Analysis, Classification Partial Discharge with wavelet...

Student:

NGO Xuan Thuy-GE5S

Professor:

Mr.Eddie SMIGIEL

Tutor:

Mr. Ruthard MINKNER

Analysis, Classification Partial

Discharge with wavelet transform and

artificial neural network

Electrical Engineering: promotion 2011 September 2011

Purpose of my internship

Improve the measurement circuit of partial discharge created by Trench company

Capture and save the partial discharge signals into computer

Realize the analysis the signals with wavelet transform and chose the appropriate

wavelet for the analysis

Create an artificial neural network to classify and recognize the defaults of these

partial discharge signals.

Test the performance of the algorithm chosen and conclude

Résumé: Décharge partielle est un phénomène très connu dans les appareils à haute tension.

Elle s‘est produite à cause des erreurs de production et aussi des défauts présentés dans les

matières d‘isolation utilisées dans ces appareils. Une fois que des décharges partielles

apparaissent, elles peuvent endommager le système d‘isolation de l‘appareil et donc mettre

hors-service ou pire détruire l‘appareil à partir d‘une certaine valeur de décharge. Dans la

chaine de production de l‘entreprise Trench, qui produit des transformateurs de mesure à

haute tension, il y a plus de 20% de produits qui sont défaillants à cause de ce phénomène. Le

but de mon stage est d‘étudier les décharges partielles présenté dans ces transformateurs pour

déterminer les causes (les défauts) de ces phénomènes afin de pouvoir récupérer les produits

défaillants. Le stage est divisé en trois phases principales : améliorer le schéma de mesure des

décharges partielles, l‘analyse les signaux des décharges partielles avec la transformée en

ondelettes (l‘outil de traitement signal) et classifier des différentes types des décharges avec le

réseau de neurone artificiel.

Abstract: Partial discharge is a well-known phenomenon in High Voltage (HV) apparatus. It

occurs because of production‘s errors and also the defaults which are introduced in the

isolating system used in these apparatus. Ones the partial discharge occurs, it can damage the

isolating system of apparatus and so can disable or destroy the apparatus from certain value of

discharge. In the production line of Trench Company, which produces transformers in High-

Voltage, there are more than 20% of products that are defective because of this phenomenon.

The purpose of my internship is to study the partial discharges occurred in these transformers

to determine the cause (defects) of these phenomena in order to recover the faulty products.

My internship is divided into three main phases: improving the measurement circuit of partial

discharge, analysis of partial discharge signals with the wavelet transform (the signal

processing tool) and classify different types of partial discharges with an artificial neural

network.

Table of Contents 1 Introduction ............................................................................................................ 1 2 Presentation of the company ................................................................................ 2

2.1 The Trench Group ....................................................................................................2 2.2 The company Trench Switzerland AG ......................................................................3 2.3 Research and Development department (R&D) .......................................................4

3 Partial discharge introduction ............................................................................... 5 3.1 Partial discharge.......................................................................................................5 3.2. Measurement of Partial discharges signals ..............................................................7

4 Final measurement circuit of our project ............................................................. 9 Fig. 4.2: PD test circuit elements ...................................................................................... 10

4.1 Some important parts in the measurement circuit ...................................................10 Coaxial shunt (100 ohm) see the fig 4.1..................................................................................10 4.2 Some problem with the measurement circuit ..........................................................11

5 Some result with the measurement circuit created ........................................... 12 5.1 With cylindrical capacitors ......................................................................................12 Test 2 .................................................................................................................................13 5.2 LOPOs ...................................................................................................................14

6 Wavelet Transform analysis ................................................................................ 16 6.1 Introduction ............................................................................................................16 6.2 Fourier transform and Wavelet transform ...............................................................17

6.2.1 Fourier transform .............................................................................................17 6.3 Wavelet Analysis ....................................................................................................19

6.3.1 What is wavelet analysis .................................................................................19 6.3.2 The continuous wavelet transform ...................................................................19 6.3.3 The discrete wavelet transform .......................................................................24

6.4 Application wavelet analysis with partial discharge signal .......................................27 6.4.1 Wavelet analysis signals with MATLAB software. ............................................29 6.4.2 Use command lines for the wavelet analysis. ..................................................30 6.4.3 Using Graphic User Interface of wavelet toolbox .............................................36

7 Artificial Neural Network (ANN) ........................................................................... 40 7.1 Introduction of artificial neural network ...................................................................41 7.2 Perceptron neural network .....................................................................................43 7.3 The back-propagation algorithm .............................................................................46 7.4 Artificial neural network created for partial discharge classification .........................48

8 Graphic User Interface (GUI) ............................................................................... 62 9 Conclusion ............................................................................................................ 75

This Semesterwork bases on a written contract between the Company Trench/Siemens CH, the School INSA Strasbourg and the two students Goeffrey BERTIN and Xuan Thuy NGO.

The report is literary property of the Students Mr. BERTIN and Mr. NGO and the R&D department of the company Trench SA/FR and Siemens AG/CH. The companies Trench SA/FR and Siemens AG/CH own all rights of the Semesterwork.

It is forbidden to publish this report in the next five years and only Mr. SMIGIEL and another Person of the School INSA Strasbourg are allowed to read this report.

During the presentation of this Semester-work the content can be explained, drawn, etc, or can be shown with a beamer. No printed explanations, drawings, etc are allowed to be distributed. Basel, 21. July 2011 Dr. Ing. Ruthard MINKNER Trench SA/FR and Trench AG/Siemens/CH

We wish to thanks Mr. MINKNER and Mr. SCHMID to allow us to carry out this project. We

also want to thank Mr. MINKNER for all his interest about this internship and for bringing

his knowledge to help us during this period. . Also a special thank you to our tutor professor Mr.

SMIGIEL for his support. Finally we would like to say many thanks to all the people who made

our work placement such a pleasant stay and particularly to the department R&D of Trench

Switzerland AG.

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Analysis, Classification of partial discharge with

wavelet transform and artificial neural network

NGO Xuan Thuy-GE5S

1 Introduction

For my final internship (―Projet de Fin d‘Etude‖ in French), I decided to join the

Trench Group company in Basel, Switzerland, during a 6 months period from the 1st of

February to the 29th of July 2011.

During the first semester, from October to February, I already had the opportunity to

work with this company for a project named: ―Partial Discharges analysis with wavelet

method‖. This work experience is the continuity of this project and consists in an

improvement of the wavelet method and inserts the delicate part of Partial Discharge

measurement that we didn‘t deal with in the previous work.

The problematic is the following. Trench group product several kinds of instrument

transformers. In these devices, partial discharges phenomena can occur (developed in chapter

3). A partial discharge limit has been fixed by IEC standard for instrument transformers.

Exceeding this limit, the device is considered like faulty and can‘t be sold by the company. As

all transformers can‘t be operational at the production line output, faulty devices have to be

checked and reintroduced somewhere in the production line. The problem is that sometimes, it

is difficult to determine the internal defect of the device and therefore, it can cost time for the

company and then losing money.

Therefore, partial discharge detection is important for the evaluation construction and

to recognize defects in these designs. The trend towards the automation of this process to test

bushings, instrument transformers and other insulated devices is evident. As the conventional

method of oscillographic observation provides only a limited recognition of defects, a better

method has to be developed. This method can be performed by measuring the current impulse

of partial discharges between the test object and earth. Then, these impulses can be analyzed

with a wavelet method which can help to classify the defects thanks to an artificial neural

network.

Task of the Semesterwork:

Description and frequency response measurement with one or two suitable sensors to

recognize partial discharge impulses and register the information in a laptop memory.

Development of an analysis method with the wavelet theory

Classification the partial discharges with an artificial neural network

Create an graphic user interface in Matlab for user who haven‘t knowledge about

wavelet and artificial neural network.

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2 Presentation of the company

2.1 The Trench Group

The Trench Group is a worldwide reputable company in the area of high voltage

technology developments. Till the year 1990 it was especially active in North America, where

grew by means of some fusions with other companies of the high voltage sector. Through

them it became a worldwide firm that nowadays possesses production installations in almost

every continent. Since 2004, the Trench Group has become a hundred percent subsidiary firm

to the multinational Siemens Group company.

Fig. 2.1.1: Extension of the Trench Group over the world at present

As it is seen, it has installations in several different countries, those which dedicate

themselves to the development of widely different technologies and the devices used for

them.

In this sense, we can focus on the kind of technology developed in each country:

In Austria, air cire by type reactors, iron core oil filled reactors and earth fault location

systems are produced.

In Brazil, the factory of Contagem manufactures air core reactors from 600 V to 345 kV,

50 kVA to 60 MVA and line traps from 72 kV to 800 kV, from 0.1 to 2 mH.

In Canada, there are four different installations belonging to the Trench Group. The main

products developed there are bushings for reactors or transformers of oil-to-air and oil

Linz, AUSTRIA

Bamberg, GERMANY

St. Louis, FRANCE

Basel, SWITZERLAND

Cairo Montenotte (SV), ITALY

Hebburn, ENGLAND

Shanghai, CHINA

Shenyang, CHINA

Contagem, BRAZIL

Ajax/Scarborough,

CANADA

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Image II.2. Installations of Trench Switzerland AG (red) and Haefely Test AG in Lehenmattstraβe, Basel. Image II.2. Installations of Trench Switzerland AG (red) and Haefely Test AG in Lehenmattstraβe, Basel

impregnated paper types, different kinds of current, voltage and combined transformers in

ranges that can go from 72.5 KV to 245, 550 or even 800 KV depending on the kind of

equipment, air core dry type reactors and some others devices to be used in relation to PLC(1)

technology.

In China, in Shanghai installations, SF6-insulated instrument transformer, coil products –

such as line traps, smoothers or filters – and low power instrument transformers are produced,

as well as HV AC and DC bushings – both oil impregnated paper and epoxy resin

impregnated paper – up to 1000 kV, in Shenyang.

