diagonostic of transformer winding movement - circle
TRANSCRIPT
DIAGONOSTIC OF TRANSFORMER WINDING MOVEMENT
by
QIAOSHU JIANG
B.Sc, North Institute of Electric Engineering, P.R. China, 1993 M.B.A., Dalian University of Technology, P.R. China, 2000
A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
in
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(Department of Electrical and Computer Engineering)
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THE UNIVERSITY OF BRITISH COLUMBIA
March 2004
©Qiaoshu Jiang, 2004
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ABSTRACT
Power transformers p lay a v i ta l role i n the operation o f a power gr id . A power
transformer converts electr ici ty from one potential level to another, and it is one o f the
most important and expensive pieces in a power gr id . H o w e v e r , transformer failures
happen, w h i c h lead to power outages, h igh cost o f repair or replacement, personal injuries
and environmental damages. W i n d i n g movement and/or dis tor t ion account for a large
percentage o f transformer failures. The focus o f this thesis is to explore an effective
w i n d i n g movement detection technique.
The current diagnostic techniques used for detecting w i n d i n g movements are
discussed and compared in this thesis. The Frequency Response A n a l y s i s ( F R A ) technique
is today's most c o m m o n l y used and effective technique; however , it h i g h l y depends on the
test frequency range, test set-up, external circuits and different phys i ca l structures o f
different transformers. T h e F R A ' s dependence on so many parameters can result i n
inaccurate data.
Based on the wave propagation property and the frequency dependent t ransmission
l ine model , a new approach for w i n d i n g movement detection is proposed i n this thesis, the
Transmiss ion L i n e Diagnos t ics ( T L D ) . In this method, by measur ing the input and output
voltages and the currents, the surge impedance Z c o f the w i n d i n g can be unique ly obtained.
Z c is the signature o f the w i n d i n g and it is independent o f the external c ircui ts . A n y
movement o f the w i n d i n g w i l l reflect in a change o f Z c . Different from the complex
transfer function o f numerous resonant frequencies i n F R A , Z c obtained b y T L D is a
s imple exponent ia l - l ike curve, whose ver t ical shift gives obvious ind ica t ion to the overa l l
axial or radial w i n d i n g movements . Furthermore, T L D is ve ry efficient i n l o w frequency
range; for example, 2 M H z is the m a x i m u m frequency used w h e n per forming the
experiments i n this thesis. W i t h a l l these advantages, T L D can be effectively applied to on
line transformer w i n d i n g condi t ion moni tor ing i n the future.
TABLE OF CONTENTS A B S T R A C T ii
T A B L E OF CONTENTS Hi
LIST OF T A B L E S v
LIST OF FIGURES vi
LIST OF ABBREVIATIONS viii
A C K N O W L E D G E M E N T ix
C H A P T E R 1 Overview ,.1
1.1 Introduction to P o w e r Transformers 1
1.2 Transformer Fai lures 5
1.3 Causes o f W i n d i n g M o v e m e n t 11
1.4 Current ly A v a i l a b l e W i n d i n g Diagnos t ic Too l s 15
1.5 Thesis O v e r v i e w 21
CHAPTER2 Transformer Models 23
2.1 M o d e l l i n g B a c k g r o u n d 23
2.2 Phys ica l Transformer M o d e l S imula ted as a Transmiss ion L i n e 27
2.3 Decoupled H i g h Frequency Transformer M o d e l 32
2.4 Equivalent 71 M o d e l by N o d a l A n a l y s i s 35
C H A P T E R 3 Transformer as a Transmission Line 39
3.1 The W a v e Propagat ion High-f requency Transformer M o d e l 41
3.1.1 Frequency-dependent L i n e M o d e l 42
in
3.1.2 Non-fau l ted W i n d i n g M o d e l 45
3.1.3 Faul ted W i n d i n g M o d e l 48
3.2 Laboratory Exper iments and S imula t ion Results 50
3.2.1 Init ial Exper iments Performed i n the U n i v e r s i t y Labs 50
3.2.2 Exper iments Performed in the Powertech Labs 60
3.2.3 Conf igura t ion o f a S ingle Phase Transformer for Tests 66
3.2.4 Exper iments Performed w i t h a N e w Transformer i n the U n i v e r s i t y L a b 72
3.3 N e e d for Base l ine H i s t o r i c a l Da ta 84
3.4 T L D for Other L o n g W i n d i n g Equipment 87
C H A P T E R 4 Conclusions and Recommendations for Future Work. 89
4.1 General Conc lus ions 89
4.2 Recommendat ions for Future W o r k 91
BIBLIOGRAPHY 93
APPENDIX A 98
IV
L I S T O F T A B L E S
Table 1 . 1 - Standardized Test Vol tages for Rated Vol tages 4
Table 1.2 - Causes for Transformer Failures 7
Table 1.3 - Fai lures for Larger Transformers w i t h On- load Tap Changers 8
Table 1.4 - Transformer Component Fai lures 9
Table 1 . 5 - Number s and A m o u n t s o f Losses due to Transformer Fa i lu re 10
v
LIST OF FIGURES
Figure 1.1 - A P o w e r Transformer 1
Figure 1.2 - C o r e T y p e Transformer 2
Figure 1.3 - She l l T y p e Transformer 3
Figure 1.4 - Dis to r t ion o f a Transformer W i n d i n g 12
Figure 2.1 - 1 6 7 k V A Sing le Phase Dis t r ibu t ion Transformer 27
Figure 2.2 - The Transformer C i r c u i t by Phys i ca l Parameters 28
Figure 2.3 - Frequency Response for the P h y s i c a l Transformer M o d e l w i t h 8 Sections 31
Figure 2.4 - Decoup led C i r c u i t I by H i g h Frequency Transformer M o d e l 33
Figure 2.5 - Decoup led C i r cu i t II b y H i g h Frequency Transformer M o d e l 33
Figure 2.6 - Symmet r i ca l C i r c u i t b y H i g h Frequency Transformer M o d e l 34
Figure 2.7 - S imula t ion Resul t for the H i g h Frequency Transformer M o d e l 35
Figure 2.8 - Equiva len t % M o d e l by N o d a l A n a l y s i s 36
Figure 2.9 - S imu la t i on Resul ts for Equivalent % M o d e l U s i n g N o d a l A n a l y s i s 38
Figure 3.1 - A Transmiss ion L i n e 42
Figure 3.2 - Equiva len t Frequency-dependent L i n e M o d e l 44
Figure 3.3 - Connec t ion o f the W i n d i n g under Investigation 45
Figure 3.4 - W i n d i n g M o d e l 46
Figure 3.5 - Faul ted W i n d i n g M o d e l 48
Figure 3.6 - Exper iment Set-up 51
Figure 3.7 - The l O k V A Transformer in the Un ive r s i t y L a b 52
Figure 3.8 - Z c wi th Different External Insulating Distances 57
Figure 3.9 - Z c Obta ined from Different Exper iment Loca t ions 59
F igure 3 . 1 0 - O r i g i n a l T i m e D o m a i n Measurements i n a U t i l i t y Research L a b 61
Figure 3.11 - M o d i f i e d T i m e D o m a i n Measurements i n a U t i l i t y Research L a b 62
Figure 3.12 - S imu la t i on Results o f Z c i n a U t i l i t y Research L a b 64
Figure 3.13 - S imula t ion Resul ts o f T rave l l i ng T i m e and Equiva len t Leng th
in a U t i l i t y Research L a b 65
Figure 3.14 - O v e r a l l V i e w o f the Transformer under Test 67
Figure 3.15 - Cross-sect ion V i e w o f the Transformer under Test 67
VI
Figure 3.16 - Cross-sec t ion V i e w o f the Transformer 69
Figure 3.17 - I l lustrat ion o f the S k i n Dep th o f a Conduc t ing M a t e r i a l 71
Figure 3.18 - Z c for Different Inner Separation by T L D M e t h o d w i t h M o d e l II 73
Figure 3.19 - Z c for Different Inner Separation by T L D M e t h o d w i t h M o d e l I 74
Figure 3.20 - Shortest Dis tance among Z c 5 , Z c 7 and Z c 8 75
Figure 3.21 - Shortest Dis tance Percentage C o m p a r i s o n W h e n b is S m a l l 76
Figure 3.22 - Z c for B i g g e r Inner Separation by T L D M e t h o d 77
Figure 3.23 - Shortest Dis tance among Z c l , Z c 2 and Z c 4 77
Figure 3.24 - Shortest Dis tance Percentage C o m p a r i s o n W h e n b is Large 78
Figure 3.25 - Z c for Different Outer Separation by T L D M e t h o d 78
Figure 3.26 - Shortest Dis tance among Z c 8 , Z c 9 and Z c l O 79
Figure 3.27 - Shortest Dis tance Percentage Compar i son among Z c 9 , Z c 8 and Z c l O 79
Figure 3.28 - Z c C o m p a r i s o n for A x i a l W i n d i n g M o v e m e n t 80
Figure 3.29 - Shortest Dis tance & Distance Percentage C o m p a r i s o n
for A x i a l W i n d i n g M o v m e n t 81
Figure 3.30 - Z c C o m p a r i s o n for Faul t Situations 83
Vll
LIST OF ABBREVIATIONS
BILs - basic insulation levels
D G A - dissolved gas analysis
L R M - leakage reactance measurement
LVI - low voltage impulse
F R A - frequency response analysis
FRA(S) - swept frequency response analysis
FRA(I) - impulse frequency response analysis
HIFRA - high-frequency internal frequency response analysis
T L D - transmission line diagnostics
EMI - electromagnetic interference
OWA - objective winding asymmetry
SDE - spectral density estimate
vni
A C K N O W L E D G E M E N T S
M y deepest and sincere gratitude goes to m y supervisors, D r . Sr ivastava and D r .
M a r t i , for g i v i n g me the chance for further studies i n the f ie ld o f power engineering and
explore the cha l lenging w o r l d o f research. Par t icular ly for their persistent inspirat ion,
valuable guidance, tremendous support (academical ly and f inancia l ly) and angelic patience.
Thei r inexhaustible pursuit, enthusiasm and h igh demand o f excel lence towards research
made a very profound impress ion and set up a mode l for me to fo l low. N o t o n l y be ing
excellent supervisors, they are also as understanding and considerate as m y o w n father.
Wi thout them, I w o u l d not be here today and they w i l l p robably never real ize h o w much I
learned from them, in both the academic w o r l d and the real w o r l d . It is rea l ly a pleasure to
have them as m y supervisors.
A special thanks goes to D r . M a y W a n g and M r . John Vandermaar , from Powertech
Labs Inc., for their k i n d assistance and support. T h e y generously donated their t ime and
knowledge for useful d iscuss ion at every single meeting. Espec ia l ly , D r . M a y W a n g who
found time in her extremely busy schedule to assist in per forming experiments at their lab
and preparing data files.
M a n y thanks go to a l l m y friends and fe l low students w i t h w h o m I cou ld talk to,
learn from and explore together. Espec i a l ly T o m D e R y b e l , who was o f enormous help
during m y experiments. A l s o a thank y o u for A l a n X u , Kenne th W i c k , K h o s r o K a b i r i ,
W e i d o n g X i a o , V i c k S u n and Y u L u o who helped me and encouraged me when I needed it
the most. The i r friendship and support is one o f m y greatest assets!
Last but not the least, I am very grateful to m y parents and m y sister, who are
always there to give me their love, understanding and support. T h e y are the source o f a l l
m y strength and hope, and I k n o w they are there to see al l m y dreams come true.
IX
CHAPTER 1 Overview
1.1 Introduction to Power Transformers
In an A C power system, power transformers are used to convert electric power
from one potential l eve l to another. A power transformer comprises o f two or more
windings that are coup led through a c o m m o n magnetic core. A t ime-va ry ing flux
created by one w i n d i n g induces voltages i n a l l o f the other w ind ings . A n example o f a
power transformer is s h o w n i n F igure 1.1.
Figure 1.1 A Power Transformer
The ma in components o f a transformer include: a laminated i ron core, two or
more windings , an insula t ion med ium, a tank, bushings and accessories. Transformers
can be categorized into different types according to different cri teria. Depend ing on the
insulat ion m e d i u m , transformers can be categorized as: d ry type transformers and f lu id-
filled transformers. I f the core and coi ls are i n a gaseous or d ry c o m p o u n d insula t ion, the
1
transformer is ca l led dry-type transformer; w h i l e f lu id- f i l l ed transformers have the core
and coi ls impregnated w i t h an insulat ing f lu id and immersed i n the same insulat ing
medium. Depend ing on the construction o f the core, transformers can be categorized as
core-type or shell-type transformers. In core-type transformers, s h o w n i n F igure 1.2 [1],
the windings are wrapped around two sides o f a s imple rectangular w i n d o w i ron core;
wh i l e i n shell-type transformers, shown i n F igure 1.3 [1], the wind ings are on ly wrapped
around the center leg o f a three-legged i ron core.
A n i ron core is used because o f its h igh relative permeabi l i ty . A s a result o f its
higher relative permeabi l i ty , a smaller magnet iz ing current is required as compared to a
non-ferromagnetic core. Furthermore, the i ron core is usual ly laminated i n order to
m i n i m i z e eddy current losses, w h i c h are generated i n the core b y the t ime va ry ing
magnetic f lux.
wvAv.electron ics2O0O.com C O R E T Y P E transformer.
Figure 1.2 Core Type Transformer
2
w v/w.e lee Iron ic s20 O0*c o m
W I N D I N G S
COKE materia I mack? up of thin laminate iron sheets, each sheel is coated with an insulating varnish and the entire core is then pressed together.
Figure 1.3 Shell Type Transformer
The insulat ion must be capable o f withstanding voltages greatly exceeding the
rated w i n d i n g voltages. Vol tages m u c h larger than the rated values can appear across the
windings o f the transformer dur ing network transients, such as swi tch ing operations,
l ightning strikes, short c i rcui t faults, and fluctuations i n the load. Table 1.1 shows the
insulat ion levels for different voltage ratings, w h i c h are defined as the values o f the
required test voltages [2]. B I L , that is basic insulat ion levels , are g iven i n the c o l u m n 3
and co lumn 7 for Europe and N o r t h A m e r i c a respectively.
3
Table 1.1 Standardized Test Voltages for Rated Voltages
Coordination of IEC Publication 71, 1972 Insulation European practice and other countries U.S.A. and Canada
Rated Test Lightning Impulse Switching surge Rated Test
Lightning Impulse
voltage voltage 50 Hz,
voltage voltage 250/2500
voltage voltage 60Hz,
voltage
Vm 1min 1.2/50 usee Msec 1min 1.2/50 usee KV in KV in KV in KV in RMS R M S KV in peak KV in peak R M S R M S KV in peak 3.6 10 40 4.76 19 60 7.2 20 60 8.25 26 75 12 28 75 15 36 95 17.5 38 95 15.5 50 110 24 50 125 25.8 60 125 36 70 170 38 80 150 100 185 450 100 185 450 145 275 650 145 275 650 175 325 750 175 325 750 245 460 1050 245 460 1050 300 380 1050 850 362 450 1175 950 420 520 1425 1050 525 620 1550 1175 765 830 2100 1425 Note: 1 .Vm is the maximum service voltage of the network between phases.
2.Test voltage is the voltage to earth.
The wind ings are usual ly made o f copper or a l u m i n i u m . The w i n d i n g conductors
may be either wires or sheets. Successive layers are insulated b y sheets o f insulat ion.
Ceramic bushings are used to isolate the windings from grounded structures o f the
transformer such as the o i l tank. Transformers w i t h increas ingly larger voltages require
increasingly longer bushings to prevent an external flashover. M i n e r a l o i l is t yp ica l ly
used as insulat ion m e d i u m . It is also used to coo l the transformer.
Transformers are one o f the most essential elements o f an electric power system.
They are w i d e l y used i n electric networks because the generation, t ransmission, and
distr ibution o f power require different voltage levels. F o r example, i n a large power
uti l i ty, the number o f transformers can exceed 1000. T h e y l ink electric loads to power
supplies through an interconnected power network and satisfy the requirements o f both
parts. The use o f transformers helps to reduce losses i n an A C power system.
Transformers are one o f the most expensive pieces o f equipment i n a power gr id .
