International Journal

Internal Fault of Control,inAutomation,

Classification Transformerand Systems,
Windings vol.Combination
using 4, no. 3, pp.of365-371,
DiscreteJune 2006Transforms and
Wavelet 365

Internal Fault Classification in Transformer Windings using Combination

of Discrete Wavelet Transforms and Back-propagation Neural Networks
Atthapol Ngaopitakkul and Anantawat Kunakorn*

Abstract: This paper presents an algorithm based on a combination of Discrete Wavelet

Transforms and neural networks for detection and classification of internal faults in a two-
winding three-phase transformer. Fault conditions of the transformer are simulated using
ATP/EMTP in order to obtain current signals. The training process for the neural network and
fault diagnosis decision are implemented using toolboxes on MATLAB/Simulink. Various cases
and fault types based on Thailand electricity transmission and distribution systems are studied
to verify the validity of the algorithm. It is found that the proposed method gives a satisfactory
accuracy, and will be particularly useful in a development of a modern differential relay for a
transformer protection scheme.

Keywords: Discrete wavelet transforms, internal faults, neural network, transformer windings.

1. INTRODUCTION and artificial intelligent tools, the development of

more sophisticated protection systems as well as fault
Protective devices are an important part for diagnosis for the power transformer has been
detecting fault conditions in a power system. The progressed with the applications of wavelet transform
appropriate protection scheme must be selected to (WT) and artificial neural networks (ANNs) [7-10].
ensure the safety of power apparatus and reliability of This paper presents an application of Wavelet
the system. Generally, power transformers can be transform and a decision algorithm based on back
protected by overcurrent relays, pressure relays and propagation neural networks in order to detect the
differential relays depending on purposes [1]. For internal faults at the windings of a two-winding
differential protection, the differential current, which transformer. The transformer model with the stray
is generated by a comparison between the primary capacitances is used so that internal fault signals with
current and the secondary current detected via current high frequency components can be calculated. The
transformers, is required. The differential protection is simulations, analysis and diagnosis are performed
aimed at detecting internal faults in transformer using ATP/EMTP and MATLAB. The current
windings. In a normal operation or in a fault condition waveforms obtained from ATP/EMTP are extracted to
due to the external short circuits, the differential several scales with the Wavelet transform, and the
current is relatively small, and the differential relay coefficients of the first scale from the Wavelet
should not function [1,2]. However, there are some transformer are investigated. The comparison of the
factors that can cause a needless operation of the coefficients is performed and used as an input for
differential protection such as effects from training processes of the neural networks. The
magnetizing inrush current. To avoid the malfunction construction of the decision algorithm is detailed and
of the differential relay, the discrimination between implemented with various case studies based on
internal faults, magnetizing inrush current and Thailand electricity transmission and distribution
external short circuit current is required [1-3]. Several systems.
transformer models and decision algorithms have been
proposed and discussed for such a task [4-6]. Recently, 2. WAVELET TRANSFORMS
with the advance of signal processing technologies
__________ Normally, the traditional method of signal analysis
is based on Fourier transforms. Fourier transform is a
Manuscript received August 30, 2005; accepted February 7,
2006. Recommended by Editorial Board member Yuan Fang process of multiplying a signal by a sinusoid in order
Zheng under the direction of Editor Jin Young Choi. to determine frequency contents of a signal. The
Atthapol Ngaopitakkul and Anantawat Kunakorn are with output of the Fourier transform is sinusoids of
Department of Electrical Engineering, Faculty of Engineering, different frequencies. It is found that Fourier
King Mongkuts Institute of Technology Ladkrabang, transform is not appropriate to analyse faults in a
Bangkok 10520, Thailand (e-mail: kkananta@kmitl.ac.th).
power system with transient based protection methods,
* Corresponding author.
366 Atthapol Ngaopitakkul and Anantawat Kunakorn