In France, the installations of St. Louis work in the field of oil insulated instrument

transformers and bushings, sharing the branches of Engineering, R&D, Sales and Marketing,

Purchasing and Production with Trench Switzerland AG.

In Germany, it is placed the technological centre for gas-insulated equipment of the

Trench Group.

In Italy, it has the center for the design and manufacturing of high voltage instrument

transformers, having the European production of capacitor voltage transformers and grading

capacitors for the whole group concentrated in this installation, with a significant

manufacturing of SF6 instrument transformers.

In England, the one known as "The Bushing Company" is located, pioneer in the design

and manufacture of bushings for transformers and switchgear since 1929.

And finally, Trench Switzerland AG, that will be described as follows because of being in

which this work has been developed.

2.2 The company Trench Switzerland AG

Trench Switzerland draws from over 95 years of experience in the field of oil

insulated instrument transformers and bushings.

Its history comes from the foundation by Emil Haefely in 1904 of his own firm. At the

beginning it was based on a patented design for manufacturing of resin-impregnated paper

insulators – this material, known as haefelite, will be mentioned in section 4.2.6.1 –, growing

quickly and being expanded into testing in 1922. Over the years, this company evolved to

become a specialist in the fabrication of electrical devices such as bushings, capacitors and in

insulation technology and high-voltage testing equipment. It meant that there were two big

areas of development into the company, one dedicated to transmission technology and other

one dedicated to high-voltage testing. Nowadays, the first of these mentioned branches

belongs to the Trench Group, being now Trench Switzerland AG, while the second one –

Haefely Test AG – belongs to the Special Technologies Platform of Hubbell Inc. Because of

this, both companies have today their installations in the same area, the one showed in this

picture.

(1) System for carrying data on a conductor also used for electric power transmission PLC (Power Line Carrier):

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(2) LOPO: Acronym of LOW POWER, referred to the low power transducers technology.

Fig. 2.1.2: Installations of Trench Switzerland AG (red) and Haefely Test AG in

Lehenmattstraβe, Basel

Focusing on Trench Switzerland AG, as it has been said before, today it shares

Engineering, R&D, Sales and Marketing, Purchasing and Production with Trench France SA.

Its main area is focused on measurement transformers (current transformers, inductive and

capacitive voltage transformers, RC voltage dividers) and bushings, having with them more

than a hundred years of experience.

Since July, 1st 2011, the company became officially Siemens Switzerland AG.

2.3 Research and Development department (R&D)

This Masterwork has been mainly carried out in close collaboration with the engineers

of the department R&D, what makes particularly required the following clarification of the

kind of work developed there.

This department is part of the Engineering branch, and is mainly dedicated to the next

tasks:

- Research of new materials and developments.

- Organization of the interchange of technology between the different locations.

- Standardization of Trench Group/Siemens products.

- Production optimization for the whole Group.

- Development and presentation of the new products.

- Promotion of the LOPO(2) technology.

As a result of these functions, some parts of the installations of the company, such as

the testing rooms and the workshops are exclusively used by this department, what also means

that every new student is working here for the development of his work.

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3 Partial discharge introduction

3.1 Partial discharge

Referring to [1], partial discharges (PD) are localized electrical discharges within an

insulation system, restricted to only a part of a dielectric material, and thus only partially

bridging the electrodes. The insulation may consist of solid, liquid or gaseous materials, or of

any combination. The term ―partial discharge‖ is relatively new, as it includes a wide group of

discharge phenomena. The type of discharge is often divided into 3 groups due to their

different origin.

Corona discharges: i.e. discharges in gases or liquids caused by a locally enhanced

field from sharp points on the electrodes. Corona is often harmless, but by-products

like ozone and nitric acids may chemically deteriorate closely lying materials.

Internal discharges:

o Cavity discharges: i.e. discharges from gas-filled voids, delaminations,

cracks, etc. within solid insulation. A refined classification could be made to

cavities that are on one side bounded by the metallic electrode, and to cavities

that are completely surrounded by the insulating material. Voids may have its

origin from

o cast insulation like epoxy spacers in SF6 bus bars, from dried out regions in

oil-impregnated paper-cables, from gas-bubbles in plastic insulation, etc.

Delaminations occur in laminated insulation like the stator-bar insulation of

large electrical machines that often is composed of mica based types with

binding enamel like epoxy. Cracks could for example occur in mechanically

stressed insulation, e.g. in loose stator bars that are vibrating.

o Treeing discharges: i.e. current pulses within an electrical tree. The electrical

tree may start from a protrusion on the electrode or from imperfections like

contaminating particles embedded in solid insulation.

Surface discharges: i.e. discharges on the surface of an electrical insulation where the

tangential field is high, e.g. the porcelain or polymeric housing of high-voltage

devices. Other common sources of surface discharges are terminations of cables or the

end-windings of stator windings.

Fig. 3.1.1: Some types of partial discharge (a) Corona discharge, (b) Surface discharge, and

(c) Cavity discharge.

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The significance of partial discharges on the life of insulation has long been

recognized. Every discharge event causes a deterioration of the material by the energy impact

of high energy electrons or accelerated ions, causing chemical transformations of many types.

As will be shown later, the number of discharge events during a chosen time interval is

strongly dependent on the kind of voltage applied and will be largest for a.c. voltages. It is

also obvious that the actual deterioration is dependent upon the material used. Corona

discharges in air will have no influence on the life expectancy of an overhead line; but PDs

within a thermoplastic dielectric, e.g. PE, may cause breakdown within a few days. It is still

the aim of many investigations to relate partial discharge to the lifetime of specified materials.

Such a quantitatively defined relationship is, however, difficult to ensure. PD measurements

have nevertheless gained great importance during the last four decades and a large number of

publications are concerned either with the measuring techniques involved or with the

deterioration effects of the insulation. The detection and measurement of discharges is based

on the exchange of energy taking place during the discharge. These exchanges are manifested

as: (i) electrical pulse currents (with some exceptions, i.e. some types of glow discharges); (ii)

dielectric losses; (iii) e.m. radiation (light); (iv) sound (noise); (v) increased gas pressure; (vi)

chemical reactions. Therefore, discharge detection and measuring techniques may be based on

the observation of any of the above phenomena. The oldest and simplest method relies on

listening of the acoustic noise from the discharge, the ‗hissing test‘. The sensitivity is,

however, often low and difficulties arise in distinguishing between discharges and extraneous

noise sources, particularly when tests are carried out on factory premises. It is also well

known that the energy released by PD will increase the dissipation factor; a measurement of

tan υ in dependency of voltage applied displays an ‗ionization knee‘, a bending of the

otherwise straight dependency. This knee, however, is blurred and not pronounced, even with

an appreciable amount of PD, as the additional losses generated in much localized sections

can be very small in comparison to the volume losses resulting from polarization processes.

The use of optical techniques is limited to discharges within transparent media and thus not

applicable in most cases. Only modern acoustical detection methods utilizing ultrasonic

transducers can successfully be used to localize the discharges. These very specialized

methods are not treated here. The most frequently used and successful detection methods are

the electrical ones, to which the new IEC 60270 Standard [19] is also related. These methods

aim to separate the impulse currents linked with partial discharges from any other phenomena.

The adequate application of different PD detectors which became now quite well defined and

standardized, presupposes a fundamental knowledge about the electrical phenomena within

the test samples and the test circuits.

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3.2. Measurement of Partial discharges signals

The partial discharge phenomena are produced in an object which has two electrodes and one

isolation material between these two electrodes. This system can be considered like one

capacitor (figure 3.2.1).

Fig. 3.2.1: Simulation of a PD test object. (a) Scheme of an insulation system comprising a

cavity. (b) Equivalent circuit.

In the figure 3.2.1, we have an object which has 2 electrodes (A and B). The isolation system

between these two electrodes has one default (one cavity). This object is placed on high

voltage (the electrode A is connected to high voltage and the electrode B connected to earth).

From one certain value of voltage we will obtain the partial discharges signals. The reason is

from certain value of voltage, the electrical field created by this voltage is bigger than

dielectric rigidity of cavity within the isolation system. So some electrons will go to electrode

B to electrode A to decrease this electrical field and also produce the partial discharge

phenomena. Theses partial discharges are very quick (some nanosecond) and also very

difficult to measure. For the measurement of theses discharges, we use a capacitor which is

connected in parallel to object (figure 3.2.2). This capacitor is called ‗coupling capacitor‘.

Fig. 3.2.2: the PD test object Ct within a PD test circuit with coupling capacitor Ck

When the system in figure 3.2.2 is supplied on high voltage, the test object and coupling

capacitor is charged with certain charge amount according to their value. When a partial

discharge occurs, we found a dropping of voltage (dropping of Vs) between two electrodes of

test object and the charge amount of test object will be decreased. Now the report between the

charge amount of test object and the one of coupling capacitor is not respected (this is due to

their capacitor value). So some charge will immediately be sent from coupling capacitor to

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test object in order to respect the charge amount report between these two. This phenomenon

creates a current i(t) which characterize the number of charges exchanged within the test

object during the partial discharge phenomena. Now we must just measure this current (i(t)) to

obtain all information about partial discharge signal. We can consult [2] to get more

information about the theory of partial discharge measurement.

In the literature we can found 3 standard measurement process used to obtain partial signal

information (figure 3.2.3) [3].

Fig. 3.2.3: Standard PD test circuits recommended in IEC 60270

So the first circuit is the measurement of current in the side of test object. The second is the

measurement of current in the side of coupling capacitor and the last one is using a bridge

between these two capacitors (coupling capacitor and object). For our project, we use the

circuit which measures the current in the side of test object.

