MEV


 

 

Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 
 

Journal of Mechatronics, Electrical Power, 
and Vehicular Technology 

 
e-ISSN: 2088-6985  
p-ISSN: 2087-3379  

 

 

mev.lipi.go.id 

 
 

 
doi: https://dx.doi.org/10.14203/j.mev.2022.v13.60-71 
2088-6985 / 2087-3379 ©2022 National Research and Innovation Agency  
This is an open access article under the CC BY-NC-SA license (https://creativecommons.org/licenses/by-nc-sa/4.0/) 
MEV is Scopus indexed Journal and accredited as Sinta 1 Journal (https://sinta.kemdikbud.go.id/journals/detail?id=814) 
How to Cite: R. Nurdiansyah et al., “State of charge estimation of ultracapacitor based on equivalent circuit model using adaptive neuro-fuzzy 
inference system,” Journal of Mechatronics, Electrical Power, and Vehicular Technology, vol. 13, no. 1, pp. 60-71, July 2022. 

State of charge estimation of ultracapacitor  
based on equivalent circuit model using  
adaptive neuro-fuzzy inference system  

Rizal Nurdiansyah a, *, Novie Ayub Windarko a, Renny Rakhmawati a,  
Muhammad Abdul Haq b 

a Electrical Engineering Department, Politeknik Elektronika Negeri Surabaya 
Jl. Raya ITS, Surabaya, 60111, Indonesia 

b Department of Electrical Engineering and Computer Science, Tokyo Metropolitan University 
1-1 Minami-Osawa, Hachioji-shi, Tokyo, 192-0397, Japan 

 
Received 31 May 2022; 1st revision 23 June 2022; 2nd revision 28 June 2022; Accepted 29 June 2022; Published online 29 July 2022 

 
 

Abstract 

Ultracapacitors have been attracting interest to apply as energy storage devices with advantages of fast charging capability, 
high power density, and long lifecycle. As a storage device, accurate monitoring is required to ensure and operate safely during 
the charge/discharge process. Therefore, high accuracy estimation of the state of charge (SOC) is needed to keep the 
Ultracapacitor working properly. This paper proposed SOC estimation using the Adaptive Neuro-Fuzzy Inference System 
(ANFIS). The ANFIS is tested by comparing it to true SOC based on an equivalent circuit model. To find the best method, the 
ANFIS is modified and tested with various membership functions of triangular, trapezoidal, and gaussian. The results show that 
triangular membership is the best method due to its high accuracy. An experimental test is also conducted to verify simulation 
results. As an overall result, the triangular membership shows the best estimation. Simulation results show SOC estimation 
mean absolute percentage error (MAPE) is 0.70 % for charging and 0.83 % for discharging. Furthermore, experimental results 
show that MAPE of SOC estimation is 0.76 % for random current. The results of simulations and experimental tests show that 
ANFIS with a triangular membership function has the most reliable ability with a minimum error value in estimating the state 
of charge on the Ultracapacitor even under conditions of indeterminate random current. 

Copyright ©2022 National Research and Innovation Agency. This is an open access article under the CC BY-NC-SA license 
(https://creativecommons.org/licenses/by-nc-sa/4.0/).  

Keywords: Ultracapacitors; state of charge; adaptive neuro-fuzzy inference system; energy storage devices; equivalent circuit 
model. 

 
 

I. Introduction 
Ultracapacitors (UCs), also known as 

Supercapacitors (SCs) or electric double-layer 
capacitors (EDLC), are now increasingly being used 
in electrical applications as energy storage devices. 
An Ultracapacitor is a type of electric double-layer 
capacitor with a broad operating temperature range, 
low internal resistance, excellent durability, high 
power density, and high discharge capability to 
supply peak power requirements [1][2]. The use of 
Ultracapacitors as energy storage devices is 
currently being increasingly used in electrical 
applications such as hybrid energy storage systems 

(HESS), electric vehicles (EVs), powertrains, and 
several other electrical applications [3][4][5]. The 
limitations of batteries in electric vehicles are their 
limited life cycle, low discharge rates, and special 
techniques needed to extend their life [6][7]. The 
latest solution to overcome this problem is to use an 
Ultracapacitor as an additional power source for the 
main propulsion of electric vehicles and as a source 
of electrical energy in regenerative braking, which 
requires a short time [8]. Ultracapacitor has fast 
charging capability with a charging current of up to 
tens of amperes and high discharge capability with a 
maximum discharge current of up to hundreds of 
amperes in one cycle [9]. Fast charging capability is 
supported by the discovery of new materials with 
nanostructures, making the Ultracapacitor has a 
larger capacitance even though its energy density is 

 
 
* Corresponding Author. Tel: +62 858 5150 3369 

E-mail address: nurdiansyahrizal@pe.student.pens.ac.id  

https://dx.doi.org/10.14203/j.mev.2022.v13.60-71
http://u.lipi.go.id/1436264155
http://u.lipi.go.id/1434164106
https://mev.lipi.go.id/mev
https://mev.lipi.go.id/mev
https://dx.doi.org/10.14203/j.mev.2022.v13.60-71
https://creativecommons.org/licenses/by-nc-sa/4.0/
https://sinta.kemdikbud.go.id/journals/detail?id=814
https://crossmark.crossref.org/dialog/?doi=10.14203/j.mev.2022.v13.60-71&domain=pdf
https://creativecommons.org/licenses/by-nc-sa/4.0/
mailto:nurdiansyahrizal@pe.student.pens.ac.id


R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 
 

 

61 

not greater than that of a lithium-ion battery [10]. 
Ultracapacitors can be used in extreme temperatures 
because they have a wide operating temperature 
range and are supported by long cycle life, giving 
them an advantage over other energy storage 
devices [11]. Technological developments 
increasingly encourage Ultracapacitor, which has 
many advantages as an energy storage device to 
replace batteries [12]. 

In their implementation, some utilize 
Ultracapacitor-battery hybrids to get optimal 
performance from both energy storage devices [13]. 
It is also possible to use an Ultracapacitor as the 
primary energy storage device in electric vehicles, 
for example, electric scooters and buses [14]. Fast 
charging capabilities make Ultracapacitor a 
breakthrough in battery replacement technology 
[15]. The power supply for driving electric vehicles 
with high traction encourages using Ultracapacitors 
with the advantages of high-power density and 
super-fast charging [16]. The high efficiency of the 
Ultracapacitor is due to the low resistance of the 
constituent material supported by a high-power 
density, which makes it capable of high current 
discharge and low power dissipation [17]. The 
Ultracapacitor's life cycle is much longer than other 
energy storage devices. The level of security using 
Ultracapacitor needs to be considered with SOC 
monitoring [18].  

