An in-depth study of the electrical characterization of supercapacitors for recent trends in energy storage system

Journal of Energy Storage 57 (2023) 106198
2352-152X/© 2022 Elsevier Ltd. All rights reserved.
Review Article
An in-depth study of the electrical characterization of supercapacitors for
recent trends in energy storage system
Sambit Satpathy a,*
, Neeraj Kumar Misra b
, Dhirendra kumar Shukla c
, Vishal Goyal d
,
Bidyut K. Bhattacharyya e
, Chandra Shekhar Yadav f
a
GLA University, Mathura
b
Vellore Institute of Technology (VIT) - AP University, Amaravati, Andhra Pradesh, India
c
Galgotias University, Greater Noida, UP, India
d
GLA University, UP, India
e
Georgia Tech, 3D packaging lab, GA, Atlanta, USA
f
NIET, Greater Noida, UP, India
A R T I C L E I N F O
Keywords:
Supercapacitor
Energy storage system
Drude model
Intelligent modelling
Engineering applications
A B S T R A C T
The Energy Storage System (ESS) is geared toward sophisticated systems with increased operating time for a
variety of real-time applications such as an electric vehicle, a WSN (Wireless Sensor Network), a Capa bus, and so
on. Its primary focus is on supplying these kinds of systems with additional capacity in recent development, and
this will continue to be its primary focus. Because of their exceptionally high specific power, rapid charging, and
low ESR (Effective Series Resistance), electric double-layer (EDLC) capacitors or supercapacitors are encouraged
for use because they can be integrated more easily with battery technology that can be used in electric vehicles
and other electronic devices. The supercapacitor calls for a precise and accurate characterization in order to
facilitate the development of improved applications and more effective energy storage devices and technologies.
In this article, we studied various supercapacitor electrode components, electrolytic solutions, analogous circuit
models, electrical energy storage properties, and some real-time supercapacitor applications in the automotive,
manufacturing, construction, and consumer electronics industries. In addition, we have discussed on hybrid
material that was just recently developed with the goal of enhancing the conductivity and effectiveness of
supercapacitors. Aside from this, we have discussed about the behaviour of supercapacitors in terms of how their
behaviour is dependent on current and voltage with detailed analysis.
1. Introduction
In a wide variety of different industrial applications, energy storage
devices are utilized either as a bulk energy storage or as a dispersed
transient energy buffer [1,2]. When selecting a method of energy stor
age, it is essential to consider energy density, power density, lifespan,
efficiency, and safety [3]. Rechargeable batteries, particularly lithium-
ion batteries, are currently the most popular option due to their high
energy density and reasonable cycle life [4]. However, they have limi
tations because of their low power density and high ESR (effective series
resistance), which could severely restrict their power-delivery capacity
when subjected to high current loads. These limitations could prevent
them from being used in certain applications. Furthermore, high
current-rate and transient loading conditions are known to shorten
battery life [5]. In order to make up for these deficiencies, redundant
architecture is frequently implemented for pulse and peak power
fulfilment. This, of course, results in an increase in the overall cost.
Supercapacitors which are also known as Electric Double-Layer Capac
itors (EDLCs), are being extensively researched and widely regarded as
promising energy storage systems, owing to their attractive character
istics such as high-power density and high recyclability [6,7]. Despite
having a low energy density, they have additional benefits such as low
internal resistance, a wide temperature range in which they can operate,
and high performance. Because of these benefits, they are particularly
well-suited for use in applications related to consumer electronics, either
on their own or in conjunction with other high-energy devices. [8].
In order to guarantee the effective operation of supercapacitor sys
tems in a manner that is also secure and dependable, it is necessary to
* Corresponding author.
E-mail address: sambitmails@gmail.com (S. Satpathy).
Contents lists available at ScienceDirect
Journal of Energy Storage
journal homepage: www.elsevier.com/locate/est
https://doi.org/10.1016/j.est.2022.106198
Received 22 June 2022; Received in revised form 27 October 2022; Accepted 19 November 2022

2
put in place a management system that is enabling [8]. The management
of cell equalization is considered to be one of its most important re
sponsibilities. Other duties include thermal or temperature manage
ment, management of power systems, visualization of safety, and other
tasks that are dependent on systems and control engineering. According
to Sharma et al. [9], precise and effective modelling is essential for the
creation of management systems, when it comes to concerns like elec
trical, thermal, and ageing. In addition to this, accurate state estimation
provides insights into the reduction of cell non-uniformity and the
enhancement of power control in supercapacitor systems. Over the
course of the past few years, a number of articles have been published
that discuss recent developments in supercapacitor modelling, state es
timates, and industrial applications. This article provides a compre
hensive discussion of recent supercapacitor studies that were found in
the previous body of work in the literature from the perspective of
control and management. The primary goal being to methodically
summarise the current state of the art in supercapacitor modelling,
electrical, chemical characteristics, and many industrial applications
from the point of view of power control [10].
The whole article is set out as follows: Section 1 is an introduction to
a supercapacitor, followed by Section 2, which discusses the energy
storage mechanism. This section illustrated the three different energy
storage mechanisms such as double-layer, pseudocapacitance, and
faradic behaviour with their pictorial representation. Section 3 reviews
the symmetric, asymmetric, and hybrid electrodes of the supercapacitor,
as well as comparing different energy storage elements using a Ragone
plot to determine power density and energy density. The electrolyte is a
critical parameter in a supercapacitor, as defined in Section 4. We
looked at organic electrolytes, aqueous electrolytes, and ionic liquids in
this module. This article concentrates primarily on the electrical
behaviour and properties of supercapacitors throughout its entirety. As a
consequence of this, Section 5 provides a concise summary of the
supercapacitor's electrical efficiency, covering topics such as voltage-
dependent capacitance, self-discharging, ohmic phenomena, and high-
frequency behaviour. Furthermore, we experimentally discovered the
current-dependent behaviour of the parallel-leakage resistance, which
led to the development of a gamma function-based supercapacitor
charging methodology. In addition to that, a new method that is both
less complicated and more accurate has been derived for determining
the voltage-dependent capacitance value. Monitoring the utilisation of
the supercapacitor in real time is mention in Section 6. The use of
supercapacitors in consumer electronics, mobile systems, and various
transportation sectors has been discussed here (specifically in regener
ative breaking). The modelling of the supercapacitor is one of its most
important components; as a result of the modelling, it is possible to
develop new characteristics. We have concentrated on four distinct
modelling approaches for a supercapacitor by taking into consideration
this point in the Section 7. These approaches are the electrochemical
model, the fractional-order model, the intelligent model, and the
equivalent model.
1.1. Innovation and novelty
As a review paper the aim of the article is to discuss all the electrical
properties, applications of supercapacitor to make it more popular in the
field of green/renewable energy. Additionally, we have added a new
characteristics of supercapacitor such as the current dependent behav
iour of parallel-leakage resistance of supercapacitor. Based on this
behaviour, this article shows how an accurate measurement of a
capacitor was made.
2. Energy storage mechanism
Fig. 1 depicts various aspects of a supercapacitor's electrical energy
storage system, including the energy storage structure, various elec
trodes, electrolytes, electrical performances, and applications [9]. The
concept of energy storage is the focus of this section. Supercapacitor
electrodes and electrolytes are provided by a large variety of materials to
determine the energy storage mechanisms in them. For understanding
and the efficient use of supercapacitors, awareness of these processes is
important. There are two major experimental studies to describe the
supercapacitor electrode, and they are convenient methods for under
standing the various mechanism of energy storage. Out of these two
methods, one is cyclic voltammetry (see Fig. 2(a, b)), and another one is
galvanostatic discharge, as seen in Fig. 2(c) and (d) [10]. In the cyclic
voltammetry method, we need to measured current vs. applied voltage,
which getting from the cyclic voltammogram trace. The galvanostatic
discharge, on the other hand, consists of a constant current discharge of
the electrode. The three basic behaviour (Pseudocapacitance, double-
layer, and faradic) explain below which are demonstrated by super
capacitor electrodes. Their electrical characteristics are compared and
contrasted based on cyclical voltammetry and galvanostatic discharge
methods.
Energy Storage
System(ESS):
Supercapacitor
Energy storage
mechanism
Double layer behaviour
Pseudocapacitive behaviour
Faradic behaviour
Supercapacitor based on
their electrodes
Symmetric
Asymmetric
Hybrid
Supercapacitor based on their electrolytes
Electrical performance
Voltage dependent capacitance
Charge distribution with electrode
Self discharging
Ohmic phenomena
High frequency behaviour
Engineering Applications Transport sector
Energy sector
Industrial sector
Consumer electronics
Fig. 1. Different elements of electrical energy storage system of supercapacitor [9].
S. Satpathy et al.