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4 Final measurement circuit of our project

The final whole circuit solution we kept is the following:

Ck

1nF

Coaxial Rshunt

100 Ohm

Rfilter 47 Ohm

Lfilter

39µH

Coaxial cable

10m 50 Ohm

Oscilloscope

AC Signal

50 Hz

V

Test object

AKV

Isolation transformer

PD measuring system

1 2 3 4

12

13

5

6

7

8

9

11

10 50 Ohm

Fig. 4.1: PD test circuit diagram

1- Variac used to change the supply voltage

2- Transformer

3- Coupling capacitor

4- Test object

5- Coaxial shunt (100 ohm)

6- Epcos 90 08 0 used for overvoltage security

7- Filter resistor

8- Filter inductance 39µH

9- Oscilloscope Tektronix TDS 3024B

10- Internal resistor of the oscilloscope (50 Ohm)

11- Isolation transformer to ensure earth connection

12- AKV used to measure impedance and peak detection

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Here we can see the different parts of this circuit:

Fig. 4.2: PD test circuit elements

4.1 Some important parts in the measurement circuit

Coaxial shunt (100 ohm) see the fig 4.1

The coaxial shunt is a special resistor which is placed between the test object and earth. This

one is used to pick up the signal of current created by partial discharge phenomena. The

principal is to pick up the voltage between two terminals of coaxial shunt. This voltage is the

image of current come through object. The specialty of this Shunt is that it is purely

resistance. It‘s created with the resistances which have no inductance or capacitance value so

we can observe the partial discharge signals with a maximum performance. The figure below

shows the coaxial shunt created for the project.

Fig. 4.1.1: 100 Ω coaxial shunt

More information about coaxial shunt can be found in the final year report of Mr. Jeoffey

BERTIN

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Filter (filter resistor and filter inductance)

These two components are used to create a high pass filter. This filter is used to eliminate the

50Hz signal which is the signal created directly from High voltage (The frequency of high

voltage is 50 Hz). The filter band is preciously calculated in order to keep the waveform of

partial discharge signals (the band pass of this filter is 250 kHz).


This transformer is used to ensure that there is only one earth connection. It‘s very important

to eliminate noises which can be come from other voltage source and also other earth

connection.

AKV used to measure impedance and peak detection

This is a standard device used to measure the amplitude of partial discharges. It‘s very

important to know if the partial discharge limit is exceeded or not. So this device is always

allowed before the measurement to avoid the destruction of measurement system.

4.2 Some problem with the measurement circuit

During the project, there are two main problems occurred in the measurement of partial

discharge signals:

Reflexion phenomenon

Loop inductance effect

Reflexion phenomenon

This is a known problem of the signal‘s transmission in high frequency. This phenomenon is

come from the difference of impedance of each part of circuit used for the transmission of

signal. The principal of this reflexion phenomenon is the same than reflexion phenomenon in

optical field. During the transmission of electrical signal, if the signals see a change of

impedance in his way, a part of signal will continue his way and another part will come back

to the point that gave birth. And this phenomenon will completely modify the waveform of

partial discharges signals. To correct this problem, some impedance adaptations are used to

eliminate the reflexion phenomena. More information about this phenomenon are given in [4]

and also in the final years report of Mr. Jeoffrey BERTIN (GE5E).

Loop inductance effect

In electrical circuit, all the loops created by cables, copper, etc… are equivalent to

inductances. This inductance can modify the waveform of partial discharge signals. It is

important to notice that the waveform change with the impedances of the circuit. Hence, the PD

waveforms can be different from one place to another with the same test object. For an accurate classification of the PD waveforms, we have to be sure they come from the same test circuit.

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5 Some result with the measurement circuit created

5.1 With cylindrical capacitors

Fig. 5.1.1: Capacitor diagram

They are composed of two cylindrical metallic parts separated by several layers of

polypropylene film.

The thickness of a layer δf is always the same: δf = 36 µm.

The distance between the two metallic part δis is given by N*δf where N is the number

of layers.

The capacitance can be calculated with the following equation:

C = 2π.εr.ε0.l/ln(r2/r1)

(9.1.1.1)

l is the shared distance between the two metallic cylinder.

r2 is the radius of the external cylinder.

r1 is the radius of the internal cylinder.

εr is the relative permittivity of the insulation between the two cylinder (εr ≈ 2.2 for

polypropylene).

Test 1

o Test object reference: MSIL 1-2

o Number of layers: 2

o Voltage: 463 V

o PD level: 100pC

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Fig. 5.1.2: MSIL 1-2 PD waveform – 400 ns/div

Test 2

o Test object reference: MSIL 3-2

o Number of layers: 2

o Voltage: 692 V

o PD level: 200pC

Fig. 5.1.3: MSIL 3-2 PD waveform – 400 ns/div

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5.2 LOPOs

LOPO is an acronym of LOW POWER, referred to the low power transducer

technology. They are 3 kind of LOPO designed by Trench group:

The type VT which include a Voltage Transducer

The type CT which include a Current Transducer

The type VCT which include a Voltage Transducer and a Current Transducer

For our work, we only tested VT or CT transducers but the VCT is just a combination

of these ones.

The next drawing shows an internal view of a VCT transducer where we can see all

the elements which compose it.

Fig. 5.2.1: VCT internal view

The current transducer is composed of a typical current transformer and a shunt

connected to the secondary. Thus, a relation between the primary current and the output

voltage allows to get the current value.

The voltage transducer is composed by a compensated R-divider.

The electrical insulation of those devices is an epoxy resin with a dielectric strength

between 18 and 22 kV/mm.

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Test 1

o Test object reference: CT16

o Voltage: 2.3 kV

o PD level: 250pC

Fig. 5.2.2: CT16 PD waveform – positive alternation

Test 2

o Test object reference: VT9

o Voltage: 9.2 kV

o PD level: 30pC

Fig. 5.2.3: VT9 PD waveform – positive alternation

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6 Wavelet Transform analysis

6.1 Introduction

The data is obtained via Tektronix Oscilloscope TD3004. This data give the waveform

of the current created by the partial discharge phenomena.

Ck

1nF

Coaxial Rshunt

100 Ohm

Rfilter 47 Ohm

Lfilter

39µH

Coaxial cable

10m 50 Ohm

Oscilloscope

AC Signal

50 Hz

V

Test object

AKV


PD measuring system

1 2 3 4

12

13

5

6

7

8

9

11

10 50 Ohm

Fig. 6.1.1: PD measuring circuit and one type of PD obtained

The figure 6.1.1 above show the PD measuring circuit and also the signal come from

Tektronix Oscilloscope. Now we use the signal processing tool to pick up all characters of

signal used for the classification and recognition of partial discharge. For this analysis, we

choose the wavelet transform to pick up the feature vector used for the neural network (The

notion of feature vector and neural network analysis will be shown in the next chapter).

Wavelet analysis is a processing tool which is more suitable for the non stationary

signal with fast change (rise time) like partial discharge signals than Fourier analysis. Another

advantage of wavelet analysis is that this one has also frequency resolution and time

resolution contrary to Fourier analysis which has only frequency resolution. In this chapter,

we will talk about Fourier transform and also wavelet transforms to see the differences

between them.

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6.2 Fourier transform and Wavelet transform

6.2.1 Fourier transform

Signal analysts already have at their disposal an impressive arsenal of tools. Perhaps

the most well-known of these is Fourier analysis, which breaks down a signal into constituent

sinusoids of different frequencies. Another way to think of Fourier analysis is as a

mathematical technique for transforming our view of the signal from a time-based one to a

frequency-based one [5].

Fig. 6.2.1.1: Fourier transforms analysis

Fourier analysis has a serious drawback. In transforming to the frequency domain, time

information is lost. When looking at a Fourier transform of a signal, it is impossible to tell

when a particular event took place.

If a signal doesn‘t change much over time — that is, if it is what is called a stationary signal

[5] — this drawback isn‘t very important. However, most interesting signals contain

numerous non-stationary or transitory characteristics: drift, trends, abrupt changes, and

beginnings and ends of events. These characteristics are often the most important part of the

signal, and Fourier analysis is not suited to detecting them. To correct this, Dennis Gabor

(1946) invented a new technique called the Short-Time Fourier Transform (STFT), maps a

signal into a two-dimensional function of time and frequency (Figure 6.2.1.2).

Fig. 6.2.1.2: principal of Short Time Fourier Transform

The STFT represents a sort of compromise between the time- and frequency-based

views of a signal. It provides some information about both when and at what frequencies a

signal event occurs. However, we can only obtain this information with limited precision, and

that precision is determined by the size of the window (See Annex 4).

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Wavelet analysis represents the next logical step: a windowing technique with

variable-sized regions. Wavelet analysis allows the use of long time intervals where we want

more precise low frequency information, and shorter regions where we want high frequency

information.

Here‘s what this looks like in contrast with the time-based, frequency-based, and

STFT views of a signal:

Fig. 6.2.1.3: The differences views of signal via FT, STFT and Wavelet analysis

Our study case is partial discharge phenomena. These types of signal are extremely

quick (rise time is some ns) and with enormous of variation. These aren‘t stationary signal

and we need both frequency and time information. It isn‘t suitable analyze these signals with

Fourier analysis so that why we want use Wavelet transform for the signal processing

analysis.

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6.3 Wavelet Analysis

6.3.1 What is wavelet analysis

A wavelet is a waveform of effectively limited duration that has an average value of

zero.

Compare wavelets with sine waves, which are the basis of Fourier analysis. Sinusoids

do not have limited duration — they extend from minus to plus infinity. And where sinusoids

are smooth and predictable, wavelets tend to be irregular and asymmetric.

Fig. 6.3.1.1: Sine wave and wavelet (db10)

This figure shows the differences between sine wave and wavelet. Sine wave is

periodic but wavelet isn‘t.

Fourier analysis consists of breaking up a signal into sine waves of various

frequencies. Similarly, wavelet analysis is the breaking up of a signal into shifted and scaled

versions of the original (or mother) wavelet.

Just looking at pictures of wavelets and sine waves, we can see intuitively that signals

with sharp changes might be better analyzed with an irregular wavelet than with a smooth

sinusoid, just as some foods are better handled with a fork than a spoon.

It also makes sense that local features can be described better with wavelets, which have

local extent.

6.3.2 The continuous wavelet transform

Mathematically, the process of Fourier analysis is represented by the Fourier transform:

Which is the sum over all time of the signal f (t) multiplied by a complex exponential.

