ANFIS Based DC Offset Removal Technique for
Numerical Distance Relaying
Ola A. Ananbeh
Electrical Engineering Department
The University of Jordan
Amman, Jordan
o.ananbeh@ju.edu.jo
Eyad A. Feilat
Electrical Engineering Department
The University of Jordan
Amman, Jordan
e.feilat@ju.edu.jo
Abstract— In this paper, an adaptive neuro-fuzzy inference
system (ANFIS) is proposed to extract the fundamental
component of the fault current utilizing the advantages of fuzzy
logic and neural networks. The grey wolf optimizer algorithm
(GWO) is utilized to estimate the fault current parameters. The
proposed model is tested using both synthesized and simulated
signals using Matlab software. The simulation is performed for
different operating conditions by altering DC decaying current,
time constant, harmonics, fault locations, fault resistance, and
inception angels. The performance of the proposed technique is
compared with that of the half cycle discrete Fourier transform
(HCDFT) in the presence of the DC decaying current. The
simulation results show that the ANFIS based technique
accurately estimates the DC decaying current and extracts the
fundamental component from the fault current within half a
cycle following fault inception.
Keywords—digital relaying, distance protection, ANFIS, grey
wolf optimizer, signal processing, dc decaying offset
I.
INTRODUCTION
Digital relays are implemented in the transmission lines
protection system to prevent equipment damage by isolating
the infected section where a fault may occur. Distance relays
are the most commonly used relays because of their quick
response in solving the problem. The relay should accurately
estimate the fundamental component of the fault current to
evaluate the impedance from the fault location to the relay.
Usually, the digital relays utilize Discrete Fourier Transform
to estimate the fundamental component of the fault current.
The presence of the DC decaying component in the fault
current causes mal-operation of the digital relay and hence
leads to undesired circuit tripping in the non-faulted section of
the transmission line due to impedance relay overreach [1-2].
The setting value of the protection relay is set based on the
system fundamental current and voltage in impedance relays.
Therefore, to achieve accurate fault detection, the fundamental
current component must be extracted from the fault current
signal. Eliminating the DC component from the fault current
signal will guarantee the selectivity, security, and
dependability of the impedance or overcurrent protection
scheme [3].
Several studies have been made to solve the DC decaying
problem either by directly detecting the fundamental
component or by eliminating the DC decaying component [515]. These studies are classified, based on the methodology of
finding the DC component, into three basic techniques. In the
first technique, the DC component is initially estimated and
then subtracted from the original fault current signal. Filterigbased techniques are used directly to extract the fundamental
current component without removing the DC decaying current
component. Moreover, both DC decaying current and
Dia Abu Al Nadi
Electrical Engineering Department
The University of Jordan
Amman, Jordan
dnadi@ju.edu.jo
harmonic current components are extracted simultaneously
using advanced signal processing techniques [7-15].
In this paper, an adaptive neuro-fuzzy inference system
(ANFIS) model is implemented for fast and accurate removal
of the DC decaying current and other harmonics components
that might exist in the fault current signal and hence accurate
detection of the impedance seen by the distance relay. The
effects of changig the magnitide of the dc component, time
constant, and fault location on the performance of the
proposed are investigated. Comparison with half-cycle
discrete Fourier transform is also examined [4-6].
II.
