve. As
far voltage curve is a mirror reflection of discharge curve,
though temperature behaves totally different. Temperature
difference might be explained by different chemical reactions
during charge and discharge, though it is just suggestion, those
reactions are not unknown.
Next step was taking the EIS measurements. The measurements
were made at 13 states of battery charge points shown at the
legend of the picture. Tests were taken using data shown in the
table 3. Analyzing the polarization curve helped with choosing
Picture 29 Charge curve (0.5C)
the points at which the measurements were taken. Bigger focus
was made on points where significant changes were noticeable. Very interesting observation was made. When
taking a closer look on the impedance imaginary part 𝑧𝑗 vs. frequency plot (picture 30), where red markers
present 𝑧𝑗 at 0.1Hz, black diamond markers 𝑧𝑗 at 1Hz, black stars 𝑧𝑗 at 10Hz and blue squares 𝑧𝑗 at 20Hz.
Max amplitude
Frequency range
Points per decade
Sampled periods
Filter strength
10
50-0.1
30
4
4
A
Hz
.
.
.
Tabel 3 Data used for EIS measurements
It is observable that till the V=3.88 the internal value of 𝑧𝑗 was decreasing (solid line), after crossing this state of
charge the value of 𝑧𝑗 starts to rise. At battery voltage U=3.4 V(dashed black line) 𝑧𝑗 at low frequencies rises to
5 ∙ 10−4 Ω, at 3.3 V (lack solid line) 𝑧𝑗 rises up to 0.002Ω and for 3.0 V(cyan) rises till 0.006Ω. Red markers at
the picture 31 presents 𝑧𝑗 at 0.1Hz, black diamond markers 𝑧𝑗 at 1Hz, black stars 𝑧𝑗 at 10Hz and blue squares 𝑧𝑗
at 20Hz. Tracking the changes of 𝑧𝑗 for mentioned frequencies for different battery voltage levels is presented on
picture 30 and 31. Significant changes at low frequencies are observed, and tendency with previously described
turning point.
Picture 31 Imaginary impedance part changes
Picture 30 Imaginary impedancje part changes for
specific frequencies
Real part of the impedance decrease asymptotically (picture 32)and show the same trend as the imaginary with
same turning point. Also at low frequencies for discharge states battery real impedance part 𝑧𝑟 rises significantly
at 3.4 V (dashed black line) 𝑧𝑟 rises till 2.8 ∙ 10−3 Ω, at 3.3 V (black solid line) 𝑧𝑟 rises till 5.3 ∙ 10−3 Ω, at 3.0
V(cyan line) 𝑧𝑟 rises till 8.5 ∙ 10−3 Ω. Picture 33 represents the Bode plot, which consist of magnitude/frequency
dependency and phase/frequency relationship. Observable is significant rise of the system magnitude at low
voltage states of the battery. As it will be shown later in the battery voltage range of 4.22-3.88 magnitude ranges
from 2.1 ∙ 10−3 to 1.85 ∙ 10−3 than for low battery voltages magnitude rises till 0.011 at 3.0V what is 5.2 times
25
Electrochemical Impedance Spectroscopy
2010
higher value than for charged battery. Phase though
decreases up till -43.6 degrees. By having a closer look
at phase and magnitude similar tendency to imaginary
impedance plot was noticed, where the turning point
was observed at 3.88V. In the voltage range 4.22-3.88
System magnitude decreases from 2.1 ∙ 10−3 till 1.85 ∙
10−3 respectively and phase increases in the range of 1.5:-3 degrees. Pictures 34 an 35 represents imaginary
capacitance 𝐶𝑗 and real part capacitance 𝐶𝑟 changes
towards frequency changes. In both cases for low
battery voltages representing its discharge state
significant decrease of capacitance was observed
Picture 32Real impedance part changes
According to 𝑂𝑟𝑎𝑧𝑒𝑚 3 low frequency limit can be
interpreted as double layer capacitance. Seen peak on
imaginary characteristics corresponds to 𝑓𝑐 =
(2𝜋𝑅𝑒 𝐶)−1 and is very useful for calculating semicircles
peaks of impedance curves.