(Recall that a complex exponential can be broken down into real and imaginary sinusoidal

components.)

(6.3.1)

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The results of the transform are the Fourier coefficients F (w), which when multiplied by a

sinusoid of appropriate frequency w; yield the constituent sinusoidal components of the

original signal. Graphically, the process looks like:

Fig. 6.3.2.1: demonstration of Fourier Transform

Similarly, the continuous wavelet transform (CWT) is defined as the sum over all time

of the signal multiplied by scaled, shifted versions of the wavelet function ψ:

Where g(s,η) is coefficient of wavelet transform with wavelet scaled by s and shifted by η.

f(t) is the original signal.

The results of the CWT are many wavelet coefficients C, which are a function of scale

and position.

Multiplying each coefficient by the appropriately scaled and shifted wavelet yields the

constituent wavelets of the original signal:

Fig. 6.3.2.2: demonstration of wavelet transforms

Scaling a wavelet simply means stretching (or compressing) it (Figure 6.3.2.3) (See Annex 1).

(6.3.2)

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Fig. 6.3.2.3: The scaling of wavelet

Shifting a wavelet simply means delaying (or hastening) its onset. Mathematically,

delaying a function f(t) by k is represented by f(t-k):

Fig. 6.3.2.5: the shifting function

Regarding this figure, we found that the shifted wavelet function ψ (t-k) is just

translated to the right with respect to the function ψ (t).

Five easy steps to a Continuous Wavelet Transform

The continuous wavelet transform is the sum over all time of the signal multiplied by

scaled, shifted versions of the wavelet. This process produces wavelet coefficients that are a

function of scale and position.

It‘s really a very simple process. In fact, here are the five steps of an easy recipe for

creating a CWT:

Take a wavelet and compare it to a section at the start of the original signal.

Calculate a number, C, the represents how closely correlated the wavelet is with this

section of the signal. The higher C is, the more the similarity. Note that the results will

depend on the shape of the wavelet you choose.

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Shift the wavelet to the right and repeat steps 1 and 2 until you‘ve covered the whole

signal.

Scale (stretch) the wavelet and repeat steps 1 through 3.

Repeat steps 1 through 4 for all scales.

When the continuous wavelet transform is done, we‘ll have the coefficients produced

at different scales by different sections of the signal. The coefficients constitute the results of

a regression of the original signal performed on the wavelets.

How to make sense of all these coefficients? We could make a plot on which the x-

axis represents position along the signal (time), the y-axis represents scale, and the color at

each x-y point represents the magnitude of the wavelet coefficient C (Figure 6.3.2.6). These

are the coefficient plots generated by the graphical tools.

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Fig. 6.3.2.6: Wavelet transforms of sinus wave + noise with wavelet db2

Figure 6.3.2.6 show an example of magnitude of all coefficients of continuous wavelet

transform. Their magnitudes are presented by the color (large coefficients are light and small

coefficients are dark). In 3D view, we can see better the representation of coefficients like the

figure below.

Fig. 6.3.2.7: Coefficients of CWT in 3D plot

In this plot, we can see the differences of all coefficients. To realize wavelet analysis,

we can use differences families of wavelet. Some wavelets are shown in the Wavelet toolbox

tutorial (P53-P57).

Time Scale

Magnitude

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It is a different view of signal data than the time-frequency Fourier view, but it is not

unrelated because there is a relation between scale coefficient and frequency of signal that is

shown below.

Relation between scale coefficient and frequency of signal

The wavelet analysis will produce a time-scale view and not time-frequency view. But

there is a relation between scale and frequency

Low scale a => compressed wavelet => rapidly changing detail => High frequency w.

High scale a => stretched wavelet => slowly changing, coarse features => Low

frequency w.

It‘s important to understand that the fact that wavelet analysis does not produce a

time-frequency view of a signal is not a weakness but a strength of the technique.

Not only time-scale is a different way to view data, it is a very natural way to view data

deriving from a great number of natural phenomena (See Annex 2).

With the continuous wavelet transform, there are 3 properties that make it difficult to

use directly. The first is the redundancy of the CWT. In (6.3.2) the wavelet transform is

calculated by continuously shifting a continuously scalable function over a signal and

calculating the correlation between the two. Even without the redundancy of the CWT we still

have an infinite number of wavelets in the wavelet transform and we would like to see this

number reduced to a more manageable count. This is the second problem we have. The third

problem is that for most functions the wavelet transforms have no analytical solutions and

they can be calculated only numerically or by an optical analog computer. So to remedy these

problems, the discrete wavelet transform is used. The next chapter will talk about this

algorithm

6.3.3 The discrete wavelet transform

As we know, Calculating wavelet coefficients at every possible scale is a fair amount

of work, and it generates an awful lot of data. What if we choose only a subset of scales and

positions at which to make our calculations?

It turns out, rather remarkably, that if we choose scales and positions based on powers

of two — so-called dyadic scales and positions — then our analysis will be much more

efficient and just as accurate. We obtain just such an analysis from the discrete wavelet

transform (DWT) (See Annex 3).

An efficient way to implement this scheme using filters was developed in 1988 by

Mallat. The Mallat algorithm is in fact a classical scheme known in the signal processing

community as a two-channel sub-band coder (See Annex 3).

This very practical filtering algorithm yields a fast wavelet transform — a box into

which a signal passes, and out of which wavelet coefficients quickly emerge.

The principal of discrete wavelet transform is passing the signal in two additional

filters (low-pass filter and high-pass filter) to obtain the coefficients of discrete wavelet

transform. The coefficients of low-pass filter are created by the scaling function (See Annex

3) and the coefficients of high-pass filter are created by wavelet function (See Annex 3).

http://polyvalens.pagesperso-orange.fr/clemens/wavelets/wavelets.html#eq1

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In DWT, we talk about 2 terms approximation and detail. Approximation is all

coefficients obtained at the output of low pass filter (it contains the information of low

frequencies). The detail is all coefficients obtained at the output of high pass filter (it contains

the information of high frequencies).

Fig. 6.3.3.1: filtering process of the first level

In figure 6.3.3.1, the original signal, S, passes through two complementary filters

(scaling filter and wavelet filter) and emerges as two signals. A means approximations and D

means details. In this case, A and D are the approximation and detail of the first level of

decomposition.

Unfortunately, if we actually perform this operation on a real digital signal, we wind

up with twice as much data as we started with. Suppose, for instance, that the original signal S

consists of 1000 samples of data. Then the approximation and the detail will each have 1000

samples, for a total of 2000.

To correct this problem, we introduce the notion of down-sampling. This simply

means throwing away every second data point. While doing this introduces aliasing (a type of

error) [8] in the signal components, it turns out we can account for this later on in the process.

Fig. 6.3.3.2: Generate wavelet coefficient by filtering method

The process on the right, which includes down-sampling, produces DWT coefficients.

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Fig. 6.3.3.3: example of DWT of a sinusoidal signal with noise at the first level

The figure above shows the discrete wavelet transform at the first level using filtering

method. The signal ‗S‘ is pass through two complementary filters and down-sampling phase

to generate DWT coefficients. cA means coefficients of approximation and cD means

coefficients of detail.

The decomposition process can be iterated, with successive approximations being

decomposed in turn, so that one signal is broken down into many lower-resolution

components. This is called the wavelet decomposition tree.

Fig. 6.3.3.4: wavelet decomposition tree

Looking at Figure 6.3.3.4, a signal‘s wavelet decomposition tree can yield valuable

information.

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Fig. 6.3.3.5: An example of wavelet decomposition tree

The figure 6.3.3.5 shows the principal of wavelet decomposition tree. The bandwidth

of signal is divided by 2 for each level of decomposition (because there are two

complementary filters). For each level, we pass the approximations into 2 others

complementary filters and at the outputs of these 2 news filters we get news coefficients of

details and approximation. With this technical, we have information about differences

frequency band. cA3 contains information of low frequencies. cD1 contains information of

highest frequencies. cD2 and cD3 contain information of frequencies between cA3 and cD1.

Since the analysis process is iterative, in theory it can be continued indefinitely. In

reality, the decomposition can proceed only until the individual details consist of a single

sample or pixel. In practice, we‘ll select a suitable number of levels based on the nature of the

signal, or on a suitable criterion. For a signal of length N, the signal can be projected onto a

maximum of log2N scales. For most signals it is adequate to go up to a scale (log2N)-3 [9].

6.4 Application wavelet analysis with partial discharge signal

As mentioned before, partial discharge signals are captured by the oscilloscope

Tektronix TDS3024B. The oscilloscope samples the signals and sends this information to

computer via Ethernet cable. So each data has 10000 samples with this kind of oscilloscope.

These data are saved in isf files.

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Fig. 6.4.1: Capturing data process

Fig. 6.4.2: Data captured from oscilloscope

In the figure 6.4.2, we have an example of data sent to computer from oscilloscope

TDS3024D via Ethernet cable. This data has 10000 samples, each sample represent the

magnitude of current pass through coaxial shunt resistor. Effectively, the data send to

computer has 10004 values (10004 samples). The first four values contain the configuration

information of oscilloscope. The first one is the total number of samples of data (this one is

always equal to 10000 which is the number of sample of data, see figure 6.4.2). The second

one is the sampling time. And two others values which show some other configurations.

Before starting the wavelet analysis, we must exclude these four values from data. It‘s very

simple with computer.

Ethernet cable

Numeric data With 10000 Samples (isf format)

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6.4.1 Wavelet analysis signals with MATLAB software.

To perform the wavelet analysis of partial discharge signals, we decided to use

MATLAB software.

MATLAB is a high-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use environment where problems

and solutions are expressed in familiar mathematical notation. Typical uses include:

Math and computation

Algorithm development

Modeling, simulation, and prototyping

Data analysis, exploration, and visualization

Scientific and engineering graphics

Application development, including Graphical User Interface building

MATLAB features a family of application-specific solutions called toolboxes. Very

important to most users of MATLAB, toolboxes allow you to learn and apply specialized

technology. Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems. Areas in which

toolboxes are available include signal processing, control systems, neural networks, fuzzy

logic, wavelets, simulation, and many others.