A large power transformer i n a 5 0 0 k V system m a y cost up to a m i l l i o n dollars. In 1996,
the total sale o f power transformers i n the Un i t ed States was over U S $ 11 m i l l i o n . In
terms o f numbers, more than 8000 transformers, o f at least 2 M V A and up to more than
100 M V A , were sold i n the same year a l l over the w o r l d [3].
Since transformers p lay a v i ta l role i n the operation o f A C or H V D C electric
networks, it is important to ensure that they are operating eff icient ly and re l iably .
1.2 Transformer Failures
Inevitably in service transformer failures occur. Genera l ly , the failures can be
d iv ided into two categories: internal failures and external failures. Internal faults are
faults that happen inside the tank, such as short circui t between wind ings , short circuit
between turns, insula t ion deterioration, loss o f w i n d i n g c l amping , part ial discharges and
w i n d i n g resonance. Exte rna l faults are related to bushing, leads and accessories that are *
5
outside the tank, and m a y be caused b y system swi tch ing operations, l igh tn ing strikes and
short circuits . The internal faults can be further d iv ided into two m a i n categories:
thermal faults and electric faults. The rma l faults cause the transformers to overheat.
A c c o r d i n g to the severity o f the faults, thermal faults are often categorized as slight
overheating ( lower than 1 5 0 ° C ) , l o w temperature overheating ( 1 5 0 - 3 0 0 ° C ) , m e d i u m
temperature overheating ( 3 0 0 - 7 0 0 C 0 ) , and h igh temperature overheating (higher than
7 0 0 ° C ) . E lec t r ic faults lead to the degradation o f the insulat ion under h igh electric f ield.
A c c o r d i n g to the degree o f discharge intensity, electric faults are further d iv ided into
partial discharge, spark discharge and arc discharge.
There are many different ways to categorize transformer failures. The above
categorization is one way . Fai lures can also be split according to "c i rcu i t ry" , structure o f
ma in body, and fault locat ion. B y circui t ry , failures can be d i v i d e d into electric faults,
magnetic faults, and o i l path faults; by structure o f the m a i n body o f the transformers,
failures can be d iv ided into w i n d i n g faults, core faults, o i l faults, and accessory faults; by
fault location, failures can be d iv ided into insulat ion faults, core faults and tap-changer
faults, etc. A l l o f the above failures can either reflect thermal failures, electric failures or
both. Thus, transformer failures m a y be caused by a mult i tude o f reasons.
A survey over the last several decades on thousands o f transformer failures
conducted b y Har t ford Steam B o i l e r l isted several reasons o f transformer failures as
shown in Table 1.2 [4].
6
Table 1.2
Causes for Transformer Failures
1975 1983 1998
Related to
winding
movement
Lightning Surges 32 .3% 30 .2% 12.4% *
Line Surges/External Short Circuit 13.6% 18.6% 2 1 . 5 % *
Poor Workmanship-Manufacturer 10.6% 7.2% 2 .9% *
Deterioration of Insulation 10.4% 8.7% 1 3 %
Overloading 7.7% 3.2% 2 .4%
Moisture 7.2% 6.9% 6 .3%
Inadequate Maintenance 6.6% 13 .1% 11 .3% *
Sabotage, Malicious Mischief 2.6% 1.7% 0
Loose Connections 2 . 1 % 2 .0% 6% *
All others 6.9% 8.4% 2 4 . 2 %
A s can be seen i n Table 1.2, l ightning surges, swi tch ing surges, deterioration o f
insulation and inadequate maintenance are the m a i n reasons o f transformer failures.
A n international survey [5] conducted by the C I G R E W o r k i n g Group on failures
in large power transformer i n service shows the percentage o f failures related to the
structural components o f the transformers, as g iven i n Table 1.3.
7
Table 1.3
Failures for Large Power Transformers with On-load Tap Changers
Location Percentage
On-load tap changers 4 1 %
Windings 19%
T a n k / F l u i d 14%
Accessor ies 12%
Termina l 10%
C o r e 4 %
Tota l 100%
Table 1.3 shows that on- load tap changers, wind ings , and tank/f lu id are the m a i n
parts that cause failures i n large power transformers.
A n article [6] i n E lec t r i c i ty Today tabulates transformer failures b y their
components as g iven in Table 1.4.
Table 1.4 c lear ly shows that components o f insula t ion system contribute the most
significant por t ion o f transformer failures. In particular, the failure o f the insula t ion
protecting the wind ings contributes more than 7 1 % o f total failures.
8
Table 1.4 Transformer Component Failures
Transformer Component Failures
High Voltage Windings* 48%
Low Voltage Windings* 23%
Bushings* 2%
Leads 6%
Tap Changers 0%
Gaskets 2%
Other 19%
Total 100%
* Components o f Insulation System
A survey o f records o f modern power transformer b reakdown that occurred over a
period o f years concludes that between 70 and 8 0 % o f the failures are f ina l ly traced back
to short-circuits between w i n d i n g turns [7].
C h e m i c a l reactions such as pyrolys is , oxida t ion and hydro lys i s age the insulat ion
material. The moisture content, presence o f oxygen, and temperature levels affect the
speed o f these chemica l reactions.
The surveys presented here are typ ica l o f results obtained f rom other publ ished
surveys. F r o m these results, one can see that failures o f transformers are i n a large part
due to problems w i t h their wind ings . Furthermore, w i n d i n g faults occur w h e n the
insulation around the w i n d i n g is compromised . In general, the insula t ion o f the w i n d i n g
is compromised either b y ageing or b y mechanical forces act ing upon it or both.
9
The failure o f a transformer can be potential ly devastating to the personnel safety
and to the environment. Transformers m a y fai l exp los ive ly causing great personal
injuries to people around them and damage to the surrounding equipment. The
environment can be adversely affected by the leakage o f o i l . A failure also has a large
economic impact due to its h igh cost o f replacement and repair and lost revenue wh i l e it
is out o f service. D u r i n g its outage, the customers o f a u t i l i ty can be greatly
inconvenienced, w h i c h c o u l d result i n a loss o f g o o d w i l l towards the ut i l i ty , especial ly i n
a deregulated power market. Table 1.5 illustrates the economic impact o f transformer
failures. Th i s table o r ig ina l ly appeared in a w o r k i n g group report to the 2 9 t h Conference
o f the International M a c h i n e r y Insurer's Assoc ia t ion [8]. The report is based on 75 cases
o f failures o f large o i l - c o o l e d transformers rated at 1 0 0 M V A and above f rom 1989 to
1996. A s can be seen i n the table, the average loss per case is i n excess o f U S $ 1.5
m i l l i o n .
Table 1.5
Numbers and Amounts of Losses due to Transformer Failure
I Year
. Total Number . . . . . »MVA I Amount (US $) millions i
Average per case $ millions
Average per case MVA
(a) 1(b) 1 12T360 I 1989 J5_ _ IQ _ 12T360 I 2 472 5
1990 j8 6 2205 12.797 1.600 368 1991 I 14 10 | 2828 "26.359 I 1.883 283 1994 T O T A L S j f ^ " ~ _ _ _
11 4482 37.70_6_ [152.650
2.900 407 1994 T O T A L S j f ^ " ~ _ _ _ [59 22048
37.70_6_ [152.650 2.035 3
N O T E : (a) total number of cases for which loss amounts are known.
(b) total number of cases for which M V A capacity is known, in addition to loss amount
10
1.3 Causes of Winding Movement
A short c i rcui t fault, for example, created b y l ightn ing strike or ground fault, is
the most l i k e l y factor to cause the w i n d i n g movement. A s s u m i n g a copper w i n d i n g is
wound on a ferromagnetic core and the transformer is i n service, the currents carried by
the windings w i l l produce the predominant flux i n the axia l direct ion. The interaction o f
the current in the co i l s i n the circumferential d i rect ion and the ax ia l f lux f ield w i l l
therefore produce a radial outward electro-magnetic force. There is , however , a leakage
flux around ind iv idua l turns and near the ends o f the wind ings w h i c h has a component i n
the radial direct ion. T h i s radia l f lux induces an ax ia l i nward electro-magnetic force.
Under normal operation o f power transformer, the wind ings are designed to withstand the
mechanical pressure described above. However , when short circui ts happen, the electro
magnetic forces induced in the windings are increased dramat ica l ly and threaten the
insulation layers severely. F o r example, i f a transformer's leakage impedance is 10%, its
short circuit current w i l l be 10 times the rated current and the mechanica l stress w i l l be
roughly 100 times o f the normal stress under the rated load current.
Short c i rcui t force studies have special meanings for autotransformers.
Autotransformers are n o r m a l l y used for coup l ing t ransmission systems where both input
and output sides are at h igh voltage, such as 2 3 0 / 5 0 0 K V or 5 0 0 / 7 6 5 K V . T h e y usual ly
have very l o w impedance, about 5% to 8%. F o r a leakage impedance o f 5% the
mechanical stresses dur ing a short circui t w i l l be i n the order o f 400 times the normal . T o
withstand the h igh pressure from both h igh voltage level and large short c i rcui t force,
11
these autotransformers have to be designed and manufactured to be m u c h stronger than i n
a normal two w i n d i n g transformers.
A s discussed above, w h e n a short circuit happens, the w i n d i n g w i l l stretch out in
the radial d i rec t ion and compress i n the axia l direction. T h e radial forces i n a 1 0 M V A
transformer can exceed 100,0001bs [9]. Such huge electro-magnetic forces w i l l inevi tably
loosen the w i n d i n g c l amp structure, w h i c h is the ma in mechanica l support o f the w i n d i n g
and cause the distort ion or movement o f the wind ing . A twisted transformer w i n d i n g is
shown in Figure 1.4 [10].
Inrush currents, due to the power ing up o f the transformer c i rcu i t and v ibra t ion
force increase the electro-magnetic forces i n the same w a y as short c i rcui ts . The frequent
fluctuation i n generation or load w i l l also put burdens to the electr ical and mechanica l
Figure 1.4 Distortion of a Transformer W i n d i n g
12
strength o f the wind ings , accelerate the loosening o f the w i n d i n g c lamps, and eventually
cause the w i n d i n g to m o v e or even break down.
The m a i n reason o f w i n d i n g movement is the loosening o f the c lamps ho ld ing the
windings . The c lamps can be loosened by the vibra t ion forces, external forces, l ike short-
circuits forces discussed above, or b y the compress ion and deterioration o f the so l id
insulation.
In service, the inter-turn insulat ion, usual ly an o i l impregnated insula t ing tape,
undergoes changes. O v e r a per iod i n service the taped insula t ion loses its elasticity.
Moreover , under short-circuit forces the taped insulat ion m a y be permanent ly
compressed or damaged. These mechanical changes i n the taped w i n d i n g insula t ion m a y
signif icant ly contribute to w i n d i n g looseness. Overvol tages caused b y system transients,
mechanical deterioration due to the short circuits fault, v ibra t ion or inrush current, the
rise o f temperature inside the w i n d i n g and o i l , and the penetration o f the moisture in the
paper insulat ion w i l l lead to the reduction o f the dielectric strength o f the ce l lu lose paper.
W i n d i n g movement m a y rupture the insulat ion paper and the rupture o f the insula t ion can
further deform the w i n d i n g .
Overheat ing caused b y sustained heavy overloads or faulty c o o l i n g system, is
another contr ibut ing factor to the w i n d i n g movement. The temperature for the normal
ageing o f a power transformer is 9 8 ° C . E v e r y rise or drop o f 6 ° C either doubles or halves
the electrical ageing [11]. Exceed ing the w i n d i n g hot-spot temperature l i m i t w i l l
13
accelerate the ageing process o f the w i n d i n g and therefore shorten the transformer's
service life dramat ical ly . In addit ion, temperatures higher than the design affect the
c lamping forces. A transformer fault detection study [12] in Swi tze r land shows that
c lamping forces vary up to 10% w i t h the temperature variations.
Structural defects due to poor quali ty control dur ing manufacture m a y trigger
w i n d i n g failure i n m a n y ways . A w i n d i n g bulge or sharp edge o f the c o i l m a y cut through
the insulation and cause short circui t between turns; deformed or disconnected leads, and
bad connection m a y decrease the tightness o f the w i n d i n g and bad ly made joints may
come apart and produce an open-circuit w i n d i n g [2].
The huge impact o f transformer failures on security o f power systems motivates
the development o f mon i to r ing systems and testing strategies. S ince a large number o f
failures are due to the wind ings , an efficient on-l ine diagnostic technique for detecting
w i n d i n g movement is a necessity. The work presented i n this thesis addresses this need.
1.4 Currently Available Winding Diagnostic Tools
A n efficient on- l ine technique for moni tor ing transformer w i n d i n g movement is
o f considerable interest due to the large number o f aging transformers and the economic
considerations under the deregulated electric power markets. Cur ren t ly developed
diagnostic techniques are discussed be low.
14
Transformer w i n d i n g movement detection can be done b y an internal v i sua l
inspection. It requires dra in ing the o i l i n the transformer, to per form a direct inspection
o f windings and c lamps, and to observe any signs o f looseness. Conven t iona l ly , such
inspections are conducted on a time-based regular maintenance schedule; therefore, it
may result in long-t ime transformer outage and consequent h igh costs. Sometimes, an
increase o f the audible noise can also indicate w i n d i n g looseness. N o w a d a y s , condi t ion-
based maintenance is b e c o m i n g the new trend and w i l l eventual ly replace the time-based
maintenance.
Short-circui t impedance measurement is another technique to detect w i n d i n g
movement. One s i m p l y shorts the l o w voltage w i n d i n g terminals and measures the input
voltage, current and power. The result is then compared w i t h the impedance before the
transformer experienced a system short circuit . A c c o r d i n g to the I E C 60076-5, 2 %
deviat ion o f the test results is the m a x i m u m value w h i c h can be accepted. The drawback
o f this technique is that it is an off-l ine diagnosis and usual ly done i n a laboratory. In
addition, it is on ly effective for a significant movement or dis tor t ion or looseness o f the
transformer windings .
D i s s o l v e d Gas A n a l y s i s ( D G A ) distinguishes the different types o f insulat ion
faults depending on the compos i t ion o f gases liberated b y so l id insulat ion or o i l
breakdown. It can indirect ly detect the w i n d i n g displacement when this movement
results in partial discharges. F o r example, when a partial discharge occurs, the most
abundant gas among a l l the other d isso lved gases is hydrogen. H o w e v e r , the method
15
cannot locate where the displacement happened and h o w severe the displacement is.
A l s o , in most cases the in i t i a l w i n d i n g displacement does not result i n partial discharges
and may go undetected b y D G A .
A w i n d i n g ratio test measures the numbers o f turns o f both p r imary and secondary
windings and calculates the ratio between them. B y compar ing the measured w i n d i n g
ratio w i t h the ratio o f rated p r imary and secondary voltages as shown on the nameplate o f
the transformer, shorted turns or open w i n d i n g faults m a y be detected. H o w e v e r , an
outage and isola t ion o f the transformer is required for the purpose o f measurements.
A w i n d i n g resistance test is s imi lar to the w i n d i n g ratio test except that it
measures the w i n d i n g resistance rather than the number o f w i n d i n g turns. A d d i t i o n a l l y , a
very precise ohmmeter is needed, w h i c h w i l l assure the accuracy o f a fraction o f an ohm.
The measured resistance w i l l be compared w i t h the previous measurement referred to the
same temperature. Measurements are conducted for different phases and different tap-
changer posi t ions. Th i s method detects the condi t ion o f the w i n d i n g conductor directly.
However , it requires a transformer outage and is usual ly performed i n the factory or a
laboratory.
Leakage reactance measurement ( L R M ) can be achieved w i t h the same test set-up
as the short c i rcui t impedance measurement. L R M is based on the increased leakage
reactance, result ing f rom the radial outward force on the outer w i n d i n g and the radial
inward force on the inner w i n d i n g induced b y short circuits . The m a i n advantage o f L R M
16
method is that it is sensitive to w i n d i n g distort ion and insensit ive to temperature or
presence o f contaminat ion. Howeve r , it is not on ly an off- l ine and in-laboratory method,
but also insufficient for frequencies more than 200 K H z [12], when compared w i t h the
F R A method, w h i c h w i l l be discussed in the later part o f this section. Furthermore, the
deviat ion o f measurement obtained from L R M is hardly found for some type o f phys ica l
w i n d i n g displacement [13] for example, when the outward w i n d i n g is s i m p l y bent inward
to the core without any ax ia l displacement, even when the distort ion o f the w i n d i n g is
severe.