CURRENT WAVEFORM DURING FAULT
During normal operating conditions of power systems, the
current waveforms have pure sinusoidal forms of nominal
50/60 Hz power frequency. However, when a fault occurs on
a transmission line, a decaying DC component appears. The
fault current signal can be expressed as [4]:
𝑝
𝑖(𝑡) = 𝐼𝑂 𝑒 −𝑡⁄𝜏 + ∑𝑛=1 𝐼𝑛 𝑠𝑖𝑛(𝑛𝜔𝑡 + 𝜃𝑛 )
(1)
where Io represents the DC component magnitude,  is the
time constant, p is the maximum harmonic order, 𝜔 is the
angular frequency, and In and 𝜃𝑛 is the amplitude and the
phase of the nth harmonic current, respectively. The DC time
constant  varies depending on the X/R of the faulted line,
fault location and fault resistance [5]. As polynomial
representation of nonlinear functions is easy to study, the
exponential term e-t/ can be expanded using Taylor series. By
utilizing the first two terms of Taylor’s series expansion, the
fault current can be represented as [3]:
𝒑
𝒊(𝒕) = 𝑰𝑶 (𝟏 − 𝒕⁄𝝉) + ∑𝒏=𝟏 𝑰𝒏 𝒔𝒊𝒏(𝒏𝝎𝒕 + 𝜽𝒏 )
(2)
In the proposed technique, the DC offset removal is achieved
as follows. First, the parameters of the fault current signal
including Io,  , In and n, are determined using the GWO
algorithm. Second, input-output patterns that includes
samples of the current signal over one cycle as input patterns
and the corresponding current signal parameters as output
patterns are generated for several cases of fault location, fault
resistance and inception angle. Then, these input-output
patterns are used to train the ANFIS network. Finally, the
performance of the proposed technique is tested under
different fault conditions to assess the performance and
effectiveness of the proposed technique.
III.
GREY WOLF OPTIMIZEER
Metaheuristic optimization algorithms are becoming
popular in recent years due to their robustness and
effectiveness in optimal parameter estimation. In GWO
algorithm, the search is guided by three best wolves in each
iteration. In each iteration, the GWO has two candidates,
generated by the GWO to move the wolf xi form its position
to a better position. The flowchart of the GWO is depicted in
Fig. 1 [16-18].
𝑋𝑖2 (𝑡) = 𝑋𝛽 (𝑡) − 𝐴𝑖2 × 𝐷𝛽 (𝑡)
𝑋𝑖3 (𝑡) = 𝑋𝛿 (𝑡) − 𝐴𝑖3 × 𝐷𝛿 (𝑡)
𝑋(𝑡 + 1) =
Initialize parameters, randomly generated wolves
𝑋𝑖1 (𝑡)+ 𝑋𝑖2 (𝑡)+𝑋𝑖3 (𝑡)
3
𝐷 = |𝐶 × 𝑋𝑝 (𝑡) − 𝑋(𝑡)|
𝑅𝑖 (𝑡) = ‖ 𝑋𝑖 (𝑡) − 𝑋𝑖−𝐺𝑊𝑂 (𝑡 + 1)‖
Calculate fitness, choose the first three best
wolves α, β and δ
Update position of W wolf
Evaluation operation, after crossover and
selection, select good individuals as next
generation then update α, β and δ
Update wolves, eliminate R worst wolves, and
randomly generate R new wolves
Update parameters α, A and C
Yes
Iter < max_itr
No
Output the position and
fitness value of wolf α
Fig. 1.
GWO Flowchart
The GWO algorithm includes three phases:
A. Initializing phase
An N wolves are distributed in the search space randomly
in a given range, the whole population of wolves are stored in
a Pop matrix which has N rows and D columns, where D is a
problem dimension number.
B. Movement phase
In GWO, for each wolf a new position is allocated to help
the three leaders. As a group hunting, each individual wolf
learns from the other candidates to be in a new position Xi(t).
In the Canonical GWO search strategy, the best three wolves
are considered as α, β and δ and the linearly decreased
coefficients a, A and C are found by Eqs. (3), (4) and (5). The
prey encircling founded by the positions Xα, Xβ and Xδ is
calculated using Eq. (6). The new candidate for the new
position and each new position dimension are calculated
using Eqs. (7) and (8), respectively. Using Euclidean
distance, Ri (t) a radius between the candidate position and the
current position is determined as given in Eq. (9). These
equations describe the hunting behavior. When the prey stops
moving, the wolves start to attack and the hunting process
stops.
𝐴 = 2 × 𝑎 × 𝑟1 − 𝑎(𝑡)
(3)
𝐶 = 2 × 𝑟2
(4)
𝑎(𝑡) = 2 − (2 × 𝑡)/𝑀𝑎𝑥𝐼𝑡𝑒𝑟
(5)
𝑋𝑖1 (𝑡) = 𝑋𝛼 (𝑡) − 𝐴𝑖1 × 𝐷𝛼 (𝑡)
(6)
(7)
(8)
(9)
C. Selecting and updating phase
By comparing the fitness value of the GWO and DLH
candidates, the superior candidate is selected. If the fitness
value of the selected candidate less than the previous position,
the new position is updated. Otherwise, the position remains
unchanged on the population. Next, the iteration is increased
by one until the maximum iterations is reached [19, 20].
