Electric Power Systems Research 79 (2009) 1538–1545
Contents lists available at ScienceDirect
Electric Power Systems Research
journal homepage: www.elsevier.com/locate/epsr
A new and accurate fault location algorithm for combined transmission lines
using Adaptive Network-Based Fuzzy Inference System
Javad Sadeh ∗ , Hamid Afradi
Electrical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box: 91775-1111, Mashhad, Iran
a r t i c l e
i n f o
Article history:
Received 5 September 2008
Received in revised form 13 April 2009
Accepted 30 May 2009
Available online 26 June 2009
Keywords:
Transmission line protection
Fault location algorithm
Combined overhead and underground
transmission line
Adaptive Network-Based Fuzzy Inference
System (ANFIS)
a b s t r a c t
This paper presents a new and accurate algorithm for locating faults in a combined overhead transmission
line with underground power cable using Adaptive Network-Based Fuzzy Inference System (ANFIS). The
proposed method uses 10 ANFIS networks and consists of 3 stages, including fault type classification,
faulty section detection and exact fault location. In the first part, an ANFIS is used to determine the
fault type, applying four inputs, i.e., fundamental component of three phase currents and zero sequence
current. Another ANFIS network is used to detect the faulty section, whether the fault is on the overhead
line or on the underground cable. Other eight ANFIS networks are utilized to pinpoint the faults (two for
each fault type). Four inputs, i.e., the dc component of the current, fundamental frequency of the voltage
and current and the angle between them, are used to train the neuro-fuzzy inference systems in order to
accurately locate the faults on each part of the combined line. The proposed method is evaluated under
different fault conditions such as different fault locations, different fault inception angles and different
fault resistances. Simulation results confirm that the proposed method can be used as an efficient means
for accurate fault location on the combined transmission lines.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
In power systems, transmission and distribution lines are vital
links that achieve the continuity of service from the generating
plants to the end users. Protection systems for transmission lines
are one of the most important parts in power systems. Fault location
is a desirable feature in any protection scheme. The increasing complexities of the modern power transmission systems have greatly
raised the importance of the fault location research studies in recent
years. The restoration can be accelerated if the location of a fault
is known or can be estimated with reasonable accuracy. Following
the occurrence of a fault, the utility tries to restore power as quickly
as possible, as rapid restoration of service reduces customer complaints, outage time, operating cost, loss of revenue and maintains
system stability. To aid rapid and efficient service restorations, an
accurate fault location technique is needed.
Transmission line fault location techniques can be classified into
two main categories: techniques based on the fundamental power
frequency component [1–5], and techniques utilizing the higher
frequency components of the fault signals [6–9]. The latter are also
referred to as traveling wave methods, due to their use of travel-
∗ Corresponding author at: Faculty of Engineering, Electrical Department, P.O.
Box: 917775-1111, Mashhad, Iran. Tel.: +98 511 8763302; fax: +98 511 8763302.
E-mail addresses: [email protected], [email protected] (J. Sadeh).
0378-7796/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2009.05.007
ing wave theory. Each of these two groups can be further divided
into two subgroups: to use single-end information or to use information from both ends of the faulted line. Algorithms that use
measurements of current and voltage at both terminals of the line
are generally more accurate than the ones using data only from the
local terminal. However, in many transmission lines, a communication channel between the local and remote line terminals is not
available, thus make it necessary to use data from the local terminal
only. Fault location algorithms based on only local terminal current and voltage data need some simplifying assumptions to make
the fault distance calculation possible, affecting the accuracy of the
results. However, fault location techniques using single-ended data
could be more attractive for researchers.
Recently, the electricity demand density has increased rapidly
in metropolitan areas. All over the world, large scale underground
power cable installations start to replace overhead transmission
lines due to environmental concerns in densely populated areas. To
operate combined transmission lines (lines consisting of overhead
and underground cable portions) with high efficiency, numerous
related technologies are required. One of them is the fault location and protection. Underground cable faults may be series faults
in which the cable is cut without the electrical insulation being
broken, or shunt faults in which a break in the electrical insulation occurs without the conductor itself being cut. On the other
hand, overhead line faults may be caused by lightning strokes,
falling trees, fog, and salt spray on contaminated insulators. In
J. Sadeh, H. Afradi / Electric Power Systems Research 79 (2009) 1538–1545
transmission systems consisting of an overhead line in combination
with an underground power cable, the main problem in the fault
location techniques is the unequal impedances of the underground
cables and the overhead lines.