W i n d i n g dis tor t ion can eventually develop into transformer failures, w h i c h can be
catastrophic. A g i n g o f the insulat ion has cumulat ive effects on transformer w i n d i n g
distortion. A n effective on-l ine condi t ion moni tor ing for transformer w ind ings is
required to provide instant detection o f the w i n d i n g integrity. Cur ren t ly several on-l ine
moni tor ing and diagnostic techniques are used for moni to r ing the wind ings
V i b r a t i o n test is an on-l ine moni tor ing technique. It moni tors the v ibra t ion
signals recorded on the tank w a l l by acoustic sensors and indicates the devia t ion or
change o f the internal w i n d i n g posi t ion. Since the acoustic sensors are usual ly mounted
on the tank w a l l , v ibra t ion testing doesn't require transformer outage. H o w e v e r , it is on ly
effective for detecting large w i n d i n g movement and can o n l y be used as reference
information [14]. F o r an external ly installed vibra t ion sensor, it is even harder to
dist inguish whether the disturbance is caused by the w i n d i n g distort ion or by the
surrounding environment.
17
L o w voltage impulse ( L V I ) method is a w e l l k n o w n technique for w i n d i n g
movement detection, w h i c h was proposed b y W . L e c h and L . T y m i n s k y i n Po land in
1960 and first publ i shed i n 1966 [15]. L V I technique was o r ig ina l l y used off-l ine and
later developed into on- l ine moni tor ing . It applies a few mic rosecond duration low
voltage impulse to one w i n d i n g and records the voltage or current response i n the other
w i n d i n g or wind ings . Recorded response currents or voltages are compared dur ing some
time interval. H o w e v e r , the response waveform is heav i ly r e ly ing on the input waveform.
It adds more d i f f icul ty to determine whether the changed response is due to the deviat ion
o f the input wavefo rm or the displacement o f the transformer w i n d i n g .
W i t h the acquis i t ion o f modern digi tal signal processing techniques, L V I method
has been developed into a c o m m o n l y used technique, ca l led Frequency Response
Ana lys i s ( F R A ) technique. There are two types o f F R A methods: F R A (I) and F R A (S).
In F R A (I), L V I measurements are first ly taken and then converted into frequency
domain by us ing Four ie r transform, fast Four ie r transform, short-time Four ie r transform
or wavelet transform. B y d i v i d i n g the response current by the input voltage, one can
obtain the transfer function o f the transformer, w h i c h is actually the transformer's
transadmittance in frequency domain . Some researchers prefer transimpedance, i.e. the
quotient between the input voltage and output current, and others prefer transadmittance.
In both cases, the transfer function is freed from the input waveform, and it is a unique
"signature" o f the parameters o f the internal windings . W i n d i n g movements result i n the
change o f the R L C parameters o f the w i n d i n g , such as inter-turn capacitance, ground
capacitance and series inductance. Hence , b y compar ing the changed "signature" w i t h the
18
"signature" obtained from the new transformer or f rom the previous measurements, one
can detect the deformation o f the w i n d i n g . T h e drawback o f this technique is that the
m a x i m u m frequency that can be used is usual ly no more than 4 M H z . In addit ion, the
experimental set up w i l l have a b i g impact on the test results, for example , the cables
layout, the leads connect ion and the choice o f external circuit . The impedance o f the
external measuring circui t w i l l vary w i t h the frequency, so str ict ly speaking there is no
way to avoid the devia t ion o f the external impedance for F R A methods.
F R A technique can be applied to both off-l ine and on- l ine moni to r ing o f
transformer w i n d i n g movement , for example, on-site measurements on a 2 0 0 M V A 3-
phase power transformer i n service in Germany [16]. B o t h moni to r ing systems consist o f
voltage sensors and current sensors w h i c h are mounted at the transformer, and a transient
digi tal recorder w i t h a resolut ion o f 10 bits and a sampl ing frequency o f 1 0 M H z . Off- l ine
transient moni to r ing is rea l ized by swi tch ing operation o f a SFe circui t breaker on the
high-voltage side o f the transformer w h i l e the low-vol tage side is usual ly disconnected
from the power network. O n the other hand, on-l ine condi t ion mon i to r ing is real ized by
the dominant exci ta t ion transients that occur at on ly one phase. The transfer function
(transadmittance) used here is the quotient between the spectra o f the neutral current and
the spectra o f the terminal voltage. B o t h off-l ine and on-l ine moni to r ing measurements
were taken dur ing an 11 -month period, and thus prove its feasibil i ty.
Theore t ica l ly , the frequency response obtained from the above off- l ine and on
line measurements should not be identical to each other, but the resonance frequencies for
19
both cases are the same up to 780 K H z . Therefore, a new resonance frequency can
indicate the movement o f the w ind ing . Howeve r , this method requires a large amount o f
information about the dominant excitat ion modes accumulated over a l ong per iod o f t ime
and is on ly v a l i d for up to 1 M H z .
F R A (S) is also ca l led S F R A , namely Swept Frequency Response A n a l y s i s . F R A
(S) technique was first proposed by D i c k and E r v e n i n 1978 [17]. In this method, a signal
from a network analyzer is applied and the swept frequency s ignal is generated by
injecting a s inusoidal s ignal at a frequency, one at a t ime. S F R A technique maintains the
constant energy level for each frequency. The analyzer used i n S F R A provides better
resolution due to the ab i l i ty o f autoscale. Compared w i t h F R A (I) method, S F R A has
better signal to noise ratio and wider frequency range. H o w e v e r it needs longer
measurement t ime and is usual ly very expensive.
F r o m the above discussion, we can see that currently used mon i to r ing techniques
are inadequate, especia l ly for h igh frequencies. Howeve r , F R A technique is s t i l l the most
effective method used avai lable for w i n d i n g movement detection. T o further improve the
off-line and on- l ine moni to r ing o f transformer w i n d i n g movement , a new h igh frequency
transformer mode l and data condi t ion ing technique are needed and are explored i n this
thesis.
20
1.5 Thesis Overview
This chapter introduced the general structure o f transformer and its failure modes.
In particular, failures due to the windings are h ighl ighted due to their h i g h frequency o f
occurrence. Af te r r e v i e w i n g the currently developed moni to r ing techniques and their
l imitations, it is apparent that a new on-l ine condi t ion moni to r ing diagnostic technique is
needed.
Chapter 2 discusses the p re l iminary work for high-frequency transformer
model l ing . F i r s t ly , it describes the his tor ical background and then it lists the three
transformer models appl ied i n this thesis w o r k and their results. T h e analysis o f these
models leads to a better and newer h igh frequency transformer m o d e l w h i c h w i l l open up
new avenues in the f ie ld o f transformer mode l l i ng i n the next chapter.
The proposed t ransmission l ine diagnostics ( T L D ) technique for transformer
w i n d i n g detection is analyzed i n Chapter 3. T L D is based on the t rave l l ing wave theory
and the frequency dependent t ransmission l ine mode l . U n l i k e the F R A method, the
characteristic impedance Z c is the chosen signature o f the transformer wind ings . The new
developed wave propagat ion h igh frequency transformer mode l is discussed under both a
no-fault case and a fault case. A l g o r i t h m s for Z c and fault locat ion have been derived.
Laboratory experiments have been performed i n the univers i ty labs and the ut i l i ty
research lab respectively. S imula t ion results based on the a lgor i thm for different
transformers have ver i f ied the new technique. T w o papers w h i c h c l a imed that no
21
historical data is needed i n w i n d i n g movement detection are discussed i n this chapter as
w e l l .
Chapter 4 gives the general conc lus ion o f this thesis and recommendat ions for
future work.
22
CHAPTER 2 Transformer Models
2.1 Modelling Background
Since the invent ion o f power transformer in 1885, people have developed
different transformer models for different purposes. Transformer models speci f ica l ly used
for the w i n d i n g movement detection are discussed here.
A mode l based on mult i -conductor transmission l ine theory uses a single w i n d i n g
turn as a c i rcui t element, w i t h the capacitance, inductance, and losses calculated as
distributed parameters, are bui l t up to simulate transformer w ind ings [18]. In the above
model , transfer functions (i.e. frequency response) that describe h o w the locat ion o f a
fault, such as a P D source, affects the current signals measured at the terminals o f the
wind ing , were calculated. The mode l shows how the pos i t ion o f the zeros i n the
frequency response o f the measured current signals can be used to locate the w i n d i n g
distortion. Howeve r , it needs (n+l )*(n+l ) Y matr ix for n conductors or layers or
pancakes, w h i c h is a huge amount o f calculat ion for a normal power transformer.
Ano the r mode l based on F R A is developed into condi t ion moni to r ing technique
for transformers i n service [19]. In this mode l , the appl ied voltage is measured on the
high voltage w i n d i n g us ing the H V bushing as a voltage divider . A custom designed
"secondary" is installed on the capacitance tap to obtain a suitable s ignal , w h i l e the
current is recorded on the other w ind ing . B y Four ier transformer, the transadmittance
- 2 3 -
obtained gives the characteristic o f the on-l ine transformer wind ings , but the usable
frequency is about 0.8 M H z in the f ield and up to 3 M H z i n a laboratory.
B y evaluating the leakage factors i n a transformer w i n d i n g , a m o d e l for internal
w ind ing faults study is presented [20-21]. The leakage factor between c o i l 1 and c o i l 2 is
defined as a i 2 = l - M 1 22 / ( L i L 2 ) i n the above papers, where L] and L 2 are the se l f inductance,
and M i 2 is the mutual inductance. B C T R A N is used i n the method. It is an auxi l ia ry
routine o f E M T P and is used to produce an input file readable b y E M T P . A matrix o f
inductance and a matr ix o f resistance o f the transformer w i n d i n g must be computed by
B C T R A N first, w h i c h indicates that a ful l knowledge o f the transformer w i n d i n g has to
be available. Based on the above R and L matrices, a new set o f R and L matrices must
be developed to a l l ow the s imula t ion o f any k i n d o f internal w i n d i n g fault, for example
faults between any w i n d i n g turns or faults between any w i n d i n g turn and the earth.
Th i s mode l is comple te ly compatible w i t h E M T P , but it adds lots o f compl ica t ion
due to the computat ion o f the new R , L matrices and the evaluat ion o f leakage factor. The
determination o f the leakage factor largely depends on the methods chosen and the
assumptions made. Based on the geometry information o f the transformer and
experimental results, a correct ing factor is usual ly added to increase the ca lcula t ion
accuracy o f the leakage factor. Different researchers m a y choose different correct ing
factors. Furthermore, the detailed transformer w i n d i n g data is not usua l ly obtained from
the manufacturer, w h i c h is the fundamental data base needed i n this mode l .
- 2 4 -
A n e w l y developed mode l H I F R A [22], high-frequency internal frequency
response analysis, uses an injected wide-band frequency s ignal through the transformer
bushing, i n combina t ion w i t h an internal sensor for F R A measurement. T h i s mode l
measures the signals inside the transformer tank b y us ing appropriate non-contact sensors
inside the transformer on the transformer w i n d i n g leads, and therefore, the transfer
function w o u l d then be calculated from the signals measured inside. T h i s method
increases the useful frequency range up to 1 0 M H z .
Wavele t analysis and neural network are applied to the w i n d i n g detection by the
researchers i n Texas A & M U n i v e r s i t y [23]. Based on the normal and faulty p r imary
signals obtained f rom E M T P , this method uses wavelet transform as a processor to the
improved B P neural network and E l m a n network to identify the internal turn-to-turn
faults in transformer w i n d i n g . Th is method is not suitable for high-frequencies because
the transformer mode l used in E M T P has lumped parameters. It also needs a b i g data
base as the baseline.
A n analysis o f internal w i n d i n g stresses i n E H V generator step-up transformer
was performed at Ontar io H y d r o [24]. In this analysis, a h i g h accuracy frequency
dependent transformer mode l is used to moni tor the terminal condi t ion o f a transformer
under transient condi t ions. A n internal voltage dis t r ibut ion map is created by the
measured transfer functions among terminals and various points o f the w i n d i n g , and is
used to evaluate the insula t ion stress and therefore detect the w i n d i n g displacement. Th is
high frequency transformer mode l takes ful l account o f frequency dependent parameter
- 2 5 -
effects, thus it is o n l y suitable for the transformer under study and the standard name
plate data from other transformers give no information to the mode l .
Transformer w i n d i n g turn-to-turn or turn-to-earth fault is mode led b y coupled
electromagnetic and structural finite elements [25]. Th i s mode l is based on the phys ica l
information o f the specific transformer and the s imula t ion is implemented by commerc ia l
software. A large amount o f previous experiment data are avai lable to compare w i t h the
present measurements and s imula t ion results. However , i n real i ty it is very hard to get the
physical layout o f a transformer; therefore detailed parameters are not available. S imi l a r
to the mode l in the previous paragraph, it doesn't have practical applicat ions to a large
number o f transformers i n service w i t h different phys ica l structures and electr ical
capacities.
D u e to the disadvantage o f the above transformer models , a new transformer
mode l for w i n d i n g movement diagnosis has to be established. F R A technique is the most
used and effective detection method i n w i n d i n g displacement so far. W i t h the increase o f
the frequency, the capacitance i n the transformer becomes more important than the
inductance. In F R A , it represents the higher resonances. W h e n compar ing w i t h a baseline
fingerprint or signature o f the transformer w i n d i n g w i t h measurements on the same
transformer i n service, admittance or transadmittance has more sensi t ivi ty for h igh
frequency than impedance or transimpedance. In m y tr ia l and error o f deve lop ing an
effective transformer mode l , the value o f transadmittance i n frequency domain is
considered as the fingerprint o f the transformer under study, w h i c h is the quotient
- 2 6 -
between the output current spectrum and input voltage spectrum o f the transformer i n this
chapter.
2.2 Physical Transformer Model Simulated as a Transmission Line
A 1 6 7 k V A single phase distr ibution transformer as shown i n figure 2.1 is used i n
the model s imula t ion for this chapter. The transformer's voltage rat ing is 1 4 4 0 0 V / 3 4 7 V ,
and the impedance is 2 % . T h e high voltage and l o w voltage w i n d i n g B I L s are 125 k V
and 3 0 k V respectively. T h e weight o f the transformer is 648 k g . T h e transformer looks
l ike a cyl inder , i n w h i c h the two wind ings are wrapped o n an i ron core. T h e l o w voltage
w i n d i n g is split into the inner section and outer section w i t h the h igh voltage w i n d i n g i n
between. The closest w i n d i n g to the core is the inner l o w voltage w i n d i n g , then the h igh
voltage w ind ing . T h e outer L V w i n d i n g is closest to the tank.
Figure 2.1 1 6 7 k V A Single Phase Distribution Transformer
- 2 7 -
The high voltage w i n d i n g is made o f copper c o i l w i t h a 4 m m diameter cross
section. The radius between the h igh voltage c o i l and the central point o f the i ron core is
about 13.24 c m . U n l i k e the h igh voltage wind ing , the l o w voltage w i n d i n g is made o f
a lumin ium sheets w i t h thickness o f 1.5 m m . F o r each section o f the l o w voltage sheets, it
has 16 layers. T h e distance between each layer is 0.5 m m . The radius o f the innermost
layer is 10.16 c m ; the distance from the outermost layer o f l o w voltage sheets to tank is
8.89 c m ; the diameter o f the tank is 50.8 c m . T h e height o f the w ind ings is 40.64 c m .
F r o m the above detailed phys ica l layout o f the transformer us ing the basic
electromagnetic field theory, the electr ical parameters R L C can be calculated and
therefore a phys ica l transformer mode l circui t is set up as shown i n F igure 2.2. A l l
resistance values are i n o h m ; the inductance values are i n mi l i -henry ; the capacitance
values are in pico-farad.
418
352
1 4AAA
1.653 52.8 ' l
0.00061 0.0038 0.00078 0.0038 12 2 o-
o-
=F2.46 5304 ±z 6751=F
1 ] m 2
Figure 2.2 The Transformer Circuit by Physical Parameters
- 2 8 -
F r o m the perspective o f electromagnetics, the transformer w i n d i n g conductors are
l ike t ransmission l ine conductors except that they are thinner and shorter. H o w e v e r , the
same length o f the t ransmiss ion l ine or transformer w i n d i n g " l o o k s " longer for h igh
frequency signal than l o w frequency signal . In this respect, the transformer w i n d i n g can
behave in a s imi la r w a y when a megahertz range signal is appl ied as an overhead
transmission l ine w i t h a s ignal i n the k i loher tz frequency range.
