Ain Shams Engineering Journal (2015) 6, 199–209

Ain Shams University

Ain Shams Engineering Journal

www.elsevier.com/locate/asej
www.sciencedirect.com

ELECTRICAL ENGINEERING

A novel transmission line relaying scheme for fault

detection and classification using wavelet transform
and linear discriminant analysis
Anamika Yadav *, Aleena Swetapadma

Department of Electrical Engineering, National Institute of Technology, Raipur, C.G., India

Received 4 August 2014; revised 24 September 2014; accepted 12 October 2014

Available online 15 November 2014

KEYWORDS Abstract This paper proposes fault detection and classification scheme for transmission line pro-
Discrete wavelet transform; tection using WT and linear discriminant analysis (LDA). Current signals of each phase are used for
LDA; the detection and identification of faulty phases and zero sequence currents are used for the detec-
Fault detection; tion of ground. Current signals are processed using discrete wavelet transform with DB-4 wavelet
Fault classification; up to level 3. Approximate coefficients are reconstructed using wavelet reconstruction. Performance
Shunt faults; of the proposed based scheme is tested by variations of parameters such as fault type, location, fault
Multi-location faults resistance, fault inception angle and power flow angle. The scheme is applicable for both single cir-
cuit and double circuit transmission line. All shunt faults and multi-location faults which occur in
different locations at the same time are also detected and classified by the proposed scheme within
one cycle time. The simulation results show that the proposed scheme is not affected by non-linear
high impedance fault and CT saturation.
Ó 2014 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an
open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

1. Introduction classification. Among the various techniques reported wavelet

based techniques are used for detection and classification of
Fast and reliable fault detection and fault classification faults by researchers [1,2]. Different artificial intelligence tech-
technique is an important requirement in power transmission niques such as ANN, fuzzy, ANFIS, and SVM also used for
systems to maintain continuous power flow. Many researchers detection and classification of faults. Artificial-neural-network
proposed different techniques for fault detection and (ANN) based approach is used for fault detection, fault phase
selection and fault classification in [3–5]. ANN in combination
with wavelet transform is used for detection and classification
* Corresponding author. Tel.: +91 9425852654.
of fault in [6,7]. Combination of particle swarm optimization
E-mail addresses: ayadav.ele@nitrr.ac.in (A. Yadav), aleena.
swetapadma@gmail.com (A. Swetapadma).
(PSO) and ANN is also used for classification of fault in [8].
Peer review under responsibility of Ain Shams University.
Fuzzy logic is used for fault phase identification and classifica-
tion in [9,10]. Fuzzy logic in combination with neural network
called as adaptive neuro fuzzy inference system (ANFIS) based
distance relaying has been used for protection of power system
Production and hosting by Elsevier [11]. Support vector machines (SVM) are used for classification
http://dx.doi.org/10.1016/j.asej.2014.10.005
2090-4479 Ó 2014 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
200 A. Yadav, A. Swetapadma