because in such a system the desirable information locating and classifying faults on transmission lines
may be located in both the frequency domain and the [13,14]. It is, therefore, useful to investigate the high
time domain. Due to the limits of Fourier transforms frequency components superimposed on the fault
in applications with transient signals, Wavelet current signals for a development of a transient based
transforms has been proposed as an alternative tool in protection for a transformer. As a result, in this paper
signal analysis. A wavelet is a small-localized wave of the combination of the transformer models proposed
a particular shape and finite duration that has an by Bastard et al [4] as shown in Fig. 1, with the high
average value of zero. The wavelet transform is a tool frequency model including capacitances of the
that cuts up data or functions or operators into transformer recommended by IEEE working group
different frequency components, and then studies each [15] as shown in Fig. 2, are used for simulations of
component with a resolution matched to its scale [11, internal faults at the transformer windings.
12]. The advantage of the transform is that the band of From Fig. 1, for the phase winding of the
analysis can be fine adjusted so that high frequency transformer with internal faults, the winding is
components and low frequency components are divided into two parts in the case of winding to
detected precisely. Results from the wavelet transform ground faults, and three parts in the case of interturn
are shown on both the time domain and the frequency faults.
domain. The wavelet transform can expand signals in The capacitances shown in Fig. 2 are as follows:
term of using a shift in time or translation as well as Chg = stray capacitance between the high voltage
compression in time or dilation of a fixed wavelet winding and ground
function named as the mother wavelet [9]. The Clg = stray capacitance between the low voltage
wavelet transform, which has a change in the analysis winding and ground
scaled by the factor of two, is called discrete wavelet Chl = stray capacitance between the high voltage
transform (DWT) as in (1). winding and the low voltage winding.

1 n k 2m
DWT ( m, n ) = f ( k ) m , (1) a a
2m k 2 Phase A Phase A
b b
n k2 m 2 c 2
where m = mother wavelet (in this paper,
2
Daubechies 4 is selected as a mother wavelet.)
Phase B Phase B

3. TRANSFORMER WINDING MODELS 3 4 3 4

For a computer model of a two-winding three-phase

transformer having primary and secondary windings
Phase C Phase C
in each phase, BCTRAN is a well-known subroutine
on ATP/EMTP. To study internal faults of the 5 6 5 6
transformer, Bastard et al proposed modification of Primary Secondary Primary Secondary
the BCTRAN subroutine. Normally, the BCTRAN
uses a matrix of inductances with a size of 6x6 to Fig. 1. The modification on ATP/EMTP model for a
represent a transformer, but with the internal fault three-phase transformer with internal faults[4].
conditions the matrix is adjusted to be a size of 7x7
for winding to ground faults and of 8x8 for interturn C hl
faults [4]. In the research work of Bastard et al [4], the
model was proved to be validate and accurate due to a
comparison with measurement results. However, the C hg Clg
effects of high frequency components which may
occur during the faults are not included in such a
model. Islam and Ledwich [5] described the
characteristics of high frequency responses of a
transformer due to various faults. It has been shown
that the fault types and fault locations have an Primary 115/23 kV Secondary
influence on the frequency responses of the 50 MVA
transformer [5]. In addition, it has been proved that
transient based protections using high frequency Fig. 2. A two-winding transformer with the effects of
components in fault currents can be applicable in stray capacitances[15].
 Internal Fault Classification in Transformer Windings using Combination of Discrete Wavelet Transforms and 367