IV.
ANFIS ARCHITECTURE
The adaptive neuro-fuzzy inference system (ANFIS) is one
type of artificial neural networks (ANNs) based on the
Takagi–Sugeno fuzzy inference system. This type of network
is a combination of neural network and fuzzy logic principles
where the input-output relationship is represented based on a
set of If-Then rules. This mixture gives ANFIS the benefits
of both models. The fuzzy system can be thought as a neural
network structure with knowledge distributed via connection
strengths because of the advantage of allowing a simple
translation of the final system into a set of If-Then rules. The
inference system in ANFIS is agreed with If-Then rules
which have the ability to approximate non-linear functions
[18, 19]. The adaptive system determines the parameters of
Sugeno type fuzzy inference system by applying a hybrid
learning algorithm that combines the least squares (LS)
method and the backpropagation gradient descent method for
training FIS membership function parameters to simulate a
given training data.
A. ANFIS architecture Analysis
An architecture of an ANFIS that consists of five layers and
two-fuzzy rules is shown in Fig. 2.
Rule 1: if (X1 is A1) and (X2 is B1) then (fi=p1Xl+q1X2+rl)
Rule 2: if (X1 is A2) and (X2 is B2) then (f2=p2X1+q2X2+r2)
Commonly, the ANFIS has five layers:
Layer 1 (Fuzzification layer)
In this layer, each node is an adaptive node that generates a
membership grade of the linguistic label. The output of the
ith node of the first layer O1,i is given as:
𝑂1,𝑖 =µ𝐴𝑖 (𝑥)
(10)
where the value of µ𝐴𝑖 (𝑥) depends on the corresponding
membership function. For example, if a bell membership
function is used, then:
1
µ𝑖 (𝑥) =
(11)
𝑏 , 𝑖 = 1,2, …
𝑥−𝑐 2 𝑖
1+[( 𝑎 𝑖 ) ]
𝑖
where ai, bi, and ci are the parameters for the bell membership
function that adjusts the center and the width of the
membership function. The type of the membership function
can be changed according to the problem to improve the
performance of the ANFIS model. The first layer’s
parameters are called premise parameters.
Layer 2 (Fuzzy rule layer)
In this layer, each node is a fixed node (not adaptive) where
its output is the product of all the incoming signals from the
first layer which is defined as:
𝑂2,𝑖 = µ𝐴𝑖 (𝑥)µ𝐵𝑖 (𝑦), 𝑖 = 1,2, …
(12)
Layer 3 (Normalization layer)
In this layer, every node is a fixed node labeled with “N” as
shown in Fig. 1. Each node calculates the ratio of the ith rule’s
firing strength to the sum of all rules’ firing strengths as
follows:
𝑖
𝑂3,𝑖 = ̅̅̅
𝑤𝑖 = 𝑤1𝑤+𝑤
, 𝑖 = 1,2, …
(13)
2
Layer 4 (Output membership layer)
Every node in this layer is an adaptive node with a node
function given by:
𝑂4,𝑖 = ̅̅̅𝑓
𝑤𝑖 𝑖 = ̅̅̅(
𝑤𝑖 𝑝𝑖 𝑥 + 𝑞𝑖 𝑦 + 𝑟𝑖 )
(14)
where wi is the normalized firing strength from layer 3, pi,
qi, and ri are the set of consequent parameters.