The conventional method for determining the 
state of charge is the open-circuit voltage (OCV) 
method which requires a rest period to determine 
the original voltage on the Ultracapacitor, so it is not 
possible to use it in practical applications. The 
weakness of the OCV method cannot be measured in 
an operating state because an effective 
measurement when the condition is the voltage at 
the terminals does not represent the open-circuit 
voltage in the energy storage [19]. The use of 
coulomb counting only uses current operating 
parameters without regard to the internal conditions 
of the Ultracapacitor and requires measuring 
instruments with high accuracy to avoid periodic 
errors. The Unscented Kalman Filter (UKF) 
application for SOC estimation still requires OCV-
SOC mapping to obtain accurate information about 
SOC, and complex modeling makes parameter 
identification more difficult [20]. The difference 
between Ultracapacitors and other energy storage 
devices is the ability to have a deeper discharge 
depth to be used optimally [21].  

Accurate state of charge (SOC) monitoring is one 
of the factors in maintaining the safety of 
Ultracapacitor performance to avoid overcharge or 
over-discharge conditions that cause dangerous 
conditions when used. Ultracapacitor modeling is 
needed to determine its characteristics and electrical 
behavior so that it has high accuracy in determining 
the state of charge. The Kalman Filter method uses a 
more complex equation to get the state of charge 
value. Based on experiments, estimates with the 
Kalman Filter have an error reading of about 5 % 
[22]. Several models analyze the original 
characteristics of Ultracapacitors, including classical 
equivalent circuit models, dynamic models, and 

transmission models [23][24]. The modeling that 
represents the characteristics of the Ultracapacitor is 
a combination of series resistors and capacitors with 
the addition of parallel resistors as self-discharge 
modeling [25][26]. This paper proposes modeling 
with a combination of resistor and capacitor 
components as the relevant model and is referred to 
as the equivalent circuit model (ECM). The proper 
modeling will get the process of monitoring the state 
of charge (SOC) on the Ultracapacitor. By modeling 
the equivalent circuit models, which are simple and 
relevant, they are chosen because they can model 
the characteristics of the Ultracapacitor with high 
accuracy [27]. 

This paper proposes a SOC estimation method 
using the Adaptive Neuro-Fuzzy Inference System 
(ANFIS) algorithm from various models with their 
respective levels of complexity. Artificial neural 
networks can form models in patterns such as neural 
networks obtained through learning experimental 
data to form a learning set as a system 
representation with a minimal error value by 
calculating the mean square error [28]. The learning 
stage of the artificial neural network is proven to 
have high accuracy and is relevant to be applied in 
various advanced research in the presence of 
appropriate data for the actual condition of the 
system [29]. The SOC estimation method, which is 
performed by predicting the Neural Network 
algorithm and in collaboration with the reasoning 
owned by the Fuzzy Inference System, has a high 
level of accuracy [30][31]. The learning and training 
processes make ANFIS one of the best methods for 
estimating the SOC Ultracapacitor, which has 
dynamic behavior [32].  

The experiment in this paper uses the equivalent 
circuit model (ECM) as the Ultracapacitor 
characteristic modeling, while the ANFIS method is 
used as the SOC estimation method. In addition, 
direct testing will be carried out on the hardware 
with constant current charging and discharging with 
a load in the form of a DC electronic load to obtain 
validation of the actual condition of the 
Ultracapacitor. The results obtained will be 
compared between theoretical calculations with an 
equivalent circuit model, SOC estimation using the 
ANFIS, and experimental data conducted in the 
laboratory. 

II. Materials and Methods 
A. Ultracapacitor modeling 

A series resistor and capasitor (RC) circuit is the 
simplest form of modeling the equivalent circuit 
model applied to an Ultracapacitor. This model 
consists of a resistor representing the internal 
resistance and a capacitor indicating the charge 
capacity during charging and discharging of the 
Ultracapacitor. Figure 1 shows the simple modeling 
of an Ultracapacitor with an equivalent circuit model. 

Based on the Ultracapacitor equivalent circuit's 
modeling, the following equations (1) and (2) are 
obtained based on Kirchhoff's voltage law. 𝑉𝑡 is the 
terminal voltage obtained by measuring the voltage, 
𝑣𝑐 is the authentic voltage of the Ultracapacitor, 𝑖 is 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 

 

62 

the current in charge and discharge conditions, and 
𝑅𝑠  is the equivalent series resistance of the 
Ultracapacitor. 

𝑉𝑡 = 𝑣𝑐 + 𝑖 ∙ 𝑅𝑠 (1) 

𝑣𝑐 = 𝑉𝑡 − 𝑖 ∙ 𝑅𝑠 (2) 

Ultracapacitor modeling primarily aims to 
simulate the characteristics under charge and 
discharge conditions. The change in terminal voltage 
during the Ultracapacitor's service life indicates the 
charging and discharging process. The advantages of 
using Ultracapacitors as energy storage devices are 
their ability to store energy long-term and high 
output power. In addition to the Ultracapacitor 
operating conditions, the terminal voltage can 
slowly decrease due to self-discharge. Self-discharge 
is caused by two conditions: ion diffusion and 
leakage current. 

This paper uses five Ultracapacitor units in series 
for a higher nominal voltage with a lower 
capacitance. Table 1 shows the data of the 
Ultracapacitors used in this research. Table 1 
mentions the datasheet as an initial reference for the 
internal parameters of the Ultracapacitor in the SOC 
estimation on the Simulink. In the advanced stage, 
this data will be validated through testing by 
researchers to determine the actual value of the 
internal parameters so that the SOC estimate follows 
the actual conditions to be applied to Simulink and 
the designed Ultracapacitor hardware. 

The parameter values of the Ultracapacitor 
components used in this paper are based on the 
SAMWHA Ultracapacitor datasheet. The following 
equation can validate parameter values based on the 
tests performed. The following equation can be used 
to determine the equivalent parallel resistance (𝑅𝑝) 
value. 𝐶 is the capacitance of Ultracapacitors, 𝑉1 is 

the initial voltage, and 𝑉2 is the final voltage after 
charging. 

𝑅𝑝 =
−10800

𝑙𝑙 (𝑉2/𝑉1) 𝐶
 (3) 

In this model, the aim is to find out the value of 
the Ultracapacitor parameters that are not listed in 
the datasheet in this paper, namely the equivalent 
parallel resistance, which has been described in 
equation (3), and to validate the actual value of 
equivalent series resistance and capacitance. To 
determine the value of equivalent series resistance, 
equation (4) can be used, where ∆𝑉 is the change in 
voltage from the charging state to the open-circuit 
voltage and ∆𝐼  is the current value used in the 
testing process. 

