Akku4Future
Report for Workpackage 6
Dav id Lindner, Florian Niederm ayr
29.09.2014
Table of Contents
Abbreviations .......................................................................................................................................... 3
1
Introduction .................................................................................................................................... 4
2
State of Science ............................................................................................................................... 4
2.1
2.1.1
Discharge test method .................................................................................................... 5
2.1.2
Open circuit voltage method .......................................................................................... 5
2.1.3
Coulomb counting ........................................................................................................... 6
2.1.4
Battery model-based method ......................................................................................... 7
2.1.5
Impedance measurements ............................................................................................. 8
2.1.6
Artificial neural network method.................................................................................... 9
2.1.7
Fuzzy logic method........................................................................................................ 10
2.1.8
Support Vector Machine method ................................................................................. 11
2.1.9
Kalman-filtering method ............................................................................................... 11
2.1.10
Hybrid methods ............................................................................................................ 13
2.2
Durability model-based open-loop SOH estimation method ....................................... 14
2.2.2
Battery model-based parameter identification closed-loop SOH estimation method. 15
5
SOF estimation ...................................................................................................................... 15
State of Technology ...................................................................................................................... 16
3.1
4
SOH estimation ..................................................................................................................... 14
2.2.1
2.3
3
SOC estimation........................................................................................................................ 4
Topologies ............................................................................................................................. 16
3.1.1
Centralized .................................................................................................................... 16
3.1.2
Modular......................................................................................................................... 16
3.1.3
Master-slave.................................................................................................................. 17
3.1.4
Distributed .................................................................................................................... 17
3.1.5
Topology comparison.................................................................................................... 18
Further applications of impedance spectroscopy......................................................................... 19
4.1
Impedance spectroscopy in food industry ............................................................................ 19
4.2
Impedance spectroscopy in biomedicine ............................................................................. 21
4.3
Impedance spectroscopy in building industry ...................................................................... 23
Bibliography .................................................................................................................................. 27
Abbreviations
SOC
state of charge
SOH
state of health
SOF
state of function
OCV
open circuit voltage
IS
impedance spectroscopy
ANN
artificial neural network
SVM
support vector machine
EKF
extended Kalman filter
UKF
unscented Kalman filter
REKF
robust extended Kalman filter
SEI
solid-electrolyte interface
SIP
spectral induced polarisation
EIS
electrochemical impedance spectroscopy
1 Introduction
Currently, Li-ion batteries are widely used in many different applications, starting with small portable
devices like smartphones and ending with large electric systems like electric vehicles. Especially their
high specific energy density makes them very attractive for high-performance applications.
However, for an effective and well working energy storage system it is essential to protect the
battery and to control its performance. Therefore, a lot of research has been done – and is still being
done – in developing battery management systems.
One of the most important features of a battery management system is definitely the estimation of
the battery states, i.e. state of charge (SOC), state of health (SOH), and state of function (SOF). The
detailed definitions of these terms will be given in the respective chapters.
So, in this report an overview of the state of science and the state of technology in battery states
estimation will be given explaining the most commonly discussed methods and mentioning some
exemplary literature. Finally, examples for other fields of applications of some explained methods
are given.
2 State of Science
2.1 SOC estimation
A general definition of SOC is shown in eq. (1) where Q is the charge balance and C is the capacity.
(1)
However, the specific definition of SOC is not always consistent in literature. The reason is, that
different definitions of capacity are used for the SOC definition [1]. One can use the nominal capacity
which is the capacity declared by the manufacturer, the measured capacity which is measured at any
moment in time under specified conditions, or the practical capacity which is the actually available
capacity for the system. Depending on which capacity definition is used, the SOC is defined
accordingly. Fig. 1 illustrates the different SOC definitions, namely the “normal” SOC (using the
nominal capacity), the relative SOC (using the measured capacity) and the practical SOC (using the
practical capacity). Mostly, the practical SOC definition is used for application because only there the
value corresponds to the discharging endpoint.
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Fig. 1: Different definitions of SOC [2].
The following sections now describe different frequently used approaches for battery SOC
estimation methods.
2.1.1 Discharge test method
The discharge test method is a reliable method to determine the battery SOC under controlled
conditions (discharge rate, ambient temperature). The remaining charge and thereof the SOC can be
estimated accurately, but the method is not useful for applications because the battery has no
power afterwards and has to be reloaded. These facts make this method too time consuming and
not suitable for on-line estimation [3].
2.1.2 Open circuit voltage method
The open circuit voltage (OCV) of the battery is a good indicator for the SOC because of the one-toone correspondence between OCV and SOC, and because there is almost no influence from the
service life of the battery [4]. The problem is that the OCV is depending on many battery parameters
and needs a long relaxation time for measuring an accurate value. It is, therefore, difficult to obtain
the OVC accurately in an application if there is not enough time for relaxation. For example a
C/LiFePO4 battery needs more than three hours for relaxation at low temperatures [5] and this is, for
instance, not working for HEV packs. Also hysteretic phenomena play a role so that at the same SOC
state the measurements after charging differ from measurements after discharging (Fig. 2).