For our project, we must use ―wavelet toolbox‖ to analysis signal and ―neural network

toolbox‖ to classify the types of partial discharge.

Wavelet toolbox:

Wavelet Toolbox™ software extends the MATLAB®

technical computing

environment with graphical tools and command-line functions for developing wavelet-based

algorithms for the analysis, synthesis, denoising, and compression of signals and images.

Wavelet analysis provides more precise information about signal data than other signal

analysis techniques, such as Fourier.

The Wavelet Toolbox supports the interactive exploration of wavelet properties and

applications. It is useful for speech and audio processing, image and video processing,

biomedical imaging, and 1-D and 2-D applications in communications and geophysics.

There are two ways to use CWT (continuous wavelet transform) and DWT (discrete

wavelet transform). The first one is using command lines and the second one is using graphic

user interface of wavelet toolbox.

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6.4.2 Use command lines for the wavelet analysis.

The first step is launch MATLAB software:

Fig. 6.4.2.1: MATLAB’s interface I.4.2.1

The figure 6.4.2.1 shows the interface of MATLAB. There are 4 important parts:

I- Content of current folder

II- Interface used for typing command

III- Workspace: all variables and data which is used or created during the work

IV- History of all command typed

Second step of analysis process is to import data (signal captured from oscilloscope) to

MATLAB. Realize this by clicking to ‗menu‘ button, choose ‗import data‘, go to the folder

which contain the data of partial discharge signal and choose the data that we want to import.

The data will appear in the part III of MATLAB‘s interface

I II

III

IV

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Fig. 6.4.2.2: import the data ‘x1’

The figure above shows the importation of data ‗x1‘ to Matlab. The dimension of this

data is 10004 as mentioned above. We must exclude four first values before stating wavelet

analysis.

To exclude these four values we type this command in the part II of Matlab‘s

interface:

>> x1=x1(5:10004,:);

Fig. 6.4.2.3: exclude 4 first values of data

Now the data contain only 10000 values and we can start the wavelet analysis.

Continuous wavelet analysis

To realize the wavelet analysis, we use 2 command lines:

COEFS = CWT(S,SCALES,'wname','plot')

Where S is the name of signal example x1 in our case

SCALE is the range of scale that we want use for CWT example 1:20 (from 1 to 20)

Wname is the name of wavelet used for the analysis example db1, sym2 etc… [5]

‗plot‘ is one option to plot the coefficients generated by continuous wavelet transform

We can type >>help cwt to get more information about this command

This command sends back to us the coefficients of CWT

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For each wavelet analysis, the choice of wavelet is very important. Each wavelet will

give us a different result (because each segment of signal will be compare avec the shifted and

scaled version of wavelet). The suitable wavelet for one analysis is the one which is able to

generate the most coefficients with high value. In other word, suitable wavelet for the analysis

of one signal is the one which is correlated with the signal to analysis. So to choose the

suitable wavelet, we calculate the correlation coefficient between the wavelets and the signal.

The one, which give the best result, is the suitable wavelet. For our partial discharge signals,

db6, db7, sym7, sym8 can give good results and the Symlets 8 (sym8) was chosen as the best

compromise between the different similarity measures [9].

Fig. 6.4.2.3: symlets wavelet order 8

Once we have finished selecting the wavelet, we can realize our wavelet analysis

>>a=cwt(x1,1:60,‘sym8‘,‘plot‘);

We use this command line to realize continuous wavelet transform of ‗x1‘ with sym8

wavelet for scale coefficients coming from 1 to 60. All coefficients are saved in variable ‗a‘.

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Fig. 6.4.2.4: CWT of x1 using sym8 wavelet

In the figure 6.4.2.4, we can see the waveform of x1 and also the wavelet coefficients

of x1. For the high variation part of x1, we found that its corresponding coefficients are higher

than others part of signal. So with this we have also the information about frequency and time.

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Discrete wavelet analysis

To realize a discrete wavelet analysis, we can use the following command line:

[C,L] = WAVEDEC(S,N,'wname') for multi-level DWT

Where S is the name of signal to analysis

N is the level of decomposition

‗wname‘ is the type of wavelet used for analysis

We can type >>help wavedec to get more information about this command

This command will give us 2 variables C and L. What do these means?

C contains the coefficients of approximations and details. L contains the length of

coefficients of approximations, coefficients of details and signals.

Fig. 6.4.2.5: two level decomposition of a signal with 100 samples.

Figure 6.4.2.5 shows a simple example of DWT of signal with 100 samples. At first

level, there are 50 coefficients of approximation cA1 and 50 coefficients of detail cD1. At

second level, there are 25 coefficients of approximation cA2 and also 25 coefficients of detail

cD2.

In this case L will be a vector with 100 components. The 25 first components are the

coefficients of cA2, the 25 following components are coefficients of cD2 and the 50 last

components are coefficients of cD1.

C, in this case, is a vector of 4 components. The first component is the length of cA2 (number

of values of cA2 =25). The second component is length of cD2 (its value must be equal to the

first one). The third is length of cD1 (50) and the last one is length of S (100).

L= [a1 a2 …a25 a26 …a50 a51 … a100]

C= [25 25 50 100]

cD1 cD2 cA2

100

50 50

25 25

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Fig. 6.4.2.6: approximation and details of discrete wavelet transform 3 levels

This figure shows the decomposition at level 3 of signal ‗x1‘. We can see three details

(D1, D2, D3) and latest approximation (A3). The details contain the high frequencies

information (noise in this case) and approximation contains low frequencies information. We

can see that A3 is original signal without noise.

With 2 vectors C and L, we can reconstruct the coefficients of approximations and details of

each level via the following command lines:

cA3 = appcoef(C,L,'sym8',3); for the coefficients of approximations

cD3 = detcoef(C,L,3); for the coefficients of details

All information about this type of wavelet analysis is given in Wavelet toolbox (p.72 to

p.76).

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6.4.3 Using Graphic User Interface of wavelet toolbox

Another useful way to realize wavelet transform is to use Graphic User Interface of

wavelet toolbox. We don‘t have to type any command line to realize the analysis. All can be

done with windows and buttons.

The first step is to open the Graphic User Interface of wavelet by typing the following

command line:

>>wavemenu

Fig. 6.4.3.1: Graphic User Interface of wavelet toolbox

A window, like figure 6.4.3.1, will be opened. In this window, there are many type of

wavelet transform. For our case, we focus only on Wavelet 1-D (Discrete wavelet transform

1D) and continuous wavelet 1-D.

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Continuous wavelet transform (continuous Wavelet 1-D)

We can use the continuous wavelet analysis by clinking to the ‗Continuous Wavelet 1-

D‘ button of ‗wavemenu‘ figure. The following figure will be opened.

Fig. 6.4.3.2: CWT with Graphic User Interface

Wavelet analysis becomes very simple with Graphic User Interface (GUI). The Figure

6.4.3.2 shows the continuous wavelet transform with GUI. The continuous wavelet will be

realized via following steps:

Import data from ‗file‘ button.

Choose the family of wavelet that we want to use for the analysis.

Choose the range of scale.

Push ‗Analysis‘ button. The results will be shown as the figure 6.4.3.2

The figure 6.4.3.2 shows the coefficients of CWT of one partial discharge signal with

‗sym8‘ for scale come from 1 to 60.

We can also export the result of wavelet analysis from GUI to workspace and save it to

computer (See more details in Wavelet toolbox tutorial [5]).

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Discrete wavelet transform (Wavelet 1-D)

We can use the discrete wavelet transform by clicking to the ‗Wavelet 1-D‘ button of

‗wavemenu‘ figure. The following figure will be opened.

Fig. 6.4.3.3: DWT with graphic user interface.

The figure above shows the analysis of DWT via graphic user interface. The discrete

continuous wavelet will be realized via following steps:

Import data via ‗file‘ button. The signal will be plot on the first axe of Wavelet 1-D (s

in Figure 6.4.3.3).

Choose the kind of wavelet that we want to use ( sym8 in this example) and level of

decomposition (6 in this example)

Click to ‗analyze‘ button to get all coefficients of details and approximation

In this example, we took a discrete wavelet transform of one partial discharge (s) to

level 6 with sym8 wavelet. It gives us all details (d1 to d6) and approximation at level 6 (a6).

We can also export results from GUI to workspace and save them to computer. (See more

details in Wavelet toolbox tutorial more details).

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Conclusion

Wavelet analysis is a powerful processing tool to extract all information about signal.

The Matlab helps us to realize this analysis simpler. For our project, we use the discrete

wavelet analysis to generate details and approximation coefficients. Sym8 wavelet is used for

analysis thanks for the correlation between this one and partial discharge signal [6]. Our

signal has 10000 samples and the maximum level that we can decompose our signals is 9

(log2N-3=9) so we decompose all partial discharge data into 9 levels. The coefficients of

details and approximation will be used to classify all kind of partial discharge. The following

chapter will give more details about utilization of these coefficients.

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7 Artificial Neural Network (ANN)

The goal of our project is find out the defect in the transformer via the waveform of

partial discharge (PD) signals captured by oscilloscope. The PD signals will be analyzed by

discrete wavelet transform to generate wavelet coefficients. After, these coefficients will be

compared with a library to identify the kind of partial discharge.

Fig. 7.1: Process of recognition

To realize this recognition, two things are required Feature extraction and Feature

classification. In our project, DWT is used for the feature extraction and artificial neuron

network is used for method classification (Feature classification).

Feature extraction

Any pattern which can be recognized and classified possesses a number of

discriminatory attributes or features. Thus, the first step in any recognition process is to

consider the problem of what discriminatory features to select and how to extract these

features from the patterns. It is quite clear that the number of features needed for successful

classification depends on the discriminatory quality of the chosen features. The tools used for

selection of feature vector (a set of selected features) are generally application dependant.

