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Machine Learning Based Classification of Inrush,

External and Internal Faults in Differential

Protection of Power Transformer

Devshree Rana Neelesh Kumar

Electrical and Electronics Department Electrical and Electronics Department

M.Tech 4th

sem(ED&PS), DIMAT Assistant Professor, neelesh.patel27

Raipur, [email protected] @gmail.com

Abstract — This abstract illustrates differential protection

scheme for Power Transformer (PT) by using combined

Discrete Wavelet Transform (DWT), Principal Component

Analysis (PCA) and Support Vector Machines (SVMs)

methods. Discrimination between internal, external fault

and magnetizing inrush condition is a very challenging

task in PT differential protection scheme. Therefore,

discrete wavelet transform is used to extract the time and

frequency division information simultaneously from the

relaying signal (i.e. differential current) and then PCA is

used to reduce the dimensions of decomposed signals from

DWT. And then these reduced dimensional features of the

relaying signal is used to train and test the SVM to detect

internal fault. The PT is modelled in PSCAD/EMTDC

software to obtain the relaying under different operating

conditions. The proposed algorithm is evaluated in

MATLAB under different operating conditions of PT and

the tested data is simulated in PSCAD/EMTDC by varying

inception angle, fault location, fault resistances, loading

conditions of PT. Results show that the proposed

algorithm is stable, reliable and selective under different

operating conditions of PT

Keywords: - Power transformer (PT), Harmonic Restrained

(HR), Discrete wavelet transform (DWT), Principal

Component Analysis (PCA), Support vector machine (SVM).

1. INTRODUCTION

Medium and large power transformers are very important and

vital component of electric power systems. Due to its

importance and cost, its protection needs to be addressed

properly. The protection should be fast and reliable. Proper

continuous monitoring of power transformer can provide early

warning of electrical failure and can prevent catastrophic

losses. It can minimize damages and enhanced the reliability

of power supply. Accordingly, high expectations are imposed

on power transformer protective relays. Expectations from

protective relays include dependability (no missing

operations), security (no false tripping), speed of operation

(short fault clearing time) and stability [1]. Differential

protection scheme is generally used as the primary protection

of medium- and large-sized power transformers, in which the

value of differential current greater than no-load value

indicates an internal fault. A transformer is said to be a static

device as it contains two or more than two stationary electric

circuits which is interlinked with the common magnetic

circuits. Its purpose is to transfer the electrical energy from

one circuit to another circuit through magnetic core without

changing the frequency. It works on the principle of faradays

law of electromagnetic induction. There are two winding in

transformer the one who receives energy from the AC Mains

is called primary winding and the one who delivers energy to

the load is called the secondary winding. Power transformer is

also a kind of a transformer that is generally used in the

generating station (step-up) and at substation (step-down) to

transfer the large amount of power. These are used for

stepping up and stepping down the voltages. They are

designed in such a way that they deliver maximum efficiency

at full load.

There are different operating conditions of the power

transformer will be discussed briefly. Power transformer

operating conditions can be categorized in the following ways:

Normal operating mode is the one when power transformer

supplies the power to the load without interruption. It can be

said that the power system is in the healthy condition. In this

case rated or less than rated current flows in the transformer,

that means load could varies [1].Over-excitation is the one

when sudden removal of the large reactive load leads to the

increment in power systems terminal voltage [2].External fault

is the one they occur outside of the transformer and outside the

protection zone of the power transformer. It could be LG, LL,

LLG, LLL or LLLG fault. In this case huge amount of current

above rated current flows in the power system. Internal fault is

the one when winding of the power transformer gets short

circuited with each other and it could get grounded. The types

of internal fault are LG, LL, LLG, LLL, LLLG and TT fault.

In this case huge amount of current above rated current flows

in the power system. Magnetizing inrush is the one when

transformer gets connected from the source the huge amount

of current flows in the source side of the power transformer.

This is also called the energization of the transformer. The

magnitude of this current depends on switching angle between

0-360 degree and the residual flux presents in the transformer

core [1].The magnitude of the inrush current could be 10 times

greater than the rated current. Sympathetic inrush is the one

when any transformer gets energized in parallel with the

previous one than it affects the current in the previous

CIKITUSI JOURNAL FOR MULTIDISCIPLINARY RESEARCH

Volume 6, Issue 8, August 2019

ISSN NO: 0975-6876

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transformer. This condition is called sympathetic inrush [2].