𝑅𝑠 =
∆𝑉
∆𝐼

 (4) 

Then, the stored charge approximation method 
determines the capacitance ( 𝐶 ), as shown in 
equation (5). The ∆𝑉  value is the subtraction 
between 𝑉1  and 𝑉2 . 𝑉1  is a voltage of 0.8 of the 
nominal voltage of the ultracapacitor. Meanwhile, 𝑉2 
is a voltage of 0.4 of the nominal voltage of the 
Ultracapacitor. The value of ∆𝑄 calculates the current 
integral during the testing process, where 𝑡1 is the 
discharge time to reach 𝑉1 and 𝑡2 is the discharge 
time to reach 𝑉2. 

𝐶 = ∆𝑄
∆𝑉

=
∫ 𝐼(𝑡)𝑑𝑡
𝑡2
𝑡1
(𝑉1−𝑉2)

 (5) 

B. State of charge estimation 

The state of charge is the ratio between an 
energy storage device's total usable energy capacity. 
This research is the ratio of the available energy 
capacity to the total charge in the Ultracapacitor. 
State of Charge represents the available energy and 
is generally expressed as a percentage in 0 to 1 or 0 
to 100 %, with 100 % indicating the Ultracapacitor is 
complete and 0 % is empty. The SOC is an important 
parameter that must be known in using energy 
storage in addition to the voltage, current, capacity, 
and energy value. State of charge monitoring is 
necessary to maintain the Ultracapacitor's lifetime 
by avoiding the risk of overcharging and over-
discharging, which can affect the structural 
components of the Ultracapacitor. At a more 
advanced stage, the determination of the SOC can be 
used to control energy use. The accuracy level of SOC 
estimation on the level of measurement accuracy 
and the suitability of the modeling to get an estimate 
that follows the actual conditions of the 
Ultracapacitor. Based on the equivalent circuit model 

Table 1. 
Ultracapacitor datasheet 

Parameter Value Unit 

Rated voltage 2.7 Volt 

Capacitance 500 Farad 

Cycle life 500000 Cycle 

Lifetime 10 Year 

ESR 3.1 mΩ 

Maximum continuous current 25 Ampere 

Maximum peak current 264.7 Ampere 

Specific energy 5.59 Wh/kg 

Mass 89 Grams 

Operating temperature -40° to 65° Celcius 
 

 

 

 
(a)  (b) 

Figure 1. (a) Ultracapacitor library in MATLAB; (b) Proposed ultracapacitor modeling 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 
 

 

63 

modeling, the formula to determine the SOC on the 
Ultracapacitor can be used with the following 
formula. 

𝑆𝑆𝐶 % = � 𝑣𝑐 
𝑣𝑐 𝑚𝑚𝑚

� × 100 (6) 

In equation (6), the value of 𝑣𝑐  is the 
Ultracapacitor voltage obtained from the modeling 
results using an equivalent circuit model. For 𝑣𝑐 𝑚𝑚𝑚 
is the value of 𝑣𝑐  at the maximum point in the 
charging process. The following summary in Table 2 
compares the methods used to estimate SOC on 
Ultracapacitors, along with their advantages and 
disadvantages. The table describes each method 
used for estimating the SOC Ultracapacitor and its 
ability to get estimation results that follow actual 
conditions, which are described as advantages and 
an explanation of the disadvantages of the methods 
used in the paper in actual application. 

C. Adaptive neuro-fuzzy inference system (ANFIS) 

The research presented in this paper used the 
ANFIS to estimate the SOC of Ultracapacitor. The 
advantages possessed by artificial neural networks 
and fuzzy inference systems are collaborating to 
form ANFIS. With the ability to learn through data 
learning and fuzzy inference system reasoning, 
ANFIS is considered to work optimally to estimate 
the SOC on the ultracapacitor. The ANFIS 
architecture has five layers with different special 
functions to form a pattern based on the training 
results. Figure 2 shows that each layer has its 
function, which will be estimated using the ANFIS 
algorithm through detailed calculations to get a 
pattern that fits the model [33]. ANFIS is an 

advanced application of a fuzzy inference system 
with neural network architecture using Takagi-
Sugeno as a learning process and determining the 
desired form of membership function. The ANFIS 
architecture consists of five layers with different 
special functions in each layer, making ANFIS 
performance with more complex and detailed 
processing. There are two rules for processing ANFIS 
with if-then rules as in equations (7) and (8). 

Rule 1: if 𝑥 is 𝐴1 and 𝑦 is 𝐵1 then 𝑓1 = 𝑝1𝑥 + 𝑞1𝑦 + 𝑟1 (7) 

Rule 2: if 𝑥 is 𝐴2 and 𝑦 is 𝐵2 then 𝑓2 = 𝑝2𝑥 + 𝑞2𝑦 + 𝑟2 (8) 

𝐴1, 𝐴2, 𝐵1, and 𝐵2 are the premise parameters of 
the input membership functions 𝑥 and 𝑦, while 𝑝1, 𝑞1, 
𝑟1, 𝑝2, 𝑞2, and 𝑟2 are linear consequent parameters of 
the Takagi-Sugeno fuzzy inference system. In 
designing ANFIS, it is necessary to pay attention to 
two rules in equations (7) and (8), clustering rules 
for data learning so that data processing at each 
layer follows the training data formed. In addition, it 
is necessary to pay attention to several important 
aspects, namely the type of membership function, 
the number of membership functions, error 
tolerance, and the number of epochs in the training 
process. The following is the workflow of the five 
layers in ANFIS. 

1) Layer 1 

The fuzzification layer at node 𝑖 for 𝜇𝐴 and 𝜇𝐵 is 
shown in equations (9) and (10). Each neuron is 
adaptive to the parameters to generate a 
membership function. At input, 𝑥 will form 𝜇𝐴𝑖, and 
input 𝑦 will form 𝜇𝐵𝑖 with 𝑖 =1,2 where 1 and 2 are 
two conditions resulting from clustering 

 
Figure 2. ANFIS Architecture [33] 

Table 2. 
Advantages and disadvantages of SOC methods 

Methods Advantage Disadvantage 

Open-circuit voltage [1] Simple and easy Ultracapacitors need long times of rest to achieve voltage stability, 
causing difficulties in measurements. 

Coulomb counting [1] Simple and easy Inaccurate current measurement will cause SOC estimation error, and 
the error will increase with long-term accumulation. 

Extended Kalman Filter [2] High accuracy despite 
external interference 

This method cannot be applied directly to estimate the states of a non-
linear system. 

Open-circuit voltage – UKF [20] High accuracy Requires Ultracapacitor modeling, OCV, and UKF equations to get 
accurate results. 

Kalman Filter [22] High accuracy Estimation errors must be recalculated to get convergent results. 
 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 

 

64 

membership function fuzzy logic reasoning to 
determine membership function. 