A real t ransmiss ion l ine has distributed parameters. In every single t iny section or
fraction o f the l ine, it includes a series resistance, a series inductance and two shunt
capacitances. These R , L and C are un i fo rmly distributed along the l ine. H o w e v e r , the
physical transformer m o d e l o f F igure 2.2 has lumped parameter characteristics. F o r
understanding the F R A response we need to simulate the distributed characteristics o f the
transmission l ine, and therefore the lumped parameter transformer m o d e l has to be evenly
split into sections. The more the number o f the sections, the more distributed the
transformer w i n d i n g m o d e l is. Theoret ica l ly , an increase i n the number o f sections
creates more L C loops, w h i c h can lead to more resonance frequencies.
Whenever the w i n d i n g has some movement, its phys ica l layout w i l l be distorted
and lead to the var ia t ion o f the R L C parameters i n the mode l . Cor responding ly , the
resonances w i l l change either i n magnitude or shift i n frequency. Consequent ly , the
waveform o f the frequency response m a y distort as w e l l . B y compar ing the resonances
and the general shape o f the wave fo rm from time to t ime, one should be able to detect
whether there is noticeable change i n the w i n d i n g geometry i n some t ime per iod.
- 2 9 -
Based on the phys i ca l transformer mode l i n F igure 2.2, the s imulat ions have been
done in M i c r o t r a n w i t h the evenly d iv ided sections o f the circuit . A n impulse voltage
source V I wi th 2.5 ns r i s ing t ime is injected into the h igh voltage terminal 11 ' ; w h i l e a
13.37 ohms load resistor is connected to the l o w voltage terminal 2 2 ' . The total
s imulat ion t ime is 80 p,s. Output current 12 and input s ignal V I are transferred into
Mat l ab script to obtain the frequency response o f the transformer, i.e. transadmittance
spectrum. The M a t l a b script is as fo l lows.
%matlab script for physical transformer model in chapter 2
load origl . txt; % load simulation results from Microtran
%plot input voltage and output current in time domain close al l ; figure subplot(3,l , l) ,plot(origl(: ,2)/ le-6,origl(: ,3)); ylabel('Input voltage in V') ;gr id; axis([19.8 20.2 50 350]);xlabel('time in us')
subplot(3,l ,2),plot(origl(: ,2)/le-6,origl(: ) 5));grid; ylabel('Output current in A');axis([19 21 -0.002 0.01]); xlabel('time in us');
%plot I(f)/V(f) in frequency domain by F F T dt=2.5e-9;%time step t=origl(:,2);%32001 time step v=fft(origl(:,3)); i=fft(ongl(:,5)); N=length(t);%801 odd number %n=N%when N is even number n=length(i)-l ;%change odd number to even number nyquist=l/2/dt; freq=( 1 :n72)/(n/2)*nyquist; freq=freq-freq(l);%frequency from zero to near nyquist frequency imag=abs(i(l:n/2)); vmag=abs(v( 1 :n/2)); b=imag./vmag;%transadmi trance subplot(3,l,3),plot(freq/le6,b),grid; xlabel(*Frequency in MHz');ylabel( 'I(f)/V(f) '); axis([0 20 -0.5e-4 3e-4]);
- 3 0 -
M o r e resonances are expected w i t h the increase i n the number o f the sections.
Simulat ions have been performed from one section to eight sections i n M i c r o t r a n and
M a t l a b , Howeve r , the results are almost the same and o n l y have two dominant resonance
frequencies as shown i n F igure 2.3.
> c 300 0
2 200 o > 1 100 c
< 10 19.8H„-3 19.85 19.9 19.95 20 20.05 20.1 20.15 20.2 x 10
t 0 •5 O
i r i r _time.
3
2
e 1 o
19„„-419.2 19.4 19.6 19.8 20 20.2 20.4 20.6 20.8 21 x 10 . . . I \
i
\ A ^ _ ;
! i i i 6 8 10 12 14 16 18 20
Frequency in MHz
Figure 2.3 Frequency Response for the Physical Transformer Model with 8 Sections
The reason o f o n l y two resonance frequencies is expla ined as fo l lows . W h e n the
transmission l ine is so long that an equivalent n c i rcui t is required instead o f the nomina l
71 circuit , the hyperbol ic correct ing functions must be appl ied to the l ine ' s parameters.
The boundary length Lb for overhead l ine and cable are calculated as the function o f
frequency appl ied as shown i n formula (2.1) and (2.2). In other w o r d , Lb is the m a x i m u m
length o f each section i n our model .
10,000 L b = for overhead l ine (2.1)
- 3 1 -
3,000 for cable (2.2)
For a t ransmiss ion l ine w i th power frequency, L b is 170 k m ; w h i l e for a cable w i t h
power frequency, Lb is about 50 k m . The transformer w i n d i n g is something i n between
the overhead l ine and cable, so i f we combine formula (2.1) and (2.2) into formula (2.3)
and the m a x i m u m frequency we are interested is around 2 0 M H z , then Lb w i l l be 0.25
meters. B y the size o f the transformer w i n d i n g , we can calculate the total length o f the
wind ing , w h i c h is around 200 meters. B y d i v i d i n g the total length w i t h L b ; we can get the
m i n i m u m number o f sections needed for this mode l , w h i c h is 800 sections i n our case.
Such a huge number o f sections makes the transformer parameters as distributed as a real
transmission l ine, but more cr i t ica l ly , it l imi ts the effectiveness o f this phys i ca l model .
Fo r h igh capacity power transformers w i t h m u c h longer wind ings , the calculat ions i n this
model are too huge to be realist ic.
Another b i g disadvantage o f this phys ica l transformer mode l is that usual ly the
detailed design parameters o f transformers are not available.
2.3 Decoupled High Frequency Transformer Model
A s impl i f i ed h igh frequency transformer mode l is used i n M i c r o t r a n to simulate
the w i n d i n g performance [26]. B y using the R L C convers ion formulae (shown i n the
5,000 for transformer w i n d i n g (2.3)
- 3 2 -
appendix) f rom the paper, the coupled-coi ls constant parameter transformer mode l i n
Figure 2.2 can be decoupled first ly as shown i n F igure 2.4.
418
8. 48
2.7 11.8
:346 -8952
0.00078 0.0038
6751
~[~Hbr~45
12 —=»•-
1 m
Figure 2.4 Decoupled Circuit I by High Frequency Transformer Model
D u e to the two sections o f the l o w voltage w i n d i n g , the above figure is s t i l l
coupled. B y s i m p l y dropping the paral lel branch w i t h 8.48 p F capacitance and the shunt
branch wi th -8952 p F capacitance, we can apply the convers ion formulae again and get
the totally decoupled h igh frequency transformer as shown in F igure 2.5.
10.1
1' j m 2 ,
Figure 2.5 Decoupled Circuit II by High Frequency Transformer Model
T o further improve the obtained circuit , an imaginary neutral plate is added to it
and al l the R L C parameters are equal ly split into two parts. The modi f i ca t ion makes the
- 3 3 -
circuit symmetr ica l , w h i c h is usual ly the case i n a real power transformer. The obtained
symmetr ical c i rcui t is shown in F igure 2.6. A decoupled and symmetr ica l c i rcui t
representation is easier to analyze and use the available software. M o r e o v e r , the results
are easy to interpret.
5. OS
12 2 —} o
1 1 2 . 0 2 9-15
? =b-5089
4= -5069 =b 2 5 . 4 5
2 5 . 4 5
5. 05
Figure 2.6 Symmetr ical C i rcu i t by H i g h Frequency Transformer M o d e l
Simula t ing the symmetr ica l c ircui t i n M i c r o t r a n and do ing Four ie r analysis i n
Mat l ab gives the results as shown i n F igure 2.7. O n l y one resonance is found. The m a i n
disadvantage o f this mode l lies in the s t i l l lumped parameters in M i c r o t r a n transformer
data card. A l s o , w i th the increase o f frequency, the capacitance and sk in effect w i l l have
b ig effects i n the performance o f the circuit . The parameters used here are not frequency
dependent parameters.
The dropping o f one paral le l capacitance branch and one shunt capacitance done
in the second decoupl ing convers ion is another b i g factor that invalidates this h igh
frequency mode l . F o r different values o f h igh frequencies, these two branches sometimes
- 3 4 -
act l ike an open circui t , sometimes act l ike a short circui t , or the si tuation i n between.
Therefore, above e l imina t ion o f branches is o n l y a very rough approximat ion and results
in more inaccuracies.
1.5
-
0 • 2 3 » 5 S 7 8 X 1 0 s
-
...I i L i i _ . J. 2 3 4 S 6 7 8 9 x 10'* time in scond
X 1 u
L \ I •'
. L , Frequency in Hz x 10*
Figure 2.7 Simulation Result for the High Frequency Transformer Model
2.4 Equivalent n Model by Nodal Analysis
A n y transformer can be described as a two-port system as shown i n F igure 2.8.
F r o m the l ine hyperbol ic equations, i.e. formula (2.4) and (2.5) [27], an equivalent n
circuit can be der ived to represent the entire l ine length, w h i c h takes the frequency
dependence o f the parameters into account. Instead o f injecting any s ignal into the circuit ,
the equivalent admittance o f the who le circui t by nodal analysis is evaluated as the
transfer function for this mode l .
- 3 5 -
k
V k
cxi
Z l
V m
Figure 2.8 Equivalent n M o d e l by Noda l Analysis
Z l = ( Z ' i ) S i n h y } = Rl(co) + jcoL\(co) (rl)
(2.4)
y 2 = ( r / ) t a n h ( ^ / 2 )
( r / / 2 )
Where ,
Z ' : impedance per meter
Y ' : admittance per meter
1: total length o f the l ine or w i n d i n g
• Y' propagat ion constant o f the l ine
(2.5)
Th i s equivalent % mode l can not be used direct ly i n t ime-domain simulat ions
because the c i rcui t parameters are functions o f frequency. It is on ly useful for one-
frequency at a t ime for steady state solutions, so it is s imulated i n M a t l a b . The script is as
fo l lowing . The s imula t ion result is shown i n F igure 2.9.
%matlab script for the equivalent pi model by using hyperbolic correction %for the whole transformer, using p i circuit for both windings f=[le3:le2:10e6]; w=2*pi.*f; Sb=l67000;
- 3 6 -
Vbl=14400; Vb2=347; Z b l = V b l * V b l / S b ; Zb2=Vb2*Vb2/Sb; cl2=352e-12; z l 2 = l . / ( j . * w . * c l 2 ) . / Z b l ; cl3=418e-12; z l 3 = l . / ( j . * w . * c l 3 ) . / Z b l ; c30=50.9e-12; z30=17(j.*w.*c30)7Zb2; %a=0.7*3e8; % YphaseO=-len/a. * w/pi ; %tao=len/a;%8.37e-7;
%for high voltage winding Cl=0.014e-12; Ll=3e-4; lenl = 175.83; z l = G . * w . * L l ) . * l e n l . * s i n h O . * w . * l e n l . * s q i 1 ( L l * C l ) ) 7 ( j . * w . * l e n l . * s q r t ( L l * C l ) ) . / Z b l ; y 21=j .^v .*Cl .* len l .na i ihO.*w.* len l .*sqr t^^ z21=27y217Zbl ;
%for inner section of low voltage winding C2=398e-12; L2=2.85e-4; len2=13.33; z2=(j.*w.*L2).*len2.*smh(j.*w.*len2.*sqrt(L2*C2))./0'.*w.*len2.*sqrt(L2*C2))./Zb2; y22=j.*w.*C2.*len2.*tanhQ.*w.*len2.*sqrt(L2*C2)./2)7(j.*w.*len2.*sqrt(L2*C2)72); z22=27y227Zb2;
%for outer section of low voltage winding C3=452e-12; L3=2.54e-4; len3=14.94; z3=(j.*w.*L3).*len3.*smh(j.*w.*len3.*sqrt(L3*C3))70'.*w.*len3.*sqrt(L3*C3))7Zb2; y23=j.*w.*C3.*len3.nanh(j.*w.*len3.*sqrt(L3*C3)72)70'.*w.*len3.*sqrt(L3*C3)72); z23=27y237Zb2;
%calculate equivalent circuit %step 1 z4=z21.*z227(z21+z22); z5=z23.*z227(z23+z22); z6=z23.*z307(z23+z30); %step 2: y to delta za=(z 1. *z2+z 1. *z4+z2. *z4)7z4: zb=(z 1. *z2+z 1. *z4+z2. *z4) 7z2 zc=(zl .*z2+zl .*z4+z2.*z4)7zl : %step 3 zf=zl2.*za7(zl2+za); zd=z21.*zb7(z21+zb); ze=z5.*zc7(z5+zc); %step 4: y to delta zg=(zf. *z3+zf. *ze+z3. *ze)7ze; zh=(zf. *z3+zf. *ze+z3. *ze)7z3; zi=(zf. *z3+zf. *ze+z3. *ze) 7zf; %step 5
- 3 7 -
zk=zd.*zh./(zd+zh); zm=zi.*z6./(zi+z6); zn=zi+zm; ye=abs((zk+zn)./(zk.*zn))./Zbl; y=fft(ye); plot(f/le6,y);xlabel('Frequency in MHz');ylabel( 'Admittance'); title( 'Applying Correction Factor to P i Mode l for the Transformer');grid;
A p p l y i n g Co r rec t i on F a c t o r to P i M o d e l for the T rans fo rmer
• ,1 J . ,i i i . , i . Il i , i . .. i . .1... I
F r e q u e n c y in M H z
Figure 2.9 Simulation Results for Equivalent n Model Using Nodal Analysis
The result yie lds many resonance frequencies, w h i c h is s imi la r to the typ ica l
experimental F R A results i n p rev ious ly publ ished papers. C o m p a r e d w i t h the first two
models in this chapter, it can be found that the distributed-parameters are the key factors
to the effective m o d e l l i n g o f the transformer w ind ing . H o w e v e r , instead o f us ing the
F R A technique, a better mode l l i ng technique can be developed by us ing a different
signature o f the w i n d i n g , i.e. the characteristic impedance Z c . " A dis t inguishing feature
o f the circuit w i t h distr ibuted constants is its abi l i ty to support t rave l l ing waves o f current
and vol tage" [28]. T h i s leads to the explorat ion o f the transformer w i n d i n g mode l l i ng
based on the t ravel l ing wave theory o f a t ransmission system i n the next chapter.
- 3 8 -
CHAPTER 3 Transformer as a Transmission Line
The t ravel l ing wave theory for transmission systems is the foundation o f this
thesis. It has been extensively studied since 1930. In short, any disturbance, no matter
whether it is electr ical , magnetic, mechanical or audio, w i l l cause a wave to propagate in
the surrounding med ium. O n power transmission systems, for example , on a transmission
l ine, any electromagnetic disturbance caused b y swi tch ing operations, faults or l ightning
strikes w i l l result in the in i t ia t ion o f t ravel l ing electromagnetic waves. These waves
propagate a long the t ransmiss ion system unt i l they reach a discont inui ty , such as the end
o f the l ine, where they m a y be reflected and/or refracted and modi f i ed . The waves m a y
also be attenuated and distorted b y corona and other losses unt i l they are comple te ly
dissipated and die out [29]. The ve loc i ty o f electromagnetic waves v 0 i n free space is
constant, but is dependent on the dielectric med ium. B y formula (3.1) [28], regardless o f
the l ine geometry or conductor material , the electromagnetic wave a lways travels at the
speed o f l ight, i.e. 300km/ms . Approx ima te ly , it takes a wave 3.3 ms to travel 1000 k m in
free space.
1 ( 3 . 1 )
\IQ: permeabil i ty o f free space, 47c* 10" H / m ;
So: permit t iv i ty o f free space, 8.854* 10" 1 2 F / m .
39
Another important term in t ravel l ing wave theory is the characteristic impedance
Z c , also cal led surge impedance, w h i c h is the ratio between the voltage wave and the
current wave. Z c represents the impedance w h i c h t ravel l ing waves encounter i n the front
along the l ine, so Z c is constant for the entire length o f a un i fo rmly distributed l ine.