Over the past couple of decades, several different approaches have been adopted for the

choice of features in PD pattern recognition. These different approaches can be broadly

grouped into the following methods/tools:

PD signal Captured by

oscilloscope

Feature extraction

Feature classification

Classification methods

Reference

Result

Kind of partial discharge

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statistical methods

pulse shape parameter approach

signal processing tools (Fourier transform, wavelet transform)

image processing tools and time-series approach

So these are some principal methods for feature extraction. Their details can be found

in [14].

Classification method

Once the feature vector is created, it will be sent to a classification method to

recognize the kind of defect that is the source of corresponding partial discharge. There are

quite a good number of classifiers available in the literature for pattern recognition. The

various approaches are based on: decision functions, distance functions, likelihood functions,

artificial neural networks, trainable classifiers etc. All the different classifiers proposed for PD

may be grouped as distance classifiers, statistical classifiers, ANN-based classifiers and fuzzy

logic based classifiers [15].

In this project, the signal processing tools with discrete wavelet transform is chosen for

feature vectors extraction and ANN (Artificial neural network) is chosen for classification

method. In the next chapter, the artificial neural network will be talked more in details and

also how the feature vectors are used.

7.1 Introduction of artificial neural network

An artificial neural network is a system based on the operation of biological neural

networks, in other words, is an emulation of biological neural system. Why would be

necessary the implementation of artificial neural networks? Although computing these days is

truly advanced, there are certain tasks that a program made for a common microprocessor is

unable to perform; even so a software implementation of a neural network can be made with

their advantages and disadvantages.

Advantages:

A neural network can perform tasks that a linear program can not.

When an element of the neural network fails, it can continue without any problem by

their parallel nature.

A neural network learns and does not need to be reprogrammed.

It can be implemented in any application.

It can be implemented without any problem.

Disadvantages:

The neural network needs training to operate.

The architecture of a neural network is different from the architecture of

microprocessors therefore needs to be emulated.

Requires high processing time for large neural networks.

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Another aspect of the artificial neural networks is that there are different architectures,

which consequently requires different types of algorithms, but despite to be an apparently

complex system, a neural network is relatively simple. There are 2 popular architectures:

Feed-forward neural networks, where the data from input to output units is strictly

feed-forward. The data processing can extend over multiple (layers of) units, but no

feedback connections are present, that is, connections extending from outputs of units

to inputs of units in the same layer or previous layers.

Fig. 7.1.1: Feed-forward neural network

Recurrent neural networks that do contain feedback connections. Contrary to feed-

forward networks, the dynamical properties of the network are important. In some

cases, the activation values of the units undergo a relaxation process such that the

neural network will evolve to a stable state in which these activations do not change

anymore. In other applications, the changes of the activation values of the output

neurons are significant, such that the dynamical behavior constitutes the output of the

neural network (Pearlmutter, 1990).

Fig. 7.1.2: Recurrent neural networks

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So the principal of all neural networks is: we put one set of value in inputs, the neural network

will take some calculation (depend on parameters of the neural network) and we obtain one

set of value in output. This method is very powerful for the classification.

All introduction and definition of neural network is given in the Annex 5. In summary, to

creating a neural network, we need the following steps:

Collect data for neural network

Extract the feature vectors

Define the number of input layer, output layer and hidden layer (if necessary)

Initial weights and bias between each connexion of ANN

Train the neural network to find the right values of weights and bias

Use the neural network

Return to our project, our goal is to identify the kind of partial discharge thanks to

information come from partial discharge signal. The process of our project is:

The discrete wavelet transform gives the feature vectors which are coefficients of

details and approximation (see chapter discrete wavelet transform). These feature vectors will

be sent to the input of neural network. The output of neural network is the kind of partial

discharge (kind of defect) corresponding to the inputs.

The neural network used for our project is Perceptron. The training algorithm is back-

propagation. The next chapter will talk in details the Perceptron neural network and also back-

propagation algorithm.

7.2 Perceptron neural network

Fig. 7.2.1: Simple Perceptron with one input and one output

Collect data from

oscilloscope

Feature extraction

DWT

Artificial neural

network

Kind of partial

discharge

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Perceptrons are the simplest architecture to learn when studying Neural Networking.

It‘s a kind of Feed-forward neural networks. Since making connections of perceptrons into

a neural structure is a bit complicated, let‘s take a perceptron by itself. A perceptron has a

number of external input pattern, one internal input (called a bias b), an activation function,

and one output. In the figure 7.2.1, you can see a picture of a simple perceptron with only one

external input unit (p), one weight (w) one activation function (f), one output (a) on the left

and the same with one bias (b) on the right. It resembles a neuron.

Fig. 7.2.2: Complete scheme of simple Perceptron

Figure 7.2.2 shows the complete scheme of a simple Perceptron with one input layers

and one output layers.

Usually, the input values are boolean (just two possible values 1 and 0, true and false),

but they can be any number. The outputs of the Perceptron can have value from 0 to 1 (it‘s

depend for activation function chosen).

All of the inputs (including the bias) have weights attached to the input patterns that

modify the input values to the neural network. The weight is just multiplied with the input.

There is another structure of Perceptron which is Multi-layers Perceptron.

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Fig. 7.2.3: Multi-layers perceptrons

The principal of multi-layer Perceptron (Figure 7.2.3) is the sample than simple

Perceptron. But with multi-layers Perceptron, there are 3 layers (input layers, hidden layers

and outputs layers). For some applications which are not possible with simple Perceptron, the

multi-layer Perceptron can give a better result. For our case, we use multi-layer Perceptron

The activation function is one of the key components of the Perceptron as in the most

common neural network architectures. It determines, based on the inputs, whether the

Perceptron activates or not. There are several activation functions like sigmoid function, step

function (threshold), linear function.

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Fig. 7.3.4: Activation functions of ANN

Figure above shows some activation functions frequently used and their symbols. For

each activation function, we can obtain a different result at the output of neural network.

Example, function threshold (‗pas unitaire‘) give only 2 values at the output (0 or 1). For

others functions, we can obtain a value coming from 0 to 1. For our artificial neural network,

sigmoid function is chosen.

7.3 The back-propagation algorithm

The back-propagation is a training algorithm used to adjust weight and bias of an

artificial neural network feed-forward (Perceptron in our case). When we create the neural

network, the weight and bias are initialized with random values. The back-propagation

algorithm will modify these weights and bias in order to minimize means square errors

between the inputs and outputs of neural network. To realize training with back-propagation,

an input vectors and a target vectors is needed.

To realize the training with back-propagation, we must differentiate 3 terms:

Input vectors: they are the vectors will be sent to inputs layer of neural network

Output vectors: they are the values at the output of neural network when the input

vectors is put in inputs layers (they are real values)

Target vectors: it‘s is the values that neural network must give at output when input

vectors is put in inputs layers (they are perfect values or target values).

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For example ‗p‘ is input vectors of neural network, ‗t‘ is target vectors of neural

network and ‗a‘ is the output vectors of neural network. The goal is minimize the cost

function F (means square errors) which is defined as:

Where Q is number of inputs vectors used for training phase. This minimization can

be done thanks to delta rules:

The algorithm LMS (Least Mean Squared) estimates the kth iteration the mean

square error e² by calculating the derived of mean square errors based on the weight and the network. Thus:

For j= [1…R] .R is the length of input vector

So we have equation

We can simplify the expression above by

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This means that the weights and biases of the network must change

Where α is the learning rate. In the case of multiple neurons, we can write

The expression (7.3.1) is the most important expression that we must to keep. The

following steps are needed for the training with back-propagation

Collect data for training (input vectors and target vectors)

Choose the learning rate α

Put each input vector to input layer

Calculate the output vector

Find out the error between target vector and input vector

If there is errors between target vector and input vector and this error is superior than

an accepted value, modify the weights and bias thanks to expression (7.3.1)

Repeat these steps until all errors are inferior to the accepted value.

This is the back-propagation used to train neural network feed-forward (Perceptron in

our case).

7.4 Artificial neural network created for partial discharge classification

To classify all kind of partial discharge, the multi-layer Perceptron is used. This

Perceptron contains:

One inputs layer

One output layer

One hidden layer

The activation functions used are sigmoid function

Inputs layer

The number of inputs layer is equal to length of feature vectors [17]. According to the

beginner of this chapter, we use discrete wavelet transform to extract feature vectors. Our

original signals have 10000 samples. We will decompose our signal up to level 9 with discrete

wavelet analysis. After this analysis, we will find 10000 coefficients of approximation (cA9)

and details (from cD1 to cD9). If these coefficients used directly for feature vector, the inputs

layer will have 10000 neurons. As we discussed before, one disadvantage of neural network is

‗Requires high processing time for large neural networks‘ (see chapter 7.1). So with 10000

neurons in inputs layer, computer needs a lot of time to make the calculations. So we need

reduce the number of neuron at inputs layer (the number of components of feature vector).

(7.3.1)

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By researching on the internet, we decided to use statistical method to reduce the

number of components of feature vector described in [9] [14]. The principal idea of this

method is that we will calculate four coefficients of statistic (means, variance, skewness, and

kurtosis) for all coefficients of details and approximation of each level.

For example x=[x1,x2,x3,…,xN], the definition of these four coefficients of statistic of

x are:

These coefficients can have expressions below:

Where η is means of x, ζ is variance of x, γ is skewness of x and κ is kurtosis of x

We calculate all means, variance, skewness and kurtosis of all details (from cD1 to

cD9) and approximation (cA9). In final, we can reduce to 40 (statistical coefficients of 9

levels of details and 1 level of approximation) of 10000 coefficients of DWT. Now, the

feature vectors have 40 components in place of 10000 components.

So with discrete wavelet transform and statistical method, we obtain the feature

vectors of 40 components. The inputs layer has 40 neurons

Hidden layer

Hidden layer is the intermediate layer between input layer and output layer. There

isn‘t formula to calculate the number of neuron of this layer. We must try with different

values and choose the values which give the best results. For our experience, with 20 neurons

(7.3.2)

(7.3.3)

(7.3.4)

(7.3.5)

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at hidden layer, we obtain a good result so we decided to create the neural network with 20

neurons at hidden layers.