Layer 5 (Defuzzification layer)
This layer has a single output which is the summation of all
incoming signals from layer 4. Thus, the overall output is:
∑
𝑂5,𝑖 = ∑𝑖 ̅̅̅𝑓
𝑤𝑖 𝑖 = ∑𝑖 𝑤𝑤𝑖𝑓𝑖 , i=1,2,…
(15)
𝑖 𝑖
In sum, when the values of the premise parameters are fixed,
the adaptive network's total output can be described as a
linear combination of subsequent parameters. Thus, the
function of a constructed network is identical to that of a
Sugeno fuzzy model and can be expressed as a function of
consequent parameters as follows:
𝑤1
𝑤2
𝑓=
𝑓 +
𝑓
𝑤1 + __𝑤2 1 __𝑤1 + 𝑤2 2
= 𝑤1 𝑓1 + 𝑤2 𝑓2
= (𝑤
̅̅̅1̅𝑥)𝑝1 + (𝑤
̅̅̅1̅𝑦)𝑞1 + (𝑤
̅̅̅1̅)𝑟1 + (𝑤
̅̅̅̅𝑥)𝑝
̅̅̅̅𝑦)𝑞
2
2 + (𝑤
2
2+
(𝑤
̅̅̅̅)𝑟
(16)
2 2
Fig. 2. Basic ANFIS architecture
B. ANFIS Training and Testing
The network learns in two main phases, the forward phase,
and the backward phase. In the forward phase, the least
square estimate is identified by the consequent parameters. In
the backward phase, the error signals propagate from the
output layer back to the input layer. These error signals are
the derivatives of the squared error for each output node. The
premise parameters in the backward phase are updated by
using the gradient descent algorithm. The training phase of
the neural network is a process of determining parameter
values that sufficiently fit the training data. The training
performance is assessed in terms of the root mean square
index (RMSE) given by:
𝑅𝑀𝑆𝐸 = √
̃
2
∑𝐾
𝑛=1(𝑂𝑛 −𝑂𝑛 )
𝐾
(17)
where 𝑂̃𝑛 is the nth actual output, 𝑂𝑛 is the nth target output
and K is the number of output patterns.
After training the ANFIS network, the generalization
capability of the network is assessed by examining its
performance using testing patterns that are different from the
training patterns. Usually, 80% of the data are used for
training phase whereas the remaining 20% of the data are
reserved for testing. Both training and testing patters are
selected randomly.
V.
PERFORMANCE EVALUATION AND SIMULATION
RESULTS
The performance of the proposed algorithm is evaluated by
using synthesized fault current signal and simulated fault
current signal in Matlab/Simulink software. The effectiveness
and robustness of the technique was assessed with respect to
variation of magnitude of the DC component, fundamental
components, harmonic component, time constant and
inception angle. The performance of the ANFIS network was
compared with that obtained by the HCDFT.
The proposed ANFIS network has five inputs that represent
five samples of the fault current sampled over a half cycle and
one output that represent one parameter of the fault current. In
this study, Gaussian-shaped member function were chosen.
After several cases of training, it was found that three
membership functions give the most accurate results. Several
ANFIS networks were trained simultaneously where the
number of the networks equals the number of current signal
parameters that will be estimated. The accuracy of training
was decided by fixing the number of training epochs up to 100
epochs.
A. Synthesized Fault Current Signal
Equation 2 is used to generate a synthesized fault current
signal. The signal is sampled at a sampling frequency of 500
Hz with 10 samples per cycle (50 Hz cycle) at a rate of 2 ms
per sample. This sampling frequency is high enough to extract
up to the 5th harmonic current component. A moving window
is applied every half cycle up to a window size of 5 cycles.
The input-output training patterns were generated by varying
the magnitudes of the fundamental component I1 and the DC
peak from 0.2–1.0 pu, the time constant  from 20 ms-100 ms,
the fault inception angle from 0o-90 o, 30% and 20% 3rd and
5th harmonic current components, respectively. The inputs
include samples of the current signal whereas the outputs
represent the parameters of the fault current signal. As a result,
a total of 8100 input-output patterns were generated to
examine the performance and generalization capabilities of
the proposed ANFIS network during training and testing
phases.
B. Computer-Simulated Fault Current Signal
In this part, the effectiveness of the proposed technique is
demonstrated by generating a fault current signal by
simulating a simple power system being protected by mho
distance relay Rab located at Bus a, as depicted in Fig. 3. The
system is comprised of two power sources connected through
a 240-km line rated for 132 kV voltage level. The line is
divided into three sections with positive-sequence impedance
Z1 = 0.068 + j0.38 Ω/km. Zone 1 of the relay is set to cover up
to 80% of the protected line impedance, Zone 2 covers 120 of
the protected line where as Zone 3 covers 100% of the
protected line and 100% of the adjacent line.