U n l i k e the ve loc i ty o f t ravel l ing waves, Z c heav i ly depends o n the geometry o f the
transmission systems. F o r example, for a single conductor above an ideal ground, Z c is
about 500 Q ; w h i l e for two paral lel conductors, Z c is about 200 to 300 Q . A n y change i n
Z c represents a d iscont inui ty i n the l ine, w h i c h m a y indicate an unusual condi t ion o f the
l ine, for example, a short c i rcui t fault.
T rave l l i ng wave theory has been applied for accurate locat ion o f faults on power
transmission systems. Te c hno logy is available to determine fault locat ion w i t h i n a
transmission span o f 300 meters on 500 k V transmission lines [30]. A n y fault on the
transmission l ine represents a discont inui ty i n the wave propagat ion a long the l ine, w h i c h
is caused b y the change o f the surge impedance. E a c h wave can be decomposed into
different frequencies depends on the type o f faults. These waves travel and reflect
towards the two ends o f the l ine at the ve loc i ty o f light i f one assumes the wave
propagation i n the air has no dielectric loss. In practice, the t ravel l ing speed along the
transmission line i n the air is a lit t le bit less than the speed o f l ight. B y observing the
t ravel l ing t ime f rom one discont inui ty to another or end o f the l ine, one can calculate the
fault distance by the product o f the ve loc i ty o f l ight and the t ravel l ing t ime. In this way , a
fault can be accurately located.
40
In practice, transformer w i n d i n g is l ike a t ransmission l ine w h e n the wave
frequency is very h igh . A c c o r d i n g to the w e l l k n o w n formula (3.2), for the power
frequency 60 H z , the wavelength a long the transmission l ine is 5000 k m ; w h i l e for a
higher frequency o f 2 M H z , the wavelength a long the transformer w i n d i n g is on ly 150 m .
In other word , h igh frequency waves make the transformer w i n d i n g long enough to
behave l ike a t ransmission l ine for wave propagation. In addit ion, measurements on many
actual transformers have revealed that the internal capacitance between turns or coi ls are
so smal l that the electromagnetic waves travel on conductors w o u n d into coi ls o f
negl igible internal capacitance, that is, ignor ing the dielectric permit t iv i ty , w i t h the same
speed as on a straight l ine conductor [31]. L i k e fault locat ion technique i n transmission
line, wave propagat ion theory can be put into the use o f transformer w i n d i n g movement
diagnosis, w h i c h is named the Transmiss ion L i n e Diagnost ics ( T L D ) method b y D r . Jose
M a r t i .
v 0 = f * A . ( 3 . 2 )
f: frequency
X: wavelength o f that frequency
3.1 The Wave Propagation High-frequency Transformer Model
B y taking advantage o f the wave propagation property and frequency-dependent
transmission l ine mode l [32], one can simulate the real transformer w i n d i n g as a h igh
frequency distributed t ransmission l ine, obtain the characteristic impedance and
propagation constant o f the w i n d i n g , calculate the t ravel l ing t ime for certain frequency
41
for the total equivalent length o f the w ind ing . B y compar ing the change o f the
characteristic impedance Z c we can detect whether there is w i n d i n g distort ion or
movement. The fault locat ion results i n an equivalent sublength, w h i c h can be compared
wi th the total equivalent length and further used to determine where the w i n d i n g
movement or dis tort ion has occurred. •
Th is section is split into three subsections. A frequency-dependant mode l for a
transmission l ine is presented i n the first subsection. Th i s m o d e l forms the basis for a l l o f
the later development o f models i n this thesis. The mode l for a non-faulted w i n d i n g is
derived i n the second subsection. The last subsection details the modi f ica t ion to the
model for the case when a fault occurs in the w ind ing .
3.1.1 Frequency-dependant Line Model
This subsection shows the derivat ion o f a frequency-dependant l ine mode l for a
transmission l ine. T h i s mode l was o r ig ina l ly presented b y D r . J . R . M a r t i i n 1982 [32].
G i v e n a t ransmission l ine as shown i n F igure 3.1, the f o l l o w i n g wave equations
can be obtained:
it, o • c > . c
Figure 3.1 A Transmission Line
42
V, = Vfie'^ +Vbke^' (3.3)
I, = j ^ V » e ~ ' ' ' - ^ V * e + r ' * (3.4) c c
where:
Vf = Z C I f (3.5)
V b = - Z J b (3-6)
Zc - is the characteristic impedance o f the l ine (3.7)
•Y' is per unit length propagation constant o f the l ine (3.8)
Z ' is the per unit length impedance o f the l ine
Y' is the per unit length admittance o f the l ine
B y c o m b i n i n g equations (3.3) and (3.4), a forward perturbation function can be
found as g iven in equation (3.9) under the condi t ion Vk + Z c I k = TV^ at x=0.
K+ZJ,=(K+ZJt)e-r'' (3.9)
Therefore, at node m , equation (3.9) becomes:
Vm ~ Z J ' m = ( V k + Z c I k ) e - ? > (3.10)
where:
43
K,=-L
I is the length o f the t ransmission l ine
(3.11)
A n equivalent c i rcui t as shown i n Figure 3.2 fo l lows f rom equations (3.10) and
(3.11).
——c
+
m
Figure 3.2 Equivalent Frequency-dependent L i n e M o d e l
Ekh and Emh are his tory functions and are defined as:
Emh = (Vk + ZJk)e •y'l (3.12)
Ekh = (Vm-ZJm)e -y'l (3.13)
F r o m Figure 3.2 and the above equations, we can f ind that a compl ica ted
distributed frequency-dependent t ransmission l ine is s i m p l y mode led as two separate
lumped circuits . E a c h c i rcui t includes the characteristic impedance o f the t ransmission
line, the wave propagation constant, and a history function. F o r a g iven t ransmission
line, its characteristic impedance and propagation constant are f ixed, since they are
44
determined by the geometry and compos i t ion o f the t ransmission l ine. T y p i c a l Z c o f a
transmission l ine is a smooth almost exponential curve, w h i c h decreases w i t h frequency.
3.1.2 Non-faulted Winding Model
The wind ings o f the transformer behave as transmission lines i f the frequency o f
the exci t ing voltage is suff iciently high. A n ind iv idua l w i n d i n g is mode led b y a b lack
box w h i c h has a specific structure. The frequency-dependent mode l that was presented i n
the previous subsection is used for the structure o f the b lack box . T h i s subsection details
the derivat ion o f the parameters o f the b lack box g iven that the input voltage, input
current, and output current are k n o w n or have been measured. T h e u n k n o w n parameters
o f the mode l are the characteristic impedance and propagation constant o f the equivalent
line model . T h i s m o d e l is for a normal , non-faulted w ind ing .
The w i n d i n g under investigation is phys ica l ly connected as shown in F igure 3.3.
Figure 3.3 Connection of the Winding under Investigation
The transmission l ine mode l for the w i n d i n g as connected i n F igure 3.3 is shown
in Figure 3.4.
coil 1: a l , a2 coil 2: b1, b2 coil 3: c 1 , c2
1 for sending end 2 for receiving end
45
al ^ Z,
•* a2
Figure 3.4 W i n d i n g M o d e l
A p p l y i n g K i r c h o f f s vo l t age l a w around the vo l t age l o o p o f the r ight-hand s ide
circuit o f F igure 3.4 gives:
Emh=(Zc+R)In (3.14)
Where:
I,„=lmZ0m is the measured output current
Substituting the def in i t ion o f Emh f rom Equat ion (3.12) y ie lds :
V k e > + Z c I k e > = Z e I m + R I m (3.15)
Where:
Vk=E s Z 0° is the measured input voltage
Ik=l k Z 6 is the measured input current
Equa t ion (3.15) contains two complex unknowns, thus another equation must be
obtained. The second equation comes from apply ing K i r cho f f s voltage l aw around the
voltage loop o f the left-hand side c i rcui t as g iven b y Equa t ion (3.16):
46
(3.16)
U s i n g the def in i t ion o f Ekh f rom equation (3.13) and not ing the direct ion o f Im
yields:
V k - Z e I k = R I m e * - Z J m e - ' (3.17)
Equat ions (3.15) and (3.17) can n o w be solved numer i ca l ly to obtain the values
for the characteristic impedance Z c and propagation constant 7 . N o t e that the
propagation constant 7 obtained by this method is the actual value not the per-unit length
value, i.e. y = y'*l. W h i l e f rom formula (3.18), w e can g e t r , w h i c h is the t ravel l ing t ime
o f wave propagation corresponding to ce r ta in ly . F o r m u l a (3.19) enables us to find the
equivalent length o f the w i n d i n g , i.e le, w h i c h is i n between the phys ica l length o f the
w i n d i n g and the height o f the w ind ing . v 0 is the ve loc i ty o f electromagnetic wave
propagation , w h i c h is 3e + 8 m/s in air.
co * T = imaginary _ part(y) (3.18)
/ e = v 0 * r (3.19)
F r o m the above, we can see that by taking measurements o f currents and voltages
on the two ends o f the w i n d i n g , we obtain the Z c and 7 , w h i c h are the fingerprints o f the
w i n d i n g without k n o w i n g the internal detailed phys ica l parameters o f the transformer. Z c
and 7 are further used i n the next section to detect the w i n d i n g displacement.
47
3.1.3 Faulted Winding Model
The mode l shown in the previous subsection is modi f i ed to account for a fault at
impedance Z t w i t h an u n k n o w n locat ion i n the w ind ing . The w i n d i n g is split into two
sections w i th effective lengths o f /, a n d / 2 . The modi f ied mode l is shown in Figure 3.5.
Figure 3.5 Faulted W i n d i n g M o d e l
A s wi th the non-faulted w i n d i n g , the input voltage, input current, and output
currents are k n o w n . The two sections on either side o f the fault have, i n general,
different propagation constants; yx for the leftmost section and y2 = y -yx for the
rightmost section. K i r c h o f f s voltage law is applied to a l l o f the loops, as was done wi th
the s impler non-faulted w i n d i n g . Four equations result f rom the four loops i n the model ,
since there are o n l y four unknowns , namely, Vf, 1f,Zx, and / , , the m o d e l has a unique
solution. The four equations are g iven by:
V k - Z J k = ( V f - Z c I f ) e - *
( V k + Z c I k ) e * = V f + Z J f
v,z. (LR-i,,,zje-^--^ = vf-zcif
(3.20)
(3.21)
(3.22)
48
(Vf + ZJf - 7 ^ ) e ^ =ImR + ZcIm (3.23)
Equat ions (3.20) - (3.23) can be solved numer ica l ly to obtain the value o f y] by
the Ma t l ab program. A b o v e formulae are defined as function F l to F 4 respect ively i n the
Mat lab . The M a t l a b script is shown as fo l l owing :
% Matlab script for solving the nonlinear equations % Define the nonlinear equations
F\ = V k - Z J k - { V f - Z c I f ) e *
F2=(yk+ZJk)e«-Vf+ZJf
F4 = (Vf + ZcIf -7^L)e^-lmR + ZcIm
F = ' [F1;F2;F3;F4] ' ; % Set initial values x0 = [0; 0;0;0]; options = optimset('Display','iter');
% Solve [x,fval] = fsolve(F,xO, options)
Since the per-unit length propagation constant is assumed not to change as the
result o f a fault, the locat ion o f the fault is s i m p l y g iven by :
l e \ ~ l e (3.24) r
The fault impedance, Zx, is also determined b y the so lu t ion o f Equat ions (3.20) -
(3.23) by Mat l ab . The determination o f the fault impedance Zx can give insight into
49
what type o f fault occurred, for example, i f Z x is very smal l , it impl i e s a short circuit
happens inside the transformer.
Note: F o r the convenience o f notation, i n the fo l l owing sections, V i n , I in , V o u t and lout
w i l l replace the V k , Ik, V m , Im o f above formulae respectively.
3.2 Laboratory Experiments and Simulation Results
Exper imenta l works have been performed i n the univers i ty undergraduate labs,
the universi ty H i g h Vo l t age L a b and the ut i l i ty research lab (Powertech Labs . Inc).
3.2.1 Initial Experiments Performed in the University Labs
The exci ta t ion o f input signal can be created b y two means i n the laboratory: a
function generator or a network analyzer. A good network analyzer can produce discrete
frequencies one at a t ime wi th a h igh resolution, record a l l the input and output signals i n
the t ime and frequency domains , and calculate the transfer function both i n magnitude
and phase angle. H o w e v e r , the equipment is very expensive. A n alternative w a y is to use
a s imple function generator, w h i c h either injects a s inusoidal s ignal , at a g iven frequency,
to the tested transformer or produces a l ow voltage impulse signal for the test, h i our
experiment, a s inusoidal s ignal was adopted as the input voltage source. The W A V E T E K
function generator used has a m a x i m u m frequency o f 2 M H z w i t h the 50 k H z frequency
resolution. The osc i l loscope is Tekt ronix T D S 220 w i t h 2 channels. The experimental
circuit is set up as figure 3.6.
50
T r a n s f o rme r"
o I i n > >
A A / V R i n
c V i n
o OS
6
F i g u r e 3.6 E x p e r i m e n t Set -up
In the above figure, the input resistor R i n is 20 Q w i t h 0 .5% precis ion. The output
resistor is made o f one 20 Cl and one 30 Q resistors i n series both w i t h 0 .5% precis ion. A
function generator injects l o w voltage s inusoidal wave into the c i rcui t at every 100 k H z
from 500 k H z to 2 M H z .
The first set o f transformers for test is four 1 6 . 7 k V A 2 4 0 V / 2 8 0 V variacs i n series.
The negative terminals have been shorted together. The connect ing cables between them
are made as short as possible , since the cable i t se l f can act l i ke a t ransmission l ine.
Because o f the smal l gauge o f the wind ings o f these Var i acs and antenna effect, on ly a
very smal l amount o f current is drawn inside the windings . Stray capacitance is
everywhere, w h i c h causes b i g loss. F o r an open circui t test, the output voltage is on ly a
few tens o f m V when the input voltage is a few tens o f vol ts . Therefore, the
measurements are not acceptable.
51
The second transformer tested is a 3-phase 60 cyc le l O k V A transformer as shown
in Figure 3.7. The voltage rating is 2 2 0 / 2 2 0 V and total weight is 275 pounds. In order to
have a so l id ground, the core and the chassis are shorted together. In i t ia l ly , the
experiments are performed i n an undergraduate lab. H o w e v e r , antenna effect and bad
grounding condit ions have a huge influence on the measurement, w h i c h leads to a l o w
signal-to-noise ratio. In order to improve the accuracy o f the experiments, the transformer
has been moved into a special H i g h Vol tage lab, where good sh ie ld ing and good
grounding are obtained. B o t h the w a l l and the floor o f the h igh voltage lab are made o f
a lumin ium, w h i c h provide evenly distributed stray capacitance and hence make it more
l ike the enclosed co i l s inside a tank environment. T o avoid electromagnetic interference
( E M I ) , both the function generator and the osci l loscope are shielded b y an a l u m i n i u m
case.
Figure 3.7 The l O k V A Transformer in the Universi ty L a b
F r o m F igure 3.7, w e can see the transformer is a dry type transformer without a
tank. In order to simulate the phys ica l transformer w h i c h is usua l ly inside a metal case,
we wound an a l u m i n i u m fo i l to the top o f the w ind ing . W e also use the insula t ion sticker
and paper ba l l to separate the a lumin ium cyl inder from the w i n d i n g w i t h different
52
separations. The change o f the separation between the w i n d i n g and the a l u m i n u m tank
w i l l vary the inductance o f the w i n d i n g and the capacitance i n between, and therefore
vary the values o f Z c for different frequencies.
Ideally, accord ing to formula (3.25) and (3.26) [31] be low, we can see that the
changes in the w i n d i n g distances (i.e. the separation b and d) vary both the capacitance
and the inductance. The increase o f the separation reduces the capacitance between the
w i n d i n g and the ground and raises the self-inductance o f the w i n d i n g . F o r m u l a (3.27)
d, w h i c h is usual ly the case for real transformers, the denominator o f the fraction equals
1, hence the Z c is d i rect ly proport ional to b. W e can conclude here that the internal
insulation distance plays a key role i n the value o f Z c . W h e n b is i n the same order as d,
both o f them determine the value o f Z c .