It is, therefore, necessary to create look-up-tables including many different values for the relevant
parameters (temperature, charging/discharging current) to calculate SOC accurately from OCV.
Creating such tables is very time-intensive so that it is useful to combine OCV measurement with
other methods (see chapter 2.1.10). In [6] an on-line SOC estimation method based on the impulse
response concept is developed where the OCV is predicted by obtaining the impulse response of the
Li-ion battery to an input current impulse.
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Fig. 2: Charge and discharge OCV curves of C/LiFePO4 battery [4].
2.1.3 Coulomb counting
The coulomb counting method (also known as Ampere-hour integral) is a method which tries
estimate the SOC by measuring the consumed charge of the battery. It observes the charging and
discharging current of the battery and estimates
in base of that measurements.
Mathematically, this method is represented by the following equation (2):
∫
(2)
.... SOC at initial time
.... Capacity of the battery in standard condition
.... Coulombic efficiency (
while discharging and
while charging)
.... Current as a function of time (negative at charge, positive at discharge)
If the initial value
is precise, coulomb counting is a quite accurate and especially simple
method for determining SOC.
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However, if
is not precise, the method is inaccurate and not very useful. Moreover, the
coulomb efficiency depends on the operation mode (SOC, temperature, current etc.) and is
therefore difficult to obtain. Also the current sensors normally have a little offset which is further
deteriorating the estimation.
All these factors make the SOC error increase with time (Fig. 3), especially in standby batteries and in
HEV packs [7].
Fig. 3: Long-term drift of SOC estimation because of the offset in the current measurement [7].
Nevertheless, coulomb counting in practice is used very often (see chapter 3) because of its
simplicity. The errors in results are attempted to get minimized by combinations with other methods
(see chapter 2.1.10). Another method to reduce the errors is the so called modified coulomb
counting method. This method uses the corrected current to improve the measurement. The
corrected current is depending on charging and discharging current of the battery in the way
describes by equation (3). Here
and are constants obtained from experimental data [8].
(3)
The SOC of the battery is now calculated again by equation (2) using instead of . The results in
the experiments show, that the accuracy of the estimation improves while using the modified
coulomb counting method in comparison with the normal coulomb counting [8] method.
2.1.4 Battery model-based method
Battery models are very useful for on-line parameter estimation of a battery so that difficulties (e.g.
long waiting times) can be avoided. Generally, two types of models are used: equivalent circuit
models and electrochemical models. A comparison of twelve commonly used equivalent circuit
models can be found in [9] and some electrochemical models are explained in [10].
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The difficulty in using battery models is to find the right balance between complexity and need of
precision, i.e. the goal is to get a maximum of accuracy with a minimum of computational cost. In
this regard, equivalent circuits are more suitable for applications than electrochemical models
because most electrochemical models are rather complicated and usually require huge
computations [9].
2.1.5 Impedance measurements
The impedance contains much information about the internal reactions inside a battery and is
therefore also sensitive to the SOC of a battery [11]. Since the impedance is frequency-dependent, it
is reasonable to measure impedance at different frequencies. This method is called Impedance
Spectroscopy (IS). For instance, Tenno et al. in [12] characterized battery impedance through the
voltage response pulses to short current pulses. For graphic illustration of the IS measurement
results the Nyquist-plot (Fig. 4) is suitable. It shows the real part of the impedance on the x-axis and
the negative imaginary part on the y-axis as a function of frequency. The frequency is small at the
right side of the curve and is increasing as the curve goes to the left.
Fig. 4: Nyquist plot of the complex impedance of a lead-acid battery cell [13].
A big benefit of IS is the fact, that it allows the parameterisation and the derivation of the structure
of impedance models [14]. An impedance model is generally a complex function of current, voltage
and frequency and sometimes it can be described with an electric circuit diagram. Some examples
for impedance based models can be found in [15] where Buller investigated some linear battery
models, and in [16] where a Li-ion polymer cell model is developed using a relatively simple
equivalent circuit.
The impedance provides also information about ageing of the battery so that impedance
measurements are also suitable for SOH estimation (see chapter 2.2). A big disadvantage of this
method is the fact that for IS a signal with frequency sweep has to be applied and this makes IS
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expensive and uncomfortable for portable devices. Furthermore, impedance is very temperature
sensitive which is another disadvantage, especially for portable devices [17].
2.1.6 Artificial neural network method
An Artificial neural network (ANN) tries to imitate the neural network of the human brain. It has
become a common tool for modelling complex or even unknown systems because of his simplicity in
handling data from such systems [18]. The big advantage of ANNs for SOC estimation is its ability to
handle data with nonlinear dependencies and its universality due to the fact, that it is not necessary
to take into consideration all the details of the battery. A little disadvantageous is the need of
powerful processing chips because of the big computational cost of this method [4].