Picture 33 Bode characteristics
Picture 35 Imaginary part of capacitance changes
Picture 34 Real part of capacitance changes
Picture 36 represent nyquist plot, in other words the imaginary impedance part versus real part plot (frequency
domain). It represents the changes of the impedance in different battery states of charges in the frequency range
of 50-0.1 Hz. Firstly it is important to emphasize that for creating initial model of the battery according to the
EIS measurements more than one spectrum is needed. Observation of the battery behavior at different state of
charges is necessary. Similar as in previous examples markers were used for tracking impedance changes at
certain frequencies. According to the curves it is possible to conclude that all curves start with a straight line
with the angle 69 degrees. Comparing the solid line curves, which represent the battery state of charge from 4.2
till 3.88 V, it is possible to distinguish 2 semicircles which represent dynamic behavior of the battery.
Characteristic ending of the curves was noticed, line app. 45 degree angle. At lower voltages the internal
impedance of the battery is rising to the values pointed out before. At lower voltages of the battery the
impedance semicircles amplitude decrees and curve is more similar to the straight line, what can be understood
as loosing dynamic performance ability. According to the impedance curves and made observations of those
curves it is possible to make first attempt of creating an equivalent model of the Kokam 53Ah lithium battery.
26
Electrochemical Impedance Spectroscopy
2010
Starting from the high frequencies an characteristic constant phase shape is observable with following it
semicircle. Because the span of smoothing
function was set to small value of 0.1 it might
seem that there is a third and fourth semicircle.
The curve does not have perfect shapes, though
sharpening it might cause unwanted faults in
model estimation. Picture 37 presents proposed
model for tested battery it consist of
resistance 𝑅𝑠 , which represents electric
conductivity of the electrolyte, separator and
electrodes. 𝑅𝑠𝑒𝑖 and 𝐶𝑃𝐸𝑠𝑒𝑖 are representing
resistance and capacitance of solid-state
interfacial layer formed on the surface of the
electrodes, and corresponds to high frequency
semicircle. 𝑅𝑐𝑡 and 𝐶𝑃𝐸𝑑𝑙 are faradic charge
transfer
resistance
and
double
layer
capacitance, which corresponds to medium
Picture 36 Nyquist graph of Kokam 53 Ah battery
frequencies. W represent the Warburg
impedance related to a combination of the
diffusional effects of lithium ion on the interface between the active material particles and electrolyte, which Is
generally indicated by a straight sloping line at low frequencies. The combination of W and 𝑅𝑐𝑡 is called faradic
impedance and reflects kinetics of the battery.2
Picture 37 Proposed impedance model for Kokam 53Ah lithium battery
27
2010
Electrochemical Impedance Spectroscopy
6.1.1
Kokam lithium polimer battery 25 Ah
Picture 38 Kokam 25Ah battery
Typical Capacity1
Nominal Voltage
Charge conditions
Max. Current
Voltage
Discharge conditions
Continuous Current
Peak Current
Cut-off Voltage
Cycle life [@ 80% DOD]2
Operating Temperature
Charge
Discharge
Dimension
Thickness(mm)
Width(mm)
Length(mm)
Weight
1)
25.0 Ah
3.7 V
25.0 A
4.2±0.03 V
25A (1C)
125 A
2.7 V
>800 Cycles
0~40℃
-20~60℃
6.5±0.2
215±2.0
220±2.0
620±20
Typical Capacity: 0.5C, 4.2 ~2.7V at 25℃
2) Voltage range: 4.15V~3.40V
Tabel 4 Kokam 25Ah lithium battery specifications
Another battery that was tested is Kokam 25Ah lithium
battery. The test was run under conditions presented in
table As it was mentioned before it has nickel manganese
cobalt cathode and carbon based anode. It is the same type
as the previously tested battery Kokam 53 Ah. The dc
polarization curve shown at picture 40 looks similar as for
the 53Ah battery, also the temperature curve seems to be
alike. First difference was noticed while looking at
temperature vs voltage plot(picture 39), where we can see
that in the battery voltage range 4.15 till 3.3 the temperature
rise can be shown as 45 degrees slope, after that the battery
Picture 39 Polarization cuve
starts losing its dynamic performance, hence voltage drop is
significant in short period of time. At this point temperature rise
angle slope is decreasing up to 23.3 ℃ at 2.6 V. Battery starting
was 18℃, what gives 5.3℃ rise during the 0.5C discharge. Table 5
presents set up parameters for EIS measurements. Pictures 41 and
42 represent Kokam 25Ah battery 𝑧𝑗 behavior at different states of
charge. Similar to 53Ah battery pattern was observed, with turning
point between 3.9 and 3.8V. Picture 42 presents imaginary
impedance parts of different states of charge towards frequency
and it can be assumed that:
Picture 40 Temperature vs voltage characteristic
28
2010
Electrochemical Impedance Spectroscopy
Max amplitude
Frequency range
Points per decade
Sampled periods
Filter strength
10
50-0.1
30
4
4
A
Hz
.