of fault in [12]. In [13] phase space based fault detection

scheme for distance relaying is proposed. Fault classification
and faulted phase selection schemes are also proposed based
on the symmetrical components of reactive power for single-
circuit transmission lines [14]. Detection and classification of
faults in power transmission lines using functional analysis
and computational intelligence is proposed in [15].
Moreover the reach setting or the protection range reported
in all above discussed papers is much lesser than 90% of the
line length i.e. if the fault occurs in between 90% and 100% Figure 1 Wavelet analysis of signal S up to level 3.
of the line, these scheme will not be able to detect the fault.
However if any protection scheme can provide protection to decomposition level up to level 3 to detect fault quickly than
larger portion of the line length then that scheme will be ben-
other higher levels.
eficial for protection of transmission line. Many researchers The decomposed components can be assembled back into
did not mention about the fault detection time which is the the original signal without loss of information which is called
most important task in transmission line relaying. Fault detec-
wavelet reconstruction, or synthesis or inverse discrete wavelet
tion time is important because from this it can be observed that transforms (IDWT). Wavelet Reconstruction is used here for
how quickly the normal flow of power can regain. Thus in this the approximate coefficients. Signals use zero padding to con-
paper a protection scheme is designed using wavelet transform
struct the original signal. Reconstruction process of proposed
and linear discriminant analysis to detect the fault, identify the method is shown in Fig. 2. After reconstruction required num-
faulty phases and classify the type of shunt faults that may bers of samples are taken from the signal for further use in the
occur in power transmission lines. Instead of designing 10
training of LDA network.
modules for 10 types of fault only 4 modules are designed to
identify the faulty phases and classify the faults. Only three line
3. Linear discriminant analysis
currents and zero sequence current measurement are sufficient
to implement this technique. The number of samples given in
training is quarter cycle data (5 samples) after pre-processing Linear discriminant analysis is used to study the difference
through discrete wavelet transform. The time taken by this between two or more groups of objects with respect to several
method is about within one cycle (20 ms). variables simultaneously, determining whether meaningful dif-
ferences exist between the groups and identifying the discrim-
2. Discrete wavelet transform inating power of each variable [18]. Any data set contains
observations with measurements on different variables called
predictors and their known class labels. For new observations
Wavelets have both scale and a time aspect that is why it is
with predictor values, classes can be determined based on the
used for signal analysis in power system protection [16]. Wave- old data set in case of classification of data [19]. The observa-
let analysis represents a windowing technique with variable- tions with known class labels are usually called the training
sized regions which allows the use of long time intervals where
data. Training data are used to train the LDA network. After
more precise low-frequency information is required and training re-substitution error is computed to know the propor-
shorter regions where high-frequency information is required. tion of misclassified observations on the training set. Then the
Advantage of wavelets is the ability to perform local analysis confusion matrix on the training set is computed to obtain the
which analyzes a localized area of a larger signal. Wavelet different sets of misclassification data. A confusion matrix con-
analysis is capable of revealing aspects of data that other signal tains information about known class labels and predicted class
analysis techniques may miss. Wavelet analysis is the breaking labels [20]. The element (i, j) in the confusion matrix is the
up of a signal into shifted and scaled versions of the original
number of samples whose known class label is class i and
wavelet to obtain a better resolution. whose predicted class is j. The diagonal elements represent
For analysis of power system transients, DB wavelets have correctly classified observations.
been used in majority of the power system transient detection
algorithms and also DB wavelets are described as best mother
wavelet of choice of the power system researchers in [17]. So in
cA3 Zero Padding
the proposed work DB wavelet is taken as mother wavelet. In
wavelet analysis signals divided into two parts approximations
and details. The approximations are the high-scale, low-fre-
quency components of the signal. The details are the low-scale, cA2 Zero Padding
high-frequency components. Decomposition of a signal S up to
level three is shown in Fig. 1. The decomposed signal contains
the approximate and detail coefficients up to certain level. Pro- cA1 Zero Padding
posed method is first designed by using different levels of
decomposition of wavelet up to level 5. But the accuracy of
the method remains constant after level 3. So if level higher Original signal, S
than level 3 will be considered it will take more time for
decomposition due to which processing time will increase but Figure 2 Wavelet coefficient reconstruction up to level 3 to get
the accuracy will be same as level 3. So it is better to take signal S.
A novel transmission line relaying scheme for fault detection and classification using LDA 201

BUS1 BUS2

100km

Source 1 Source 2
400kV 400kV

Load Load
100kW 200kW
100kVAr

Figure 3 Single line diagram of proposed power system network.

2500 When another labeled data set is not present, it can be sim-
Input Currents Ia,Ib,Ic and Iz (amp)

Ia
2000 ulated by doing cross-validation. N-fold cross-validation is
Ib
used for estimating the test error on classification algorithms.
1500 Ic
Iz
It randomly divides the training set into N disjoint subsets.
1000 Each subset has roughly equal size and roughly the same class
proportions as in the training set. Because cross-validation
500
randomly divides data, its outcome depends on the initial ran-
0 dom seed.
X: 80
-500 Y: 2.116e-006

-1000 Table 1 Confusion matrix of fault detection training module.

-1500 Predicted value Actual value
20 40 60 80 100 120 140 160 180 200
Time (ms) No fault Fault
No fault 100 0
Figure 4 Three phase current signals Ia, Ib, Ic and zero sequence Fault 0 1900
current signal Iz during AG fault at 80 ms.