A typical ANN is build up of three layers: an input layer, a hidden layer and an output layer (Fig. 5). It
is composed by neurons which are connected to work together and to process the information
coming from the input layer. The connecting lines illustrate the weights which are in principle
functions between the layers. To find appropriate values for these weights it is necessary to train the
ANN before using it for estimations. This training phase is the biggest limitation of an ANN because a
lot of different data is needed to get an accurately working network [19].
Fig. 5: Different layers of a typical Artificial Neural Network [19].
Examples for applications of ANNs for SOC estimation can be found in [20] where an ANN is used for
capacity estimation of a lead-acid battery, and in [21] where internal battery parameters of different
types of batteries were used as inputs of the ANN to get SOC as the output.
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2.1.7 Fuzzy logic method
With the fuzzy logic method it is possible to model nonlinear and complex systems by processing the
measured data using the rules of the fuzzy logic theory. A practical method for estimating SOC using
fuzzy logic has been developed in [22], where also the concept of fuzzy logic is described. The fuzzy
logic method allows a certain level of uncertainty in the calculations. The measured data can be
categorized by crisp or fuzzy sets. Crisp sets categorize data with certainty, while data sets in fuzzy
sets have uncertain values. For example a crisp set could be a set of temperatures between 30°C and
40°C, a fuzzy set could be categorized by the expression “warm”. The subset categorized by the
expression “warm” is defined by its so called membership function and each element in a fuzzy set
gets a degree of membership which indicates the degree of belonging to the different subsets.
An example of a fuzzy set with three subsets is shown in Fig. 6. The process of determining the
degree of membership of the crisp data is called the fuzzification of the data.
Fig. 6: Membership function for temperature [22].
A simple fuzzy system where both the inputs and the outputs are crisp sets is shown in Fig. 7. The
fuzzy system, after determining the degree of membership, has four conceptual components:
-
A rule base describing the relationship between input and output variables
A database that defines the membership functions for the input and output variables
A reasoning mechanism that performs the inference procedure
A defuzzification block which transforms the fuzzy output sets to a crisp output
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Fig. 7: Fuzzy system with crisp inputs and outputs [22].
The fuzzy logic method is a powerful method, but it requires a big amount of testing data, relatively
large computations and a good understanding of the batteries themselves for an accurate SOC
prediction [4]. An example for fuzzy logic based SOC estimation can be found in [23] where a SOCmeter for Li-ion batteries used in portable defibrillators is developed. Also extended fuzzy logic
methods are investigated for application in battery management systems, e.g. a wavelet-fuzzy logic
based energy management system is examined in [24].
2.1.8 Support Vector Machine method
The support vector machine (SVM) can be used as a regression algorithm for nonlinear problems and
is therefore also suitable for SOC estimation of Li-ion batteries. In [25], Hansen and Wang
investigated the implementation of a SVM-based SOC estimation method. The input vector included
current, voltage and SOC calculated from the previous step and the voltage change in the last
second, and the output was SOC. The SOC estimation model was trained using just steady state data
and the reported errors were around 5%. Moreover, the authors emphasize, that regressions using
the SVM method are more stable than least-squares estimation because of its insensitivity to small
changes. Nevertheless, a good SVM regression model requires fine tuning of the different
parameters, and this process is likely to be time-consuming [18].
2.1.9 Kalman-filtering method
A Kalman filter is an algorithm to estimate the inner states of a battery, among others, SOC and SOH.
The estimation is based on a battery model which includes the wanted unknown quantities in its
state description.
Since Kalman-filtering is a very effective and widely used tool, its basic concept will now be
explained referring to the introduction of Welch and Bishop [26].
The goal of using a Kalman filter is to estimate the state
of a discrete-time controlled process
governed by the linear difference equation (4) with a measurement
that has the form of
equation (5).
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(4)
(5)
The matrix
relates the state
( at time step ) to the state
( at time step
), the
matrix relates the control input
to the state
and the matrix
relates the state to
the measurement . The variables
and
are random variables and represent the noise in the
process and in the measurement, respectively.
The Kalman filter algorithm is working in two alternating steps, the time update step (predictor
equations) and the measurement update step (corrector equations). In the time update step the
filter estimates the process state a priori at a specific time and in the measurement update step the
filter obtains feedback from the measurement to obtain an improved a posteriori estimation. This
process with the associated equations is illustrated in Fig. 8. Here ̂ and
denote the a posteriori
state estimation and the a posteriori estimation error covariance, while ̂ and
denote the
corresponding a priori estimations. The matrix
is the so called Kalman gain factor that minimizes
the a posteriori error covariance, the matrix
denotes the measurement error covariance and the
matrix
represents the process noise similar to the variable
. In the time update step the
equations project the state and covariance estimations from time step to step
. In the
measurement update step first the Kalman gain
is calculated, then the a posteriori state estimate
is generated by incorporating the measurement
and finally the a posteriori error covariance
estimate is computed.