4. CASE STUDIES AND FAULT DETECTION

ALGORITHMS

A 50 MVA, 115/23 kV two-winding three-phase

transformer was employed in simulations with all
parameters and configuration provided by a
manufacturer [16]. The scheme under investigations is
a part of Thailand electricity transmission and Fig. 3. The system used in simulations studies.
distribution system as depicted in Fig. 3. It can be
seen that the transformer as a step down transformer is
connected between two subtransmission sections. The
primary and secondary current waveforms, then, can
be simulated using ATP/EMTP, and these waveforms
are imported into MATLAB/Simulink for a
construction of fault diagnosis process.
To implement the transformer model and cover all
regions of operating conditions training and testing
data were simulated with various changes in system
parameters as follows:
- The angles on phase A voltage waveform for the
instants of fault inception were 30o and 210o.
- Two types for internal faults at the transformer
windings (both primary and secondary) which are
winding to ground faults and interturn faults, were
investigated.
- For the winding to ground faults, the fault locations Fig. 4. Wavelet transform of differential currents
were designated on any phases of the transformer (Turn to ground fault at 40% in length of the
windings (both primary and secondary) at the length high voltage winding).
of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and
90% measured from the line end of the windings. applied to the quarter cycle of current waveforms after
- For the interturn faults, the position of point a on the the fault inception. With several trial and error
transformer winding, as shown in Fig. 1, was varied at processes, the decision algorithm on the basis of
the length of 10%, 20%, 30%, 40%, 50%, 60%, 70% computer programming technique is constructed. The
and 80% measured from the line end of the windings. most appropriate algorithm for the decision with all
- For the interturn faults, the position of point b on the results from the case studies of the system under the
transformer winding, as shown in Fig. 1, was varied at investigations can be concluded as follows[17]:
the length of 10%, 20%, 30%, 40%, 50%, 60%, 70% For detecting the phase with a fault condition,
and 80% measured from the line end of the windings. for td = 0.000005 : 0.000005 : 0.1
- Fault resistance was 5 .
(td + t1) 5 * X max(0 td) )
(X diff diff
With fault signals obtained from the simulations, if
the differential currents, which are a deduction
between the primary current and the secondary current then diff
X chk =1
in all three phases as well as the zero sequence, are
calculated, and the resultant current signals are else
extracted using the Wavelet transform. The diff
X chk =0
coefficients of the signals obtained from the Wavelet end
transform are squared for a more explicit comparison. end
Fig. 4 illustrates an example of an extraction using
Wavelet transform for the differential currents and where
zero sequence current from scale1 to scale 5 for a case
of phase A to ground fault at 40% in length of the high t1 = 5 sec (depending on the sampling time
voltage winding. used in ATP/EMTP),
After applying the Wavelet transform to the X diff
(td + t1) = coefficient from Wavelet transform for the
differential currents, the comparison of the
differential current detected from phase X
coefficients from each scale is considered so that the
at the time of td+t1,
fault classifications can be analysed. In case of
internal faults and external faults Wavelet transform is Xdiff
max(0t) = coefficient from Wavelet transform for the
368 Atthapol Ngaopitakkul and Anantawat Kunakorn

differential current detected from phase X Newton algorithm, Levenberg-Maquardt algorithm,

at the time from t =0 to t = td, Resilient Backpropagation, Conjugate Gradient
X diff
chk = comparison indicator for a change in algorithm etc. Each method has difference efficiency
coefficient from Wavelet transform and training time. A comparison of the various
diff diff diff training algorithms has been mentioned, and it is
( Acheck , Bcheck , Ccheck ), used for separation shown that Levenberg-Marquardt algorithm has the
between normal conditions and faults. fastest convergence [18]. As a result, Levenberg-
Marquardt algorithm is selected as adjustment weight
By performing many simulations, it has been found and bias in this paper.A training process for the back
that when applying the previously detailed algorithm propagation neural network can be divided into three
for detecting internal faults at the transformer winding, parts as follows [18]:
the coefficient in scale 1 from DWT seems enough to
indicate the internal fault inception of the transformer. 1) The feedforward input pattern, which has a
As a result, it is unnecessary to use other coefficients propagation of data from the input layer to the hidden
from higher scales in this algorithm, and the layer and finally to the output layer for calculating
coefficients in scale 1 from DWT are used in training responses from input patterns illustrated in (2) and (3).
processes for the neural networks later.
a2 = f 2
(lw 2,1
( )
* f 1 iw1,1 * p + b1 + b 2 , ) (2)
( )
5. NEURAL NETWORK DECISION
ALGORITHM AND SIMULATION RESULTS o / p ANN = f lw 3 3, 2
*a + b ,
2 3
(3)