Fig. 3. Single-line diagram of the simulaated system
The fault current signal is obtained by solving the
governing differential equation using Euler numerical
integration method as follows [21]:
𝐸1 (𝑡) = 𝑥𝑅𝐿 𝑖(𝑡) + 𝑥𝐿𝐿
𝑑𝑖
𝑑𝑡
(18)
where xRL and xLL are the corresponding resistance and
inductance between the relay Rab and the fault location at
distance x. Using two consecutive samples ik and ik+1 sampled
at a sampling time t, the solution of the fault current is
obtained
𝑖𝑘+1 = 𝑖𝑘 +
∆𝑡
𝑥𝐿𝑓
( −𝑥𝑅𝐿 𝑖𝑘 + 𝐸1𝑘 )
(19)
(a) Current componnet (Io)
(b) Current componnet (Io/ )
Fig. 5. Estimated DC Components of the synthesized fault current
The estimated values of the fundamental current component
(I1) and the phase angle (1) of the synthesized fault current is
depicted in Fig 6. Examining both figures one can notice that
both components were estimated accurately as compared to
the actual values.
Equation (19) can be expanded using Fourier expansion as
𝑖(𝑡𝑘 ) = 𝐼𝑜 𝑒
−𝑡𝑘⁄
𝜏
+ 𝑎𝑛 sin(𝜔𝑛 𝑡𝑘 ) + 𝑏𝑛 cos(𝜔𝑛 𝑡𝑘 ) (20)
After obtaining the fault current, the GWO is applied to extract
the parameters of the fault current signals, namely Io, a1, b1
and . The magnitude and angle of the nth current component
can be calculated as follows
𝐼𝑛 = √𝑎𝑛2 + 𝑏𝑛2
𝜃𝑛 =
𝑏
𝑡𝑎𝑛−1 ( 𝑛 )
𝑎𝑛
(21)
(22)
Several three-phase faults at several locations in Zone 1
(10%-80%), Zone 2 (90%-120), and Zone 3 (13%-200%) in
steps of 10% are conducted at different fault inception angles
(0 o -90o) and with different fault resistances (0-10 ) are
conducted to generate the training and testing input-output
patterns. The current signal is sampled at 3000 Hz with 60
samples per cycle. Consequently, 4180 input-output patters
were generated.
(a) Magnitude of (I1)
(b) Phase angle (1)
Fig. 6. Estimated values of the fundamental current componnet (I1) and
phase angle (1) of the synthesized fault current
Likewise, the magnitudes of the third and fifth harmonic
components (I3) and (I5) of the synthesized fault current
were exactly estimated as demonstrated in Fig. 7.
Figure 4 shows the RMSE convergence of the ANFIS
networks for both synthesized and simulated fault currents.
(a) Magnitude of (I3)
(b) Magnitude of (I5)
Fig. 7. Estimated values of the third and fifth harmonic componens (I3)
and (I5) of the synthesized fault current
(a) Synthesized Currnet
(b) Simulated Current
The estimation results of the modal components of a simulated
fault current signal, shown in Fig. 8, are presented.
Fig. 4. RMSE Training convergence
The estimated DC decaying current components (Io) and
(Io/) of the synthesized fault current are shown in Fig. 5. It
can be seen that the estimated DC terms are very close to the
actual values; meaning that that the ANFIS model can
accurately determine the DC offset magnitude of the fault
current.
Fig. 8. Simualted fault current signal obtained by Euler and E-GWO
The harmonic components of the simulated fault current
signal were estimated using E-GWO. The results of the
E-GWO are compared with that obtained by the ANFIS
model. The estimation of the DC terms of the simulated
fault current signal is illustrated in Fig. 9 The results
obtained by ANFIS network matches the results obtained
by E-GWO with high degree of accuracy.
(b) Current componnet (Io/)
(a) Current component (Io)
Fig. 9. Estimated DC Components of the simulated fault current
The ANFIS estimation of the Fourier components of the
fundamental current (a1) and (b1) of the simulated fault current
signal is presented in Fig. 10. Comparing the ANFIS
estimation with that obtained by E-GWO, one can see that the
results are almost identical.
different values of fundamental peak current, fundamental
angle and time constant of the DC decaying component.