Fig. 8: Complete picture of the operation of the Kalman filter [26].
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This Kalman filter is working for a linear measurement-to-process-relationship but in many cases
(e.g. for SOC estimation) the relationships are nonlinear and so the so called extended Kalman filter
(EKF) is necessary. Here the process is governed by the equation (6) with the measurement in the
form of equation (7) where and are nonlinear functions. The EFK works similarly to the Kalman
filter by linearizing the nonlinear functions around the current estimate using the partial derivatives
of the functions [26].
(6)
(7)
There are some other variations of Kalman filters which will not be explained here, e.g. the
Unscented Kalman filter (UKF) or the robust extended Kalman filter (REKF).
In [27], [28] and [29], Gregory L. Plett investigated the use of Kalman filters for battery management
systems and examined five algorithms using EKF, namely the combined model, the simple model
(Rint model), the zero-state hysteresis model, the one-state hysteresis model and the enhanced selfcorrecting model.
In [30] and [31] different battery equivalent circuits are investigated using a REKF and an EKF,
respectively. Some other examples for implementations of Kalman filters for SOC estimation can be
found in [32] (EKF for electric vehicle battery SOC estimation), in [33] (EKF based on an
electrochemical model), in [34] (UKF based on an enhanced battery model) and in [35] (UKF based
on the “Partnership for a New Generation of Vehicles” equivalent battery model).
2.1.10 Hybrid methods
To benefit from the advantages of each SOC estimation method and thereby optimize the
estimations, hybrid methods are developed. Naturally, any combination of the methods mentioned
above is conceivable and in this section some examples for hybrid methods should be given.
In [17] an SOC estimation algorithm was implemented by combining Coulomb Counting and OCV
measurement.
Lee et al. developed a State-of-charge and capacity estimation method in [36], applying a dual EKF to
OCV measurements.
In [37] LiFePO4-based Li-ion secondary batteries are investigated using a battery model for OCV
estimation which included an impedance model, a hysteresis model and an OCV recovery model
part.
A SOC estimator based on Coulomb counting using an adaptive EKF is developed in [38]. In this
method the Kalman filter is applied to correct the initial value used in the Coulomb counting
method.
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Do et al. in [39] improved the impedance spectroscopy based parameter estimation in Li-ion
batteries for hybrid electric vehicles using an EKF.
Impedance spectroscopy measurement have been combined with fuzzy logic methods, for instance,
in [40] and [41] where the parameters for a fuzzy logic model are derived from electrochemical
impedance spectroscopy measurements for SOC (and also SOH) estimation.
In [42] SOC is estimated combining an ANN with an EKF. The ANN is first trained offline and then
used for finding a battery model which is necessary for the EKF to estimate the SOC.
Andre et al. developed a method of SOC (and SOH) estimation in [43] combining a dual Kalman filter,
consisting of a standard Kalman filter and a UKF, with a SVM. By joining minimum variance
estimation and machine learning in this way they claimed to get a robust and powerful real-time
SOC (and SOH) estimation method with an estimation error below 1%.
As mentioned above, this was just an exemplary extract of all the possible hybrid methods and the
purpose was to give an idea of possible combinations.
2.2 SOH estimation
There is no consistent definition of SOH in literature, but in principle SOH can be seen as a value
which represents the actual condition of a battery compared to its initial (ideal) condition. SOH can
be calculated from different parameters like internal resistance, capacity, impedance, power density,
self-discharge rate etc. The important factor which determines the SOC is ageing, influenced by
extreme temperatures (high and low), overcharge, overdischarge and high charge/discharge rate.
Basically the SOH estimation methods can be divided in two categories, namely the durability modelbased open-loop SOH estimation method and the battery model-based parameter identification
closed-loop SOH estimation method [4].
2.2.1 Durability model-based open-loop SOH estimation method
This method estimates directly the capacity and the internal resistance changes based on battery
durability models which include durability mechanism models and durability external characteristic
models. Durability mechanism models are models which describe the internal side reaction
mechanisms of batteries. They are used to estimate microscopic quantities of the battery like ion
concentration and solid-electrolyte interface (SEI) resistance for a deep understanding of these
mechanisms and, in this way, of the batteries ageing. However, the durability mechanism models are
not practical for application because the age mechanisms of batteries are complex and therefore
computations are large and parameters are hard to define accurately.
Durability external characteristic models use external characteristics of the battery like capacity loss
and internal resistance increase for SOH estimation. These parameters can easily be estimated and
therefore the durability external characteristic models are suitable for applications, although a big
number of measurements is necessary for an accurate SOH estimation.