𝑆𝑖
1 = 𝜇𝐴𝑖(𝑥) ,    𝑖 = 1,2 (9) 

𝑆𝑖
1 = 𝜇𝐵𝑖(𝑦) ,    𝑖 = 1,2 (10) 

2) Layer 2 

The fixed node layer 𝑤𝑖 produces output in the 
form of multiplication of all incoming signals by the 
node, representing the activation of the fuzzy rule. 
Equation (11) shows the multiplication of 𝑤𝑖 using 
𝜇𝐴𝑖 and 𝜇𝐵𝑖 with 𝑖 for conditions 1 and 2, which have 
been formed in the previous layer. 

𝑆𝑖
2 = 𝑤𝑖 = 𝜇𝐴𝑖(𝑥) ∙ 𝜇𝐵𝑖(𝑦),    𝑖 = 1,2 (11) 

3) Layer 3 

The nonadaptive normalization layer performs an 
activation function. 𝑤𝚤��� is a normalization of the fuzzy 
rule activation form with the value of 𝑤𝑖 divided by 
the total values of 𝑤1 and 𝑤2. Determination of the 
value at layer 3 is shown in equation (12). 

𝑆𝑖
3 = 𝑤𝚤��� =

𝑤𝑖
𝑤1+𝑤2

 ,    𝑖 = 1,2 (12) 

4) Layer 4 

The adaptive defuzzification layer for 𝑤𝚤���  is 
multiplied by 𝑝𝑖 , 𝑞𝑖 , and 𝑟𝑖 . 𝑤𝚤���𝑓𝑖  is useful for 
denormalizing the values obtained at layer 3. To get 
the parameter values for the coefficients of 𝑝𝑖, 𝑞𝑖, and 
𝑟𝑖 with 𝑖 for 1 and 2, using the Recursive Least Square 
Estimator (RLSE) calculation. The following equation 
(13) is used to get the value on layer 4. 

𝑆𝑖
4 = 𝑤𝚤���𝑓𝑖 = 𝑤𝚤��� ∙ [(𝑝𝑖 ∙ 𝑥) + (𝑞𝑖 ∙ 𝑦) + 𝑟𝑖)],    𝑖 = 1,2 (13) 

5) Layer 5 

The single fuzzy node output layer is fixed to 
return all outputs by adding up all the inputs 
obtained from the fourth layer to determine the 
output layer using the function in equation (14). In 
the final calculation, layer 5 is obtained from the 
output layer 4 from the results of 𝑤𝚤���𝑓𝑖. The output 
from layer 5 is the estimated value of the 
Ultracapacitor's authentic voltage, which will be 

used as the main parameter for SOC estimation using 
the ANFIS algorithm. 

𝑆𝑖
5 = ∑𝑤𝚤���𝑓𝑖 =

∑𝑤𝑖∙𝑓𝑖
∑𝑓𝑖

,    𝑖 = 1,2 (14) 

III. Results and Discussions 
In this experiment, the Ultracapacitor energy 

storage system will be tested for charging using a DC 
Power Supply and discharging using a DC electronic 
load with a variable current to model the actual 
conditions in a non-linear load. Figure 3 shows a 
research diagram for estimating SOC. The equivalent 
circuit model in Figure 1 and equation (6) in this 
system is used as true SOC because it is an 
application of estimation with modeling to 
determine open-circuit voltage, which is commonly 
used for SOC estimation in addition to coulomb 
counting. While the system is running, the measured 
voltage is the charging voltage. Estimating the 
authentic voltage on the Ultracapacitor obtained 
through modeling for estimation using the open-
circuit voltage method is necessary. The authentic 
voltage on the Ultracapacitor is the essential 
parameter to determine the state of charge. In 
simple terms, it is the authentic voltage of the 
Ultracapacitor without the influence of equivalent 
series resistance. In this paper, five Ultracapacitor 
units are used in series with the simulation on 
Simulink MATLAB and hardware testing of 
measuring terminal voltage and current under 
charge and discharge conditions. 

The data required is the measurement of current 
and voltage at the terminal of the Ultracapacitor 
energy storage system. The Ultracapacitor is 
mathematically analyzed to adjust the electrical 
behavior and estimate the SOC with a modeling 
system based on the equivalent circuit model. RC 
circuit in series with a parallel resistor as a self-
discharge model, as shown in Figure 1. The ANFIS 
built will be used as an estimator to determine the 
SOC value from the results of the supervised learning. 
The data obtained from the logging results will be 
processed simultaneously through modeling and the 
ANFIS estimator. Performance testing will be 
performed using the root mean square error (RMSE), 
mean square error (MSE), mean absolute error 

 

Figure 3. Block diagram of the comparative analysis estimations SOC 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 
 

 

65 

(MAE), and mean absolute percentage error (MAPE) 
methods. 

From the results of characteristic testing with 
varying current patterns on charging and 
discharging conditions that have been carried out on 
Ultracapacitor energy storage, training will be 
carried out on the ANFIS toolbox to build a Fuzzy 
Inference System. The required training data are 
voltage and current on charging and discharging 
conditions, with the target data being the authentic 
voltage on the Ultracapacitor. The training process 
from the data obtained from testing the 
Ultracapacitor characteristics is carried out on the 
MATLAB toolbox. Figure 4 shows the training results 
using a hybrid method to get an algorithm following 
the original system. ANFIS training is used to form a 
fuzzy inference system pattern in the estimation 
process through the learning process. A hybrid 
method of artificial neural networks is used to form 
a network pattern that is appropriate and adaptive 

to system performance that varies with charging and 
discharging conditions. 

The flowchart of the ANFIS architecture is shown 
in Figure 5. There are a series of processes, so the 
mechanism can work optimally according to the 
expected target. In the early stages, there is data 
sharing for training and testing, for training data 
using data from test results with the patterned 
current. In comparison, testing data using data from 
tests with random currents. Based on the results of 
the ANFIS development, the average testing error of 
6.9917e-9 indicates optimal learning outcomes and is 
following the desired target. 

A. Simulation results  

From the training and data testing results to 
building ANFIS, performance testing is carried out on 
charging and discharging conditions in the 
simulation. Current sources are randomly assigned 
to check the capability of the ANFIS as an estimator. 

   
(a)  (b) 

Figure 4. (a) Training error with 100 epochs; (b) Training data with authentic ultracapacitor voltage as target 

 

 
Figure 5. Flowchart of ANFIS architecture 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 

 

66 

In this simulation, the capacitance value of 100 
farads and the equivalent series resistance of five 
Ultracapacitor units of 15.5 mΩ is determined based 
on the reference obtained from the datasheet. 
Figure 6 shows the charging and discharging 
process plot results in MATLAB. 