.
.
Tabel 5 EIS test conditions
in the voltage range 4.15-3.9, which represents
battery being charged 𝑧𝑗 has decreased in the higher
frequencies, though at low <2 Hz fast rise is
noticeable. After crossing the turning point internal
imaginary impedance rises and reaches 3.8 ∙ 10−3 Ω
level what is 14 times bigger value than for 𝑧𝑗 at full
charge state 2.7 ∙ 10−4 Ω . Red markers at the picture
40presents 𝑧𝑗 at 0.1Hz, black diamond markers 𝑧𝑗 at
1Hz, black stars 𝑧𝑗 at 10Hz and blue squares 𝑧𝑗 at
20Hz. Tracking the changes of 𝑧𝑗 for mentioned
frequencies for different battery voltage levels is
presented on picture 42.
Picture 41 Imaginary impedance part changes towards frequency
at different states of charge.
Picture 43 present 𝑧𝑟 changes and they characterize
with the same pattern as in previous cases, it rises
from 2.5 ∙ 10−3 Ω at full charge state till 7 ∙ 10−3 Ω at
full discharge state. Picture 44 present bode
characteristics, as for the phase the lower voltage
level of the battery the bigger changes in the phase
are noticed. At low frequencies characterize with big
phase changes the peak was noticed at 0.7 Hz, where
it reached -30 degree angle. At high frequencies the
phase differences at different voltage levels are
becoming less significant. Magnitude resembles
asymptotical behavior, increases significantly at Picture 42 Imaginary impedance part changes for specific
lower frequencies, though decrease at high frequencies.
frequencies. Pictures 44, 46 and 47 presents batteries
capacitance behavior, divided into real and imaginary
characteristic. In subchapter dedicated for kokam 53 Ah
battery description was given for those characteristics,
their meaning. Noticeable is decrease of the capacitance
both real and imaginary while battery being discharged.
For imaginary the decrees is up to 13 times big, for real
5 times. As frequency increase differences of
capacitance for at different voltage levels becomes
smaller.
Picture 43 zr changes at different battery voltage levels
29
2010
Electrochemical Impedance Spectroscopy
Picture 44 Imaginary capacitance changes
Picture 47 Imaginary capacitance changes
Picture 45 Real capacitance Changes
Picture 46 Bode characteristics
Picture 48 represent Kokam 25 Ah battery internal impedance changes displayed using nyquist plot. At high
frequencies impedance can be represented as straight line with 67 65 degree angle, and it ends with a semicircle.
In middle frequencies 2 semicircles become vivid, which are followed by a constant phase line of 45 degrees. As
at Kokam 53 Ah battery used 𝑅𝑐𝑡 and 𝐶𝑃𝐸𝑑𝑙 for describing faradic charge transfer resistance and double layer
capacitance, which corresponds to medium frequencies. In Kokam 25Ah two parallel connections are going to
represent described phenomena. Picture 49 presents proposed model for the battery.
Picture 48 Nyquist plot
30
2010
Electrochemical Impedance Spectroscopy
Picture 49 Proposed impedance model for Kokam 25 Ah lithium battery
6.2
Lithium ion polymer battery 20Ah (LIPB)
Model name: ePLB C020B.