Various fault location algorithms for overhead transmission
lines and underground cable transmission lines have been developed so far [1–9] but the field of fault location in combined lines
is not matured yet. In Ref. [10] a digital distance relaying algorithm is presented for combined overhead transmission lines with
underground power cables. This reference describes an accurate
calculation algorithm of the line impedance with the compensation factor at the relay point, as well as the method to discriminate
the fault section between both sections when the single line-toground fault has occurred. In Ref. [11] a fault location scheme for
transmission systems consisting of an overhead line combined with
an underground power cable is proposed that requires synchronized phasor measurements data at one end of the transmission
line and at the far end of the power cable. Fault location is determined using distributed line model, modal transformation theory
and Discrete Fourier Transform. Wavelet-based traveling wave fault
location algorithm is presented in Ref. [12] for combined transmission lines.
With the great developments of ANN training and design methods, a series of contributions have been introduced to estimate the
fault distance of the faulted line. This is mainly accomplished by
those ANN types that use supervised training to map the hidden
relations between the available data and the unknown fault distance through the collected training data [13–15]. So far, Fuzzy
1539
Logic (FL) systems have no solid contributions for fault location
purposes. The main reason behind this is the difficulty in optimizing the constructed FL network parameters. However, the recent
training methods for optimizing the parameters for FL networks are
expected to change the situation drastically and turn the FL into efficient and successful tools. As is clear from the above explanations,
the fault location problem, especially for the combined overhead
line and underground cable, is the very type of the problems which
ANN-FL tool is designed to handle in an efficient manner.
In general, a neuro-fuzzy system is an intelligent model which
has both the learning capabilities of the neural networks plus
the knowledge illustration of fuzzy logic systems using linguistic
expressions.
Application of the artificial neural network to fault location in
the combined transmission line is proposed in Ref. [16]. The algorithm consists of two parts. In the first part the faulty section is
determined, and in the second part the exact location of fault is calculated. Wavelet and neuro-fuzzy-based fault location algorithm is
proposed in Ref. [17]. In this reference, neuro-fuzzy system consists
of two parts as in Ref. [16]. The algorithm has the ability to consider
the high impedance fault in overhead section and the simulation
results confirm the accuracy of the algorithm.
In this paper an accurate fault location algorithm for combined
overhead transmission line with underground power cable is proposed which is based on Adaptive Network-Based Fuzzy Inference
System (ANFIS). Four inputs are used to train the ANFISs in order
to classify the fault type, detect the faulty section and accurately
locate the faults on each part of the combined line. The proposed
method is tested under different fault conditions such as different
fault locations, different fault inception angles and different fault
resistances. The simulation results confirm the validity and high
accuracy of the new algorithm.
2. Adaptive Network-Based Fuzzy Inference System [18]
2.1. ANFIS architecture
An adaptive network is a multilayer feedforward network in
which each node performs a particular function on the incoming signals, as well as on the set of parameters pertaining to this
node. The formula for the node functions may vary from node to
node, and the choice of each node function depends on the overall
input–output function which the adaptive network is required to
carry out. The parameter set of an adaptive network is the union
of the parameter sets of each adaptive node. In order to achieve
a desired input–output mapping, these parameters are updated
according to given training data and a gradient-based learning procedure. In the rest of this section, the architecture of ANFIS as an
adaptive network is described.
For the purpose of illustration, the simplifying assumption is
considered that the fuzzy inference system under consideration has
two inputs x and y and one output f. Suppose that the rule base
contains two fuzzy if-then rules of Takagi–Sugeno’s type [19]:
• Rule 1: if x is A1 and y is B1 then f1 = p1 x + q1 y + r1 .
• Rule 2: if x is A2 and y is B2 then f2 = p2 x + q2 y + r2 .
Then the fuzzy reasoning is illustrated in Fig. 1(a) and the corresponding equivalent ANFIS architecture is shown in Fig. 1(b). The
node functions in the same layer are of the same function family, as
described below:
• Layer 1: Every node i in this layer is an adaptive node with a node
function:
Fig. 1. (a) Fuzzy reasoning and (b) equivalent ANFIS.