In the results, the variation of the membership 
function is conducted to determine the most optimal 
ANFIS performance for SOC estimation (Figure 7). 
The charging and discharging currents are made 
similar to the actual conditions in using non-linear 
loads to test the estimator's performance under 
conditions with drastic changes. Over time, the SOC 
will increase when charging and decrease when 
discharging. An Ultracapacitor can handle this 
condition because it has a high discharge rate, a 
wide operating temperature, and a long lifecycle, 
making it safe to use in extreme conditions. 

Table 3 shows the calculation of ANFIS 
performance testing using the RMSE, MSE, MAE, and 
MAPE methods and the results of three different 
membership functions to determine the best model 
for the ANFIS estimator. Based on the test, ANFIS has 
a high accuracy performance with MAPE calculation 
error values of 0.70 % in charging conditions and 
0.83 % in discharging conditions for actual data 
compared to the estimated equivalent circuit 
modeling. The accuracy level is excellent if the 
prediction data is close to the actual data. The blue 
graph shows the true SOC obtained using equation 
(6) from the estimation results. The true SOC will 
compare the ANFIS estimator shown in the red 
graph for the triangular membership function, the 
yellow graph for the trapezoidal membership 
function, and the green graph is the gaussian 
membership function. Table 4 shows the results of 

 

(a) 

 

  

(b) 

 

Figure 6. (a) Charging Current and Voltage; (b) Discharging Current and Voltage 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 
 

 

67 

calculating the average error value in the SOC 
estimation with previous research using the 
equivalent circuit model. The SOC estimation 
research using ANFIS showed better results than the 
Extended Kalman Filter method. 

B. Experimental results  

This research uses a hardware design, as shown 
in Figure 8, with the results presented using MATLAB 
to determine the performance of ANFIS for 
estimating the state of charge. Observation of 
voltage and current on charging and discharging 

conditions using the Yokogawa DL-3031 
Oscilloscope with programmable DC power supply, 
which functions as a charger, and DC electronic load 
as a load that works to represent use as energy 
storage in electric vehicles and other electrical 
applications. 

The charging uses constant current from 
programmable DC power supply mode by testing 
various current values to obtain varying charging 
conditions. Ultracapacitor charging on real hardware 
was taken using a Yokogawa DL-3031 Oscilloscope 
with an increase in terminal voltage from the initial 
condition to full 13.5 Volts and a variable constant 
current. From the characteristic test carried out with 
the results in Figure 9, a calculation analysis can be 
carried out to determine the internal parameters of 
the Ultracapacitor with equation (3) to determine 
the value of equivalent parallel resistance, equation 
(4) to determine the value of equivalent series 

(a) 

 
  

(b) 

 

Figure 7. (a) Estimations SOC ANFIS with various MF on charging; (b) Estimations SOC ANFIS with various MF on discharge 

 

Table 3. 
Comparison estimation SOC with various membership functions 

ANFIS membership  
function 

RMSE MSE MAE MAPE 

Charge Discharge Charge Discharge Charge Discharge Charge Discharge 

Triangular 0.0201377 0.0198281 0.0004055 0.0003932 0.0004027 0.0003965 0.7085133 0.8398471 

Trapezoidal 0.0201625 0.0197755 0.0004065 0.0003911 0.0004032 0.0003954 0.8328958 1.1025848 

Gaussian 0.0201474 0.0197879 0.0004059 0.0003916 0.0004029 0.0003957 0.7569106 1.0405872 

 

Table 4. 
Comparison with previous research 

Methods 
Average error 

Charge Discharge 

ECM-EKF [2][22] <5.00 % <5.00 % 

ECM-ANFIS 0.99 % 0.92 % 
 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 

 

68 

resistance, and equation (5) to determine the value 
of capacitance. 

Based on the characteristic test data shown in 
Table 5 with the variation of the current source, it is 

known that the average value of equivalent series 
resistance (𝑅𝑠)  is 0.10828 Ω, equivalent parallel 
resistance (𝑅𝑝) 26.006 Ω, and capacitance (𝐶) 80.748 
Farads. Changes in the capacitance value from its 

(a) 

 

             (b) 

 

Figure 8. (a) Experimental setup; (b) Ultracapacitor energy storage system 

 

(a) 

 
  

(b) 

 
Figure 9. Ultracapacitor characteristic testing (a) 5A, 10 A, and 15 A testing; (b) 15 A, 20 A, and 25 A testing 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 
 

 

69 

original condition can be caused by being degraded 
due to use. Meanwhile, the value of 𝑅𝑠 can is caused 
by the connecting conductor on each Ultracapacitor. 
After testing the characteristics and getting actual 
parameters on the hardware, testing is carried out to 
determine the success of the estimation process. 
Current sources with varying random values are 
used for the charging process to determine the 
ANFIS capability built to accurately estimate the SOC 
value. Figure 10 is a charging process with a random 

current, making the voltage increase in the 
Ultracapacitor non-linear. Therefore, ANFIS can be 
relied on to handle these conditions. 

Figure 11 shows that the estimation graph using 
ANFIS with three different membership functions 
has results that coincide with true SOC conditions. 
However, out of the three ANFIS membership 
functions used, the triangular membership function 
has the most superior performance, with the lowest 
MAPE at 0.76 %.  

In Figure 12, the following data is presented for 
the calculation of RMSE, MSE, MAE, and MAPE from 
the comparison between the true SOC value and the 
estimated SOC using various ANFIS membership 
functions. 

Based on hardware experiments, the results of 
the error calculation using the RMSE, MSE, MAE, and 
MAPE methods are shown to determine the 
performance of ANFIS in estimating the state of 

Table 5. 
Ultracapacitor parameter value from characteristic test results 

Charging current 𝑹𝒔 𝑹𝒑 𝑪 
5 A 0.1266 30.04 80.91 

10 A 0.1147 25.11 81.35 

15 A 0.1066 24.15 80.19 

20 A 0.0970 25.15 81.29 

25 A 0.0965 25.58 80 
 

 

 
Figure 10. Charging current (top) and voltage (bottom) 

 
 

 
Figure 11. Estimations of SOC ANFIS with various MF 



R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 

 

70 

charge on the ultracapacitor. The chart above is the 
result of a comparison of the estimation results by 
ANFIS with three different memberships, namely 
triangular, trapezoidal, and gaussian, to determine 
the most efficient form of membership function in 
the estimation process. The blue chart represents the 
performance of the triangular membership function, 
the orange chart represents the performance of the 
trapezoidal membership function, and the gray chart 
represents the performance of the gaussian 
membership function from the error calculation 
results using the four relevant methods used as a 
reference to determine learning performance. 