Artificial neural networks are an attempt to where

simulate the human brains non-linear and parallel p = input vector of ANNs,
processing capabilities. Although there are many types iw1,1 = weights between input and the first hidden
of neural networks, only a few of neuron-based layer,
structures are being used commercially. One particular lw2,1 = weights between the first and the second
structure, a back-propagation neural network, is the hidden layers,
most popular tool for applications such as pattern lw3,2 = weights between the second hidden layer and
recognition fault classification etc. A structure of a output layers,
back propagation neural network consists of three b1, b2 = bias in the first and the second hidden layers
layers which are an input layer, at least one hidden respectively,
layer and an output layer. Each layer is connected with b3 = bias in output layers,
weights and bias. In this paper, a three-layer back f1, f2 = activation function(Hyperbolic tangent sigmoid
propagation neural network with one input layer, two function : tanh),
hidden layers and one output layer is employed as f3 = activation function(Linear function).
shown in Fig. 5.
Hyperbolic tangent sigmoid functions are used as 2) The back-propagation for the associated error
an activation function in all hidden layers while linear between outputs of neural networks and target
function is used as an activation function in output outputs; The error is fed to all neurons in the next
layers. In addition, there are many adjustment weight lower layer, and also used to an adjustment of weights
and bias in the neural network toolbox such as quasi- and bias.

Input Layer 1st Hidden Layer 2nd Hidden Layer Output Layer

Fig. 5. Back propagation with two hidden layers [18].

 Internal Fault Classification in Transformer Windings using Combination of Discrete Wavelet Transforms and 369

3) The adjustment of the weights and bias by and output neurons, number of training cases and the
Levenberg-Marquardt (trainlm). This process is aimed type of activation function in hidden layer etc. The
at trying to match between the calculated outputs and initial number of neurons for the first hidden layer can
the target outputs. Mean absolute percentage error be calculated as shown in (5).
(MAPE) as an index for efficiency determination of
the back-propagation neural networks is computed in z=
2
(r + q ) , (5)
(4). 3

1 n o / p ANNi o / pTARGETi where

MAPE = * * 100% , (4) z = Initial number of neurons in the first hidden layer,
n i =1 o / pTARGETi
r = Number of neurons input,
q = Number of neurons output.
where n = number of test sets.

A training process was performed using neural When the initial number of neurons in the first
network toolboxes in MATLAB [18]. A structure of hidden layer had been determined, the final number of
the back propagation neural network consists of 4 the neurons in the same layer had to be calculated in
neuron inputs and 8 neuron outputs. The inputs are the order to stop the training process. The final number
maximum coefficients of the differential currents and can be obtained from:
zero sequence current as mentioned in the previous
z _ st = z + z1 , (6)
section. In this paper, there are 360 sets for training.
The output variables of the neural networks are where
designated as either 0 or 1 with various types of faults z_st = the final number for the neurons in the first
as shown in Table 1. hidden layer,
Before starting the training process, a number of
neurons in each hidden layer have to be fixed 5 2 z6
according to various factors such as: number of input 4
7 z 10
z1 = if
Table 1. Output patterns from neural networks for 3 11 z 13
various fault types. 2 14 z.