Some examples for durability mechanism models can be found in [44] where a review of the
batteries ageing mechanisms and their consequences occurring during a battery life is given. An
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implementation of an advanced durability mechanism model is developed in [45] where a third
order, single particle, positive electrode model of Li-ion cells is realized using least square and
recursive parameter estimators. In [46] and [47] different approaches for battery lifetime prediction
using durability external characteristic models are presented and compared. An example for an
advanced durability external characteristic model can be found in [48] where a battery life
prediction error within 15% is reached using stress coupling analysis which considers many factors
like temperature, charge and discharge rate, charge and discharge cut-off voltage etc. Another
example can be found in [49] where Dubarry et al. developed a diagnostic and prognostic model
synthesizing processes like loss of active material, loss of lithium inventory and formation of parasitic
phases.
2.2.2
Battery model-based parameter identification closed-loop SOH estimation
method
The battery model-based parameters identification closed-loop method is not just focusing on SOH
changes caused by ageing, but it uses existing battery models such as the models mentioned in
Section 2.1 and estimates the battery model parameters like capacity or internal resistance using
Kalman filters, ANNs and other algorithms. From these parameters the SOH is derived.
For example, Plett in [29] estimates not only SOC, but also SOH using an EKF with the Rint model,
and, as already mentioned, SOH is also estimated in [41] and [43]. In [50] there is used a Kalman
filter too, combined with a linear fitting method for the parameters estimation. Other examples can
be found in [51] and [52] where Remmlinger et al. developed a battery internal resistance on-line
identification method based on special battery equivalent circuits. A model based on impedance
spectroscopy and recurrent neural networks is investigated in [53] where a real-time automated
system for monitoring SOH is developed, taking to account several important phenomena and
dependencies in Li-ion cells.
2.3 SOF estimation
The SOF of a battery is a battery state which cannot be defined universally because it depends on
the system for which the battery is used. In words the SOF can be defined as the capability of the
battery to perform a specific duty, which is relevant to the functionality of a system powered by the
battery [54]. Generally, SOF is a function of SOC, SOH and temperature, but the concrete
dependency has to be defined for each system separately.
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3 State of Technology
Commercially available battery management systems in principle focus on battery balancing,
protecting and charge control. The SOC estimation is mostly done by coulomb counting in
combination with voltage measurements. Some of the few exceptions therefrom are three battery
management systems designed by Texas Instruments which are based on a technology using
impedance measurements (“Impedance Track” technology) [55].
Further details about the working principles and the SOC estimation algorithms of the different
battery management systems are difficult to detect because, naturally, the companies are unwilling
to betray their whole knowledge. Therefore, the topological differences of commercially available
battery management systems will be described.
3.1 Topologies
Battery management systems can be installed in different ways, i.e. with different topologies. In this
section, following the explanations in [7], a classification of topologies according to functionality is
presented and some examples for applications of each topology in commercially available battery
management systems are given.
3.1.1 Centralized
A centralized battery management system (Fig. 9) consists of one module from which the wires go to
the individual cells. This topology is very compact, relatively cheap, and if repair is required, it is
comfortable to replace just one single module.
An example for a commercially available battery management system with this topology is the Flex
BMS48 from Convert the Future [56].
3.1.2 Modular
A modular battery management system (Fig. 10) consists of multiple, identical modules and each
module is connected with a certain number of cells in the same way as for the centralized topology.
Normally, one of the modules is chosen as the master module with the task, linked with each of the
other modules, to manage the whole pack and to communicate with the rest of the system. The
advantages of this topology are basically the same as the ones of the centralized topology.
Additionally, the wires are easier to handle for a big number of cells and expansions to larger packs
can simply be done by adding more modules. However, this topology is slightly more expensive than
the centralized one because more modules and more wires are needed and some of the inputs of
the modules may be remain unused for a better spatial arrangement of the packs.
An example for a modular battery management system is the solution of Reap Systems [57].
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Fig. 9: Centralized topology block diagram [7].
Fig. 10: Modular topology block diagram [7].
3.1.3 Master-slave
A master-slave battery management system (Fig. 11) has a similar topology to the modular system.
Multiple identical modules, the slaves, measure the voltage of a certain number of cells and the
master module handles communications with the system and computations. This topology has
almost the same advantages and disadvantages as the modular system, just the cost can be slightly
less because the slave modules are designed to only measure voltage.
An example for a master-slave battery management system is the BMS Master 9-M from REC [58].
3.1.4 Distributed
The distributed battery management system (Fig. 12) consists of a controller module and in many
cell boards, one for each battery cell. The cell boards are placed directly on the cells and contain all
the electronics, while the controller unit handles computations and communications. Therefore, the
distributed topology is significantly different from all the other topologies where the electronics are
separated from the cells. The distributed topology is more expensive than the other topologies
indeed, but the measurements are also more accurate because of the direct connections between
cells and measuring electronics.