[31] further defines that Z c is d i rect ly proport ional to b
. W h e n b is m u c h less than l + b/d
C = ecoh b + d
AO9 F (3.25) 4;rv„ bd
L = 47TLi-N2 bd
.10 -9 H (3.26) h b + d
(3.27)
Where ,
| i : magnetic permeabi l i ty o f the material
e: permit t iv i ty o f the insula t ion material
N : total number o f the turns o f the w i n d i n g
53
h: ax ia l length o f the w i n d i n g
b: average internal insulat ing distance, i.e. distance between the inter w i n d i n g and
the core
d: average external insulat ing distance, i.e. distance between the outer w i n d i n g
and the tank
v 0 : ve loc i ty o f l ight i n a vacuum, 300m/us.
The relationship that Z c is direct ly proport ional to the inner separation can be
proved in another way . T a k i n g a s imple case, for two paral le l plates, the capacitance is
inversely proport ional to the separation between the plates b y the w e l l - k n o w n
relat ionship/formula (3.28).
C = k , A / D (3.28)
Where ,
k i : constant
A : area o f the plate
D : the distance between two plates
\Z' IR + jwL B y extending the formula (3.7), w e get Zc = — - = , w i t h the
V Y \ G + jwC
increasing o f frequency, R and G are negl igible , therefore w e get the fo rmula (3.29). In
formula (3.30) [31], v 0 is a constant, i.e. the speed o f light. C o m b i n i n g these two
formulae, we can get the direct relationship between Z c and C (3.31).
Z c = i l ( 2 9 )
54
LC (30)
1/v, 0 k. Z c = (31)
C C
C o m p a r i n g formulae(3.28) and (3.31), we get
Z c = - ^ - D = k»D k,A
(32)
F r o m the above w e can f ind that formula (3.32) is consistent w i t h formula (3.27),
w h i c h leads us to focus more on the var ia t ion o f the separation between the w i n d i n g and
the core o f a transformer. It also gives us some general idea that Z c increases w i t h the
increase o f the separation; it can be either the separation between the w i n d i n g and the
core, or the separation between the w i n d i n g and the tank.
H o w e v e r , i n the above ideal situation, Z c is l inear to the separation and
independent o f frequency, w h i c h is usual ly not the case for pract ical transformers. M o r e
often, transformers are made o f concentric core and tank, w h i c h prov ide nonl inear
capacitances and Z c as w e l l . F o r example, the capacitance is the logar i thm o f the
separation o f two concentric cyl inders ; also, the dielectric constant becomes frequency
dependent. Therefore, separation between the w i n d i n g and the core, separation between
the w i n d i n g and the tank, and frequency are the m a i n factors to be var ied and discussed
in our technique.
55
B y measur ing the input voltage, input current and output voltage, w e simulate the
w i n d i n g performance o f the l O k V A transformer i n M a t l a b based o n the formulae
described i n section 3.1. The M a t l a b script is as f o l l o w i n g :
%Matlab script for experiments performed in the univeristy lab
%Frequency scan
%Experimental results of input voltage, input current and output current
%are 3 knowns. Hence, we set them as constant A, B, and C.
"/•Source voltage is the reference voltage which has zero phase angle
close all;
Rin=20;%input resistor is adjustable
A=data(.,4) *exp(2*pi*1000*data(:,l)*le-9.*data(:,5)*j)/2;%input voltage Vk(to the winding)
B=(data(:,2)/2-A)/Rin;%input current Ik
R=50;%output resistor is adjustable
C=data(:,6).*exp(2*pi*1000*data(:,l)*le-9.*data(:,7)*j)/R/2;%output current Im
kl=A+B*R;
k2=C+B.*C*R./A;
ml=C-B.*B./C;
m2=B+C.*C*R./A;
nl=C.*R+A.*B./C;
n2=C.*C*R*R./A-A;
%set the parameters aa, bb, cc for solving Zc
aa=ml .*k2;
bb=nl.*k2-ni2.*kl;
cc=-n2.*kl;
Zc=(-bb+sq rt(bb. *bb-4 *aa. *cc))./(2 *aa);
Zc_mag=abs(Zc);
Zc_angle=unwrap(angle(Zc));
%Zc plots
figure(l)
subplot(2,l,l);
plot(data(:,l ),Zc_mag);ylabel('Magnitude of Zc');grid;title('Zc');
axis([500 2000 100 1300]);%parameters are adjustable & The command may not be needed.
subplot(2,l,2);
plot(data(:,l ),Zc_angle/pi);xlabel('Frequency in KHz');ylabel('Phase angle of Zc in pi');grid;
56
The characteristic impedance Z c o f the transformer w i n d i n g is obtained in the
unshielded undergraduate lab as shown in F igure 3.8. The results have been graphical ly
smoothed out because the geometrical irregulari ty o f the transformer results i n the
osci l la t ion o f Z c . The w i n d i n g o f the transformer is very short. In the normal lab, there
are stray capacitances a l l over the place, to the support ing poles, to the w a l l , to the nearby
objects, to the floor, and to the chassis. A l l create the irregulari ty and uncertainty, w h i c h
degrades the t ransmission l ine behaviour o f the w ind ing . An tenna effect is another factor
w h i c h worsens the exper imental condi t ion . M o r e important, the ground is not evenly
distributed, w h i c h is not the situation for an over head t ransmission l ine.
6 c
1100
1000
900
800
700
600
500
400
300
200
Zc with different seperat ions between the outer winding and the a luminum coil
100
without foil c l o s e foil 0 .5cm seperat ion
O 5cm seperat ion \
\
without foil c l o s e foil 0 .5cm seperat ion
O 5cm seperat ion
without foil c l o s e foil 0 .5cm seperat ion
O 5cm seperat ion
' \ i \ :
• •
0.5 0.6 0.7 0.8 0.9 1 1.1 frequency in M H z
1.2 1.3 1.4 1.5
Figure 3.8 Zc with Different External Insulating Distances
In the experiments, the internal insulat ing distance b is f ixed, and the on ly thing
we can change is the outer insulat ing distance d. W i t h the increase o f d, Z c decreases
57
correspondingly. In F igure 3.8, we can f ind that when changing the transformer tank from
closed fo i l to open fo i l , i.e. increasing d, Z c goes up dramatical ly . Z c o f open fo i l is
almost one and a h a l f t imes o f Z c o f close fo i l . W e can f ind the same phenomenon
between 0.5 c m and 5 c m separations. The Z c curve o f 5 c m separation is a lways above
the Z c curve o f 0.5 c m separation. T h e y are l ike i n paral le l , w h i c h demonstrates that the
increment o f Z c from one separation to another separation is f ixed, determined by the
f r ac t ion——^—. H o w e v e r , the osc i l la t ion o f the curves reflects the inferior experimental l + b/d
condit ions, l ike bad grounding and antenna effect.
After m o v i n g the transformer into the H V lab, the grounding and sh ie ld ing
condit ions improve dramatical ly , but the presence o f other H V gas insula t ion testing
equipments i n the H V lab creates the extra irregulari ty p rob lem. S i m u l a t i o n results
among different locat ions are shown as F igure 3.9. It shows that the loca t ion or the
experimental cond i t ion plays a cr i t ical role i n the accuracy o f the s imula t ion results.
F r o m the F igure 3.8 and 3.9, we can find that no matter h o w b i g the external
insulating distance is and no matter where the experiment is performed, the general shape
o f Z c o f the transformer w i n d i n g is just l ike the characteristic impedance o f t ransmission
line.
58
Zc at different locations
E .c O
cn c •a c
u N Q) u c
a> o. E o to 'l 0) T> CD
1400
1200
1000
ro x: o
800
600
400
2 200
-©-
— in lab 1 - - - in lab 2 O in HV lab
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 frequency in MHz
1.3 1.4 1.5
Figure 3.9 Zc Obtained from Different Experiment Locations
Howeve r , there are s t i l l some other factors w h i c h l imi t the accuracy o f the
s imulat ion. Factors l ike the m i n i m a l frequency resolution, the recording length o f the
samples and the data-reading b y human (when us ing the cursor to get the phase angle),
the bad grounding condi t ion , the uncontrol led stray capacitance, the sma l l s ignal to noise
ratio, the temperature ( i f the w i n d i n g is too thin and therefore susceptible to temperature
change), the test set-up and especial ly the o ld equipment, they a l l reduce the accuracy o f
the s imulat ion results. F o r example, the l inks o f the wire or the scope cables w i l l create
an extra phase delay because they act l ike a t ransmission l ine for h igh frequency wave as
w e l l . In order to improve the accuracy o f the s imula t ion results, experiments need to be
59
implemented in a ut i l i ty research lab w h i c h has advanced function generator and better
digital osci l loscope.
3.2.2. Experiments Performed in the Powertech Labs
Under private communica t ion [33], s imi lar experiments are performed o n a
1 6 7 k V A distr ibut ion reactor i n a u t i l i ty research lab (Powertech Labs . Inc.). A fast pulse
generator, a h igh prec i s ion measur ing equipment and automatic data recording were used.
A s the above, three parameters are recorded i n the t ime domain : input voltage, input
current and output current. The internal impedance o f the pulse generator is 50 Q.. W h i l e
the output current is measured on a l f i shunt. Different f rom the previous experiments i n
the U B C lab, the input is not a s inusoidal signal . Instead, an impulse s ignal is injected.
The sampl ing frequency is 500 M H z , w h i c h impl ies that the m a x i m u m frequency from
the signal w e can get is 25 M H z . Hence , the time-step is 2 ns. The number o f the
sampl ing points is 30,000 and the t ime w i n d o w is 60 p.s. The m i n i m a l recording data
value is l e " . The o r ig ina l measurement obtained from the research lab is shown i n
Figure 3.10. In order to have a detailed look o f the wavefo rm when the impulse signal is
injected, figure 3.10 on ly shows the waves from 11.8 [is to 13 u.s.
60
CD
E CO c 0
-0.5 11.8
CD
aS 0.2 CL E
co 0
e -0.2 CD I -0.4
11.8
input voltage
1 2 2 inpat ient 1 2 - 6 1 2 - 8
12 12.2 ou tpii&urrent 12.6 12.8
12 12.2 12.4
time in (JS
12.6 12.8
13
I I I
h i . ^ a I
I v
f - i y — - v - y
i i i i
13
I
l i . A J t \ / V ^ / •
\ / -i i
v. \
/ J
13
Figure 3.10 Original Time Domain Measurements in a Utility Research Lab
The data obtained from the research lab is not put into use direct ly. Some
modif icat ions have been made. F i r s t ly , the t ime w i n d o w is chopped for a l l three
waveforms to el iminate noises and unreliable parts. F r o m the data file obtained [33], we
can find that there are lots o f noise during the who le t ime per iod. Af ter examin ing the
input voltage data file, we find that at 11.988 u.s, the input impulse voltage is being
injected; wh i l e at 12.108 tis, the impulse signal has its first zero cross ing. In order to
remove the noise, we set the signal before 11.988 LIS and after 12.108 LIS to 0. Therefore,
61
a better impulse input s ignal is generated without noise before and after.
Correspondingly , the input current and output current are chopped at 11.988 u,s
and l2 .108 u.s as w e l l , and on ly the signals i n the t ime interval 11.988 ps and 12.108 p.s
are kept nonzero. Furthermore, i n order to get almost continuous frequency response, the
time w i n d o w has been extended to double as before. B y chopp ing and extending the t ime
w i n d o w , an impulse response is represented i n a better way . F igure 3.11 b e l o w shows the
modi f ied measurements i n the t ime domain .
C D O ) C D
~o >
15
10
5
0
11.8 0.5 r —
C D Q -
E C D
C D
-0.5 11.8
C D
S 0.2
C D 0
= -0.2 C D
-0.4 11.8
12
12
12
input voltage
1 2 2 inpat ient 1 2 ' 6 1 Z 8
12.2 12.4 time in ps
12.6
1 2 2 outpul̂ urrent 1 2 6 1 2 8
12.8
13
13 I 1 1 1
A A \
1 ,y/
i i i i
13
Figure 3.11 Modified Time Domain Measurements in a Utility Research Lab
62
B y app ly ing the formulae developed i n section 3.1, we can obtain the
characteristic impedance Z c o f the w i n d i n g i n both magnitude and phase as shown i n
Figure 3.12, based o n the f o l l o w i n g Ma t l ab script. Furthermore, the t ravel l ing t ime and
equivalent length o f the w i n d i n g for different frequencies are obtained, as shown i n
Figure 3.13.
%Matlab script for experiments performed in a utility reserach lab %lnject Impulse Signal %chop the time window from first zero crossing %add another 30,000 points—i.e. zero padding
close all; dt=2e-9; n=60000;%number of points tmax=dt*n; t=[dt:dt:tmax]; fmax=l/dt;%sampling frequency is 500MHz df=fmax/n;%frequency resoluation freq=[df:df:fmax]; f=transpose(freq); w=2*pi*f;
v_in=data(:,3); ijn=data(:,4).*50; i_out=data(:,5);
v_in_f=fft(v_in);%convert input voltage into frequency domain i_in_f=fft(i_in);%convert input current into frequency domain i_out_f=fft(i_out);%convert output current into frequency domain
%Experimental results of input current, input voltage and output current %are 3 knowns. Hence, we set them as constant A, B, and C. A=v_in_f; B=i_in_l'; C=i_out_f; R=l;% resistor connected to the bottom end of the reactor in ohms
kl=A+B*R; k2=C+B.*C*R./A; ml=C-B.*B./C; m2=B+C.*C*R./A; nl=C.*R+A.*B./C; n2=C.*C*R*R./A-A;
%set the parameters aa,bb,cc for solving Zc aa=ml .*k2; bb=nl.*k2-m2.*kl; cc=-n2.*kl; Zc=(-bb+sqrt(bb.*bb-4*aa.*cc))./(2*aa); Zc_mag=abs(Zc); Zc_anglc=unwrap(angle(Zc));
%plots %time domain plots figure (I) subplot(3,1,1 ),plot(t/l e-6,v_in);grid; title('input voltage');ylabel('voltage in volt'); axis([l 1.813-215]);%The parameters are changeable according to when the impulse signal is injected.
63
%This command may not be needed if we want the full range plot. subplot(3,l,2),plot(t/le-6,i_in);grid; title('input current');ylabel('cun"ent in ampere'); axis([l 1.8 13 -0.5 0.5J);%changeable or not needed. subplot(3,l,3),plot(t/le-6,i_out);grid; title('output cunent');xlabel('time in |is');ylabel('current in ampere'); axis([l 1.8 13 -0.4 0.3]);%changeable or not needed.
%FRA plots figure (2) subplot(2,l,1 ),plot(t/le-6,i_in./i_out);grid;%v_out=i_out, Rout=lohm title('Transadmittance of the Reactor');xlabel('time in us');ylabel('Transadmittance in Siemens'); axis([11.8 13 -100 150]);%changeable or not needed subplot(2,l,2),plot(f/le6,(i_in_0/(i_out_0);grid; title('Frequency Response of the Reactor');xlabel('fiequency in MHz');ylabel('Transadmittance in Siemens'); axis([0 25 -50 100]);%Only take the values up to Nyquist frequency & parameters are adjustable
%TLD plots (Zc) figure(3) subplot(2,l,l); piot(freq/l e6,Zc_mag);ylabel('Zc');title('Magnitude of Zc');grid; axis([0 25 0 300]);%parameters are adjustable subplot(2,l,2); plot(freq/le6,Zc_angle/pi);xlabel('Frequency in MHz');ylabel('Phase angle of Zc');title('Phase angle of Zcl in pi');grid; axis([0 25 -1300 100]);%parameters are adjustable
Magnitude of Zc for the transformer winding
_\
\
\
0 5 10 15 20 25
Phase angle of Zc
0 5 10 15 20 25 Frequency in MHz
Figure 3.12 Simulation Results of Zc in a Utility Research Lab
64
travel time
0.5
S 0
-0.5
1 \
\ :
1 I . I 1 1 1 1 1
200 r
£ 150 -% E c 100 -
SI
leng
l
50 -
0 2 4 6 8 10 12 14 16 18 20
equivalent length
I I
\
\ —
. i i i i i i - " I 1 r -
0 2 4 6 8 10 12 14 16 18 20 Frequency in MHz
Figure 3.13 Simulation Results of Travelling Time and Equivalent Length in a Utility Research Lab
F r o m figure 3.12, we can f ind the Z c o f the transformer w i n d i n g has the exact ly
same wave shape as the Z c o f a typ ica l t ransmission l ine up to 1 7 . 5 M H z . W i t h the
increase o f the frequency, the magnitude o f Z c decays exponent ia l ly and the phase angle
o f Z c decreases l inear ly . Therefore, w e can ver i fy that it is v a l i d to m o d e l the transformer
w i n d i n g as a t ransmiss ion l ine as long as the frequency is h i g h enough. The s ignal w i t h
h igh frequency travels fast and has a smal l wavelength so that the transformer w i n d i n g is
long enough to a l l o w the wave to travel along as i f the wave travels a long the
transmission l ine .