3
2.1. Pseudocapacitance behaviour
Pseudocapacitive electrodes exhibit a capacitor-like behaviour as
their cyclic voltammogram is similar to their double-layer rectangular
form (see Fig. 2(a)) and also have a linear galvanostatic discharge,
which can observe from Fig. 2(c). Pseudocapacitive electrodes can give a
considerably greater specific-capacitance compared to double-layered
electrodes; this makes them promising for applications that needed a
high energy density (see Fig. 3). Still, they suffer two major problems, i.
e., lesser cyclability and lower power-density that are associated with
the electrochemical reactions. This electrochemical reaction involves
irreversibility and allows the electrode to age more rapidly as the dy
namics of the reaction decrease its strength. The development of pseu
docapacitive electrodes is a result of RuO2's peculiar electrochemical
behaviour [11]. Several cheap metal oxides have also been tested for
pseudocapacitors as possible electroactive materials [12–13]. The
metal-oxide materials and hydroxides are of considerable importance
because of their abundance, a high value of specific capacitance, and
low toxicity materials currently being studied. Metal carbides [14–15]
and conducting polymers are inherently shown pseudocapacitive
behaviour, in comparison to the metal oxides. Compared to inorganic
materials, the major downside of conductor polymers is that although all
of them have zero volumes for ions to cross, the conductive polymers
that do not have an adequate amount of space to carry their ions and the
intercalation creates extreme changes in the thickness of the electrode.
One of the pioneering conduction materials is Polyaniline (PANI). Due to
the progress made in technology, integrating PANI with other electro
active materials to improve the electrochemical efficiency of the
supercapacitor, this material has been paying more attention in the past
few years [16–17]. The plurality of available supercapacitor electrodes
must be taken into account, as the existence of functional groups
contributing to a pseudocapacitive secondary response [18], which is a
marginal part of the pseudocapacitive category.
2.2. Double-layer behaviour
The aggregation of two charges at the electrode-electrolyte interface
makes up the double-layer mechanism, which is the primary storage
mechanism for electrodes that are composed of carbon powders or
Fig. 2. Electrochemical characteristics of capacitor materials (a) the reaction to a linear change in the voltage with constant current in cyclic voltagrams, (b) Faradaic
redox peaks can be seen in capacitors, (c) Galvanostatic discharging behaviour, (d) The example, how a bulk material shows the voltage plateau [10–11].
(a)
(b)
(c)
(d)
Fig. 3. The numerous mechanisms for the capacitive energy storage are shown:
(a) Carbon particles, (b) Porous carbon, (c) Redox pseudocapacitance, (d)
intercalation Pseudocapacitance [11].
S. Satpathy et al.

4
fibres. On the one hand, an excessive number of electrons or an insuf
ficient number of electrons in the electrode, specifically on or close to
the interface region. In the meantime, counterbalance of charge density
on the solution side of the two layers at the electrode interfaces of cat
ions or anions accumulated by the electrolyte [12] and provided that the
surface density of these charges, electrostatically deposited at the elec
trode interfaces, that depending on the voltage applied to the electrodes
[13] cations or anions accumulated by the electrolyte. Thus, rectangular
cyclic voltammograms, as seen in Fig. 2(a), describe double-layer
capacitance with a constant current response to a linear voltage shift.
In addition, for this kind of material, the galvanostatic discharge is linear
(see Fig. 2(c)) [19]. The double-layer effect is carried out at each
interface, which is a common scenario in most electrochemical energy
storage systems between electronic and ionic conduction materials.
However, it is a parasite in devices such as electrolyzes, fuel cells, and
batteries [20–21] rather than the main energy Storage Mechanism.
Conversely, this property is based on the supercapacitor operating the
ory, and its electrodes are built to optimize this effect.
2.3. Faradic behaviour
The storage mechanism serves as the foundation for the redox re
actions that take place between metal ions within the crystalline struc
ture of the electrode. In most cases, metal cations will be intercalated
and then deintercalated; however, in order for this process to be suc
cessful, redox reactions involving electrode materials are required. This
mechanism also involves phase transformation along with alloying re
actions for charge passage, and it is this behaviour that is described as
being pseudocapacitive. The voltage of the electrodes is typically
determined by the structure and concentration of the solution as well.
Therefore, these materials display a galvanostatic discharge voltage
plateau (see Fig. 2(d)) and a faradaic redox peak in CV (cyclic voltam
mograms) in Fig. 2(b). In Faradaic electrodes, the power (capacity)
obtained is many times greater (10 to 100 times) than in capacitive
electrodes. Unfortunately, in several papers, many battery-like elec
trodes like Ni (OH)2 or other material with a faradic behaviour were
treated as pseudocapacitive materials, which lead to readers' confusion
[22]. Though battery materials are electrochemically reversible, their
redox properties are far worse than pseudocapacitors materials, and ion
diffusion within the crystalline structure limits their charging and
release strength. It must be remembered that pseudocapacitive or
battery-like behaviour can be accomplished by the same electroactive
material. This problem is due to the different lattice structures, config
urations, and nano-architectures that can be accomplished during the
manufacturing phase in the electroactive material [23].
3. Supercapacitor based on their electrode
The application of supercapacitor is going to be the most useful for a
given device. A classification of supercapacitors, which highlights their
individual properties, is yet another helpful tool that can be used to
select the appropriate supercapacitors for each application [24]. This
electrode classification is the most common method for supercapacitors
and for defining their benefits and drawbacks, as well as for tackling
important parameters and characteristics to make the appropriate
supercapacitor selection. In addition, this classification is the most
widely used method for supercapacitors. The supercapacitor can be
divided into three major classes, which are hybrid, asymmetric, sym
metric, as detailed below. Table 1 summarizes the usual characteristics
and pictorial representation (see Fig. 4) of any form of the super
capacitor. In Fig. 4 has shown the comparison between different energy
storage elements in terms of energy density and power density.
3.1. Symmetric supercapacitors
The double-layer material is used for both of the electrodes at the
same time. These are the supercapacitors that have seen the most
widespread application and have the highest level of sophistication
among their electrodes [25]. In these supercapacitors, researchers aim
to take advantage of nanotube carbon [26], aerogels carbon [27], and
graphene. Its energy density, roughly 5 Wh/kg, is comparatively low,
and power density is as high as 9 kW/kg [28]. Symmetric super
capacitors are the perfect alternative for different applications, where
protection, low maintenance, and long service life are important, and
the high-power density is also appropriate without affecting the low
energy density.
3.2. Asymmetric supercapacitors
Supercapacitors, which have electrodes made of two distinct
capacitor materials and are able to achieve high power and energy
densities, are the type of capacitors that use this term [24]. The energy
density of a MnO2 Graphene and Graphene asymmetric supercapacitor
was reported to be 30.4 Wh/kg, while the power density of the device
was 5 kW/kg. These supercapacitors are still relatively costly and may
be affected by reduced efficiency and rated voltage due to the need for
watery electrolytes [25] and short service life (79 % of performance
retention after 1000 cycles is reported in [29]). Asymmetrical super
capacitors can also be sufficient for applications with mandatory energy
and power density balance and costs, not a big concern.
3.3. Hybrid supercapacitors
This particular variety of supercapacitor has an energy density that is
higher than 100 W/kg and consists of a capacitor-like electrode in
addition to a faradaic electrode. Additionally, it has a high specific
power [30]. The power density of approximately 4.5 kW/kg (See
Table 1), by comparison, is smaller than that obtained with a symmet
rical supercapacitor [29]. It is less advanced in its development than
symmetric and asymmetric supercapacitors. While hybrid super
capacitors are now freely available on the market [31], and from the
research point of view, numerous articles on new materials and devel
opment processes have been published [32]. The literature [33] shows
the power density and energy density characteristics of the hybrid
supercapacitors. This paper provides only content values (the weight of
the electrodes and electrolyte is taken into account). Additionally, it
records 257 Wh/kg and 867 W/kg (material level), with retention of the
output of 79.2 % after 15,000 cycles.
3.4. Hybrid AI materials supercapacitors (electrode)
EDLCs, also known as electric double-layer capacitors, Due to their
Table 1
Key features of various types of supercapacitor based on their electrodes [10].
Various parameters Hybrid Asymmetric Symmetric
Electrodes Carbon,
Intercalation
materials
Metal oxide, carbon,
conducting
polymers
Carbon
materials
Electrolytes Organic Aqueous Organic
Energy density
(Wh/kg)
100 30 5
Power density
(kW/kg)
4 5 9
Operating
Temperature
(Degree C)
− 40/60 − 25/60 − 40/60
Energy Storage
mechanism
Double-layer and
faradic
Double-layer and
Pseudo capacitance
Double-layer
Advantage Higher energy
density
Trade-off energy and
power
Higher power
density
Disadvantage Lower power
density
Higher price, less
efficiency and
lifetime
Lower energy
density
S. Satpathy et al.