Recovery inrush is the one when sever external fault gets

removed it affects the characteristics of the currents in the

power transformer.

Power transformers are devices that require continuous

monitoring and fast protection because they are essential to the

electrical power systems. About 10% of faults take place into

power transformers, in which 70% of these faults are caused

by short-circuits in its windings. In case of magnetizing inrush

and sympathetic inrush large current flows in the source side.

This large current from the source results in large differential

current, which in turn causes the relay to operate undesirably.

Owing to this reason, conventional differential relays are

blocked for few initial cycles of energization which makes the

relay operation delayed on switching-in of the transformer on

faults. And also in case of high amplitude current due to

external fault causes CTs to saturate this results in the high

amplitude differential current. Therefore, discrimination

between magnetizing inrush, external fault and internal fault

condition is the key to improve the security of the differential

protection scheme. Traditionally, two types of approaches are

used for the purpose of discrimination between inrush and

internal fault, that is, harmonic restraint (HR) and waveform

identification (WI) concepts [2].The HR is based on the fact

that the second harmonic (sometimes the fifth) component of

the magnetizing inrush current is considerably larger than that

in a typical fault current. The literature reveals the extensive

use of the HR method. However, the HR-based method fails to

prevent false tripping of relays because high second harmonic

components during internal faults and low second harmonic

components are generated during magnetizing inrush for

transformers having modern core material [1].Therefore, the

techniques based on detection of second/fifth harmonic

component are not useful to discriminate between the

magnetizing inrush and internal fault condition of modern

power transformers. The second method consists of

distinguishing magnetizing inrush and over-excitation

condition from internal fault condition on the basis of WI

concept. The development of advanced digital signal-

processing techniques and recently introduced artificial neural

network (ANN) provide an opportunity to improve the

conventional WI technique and facilitate faster, secured and

dependable protection for power transformers. However, a

large number of training data samples, slow convergence

during training, and a tendency to over-fit data are the

limitations of ANN-based schemes. The importance of the

protection and limitations of the existing techniques inspired

to do research in this area.

2. DIFFERENTIAL PROTECTION

Differential current relay is use to protect power transformer

in case of internal fault. It is mainly two types, Simple

differential relay and Percentage differential relay. Percentage

differential relay without restraining coil is considered as a

simple differential relay. Number of turns in restraining coil

and operating coil decides the slope of the differential relay.

Slope of the differential relay is in between differential current

vs. restraining current (biased current).

Figure.1. Percentage differential relay

The percentage differential relay can be made more immune to

mal-operation on 'external fault' by increasing the slope of the

characteristic. That‟s why the dual slope percentage

differential current relay is used. Where slope1 gives high

sensitivity for internal faults and slope2 gives high security for

external fault [3]. The magnitude of slope2 is greater than

slope1 to achieve proper sensitivity and security. Knee point

of dual slope differential current is decided where saturation of

CT is started.

Figure 2. Operating characteristics of percentage

differential relay

3. DISCRETE WAVELET TRANSFORM

Discrete signal is comprises by using scaling and wavelet

function is:

, -

√ ∑ , - , -

√ ∑∑ , - , -

(1)

Where,

, - is scaling function

, - is wavelet function

, - is approximate coefficient

, - is detailed coefficient

is shifting parameter

is shifting parameter

Approximate (2) and detailed (3) coefficients are:

, -

√ ∑ , - , -

(2)

, -

√ ∑ , - , -

(3)

In simple way it means that sampled input signal passes

through LPF and HPF simultaneously and then it gets down-

Equipment under

protection

CB CBCT

n:1

CT

n:1 ILIS

I2

I1

(I1 - I2)

Nr/2Nr/2

No

Restraining coil

Operating coilPercentage

differential

relay

Trip Trip



ISSN NO: 0975-6876


sampled by two. Output of the HPF is a convolution between

input signal and coefficients of HPF and then it gets down-

sampled by two. This is called detailed coefficient and it

contains upper half of the frequency present in the input

signals [8]. And Output of the LPF is also a convolution

between input signal and coefficients of LPF and then it gets

down-sampled by two. This is called approximate coefficient

and it contains lower half of the frequency present in the input

signals. And then again output of LPF goes to same kind of

LPF and HPF and gets down-sampled by two, and this process

goes on until goal will be reached.