W h e n the frequency is re la t ively l o w , for example i n our case lower than 0 . 5 M H z ,
the corresponding wavelength o f the frequency is very long. Espec i a l l y , i f the wavelength
is longer than the phys i ca l length o f the w i n d i n g , the injected s ignal w i l l not rea l ly travel
65
along the w i n d i n g l ike a long a t ransmission l ine. In other words , the w i n d i n g is not long
enough to act l ike a t ransmission line for any l o w frequency signals. T h i s explains the
phase angles for the lower frequency range.
W h e n the frequency is extremely h igh, the Z c response is becomes more sensitive
to the test set-up, the noise and the accuracy o f the measur ing equipment. W e can find i n
figure 3.12 that the magnitudes o f Z c above 17.5 M H z begin to increase. It should be
corrected b y further improvement on the overa l l test design and more advanced
measuring equipment.
F r o m figure 3.13, we can see that the results are consistent w i t h the conc lus ion i n
section 3.1.2. L i k e i n a t ransmission l ine, h igh frequency signal oscil lates faster.
Moreover , the equivalent length o f the w i n d i n g decreases w i t h the increase o f the
frequency. It proves again that the transmission l ine diagnostic mode l i n transformer is
va l id and efficient. '
3.2.3 Configuration of a Single Phase Transformer for Tests
In order to further the study o f the w i n d i n g movement diagnosis, a single phase
power transformer is assembled i n the laboratory as shown i n F igure 3.14 and 3.15. T w o
identical d isk- type copper co i l s are used as the two wind ings . Conduc tors o f both the
windings have square cross sections about 0.2 c m . They are w o u n d as concentric disks.
The radius o f the innermost layer is 8.5 inches, w h i l e the radius o f the outermost layer is
12.5 inches. The number o f the disks for each w i n d i n g is 23, and the number o f layers is
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28. The height o f each w i n d i n g is 4.75 inches. The insula t ion between turns and layers is
varnish. The insulat ions between the two windings and between the lower w i n d i n g and
ground are wooden spacers. The two windings are connected i n series.
Figure 3.14 Overa l l V iew of the Transformer under Test
Figure 3.15 Cross-section View of the Transformer under Test
67
A c c o r d i n g to the formula (3.33) be low, w e roughly calculate the total length o f
the windings ( L ) , w h i c h is 7081 feet, that is, 2158 meters. C o m p a r i n g L w i t h the
wavelength o f 600 meters at 0.5 M H z obtained by formula (3.2), w e k n o w that in a
homogeneous lossless m e d i u m , the wave travels about 3 wavelengths at such frequency.
In the other w o r d , it provides 3 ful l waveforms. S i m i l a r l y , the wavelength is 150 meters
for a 2 M H z s ignal , w h i c h w i l l g ive us about 14 fu l l waveforms o f the s ignal . A g a i n , the
higher the frequency is, the shorter the wavelength w i l l be, and therefore the more ful l
waveforms w i l l be obtained. Therefore, the wind ings w i t h such length are reasonable and
practical for our t rave l l ing wave based transmission l ine diagnostic m o d e l l i n g .
L=2 * 7i * average w i n d i n g radius * number o f the turns * number o f the layers (3.33)
The core is made up o f the very thin a l u m i n i u m cyl inder , w h i c h is w o u n d from an
a lumin ium sheet. C o m p a r e d w i t h a lumin ium, steel is a ve ry good type o f magnetic
material due to its h igh permeabi l i ty , around 2000 times o f air and a l u m i n i u m . However ,
steel is usual ly very heavy and hard to bend. A l t h o u g h a l u m i n i u m doesn' t have as good a
magnetic permeabi l i ty as steel, it is suitable for h igh frequency study due to the sk in
effect explained later.
The a l u m i n i u m cy l inder or sheet is 31 inches ta l l . The w h o l e transformer is put on
the top o f a mob i l e w o o d e n stand w i t h wheels underneath. T h e height o f the stand is
around 6 inches and the w o o d e n spacer between two wind ings is around 5 inches. In
order to shield the magnetic f lux and to reduce end effect and p r o x i m i t y effect, the height
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o f the core has to be larger than the total height o f the w ind ings , i.e. overheads has to be
added up to the total height. Here w e chose the height o f the core to be about two times
the total height o f the wind ings . Af te r rounding it, the m a x i m u m radius o f the h o l l o w
core is approximate ly 8.5 inches, w h i c h equals the radius o f the most inner layer o f each
wind ing . In such a w a y , w e can s i m p l y adjust the separation between the wind ings and
the core, i.e. b i n formula (3.27), b y compressing or expanding the ve ry th in a lumin ium
cyl inder . A cross-sect ion v i e w o f the transformer is shown i n F igure 3.16.
Figure 3.16 Cross-section View of the Transformer
The thickness o f the core is calculated based on the sk in depth i n a conduct ing
material. W h e n a magnet ic f ield B travels inside a lossy conduc t ing m e d i u m , it attenuates
i n magnitude exponent ia l ly according to the attenuation constant a as s h o w n i n Equa t ion
69
(3.34). S k i n depth is defined i n Nannapaneni R a o ' s book [34] as "The f ie ld is attenuated
by a factor e-1 or -.368 i n a distance equal to 1/ a. Th i s distance is k n o w n as the sk in
depth and is denoted by the symbo l 8". S k i n depth sometimes is also named space
constant [28]. Equat ions (3.35) and (3.36) from R a o ' book derive and ver i fy the
relationship between a and 8. F r o m these equations, we can f ind that for a g iven magnetic
material, the depth o f the magnetic f ie ld penetration is inverse propor t ional to the square
root o f frequency appl ied. The higher the value o f the frequency, the larger the value o f
the attenuation constant a, the smaller the value o f the sk in depth 8, and therefore the
shal lower the magnetic wave can penetrate. Th i s phenomenon is i l lustrated i n F igure
3.14.
B = B 0 * e " a (3.34)
Bo is the surface magnetic f lux density
a = ^nfuia (3.35)
S = -=L= (3.36) Jnf/ua
Where,
o is the conduct iv i ty o f the material
F r o m figure 3.17, we can observe that at skip depth, the flux density declines to
about one third o f surface f lux density; at a depth o f two sk in depths, the f lux density
decreased to about one seventh o f surface flux density; at a depth o f three sk in depths, the
flux density is o n l y f ive percentage o f the surface f lux density. F r o m the last observation,
70
we can design our a l u m i n i u m core w i t h proper thickness i n order to m i n i m i z e the leakage
magnetic f lux. The m i n i m u m frequency w e are interested i n is 0 . 5 M H z , the permeabi l i ty
and conduct iv i ty o f a l u m i n i u m are 47i*10" 7 henries/meter and 3 .82*10 7 siemens/meter
respectively. Put the above parameters into equation (3.36), w e get the sk in depth o f
a lumin ium is 0 .115mm. Therefore w e choose our a l u m i n i u m sheet w i t h 0 .5mm thickness,
w h i c h is larger than 3 s k i n depths.
Depth of penetration into a conducting material
c CD tJ
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.5 1 1.5 2 penetration in skin depth
2.5
Figure 3.17 Illustration of the Skin Depth of a Conducting Material
The tank is chosen and configured i n the same w a y as the core. It is made o f
a lumin ium sheet, w h i c h provides very good electromagnetic shie ld ing. The height o f the
tank is same as the core. The radius is adjustable by compress ing or expanding as w e l l .
The m i n i m u m radius that the tank can round is 12.5 inches, i.e., the radius o f the most
outer w i n d i n g ; w h i l e the m a x i m u m radius that the tank can provide is 18.5 inches.
71
The choos ing o f the parameters above for both the core and the tank facilitate the
changing o f b and d in formula (3.27), w h i c h are the keys factors o f Z c .
3.2.4 Experiments Performed with a New Transformer in the
University Lab
W e use the same wave fo rm generator to produce one s inusoidal s ignal one at a
t ime to the one terminal o f the w i n d i n g , w i t h starting frequency o f 500 K H z and up to
2 M H z generated b y the same wavefo rm generator. The experiment c i rcui t is same as
figure 3.6 except that here both R i n and Rout are 220 ohms. A s discussed i n the T L D
method, we measure the input voltage, input current and output voltage both i n
magnitude and phase angle. Af ter impor t ing the measurements into the M a t l a b script i n
section 3.2.1, w e can get the experimental results o f Z c . T o reduce the measurement
errors and E M I nearby, w e smooth the experimental results by curve fi t t ing us ing Ma t l ab
routines. Here w e use the first order exponential f i t t ing m o d e l I and second order
exponential f i t t ing m o d e l II respectively. In the f o l l o w i n g part, we w i l l discuss about the
w i n d i n g overa l l movement both i n axia l and radial direct ion o f the transformer.
F i r s t ly , discuss about the radial w i n d i n g movement . W e vary the inner separation
b wh i l e keeping the outer separation d constant. In practice, the w i n d i n g is usual ly very
close to the core, so we vary b from 0 to 0.25 inches and to 0.5 inches, d is usual ly very
b ig compared w i t h b, so here w e set d as 2.25 inches. The Z c result curves obtained for
different inner separations are shown i n figure 3.18 and figure 3.19. B o t h figures show
that for g iven b and d, the surge impedance Z c exponent ia l ly decreases w i t h the increase
72
o f frequency, w h i c h is consistent w i t h the Z c o f a t ransmiss ion l ine. Furthermore, when b
is decreasing; in other w o r d , the inner w i n d i n g is expanding to the core as analyzed i n
chapter 1, Z c ver t i ca l ly shifts down. F o r example, i n figure 3.18, w h e n w e reduce inner
separation from 0.5 inches to 0.25 inches and then to 0 inch , Z c is correspondingly
shifted from the upper curve to the midd le curve and then to bot tom curve. It verifies the
conc lus ion in formula (3.32), i.e. Z c is direct ly proport ional to inner separation b when b
is much less than d. F igure 3.19 gives the same result and conc lus ion about the numerica l
relationship between Z c and b.
Surge Impdeance when b is very small b5=top; b7=0.25"; b8=0.5"; d=2.25" Model 2: Zc=a*exp(b*f)+c*exp(d*f)
0.000 I— 1 r— , ; , , 1 500 700 900 1100 1300 1500 1700 1900
Frequency in KHz
Figure 3.18 Zc for Different Inner Separation by T L D Method wi th Mode l II
T a k i n g Z c at 5 0 0 K H z i n figure 3.18, we can f ind that w h e n b changes from 0 to
0.25 inch, i.e. 3 % (0.25/8.5) separation change based on the inner radius o f the w ind ing ,
73
Z c changes 12% ((470-420V420) . I f the change percentage o f Z c is l inear to the change
percentage o f b, then w h e n b changes from 0 to 0.5 inch , i.e. 6% (0.5/8.5), Z c should
correspondingly change to 24%. However , Z c only changes 18% ((495-420)/420). T h i s
shows that the smal ler the separation, the more sensitive the Z c is. In reali ty, b is usua l ly
close to zero, w h i c h w i l l lead the T L D method to a very h igh accuracy. F igure 3.19 also
proves the nonl inear i ty between the change percentage o f b and the change percentage o f
Z c . It shows the h i g h sensi t ivi ty o f Z c when b is very close to the core as w e l l .
Surge Impedance Zc when b is very small b5=top; b7=0.25"; b8=0.5"; d5=d7=d8=2.25"
Fitting Model I: Zc=a*exp(b*f)
500.000
450.000
400.000
350.000
500 700 900 1100 1300 1500
Frequency in KHz
1700 1900
Figure 3.19 Zc for Different Inner Separation by T L D Method with M o d e l I
F r o m the curves i n figure 3.18 and figure 3.19, w e f ind that the distance between
the two curves is not a lways the same. The discussion about the shortest distances
between any two curves is made here and plots are as shown i n figure 3.20. The curves
74
are almost straight l ines, where the data is w e l l behaved. F igure 3.21 shows the
percentage compar i son o f the shortest distance among any two curves, where the data
w e l l behaved as w e l l .
shortest distance C21 between Zc7 and Zc5 & b5=top; b7=0.2S"
shortest distance C31 between Zc8 and ZcS & b5=top; b8=0.5"
M
shortest distance C31 between ZcS and Zc7 & b7=0.25"; b8=0.S"
u
500 1000 1500 2000
Figure 3.20 Shortest Distance among Zc5 , Zc7 and Zc8
75
35
30
25
20
15
10
Shortest Distance Percentage Comparison among Zc5,Zc7 and Zc8
K75=(Zc7-Zc5)/Zc5*100% K85=(Zc8-Zc5)/Zc5*100% K87=(Zc8-Zc7)/Zc7*100%
500 1000 1500 2000
Figure 3.21 Shortest Distance Percentage Comparison When b is Small
W h e n b is large, we do the same measurements and plot Z c versus frequency as
shown in figure 3.22. A g a i n , it shows Z c exponent ia l ly decreases w i t h the increase o f the
frequency for the same separation b. A l s o , Z c shifts ver t ica l ly w i t h the change o f the
separation. It is consistent w i t h the results i n figure 3.18 and figure 3.19, that is , Z c
decreases w i t h the decrease o f the inner separation b. In other words , w h e n a short circui t
happens, the inner w i n d i n g bulges out and therefore reduce the inner separation. A s a
result o f the reduced b, Z c decreases as w e l l . B y compar ing the percentage changes o f b
and Z c , we conclude again that smaller the b, the more sensitive the Z c is. F o r example,
when b changes from 7 .5% to 2 2 . 5 % (i.e. b changes from 2.25 inches to 3.75 inches), Z c
changes from 9 .3% to 11 .3% based on the Z c at 500 k H z .
76
Surge Impedance Zc when b is large b1=1.5";b2=2.25";b4=3.75";d1=d2=d4=2.25"
200 000
-•—Zc1
~f|—Zc2
-A—Zc4
700 1100 1300 1500
Freqeuncy In KHz
1700 1900
Figure 3.22 Zc for Bigger Inner Separation by T L D Method
Shortest distances between the above curves are shown in figure 3.23. L i k e the
curves in figure 3.20, they are almost straight lines as w e l l . T h i s should be analyzed i n
further work o f the T L D method. The shortest distance percentage compar i son is shown
in figure 3.24.
shortest distance c21 between Zc2 and Zc1 & b1 = 1.5; b2-2 .25
40
30
20
10 -
500 1000 1500 2000
shortest distance c31 between Zc4 and Zc1 & b1 = 1.5. b4=3.75
60
40
. . . ! . . _
Figure 3.23 Shortest Distance among Z c l , Zc2 and Zc4
77
11
10
g
8
7
e
5
4
S h o r t e s t D i s t a n c e P e r c e n t a g e C o m p a r i s o n a m o n g Z c 1 , Z c 2 a n d Z c 4
K 2 1 = ( Z c 2 - Z c 1 ) / Z c 1 * 1 0 0 % K 3 1 = ( Z c 4 - Z c 1 ) / Z c 1 - 1 0 0 %
Figure 3.24 Shortest Distance Percentage Compar ison W h e n b is Large
N o w we va ry the outer separation d whi le keeping the inner separation b constant.
Here, d changes from 1.5 inches to 2.25 inches and then to 3 inches, b stays at 0.5 inches.
S imula t ion results are shown i n figure 3.25. Z c obtained shows the same shape and shift
tendency as Z c w h e n v a r y i n g b.