An example for a distributed battery management system is the Lithiumate Pro from Elithion [59].
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Fig. 11: Master-slave topology block diagram [7].
Fig. 12: Distributed topology block diagram [7].
3.1.5 Topology comparison
In Fig. 13 a comparison of the mentioned topologies is shown.
The distributed topology seems to be the most suitable one, but also the master-slave topology is
interesting for application, especially from a pricing perspective. Therefore, most of the
commercially available battery management systems are implemented using one of these two
topologies.
A very detailed list and a comparison off almost all battery management systems available on the
market can be found in [60].
Fig. 13: Comparison of battery management system topologies [7].
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4 Further applications of impedance spectroscopy
The impedance spectroscopy method is not only suitable for battery states estimation, but it can be
used for many investigations in different subjects because of its ability to characterize the frequencydependent electrical behavior of a system. Some examples for the fields of application of the
impedance spectroscopy method will be described in this section focusing on three subjects, namely
food industry, biomedicine and building industry.
4.1 Impedance spectroscopy in food industry
In food industry, impedance spectroscopy can be used to assess the physiological condition and the
quality of different foods like meat, fish or fruit.
This has, for instance, been done in [61], where the electrical impedance of kiwifruit was studied
during fruit ripening. Impedance spectra of the whole fruit, the outer pericarp, the inner pericarp
and the core of the fruit were recorded using alternating current at frequencies between 50 Hz and
1 MHz. The measured spectra were interpreted with a kiwifruit cell model (Fig. 14) which consists of
resistances of apoplast, cytoplasm and vacuole and in the capacitances of the plasma membrane and
of tonoplast.
Fig. 14: Circuit diagram used to interpret kiwifruit impedance spectra [61].
The measurements showed that the resistances of the outer pericarp, the inner pericarp and the
core were significantly different because of the differences in firmness and volume of the respective
extracellular fluid and in the sugar and ionic content of the cells. However, there was surprisingly
little change in the impedance characteristics of the fruit during the ripening process. This was
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unexpected since previous investigations on other fruit observed decreasing impedance during fruit
ripening. The proposed explanation therefor is that the mobility of electrolytes within the cell walls
of the kiwifruit did not change during ripening because of the formation of a gel which immobilized
the electrolytes.
Another example of an application of impedance spectroscopy in food industry can be found in [62].
Here, a low-cost non-destructive system for measurement of salt levels in food products such as
cured ham or pork loin is developed. The system consists of a PC application for evaluation, of an
electronic equipment for the implementation of impedance spectroscopy and of a concentric needle
electrode (Fig. 15) that is introduced into the food sample.
Fig. 15: Coaxial needle electrode [62].
In order to calibrate the system, solutions with different NaCl concentrations were measured and
statistically processed. The results show a good correlation between predicted and observed NaCl
concentrations. The measurement system was also tested on meat samples and showed reliable
results as well.
Some other investigations of foods by impedance spectroscopy have been done by Fuentes et al. in
[63] and [64].
In [63] the effect of temperature on potato microstructure and texture is investigated and a
correlation between temperature of the heat treatments and impedance has been observed and
explained by rupture and leakage processes taking place in potato microstructure.
In [64] a rapid, low cost and easy-to-use system for distinguishing fresh and frozen-thawed sea
bream was studied. Systems with different electrodes were investigated and compared. The results
show that impedance spectroscopy is able to assess damages in fish structure and other changes on
sea bream caused by freezing-thawing processes, but they show also that the choice of the type of
electrode is crucial for a working system.
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4.2 Impedance spectroscopy in biomedicine
The ability of impedance spectroscopy to provide information about changes and processes in
different types of tissues makes this method also suitable for biological, medical and biomedical
areas. Some exemplary applications of impedance spectroscopy in this field will be described in this
section.
In [65] Clemente et al. used the electrochemical impedance spectroscopy (EIS) method to investigate
muscular tissue in different physiological conditions. Muscles change their characteristics when they
perform physiological functions and the changes in the electrical properties of muscular tissue are
analysed using EIS. The goal of this research was to characterize different muscular conditions, i.e.
rest, contraction and four minutes after contraction with preferably one simple value. In order to do
this, the area under the Nyquist plot is proposed to be an index for the impedance changes due to
different muscle tissue conditions. It is claimed that the EIS has potential in this field of application,
although further research is needed for getting a reliable method for muscle tissue investigation
based on EIS.
The electrical impedance of muscles during isometric contraction was already observed by Shiffman
et al. in [66] using the dynamic electrical impedance myography technique. They did non-invasive
impedance measurements on the anterior forearms of six healthy men and woman with ages from
19 to 70 years. The impedance war measured at a frequency of 50 Hz during voluntary isomeric
contraction of the finger flexor muscles with a defined force (Fig. 16). The results showed that the
resistance and reactance increased under this contraction of the finger flexor muscles and that the
relationship between impedance and force is nonlinear, depending on the type of test, the history of
prior exercises and the health status of the acting person.