IV. Conclusion 
Based on the research results to estimate SOC, 

the equivalent circuit model is a relevant circuit for 
Ultracapacitor modeling because it has a simple and 
accurate model. It is also supported by ANFIS 
intelligence as an estimator capable of estimating 
the SOC value with high accuracy. ANFIS with 
triangular membership function as a method for 
predicting SOC estimation on ultracapacitors works 
optimally and has high accuracy with MAPE 
calculation of 0.70 % for charging while 0.83 % for 
discharging compared to true SOC. While in the 
hardware experiment, the results of the SOC 
estimation with the triangular membership function 
are small at 0.76 %. It is hoped that SOC research can 
develop with simplification and better performance 
in the future. Ultracapacitors as energy storage 
devices, both hybrid and primary, can be developed 
and applied to electric vehicles and other electronic 
applications because of their excellent performance. 

Acknowledgment 

The authors are grateful to Politeknik Elektronika 
Negeri Surabaya and Renewable Energy Laboratory 
for the permission to use the Ultracapacitor for this 
research and to publish this paper. We would also 
like to thank those who have helped and supported 
us in preparing this manuscript. 

Declarations 
Author contribution  

Rizal Nurdiansyah: Writing - Original Draft, Writing - 
Review & Editing, Conceptualization, Software, Hardware, 
Formal analysis, Investigation, Visualization, Validation. 
Novie Ayub Windarko: Writing - Original Draft, Formal 
analysis, Conceptualization, Investigation, Visualization, 
Validation, Data Curation, Resources, Supervision. Renny 
Rakhmawati: Formal analysis, Conceptualization, 
Investigation, Supervision. Muhammad Abdul Haq: Formal 
analysis, Supervision. 

Funding statement  

This research did not receive any specific grant from 
funding agencies in the public, commercial, or not-for-
profit sectors.  

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.  

Additional information  

Reprints and permission: information is available at 
https://mev.lipi.go.id/. 

Publisher’s Note: National Research and Innovation 
Agency (BRIN) remains neutral with regard to jurisdictional 
claims in published maps and institutional affiliations. 

References 
[1] C. Liu, Q. Li, and K. Wang, “State-of-charge estimation and 

remaining useful life prediction of supercapacitors,” Renew. 
Sustain. Energy Rev., vol. 150, p. 111408, Oct. 2021. 

[2] A. Afandi, B. Sumantri, and N. A. Windarko, “Estimation state 
of charge (SOC) of Ultracapacitor based on classical equivalent 
circuit using Extended Kalman Filter,” in 2020 International 
Electronics Symposium (IES), Surabaya, Indonesia, Sep. 2020, 
pp. 31–36. 

[3] P. Fornaro, P. Puleston, and P. Battaiotto, “On-line parameter 
estimation of a Lithium-Ion battery/supercapacitor storage 
system using filtering sliding mode differentiators,” J. Energy 
Storage, vol. 32, p. 101889, Dec. 2020. 

[4] K. Alobeidli and V. Khadkikar, “A new Ultracapacitor state of 
charge control concept to enhance battery lifespan of dual 
storage electric vehicles,” IEEE Trans. Veh. Technol., vol. 67, no. 
11, pp. 10470–10481, Nov. 2018. 

[5] T. Rout, A. Chowdhury, M. K. Maharana, and S. Samal, 
“Analysis of energy management system for photovoltaic 

 

Figure 12. SOC estimation error values with method calculations: RMSE, MSE, MAE, and MAPE 

https://mev.lipi.go.id/
https://doi.org/10.1016/j.rser.2021.111408
https://doi.org/10.1016/j.rser.2021.111408
https://doi.org/10.1016/j.rser.2021.111408
https://doi.org/10.1109/ies50839.2020.9231736
https://doi.org/10.1109/ies50839.2020.9231736
https://doi.org/10.1109/ies50839.2020.9231736
https://doi.org/10.1109/ies50839.2020.9231736
https://doi.org/10.1109/ies50839.2020.9231736
https://doi.org/10.1016/j.est.2020.101889
https://doi.org/10.1016/j.est.2020.101889
https://doi.org/10.1016/j.est.2020.101889
https://doi.org/10.1016/j.est.2020.101889
https://doi.org/10.1109/tvt.2018.2871038
https://doi.org/10.1109/tvt.2018.2871038
https://doi.org/10.1109/tvt.2018.2871038
https://doi.org/10.1109/tvt.2018.2871038
https://doi.org/10.1109/icsesp.2018.8376737
https://doi.org/10.1109/icsesp.2018.8376737


R. Nurdiansyah et al. / Journal of Mechatronics, Electrical Power, and Vehicular Technology 13 (2022) 60-71 
 

 

71 

system with battery and supercapacitor using fuzzy logic 
controller,” in 2018 Technologies for Smart-City Energy 
Security and Power (ICSESP), Bhubaneswar, Mar. 2018, pp. 1–
4. 

[6] A. Amin, K. Ismail, and A. Hapid, “Implementation of a LiFePO4 
battery charger for cell balancing application,” J. Mechatron. 
Electr. Power Veh. Technol., vol. 9, no. 2, p. 81, Dec. 2018. 

[7] B. Traore, M. Doumiati, C. Morel, J.-C. Olivier, and O. Soumaoro, 
“Energy management strategy based on a new adaptive 
filtering algorithm for battery-ultracapacitor electric vehicles,” 
in 2020 15th IEEE Conference on Industrial Electronics and 
Applications (ICIEA), Kristiansand, Norway, Nov. 2020, pp. 
392–396. 

[8] A. R. Al Tahtawi and A. S. Rohman, “Simple supercapacitor 
charging scheme of an electric vehicle on small-scale 
hardware simulator: a prototype development for education 
purpose,” J. Mechatron. Electr. Power Veh. Technol., vol. 7, no. 
2, pp. 77–86, Dec. 2016. 

[9] H. Yang, “Estimation of supercapacitor charge capacity bounds 
considering charge redistribution,” IEEE Trans. Power 
Electron., vol. 33, no. 8, pp. 6980–6993, Aug. 2018. 

[10] Q. Zhu et al., “A new view of supercapacitors: Integrated 
supercapacitors,” Adv. Energy Mater., vol. 9, no. 36, p. 
1901081, Sep. 2019. 

[11] H. Jiang, L. Xu, J. Li, Z. Hu, and M. Ouyang, “Energy 
management and component sizing for a fuel 
cell/battery/supercapacitor hybrid powertrain based on two-
dimensional optimization algorithms,” Energy, vol. 177, pp. 
386–396, Jun. 2019. 

[12] I. Jarraya, F. Masmoudi, M. H. Chabchoub, and H. Trabelsi, “An 
online state of charge estimation for Lithium-ion and 
supercapacitor in hybrid electric drive vehicle,” J. Energy 
Storage, vol. 26, p. 100946, Dec. 2019. 