5
enormous energy storage capacity, extended maintenance-free life,
excellent cycling efficiency, and high power density, supercapacitors
have received a lot of interest (Stoller and Ruoff [48]; Berrueta et al.
[10]; Song et al. [22]). Double-layer capacitors are crucial components
of goods like batteries and electric cars. In the meantime, their low en
ergy density prevents them from being widely used; one approach is to
use machine learning to speed the creation of novel capacitor materials.
According to Zhang et al. [1], carbon-based materials are frequently
used as double-layer capacitor electrodes because of their high specific
surface area, high porosity, high electrical conductivity, low cost,
simplicity of production, and environmental friendliness.
4. Supercapacitor based on their electrolytes
Different forms of electrolytes are used in a supercapacitor, such as
organic, aqueous, ionic liquids. We have briefly discussed these elec
trolytes below.
4.1. Organic electrolytes
The fundamental part of these electrolytes is an organic solvent such
as acetonitrile (ACN) or propylene carbonate (PC). In the solvent dis
solved salt like Et4NBF4 is present, whose organic ions are relatively
wide. In order to contribute to energy storage, these ions should be able
to enter the electrode pores. Electrodes with micropores that can't host
organically produced electrolytes are also not suitable. The absence of
the micropores also increases the power output of the supercapacitor.
Their decomposition tension can be up to 2.2 to 3 V [35], which con
tributes to the device's both high-power density and energy density.
Because of their low viscosity, high conductivity, and electrochemical
stability, PC and ACN are the most frequently used organic solvents.
These solvents make it possible to produce high-energy supercapacitors,
which also provide high power and cyclic stability [36]. However, there
are some safety issues about the flammable and poisonous AN solvent
[37]. While there is a common use of organic electrolytes, research is
currently focused on the creation of modern, healthy solvents that have
higher energy densities [38]. There has already been presented a solvent
with a decomposition voltage of up to 4 V [39]. The trade-off of this rise
in the voltage window nevertheless is a major reduction of the super
capacitor's maximum power.
4.2. Aqueous electrolytes
These electrolytes are made up of very small molecules of acid that
are dissolved in water, such as H2SO4 for example. Because of the
minute size of these inorganic ions, it is preferable for micropores of the
electrodes (with a diameter of approximately 1 nm), which may contain
T‑carbons or carbide-derived carbohydrates, to be present. The aqueous
electrolytes have a lower decomposition voltage than organic electro
lytes. Since water dissociates at a voltage of 1.23 V from H2 and O2 a
maximum voltage of 0.6 V to 1.4 V [35], the stability for aqueous
electrolytes is restricted. The most prominent trends in research are to
increase their decomposition voltage by using an aqueous electrolyte
with high energy of solvation, which has already been reported to be up
to 2.2 V [40]. On the other hand, it is necessary to improve the cycle
stability of aqueous electrolytes and to use a protic ionic liquid as a
solvent for aqueous electrolytes [41].
4.3. Ionic liquid electrolytes
In the beginning, these compounds were thought of as an alternative
solvent for aqueous electrolytes; as a result, their applicability was
limited as a result. However, in modern times, they are thought of as an
alternative to solid electrolytes, particularly due to the fact that their
voltage window is significantly larger than that of organic electrolytes.
In light of this, it is an excellent electrolyte that helps to contribute to a
very high energy density [42]. It also has a less toxic portion than the
organic electrical electrolyte, increasing the optimum temperature at
[43] and lower volatility [44]. The present high price of ionic liquids is
not based on the material itself but on the cleaning costs required. A
better interpretation of these products as a supercapacitor electrolyte
could result in decreased cleanliness requirements, which means the
ionic liquid of the supercapacitor price will be reduced [42]. These
materials are still early in production, and a considerable research
initiative to enhance their characteristics is also being made. In this
regard, the first is the design and characterization of additives to
enhance the efficiency of such devices [45]; and secondly, to achieve
solvent-free (or solid State) supercapacitors providing exceptional ionic
transport properties [46].
)
g
k
/
W
(
y
t
i
s
n
e
D
r
e
w
o
P
Energy Density (W h/kg)
0.01 0.1 1 10 100 1000 10000
10000000
1000000
100000
10000
1000
100
10
1
l
a
n
o
i
t
n
e
v
n
o
C
Capacitor
Hybrid
supercapacitors
Organic asymmetric
supercapacitors
Aqueous asymmetric
supercapacitors
Pseudocapacitors
EDLC
Fuel
Cells
Batteries
Different type of
supercapacitors
Fig. 4. Ragone plot for multiple energy storage system, specifically different types of supercapacitors. [34].
S. Satpathy et al.