Fig. 16: Illustration of the physical arrangement and of the data acquisition system [66]
Page 21 of 32
Moreover, it was shown that the changes of the impedance reflect primarily the physiological
changes in the muscle and not the morphological ones. For example, the impedance changes many
milliseconds before the muscles are contracting and the impedance does not return to its original
value after the relaxation of the muscle either.
A comparison of their results with a preliminary study of patients with various neuromuscular
diseases showed quantitative and qualitative differences in the impedance measurements which
could be suitable for future medical applications [66].
Another medical examination method based on impedance measurements, called impedance
tomography, is developed in [67]. This system is able to take images of the electrical impedance of
the human thorax with a frame rate of 80 frames per second in the frequency range of 12.5 kHz to
800 kHz. The experiments showed that meaningful illustrations of the impedance distribution can be
reconstructed by this system.
Compared to other imaging methods like magnetic resonance tomography or ultrasound imaging,
impedance tomography has relatively low spatial resolution. However, the human thorax is a
conductive body with irregular boundaries and therefore the high spatial resolution is not absolutely
essential. The main advantage of impedance tomography compared to other methods is the high
time resolution. It has been shown that meaningful images can be obtained for illustrations of
activities of lung and heart. It is for example possible to monitor an accumulation of fluids in the lung
and to localize it constantly or to determine the volume of a heart. Furthermore, since small currents
in the mentioned frequency range are used, there is no risk to the patient, which makes this method
suitable for medical applications [67].
An example for a more biological application of impedance spectroscopy can be found in [68]. Here,
redox enzyme kinetics are investigated using three mathematical models which describe the
mechanisms of a bio-enzymatic process. As a model system an enzyme horseradish peroxidase
adsorbed on graphite electrode was chosen and the mathematical models were based on
generalized mechanisms of horseradish peroxidase catalysed hydrogen peroxide reduction. Based
on these mathematical models, the theoretical electrochemical impedances are derived and
mechanistic details of the bio-electrochemical reactions including all relevant kinetic parameters
were obtained.
In order to discriminate the quality of the mathematical models and to find that one which describes
the enzyme kinetics best, EIS measurements are performed to compare the theoretically calculated
impedances to the measured data. In doing so, it was possible to ascertain that model of the three
which described the mechanisms of the bio-enzymatic processes in the best way [68].
These are just a few examples for application of impedance spectroscopy in biomedicine so as to
give an idea of the different fields of IS applications. A very detailed overview of biomedical IS
applications containing many examples and explaining their principles can be found in [69].
Page 22 of 32
4.3 Impedance spectroscopy in building industry
Most methods which are applied in civil engineering research for testing building materials are of a
destructive character and can therefore be applied to a particular material only once. Nondestructive testing methods like the impedance spectroscopy do not have this limitation and are
therefore suitable for investigations of building materials [70]. In this section some examples for
applications of impedance spectroscopy are given.
An attempt of investigating building materials by EIS is presented in [71]. Here, an equivalent circuit
model for EIS of concrete has been proposed (Fig. 17). This model takes into account the resistance
of the continuously connected micro-pores in the concrete (
), the resistance of the
discontinuously connected micro-pores blocked by cement paste layers in the concrete (
), the
capacitance across the concrete matrix (
) and the capacitance of the cement paste layers
blocking the discontinuously connected micro-pores in the concrete (
).
Fig. 17: Equivalent circuit model of concrete [71].
In this paper it has been shown that the proposed model is able to explain the experimental
phenomena observed in previous researches, i.e. the influences of hydration time, silica fume,
water/cement ratio etc. on the impedance spectra.
Also the hardening process of cement paste can be studied by impedance spectroscopy, for example
done in [72] where Andrade et al. measured the impedance of hardening cement paste with
different water/cement ratios in the range of 10 kHz to 15 MHz. In order to avoid the influence of
sample-electrode interfacial phenomena a non-contact air gap technique was introduced. As a result
of the measurements they were able to differentiate between the solid phase contribution and
contribution of the electrolyte inside the paste pores which are both governing the dielectric
properties of the hardened cement. Moreover, they found a linear dependence between the high
frequency dielectric constant and the cement paste porosity.
A similar study can be found in [73] where hardened Portland cement paste is investigated using a
non-contact air gap technique for the impedance measurements. For interpretation of the
impedance spectroscopy results, an equivalent circuit model is proposed which allowed determining
two time constants, one attributed to the solid cement matrix and the other one to the liquid phase
filling the pores of the cement paste.
In [74] the hydration on concrete is investigated by means of impedance spectroscopy. The
measurements allowed to track the changes in the spectrum during concrete hydration and to
Page 23 of 32
characterize the concrete hydration process stages. As a consequence it was possible to analyse
concrete aging in various environment.