If there is
Obtain the no fault in
three phase Obtain the Test it against line output
currents Ia, Ib approximate the trained will be ‘0’.
and Ic from coefficient of LDA fault
relaying three phase detection
point. currents. network. If there is a
fault in line
output will
be ‘1’.
Pre-process the three phase currents Ia, Ib, Ic
and zero sequence current Iz with discrete
wavelet transform and obtain the approximate
coefficient of currents.

Ia Ib Ic Iz

Trained Trained Trained Trained

LDA LDA LDA LDA
module module module module

A B C G
Phase Phase Phase Phase

FAULT CLASSIFICATION

Figure 5 Proposed method for fault detection and classification.

202 A. Yadav, A. Swetapadma

Table 2 Fault detection time in case of near boundary faults (near end and far end) with Rf = 0.001 X and Ui = 0°.
Fault location (km) Fault detection time (ms) Fault phase identification time (ms) Fault classification
A B C G
0.1 12 7 – – 8 AG
0.3 12 – 6 – 9 BG
0.5 12 – – 8 10 CG
0.7 12 9 6 – 8 ABG
0.9 12 – 8 7 12 BCG
1.1 12 11 – 9 10 CAG
1.3 12 9 7 – – AB
1.5 12 – 12 7 – BC
85 15 10 – 11 – CA
87 15 7 11 9 – ABC
89 15 5 – – 7 AG
91 15 – 9 – 11 BG
93 15 – – 8 12 CG
95 15 9 6 – 10 ABG
97 16 – 8 9 9 BCG
99 16 7 – 6 8 CAG
Output of LDA

2
based fault

X: 80
detection

1 Y: 0
0 X: 92
Y: 1
-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
(a)
2
Output of LDA based Fault phase Identifier and fault Classifier

X: 80
1 Y: 0
A

X: 87
0
Y: 1
-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
1

0
B

-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
1
C

-1
20 40 60 80 100 120 140 160 180 200
Time(ms)
2
X: 80
1 Y: 0
G0 X: 88
Y: 1
-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
(b)
Figure 6 (a) Output of fault detection. (b) Output of fault classification during AG fault for Rf = 0.001 X and Ui = 0° at 0.1 km.
A novel transmission line relaying scheme for fault detection and classification using LDA 203

4. Proposed method using linear discriminant analysis Training accuracy is estimated by calculating the re-substi-
tution error and cross-validation error which is 0% in LDA
The proposed method consists of three stages: developing the based method. Confusion matrix of the training is given in
model of the power system network for fault simulation stud- Table 1. Diagonal values of the confusion matrix show the
ies, pre-processing of the signals to obtain the input–output accurate number of classified data for a particular class. After
patterns/data set and designing of LDA network for fault training network is tested for different fault cases and output
detection and fault classification. MATLAB/SIMULINK of fault detection is obtained which will be discussed in next
platform has been used for the implementation of the three section.
stages involved in the proposed method such as fault simula-
tion, signal pre-processing and algorithm implementation. 4.3. Fault classification
The single line diagram of the power system network under
consideration is shown in Fig. 3. It consists of 400 kV, 50 Hz After fault is detected the phases of fault are identified using
single circuit transmission line of length 100 km. Three phase LDA. Proposed fault phase identification and fault classifica-
source of 400 kV, 50 Hz is connected to bus-1 with 100 kW tion scheme is shown in Fig. 5. For fault classification separate
and 100 kVar load, the short circuit capacity of source is modules are designed for each phase A, B, C and ground G.
1250 MVA and X/R ratio is 10. At bus-2 a load of 200 kW Input given to each classifier A, B, C is the phase currents
is connected and another 3 phase source of 400 kV, 50 Hz, and zero sequence current for ground G. Training accuracy
SCC 1250 MVA, X/R ratio is 10 is connected. is 100% in case of fault classification. After training the net-
work, test data are generated and tested for checking the per-
4.1. Inputs to the network formance of the relay for the classification of fault. First fault
phases are identified individually and from phase identification
Three phase current signals are obtained from the relaying output faults are classified.
point for different fault case studies. To analyze the current
signals during faulty condition, consider a single line to ground 5. Results and discussion
fault has occurred at 80 ms. The waveform of the three phase
currents and zero sequence current during AG fault is shown The proposed relay has been tested for around 5000 test fault
in Fig. 4. Before the inception of fault, the three phase currents cases involving different faults (LG, LL, LLL, and LLG) at 50
in all the phases are same and zero sequence current has zero
magnitude. At 80 ms, AG fault has occurred, so phase ‘‘A’’
current increases and zero sequence current also starts increas- Table 3 Fault detection time in case of varying fault
ing while other phase currents remain same as shown in Fig. 4. resistance with Ui = 180°.
Various fault parameter variations such as fault type, fault
Fault Fault Fault Fault resistance
location, fault inception angle, and fault resistance are studied.
type location (km) detection (X) time (ms)
The total number of fault cases simulated for training includ-
ing variations in fault type: LG, LLG, LL, LLL faults, fault AB 12 0 6
locations, fault inception angles, and fault resistances are BC 22 5 11
380. Three phase current and zero sequence current signals CA 32 10 10
ABC 42 10 7
are processed with DB-4 wavelet up to level 3. In the proposed
AG 52 0 15
technique approximate DWT coefficients of three phase cur- BG 62 20 18
rents obtained after wavelet reconstruction process are used CG 72 40 20
as inputs to LDA based fault detector. On the other hand in ABG 82 60 12
addition to approximate DWT coefficients of three phase cur- BCG 92 80 14
rents and zero sequence currents are also used as input to LDA CAG 99 100 17
based fault classifier. Fault detection and classification are car-
ried out in separate modules which will be described below.