Oi1 = Ai (x)
(1)
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J. Sadeh, H. Afradi / Electric Power Systems Research 79 (2009) 1538–1545
where x is the input node i, and Ai is the linguistic label associated
with this node function. In other words, Oi1 is the membership
function of Ai and satisfies the quantifier Ai . Usually Ai (x) is chosen to be bell-shaped or Gaussian with maximum equal to 1 and
minimum equal to 0, such as
Ai (x) =
1
(2)
2 bi
1 + [((x − ci )/ai ) ]
or
x − ci 2
A (x) = exp −
(3)
ai
where {ai , bi , ci } is the parameter set. As the values of these
parameters change, the bell-shaped or Gaussian functions vary
accordingly, thus exhibiting various forms of membership functions on linguistic label Ai . In fact, any continuous and piecewise
differentiable functions, such as commonly used trapezoidal or
triangular-shaped membership functions, are also qualified candidates for node functions in this layer. Parameters in this layer
are referred to as premise parameters.
• Layer 2: Every node in this layer is a fixed node labeled ˘, which
multiplies the incoming signals and sends the product out. For
instance,
wi = Ai (x) × Bi (y)
i = 1, 2
(4)
Each node output represents the firing strength of a rule.
• Layer 3: Every node in this layer is a fixed node labeled N. The
ith node calculates the ratio of the ith rule’s firing strength to the
sum of all rules’ firing strengths:
w̄i =
wi
w1 + w2
i = 1, 2
(5)
For convenience, outputs of this layer will be called normalized
firing strengths.
• Layer 4: Every node i in this layer is an adaptive node with a node
function:
Oi4 = w̄i fi = w̄i (pi x + qi y + ri )
(6)
where w̄i is the output of layer 3, and {pi , qi , ri } is the parameter set. Parameters in this layer will be referred to as consequent
parameters.
• Layer 5: The single node in this layer is a fixed node labeled ˙ that
computes the overall output as the summation of all incoming
signals, i.e.:
Oi5
= overall outpur =
wi fi
w̄i fi = i
i
i
wi
(7)
2.2. ANFIS learning algorithm
ANFIS employs two modes of learning. First, a forward pass is
made using current premise parameters to optimize rule consequent parameters using least square estimation based on output
error. This is possible since outputs are a linear function of consequent parameters. Second, a backward pass is made to alter premise
parameters using gradient-based learning. This process of learning
is named Hybrid Learning. The backward pass employs learning in
a similar way as to the back-propagation in neural networks. For
each pass, each rule antecedent parameter ˛ is changed according
to
˛ = −
∂E
∂˛
(8)
Fig. 2. The proposed ANFIS structure for fault type classification and faulty section
detection.
and
=
k
(∂E/∂˛)
˛
(9)
2
where E is the output error, is the learning rate parameter and k is
a parameter which is automatically varied during learning process
to adapt to the learning rate. k is increased if four consecutive learning epochs reduce output error and is decreased if two consecutive
learning epochs result in non-monotonic changes in error. ∂E/∂␣ is
calculated using the chain rule [18].
3. Architecture of the proposed fault location algorithm
In this section the architecture of the proposed fault location
algorithm is presented. The proposed method consists of three
stages, including fault type classification, faulty section detection,
as well as exact fault location. The presented algorithm contains 10
ANFISs, 1 for fault type classification, 1 for faulty section detection,
and the other 8 networks for accurate fault location (2 for each fault
type). Figs. 2 and 3 shows the schematic diagrams of the algorithm.
As a first step in any pattern classification technique, feature
extraction is used to reduce the dimension of the raw data and
extract useful information in a concise form. It is important to note
that different fault locations produce different frequency components in voltage and current signals. This also means that these
signals vary with fault type, location and inception angle. The crisp
inputs to ANFIS comprise a set of features based on the voltage
and current. An acceptable and simple criterion used here is that a
variable as a feature for the ANFIS input should provide more information for fault location than those not selected. In this respect, for
fault type classification (ANFIS1), the amplitude of the fundamental
frequency of three phases currents and neutral current are selected
as inputs and the outputs have been termed as A, B, C and G, which
represent the three phases and ground. Any one of the outputs A,
B, C approaching 1 indicates a fault in that phase, and if G is taken
1 indicates a fault involve ground.