6
5. Electrical performance of supercapacitors
In this section, the electrical consequences that show the causes for
the most notable electrical phenomena are investigated, and their effects
on energy storage systems are analysed. According to the specific re
quirements of each application, one of the characteristics, which are
going to be defined in the following paragraphs, requires significantly
more consideration than the others.
5.1. Voltage-dependent capacitance
The ability of supercapacitors to have variable capacitance is one of
their most valuable properties. Although the output of the super
capacitor is not normally an issue because it does not involve a signifi
cant reduction in characteristics, it is still important to note. This is
something that must be taken into consideration whenever super
capacitors are utilized as a component of an energy supply. This is
because the voltage difference over the whole range is in between 15 %
and 20 % of the rated capacity [47], which cannot be ignored in most
designs. Capacitance calculates the charge stored (q) for a given amount
of voltage difference (V), and the mathematical relationship is given by:
C =
q
V
(1)
The variable capacitance of supercapacitors is one of the most
important features of these devices. Even though the output of the
supercapacitor is not normally a cause for concern because it does not
involve a significant reduction in characteristics. This is something that
must be taken into account whenever supercapacitors are incorporated
into a system that provides energy. This influence increases in the
density of charge storage, which means the capacitance of the super
capacitor rises in line with the voltage applied [48]. As the parameter C
depends on the voltage, (1) doesn't give the same advantages as in
traditional capacitors. That is why Cdiff is a favored parameter for the
analysis of supercapacitors. And Cdiff is defined as the ratio of the
increment in the stored charge, ‘dq’ to the voltage variance ‘dV’ induced,
which is shown by (2).
Cdiff =
dq
dV
=
idt
dV
(2)
Capacitance C and the change in the capacitance ‘Cdiff’ relate to the
same supercapacitor’s property. And both the value gives the relation
ship between the change in voltage to the charge storage. While C is the
defining parameter for traditional supercapacitors, where ‘Cdiff’ is also
used to characterize supercapacitors. The difference of ‘Cdiff and C′
based
on the change of C with the applied voltage, V. If we considered the
literature [49–50], they described the linear dependency between the
capacitance and the voltage with an assumption of (C = C1 + pV1) and
also from this a correspondence relation between C and Cdiff can be
found as given by
i =
dq
dt
=
d
(
CdiffV
)
dt
(3)
Now we have put the assumption that we considered to find out Cdiff
i =
d[(C1 + pV1)V ]
dt
= [C1 + 2pV1]
dV
dt
(4)
Using the relationship between Cdiff and the voltage in (4), therefore,
we have
Cdiff = C1 + 2pV = C + pV (5)
The temperature has the potential to have an effect not only on the
voltage dependence of the supercapacitor but also on its ability to store
charge. The primary benefit of supercapacitors is their superior perfor
mance even when subjected to high temperatures. However, the dif
ference in capacitance value that is produced by such significant
temperature variations may require special consideration during the
process of designing an energy storage system in the correct manner.
Since a rise in the temperature induces the development of the Brownian
motions of the double-layer ions, and a greater distance occurs in this
double layer in increasing temperature between positive and negative
charges. This leading to a decrease in capacitance [49]. In fact, there has
been a loss of capacitance of about 0.1 % per degree centigrade [47].
This implies an 8 % divergence in capacitance if a variance in temper
ature of 80 ◦
C. The temperature typically has a lower effect on the value
capacitance than voltage, but a device built for outdoor activity will
need care. Here also we have discussed some literature, which describes
and addresses the temperature-dependent capacitance behaviour for
supercapacitor. Due to the increased viscosity of the solution, the con
ductivity of electrolytes decreases at declining temperatures. Using this
interpretation, researchers demonstrated the changes in capacitance
with temperature change [50–51]. Using impedance spectroscopy, all
values were measured at 10 MHz. The electrical energy that is trans
ferred to heat during charging and discharging increases as the resis
tance of the capacitor increases. The rise of the resistance at low
temperatures also allows the capacitance to be decreased, as seen in
Fig. 5 [52–55].
5.2. New methodology of finding capacitance (voltage-dependent) of the
supercapacitor
Finding the capacitance of a supercapacitor with a high value such as
Nippon requires a method that is both complex and complicated (700F).
On the other hand, here we have determined the capacitance of the
supercapacitor through experimentation using the results of the self-
discharge. Therefore, in the beginning, we have to charge the super
capacitor with a variety of constant currents, such as 7, 8, or 10 amps,
and once the voltage reaches the saturation level (VSat), we have to let it
discharge naturally (i.e., self-discharge). Fig. 6, describe the equivalent
circuit model of charging of supercapacitor. Where RP denotes as the
leakage-parallel resistance, VSat corresponds to the saturation voltage
and ISat. define saturation current. The DLA Nippon supercapacitor starts
self-discharge after charging the constant current, shown in Fig. 7. This
figure also reported the discharging voltage as the function of time of the
supercapacitor. Fig. 7 also gives the VSat value for different constant
charging current (ISat) and the ration between VSat to ISat gives the initial
resistance (RP). We can draw the log plot of the ISat and RP that gives η
and λ values respectively, in the form of slope and coefficient. Also,
experimentally we have found the voltage-dependent behaviour of the
parallel-leakage resistance of the supercapacitor [3,51], which is given
by (6)
RP = λI− η
P (6)
The value of RP can be determined by using (6) with the known value
of η and λ. The relationship between VSat and RP also gives the average
0
50
100
150
200
250
300
-60 -40 -20 0 20 40 60 80
)
d
a
r
a
F
(
e
c
n
a
t
i
c
a
p
a
C
Temperature (℃)
50 mS/cm
22 mS/cm
12 mS/cm
Fig. 5. Capacitance of supercapacitor as the function of Temperature [50].
S. Satpathy et al.

7
current value, i.e. I. We need to measure, dVP
dt
in order to calculate
capacitance of the discharge voltage. That's also the slope of the dis
charging time vs. discharging voltage graph (see Fig. 7). And also, the
ratio between the average value of current to dVP
dt
gives the capacitance
value for the Nippon supercapacitor. All the above writeup, helpful to
find out the capacitance that shown by Fig. 9 through flow chart.
The capacitance values of the supercapacitors can now be deter
mined using the above flow chart (see Fig. 9). It is important to note that
both maximum and minimum capacitance values are present in each
case and that they depend primarily on the voltage on the two super
capacitor terminals. Approximately the capacitance value (700F) at
operating voltages anywhere between 2.5 V to 3.5 V is quoted from the
Nippon supercapacitor producer. They calculated the capacitance using
two data points from the voltage vs. time graph and the assumption that
the voltage declines linearly with time while the capacitor is discharged
continuously. When supercapacitors are drained with a constant cur
rent, it is known that the voltage does not drop linearly with time
[52–53]. This phenomenon created a lot of uncertainty among re
searchers and these are also studied under the fractional-order model
ling [54–55]. But the supercapacitor model in our study is clear and
similar to the model in Fig. 6, the only difference is the leak resistance
value, RP, which depends on the voltage between the supercapacitor
terminals. In the Fig. 10 and Fig. 8, It's the first time where; we explained
how to calculate the capacitance values for supercapacitors using just
the data for self-discharge, since all current passes through the leakage-
resistor. It is also shown that calculation was only feasible because the RP
leak intensity depends on voltage through terminals of the super
capacitor, and the Vsat, saturation voltage cannot be continuously raised
by pumping constant current. We have a strong believe, in near future
will bring lots of interesting physical understanding of various materials,
which are used for the formation of the electric double-layer capacitor
(EDLC) and may implemented various real-time application.
5.3. Self-discharging
One of the major drawbacks that prevents the use of supercapacitors
to store power for periods longer than 30 min is self-discharge. In fact,
the authors of [56] measure that 36 % of the energy lost during the first
two hours of the supercapacitor's storage was useable energy. A leakage
current through the ion-conducting membrane is the primary cause of
the self-discharging process in the supercapacitor. A linear decrease in
the supercapacitor voltage over a duration indicates the self-discharge
effect. One of the things that need to be strengthened is the super
capacitor's self-discharging properties, and a number of research papers
on this subject have been published [57–58]. The authors here analyze
the nature of self-discharge and ionic charge distribution in electrode
pores. The supercapacitor's charge redistribution is calculated within the
first minutes or hours of voltage stabilization as a nonlinear progression
of supercapacitor voltage over time. This method would not induce a
RP,sat C
Vsat
ISat
Isat
Icap=0
RS
Fig. 6. Charging the supercapacitor using constant current Isat and charge it
upto the saturation voltage Vsat.
1.9
2.1
2.3
2.5
2.7
2.9
3.1
3.3
3.5
3.7
0 500 1000 1500 2000 2500 3000 3500
Self-
f
o
)
v
(
e
g
a
t
l
o
v
g
n
i
g
r
a
h
c
s
i
d
t
n
e
r
e
f
f
i
d
h
t
i
w
r
o
t
i
c
a
p
a
c
r
e
p
u
s
t
n
e
r
r
u
c
g
n
i
g
r
a
h
c
t
n
a
t
s
n
o
c
Discharging time (Sec)
10 Amp current
8 Amp current
7 Amp current
Fig. 7. Self-discharging voltage of the supercapacitor after fully charged by constant charging current (10, 8, 7 Amp).
S. Satpathy et al.