Output layer

The output layer is the answer of neural network when there is a value (a feature

vector) put on input layer. The number of neuron of this layer is equal to the number of defect

that we have. If we have 3 defects (3 kind of partial discharge) the number of neuron of output

layer is 3. Now the question is how neural network will answer?

It‘s very easy, for each time, only one output (one neuron) of output layer is activated

(1) and others output is deactivated (0). For example the neural network has 3 outputs which

correspond to 3 types of partial discharge (type 1, type 2, type 3), the feature vectors of partial

discharge type 1 is put on input layer and in output of neural network, the output type 1 is

equal to 1 and others outputs are equal to 0. So we can conclude that this signal is type 1.

Test our analysis method.

To test our analysis method, we use 3 transformers with 3 differences defects. These

transformers are shows in the following figure:

Fig. 7.4.1: Transformers with different defects

The figure 7.4.1 shows transformers with different defects in inside. Type 1 is a voltage

transformer where the defect is resistor fat QZ13. Type 2 is also a voltage transformer where

the defect is resistor coated silicon. Type 3 is a current transformer with vacuum bladder. For

each type of defect, we captured 110 data. 100 data will be used to train the neural network

with back-propagation algorithm. Once the neural network is trained, we use 10 last data to

test our neural network.

In this test, we try to classify these 3 types of defects. So the output layer of our neural

network has 3 neurons.

Type 1 Type 2 Type 3

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Fig. 7.4.2: Perceptron created for our classification

The figure 7.4.2 shows the configuration of neural network used for our project. Once

it‘s created, we must train the neural network to make sure that it works correctly. For training

phase, we use the back-propagation algorithm and we must create the matrix of data and

target matrix for training phase. So what are these matrixes?

The matrix data for training phase is a matrix which contains all feature vectors of

partial discharge signals that we know which type they belong. See example below to

understand

A = x1 y1 z1

x2 y2 z2

x3 y3 z3

. . .

. . .

. . .

x40 y40 z40

So A contains 3 feature vectors x, y, z that we know in advance which type of partial

discharge they belong. For example x is type 1, y is type 2 and z is type 3.

The target matrix is the matrix which contains the answer (output desired, target

output) of each feature vectors in matrix of data used for training phase. For example, with

matrix of data which has 3 feature vectors x, y, z like the example above. The target data

corresponding to matrix A for training phase is:

T= 1 0 0

0 1 0

0 0 1

The first column of T shows that the first feature vector of A is type 1. The second

column of T shows that the second feature vector of A is type 2 and the third shows that the

third feature vector of A is type 3.

For training phase, we must have a matrix of data with a lot of feature vectors in order

to give a good result. As mentioned before, we use 100 data of each type of partial discharge

for training phase. We have 3 kind of defect so we captured totally 300 signals for training

phase. And the dimension of our data matrix is 40x300. The target matrix for training phase

x y z

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has a dimension of 3x300. These matrixes can be created thanks to matlab code in the Annex

6.

Once we created the data matrix and target matrix for training phase, we can create the

neural network and train this neural network thanks to neural network toolbox of Matlab.

These following steps must be respect to create, train and use the neural network thanks to

graphic user interface of neural network tutorial:

Type this command code in matlab windows >>nprtool. The following figure will be

opened

Fig. 7.4.3: graphic user interface of neural network toolbox

Click Next to proceed. The Select Data window will be opened. Select data matrix for

‗Inputs‘ and target matrix for ‗Targets‘ as the figure 7.4.4

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Fig. 7.4.4: data matrix and target matrix selection

When we finish the data selection, click Next to go to the Validation and Test Data

window.

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Fig. 7.4.5: Validation and Test Data window

Validation and testing data sets are each set to 15% of the original data. With these

settings, the input vectors and target vectors will be divided into three sets as follows:

80% are used for training.

10% are used to validate that the network is generalizing and to stop training

before over-fitting.

The last 10% are used as a completely independent test of network

generalization.

More details about this are given in ‗neural network toolbox tutorial‘ [17] (page 3-10).

Click next to continue

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Fig. 7.4.6: Network architecture

Choose the number of hidden layer (in our case it‘s is 20) and Click next to open the

train network window

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Fig. 7.4.7 Train network

Click ‗Train‘ to train our neural network. It will try to modify all weights values in

order to get a good result with data matrix and target matrix. The following window

will be opened.

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Fig. 7.4.8: Neural network training

So this figure shows the structure of neural network and also how neural network is

trained. We can click to the ‗Confusion‘ button to open the following window which is used

to see the performance of neural network

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Fig. 7.4.9: confusion table

This figure gives all confusion during the training phase, validation phase and test

phase. The neural network will be more performance if there are less confusions in training

phase validation phase and test phase [17]. In our case, there aren‘t confusions in any phase.

So our neural network is very performance.

Once the neural network is created and trained, we must save this neural in order to

able to test after.

If the result is satisfied, click next in train network windows. If the result isn‘t

satisfied click ‗retrain‘ to realize training (each training will give the differences

weights i.e. news results).

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Fig. 7.4.910: save result window

When the result is satisfied, we must save this neural, click to ‗Save Results‘ to save

the neural network to ‗workspace‘. His default name is ‗net‘. We can change this

name as we want.

Now the neural network is created and trained. We can use our neural network. How

to use this neural network?

The diagram above shows the wave to test/use our neural network. This network is

created to recognize 3 type of partial discharge. So now we will captured new signals of these

3 types of partial discharges (which is not use for training phase) and test to see if the neural

network arrive to recognize the type of partial discharges of these signal or not.

Captured data from

oscilloscope Signal with

10000 samples

Feature vectors extraction thanks

to DWT and statistical

method

Neural network

trained

Kind of partial

discharge

identified

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For each type of partial discharge, we captured 10 news signals. These signals will be

processed by DWT (discrete wavelet transform) and statistical method to obtain their 40

components used for input of neural network.

To test the neural network, we use this command:

>>sim(net,x1)

Where net is the name of neural network saved in workspace of Matlab and x1 is the feature

vector of signal that we want to test.

Fig. 7.4.11: test the neural network with the signal type 1

The figure 7.4.11 shows the test for the signals type 1. We can see that the first

component of output is 0.9998 which is very higher than others components of output, it

indicate that the signal belong to type 1.

Fig. 7.4.12: Test the neural network with the signal type2




Fig. 7.4.13: Test the neural network with the signal type 3

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For each kind of defect, 10 data was captured to test the neural network. These data

can be recognized without confusion. So the neural network created is very performance for

classification these 3 types of defect.

If we have more defect in the transformer, we must just captured the data of these new

defects and re-create (with larger layers in output) and re-train the neural network. After, the

neural network could recognize these defects.

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8 Graphic User Interface (GUI)

During our project, Matlab software was used to realize all our analysis (discrete

wavelet transform, statistical method and also artificial neural network). These analyses

require the knowledge about Matlab software and also utilization of command lines in

Matlab. It could be difficult for someone who wants to understand and use our method. To

help user to use our method simpler, we decide to create a graphic user interface which realize

our analysis method with window and button (not command line).We program this graphic

user interface in Matlab thank to GUIDE (Graphic User Interface development environment).

GUIDE, the MATLAB graphical user interface development environment, provides a

set of tools for creating graphical user interfaces (GUIs). These tools greatly simplify the

process of designing and building GUIs. We can use the GUIDE tools to perform the

following tasks:

Lay out the GUI.

Using the GUIDE Layout Editor, we can lay out a GUI easily by clicking and

dragging GUI components—such as panels, buttons, text fields, sliders, menus, and so

on—into the layout area. GUIDE stores the GUI layout in a FIG-file.

Program the GUI.

"GUIDE automatically generates a MATLAB program file that controls how the GUI

operates. The code in that file initializes the GUI and includes function templates for

the most commonly used callbacks for each component—the commands that execute

when a user clicks a GUI component. Using the MATLAB editor, we can add code to

the callbacks to perform the functions you want.

Graphic User Interface created for the partial discharge recognition

To realize an analysis with Graphic User Interface of partial discharge, we need these

following steps

Open Matlab software

Change the current folder to the ‗partial discharge‘ folder (this folder contain the

program of graphic user interface of partial discharge).

Type >>partialdischarge at the command line and the following window will be

opened

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Fig. 8.1: Graphic User Interface of partial discharge

This window is the Graphic User Interface of partial discharge that we create to

analyze the partial discharge signals thanks to DWT and neural network. In this window we

can:

Click to images to visit the website of TRENCH Company and INSA

Click to ‗help‘ button to open ‗Help Partial Discharge‘ window. It will generate the

pdf files which explain how to use DWT, neural net work and also how to use this

Graphic User Interface. Choose the document that you want to read and click ‗Ok‘

button, this document will be opened.

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Fig. 8.2: Help Partial Discharge Analysis window.

Click to Start Analysis to start our analysis. The following window will be opened

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Fig. 8.3: graphic user interface of partial discharge analysis

Figure above shows the graphic user interface (GUI) of our partial discharge analysis process.

With this GUI, we can:

Create new neural network with new data and use the neural network created

Choose one neural network exited from a folder and utilize the neural network chosen

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Create new neural network with new data

This chapter shows each steps to create a new neural by using our process.

The first step is to collect the data needed for the analysis (the waveform data of each defect).

These data is captured from oscilloscope via computer connection (see the chapter Artificial

Neural Network).

For example we have 3 defects which can produce the partial discharge phenomena. So we

want classify this 3 types of defects. The first thing we must do is create 3 samples which

represent these 3 defects. We measure the partial discharge of these 3 samples. For each

sample (each type of defect), we capture several measurement (example 20 or 50

measurement for each sample) to computer. Normally with Tektronix oscilloscope, the

measurement will be saved in ‗isf‘ format. We put all measurement of the same sample in a

folder specific.