Picture 50 Eig 20Ah battery
Typical Capacity
Nominal Voltage
Charge conditions
CC
CV
Discharge conditions
Continuous Current
Max discharge current(constant)
Peak Current
Cut-off Voltage
Cycle life [@ 80% DOD]2
Operating Temperature
Charge
Discharge
Dimension
Thickness(mm)
Width(mm)
Length(mm)
Weight
20.0 Ah
3.65 V
10.0 A
4.15V to 1A
10A (0.5C)
100A
200 A
3.0 V
>800 Cycles
0~40℃
-30~55℃
7.2±0.2
129 ± 0.5
217±1.0
427 ± 3g
Tabel 7 EiG lithium 20 Ah battery specifications
Next tested battery is 20Ah
nickel manganese cobalt cathode, carbon based anode. It was
discharged using 0.5C current, which is 10A. Picture 53
presents the tested battery temperature and voltage curve
during the discharge. Actual discharge starts from 102 𝑠. and
characteristic function 𝑒 𝑥 shape. After crossing 3.8V point
temperature has lowered what is difficult to explain as it should
increase during the discharge. After crossing 3.6 V limit
Picture 51 Temperature curie and voltage curie in
time dependency
31
battery temperature starts rising in 𝑒 −𝑥 manner until total
2010
Electrochemical Impedance Spectroscopy
Picture 52 zj changes at different voltage levels
Picture 53 Imaginary impedance part changes
discharge. Observations of the battery imaginary impedance part are
shown on picture 51 and 52. The previously described turning point
was found at 3.79 V, from this point the impedance starts to rise. As
at charged states of battery (3.8-4.2 V) the 𝑧𝑗 do not change
significantly (picture 52) in any frequency range as for lower
voltages (3. 3-3.12) battery 𝑧𝑗 at low frequencies increase up to 1.3 ∙
10−3 Ω. Changes of 𝑧𝑗 at chosen frequencies 0.1,1,10 and 20 Hz are
presented at picture 51. As for real impedance part (picture 50)
changes at middle and high frequencies relevantly small, at low
voltages (3.3-3.12) 𝑧𝑟 increases more than 3 times, up to 1.5 ∙
10−3 Ω s in charged condition. Pictures 54 and 55 present changes
of the EiG 20 Ah battery capacitance, its real and imaginary parts.
The lower battery voltage level the lower value capacitances are
taking. At high frequencies differences of capacitances are not as
significant as for low frequencies. 𝐶𝑗 decrease till −4 ∙ 10−5 when
at higher voltages it ranges between −1.4 ∙ 10−6 and −0.6 ∙ 10−6 .
𝐶𝑟 for higher voltages ranges between −1 ∙ 10−5 and −1.25 ∙
10−5 for low voltages it decrease till −4.5 ∙ 10−5 . All values
Picture 54 Real impedance part changes
Picture 55 Real capacitance part changes
are given in farads [F]. As seen on picture 56, which present
bode diagram systems magnitude at voltage level >3.3 V do
not cross the 0.005 value. Cyan color curve presents battery at
discharge state, magnitude is significantly higher, it reaches
0.02 value, and phase shift rises up to -50 degree angle. By
having a closer look at battery nyquist plot, which show
impedance changes (picture 57) noticeable is similar battery
behavior as in Kokam 25Ah one. Two semicircles are
Picture 56 Imaginary capacitance part changes
representing middle frequency changes, second one is less
vivid but cannot be omitted. Because of this the same model as for 25Ah battery is proposed for this battery.
Picture 57 Nyquist plot
32
Picture 58 Bode diagram
Electrochemical Impedance Spectroscopy
6.3
2010
Lithium ion polymer battery 14Ah (LIPB)
Picture 59 Eig 14 Ah lithium battery
Typical Capacity
Nominal Voltage
Charge conditions
CC
CV
Rapid charge
Discharge conditions
Continuous Current
Max discharge current(constant)
Peak Current
Cut-off Voltage
Cycle life [@ 80% DOD]2
Operating Temperature
Charge
Discharge
Dimension
Thickness(mm)
Width(mm)
Length(mm)
Weight
14.0 Ah
3.25 V
7.0 A
3.65V to 0.7A
CC:14A; CV:3.65 to 0.7A
14A (1C)
140A(10C)
280 A(20C)
2.0 V
>800 Cycles
0~40℃
-30~55℃
7.2±0.2
129 ± 0.1
222±1.0
380 ± 5g
Last tested battery for this project is EiG 14Ah
lithium polymer battery. As three previous
batteries were using the same materials for cathodes this one differs. Lithium iron phosphate cathode, carbon
based anode are used. Table 9 represent 14Ah battery specifications. Noticeable is battery ability for high
current discharge. Continuous 10C current is very
unique. Picture 60 present 5C discharge, it is 70 A and
higher discharge C is impossible for used power supply.