4.2. Proposed fault detection method

Table 4 Fault detection time in case of different power flow
angles with Rf = 0.001 X and Ui = 0°.
Proposed LDA based fault detection scheme is shown in
Fig. 5. LDA based fault detection module consists of training Fault Fault Power flow Fault detection
type location (km) angle (°) time (ms)
and testing phase. Training data set for the detection of fault
consists of samples of fault and no fault cases. The number AG 0.1 5 18
of fault samples for one fault case is 5. So total number of fault BG 1 15 13
samples for training is 1900. Total number of no fault samples CG 11 25 8
ABG 21 35 6
given in training is 100. So total of 2000 samples are given as
BCG 51 45 4
input to training module. The LDA based fault detection mod-
CAG 61 5 18
ule detects the fault against the trained LDA network. Input AB 71 15 16
samples of three phase currents are given to the network and BC 81 25 9
trained using LDA. The output of the detector will be low CA 91 35 7
(0) when there is no fault in the system. The output of the ABC 99.9 45 3
detector will be high (1) when there is fault in the system.
204 A. Yadav, A. Swetapadma

different locations with varying fault resistance (0 O, 50 O and

Table 5 Fault detection time in case of different power flow
100 O) and fault inception angle (0°, 45°, 90°, 135°, 180°, 225°,
angles and faults with Rf = 0.001 X.
270°). Some of the test results are discussed below.
Fault Fault Fault inception Fault detection
5.1. Fault near boundaries type location (km) angle (°) time (ms)
AG 3 0 18
ABG 13 45 20
In order to check the performance and to evaluate the reach
AB 23 90 14
setting of the proposed technique different types of faults at
ABC 33 135 19
different locations between 85 and 99 km from the relaying BG 43 180 17
point bus-1 with increment of 2 km have been studied. To BCG 53 225 13
study performance of relay in case of close in faults various BC 63 270 20
near end faults having fault location ranging from 0.1 km to CG 73 315 18
1.5 km with step of 0.2 km are reported in Table 2. After

2
Output of LDA
based Fault
Detector

1
X: 86
0 Y: 1
X: 80
-1
20 40 60 Y: 0 80 100 120 140 160 180 200
Time (ms)
(a)
2

X: 80
1
Y: 0
A

X: 86
0 Y: 1

-1
20 40 60 80 100 120 140 160 180 200
Output of LDA based Fault Phase Identifier and fault classifier