The frequency band of detailed and approximate coefficient

after m-level of decomposition are:

,

-

,

-

Figure. 3. Decomposition LPF and HPF

Figure (3) shows the decomposition LPF and HPF of

Daubichies6 (db6) mother wavelet family, where 6 represents

the order of the filter.

Figure. 4. Decomposition filtering block diagram

After the decomposition of sampled signals, these

approximate and details coefficient pass through thresholding

block.

4. PRINCIPAL COMPONENT ANALYSIS

Here the basic application of principal component analysis is

to reduce the dimension of the input vector that goes to the

SVM for classification purpose so that the classification

accuracy of the SVM increases.

PCA finds a new set of dimensions such that all the

dimensions are orthogonal and ranked according to the

variance of data among them [7]. It means more important

principle axis occurs first.

PCA works as follows:

It first calculates the covariance matrix of „n‟

dimensional input data sets.

Calculate Eigen vectors and corresponding Eigen

values.

Arrange the Eigen vectors according to their Eigen

values in decreasing order.

Select first „m‟ Eigen vectors and that will be the new

„m‟ dimensions.

Transform the original n-dimensional data points into

„m‟ dimensions.

Figure. 5. Mapping of data from two dimensional to one

dimensional in the red line axis

5. SUPPORT VECTOR MACHINES

Support vector machines are supervised learning model with

associated learning algorithm that analyses set of data for

classification or regression purposes. Here SVM is used for

classification purposes. SVM as a classifier takes training data

sets of two categories (class1 and class2) after that it builds the

model that assigns new data set into either class1 or class2.

SVMs are based on the idea of finding a hyper-plane that best

divides a dataset into two class, in case of two-dimensional

data points the hyper-plane would be a line (one dimension

less than the dimension of the input data). A good separation

is achieved by the hyper-plane that has the largest distance to

the nearest training-data point of any class (so-called

functional margin), since in general the larger the margin the

lower the generalization error of the classifier [15]. Figure

4.12 shows three hyper-plane H1, H2 and H3, where H1

clearly does not classify the input data sets, but H2 and H3

both are able to classify. Due to the fact that H3 has high

functional margin than the H2 hyper-plane, H3 would be the

LPF

HPF

LPF

HPF

LPF

HPF 2

2

2

2

2

2

f(n)

Detail 1

Detail 2

Detail n

Approximate n



ISSN NO: 0975-6876


best hyper-plane that would lead to the minimum

generalization error

Figure.6. Choosing proper hyper-plane to classify two

types of data sets

SVMs are a group of learning machines for solving pattern

recognition problems efficiently. SVMs try to find the hyper-

plane, which separates optimally the training patterns

according to their classes (i.e. hyper-plane with maximum

boundary margin). They have a good generalization

performance over traditional approaches, since their training is

based on the principle of structural risk minimization (SRM)

(i.e. minimizing the upper bound on the expected risk), while

the training traditional approaches is based on empirical risk

minimization (i.e. minimizing the number of the training

error). SVMs have a high computational efficiency in terms

of speed and complexity [11]. They are also more preferable

when dealing with high dimensional data as they are more

robust than traditional approaches which may over-fit the data.

The description of SVMs classification can be explained as

follows:

5.1 Linearly Separable Data:-

Let us consider a linear classification problem aiming to find

optimal separating hyper-plane with maximum margin [15].

Assuming that for the set of n training data:

*( ) * + + (4)

Where,

i=1, 2, 3….n;

is a d-dimensional input vector

indicate class 1 or -1 for the corresponding

For this it is possible to find a maximum margin hyper-

plane that linearly separates the appropriate class as shown in

the figure 4.5. In such case hyper-plane can be described by

the formula ; where is a weight vector and

is a bias. Additionally it is possible to find two hyper-planes

with no points between them one is 1 and another

one is , then a distance between these two

hyper-plane is called margin

‖ ‖ .

Figure.1. Hard margin classifier

Then class 1 (1) and class 2 (-1) for the input vector is

depicted by the following formulla.