[13] S. Hussain, M. U. Ali, G.-S. Park, S. H. Nengroo, M. A. Khan, and 
H.-J. Kim, “A real-time bi-adaptive controller-based energy 
management system for battery–supercapacitor hybrid 
electric vehicles,” Energies, vol. 12, no. 24, p. 4662, Dec. 2019. 

[14] C-T. Ma, “Design and implementation of a hybrid real-time 
state of charge estimation scheme for battery energy storage 
systems,” Processes, vol. 8, no. 1, p. 2, Dec. 2019. 

[15] H. Yang, “Application of Peukert’s law in supercapacitor 
discharge time prediction,” J. Energy Storage, vol. 22, pp. 98–
105, Apr. 2019. 

[16] P. Venugopal, “State-of-charge estimation methods for li-ion 
batteries in electric vehicles,” International Journal of 
Innovative Technology and Exploring Engineering (IJITEE), vol. 
8, no. 7, p. 11, 2019. 

[17] Poonam, K. Sharma, A. Arora, and S. K. Tripathi, “Review of 
supercapacitors: Materials and devices,” J. Energy Storage, vol. 
21, pp. 801–825, Feb. 2019. 

[18] H. Chaoui and H. Gualous, “Online lifetime estimation of 
supercapacitors,” IEEE Trans. Power Electron., vol. 32, no. 9, 
pp. 7199–7206, Sep. 2017. 

[19] L. Rozaqi, E. Rijanto, and S. Kanarachos, “Comparison between 
RLS-GA and RLS-PSO for Li-ion battery SOC and SOH 
estimation: a simulation study,” J. Mechatron. Electr. Power 
Veh. Technol., vol. 8, no. 1, pp. 40–49, Jul. 2017. 

[20] P. Saha, S. Dey, and M. Khanra, “Accurate estimation of state-
of-charge of supercapacitor under uncertain leakage and open 

circuit voltage map,” J. Power Sources, vol. 434, p. 226696, 
Sep. 2019. 

[21] M. A. Awadallah and B. Venkatesh, “Accuracy improvement of 
SOC estimation in lithium-ion batteries,” J. Energy Storage, vol. 
6, pp. 95–104, May 2016. 

[22] Z. Tao, G. Shaoting, L. Xin, and J. Jing, “SOC estimation scheme 
of super capacitor based on Calman filter,” in 2016 IEEE 11th 
Conference on Industrial Electronics and Applications (ICIEA), 
Hefei, China, Jun. 2016, pp. 918–921. 

[23] J. Wang, L. Zhang, J. Mao, J. Zhou, and D. Xu, “Fractional order 
equivalent circuit model and SOC estimation of 
supercapacitors for use in HESS,” IEEE Access, vol. 7, pp. 
52565–52572, 2019. 

[24] J. I. Hidalgo-Reyes, J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, 
V. M. Alvarado-Martínez, and M. G. López-López, “Classical 
and fractional-order modeling of equivalent electrical circuits 
for supercapacitors and batteries, energy management 
strategies for hybrid systems and methods for the state of 
charge estimation: A state of the art review,” Microelectron. J., 
vol. 85, pp. 109–128, Mar. 2019. 

[25] L. Zhang, X. Hu, Z. Wang, F. Sun, and D. G. Dorrell, “A review of 
supercapacitor modeling, estimation, and applications: A 
control/management perspective,” Renew. Sustain. Energy 
Rev., vol. 81, pp. 1868–1878, Jan. 2018. 

[26] M. R. Djalal, H. Setiadi, and A. Imran, “Frequency stability 
improvement of micro hydro power system using hybrid SMES 
and CES based on Cuckoo search algorithm,” J. Mechatron. 
Electr. Power Veh. Technol., vol. 8, no. 2, pp. 76–84, Dec. 2017. 

[27] M. E. Şahin, F. Blaabjerg, and A. Sangwongwanich, “Modelling 
of supercapacitors based on simplified equivalent circuit,” 
CPSS Trans. Power Electron. Appl., vol. 6, no. 1, pp. 31–39, Mar. 
2021. 

[28] M. Rif’an, F. Yusivar, and B. Kusumoputro, “Sensorless-BLDC 
motor speed control with ensemble Kalman filter and neural 
network,” J. Mechatron. Electr. Power Veh. Technol., vol. 10, 
no. 1, pp. 1–6, Dec. 2019. 

[29] K. Faqih, S. Sujito, S. Sendari, and F. S. Aziz, “Smart guided 
missile using accelerometer and gyroscope based on 
backpropagation neural network method for optimal control 
output feedback,” J. Mechatron. Electr. Power Veh. Technol., 
vol. 11, no. 2, pp. 55–63, Dec. 2020. 

[30] A. Soualhi et al., “Heath monitoring of capacitors and 
supercapacitors using the neo-fuzzy neural approach,” IEEE 
Trans. Ind. Inform., vol. 14, no. 1, pp. 24–34, Jan. 2018. 

[31] A. Fotouhi, D. J. Auger, K. Propp, and S. Longo, “Lithium–sulfur 
battery state-of-charge observability analysis and estimation,” 
IEEE Trans. Power Electron., vol. 33, no. 7, pp. 5847–5859, Jul. 
2018. 

[32] K. V. Singh, H. O. Bansal, and D. Singh, “Hardware-in-the-loop 
implementation of ANFIS based adaptive SoC estimation of 
lithium-ion battery for hybrid vehicle applications,” J. Energy 
Storage, vol. 27, p. 101124, Feb. 2020. 

[33] H. Suryoatmojo, M. Ridwan, D. C. Riawan, E. Setijadi, and R. 
Mardiyanto, “Hybrid particle swarm optimization and 
recursive least square estimation based ANFIS multioutput for 
BLDC motor speed controller,” International Journal of 
Innovative Computing, Information and Control (ICIC), vol. 15, 
no. 3, June 2019.  
 