Time (ms)
2

X: 80
1
Y: 0
B

X: 88
0 Y: 1

-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
1

0
C

-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
2

1
G X: 87
0
Y: 1
X: 80
-1
20 40 60 Y: 0 80 100 120 140 160 180 200
Time (ms)
(b)

Figure 7 (a) Output of fault detection. (b) Output of fault classification during ABG fault for Rf = 0.001 X and Ui = 0° at 0.1 km at
80 ms for 25° power flow angle.
A novel transmission line relaying scheme for fault detection and classification using LDA 205

Output of Fault
X: 95

Detection
2 Y: 1
1
0
-1 X: 85
20 40 60 Y:80
0 100 120 140 160 180 200
Time (ms)
(a)
A Phase

2
1
0 X: 99
Output of Fault Phase Identification and Fault Classification

-1 X: 85 Y: 1
20 40 60 Y:80
0 100 120 140 160 180 200
Time (ms)
X: 95
2 Y: 1
B Phase

1
0
-1 X: 85
20 40 60 Y:80
0 100 120 140 160 180 200
Time (ms)
X: 97
C Phase

2 Y: 1
1
0
-1 X: 85
20 40 60 Y:80
0 100 120 140 160 180 200
Time (ms)
Ground G

-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
(b)

Figure 8 (a) Output of fault detection. (b) Output of fault classification during ABC fault at 65 km with fault resistance of 0.001 X and
fault inception angle of 90° at 87.5 ms.

is AG fault. Fault classification time is within half cycle time

Table 6 Fault detection time in case of non-linear high fault in this case. Proposed wavelet and LDA based relay accurately
impedance. detect the fault for all fault cases.
Fault type Fault location (km) Fault detection time (ms)
5.2. Varying fault resistance
AG 7 10
BG 27 13
The proposed method is also tested for varying fault resistance
CG 47 14
AG 67 13 including high resistance faults. High resistance fault which is
BG 87 14 not detected by many schemes proposed can be detected by the
CG 97 14 LDA method. Some of the results are shown in Table 3 for
varying fault resistance. Fault detection time is within one
cycle for varying fault resistance.
detecting the fault it identifies the fault phase and classifies the
fault. Fault detection time and fault phase identification time 5.3. Varying power flow angle
are shown in Table 2. It shows that the fault detection time
is within 20 ms of time for near boundary faults. Proposed LDA based relay is also tested for different power
Fault detection and classification at 0.1 km are shown in flow angles. Different power flow angles are 5, 15, 25, 35 and
Fig. 6. Fig. 6(a) shows the output of LDA based fault detec- 45. Faults are detected and classified in this case. Fault detec-
tion. Output is low (0) up to 80 ms of time shows that there tion time for different power flow angles is shown in Table 4.
is no fault. After 80 ms it started increasing and reach high Fault detection time is within one cycle time for different
(1) at 92 ms of time. So fault detection time in this case is power flow angles. Fig. 7(a and b) shows the outputs of fault
12 ms. Fig. 6(b) shows the output of fault phase identification detection and fault classification networks for power flow
and fault classification. Fault phases are A, B, C and G which angle of 25° during ABG fault at 80 ms respectively.
are the four plots shown in Fig. 6(b). After 80 ms of time A Fig. 7(a) shows output of fault detection which becomes high
and G phases started increasing to high shows that the fault (1) level after 86 ms. Fault detection time is 6 ms in this case.
206 A. Yadav, A. Swetapadma

Three Phase Currents (CT Primary & Secondary)

Ref.
3000 Ia1 Primary
Ib1 Primary
2500 Ic1 Primary
Ia1 Secondary X ct ratio
2000 Ib1 Secondary X ct ratio
Ic1 Secondary X ct ratio
1500
(Amperes)

1000

500

-500

-1000

-1500
20 40 60 80 100 120 140 160 180 200
Time (in ms)

Figure 9 Three-phase current waveforms during an AG fault resistance of 0.001 X and inception angle of 0° at 90 km with and without
CT saturation.

Table 7 Fault detection time in case of CT saturation. Table 10 Fault detection time in case different short circuit
Fault type Fault location (km) Fault detection time(ms) capacities of source.
AG 6 11 Short circuit Fault Fault Fault detection
BG 16 13 capacity of source type location (km) time (ms)
CG 26 15
1250 MVA AG 12 14
ABG 36 12
ABG 32 17
BCG 46 10
AB 52 18
CAG 56 16
ABC 72 15
AB 66 9
BC 76 13 2000 MVA AG 12 8
CA 86 11 ABG 32 5
ABC 96 14 AB 52 5
ABC 72 5

Table 8 Fault detection time in case of double circuit lines.