, if =1

(5)

Or

, if =

(6)

For better SVM classifier this margin should be maximum, it

means the ‖w ‖ should be minimum. This finding w and

b can be done by several optimization techniques [12]. But

this optimization problem is solved by introducing Lagrange

multipliers and then class of the unknown data x may be

determined as follows:

( ) ( )

(7)

Where,

∑ ( )

Where,

is a input vector to be classify

is a support vector

is a class of given support vector

is a Lagrange multiplier

is a number of support vector

is a bias value (calculated during training process)

5.2 Linearly Non-separable Data:-

In case when training data can‟t be able to get separated by

linear hyper-plane then these input vector gets mapped into the

one higher dimension feature space in such a way so that the

mapped data gets separated by linear hyper-plane [15]. For

this purpose nonlinear function ø is used. Then the class of

unknown data may be expressed as follows:

X1

X2H1

H2

H3

X1

X2

w

w·x -

b = 0

w·x -

b= -1

w·x -

b = 1 ||w||

2

||w||b

Support

vectors



ISSN NO: 0975-6876


( ) (∑ ( ) ( )

) ( )

( ) ( ) ( ) ( )

Then the decision function of SVM is:

( ) (∑ ( )

) ( )

The most common kernel functions are:

Linear: ( ) ( )

Polynomial: ( ) ( )

Gaussian radial basis function: ( )

( ‖ ‖ ) , for

Hyperbolic tangent: ( ) ( ),

for some (not every) and

Figure.2. Non-linear based SVM classification

5.3 Soft margin:-

It may happen that even in new feature space it is impossible

to split this space into two classes. Then, soft margin method

may be employed to moderate optimization constraints. Soft

margin method allows the classifier to misclassify some

examples, what is illustrated in figure. This method introduces

two parameters (used in training process) [15].

is a slack variable that allow patterns to be in the margin

( , margin errors) or to be misclassified (

).

Figure.3. Soft margin classifier

5.4 General features

Support vector machine is considered as a promising method

for classification due to

solid mathematical foundations,

fast optimization algorithms,

no local optima, unlike in neural networks,

SVMs maximize the margin, which corresponds to

maximizing the generalization performance,

SVMs deal with nonlinear classification efficiently

(employing the kernel trick),

Good generalization performance even in case of

high-dimensional input vector and a small set of

training data.

The following algorithm provides the power transformer

protection



ISSN NO: 0975-6876


Figure.4. DWT and SVM based PT protection algorithm

6. MODELLING, SIMULATION AND RESULTS

Power transformer protection are performed in this thesis. To

achieve that first a power system is modelled in the

PSCAD/EMTDC where a source, power transformer,

transmission line and load is connected. Where ratings of

source is 400kV 50Hz, power transformer is 315 MVA

400kV/220kV 50Hz, transmission line is 220kv 100km and

the load is 285 MW, 137MVAR. The operation of Power

Transformer can be categorized into five categories which is

normal operating condition, internal fault, external fault, over

excitation, magnetizing inrush/ Sympathetic inrush. For these

operating conditions differential current is being generated in

the PSCAD/EMTDC software. In case of inrush three things

are considered first is the residual flux, second is the switching

angle and last is the loading conditions.

Figure.11. Power transformer internal fault model with

CTs

In this case switching angle is varied from 0° to 330° in the

interval of 10° and residual flux is varied from 10% to 80% of

rated flux. When generating internal fault current three things

are considered, fault percentage of winding, fault inception

angle (time of fault) and fault resistances (0.01 ohm to 20

ohm). And this differential currents are sampled at 10 kHz.

The different operating conditions model and the differential

current waveform are shown in the figures above and below.

Figure.12. Power transformer magnetizing inrush model

with residual flux and CTs

Apply Discrete Wavelet Transform

operating signal (differential current)

Start

NO

Yes

Idiff > Ithreshold

Principal Component Analysis

SVM (Support Vector Machine)

Trip signal

Inrush / external fault

Internal fault



ISSN NO: 0975-6876


Figure.13. Power transformer with external faults

Figure.14. Differential current during magnetizing inrush

of power transformer

Figure .14. is obtained by energizing the power transformer at

210 degree (inception angle), no load and residual flux with

75% of the rated flux. During these conditions differential

currents nature is peaky in some region and flat in another

region. That is due to the saturation of the transformer core.