Another application of impedance spectroscopy for investigating cement paste is presented in [75].
Here, Tang et al. analyse the pore structure in Portland cement paste. The pore structure of cementbased materials is crucial for its strength, permeability and durability. Since the pores can be seen as
passages of ions transportation it is possible to relate the impedance response of the cement to the
pore size.
The characterisation of the pore size in [75] is based on the pore fractal theory which includes a
combination of two networks, namely a fractal electrical network and a pore structure network (a
further explanation of the theory is given in the paper and would go beyond the scope of this text).
The obtained results permitted to detect the pore size domain from µm to mm scale.
In [76] an impedance measurement method is presented which is able to monitor changes of
humidity and salt affliction in building materials. The measurements are performed using a twoelectrode design which, compared to a four-electrode design, has the advantage that there are less
boreholes necessary. This is, for instance, very important for measurements on historical buildings.
Since the electrical conductivity in this kind of objects is mainly caused by the electrolytes in the
pores of the building and since the amount of dissolved salt is dependent on the humidity of the
material, the impedance is determined by salt concentration and humidity. Thus, information about
the salt concentration and the evolution of moisture inside the building has been obtained.
Moreover, it was possible to detect transport routes and fonts of the electrolytes by spatially
distributing many sensors.
A very detailed investigation of the impedance behavior of salt affected building materials can be
found in [77] where an experiment series with different types of salt and different salt
concentrations has been performed in order to develop a system which permits to determine the
salt concentration in building materials quantitatively.
A further application of impedance measurements in building industry is the detection of corrosion
of steel in building materials which is most of the times caused by the reaction of chloride, present in
the environment, with a passive layer formed on the surface of the steel.
An example for an analysis of the chloride diffusion in steel reinforced concrete can be found in [78]
where Sánchez et al. developed a tool to determine the chloride diffusion coefficient of the concrete
using impedance spectroscopy. This coefficient describes the velocity of ingress of chloride into the
material, and thus its physical condition.
The technique developed in [78] was able to determine the chloride saturation of concrete or
mortar samples using equivalent circuits for the interpretation of the impedance measurements. The
pores of the material which are initially filled with water cause a high resistivity and the resistivity
decreases while the chloride is diffusing from the environment into the material (Fig. 18). By
measuring this diminution in real time it was possible to calculate the diffusion coefficient of the
material. In addition to these results, the impedance measurements allowed also to study the
modifications in the microstructure of cementitious materials caused by the applied electric field
during the measurements for the determination of the diffusion coefficients.
Page 24 of 32
Fig. 18: Evolution of the resistance during the migration test for a mortar sample after 28 days hardening [78].
Also Ye et al. analysed the chloride-induced corrosion of steel by impedance measurements in [79].
They studied the behavior of reinforcement steel in simulated carbon concrete pore solution
containing different concentrations of chloride using EIS and linear polarisation resistance
measurements. The results showed that EIS is a suitable method for monitoring the chloride induced
corrosion process and also a value for the chloride concentration of the simulated carbon concrete
pore solution (0.01 mol/L) could be detected which is critical for corrosion initiation. The topology of
the reinforcement steel surface has been observed with a scanning electron microscope (Fig. 19).
The pictures visually show the corrosion of the steel at different chloride concentrations.
Fig. 19: Images of reinforcement steel after 4h immersing in solutions with different chloride concentrations [79].
Page 25 of 32
In [80] the corrosion of stainless steel is investigated by EIS. Different types of stainless steel have
been analysed and as a result it is shown that the use of stainless steel rebars for concrete
reinforcement is advantageous because it is much more resistant to chloride-induced corrosion.
However, negative performance of building materials is not just caused by chloride-induced
corrosion but also by carbonation processes, and these processes can be analysed using impedance
spectroscopy as well. An example therefor can be found in [81]. Here, Dong et al. studied the
carbonation behavior of cementitious materials using EIS in combination with an electrochemical
model (Fig. 20) which is based on the so called solid/liquid double-phase model described in the
paper.
Fig. 20: Equivalent circuit model for the performed carbonation study; R stands for resistance, W for Warburg resistance
and Z for impedance [81].
Using this model the impedance measurements were in good agreement with the results of the
model analysis. The fitting parameter R_ct1 turned out to be characteristic for the carbonation
behavior of the cementitious materials, and in consequence it was possible to predict the
carbonation time and the carbonation depth effectively.
In conclusion, a German institute should be mentioned which already uses impedance
measurements for damage assessment on real buildings: the “Federal Institute for Materials
Research and Testing”. The division 8.2 of this institute is specialized on non-destructive damage
assessment and environmental measurement methods and its prime topic is to promote, to improve
and to enhance practical applications of non-destructive testing methods in civil engineering,
amongst others, methods based on impedance spectroscopy [82]. Further information including
some posters and a list of publications can be found on their website under [82].
Page 26 of 32
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