8
discharge in the supercapacitor since the electrical charge is still present
in the supercapacitor even though the voltage is lower. And this happens
due to the double layer is built using more electrode surface area [59].
For two major factors, the authors rule out the self-discharge faradaic
reactions as the cause for the nonlinear change in voltage in super
capacitors. (i) The V vs. ln t does not have the characteristic linear
pattern of a faradaic reaction, and (ii) the voltage at which this trend is
measured is described below the electrolyte's decomposition voltage.
Some research work has also been reported in which supercapacitors'
efficiency is improved by reducing self-discharge and suggesting elec
trode coatings capable of reducing the leakage current [60]. The
disadvantage of this proposal is decreasing in the average capacitance
and energy storage density by 56 %. Based on the literature mentioned
above, we know that the supercapacitor's self-discharge property is a
major phenomenon. As a result, additional research and correct char
acterization are needed to give a new path in the field of energy storage.
Here, Nippon-DLA and Green-cap supercapacitors were taken into
consideration and charged using different constant current sources (4, 5,
7 amp). Allow the capacitor to spontaneously drain, or self-discharge,
when it has been fully charged (3.5 V is regarded).
In Fig. 11(a), we demonstrate the charging of Nippon Super
capacitors using a 650 mA constant current. The power source
(PSD3304, Science Company) supplied the above current (650 mA) at
3.478 V, and after it got charged fully at 3.478 V. We have discharged
the supercapacitor naturally, using its leakage resistance Rp. This
discharge is shown in Fig. 11(b). We also noted that the average DLA
Nippon supercapacitors have capacitance values at 60C is roughly about
700F at 2.5 V.
VC
VS
=
(
1 − e
(
− t
(RP+R)C
)
)
(7)
VC
VS
=
(
e
(
− t
RPC
)
)
(8)
VS = IPRP (9)
In Eqs. (7), (8), and (9), we demonstrate the charging and discharge
of the supercapacitors. The Nippon supercapacitor used a specific con
stant current (from 0.25 amp to 1.5 amp), and this current, charges the
supercapacitor up to a certain saturation voltage which is shown in the
Table 2. In column 1 of the Table 2 shows the maximum voltage that the
supercapacitor got charged at the corresponding constant current,
which is shown in column 2. When the supercapacitor got charged
completely, then the same current was still passing through the leakage
resistance that maintaining the voltage across the supercapacitor being
constant, as shown in column 1. The values of (RP + R) obtained are
shown in Table 2, column 3. For this experiment, the value of capaci
tance ‘C' is assumed to be 700F, and using normal self-discharge, we
have found the value of RP. From the below table, it is important to
mention the value of R is very small compared to the 300mΩ, i.e., range
of lithium-ion batteries [3,61]. The parallel-leakage resistance value
depends on the charging current of the supercapacitor. The RP value is
more significant when the current for this Nippon-DLA supercapacitor is
low.
y = -0.9055x + 1.0455
R² = 0.9997
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
1.5 1.7 1.9 2.1 2.3 2.5
ln
(R
P
,sat)
ln (Isat)
Fig. 8. log plot of saturation current vs. the values of the natural log of the
supercapacitor's leakage-parallel resistance.
Start
Getting VSat and ISat
from the self-
discharging data
Find R (initial) from VSat
and ISat, and find the η
and λ from the log plot
of ISat and R
Using the η and λ we
Generated the leakage
parallel resistance (RP) using
= ( )
Now find the average
current (I), which is ratio
between discharging
voltage (VP) to RP
Calulate the slope from the
discharging data (VP , t)
and calculate
Finally, calculate the
capacitance (C), ration
between I to
Stop
Fig. 9. New methodology of finding voltage dependent capacitance of the
supercapacitor (Nippon-DLA).
0
100
200
300
400
500
600
700
800
2.2 2.4 2.6 2.8
)
d
a
r
a
F
(
e
u
l
a
v
e
c
n
a
t
i
c
a
p
a
C
Discharging voltage (V)
8 Amp
7 Amp
6 Amp
Fig. 10. Voltage dependent capacitance of the Nippon supercapacitor with
different constant charging current.
S. Satpathy et al.

9
Fig. 12 displayed the value of the resistance RP as a function of the
overall current I (shown in Fig. 11) coming from the power supply, VCC.
The empirical relationship between resistance (RP) and current from the
power supply is provided by the following Eq. (10).
RP ≈ 12.041e− 1.1991
(10)
Using (10), the magnitude of a voltage drops over Rp can be deter
mined when the supercapacitor will be fully charged. If the capacitor is
fully charged, the current by RP is the same as the total current supplied
by the power supply with the voltage V. And the voltage drop through RP
can be calculated using the following Eq. (11) also can see Fig. 13.
VP = IP RP ≈ 12.041 IPexp( − 1.199I) (11)
The above mathematical equations conclude that If anyone needs to
power these supercapacitors up to a saturation voltage of 3.69 V, the
maximum current one can pump will be about up to 1.02 Amp. The
capacitor will not charge to 3.69 V above that current. The statement
like one can pump a large amount of current to charge the super
capacitors to a given value of voltage may not be accurate since the
value of RP reduces. Using this concept researcher made fast charging
algorithm [3], which can also be implemented in any low-power con
sumer electronics application.
VP = − 0.0008I6
+ 0.0277I5
− 0.363I4
+ 2.3231I3
− 7.2418I2
+ 8.8813I
(12)
5.4. Ohmic phenomena
During the supercapacitor charge and discharge process, electronic
and ionic load transportation takes place [62]. Firstly, among the elec
trons joule effect takes place and due to this, the kinetic energy inside
electrons is converted into heat energy. On the other hand, part of the
ion, kinetic energy, is converted into heat due to friction with the other
atoms in the dilution during the electrolyte ionic charge transport pro
cess. The quantity of charges transferred and the rate of current flow
both have an impact on the voltage required to overcome these two
dissipative processes. These two occurrences were both negatively
impacted by the temperature drop. The solid electrode's working tem
perature rising causes an increase in atomic vibration, which in turn
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
0 5000 10000
Discharging
voltage
of
supercapacitor
(V)
Discharging time of supercapacitor (Sec)
0
0.5
1
1.5
2
2.5
3
3.5
0 5000 10000
f
o
e
g
a
t
l
o
v
g
n
i
g
r
a
h
C
)
V
(
r
o
t
i
c
a
p
a
c
r
e
p
u
s
Charging time of supercapacitor (Sec)
(a) (b)
Fig. 11. (a) Supercapacitor is charged by constant current of 650 mA, (b). Natural discharge of the given supercapacitor once it is charged up to its saturation value
(i.e., self-discharge) [3].
Rp = 12.041e-1.199I
R² = 0.9827
0
1
2
3
4
5
6
7
8
0 1 2
)
m
h
O
(
e
c
n
a
t
s
i
s
e
R
l
e
l
l
a
r
a
P
Charging Current (Amp)
Fig. 12. Charging current of supercapacitor vs. Parallel-leakage resistance [6].
Vp = -0.0008I6 + 0.0277I5 - 0.3635I4 +
2.3231I3 - 7.2418I2 + 8.8813I
R² = 0.9819
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5 6 7 8
)
p
V
(
p
R
n
i
p
o
r
d
e
g
a
t
l
o
V
Charging current (Amp)
Fig. 13. Voltage drops in the leakage resistance at each value of the passing
current. [6].
0
500
1000
1500
2000
2500
3000
)
F
(
e
c
n
a
t
i
c
a
p
a
C
Frequency(Hz)
0.001 0.01 0.1 1 10 100 1000 10000
Fig. 14. Variation of capacitance with the frequency with a bias voltage of 2.5
V and 20-degree centigrade temperature [67].
S. Satpathy et al.

10
causes the temperature to rise due to the Joule effect. By reducing vis
cosity and increasing molecular mobility in liquid electrolytes, the
amount of wasted energy is decreased [63]. Some experiments have
shown that the weight of ionic charging transport in the supercapacitors
is greater than that of electric charges [64], and therefore a rise in
temperature results in lower ohmic phenomena.
5.5. High-frequency behaviour
Supercapacitors are typically used for short charging and discharging
periods provided their excellent efficiency in these applications. Tenth
of seconds to 10 min is dangerous for other energy storage devices, such
as batteries, whereas supercapacitors work well in these schedules.
However, in view of the fact that the charging and discharge processes
require the passage of ions through the electrolyte but they are not
capable of handling frequencies as high as those controlled by tradi
tional capacitors. The equivalent capacitance has reduced with
increasing frequency was analysed in many papers [65–66] and
concluded that the capacitance of the supercapacitor had the behaviour
seen in Fig. 14. There is a cut-off frequency (based on the supercapacitor
materials and the production process, but typically about 1 Hz) where
the capacitance of the system is dramatically decreased, and no capac
itive activity is calculated at higher frequencies. Therefore, the
supercapacitors cannot be used to process the harmonic components of
the electrical converter (several kHz). However, some specific applica
tions are there, where we needed the intermediate frequency to be
filtered, such as the harmonics generated by the diode rectifiers (hun
dreds of Hertz). In these applications also we can use a supercapacitor,
which is studies by several researchers [67], concluding that graphene
electrodes are needed to have a functional capacity at this frequency
range. As a consequence, the cut-off frequency indicated in Fig. 14. The
graphene supercapacitor is in the range of hundreds of Hertz.
6. Engineering applications
6.1. Consumer electronics applications
In the near future, supercapacitor modules can substitute or integrate
with these batteries for all newly developed consumer electronic (CE)
products, in particular those that run on dc voltage or electricity. Since
Electric Vehicle
Regenerative Brakes
Super-Capacitor
Bank
Battery
Electrical
Engine
(a) (b)
Fig. 15. (a) Various real-time applications of supercapacitor [68], 15 (b) Example, how a supercapacitor used in a hybrid vehicle.
Fig. 16. The prototype of a supercapacitor powered battery less buck con
verter [69].
Regulated Output
By the DC-DC
converter
Output of DC-DC
converter which
powered by
supercapacitor module
Supercapacitor
Module
Fig. 17. Supercapacitor used to power supply the hand-held mobile
phone [70].
S. Satpathy et al.