Surge Impedance Zc when changing d d8=2.25"; d9=1.5"; d10=3"; b8=b9=b10=0.5"
-Zc8
-Zc9
-Zc10
1300
Frequency in KHz
Figure 3.25 Zc for Different Outer Separation by T L D Method
78
The shortest distance compar i son is shown i n figure 3.26; w h i l e the shortest
distance percentage compar i son is shown i n figure 3.27.
s h o r t e s t d i s t a n c e b e t w e e n Z c 8 a n d Z c 9 & d 9 = 1 . 5 ; d 8 = 2 . 2 5 4 0
3 0
2 0
1 0
o 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0
s h o r t e s t d i s t a n c e b e t w e e n Z d O a n d Z c 9 & d 1 0 = 3 ; d 9 = 1 . 5 6 0
5 0
4 0
1 0 0 0 2 0 0 0 f r e q u e n c y i n K H z
Figure 3.26 Shortest Distance among Zc8, Zc9 and ZclO
S h o r t e s t D i s t a n c e P e r c e n t a g e C o m p a r i s o n a m o n g Z c 9 , Z c 8 a n d Z c l O
K 2 1 = ( Z c 8 - Z c 9 ) / Z c 9 * 1 0 0 % K 3 1 = ( Z c 1 0 - Z c 9 ) / Z c 9 * 1 0 0 %
Figure 3.27 Shortest Distance Percentage Comparison among Zc9, Zc8 and ZclO
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F r o m the above experiments and simulations, we f ind that Z c o f the T L D method
is just l ike the Z c o f the t ransmission l ine. B y analyz ing the shift o f the Z c curves, the
overa l l w i n d i n g movement in the radial direction can be found.
Secondly , w e w i l l discuss the overal l w i n d i n g movement i n ax i a l direct ion. W e
s i m p l y lift up the transformer core and tank b y 1.5 inches, and then w e equivalent ly
lower the w i n d i n g b y 1.5 inches. F igure 3.28 shows the Z c compar i son results, before and
after the l i f t ing.
Zc8(before lifting) vs Zc16(after lifting) b=0.5"; d=2.25"
frequency in KHz
Figure 3.28 Zc Comparison for A x i a l W i n d i n g Movement
80
F r o m the compar i son curves o f Z c , before l i f t ing and after l i f t ing , w e f ind that
when the w i n d i n g is m o v i n g down , Z c shifts up and v ice versa. Therefore, the shifting
direction o f Z c can be used to determine the w i n d i n g movement i n ax ia l direct ion.
The shortest distance and the distance percentage compar i son are shown i n figure
3.29. A g a i n , the shortest distance percentage is a straight l ine i n the plots.
20 shortest d is tance between Zc8(before lifting) and Zc16(after lifting)
15 U
| 10
0 500 1000 1500 2000
Shortest D is tance Percen tage Compar ison among Zc8(before lifting) and Zc16(after lifting)
500 1000 1500 2000
Figure 3.29 Shortest Distance & Distance Percentage Comparison for Axial Winding Movement
F r o m above discuss ion, w e can conclude that by ana lyz ing the ver t ical shifting o f
Z c , we can detect the overa l l w i n d i n g movement i n both ax ia l and radial directions. In
addit ion, T L D method is very sensitive when the separation is smal l .
81
It was decided to do an invest igat ion into what type o f effects w i l l occur to Z c
when the same a lgor i thm above is appl ied to various internal fault situations. The
fo l lowing are the several different fault situations we used. F i r s t ly , w e assume that a short
circuit occurs at the connect ion point o f the two windings . F o r the second case, we
assume that a fault shunt branch w i t h 220 ohms resistance occurs at the same locat ion as
the first case. In the third case, w e assume that a fault shunt branch w i t h 330 ohms
resistance occurs at the same locat ion as the first case. F i n a l l y , w e assume that a fault
shunt branch w i t h 4700 ohms resistance, w h i c h is s imi la r to the arc ing resistance caused
by partial discharge, occurs at the same locat ion as the first case.
After app ly ing the a lgor i thm developed i n the section 3.1.2, the Z c results are
compared as shown in figure 3.30. W e can see that i n the short c i rcui t case Z c decreased
dramatical ly. Compared w i t h the Z c o f the or ig ina l curve under no rma l condi t ions, Z c o f
the short circui t case is roughly h a l f o f the or ig ina l curve. In the 220 and 330 ohms fault
cases, the Z c curves cross the or ig ina l curve. In the 4700 ohms fault case, the Z c curve is
above the or ig ina l curve. W e can conclude that w i t h the increase o f the fault resistance,
Z c begins to increase and crosses the or ig inal non-fault curve at certain fault impedances,
and continues to go up unt i l it is above the non-fault curve. A l s o , w e can detect a short
circuit fault by observ ing the dramatic decrease o f Z c .
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Zc Comparison when b=0.5" d=1.5"
450 ——-— —. . — , —
Frequency in KHz
Figure 3.30 Zc Comparison for Fault Situations
3.3 Need for Baseline Historical Data
A significant disadvantage o f the F R A technique is the need o f the baseline data
or reference values, because bas ica l ly it is a method o f compar i son rather than o f absolute
values. Unfortunately, the baseline data or fingerprints f rom the s imi l a r units are usual ly
not available. A l s o , for the power transformers w i t h the same voltage rat ing and power
ratings, the internal phys i ca l structures m a y be totally different and hence the F R A
signatures. E v e n for the same transformer manufacturer, the assembly process and
technique may change and evolve, therefore changing the signatures. These factors l imi t
the development o f the F R A technique in w i n d i n g movement detection.
83
The first paper w h i c h c la ims that there is no need for the previous baseline data
can be traced back to 1999 [35]. In this paper, the author states that most mechanica l
damages on ly occur to one o f the w i n d i n g assemblies, therefore the separate examinat ion
or measurement o f each w i n d i n g can be compared for the detection o f irregularities. The
basic assumption is that there is structural three-phase symmetry i n the core-and-coi l -
assembly. Spec i f i ca l ly , as stated in the paper " w h i l e the coi ls are quite ident ical and the
core is symmetr ic , tap changer and conductor configurations around the co i l s compose a
non-symmetr ic assembly" [35]. In a s imple example, i f phase A and phase C are
symmetr ica l ly located at the left and right sides o f phase B , then one should expect that
the transfer functions for phase A and phase C obtained b y exc i t ing and measur ing them
separately should be quite s imi lar . I f any o f the three phases has some geometr ical
change, the symmetry w i l l be broken. B y further examin ing the trend and extent o f the
asymmetry, one should be able to determine w h i c h phase causes the asymmetry.
Some experimental works have been publ ished. T w o transfer functions are used:
grounded neutral current and transferred voltage. Exper imenta l results show that transfer
function o f neutral current gives no significant indica t ion o f the w i n d i n g deformation for
both radial shifts and axia l shifts. In other words, it s t i l l presents good symmetr ic
properties for the three phases. O n the other hand, transfer function o f transferred voltage
o f the l o w voltage w i n d i n g indicates noticeable changes for the w i n d i n g movements , i.e.
the absence o f the symmet ry reflects the geometrical distort ion o f one o f the phases.
84
N o t on ly the choice o f the transfer function, but quite a few other factors, w i l l
determine the va l id i t y and sensi t ivi ty o f this no-need-of-reference method. The set-up o f
the test w i l l def ini tely affect the sensit ivi ty o f the experimental results and the assessment
o f the different transfer functions. Another major factor is the qual i ty o f the symmetry.
Different transformers have different extent o f symmetry/asymmetry i n the core-and-coi l -
assembly. It largely influences the sensit ivi ty o f the method for different transformers.
Furthermore, i f the results need to be interpreted i n more details, a large amount o f the
know-how database is s t i l l needed, " w h i c h includes an amount o f experimental
experiences and rules o f correlations o f transfer function characteristics and changes i n
core-and-coil assembly" [35].
A t the X H I t h International S y m p o s i u m on H i g h Vo l t age Eng inee r ing o f Augus t
2003, a second paper c l a i m i n g no need o f baseline data was presented b y researchers
from U S A and G e r m a n y [36]. The new technique is ca l led Object ive W i n d i n g
A s y m m e t r y ( O W A ) , w h i c h takes advantage o f the s imilar i t ies among the three phases.
O W A is a software-based vers ion o f F R A (I). Spectral Dens i t y Est imate ( S D E )
bu i ld ing b locks are used to formulate the f inal transfer function based o n the op t imum
transfer function models , w h i c h was o r ig ina l ly appl ied i n sound, m o t i o n and v ibra t ion
studies. T o improve the accuracy o f the estimated transfer function, averaging and
weight ing techniques have been used. A l s o , coherence function and random error
function are used to reduce the noise and random error. The improved transfer functions
then w i l l be compared across phases and provide a single cond i t ion number w h i c h
85
presents the weighted difference among phases. A c c o r d i n g to the paper, O W A technique
can a l low the normal phase-to-phase difference caused by the phys i ca l asymmetr ic
layout, and detect the abnormal phase-to-phase difference caused b y the w i n d i n g
displacement. S ince this technique is patented i n U S A , the detailed explanat ion o f the
software and f i rmware is not p rov ided i n the paper. H o w e v e r , this technique is more l ike
a software based mathematical tool . It is computat ional ly intensive and requires specific
and powerful software to assist. In addit ion, the disadvantages o f the convent ional F R A
exist here as w e l l , such as the test set up and the choice o f transfer function.
The variety o f the phys ica l layouts o f different transformers w i t h different ratings
complicates the va l id i t y and generalization o f the above two methods. The sensi t ivi ty o f
the two methods not o n l y depends on the choice o f the transfer function or the estimated
spectral density, as noted i n the second paper, but also largely depends on the extent o f
the symmetry o f the transformer structure under study. Furthermore, there are no
proposed cri teria for assessing the severity o f the w i n d i n g deformation. T h e assessment
criteria w i l l vary case b y case.
Notwi ths tanding , the l imitat ions and the disadvantages o f the above new methods,
they do shed light on the present investigation. The new bui l t -up transformer for
experiments has perfect symmetry, and therefore can be explored for the no-need-of
reference diagnostic method i n the future work .
86
Another significant advantage for the transmission l ine diagnostic technique over
the F R A technique is the independence from the changes i n the measur ing circuit . S ince
Z c is the characteristic impedance o f the w i n d i n g , it doesn't depend upon the external
circuit . N o matter whether the external measuring impedance changes or not, Z c is
always the fingerprint or signature o f the w i n d i n g . Z c keeps constant at a g iven frequency
and is independent o f both the source and the measuring impedance.
3.4 T L D for Other Long Winding Equipment
In power apparatus, wave propagation theory applies to homogenous lines,
composite l ines, cables, transformer wind ings and any other machine wind ings , for
example, large generator and motor windings . In a l l the above cases, the characteristic
impedance Z c and ve loc i ty v are defined according to the corresponding dielectr ic
constant, magnetic permeabi l i ty and phys ica l parameters.
W h i l e w i n d i n g movement contributes to a large percentage o f power transformer
failures, w i n d i n g movement and fault discontinuit ies i n other machinery m a y also lead to
equipment failure, economica l loss and a hazardous w o r k i n g environment for personnel.
W h i l e the T L D technique has been appl ied i n this thesis to the p rob lem o f w i n d i n g
displacement and internal faults i n power transformers, the idea is general and can be
applied to any situation where there is a change o f capacitance or inductance o f an
electr ical ly long w i n d i n g , due to w i n d i n g movement or internal faults. In particular, the
idea can be appl ied equal ly w e l l to large synchronous or induc t ion generators and to large
87
synchronous or induc t ion motors. Th i s is an important area o f appl ica t ion to be
investigated in future work .
88
CHAPTER 4 Conclusions and Recommendations for Future Work
4.1 General Conclusions
Nowadays , almost a l l the techniques and devices used for transformer w i n d i n g
movement detection are based on the F R A technique, w h i c h depends h i g h l y on the
frequency range, test set-up, external measuring circuits , h is tor ica l data, and different
phys ica l structures o f different transformers. In F R A , in order to have usable and stable
information, the frequency needed is usual ly around 4 M H z or above. H o w e v e r , the test
circuit w i l l act l ike an antenna and p i ck up other extraneous signals i n air, when the test
frequency is that h igh . T o overcome this l imi ta t ion , a new diagnostic technique,
Transmiss ion L i n e Diagnos t ics ( T L D ) , is explored i n this thesis.
T L D combines the wave propagation theory and a frequency dependent
transmission l ine mode l , and applies it to detect w i n d i n g movement i n transformers. In
this technique, by measur ing input and output voltage and current, the surge impedance
Z c o f the w i n d i n g can be uniquely obtained. Z c is the signature or fingerprint o f the
w i n d i n g and it is independent o f the external circuits . The change o f Z c can be easi ly
measured when the distributed parameters o f the w i n d i n g are altered, for example , by
looseness and movement . The smaller the separation between w ind ings and tank/core, the
more sensitive the Z c becomes.
The ma in advantage o f the T L D technique over F R A method is that Z c obtained
by T L D is a s imple exponent ia l - l ike curve for any transformer; w h i l e the transfer
89
function obtained b y F R A is a complex function o f numerous resonant frequencies
excited by the input s ignal , and the general shape o f the response curve varies for
different transformers. W h e n there are axia l or radial w i n d i n g movements , T L D gives
ver t ical ly shifted Z c curves; w h i l e for F R A , it is diff icult to correlate internal w i n d i n g
changes w i t h the measured response.
Ano the r significant advantage o f T L D is that app ly ing a lower frequency input
signal is sensitive enough to detect even a smal l w i n d i n g movement . It is not necessary to
go to higher frequencies. In this invest igat ion the m a x i m u m frequency used is on ly
2 M H z .
In the T L D method, we don ' t need to take the transformer out o f service and we
have less electromagnetic interference from the surrounding environment compared w i t h
the F R A method. Th i s is because we could use the lower frequency and Z c is
independent o f the external circuits .
Furthermore, w e can develop the formulae o f t ravel l ing t ime and equivalent
length to locate faults. The expressions for Z c , w i t h a fault impedance Z x , w i l l give more
indicat ion about the type o f fault. These formulae cou ld be used i n a future study o f
w i n d i n g movement detection.
90
4.2 Recommendations for Future Work
In the future, we need to further improve the accuracy o f the experimental results
by a better set up o f the experiments, for example, adapt advanced d ig i ta l osc i l loscope or
network analyzer, use h igh resolut ion signal generator, make the separation more un i form
along the who le w i n d i n g and reduce E M I .
H i s to r i ca l database for a g iven transformer design needs to be established. E v e n
when a transformer is s t i l l healthy, its structure may not be un i form, i.e. it m a y have
discontinuit ies. Hence , w e s t i l l need the baseline data to make the diagnostic technique
more practical and accurate.
W e also need to locate w i n d i n g distortions or damage or faults, par t icular ly when
several different types o f faults and/or damage m a y be present inside the transformer. I f
it is overal l movement , by the change percentage o f Z c , we m a y try to determine h o w the
separation has changed numer ica l ly . The w e l l behaved lines i n the shortest distance plots
may provide some hints for certain new algori thm. F o r part ial w i n d i n g displacement, it
may be possible to locate the bu lg ing or compress ing locations according to the t ravel l ing
t ime and the equivalent length o f the transmission system.
The T L D technique cou ld be further appl ied i n the movement and internal fault
detection i n other l ong w i n d i n g machines, for example, large synchronous or induct ion
generators and motors.
91
M o r e pract ica l ly , w e need to develop our algori thm/technique into an easy-to-use
diagnostic tester package i n order to apply the T L D technique to the cond i t ion moni tor ing
o f the in-service transformers. There are three stages for deve lop ing this appl icat ion. The
first stage is to port the M a t l a b scripts to C language; the second stage is to implement
the software in hardware (for example, a box w i t h chip inside and leads outside); the third
stage should be to create a s imple prototype inc lud ing input and output leads, d isplay
w i n d o w , tester box , user manuals and print interface.
92
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APPENDIX A
High Frequency Model for a Pair of Coupled Transformer Coils
q 2
Ri(w) L A ( w ) N i N , R 2 ( w )
A A / V - ^ ^ -
22
_ L C2g
-TC2g
C i r c u i t 1: O r i g i n a l C i r c u i t
Where ,
C i g , C 2 g : capacitance between w i n d i n g and tank
C i i ' , C 2 2 ' : capacitance between turns
C12: capacitance between w i n d i n g and w i n d i n g
R i ( w ) , R 2 ( w ) : w i n d i n g resistance
L i ( w ) , L-2(w): w i n d i n g inductance
98
C i 2 / a
-iff
R 1 2 ( w ) L l z ( w ) Nj. N 2
-11 £2
Where,
C i r c u i t 2 : E q u i v a l e n t C i r c u i t
a =
.N. R\2 = Rl +(jf~"> R *
.N Ll2=Ll+(-f-YL
99