Figure.15. Differential current during L-G fault on the

primary side of PT

Figure .15. is obtained by creating a fault at phase A (with

ground) of the primary side of the power transformer at 180

degree (inception angle) of the sinusoidal voltage, 20% of the

winding A, 10 ohm fault resistance with full load conditions

Figure.16. Differential current during LL fault on the

primary side of PT

Figure .16. is obtained by creating a fault at phase A and B

(without ground) of the primary side of the power transformer

at 180 degree (inception angle) of the sinusoidal voltage, 20%

of the winding A and B with full load conditions.

Figure.17. Differential current during LL-G fault on the

primary side of PT


(with ground) of the primary side of the power transformer at

180 degree (inception angle) of the sinusoidal voltage, 20% of

the winding A and B, 10 ohm fault resistance with full load

conditions.

Figure.18. Differential current during LLL fault on the

primary side of PT

Figure .18. is obtained by creating a fault at phase A, B and C

(without ground) of the primary side of the power transformer


of the winding A, B and C with full load conditions.

Figure.19. Differential current during LLL-G fault on the

primary side of PT


(with ground) of the primary side of the power transformer at

180 degree (inception angle) of the sinusoidal voltage, 20% of

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ISSN NO: 0975-6876


the winding A, B and C, 10 ohm fault resistance with full load

conditions.

Figure.10. Differential current during L-G fault on the

secondary side of PT

Figure .20. is obtained by creating a fault at phase A (with

ground) of the secondary side of the power transformer at 180

degree (inception angle) of the sinusoidal voltage, 20% of the

winding A, 5 ohm fault resistance with full load conditions.

Figure.11. Differential current during LL fault on the



(without ground) of the secondary side of the power

transformer at 180 degree (inception angle) of the sinusoidal

voltage, 20% of the winding A and B with full load

conditions.

Figure .212. Differential current during LL-G fault on the



(with ground) of the secondary side of the power transformer


of the winding A and B, 5 ohm fault resistance with full load

conditions.

Figure.13. Differential current during LLL fault on the



(without ground) of the secondary side of the power

transformer at 180 degree (inception angle) of the sinusoidal

voltage, 20% of the winding A, B and C with full load

conditions.

Figure.14. Differential current during LLL-G fault on the



(with ground) of the secondary side of the power transformer


of the winding A, B and C, 5 ohm fault resistance with full

load conditions.

Figure.15. Differential current during external fault


(with ground) at the end of secondary CT of the differential

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external fault



ISSN NO: 0975-6876


relay / starting of a transmission line, inception angle of 210

degree of the sinusoidal voltage, 0.01 ohm fault resistance

with full load conditions.

Figure.16. Differential current during normal operating

condition

Figure .26. is obtained when transformer operates normally

with full load and no faults or any kind of a disturbances. The

nature of differential current in this case is sinusoidal with

extremely low magnitude.

Figure.17. Single phase differential current during

magnetizing inrush condition

Figure.18. Single phase view of differential current during

internal fault

After modelling of power transformer in PSCAD these

differential current are used in the MATLAB for DWT and

SVM based transformer protection. This differential current

first decomposed into different frequency band using db6

mother wavelet. The reconstructed decomposed signals for

internal fault, external fault and inrush are shown in the

following figures.

Figure.19. Different details and approximate signals of

internal fault current


inrush current

-0.20

-0.10

0.00

0.10

0.200

.00

0.0

2

0.0

4

0.0

6

0.0

8

0.1

0

0.1

2

0.1

4

0.1

6

0.1

8

0.2

0

0.2

2

0.2

4

0.2

6

0.2

8

Dif

fere

nti

al

curr

ent

(A)

Time (second)

-5.00

0.00

5.00

10.00

0.0

2

0.0

4

0.0

6

0.0

8

0.1

0

0.1

2

0.1

4

0.1

6

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8

0.2

0

0.2

2

0.2

4

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6

0.2

8

0.3

0Dif

fere

nti

al

curr

ent

(A)

Time(second)

-40.00

-20.00

0.00

20.00

40.00

0.0

0

0.0

20

.04

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8

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Dif

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urr

ent

(A)

Time (second)



ISSN NO: 0975-6876



external fault current

From those DWT frequency band only fourth and fifth level

decomposed signal are passes through PCA for dimensions

reduction these reduced dimensional signals are called

features. This feature goes to the kernel based radial basis

function non-linear mapping SVM classifier for classification

purposes. Figure explains how each phase of the differential

currents samples passes through the protection algorithm. First

50 samples (1/4th

cycle) from pre fault and 200 samples (1

cycle) from post fault of differential current for each phase is

taken, then from these individual differential current, DWT

(db6 mother wavelet) decomposed detail4(25 samples) and

detail5( 18) computed.