Fig. 8.4: folders where all measurement are saved

In the figure above, we can see 3 folders which contain the measurements of 3 samples. Each

folder contains the measurements of one sample (the ‗isf‘ files).

The second step is to select the data to GUI of partial discharge. Open GUI of partial

discharge and use the ‗select data for a new neural network‘ to select data.

Fig. 8.5: select data to create a new neural network

To select the data to create a new neural network, we must following these steps:

Enter the total number of defect that you want to classify in case ‗total number of

defect (3 in our example)

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You enter the type of defect that you want to select now (1 or 2 or 3 in our example) in

the case ‗Type of defect‘. These numbers must be entered with care because it will

change completely our result.

Click ‗Data Select‘ to select the data. A select window will open and we go to the

folders where there are the data of the type of defect typed in case ‗type of defect‘.

Fig. 8.6: Window used to select data

Click ‗Ouvrir‘ to select data (in the figure 8.6, ten data of defect type 1 are selected)

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Fig. 8.7: Data selected

Figure 8.7 shows the result of selection of data type 1. In case ‗Description‘ we will see the

dimension of matrix input is 10000x10 because we selected 10 data of defect type 1 (each

data has 10000 values). The matrix output is created for the neural network. The case ‗Display

data‘ displays all data select for analysis. We repeat these steps to select data for others type

of defect.

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Fig. 8.8: data of all 3 types of defect selected

Figure 8.8 shows that the data of 3 types of defect are selected (10 data of each type of defect

are selected). The matrix input contains the waveform data (see type of data).

The third step is use wavelet analysis to create the feature vector data corresponding for each

waveform data. Use the case ‗Wavelet analysis‘ to realize this step. In this case, we can

choose different type of wavelet for analysis (the wavelet symlet 8 is recommended). When

we finish the choice of wavelet, we click to the ‗Wavelet Analysis‘ button to realize the

discrete wavelet transform at level 9 (see Chapter Wavelet transform).

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Fig. 8.9: Wavelet analysis withi GUI of partial discharge

The figure 6 shows the result of wavelet analysis. In case ‗description‘ we can see that the

dimension of input matrix is 40x30 in place of 10000x30 in figure 8.8. The input matrix

contains now feature vector data. This is the result of wavelet analysis + statistical method

(see Feature Vector in Chapter Artificial Neural Network). The box ‗Display data‘ displays

the coefficients of new input matrix. Now we have the input matrix and output matrix for

neural network. The next step is to create the neural network.

Use the case ‗Neural Network analysis‘ to create new neural network. Our neural network has

3 layers

Input layer configured by input matrix

Output layer configured by output matrix

Hidden layer configured by user. So you must enter the number of hidden layer to

create new neural network (20 is recommended by our experience)

When we entered the size of hidden layer, we need to click the ‗create new neural‘ button to

create a neural network. A neural network will be created and a window will be opened.

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Fig. 8.10: Neural network training

This figure shows the result of training phase. Click ‗confusion‘ button to see the result of

neural network (see neural network toolbox or chapter Artificial Neural Network to have

more information). If the result is not good, click ‗create new neural‘ button again to retrain

the neural network. If the result of neural network is good, we can close the ‗Neural Network

Training‘ window (figure 7) and use this neural now.

Now when the network was created, we can:

Save this neural network to our current folder by typing the name that you desire to

save in box ‗name of neural network to save‘ and click ‗save the neural network‘

button. A mat file will be create in our current folder and contains the new neural

network.

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We can use directly this neural network to test by clicking ‗choose data for test‘ in

‗Test Panel‘ box. This button will allow us to select new data for test. For example we

want to know one object which has which type of defect. We must captured some

partial discharge data of this object from oscilloscope (We must capture several data,

only one data is not accepted because with more data, the result will be more

accurate).We select these data thanks to ‗choose data for test‘ and after the result will

be appear in ‗Description‘ box.

Fig. 8.11: Select data for test

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Fig. 8.12: Result of test

Figure 8.12 shows the result of test with some data of type 1 (we selected 5 data of defect type

1). The ‗Description‘ box shows that the defect is the type 1. So the neural network works.

The ‗Display data‘ shows the feature vector of all data selected for test.

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Choose one neural network existed from a folder and utilize the neural network chosen

To choose a neural network existed from a folder, we use the ‗choose an existed neural‘

button (Figure 8.12). This button allows us to select one neural created before.

Fig. 8.13: Select a neural network existed before.

This figure shows the window used to select a neural network. We go to the folder which

contains the neural network that you want to select. We choose the network and click ‗Ouvrir‘

(In figure 8.13, net1 was chosen). The neural network will be import to workspace of Matlab.

Now we can use this neural network to test. To analyze with this neural network, you use the

‗choose data for test‘ button like the chapter before.

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9 Conclusion

For the measurement part, with the filter created, we arrive to eliminate the 50 Hz

signal. Without this signal, the partials discharges are simpler to captured and simpler to

analysis.

The problem of reflexion and oscillation frequency modifies our partial signal signals.

And we can obtain wrong signals. By adapting the impedance in function of coaxial cable we

eliminate the reflexion phenomena and by reducing the loop of measuring circuit we can

attenuate the oscillation frequency.

The discrete wavelet transform is chosen to analysis partial discharge signal because it

gives us all information about time and frequency. This analysis is more suitable than Fourier

transform for the type of partial discharge which is the signals with very fast variation in a

very short time.

The statistical method is used to reduce the number of coefficients used for neural

network. It will reduce the analysis time of neural network and also gives more accurate

results (so many coefficients require many weight and the neural network becomes more

difficult to train).

The neural network classifier is chosen thank to its advantages, the Perceptron neural

network is used for the analysis. The back-propagation is used to train our neural network.

The results of neural network created for 3 types of partial discharge are 95% so the neural

network works perfectly. So the problem now is just to identify all type of defect can be take

place in the transformer. Create the samples which have only one defect a time. Test these

samples and training the neural network with more output (more type of defect) and after we

can use this neural network to identify an unknown defect in the transformers.

During this final year project, we has discovered a lot of new theory about the

difficulties of measurement process, the problem of transmission at high frequencies, the

wavelet analysis and also the neural network which are very important for our professional

life in the future.

We want to thank Mr MINKER, Mr SMIGIEL our supervisors. They help us a lot to

understand many thing and also to solve all problem that we had during our project. We want

also to thank all people in TTT department of TRENCH Company for their help during our

project.

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References

[1] Hans Edin, ―Partial Discharge Studied with Variable Frequency of the Applied

Voltage‖, 2001, pp. 12.

[2] E. Kuffel, J.Kuffel, W.S. Zaengl, High Voltage Engineering – Fundamentals – Second

Edition, 2000

[3] Guide for Partial Discharge Measurements in Compliance to IEC 60270 – December 2008

[4] Cours 1998 de C. Brielmann Leitungstheorie, G. S. Moschytz, U. Brugger et J. Rosenblatt

– ‗Transmission sur lignes‘

[5] ‗Wavelet toolbox‘- Matlab -http://www.mathworks.com/help/toolbox/wavelet/

[6] ‗Standing wave‘- http://en.wikipedia.org/wiki/Standing_wave

[7] ‗Wavelets and Filter Banks‘, by Strang and Nguyen, P.1

[8] ‗Wavelets and Filter Banks‘, by Strang and Nguyen, P.91

[9] D. Evagorou, A. Kyprianou, P.L.Lewin, A. Stavrou, V. Efthymiou, A.C. Metaxas, G.E.

Georghiou ‗Feature extraction of partial discharge signals using the wavelet packet transform

and classification with a probabilistic neural network‘- IEEE, p.8

[10] ‗Wavelet tutorial‘ http://polyvalens.pagespersoorange.fr/clemens/wavelets/wavelets.html

[11] Sheng, Y. ‗WAVELET TRANSFORM’. In: The transforms and applications handbook.

Ed. by A. D. Poularikas. P. 747-827. Boca Raton, Fl (USA): CRC Press, 1996. The Electrical

Engineering Handbook Series.

[12] Mallat, S. G. ‗A THEORY FOR MULTIRESOLUTION SIGNAL DECOMPOSITION:

THE WAVELET REPRESENTATION’. IEEE Transactions on Pattern Analysis and Machine

Intelligence, Vol. 11, No. 7 (1989), p. 674- 693.

[13] Burrus, C. S. and R. A. Gopinath, H. Guo. ‗INTRODUCTION TO WAVELETS AND

WAVELET TRANSFORMS, A PRIMER’. Upper Saddle River, NJ (USA): Prentice Hall, 1998

[14] N. C. Sahoo, M. M. A. Salama. ‗Trends in Partial Discharge Pattern Classification:A

Survey’. p3 –p7

[15] N. C. Sahoo, M. M. A. Salama. ‗Trends in Partial Discharge Pattern Classification:A

Survey‘. P7 –p12

[16] http://www.learnartificialneuralnetworks.com/#Intr

[17] Neural network toolbox tutorial, http://www.mathworks.com/help/toolbox/nnet/

http://en.wikipedia.org/wiki/Standing_wave

http://www.learnartificialneuralnetworks.com/#Intr

http://www.mathworks.com/help/toolbox/nnet/

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NGO Xuan Thuy-GE5S

[18] D. Evagorou, A. Kyprianou, P.L.Lewin, A. Stavrou, V. Efthymiou, A.C. Metaxas, G.E.

Georghiou ‗Feature extraction of partial discharge signals using the wavelet packet transform

and classification with a probabilistic neural network‘- IEEE, p.8

[19] Standard IEC 60270:2000-12 ―High-voltage test techniques – Partial discharge

measurements‖. Publication of Dr. MINKNER

[20] A coaxial shunt 14 ohms. The R&D department borrowed it from Prof. Ing. A.

RODEWALD from the university of applied Sciences in Muttenz/BL/CH

[21] Wavelet transform: http://en.wikipedia.org/wiki/Wavelet_transform

http://en.wikipedia.org/wiki/Wavelet_transform

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