Classifications of Fault A1 B1 C1 G1 A2 B2 C2 G2 During the training process, the weight and biases
were adjusted, and there were 20,000 iterations in
Winding to ground phase A order to compute the best value of MAPE. The
1 0 0 1 0 0 0 0
(HV)
number of neurons in both hidden layers was
Winding to ground phase A increased before repeating the cycle of the training
0 0 0 0 1 0 0 1
(LV) process. The training procedure was stopped when
Interturn phase A reaching the final number of neurons for the first
1 0 0 0 0 0 0 0
(HV) hidden layer or the MAPE of test sets was less than
Interturn phase A 0.5%. The training process can be summarized as a
0 0 0 0 1 0 0 0
(LV) flowchart shown in Fig. 6 while various results from
Winding to ground phase B the training process can be shown in Table 2 with the
0 1 0 1 0 0 0 0 initial number of neurons for the first hidden layer
(HV)
Winding to ground phase B obtained from (5).
0 0 0 0 0 1 0 1
(LV)
Interturn phase B Table 2. Results from the training process (Performed
0 1 0 0 0 0 0 0
(HV) on a PC with Pentium IV 2.4GHz CPU, with
Interturn phase B 512 MB RAM).
0 0 0 0 0 1 0 0
(LV) Number of
Time used in
Winding to ground phase C neurons in the MAPE of Test
0 0 1 1 0 0 0 0 training process
(HV) first hidden set (%)
(minute)
Winding to ground phase C layer
0 0 0 0 0 0 1 1
(LV) 8 0.55556961 100.59
Interturn phase C 9 0.5555649 141.28
0 0 1 0 0 0 0 0
(HV)
10 0.59023954 178.32
Interturn phase C
0 0 0 0 0 0 1 0 11 0.5678628 221.12
(LV)
370 Atthapol Ngaopitakkul and Anantawat Kunakorn

Start Table 3. Outputs from the neural network for the

simulation case shown in Fig. 4.
A1 B1 C1 G1 A2 B2 C2 G2
Normalization input pattern
1 0 0 1 0 0 0 0

Initial number of neurons

Table 4. Accuracy of fault classification from the
hidden1 = z proposed algorithm.
hidden 2 = z -1 Number of
Types of faults Accuracy
case studies
Winding to ground fault
18 100%
at the high voltage side
Winding to ground fault
18 100%
for i = 1 at the low voltage side
Interturn fault
72 98.61%
at the high voltage side
Interturn fault
72 100%
at the low voltage side
Random initial weight
and biases

From Table 3, it can be seen that the index value at

Compute output and A1 is 1 and that at G1 is also 1 while others are 0.
MAPE of BP This means that there is an internal fault occurring at
the high voltage side, and the internal fault is
No classified as a winding to ground fault, which is
i=i+1 i > 20000 correlative to the condition of the transformer used in
simulations of Fig. 4.
Yes In addition, when all case studies are tested with
Store Weight, bias that various types of internal faults and different locations
computed minimum on both primary windings and secondary windings at
MAPE the three-phase transformer, the accuracy of the
results obtained from the prediction from the neural
network is illustrated in Table 4.
No hidden1 = z + z1
hidden1=hidden1+1; 6. CONCLUSIONS
or
hidden2=hidden2+1;
MAPE < 0.5%
A technique using discrete wavelet transform in
Yes
combination with back propagation neural networks
Store Weight, bias that in order to classify internal fault types of a three-phase
computed minimum transformer has been proposed. The maximum values
MAPE from the first scale at cycle of phase A, B, and C of
post-fault differential current signals and zero
sequence current obtained by the wavelet transform
End
have been used as an input for the training process of
a neural network in a decision algorithm with a use of
Fig. 6. Flowchart for the training process. the back propagation neural networks. Various case
studies have been studied including the variation of
The decision algorithm based on the neural network, fault inception angles, fault types and fault locations.
then, is tested with 180 case studies. The internal fault The results have illustrated that the proposed
conditions in the windings of the transformer are algorithm is able to predict the internal faults at
simulated on ATP/EMTP. In order to explain the windings of a transformer with an accuracy of higher
verification of the neural network algorithm, the than 98%. This technique should be useful in the
simulation results shown in Fig. 4 are used as an differential protection scheme for the transformer. The
example. For this case, when applying the decision further work will be the improvement of the algorithm
algorithm for a prediction, the output obtained from so that fault locations on the windings of the
neural network is as shown in Table 3. transformer can be identified.
 Internal Fault Classification in Transformer Windings using Combination of Discrete Wavelet Transforms and 371

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October 2003. Thailand in 1992. He received his
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frequency localization and signal analysis,
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