Fault type Fault location (km) Fault detection time (ms) Fig. 7(b) shows the outputs of fault classification network
A1G 9 16 wherein the faulty phases A, B and ground G start increasing
B2G 19 15 after 80 ms and reach to high level after 88 ms showing that the
C1G 29 11 fault type is LLG and faulty phases are A and B. As depicted
A1B1G 39 17 in Table 4, the fault classification time for different power flow
B2C2G 49 12 angles is within one cycle time. Relay operation time is within 1
C1A1G 59 15 cycle time for the LDA based relay for different power flow
A2B2 69 14
angles with 100% accuracy in all fault cases.
B1C1 79 11
C2A2 89 18
A1B1C1 99 12 5.4. Varying fault inception angle

Proposed LDA based method is tested for varying fault incep-

tion angle and the results are given in Table 5. For all the cases
Table 9 Fault detection time in case of multi-location faults. tested for varying fault inception angle, fault detection time is
Fault 1 Fault 2 Fault detection
within 1 cycle time. Fault detection and classification outputs
time (ms) during three phase ABC fault at 65 ms at 90° inception angle
are shown in Fig. 8(a and b) respectively. Fig. 8(a) shows the
AG fault at 11 km BG fault at 66 km 18
output of LDA based fault detection module which becomes
ABG fault at 34 km CG fault at 79 km 15
BC fault at 56 km AG fault at 87 km 17
high at 95 ms. Fig. 8(b) shows that the outputs of fault
AB fault at 43 km CG fault at 91 km 11 classification network wherein all the three faulty phases A,
BG fault at 81 km CG fault at 96 km 14 B and C become high after 99 ms, and ground output ‘‘G’’ is
CAG fault at 32 km BG fault at 98 km 16 low all the time.
A novel transmission line relaying scheme for fault detection and classification using LDA 207

5.5. Performance of the proposed method during nonlinear high- 5.7. Performance in case of double circuit line
impedance faults
Proposed LDA based method is also tested for double circuit
The faults with nonlinear high-impedance are simulated using lines considering the zero sequence mutual coupling effect.
MATLAB and the proposed method is tested for non-linear Current signals of both the circuits are taken as input to
high impedance fault with arc resistance of 100 X where arc LDA based method for detection and classification of faults.
resistance is function of arc current. Current threshold for The performance of the relay is tested by some fault cases in
arc extinction is 50 A. Some of the results during nonlinear both the circuits and few test results for double circuit lines
high-impedance faults are given in Table 6 which shows that are shown in Table 8. From this Table 8, it can be concluded
the proposed scheme is not affected by nonlinear high- then the proposed scheme works correctly for double circuit
impedance faults. line also.

5.6. Effect in CT saturation 5.8. Performance in case of multiple location faults

Proposed method is studied to observe effect of CT Proposed LDA based method is checked for faults occurring
saturation. Three CTs are used to measure current using in multiple locations. Multiple location faults are the faults
the saturated transformer block each rated 2000 A/5 A occur at different locations in same time; the conventional dig-
and 25 VA. To study the effect of CT saturation, CTs are ital distance relay is unable to detect multi-location fault
assumed to saturate at 8 pu. Three-phase current waveforms occurring at the same time. The performance of the proposed
during an AG fault at 99 km with Rf = 0.001 X, Ui = 0° scheme during multi-location faults has been investigated and
with and without CT saturation are shown in Fig. 9. some of the test results of multiple location faults are shown in
The test result of LDA based network for fault detection Table 9. From Table 9 it can be observed that proposed LDA
and fault classification with CT saturation is shown in based method can detect multiple location faults correctly
Table 7. within one cycle time.
Output of Fault

X: 109
2 Y: 1
Detection

1
0
X: 100
-1
20 40 60 80 Y: 0 100 120 140 160 180 200
Time (ms)
(a)
Output of LDA BAsed Fault Phase Identification and Fault Classification