Likewise, the simulated signals were obtained by simulating
three-phase faults on the transmission line and the fault current
was obtained by solving the differential Equation of the line
using Euler method. The modal components of the simulated
signals were estimated using E-GWO. Different fault
scenarios were intensively studied including a wide range of
conditions such as fault inception angle, fault resistance, and
fault location. Simulation results were so encouraging as very
high accuracy was achieved. The ANFIS model was able to
estimate the fundamental component of the fault current so
quickly within half a cycle. Therefore, it is believed that the
proposed technique is effective and can be used for digital
protection purposes. The accuracy of ANFIS estimation was
also compared with that obtained by HCDFT. The simulation
results illustrate that using ANFIS models is more accurate
than using HCDFT since no oscillations have appeared
because ANFIS models can accurately estimate the RMS
value of the fault current within half a cycle following the fault
inception.
(a) fault at the middle of zone 1
(a) Fourier current component (a1)
(b) Fourier current component (b1)
Fig. 10. Estimated values of the Fourier fundamental current componnets
(a1) and (b1) of the simulated fault current
Moreover, the estimation performance of the ANFIS
network was compared with the HCDFT estimation as shown
in Fig. 11 for a three-phase fault at the middle of zone 1 and
at the end of zone 1 of the transmission line. It was found the
ANFIS is capable to estimate the RMS value of the
fundamental current in almost half cycle as depicted in Fig.
11.
(b) fault at the end of zone 1
Fig. 11. Performance comparison between ANFIS and HCDFT Estimations
The impedance tracking following fault occurrence for
both ANFIS and HCDFT based techniques is illustrated in
Fig. 12. It can be observed that the ANFIS based scheme was
able to estimate the fault location accurately after half cycle of
fault inception as indicted in the three zone Mho
characteristics of the distance relay.
VI.
CONCLUSION
In this paper, an adaptive neuro-fuzzy interference system
was proposed to extract the fundamental component of the
fault current and to determine the DC decaying current for the
sake of applying the technique in digital protection relaying.
The performance of the proposed system was tested using
synthesized and simulated fault current signals. The
synthesized test signals were constructed numerically using
(a) fault at the middle of zone 1
[8]
[9]
[10]
[11]
(b) fault at the end of zone 1
[12]
Fig. 12. Impedance tracking by ANFIS and HCDFT
[13]
ACKNOWLEDGMENT
The authors acknowledge the support and facilities
provided by the university of Jordan.
[14]
[15]
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
S-A. Ahmadi, M. S-Pasand, M. Davarpanah, “Preventing maloperation
of distance protection due to CCVT transients,” IET Generation,
Transmission & Distribution, vol. 13, no. 13, pp. 2828-2835, 2019, doi:
10.1049/iet-gtd.2018.6559.
U. J. Patel, N. G. Chothani, P. J. Bhatt, “Adaptive quadrilateral distance
relaying scheme for fault impedance compensation,” Electrical,
Control and Communication Engineering, vol. 14, no. 1, pp., 58-70,
2018, doi: 10.2478/ecce-2018-0007.
Y-S. Cho, C-K. Lee, G. Jang, and H. J. Lee, "An innovative decaying
DC component estimation algorithm for digital relaying," IEEE
Transactions on Power Delivery, vol. 24, no. 1, pp. 73-78, 2008, doi:
10.1109/TPWRD.2008.2005682.
T. S. Sidhu, X. Zhang, V. Balamourougan, "A new half-cycle phasor
estimation algorithm," IEEE Transactions on Power Delivery, vol. 20,
no. 2, pp. 1299-1305, 2005, doi: 10.1109/TPWRD.2004.834677.
G. Benmouyal, "Removal of DC-offset in current waveforms using
digital mimic filtering," IEEE Transactions on Power Delivery, vol. 10,
no. 2, pp. 621-630, 1995, doi: 10.1109/61.400869.
K. W. Min, S. S. Santoso, “DC offset removal algorithm for improving
location estimates of momentary faults,” IEEE Transactions on Smart
Grid, vol. 9, no. 6, pp. 5503-5511, November 2018.