That means for each individual differential current total

number of decomposed samples are 43 and 43 X 3 = 129 for

all the three phases. These decomposed samples goes to the

three different PCA for three types of classifications using

SVMs. The PCA1 reduces the dimensions from 129 to 10, the

PCA2 reduces the dimension from 129 to 8 and PCA3 reduces

the dimensions from 129 to 7. Using this algorithm the final

internal fault detection accuracy achieved is 99.16% on total

number of different 2486 testing samples that is illustrated in

the table 5. 1. Apart from the internal fault detection there

exist another two SVM. The second SVM identifies in which

side of the transformer windings, fault has occurred and the

third SVM discriminates between inrush and external fault.

Table 5.2 and table 5.3 shows their classification accuracy.

Figure.22. An Algorithm for power transformer protection

In this thesis 4030 training samples, 2486 testing samples, and

6516 total samples were generated. Training data is used to

create a differential power transformer protection model and

the testing samples is used to find the accuracy of that created

differential protection model. To do that it took only one cycle

data from occurrence time of inrush, internal and external

fault. The above algorithm is performed in this thesis.

FAULT AND

INRUSH

TRAINING

SAMPLE

TESTING

SAMPLE

FALSE

DETECTION

Accuracy

Internal fault

(primary and secondary

winding fault)

3280 2000 12

99.16%

Inrush and

external fault 750 486 09

Total samples 4030 2486 21

Table.1. Classification accuracy table for internal fault,

inrush and external faults

Trip Signal

operating signal (differential current)

(Ida(250), Idb(250), Idc(250))

Start

NO

SVM 3SVM 2

SVM 1

INRUSH

AND

EXTERNAL

FAULT

INTERNAL

FAULT

Yes

PWF SWF INRUSH EXTERNAL

FAULT

Idiff > Ithreshold

Apply Discrete Wavelet Transform

(detail4(25), detail5(18))

PCA 3

129 X 7

PCA 2

129 X 8

PCA 1

129 X 10

[Ida(d4,d5) 43], [Idb(d4,d5) 43], [Idc(d4,d5) 43]

EnableEnable



ISSN NO: 0975-6876


FAULT UNIT

AND INRUSH

TRAINING

SAMPLE

TESTING

SAMPLE

FALSE

DETECTION

Accuracy

Primary winding fault

1640 1000 00

100% Secondary

winding faults

1640 1000 00


Table .2. Classification accuracy table for primary and

secondary winding faults

FAULT UNIT

AND INRUSH

TRAINING

SAMPLE

TESTING

SAMPLE

FALSE

DETECTION

Accuracy

Inrush 350 226 00

100% External fault 400 260 00


Table .3. Classification accuracy table for inrush and

external faults

7. CONCLUSION

The proposed protection based on combined wavelet, PCA

and SVM algorithm provides a differential protection for

Power Transformer. Which provides much more security than

the other existing ANN and conventional dual slope

percentage differential based protection. Here DWT extracted

the different time and frequency based information from

relaying signals then PCA is used to reduce the dimensions of

the detailed coefficients of DWT that passes through SVM

based classifier and then above protection algorithm achieved

an accuracy of 99.16% to detect the internal fault from

magnetizing inrush and external fault current. To achieve that

much accuracy it only took 1 cycle data from differential

current for the processing which leads to the fast power

transformer protection. Apart from fault detection this

algorithm also gives additional information on which side of

the transformer windings are damaged and also the external

fault and inrush conditions separately. This classify the

primary winding faults from secondary winding faults with

100% accuracy, and for the classification between inrush and

external fault it also achieved 100% accuracy.

In future the classification among all types of internal faults

(a-g, b-g, c-g, ab, bc, ca, ab-g, bc-g, ca-g, abc, abc-g) in each

side of the transformer windings will be performed with good

classification accuracy. And also to enhance the speed of

operation the data require for the processing would be reduce

and search for the new features so that SVM classify more

accurately. And this proposed algorithm can be implemented

in the real time.

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ISSN NO: 0975-6876


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