11
consumer electronics goods require constant dc voltage for operation. A
new DC-DC converter module that operates only on supercapacitors
without a battery has been developed. The designers of this concept [68]
create a dc-dc converter to supply the CE devices with the constant
voltage they require from supercapacitors, which corresponds to the
module's decreasing or falling voltage. For the first time, all devices
would be adequately controlled by the supercapacitors and produce a
steady voltage from the supercapacitors, even if the voltage decreases
with time. The supercapacitor's viability in this application demon
strates how it may open up new technical avenues for energy storage.
Although the series resistance is considerably smaller than that of the
batteries internally resistance, the supercapacitors charge even more
rapidly than the batteries [1,3]. Fig. 15(a) displays a variety of current
applications for supercapacitors, while Fig. 15(b) shows a hybrid vehicle
with a supercapacitor where a dc-dc converter and a battery is being
used.
Researchers have also shown a special analogue buck converter
circuit, that is operated exclusively by a supercapacitor [69]. This pro
totype has been designed so that batteries will be gradually modified to
future CE systems, as supercapacitors have been miniaturized. In this
topology, the circuit operated entirely by supercapacitors is seen in
Fig. 16, without any other energy source, which is the first step in the
path of battery-less consumer electronics systems. The authors [70–71]
Fig. 18. Charging of electric vehicles and the energy generated by the regenerative braking system [72].
• Intelligent
modules
• Fractional-
order
models
• Equivalent
circuit
modelling
• Electro-
chemical
modelling
Supercapacitor
modelling
method
Fig. 19. Different types of supercapacitor modelling method for its electrical
characterization.
Ri
RP
Rd Rl
CV Co
Ci Cd
Cl
R1 Rn
Rs
Cn
C1
C
RS RP
C
R1
C1
R1 Rn
C0 C2 Cn
(a) (b)
(c) (d)
Fig. 20. Equivalent circuit models of supercapacitor, (a) Conventional model, (b) RC branch, (c) Musolino et al. proposed model [82], (d) resistance-capacitance
networks [75].
S. Satpathy et al.

12
here develop an analogue circuit that is only powered by a super
capacitor without extra energy for low-power devices like cell phones. A
architecture for buck converters was shown in Fig. 16. This is initially
powered by two voltage sources with the same specifications. A positive
voltage is supplied by one, and a negative voltage by the other.
Regardless of changes or fluctuations in the input voltage, this design
generates an output voltage that is constant. These voltage sources
power up the entire circuit, including the different elements such as the
integrated circuit and the output load. This buck topology is a revolu
tionary and fascinating new concept. As shown in Fig. 17, it can assist in
driving low-power applications and electronic devices at a steady output
voltage without the use of an auxiliary battery or an external power
source. In this figure, the DC-DC converter was running the cell phone
with a working voltage of nearly 3.9 V, particularly for all mobile phones
with a battery capacity of up to 4500 mAh. Author [70–71] tested and
substituted the supercapacitor-module battery in the laboratories, which
worked properly.
6.2. Supercapacitor useful in the transportation sector
There are many options for driving Hybrid Electric Vehicle (HEV)
technologies in close proximity to a secondary power source. Fuel-
engine, electric motor drives, and energy storage elements are also
part of HEV technology. The supercapacitor is paired with a primary
source combustion engine in Fig. 15(b) as a secondary power source.
Peak power demands for acceleration are met by the secondary source.
This power supply is often used to capture regenerative braking energy
and apply it to additional acceleration or the essential energy
Surface area (specific)
Heteroatom-Doping
Pore size
Voltage
Current in capacitor
Prediction
Real Capacitance
vs
Input layer Hidden layer Output layer
Fig. 21. Artificial neural network (ANN) model to predict the supercapacitor performance [91–92].
(In this model we considered)
Surface area (specific), Voltage, Heteroatom-
doping, Pore size, current in capacitor
Performance
Efficiency
Fig. 22. Fuzzy logic to predict the supercapacitor performance and other characteristics [93–94].
S. Satpathy et al.

13
requirements of auxiliary electrical systems. HEVs claim to be low-
maintenance, higher life cycle and providing high performance due to
the addition of supercapacitor as a secondary power supply. Also, the
hybrid supercapacitor-battery energy storage system was developed by
the transport authority, which senses a spike in line voltage on an
overhead catenary system and absorbs excess braking energy in the
trains. As a result, there is a 10–20 % drop in energy usage and an 800
kW grid operator subsidy. It may have an annual turnover of $200,000
in monetary terms [73]. Fig. 18 illustrates a few instances of hybrid cars
that are propelled by energy produced by regenerative braking.
Apart from the HEV, Supercapacitors have also given major advan
tages to electric rail networks. This technology has long been used to
enable regenerative train braking and catenary voltage to be stabilized.
We can consider two cities like Cologne and Madrid, where SITRAS-SES
trackside storage systems have been developed since 2001 and 2003,
respectively, designed by Siemens using Maxwell's 1344 supercapacitors
[74]. South-eastern Pennsylvania, where trains halt and speed up
several thousand times a day, offers another example of this application.
7. Modelling of supercapacitor
Researchers and engineers are always required to have a common
framework for describing and analyzing any system. It is also thought of
as mathematical modelling. Supercapacitor system architecture includes
modelling for prediction, condition tracking, and control synthesis.
Because a model is a substitute for real systems and based on the
model's accuracy, assumption, it may be applicable for specific purposes.
Numerous supercapacitor models, including electrical behaviour, ther
mal behaviour, self-discharge, have been reported in the literature for a
variety of purposes [76–77]. The most used models are electrochemical,
equivalent circuit models, intelligent models, and fractional-order
models, which are shown in Fig. 19.
7.1. Electrical model
From the literature review, it has been observed the electrochemical
models are generally extremely accurate but have low calculation, ef
ficiency models. And the low efficiency is due to capture the actual re
action process within supercapacitors at the expense of partial
differential equations (PDEs). This impedes their use in the energy
storage system and control systems in real-time applications. The anal
ogous circuit models, by comparison, are derived under certain condi
tions from scientific knowledge and experimental evidence. That makes
the dynamics of the supercapacitor in large-scale conditions inadequate,
which leads to problems with modelling. In addition, there are no
physical representations of their parameters, which means no internal
Zα
RS
Constant
current
discharging
Circuit
Io
Zα
RS
Constant
current
discharging
Circuit
Io
(a) (b)
Fig. 23. Equivalent circuit model of supercapacitor using fractional-order
Modelling, a. R-CPE modelling, b. R-CPE-C modelling [51,96].
Fig. 24. (a, b, c, d) Switching Supercapacitor balancing circuit. (e) Simulation model of Switching Supercapacitor balancing circuit using matlab, Simulink
tool [117–118].
Table 2
Experimental data of charging of supercapacitor with different constant current
and valuating the Parallel (Rp) and Series (R) resistance.
Experimental data
Power supply
voltage (v)
Various
current value
Rp + R
(Charging) in Ω
Rp (Discharging)
in Ω
R (Ω)
3.69 0.527 7.21 7.202 0.008
3.478 0.650 5.807 5.793 0.014
3.308 1 3.208 3.203 0.005
3.26 1.25 2.602 2.601 o.001
3.21 1.5 2.201 2.197 0.004
S. Satpathy et al.