When the phases which are involved in fault are determined,
four features are extracted from digitized data and are fed to faulty
section detection block as shown in Fig. 2. Normalized values of
post-fault peaks of the fundamental component of voltage and current, the phase difference between voltage and current and the dc
component of current are obtained as features of the measured
signals and are used as inputs to ANFIS2 for detecting the faulty
section. These inputs are estimated from sampled values of the current/voltage signal using least square error estimation (LSE) method
[20] within one cycle after fault inception. This network determines
whether the fault is on the overhead or on the underground section
of the transmission line.
J. Sadeh, H. Afradi / Electric Power Systems Research 79 (2009) 1538–1545
1541
Fig. 4. System under study.
ters, an input pattern corresponding to a particular fault condition
is fed to the ANFIS and its output is compared with the desired
output pattern corresponding to that fault condition. The ANFIS
parameters are updated after all patterns have been presented to
the ANFIS.
4. Performance evaluation
In this section performance of the proposed algorithm is evaluated under different fault conditions and some of the results are
presented.
4.1. Power system model
The single line diagram of a 100 km, 220 kV combined overhead transmission line with underground power cable is shown
in Fig. 4. The line consists of a 90 km overhead transmission line
ended with 10 km underground cable. Distributed parameter model
is used for modeling of the overhead line and the underground
cable. The proposed fault location algorithm requires only the three
phase voltages and currents at the sending end of the overhead
transmission line. This system has been simulated using the well
known Alternative Transient Program (ATP) and the collected data
is processed using MATLAB to prepare the inputs for the ANFISs.
4.2. Fault type classification and faulty section detection
Fig. 3. The proposed ANFIS structure for exact fault location.
In the next step, eight ANFISs are trained for each fault type and
each faulty section, as shown in Fig. 3. Once the fault is classified
and the faulty section is determined, the relevant ANFIS for fault
location is activated. The inputs for these networks are the same as
the inputs of ANFIS2 and the output is the normalized distance of
the fault point from the sending end of the overhead line.
In order to design an ANFIS, it is crucial to train it efficiently
and correctly. The training set must be carefully chosen so that
all the different fault conditions such as different fault inception
angles, different fault resistances and different fault locations are
considered. The performance of the ANFIS is then tested using
both patterns within and outside of the training set. The approach
adapted here is based on the Hybrid Learning that is described in
Ref. [18]. In order to find the optimum values of the ANFIS parame-
Different fault types at various locations of each section of the
system under study with different inception angles and fault resistances are used for training and testing the ANFIS1 for fault type
classification and the ANFIS2 for faulty section determination. During training of the ANFIS1 any phase/ground involved in the fault is
assigned ‘1’ otherwise ‘0’, whereas during testing if the output is less
than 0.25 then it would be classed as ‘0’, i.e., a healthy phase indication, and if it is greater than 0.75 then it is classed as unity, i.e., a
faulty phase indication. Also during training of ANFIS2 the faults on
the overhead line is assigned ‘0’ and the faults on the underground
cable is assigned ‘1’.
Table 1 shows some of the test results for different system conditions which were not presented to the ANFIS during the training
process. For each case it can be seen that the ANFISs’ outputs converge to the desired values, and are either very close to zero or to
one.
4.3. Accurate fault location using ANFISs
All types of faults with different inception angles, different
locations and different fault resistances in both sections of the
combined overhead line and underground cable are simulated to
evaluate the performance of the proposed fault location algorithm.
The system under study is shown in Fig. 4. In the following sections
some of the results are presented. The percentage error is defined
as the formula given below [11]:
% Error =
Actual fault location − Calculated fault location
Total faulty section lenght
× 100
(10)
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J. Sadeh, H. Afradi / Electric Power Systems Research 79 (2009) 1538–1545
Table 1
Results of the fault type classifier and the fault section detector.