1
A Phase

-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
1
B Phase

-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
2
C Phase

X: 100
1
Y: 0
X: 106
0 Y: 1

-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
2
Ground G

X: 100
1
Y: 0
X: 108
0 Y: 1
-1
20 40 60 80 100 120 140 160 180 200
Time (ms)
(b)

Figure 10 (a) Output of fault detection. (b) Output of fault classification for un-transposed line during CG fault at 70 km with Rf
0.001 X and Ui = 0° at 100 ms.
208 A. Yadav, A. Swetapadma

5.9. Performance in case of different sources

Percentage accuracy not mentioned

Highest accuracy up to 98.44%

The power system network under study consists of 400 kV
transmission line fed from sources at both the ends and the
short circuit capacity of the two sources is considered equal
to 1250 MVA and X/R ratio = 10. If the SCC of one source
is changed, in that case the current flowing in the line will

Not mentioned
change, this requires adding the samples of no-fault condition
in the training data set. The test result of proposed fault detec-
Accuracy

98.703%
99.91%

tion and classification scheme for power system network with

100%
98%
different source capacities is shown in Table 10. It is clear that
the proposed scheme is not affected by variation in source
capacities.

99% of line length

90% of line length

90% of line length

80% of line length

80% of line length

Not mentioned
Reach setting

5.10. Performance in case of un-transposed lines

The performance of the proposed LDA based fault detection

100%

and classification scheme is also evaluated for un-transposed

line in this subsection. For this a single line to ground fault
in ‘‘C’’ phase of the 400 kV, 50 Hz un-transposed is simulated
Wavelet transform and linear discriminant analysis

using ATP-EMTP software and current signals obtained are

then pre-processed in MATLAB software and then the pro-
Use particle swarm optimization (PSO) for

posed algorithm is tested for this fault case and results are
training of ANN and wavelet transforms

shown in Fig. 10. Fig. 10 shows output of fault detection

Systematic fuzzy rule based approach

and classification during CG fault at 70 km with fault resis-

tance of 0.001 X and fault inception angle of 0° at 100 ms. It
Fuzzy neural network (FNN)

can be seen that the proposed algorithm can correctly detect

and classify the fault in un-transposed line within one cycle
Support Vector Machine

Elliptical 2-D structure

time. This is owing to the fact that the performance of LDA

network depends upon the approximate DWT coefficients
Wavelet transform

and not the magnitude of the instantaneous phase current.

Algorithm used

6. Comparison with other schemes

Proposed method is compared with other fault detection and

classification schemes as shown in Table 11. Most of the tech-
Normalized peaks of fundamental component of current

niques given in Table 11 have reach setting within 90% [1,10–

Samples of one cycle duration of line currents and zero
Three-phase voltage samples of quarter and half cycle

12,15] of line length while proposed method has reach up to

99% of line length. Proposed method requires only quarter
cycle samples (5 samples) for detection and classification which
Detailed coefficients of phase current signals,

is advantage. Accuracy of the proposed method is 100% com-

Three phase currents of quarter (1/4) cycle
Voltage and current signals of 1.4 cycles

parison to all the other methods shown in table.

and voltage waveforms of the 3 phases

7. Conclusions
measured at the sending end

This paper presents the wavelet and LDA based fault Detector
Comparison with other schemes.

and Classifier for protection of both single as well as double

circuit transmission line against various types of shunt fault
sequence current

e.g. LG, LL, LLG, and LLL. The performance of the pro-
Current signals

posed scheme is validated considering the effect of CT satura-

tion, variation in power flow angle and different fault
parameters such as fault type, fault location, fault resistance
Inputs

and fault inception angle. Inputs given to the LDA based fault
detector and classifier are approximate coefficients of three
phase currents and zero sequence current. Wavelet
Proposed method
Upender et al. [8]

Gomes et al. [15]

Parikh et al. [12]
Samantaray [10]
Dash et al. [11]

re-construction has been applied on the third level approxi-

mate coefficients to reconstruct the original signals in time
Youssef [1]
Table 11
Methods

domain. Five postfault samples of these signals are then used

to train the network which is an offline process. Once the
LDA network has been trained, it is tested for different fault
A novel transmission line relaying scheme for fault detection and classification using LDA 209

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