S. Jamali and H. Zamani, "Removal of system and CT decaying DC
component in fault signal using selective interval integration," IEEE
Transactions on Power Delivery, vol. 37, no. 2, pp. 905-912, April
2022, doi: 10.1109/TPWRD.2021.3074191.
[16]
[17]
[18]
[19]
[20]
[21]
M. Dashtdar, O. Rubanenko, N. K. Sharma, I. Hunko, S. M. S.
Hosseinimoghadam, and M. Bajaj, "Decaying DC offset removal in
fault current signals of digital relays based on LMSR method," 2021
IEEE 2nd KhPI Week on Advanced Technology (KhPIWeek), 13-17
September 2021, doi: 10.1109/KhPIWeek53812.2021.9569977.
H. Hajizadeh, S. A. Ahmadi, and M. Sanaye-Pasand, " An analytical
fast decaying DC mitigation method for ddigital relaying applications,"
IEEE Transactions on Power Delivery, vol. 36, no. 6, pp. 3529-3537,
2020, doi: 10.1109/TPWRD.2020.3044376.
V. Sok et al., "DC offset removal for phase estimation based on DNN
in power system using less than one cycle waveform," 15th
International Conference on Developments in Power System
Protection (DPSP 2020), 9-12 March 2020 2020, Liverpool, UK, doi:
10.1049/cp.2020.0110.
A. A. Abdoos, S. A. Gholamian, M. J. I. G. Farzinfar, "Accurate and
fast DC offset removal method for digital relaying schemes," IET
Generation, Transmission, and Distribution, vol. 10, no. 8, pp. 17691777, 2016.
M. Tajdinian, S. M. Kouhsari, K. Mohseni, M. Jahromi, "A novel
method for decaying DC component removal with regard to frequency
fluctuations," The international journal for computation and
mathematics in electrical and electronic engineering, Electronic
Engineering, vol. 35, no. 1, pp. 270-288, 2016.
Z. Moravej, S. Bagheri, and S. R .Ebrahimi, "A Novel Approach to
Decaying DC offset Removal in Current Signals of Digital Relays,"
29th Power System Conference – 2014, Tehran, Iran 2014.
N. S. Ashrafi and K. H. Kazemi, "An analytic method for removal of
decaying DC component from phasor estimates," Iranian Journal of
Electrical and Computer Engineering, vol. 12, no. 1, pp. 33-40, 2013.
A. Yusuff, A. Jimoh, and J. J. M. Munda, "Stationary wavelet
transform and single differentiator based decaying DC-offset filtering
in post fault measurements," Measurement, vol. 47, pp. 919-928,
January 2014.
S. Mirjalili, S. M. Mirjalili, and A. Lewis, "Grey Wolf Optimizer,"
Advances in Engineering Software, vol. 69, pp. 46-61, March 2014,
doi: 10.1016/j.advengsoft.2013.12.007.
A. Saxena, R. Kumar, and S. Mirjalili, "A harmonic estimator design
with evolutionary operators equipped grey wolf optimizer," Expert
Systems with Applications, vol. 145, [11312], May 2020,
doi:10.1016/j.eswa.2019.113125.
M I. Al Saaideh, B. B. Mazideh, D. I. Abu-Al-Nadi, “Grey Wolf
Optimizer for Optimal Design of Digital HR Filter”, 2019 10th
International Conference on Information and Communication Systems
(ICICS),
11-13
June
2019,
Irbid,
Jordan,
doi:
10.1109/IACS.2019.8809137.
N. Walia, H. Singh, A. Sharma, "ANFIS: Adaptive neuro-fuzzy
inference system-a survey," International Journal of Computer
Applications, vol. 123, no. 13, pp. 32-38, August 2015, doi:
10.5120/ijca2015905635.
N. Talpur, M. N. M. Salleh, and K. Hussain, "An investigation of
membership functions on performance of ANFIS for solving
classification problems," IOP Conference Series: Materials Science
and Engineering 226, 6-7 May, 2017, Melaka, Malaysia
doi:10.1088/1757-899X/226/1/012103.
E. A. Feilat and K. N. Al-Tallaq, "An artificial neural network approach
for three-zone distance protection," International Journal of Modelling
and Simulation, vol. 25, no. 4, pp. 291-298, 2005.