14
information is explicitly available. As a whole, the complete super
capacitor models reviewed in this paper for control/management pur
poses are shown in Fig. 20 [75].
The electrical behaviour of the supercapacitor can be mimic with the
help of RC equivalent circuit models. These models are nothing but the
simplified form of complex differential equations. [78]. Here, with
differing precision, we address various modelling methods that focus on
the number of elements and the structure of the circuit. And it also
showed that the precision is improved by.
increasing the number of circuit components. Just in Fig. 20, Four
common supercapacitor equivalent circuit models have been shown.
Fig. 20(a) is started with a simplified model, and the complexity is
steadily increased to Fig. 20(d) [79]. Satpathy et al. [3] describe Fig. 20
(a), which shows one series resistance Rs and a parallel-leakage resis
tance Rp. The practical application of this straightforward model is
severely constrained since it can only capture the dynamics of a super
capacitor for a brief period of time. Zubieta and Boner [80] focused on
power electronic applications and created a concept that included three
RC branches (see in Fig. 20(b)): such as immediate, deferred, and long-
term. Also, on a different time scale, each branch retains the super
capacitor characteristics. Buller et al. [81] suggested a frequency-
domain hierarchical model based on electrochemical impedance spec
troscopy (EIS). As seen in Fig. 20(c), the model consisted of a series
resistor, a lumped capacitor, and two parallel RC connections. Musolino
et al. [82] mention, this model represented the entire frequency-range
behaviour of a supercapacitor. Transmission line models were imple
mented to simulate the dispersed capacitance and electrolyte resistance
defined by the porous electrodes, taking transient and long-term activity
into account, as shown in Fig. 20(d). A model's complexity is determined
by the quantity of resistance-capacitance networks utilized in it [83,84].
The responsibility of calculating the capacitance and resistance of each
electrode pore dispersion is distributed to each RC network. In terms of
model complexity, accuracy, and resilience, all of these models are
helpful in representing our study employing supercapacitors, with the
dynamic model showing the highest overall efficiency. And each model
has its own set of advantages for describing or identifying a super
capacitor's specific characteristics.
7.2. Intelligent model
The efficiency of energy storage devices such as batteries, fuel cells,
and supercapacitors has been successfully predicted using intelligent
simulation techniques such as artificial neural networks (ANN) and
fuzzy logic [85–86]. Fig. 21 shows an example of a neuron body that
processes input signals and generates the response. Without a thorough
understanding of the fundamental processes, and intelligence-based
approaches are usually capable of representing the dynamic nonlinear
interaction between output and its motivating factors [87]. The real-
capacitance of the supercapacitor is predicted by an artificial neural
network in Fig. 21 [90–91]. This model has three layers: an input layer, a
hidden layer, and an output layer. The input layer is composed of five
parameters: basic surface area, capacitance voltage, heteroatom doping,
pore size, and capacitor current. Using these input and output data, the
hidden layer educated itself to create a function with a greater predic
tion accuracy. Additionally, this model predicted the real capacitance in
the output layer based on its input parameters [88–89]. To ensure the
model's consistency and generality, a large amount of high-quality
training data is needed. Because of these distinguishing characteris
tics, intelligent approaches for supercapacitor design and output pre
diction are now widely used.
Identifying model topology is a major challenge in the supervised
learning process. People often used adaptive and experiential ideas to
deal with this issue. Clustering methods are used to minimize or eradi
cate the harmful effects of collective decisions. Clustering data based on
a similarity metric is important in engineering data analysis. Traditional
partition-based clustering approaches include the classical K-means
algorithm, the fuzzy c-mean (FCM) algorithm, the maximum entropy
technique, and so on. One of the famous clustering algorithms is the
fuzzy c-mean (FCM) algorithm, which is a partition-based clustering
method. The traditional formulation, however, has three flaws: 1) the
number of clusters must be allocated ahead of time; 2) the clustering
result is especially vulnerable to initialization, and 3) there is a high
chance of being stuck in local minima. But this new fuzzy logic algo
rithm and some others that are hybrid algorithms (i.e., fuzzy logic in
addition to soft computing techniques) are helpful to reduce the degree
of attributes during the clustering time. Fuzzification, generate mem
bership function, rule-based design, and defuzzification are all compo
nents of the overall strategy, which aid in the correct modelling and
characterization of the supercapacitor depicted in Fig. 22 [93–95].
7.3. Fractional-order modelling
To boost modelling precision, fractional-order calculus has been used
in supercapacitor simulation [96,97]. Fractional-order models are made
up of intrigo-differential equations and are therefore better at capturing
supercapacitor dynamics than other circuit models. As an example, we
have demonstrated two common fractional-order models in Fig. 23, that
depicts a series resistor, a parallel resistor, in an R-CPE (constant-phase
element), and an R-CPE-C model. By developing a half-order model
capable of reliably reflecting supercapacitor behaviour while mini
mizing computational load, Riu et al. [98] established the use of
fractional-order models for supercapacitors. The fractional differentia
tion order was set in the model parameterization protocol, which
restricted the options for improving model accuracy.
7.4. Cell balancing modelling of supercapacitor
One of the most important things that Battery series balancing can
help with is making the robot's batteries last longer. Cell balancing is
often either active or passive. The active balancing is accomplished via
the supercapacitor switching technique. Since a supercapacitor has a
higher power density and a longer life cycle than a high-power battery, it
can move energy between cells without wasting time or money. There is
an analysis of how the supercapacitor and lithium battery work well
together, and a simulation of this power system shows that it works well
for a robot with a pulsed load. The supercapacitor used not only took in a
lot of spiking power to make the lithium battery lighter, but it also
balanced the cells by switching. A supercapacitor-equipped control
board is created for practical robot installation. Numerous researchers
[117] have successfully proven techniques through simulations and
experiments that have a wide range of applications.
Here in Fig. 24, we have considered many switching supercapacitor
balancing circuit. In Fig. 24(a), it has been shown the switching circuit
between the lithium-ion battery and supercapacitor. The equivalent
circuit of single cell is as shown in Fig. 24(b). The equivalent circuit of
the switching state is depicted in Fig. 24(c), and a realistic circuit will
contain resistance in the relay contact switch (Rsw) and the equivalent
series resistance (ESR) of the capacitor in Fig. 24(d). Additionally Fig. 24
(e) shows the Simulation model of Switching Supercapacitor balancing
circuit with Simulink using matlab tool [118].
8. Comparison
Apart from the aforementioned-literature study, we compare our
current research piece to the literature of other review papers. For the
compressive research, we looked at a variety of factors, including energy
storage mechanisms, electrode and electrolyte details, supercapacitor
electrical performance, engineering applications, different modelling
methods, difficulties, and future prospects, which can see in Table 3.
Raghavendra et al. [103] mention, in the current review, extensive
study on the latest literature of supercapacitors with great care. Super
capacitors' fundamental and application views are included in the global
S. Satpathy et al.