Fault type
Fault inception angle
Faulty section
–
a–g
a–g
b–g
c–g
a–b
b–c
c–a
ab–g
bc–g
ca–g
abc
abc–g
–
0
90
0
90
90
45
45
90
0
0
0
90
–
0
1
0
1
0
1
0
1
0
1
0
1
Output results of ANFIS1
Output results of ANFIS2
A
B
C
G
0.000
0.996
1.023
0.132
0.013
1.063
0.033
1.039
0.899
−0.165
1.002
1.185
1.210
0.000
0.015
−0.022
1.019
−0.191
0.978
0.991
−0.001
1.028
1.112
−0.199
0.905
1.054
−0.000
0.021
0.125
0.012
0.992
0.011
0.973
1.195
0.019
0.972
1.035
1.036
0.899
0.000
1.031
1.029
0.985
1.081
−0.109
−0.053
0.134
1.103
1.055
0.961
−0.023
1.143
4.3.1. Single line to ground faults
In this study, with considering the 5 and 0.5 km as fault distance steps in overhead and underground cable, respectively, 20
and 10◦ as fault inception angle steps in overhead and underground
cable, respectively, and four different fault resistances (0, 10, 50 and
100 ) for overhead line and solid short circuit on the underground
cable, 2132 patterns are produced for training the ANFISs, among
which 1520 patterns are associated with the overhead line and the
rest are for the underground cable. The percentage error during
–
−0.078
1.001
0.091
0.956
−0.106
1.213
0.146
0.978
−0.089
1.129
0.019
1.023
training for this type of fault on the overhead line and underground
cable are shown in Figs. 5 and 6, respectively. As shown in these figures, the maximum percentage error for the overhead line and the
underground cable are 0.0109 and 0.031, respectively, which means
that the training process is completed successfully.
Once the training procedure is done completely, the networks
are tested using simulated fault patterns not presented during the
training process. The percentage error for 70 patterns (35 patterns
for the overhead line and the same number for the underground
Table 2
Fault conditions and percentage error for single line to ground faults on the overhead line.
Fault location
8
12
12
27
27
44
44
58
58
67
67
73
73
86
86
19
19
19
Fault inception angle
325
25
125
225
75
45
145
25
275
195
95
5
335
15
155
10
25
70
Fault resistance
Percentage error
Fault location
35
55
55
55
75
35
55
7
7
47
15
40
40
10
1
10
70
35
0.018
0.004
0.018
0.001
0.006
0.009
0.003
0.013
0.003
0.005
0.005
0.018
0.002
0.010
0.002
0.003
0.016
0.009
19
19
37
37
47
47
47
62
62
62
81
85
85
85
85
87
87
Fault inception angle
40
35
135
0
15
40
10
215
15
115
75
35
55
275
195
95
35
Fault resistance
Percentage error
55
55
55
75
35
7
7
47
47
40
40
30
2
15
1
10
25
0.003
0.010
0.0277
0.014
0.006
0.003
0.003
0.002
0.005
0.012
0.009
0.004
0.005
0.004
0.013
0.011
0.013
Table 3
Fault conditions and percentage error for single line to ground faults on the underground cable.
Fault location
Fault inception angle
Percentage error
Fault location
Fault inception angle
Percentage error
91.2
91.2
93.7
93.7
95.6
95.6
97.4
97.4
98.2
98.2
91.3
98.8
95.1
96.6
96.6
97.7
97.7
95.6
3
333
235
7
77
125
265
25
95
215
125
45
175
345
355
85
185
230
0.027
0.005
0.008
0.034
0.005
0.026
0.022
0.015
0.017
0.036
0.002
0.004
0.038
0.034
0.010
0.029
0.010
0.022
95.6
93.3
93.3
93.3
93.7
93.7
93.7
97.2
97.2
92.9
92.9
92.4
92.4
95.5
95.5
91
91
330
18
357
45
14
18
185
118
30
105
33
113
15
45
165
58
158
0.002
0.008
0.014
0.021
0.001
0.034
0.032
0.032
0.015
0.008
0.004
0.020
0.001
0.020
0.026
0.024
0.011
J. Sadeh, H. Afradi / Electric Power Systems Research 79 (2009) 1538–1545
1543
Fig. 8. Percentage error during testing (underground cable).
error for the overhead line and the underground cable are 0.0277
(about 24.9 m) and 0.038 (about 3.8 m), respectively.