 
 

https://doi.org/10.1109/icsesp.2018.8376737
https://doi.org/10.1109/icsesp.2018.8376737
https://doi.org/10.1109/icsesp.2018.8376737
https://doi.org/10.1109/icsesp.2018.8376737
https://doi.org/10.14203/j.mev.2018.v9.81-88
https://doi.org/10.14203/j.mev.2018.v9.81-88
https://doi.org/10.14203/j.mev.2018.v9.81-88
https://doi.org/10.1109/iciea48937.2020.9248112
https://doi.org/10.1109/iciea48937.2020.9248112
https://doi.org/10.1109/iciea48937.2020.9248112
https://doi.org/10.1109/iciea48937.2020.9248112
https://doi.org/10.1109/iciea48937.2020.9248112
https://doi.org/10.1109/iciea48937.2020.9248112
https://doi.org/10.14203/j.mev.2016.v7.77-86
https://doi.org/10.14203/j.mev.2016.v7.77-86
https://doi.org/10.14203/j.mev.2016.v7.77-86
https://doi.org/10.14203/j.mev.2016.v7.77-86
https://doi.org/10.14203/j.mev.2016.v7.77-86
https://doi.org/10.1109/tpel.2017.2764423
https://doi.org/10.1109/tpel.2017.2764423
https://doi.org/10.1109/tpel.2017.2764423
https://doi.org/10.1002/aenm.201901081
https://doi.org/10.1002/aenm.201901081
https://doi.org/10.1002/aenm.201901081
https://doi.org/10.1016/j.energy.2019.04.110
https://doi.org/10.1016/j.energy.2019.04.110
https://doi.org/10.1016/j.energy.2019.04.110
https://doi.org/10.1016/j.energy.2019.04.110
https://doi.org/10.1016/j.energy.2019.04.110
https://doi.org/10.1016/j.est.2019.100946
https://doi.org/10.1016/j.est.2019.100946
https://doi.org/10.1016/j.est.2019.100946
https://doi.org/10.1016/j.est.2019.100946
https://doi.org/10.3390/en12244662
https://doi.org/10.3390/en12244662
https://doi.org/10.3390/en12244662
https://doi.org/10.3390/en12244662
https://doi.org/10.3390/pr8010002
https://doi.org/10.3390/pr8010002
https://doi.org/10.3390/pr8010002
https://doi.org/10.1016/j.est.2019.01.022
https://doi.org/10.1016/j.est.2019.01.022
https://doi.org/10.1016/j.est.2019.01.022
https://www.ijitee.org/wp-content/uploads/papers/v8i7/F3430048619.pdf
https://www.ijitee.org/wp-content/uploads/papers/v8i7/F3430048619.pdf
https://www.ijitee.org/wp-content/uploads/papers/v8i7/F3430048619.pdf
https://www.ijitee.org/wp-content/uploads/papers/v8i7/F3430048619.pdf
https://doi.org/10.1016/j.est.2019.01.010
https://doi.org/10.1016/j.est.2019.01.010
https://doi.org/10.1016/j.est.2019.01.010
https://doi.org/10.1109/tpel.2016.2629440
https://doi.org/10.1109/tpel.2016.2629440
https://doi.org/10.1109/tpel.2016.2629440
https://doi.org/10.14203/j.mev.2017.v8.40-49
https://doi.org/10.14203/j.mev.2017.v8.40-49
https://doi.org/10.14203/j.mev.2017.v8.40-49
https://doi.org/10.14203/j.mev.2017.v8.40-49
https://doi.org/10.1016/j.jpowsour.2019.226696
https://doi.org/10.1016/j.jpowsour.2019.226696
https://doi.org/10.1016/j.jpowsour.2019.226696
https://doi.org/10.1016/j.jpowsour.2019.226696
https://doi.org/10.1016/j.est.2016.03.003
https://doi.org/10.1016/j.est.2016.03.003
https://doi.org/10.1016/j.est.2016.03.003
https://doi.org/10.1109/iciea.2016.7603713
https://doi.org/10.1109/iciea.2016.7603713
https://doi.org/10.1109/iciea.2016.7603713
https://doi.org/10.1109/iciea.2016.7603713
https://doi.org/10.1109/access.2019.2912221
https://doi.org/10.1109/access.2019.2912221
https://doi.org/10.1109/access.2019.2912221
https://doi.org/10.1109/access.2019.2912221
https://doi.org/10.1016/j.mejo.2019.02.006
https://doi.org/10.1016/j.mejo.2019.02.006
https://doi.org/10.1016/j.mejo.2019.02.006
https://doi.org/10.1016/j.mejo.2019.02.006
https://doi.org/10.1016/j.mejo.2019.02.006
https://doi.org/10.1016/j.mejo.2019.02.006
https://doi.org/10.1016/j.mejo.2019.02.006
https://doi.org/10.1016/j.rser.2017.05.283
https://doi.org/10.1016/j.rser.2017.05.283
https://doi.org/10.1016/j.rser.2017.05.283
https://doi.org/10.1016/j.rser.2017.05.283
https://doi.org/10.14203/j.mev.2017.v8.76-84
https://doi.org/10.14203/j.mev.2017.v8.76-84
https://doi.org/10.14203/j.mev.2017.v8.76-84
https://doi.org/10.14203/j.mev.2017.v8.76-84
https://doi.org/10.24295/cpsstpea.2021.00003
https://doi.org/10.24295/cpsstpea.2021.00003
https://doi.org/10.24295/cpsstpea.2021.00003
https://doi.org/10.24295/cpsstpea.2021.00003
https://doi.org/10.14203/j.mev.2019.v10.1-6
https://doi.org/10.14203/j.mev.2019.v10.1-6
https://doi.org/10.14203/j.mev.2019.v10.1-6
https://doi.org/10.14203/j.mev.2019.v10.1-6
https://doi.org/10.14203/j.mev.2020.v11.55-63
https://doi.org/10.14203/j.mev.2020.v11.55-63
https://doi.org/10.14203/j.mev.2020.v11.55-63
https://doi.org/10.14203/j.mev.2020.v11.55-63
https://doi.org/10.14203/j.mev.2020.v11.55-63
https://doi.org/10.1109/tii.2017.2701823
https://doi.org/10.1109/tii.2017.2701823
https://doi.org/10.1109/tii.2017.2701823
https://doi.org/10.1109/tpel.2017.2740223
https://doi.org/10.1109/tpel.2017.2740223
https://doi.org/10.1109/tpel.2017.2740223
https://doi.org/10.1109/tpel.2017.2740223
https://doi.org/10.1016/j.est.2019.101124
https://doi.org/10.1016/j.est.2019.101124
https://doi.org/10.1016/j.est.2019.101124
https://doi.org/10.1016/j.est.2019.101124
https://doi.org/10.24507/ijicic.15.03.939
https://doi.org/10.24507/ijicic.15.03.939
https://doi.org/10.24507/ijicic.15.03.939
https://doi.org/10.24507/ijicic.15.03.939
https://doi.org/10.24507/ijicic.15.03.939
https://doi.org/10.24507/ijicic.15.03.939

	Introduction
	II. Materials and Methods
	A. Ultracapacitor modeling
	B. State of charge estimation
	C. Adaptive neuro-fuzzy inference system (ANFIS)
	1) Layer 1
	2) Layer 2
	3) Layer 3
	4) Layer 4
	5) Layer 5


	III. Results and Discussions
	A. Simulation results 
	Experimental results 

	IV. Conclusion
	Acknowledgment
	Declarations
	Author contribution 
	Funding statement 
	Competing interest 
	Additional information 

	References