15
market analysis, along with manufacturing firms, challenges, and cur
rent developments. A comprehensive image may be obtained by care
fully analyzing the numerous supercapacitor categories, the production
of different electrode materials, and electrolytes from the very beginning
of their development. Finally, future scope and problems are briefly
discussed and considered for the design and uses of next-generation
supercapacitors. The electrical performance and engineering applica
tions of supercapacitors are two significant aspects of this review that
are lacking. Berrueta et al. [10] discusses contemporary research and
applications of supercapacitors, emphasizing the link between material
qualities and electrical characteristics in this review article. It starts with
an overview of the energy storage techniques and materials that
supercapacitors employ.
The supercapacitors are categorized, their main properties are
described, and their electrochemical characteristics are connected to
electrical performance based on these materials. Also discussed the
usage of supercapacitors in various market areas, as well as their
development prospects. However, the purpose of this review article is
failed to illustrate the challenges and the future solution for the super
capacitor with its modelling. With the growing usage of supercapacitors
in the transportation and energy sectors, dependability, which is related
to lifetime performance and cost, becomes an essential factor to address,
according to Liu et al. [104]. This study also covers the failure processes,
lifespan modelling, and reliability-oriented design of three different
types of supercapacitors used in energy storage applications. From an
application standpoint, scientific issues and opportunities are also
acknowledged. However, this article falls short of explaining the elec
trode and electrolyte in detail, as well as engineering applications.
Satpathy et al. [3] addressed the structural design of supercapacitors as
well as numerous engineering-based applications in consumer elec
tronics, transportation, and other fields in this study. Aside from these
characteristics, the authors cover various electrical characterization of
supercapacitors, such as voltage dependent capacitance and current
dependent leakage resistance. However, the electrical modelling and
future challenges of supercapacitors are not covered in this article.
Finally, we look at all the above characteristics that have an influence on
supercapacitor characterization and briefly explain them, which can
show in Table 4.
9. Supercapacitors' challenges in real-time applications
Because of their unique designs features, supercapacitors are widely
used in medical, transportation, industrial, armed forced, portable, and
tiny electronics device sectors. However, These gadgets still have some
flaws. The following four factors primarily explain the present diffi
culties that must be resolved.
9.1. Supercapacitor's technical issues
Supercapacitors' energy densities aren't particularly high. In terms of
energy density still, there is a big gap between conventional super
capacitors and lithium-ion batteries. From the literature, it has been
understood that the energy density of lithium-ion is probability tenth
times of the supercapacitor [105–106]. Nowadays from the research
point of view, how to improve the energy density of supercapacitors is a
big challenge. The solution of this challenge is related to improvising the
manufacturing process with a novel electrode, electrolyte, and tech
nology that are probably an effective ways to enhance the storage ca
pacity of the supercapacitor. With increasing in energy density the
weight of the supercapacitor also increases, which creates an issue of
compactness. Some other ways are to increase the energy density are,
increasing the surface area of the electrode or increasing the operating
voltage. Specifically, to increase the surface area, researchers are trying
to create innovative materials and to withstand the voltage range used
different organic electrolytes. We believe, Supercapacitors' energy
densities might become similar to batteries if these gaps are adequately
addressed.
9.2. Modelling based on electrical parameters
Some aspects of the supercapacitor model may be equal to the ideal
model in some cases, but some nonideal characteristics also have been
seen. Specifically, military applications, such as power supply applica
tions for satellites and spacecraft, may provide possible hazards that
must not be overlooked. The resonance produced by the filter, the
limited quantity of energy accessible, and the energy storage super
capacitor have a developed solution. Additionally, because super
capacitors have a huge amount of energy, they may deliver quick
Table 3
Summary of various models for illustrating a supercapacitor's electrical behaviour.
Types of
behaviour
Sub class of the
behaviour
Merits Demerits References that
describe
Electrical
behaviors
(a) Fractional order
model
Better capabilities to fitting simulated and experimental
data to characterized a supercapacitor
This model has no self-discharge path [3,51,96]
(b) Electro-
chemical model
It efficient describe the inner physical chemical reactions,
and also the model has higher accuracy
Model associate with more complex mathematics [99–100]
(c) Equivalent
circuit model
This model has moderate accuracy Absence of real physical meaning and understanding [101–102]
(d) Intelligent
model
Good modelling capabilities This model is more sensitive to the training, testing
and validation data set, poor robustness
[93–95]
Table 4
Comparison of our article with other review papers with respect to various parameters.
References Author Energy storage
mechanism
Detail on electrode &
electrolyte
Electrical
performance
Engineering
applications
Modelling of
supercapacitor
Challenges & future
opportunity
[103] Ragha-vendra
et al.
[10]
Berrueta et al.
[104]
Liu et al.
[3]
Satpathy et al.
Present article
S. Satpathy et al.

16
throughput when needed. In order to investigate the influence of load
type, load changes, or external environmental, as well as unintentional
disruption on the system's stability, it is very crucial to have a depend
able design [107–108].
9.3. Industrial standardization of supercapacitor
Enterprises involved in the supercapacitor sector operate on a variety
of levels. Due to the fact that supercapacitors are a novel energy storage
technology [109–110]. Their proper growth is, directly and indirectly,
related to industry and market condition, which strives to establish a
genuine standard not only in terms of the industry but worldwide also.
To maintain this, it is necessary to develop a technical standard system
that includes terms, and various other precise methods such as electrical
performance tests, technical safety, electrode, and electrolyte specifi
cation, transportation, and so on [111–112].
10. Future research opportunities
Flexible energy storage systems have grown more popular among
academics as a result of the fast development of tiny, portable, and
wearable electronic devices. It is extremely important to design such
type storage devices or gadgets that are both flexible and compact, while
also possessing excellent electrochemical characteristics. But because of
the unbending characteristics of the electrode, traditional super
capacitors are severely restricted in their ability to change the shape of
the device. Additionally, throughout the manufacturing process, flexible
metal plates, electrodes, and electrolytes should be prepared in a way
that will maximize their ability to operate electrochemically. This in
dicates that the foundation for the subsequent generation of energy
storage technology will be an integrated flexible supercapacitor and a
portable electronic device [113–114].
To overcome the major issue of supercapacitor i.e. having low energy
density, it is necessary to build hybrid or integrating technology, in
which we combine both battery and supercapacitor. Where one can
charge an electrode with a battery-type charging method such as a
faradic process. And the other electrode may be charged with a capac
itive mechanism. In this way, we can integrate both high energy density
(battery technology) and high-power density (supercapacitor) and
developed a hybrid system. Aside from this, the developed hybrid sys
tem may apply to solve many real-time applications such as fast
charging, an extended life cycle with being inexpensive [115–116].
10.1. State of health estimation
It is method for figuring out the state of health (SOH) based on the
voltage and current of the partial charge. This is talked about and ana
lysed how to get the feature variables, which are the energy signal, the
Ah-throughput, and the charge duration in a supercapacitor during
charging and discharging. The SOH is estimated using a support vector
machine (SVM) with a radial basis function (RBF) as the kernel function.
With both full and partial charging data, the SVM looks at how well it
can predict the SOH. The results of the experiment show that the dis
cussed method is accurate for estimating the SOH. It has been found that
many researchers [118–120] made it for lithium ion battery. So, finding
and analysis the SOH for supercapacitor will our future work. And
during this SOH analysis we plan to followed of SVM, neural network
and fuzzy logic to make more accurate analysis. Also, future research
should focus on figuring out the SOH of different supercapacitors like
Nippon, Maxwell etc., since their degradation mechanisms and electrical
performance can be different [121–127].
11. Conclusion
This review article goes into detail about how supercapacitors store
energy. Its demand is also going up because there is a need for strong
energy storage solutions that can keep up with high energy demand.
This review paper talks about the technology in a general way, with a
focus on some of its electrical features and new uses. First, the energy
storage mechanism in the traditional supercapacitor was addressed.
Then, in terms of power density, and energy density we compare and
discuss different energy storage devices including the supercapacitor,
lithium-ion, fuel cell, and some other devices. In a supercapacitor,
electrodes and electrolytes are the key factors that determine the per
formance of a storage system. So, we concentrated on various electrodes
and electrolytes. The key subject of this review paper is electrical
characteristics. Therefore, we spoke about those basic properties, such
as self-discharge, voltage-dependent behaviour, ohmic phenomenon,
supercapacitor high-frequency behaviour. The current-dependent
behaviour of the parallel leakage resistance of the supercapacitor was
observed experimentally during this discussion and a new, simple
method for measuring the voltage-dependent capacitance value was also
developed. The article's novelty, which was merged with the review
effort, is the precise capacitance measurement. We discuss the sub
stantial and varied uses of the supercapacitor in consumer electronics,
transportation, and regenerative braking systems. Additionally, model
ling is needed for the supercapacitor in order to apply the newest fea
tures. Additionally, modelling is needed for the supercapacitor in order
to apply the newest features. Fractional-order, RC equivalent, and
intelligent modelling with artificial neural networks and fuzzy logic
were covered in the last module. Integration of all these review and
novelty of supercapacitor helps to enhance its features and make the
future scenario to use it in electric vehicle as secondary power supply
with lithium-ion battery.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data availability
No data was used for the research described in the article.
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Sambit Satpathy is working at Galgotias College of Engineering, Greater Noida as an
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Agartala in 2021. He has the author and co-author of 25 peer review journals. His research
area is on modelling, characterizing the electrical properties of supercapacitors.
Dhirendra K Shukla works at working at Galgotias University, Greater Noida as an
Associate Professor. He has got his Ph.D. from the Motilal Nehru National Institute of
Technology Allahabad in 2021.
S. Satpathy et al.

An in-depth study of the electrical characterization of supercapacitors for recent trends in energy storage system

An in-depth study of the electrical characterization of supercapacitors for recent trends in energy storage system

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