Fig. 5. Percentage error during training (single line to ground fault on the overhead
line).
cable) are indicated in Figs. 7 and 8. Also, the simulation conditions and the percentage error for these patterns are presented in
Tables 2 and 3, for faults on the overhead line and on the underground cable, respectively. The presented results in these figures
and tables show that the proposed algorithm has a high degree of
accuracy such that during testing process the maximum percentage
4.3.2. Three phase faults
In this case, the fault distance steps are assumed to be 5 and
0.25 km in overhead and underground cable, respectively, and fault
inception angle steps are 20 and 10◦ in overhead and underground cable, respectively. Four different fault resistances (3, 10,
30 and 50 ) for overhead line and solid short circuit on the underground cable are considered. For this condition, 3026 patterns are
produced, among which 1805 patterns are associated with the overhead line and the rest are for the underground cable. These patterns
are applied to train the ANFISs. The percentage error during training for this type of fault on the overhead line and the underground
cable are shown in Figs. 9 and 10, respectively. As shown in these
figures, the maximum percentage errors are 0.0085 and 0.0739,
respectively. These values indicate that the training process is done
successfully.
After executing the training procedure, the networks are tested
using simulated fault patterns not presented during the training
process. The simulation conditions and the percentage error for 65
patterns, 35 patterns for the overhead line and 30 patterns for the
underground cable are shown in Tables 4 and 5, respectively. Based
on the presented results in these tables, it can be seen that similar
to the previous case, the proposed method has a high degree of
accuracy such that during testing the maximum percentage error
for the overhead line and the underground cable are 0.0081 (about
7.3 m) and 0.071 (about 7.1 m), respectively. The obtained results, for
Fig. 6. Percentage error during training (single line to ground fault on the underground cable).
Fig. 7. Percentage error during testing (overhead line).
Fig. 9. Percentage error during training (three phase fault on the overhead line).
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J. Sadeh, H. Afradi / Electric Power Systems Research 79 (2009) 1538–1545
Table 4
Fault conditions and percentage error for three phase faults on the overhead line.
Fault location
6
6
6
6
16
16
16
18
22
22
22
23
23
26
26
26
26
Fault inception angle
23
325
235
235
115
15
15
10
165
165
165
45
45
25
0
165
0
Fault resistance
Percentage error
Fault location
10
10
45
65
1
7
1
7
5
14
24
35
45
5
15
30
35
0.0030
0.0002
0.0004
0.0005
0.0027
0.0036
0.0013
0.0016
0.0027
0.0005
0.0007
0.0081
0.0004
0.0017
0.0005
0.0023
0.0009
47
47
47
54
67
67
67
67
72
72
77
77
82
82
87
87
Fault inception angle
70
70
240
65
260
326
100
5
45
95
23
0
240
240
345
34
Fault resistance
Percentage error
5
15
15
45
5
10
15
45
35
35
3
33
5
15
13
37
0.0023
0.0011
0.0009
0.0036
0.0010
0.0013
0.0005
0.0014
0.0018
0.0030
0.0029
0.0004
0.0006
0.0010
0.0044
0.0001
Table 5
Fault conditions and percentage error for three phase faults on the underground cable.
Fault location
Fault inception angle
Percentage error
Fault location
Fault inception angle
Percentage error
91.0
91.25
91.75
91.9
92.0
92.2
92.2
92.9
93.3
93.7
94.1
94.1
94.7
94.7
95
63
12
50
110
41
115
120
26
335
200
25
315
10
115
185
0.071
0.006
0.065
0.001
0.062
0.006
0.006
0.0005
0.005
0.015
0.040
0.002
0.005
0.008
0.017
95.3
95.6
96.2
96.4
96.7
97.2
97.5
97.7
97.9
98.1
98.2
98.4
98.6
98.8
98.8
35
135
335
345
15
75
145
215
10
90
190
75
0
10
225
0.025
0.040
0.059
0.010
0.052
0.009
0.011
0.052
0.026
0.0005
0.025
0.011
0.019
0.025
0.049
based on the Adaptive Network-Based Fuzzy Inference System. The
algorithm consists of three stages, including fault type classification, faulty section determination and fault location. To estimate
the accuracy of the proposed algorithm, a wide variety of conditions
such as different fault types, different fault inception angles and
different fault resistances on the overhead line and on the underground cable are simulated and some of the results are presented.
Based on the obtained results, it can be concluded that the proposed
method is very effective to classify the fault type, to determine the
faulty section and to find the exact location of fault such that the
maximum percentage error is kept below 0.07%.
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Fig. 10. Percentage error during training (three phase fault on the underground
cable).
the same fault conditions, are comparable to or better than those
as published in Ref. [11].
5. Conclusion
This paper proposed a new algorithm for fault location in a combined overhead transmission line with underground power cable
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