Battery behaves is a very interesting way. While
discharge it keeps the voltage on constant level, voltage
drop is very sudden and does not characterize with much
of a efficiency. Picture 59 presents battery 𝑧𝑗 changes at
Tabel 6 EiG 14Ah lithium battery specifications
different voltage levels. Noticeable are changes while Picture 61 Discharge 5C temperature and voltage curve
discharge of battery, but presented curves does not show changes
battery internal dynamics at each particular voltage level.
Curves behave asymptotically without any observable
semicircles. Picture 61 presents nyquist plot, where
observable is battery impedance behavior. Two curves
(V=3.32 and V=3.25) present noticeable semicircles , the
rest behaves as battery was discharged. EiG battery was
tested in a wrong way, its specific behavior of working
most efficiently in a very small voltage range and for
long time made it difficult to track its dynamic behavior.
Most of the measured curves present battery leas efficient Picture 60 zj changes for diferent voltage levels
part and according to them it is possible to observe
maximum and minimum reached values but to conclude a impedance model and observe trends that occur it will
be needed to create measurements more precisely.
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Electrochemical Impedance Spectroscopy
2010
Picture 62 Nyquist plot
Summary
In this chapter four batteries were tested, from where 3 successfully. Each of the battery was described with
highlighting its most noticeable attributes. Interesting is the EiG 20Ah and EiG 14Ah batteries ability for high
current discharge possibility, though they have different materials as cathodes. Kokam batteries do not show
such ability. From shown reason Kokam and EiG batteries are going to be used for different purposes. 14Ah EiG
battery is not a good solution for electric vehicle, because it might be difficult to read battery state of charge with
such small voltage changes, though other applications, where high current is needed will be perfect for them.
Presented battery models are not satisfactory and not optimal. Values taken for simulation were chosen manually
and should be fitted using least square method. Made model resembles characteristic taken for impedance, but it
does not have ability to follow the impedance changes that describes the battery. In the future a fitting program
should be made, more precise tests in case of 14Ah battery. As for other batteries Tracked markers show that in
some cases it is difficult to show trends of changes, sometimes variations are to big, what is caused by the noise
in the system. Kramers-Kronig algorithm should be implemented for investigating the systems stability and
linearity.3
7
Summary and conclusions
For the purpose of this work a few different models of batteries were tested. Unfortunately provided
specifications for the batteries did not give any information about neither the battery construction, materials used
for electrolyte, electrodes, further contact with the company did not give any results. Luckily some basic very
helpful information about material used for cathodes and anodes of the batteries were provided by the
DongEnergy Company. According to owned information about the batteries, equipment and time barriers an
approach was made towards creating the battery impedance model. As it was mentioned before, thanks to EIS
method it is possible to acquire information about the batteries impedance. Those information are indispensible
in creating the batteries equivalent model, but it is necessary to emphasize that the model based only according
to the data acquired by EIS method represents the classic example of “ fitting the elephant “. What means that
creating an impedance-based model of the battery based only on the experimentally taken measurements is not
enough. Such model would be satisfactory only up to certain point. Proper model should be also based on other
observations and calculations, like physical calculations and chemical expertise of the battery. Such calculations
demands more detailed information about batteries, like dimensions of cathode and anode, thickness of the used
film. From those reasons this work was focused on the electrochemical impedance spectroscopy method usage
on batteries and creating an impedance-based model, but without any external supportive investigations. EIS
software on its own has shown a lot good qualities, the interface made in LabView was intuitive and easy to
34
Electrochemical Impedance Spectroscopy
2010
handle. Very useful turned out to be to store the results in the .m file so working in program Matlab was much
easier. Communication between LabView and Matlab turned out to work perfectly. Given real time graphical
representation of the measurements provides bigger control of the whole test process, moreover the user could
quickly decide if run test is going well and if some parameters should be changed for further tests. EIS software
was used before for modeling the fuel cells, in the battery case some problems occurs during the tests. Proper
battery charging should be made in 2 steps, constant current and constant voltage. Software was not able to run
with constant voltage mode what has brought some complications. For further researches on battery EIS,
developing the software will be needed. Could be a good idea to store the EIS parameters in an output file with
all the measured data, plus creating a fitting program could be useful.
8
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