relaxation phenomena in oil filled transformers
TRANSCRIPT
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
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INVESTIGATION OF ‘OFF-LINE’ RELAXATION
PHENOMENA IN OIL FILLED TRANSFORMERS
A THESIS
Submitted in partial fulfilment of the
requirements for the award of the degree
of
MASTER OF ENGINEERING (RESEARCH)
In
SCHOOL OF ENGINNEERING SYSTEMS
By
VEERENDRA LINGAMANENI
B.E (EEE)
Faculty of Built Environment and Engineering
Queensland University of Technology
BRISBANE – 4001 (AUSTRALIA)
May, 2010
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Queensland University of Technology
CANDIDATE’S DECLARATION
I hereby certify that the work which is being presented in the thesis, entitled
―Investigation of Off-Line Relaxation Phenomena in Oil Filled Transformers” in
partial fulfilment of the requirements for the award of the degree of Master of
Engineering and submitted in the School of Engineering Systems of the University is
an authentic record of my own work carried out under the supervision of
Prof. Gerard Ledwich and Prof. Birlasekaran Sivaswamy, School of Engineering
Systems, Queensland University of Technology, Brisbane.
The matter presented in this thesis has not been submitted by me for the
award of any other degree of this or any other University.
(Veerendra Lingamaneni)
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ACKNOWLEDGEMENT
This thesis is a living testimony to the numerous contributions of a galaxy of
distinguished personalities whom I had the good fortune of being associated with. I
deem it an honour and duty to acknowledge all help I received from these luminaries.
I am awed and overwhelmed as I bow to my most revered ‗mentor‘ Prof. Gerard
Ledwich, Chair in Power Engineering, Faculty of Built Environment and
Engineering, QUT. There is much for me to learn from his artistic touch to academics
and his meticulousness. It is an eternal honour to have worked as his student for such
a long spell. His support, personal guidance, thought provoking discussions and
encouragement helped me glide through the upheavals, which are inevitably in-built
into a research work.
Words desert me when I rise to offer my humble respects to my second guide,
Prof. Birlasekaran Sivaswamy, Faculty of Built Environment and Engineering,
QUT. ―It is the master who makes things easy‖ holds true for him. It is a great honour
to work under his supervision. His fathomless knowledge always turned a pearl of
advice to satiate my academic inquisitions. The support and kindness that he has laid
on to me is much appreciated.
I heartily thankful to the QUT for the scholarship they provided to me. Without their
support, it may not possible to conduct this research in a smooth fashion.
I avail the privilege to pour on paper, my regards to my parents,
Venkatarao Lingamaneni and Bhaskaramba Lingamaneni. Their blessings, love,
care, inspiration, seen and unseen blessings kept me sailing through the storms.
The active support provided by my revered wife Jyothsna Lingamaneni, and my
revered brother Srimanth Lingamaneni who has been a parent, a guide, a patron
also a trouble saver is acknowledged.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
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I thank all the souls who helped me in this herculean task.
Finally, I thank God, for all the blessings that he has showered on me and helped me
to achieve my true potential in this temporal world.
Veerendra Lingamaneni
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ABSTRACT
Power transformers are one of the most important and costly equipment in power
generation, transmission and distribution systems. Current average age of
transformers in Australia is around 25 years and there is a strong economical tendency
to use them up to 50 years or more. As the transformers operate, they get degraded
due to different loading and environmental operating stressed conditions. In today‘s
competitive energy market with the penetration of distributed energy sources, the
transformers are stressed more with minimum required maintenance. The modern
asset management program tries to increase the usage life time of power transformers
with prognostic techniques using condition indicators. In the case of oil filled
transformers, condition monitoring methods based on dissolved gas analysis,
polarization studies, partial discharge studies, frequency response analysis studies to
check the mechanical integrity, IR heat monitoring and other vibration monitoring
techniques are in use.
In the current research program, studies have been initiated to identify the degradation
of insulating materials by the electrical relaxation technique known as dielectrometry.
Aging leads to main degradation products like moisture and other oxidized products
due to fluctuating thermal and electrical loading. By applying repetitive low
frequency high voltage sine wave perturbations in the range of 100 to 200 V peak
across available terminals of power transformer, the conductive and polarization
parameters of insulation aging are identified. An in-house novel digital instrument is
developed to record the low leakage response of repetitive polarization currents in
three terminals configuration. The technique is tested with known three transformers
of rating 5 kVA or more. The effects of stressing polarization voltage level,
polarizing wave shapes and various terminal configurations provide characteristic
aging relaxation information. By using different analyses, sensitive parameters of
aging are identified and it is presented in this thesis.
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TABLE OF CONTENTS
Title Page No
CANDIDATE’S DECLARATION 2
ACKNOWLEDGEMENT 3
ABSTRACT 5
TABLE OF CONTENTS 6
LIST OF FIGURES 11
LIST OF TABLES 13
NOMENCLATURE AND ACRONYMS 14
CHAPTER 1: INTRODUCTION 15
1.1 MOTIVATION 15
1.2 OBJECTIVES 19
1.3 OVERVIEW OF THE THESIS 19
1.4 SUMMARY 21
CHAPTER 2: LITERATURE REVIEW ON RELAXATION
PHENOMENA 22
2.1 OIL FILLED TRANSFORMER 22
2.2 TRANSFORMER FAILURE 23
2.3 CONDITION MONITORING 25
2.3.1 FREQUENCY RESPONSE ANALYSIS 28
2.3.2 RECOVERY VOLTAGE METHOD 29
2.3.3 PARTIAL DISCHARGE MONITORING 31
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2.3.4 TEMPERATURE MONITORING 32
2.3.5 VIBRATION MONITORING 33
2.3.6 CURRENT MONITORING 33
2.3.7 BUSHING AND CT MONITORING 33
2.4 ONLINE OIL MONITORING 34
2.4.1 COMBUSTIBLE GAS MONITORING 35
2.4.2 MULTI GAS MONITORING 35
2.4.3 OIL QUALITY MONITORING 36
2.5 RELAXATION PHENOMENA 37
2.5.1 INSULATION RESISTANCE MEASUREMENT 38
2.5.2 POLARISATION AND DEPOLARISATION CURRENT
MEASUREMENT 38
2.5.3 DIELECTROMETRY METHODS 39
2.6 SUMMARY 41
CHAPTER 3: DEVELOPED INSTRUMENTATION AND TEST
ARRANGEMENTS 42
3.1 RELAXATION INSTRUMENTATION 42
3.2 DEVELOPED RLAXATION INSTRUMENT 44
3.2.1 FUNCTION GENERATOR 45
3.2.2 LEAKAGE CURRENT RESPONSE MEASURING SYSTEM 46
3.2.3 DATA ACQUISITION AND STORAGE 46
3.3 DEVELOPED RELAXATION INSTRUMENT SPECIFICATIONS 49
3.4 TESTED HV TRANSFORMERS 50
3.4.1 POLARISATIONINDEX 50
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3.4.2 OIL/(INSULATION+CORE+WINDING)RATIO 51
3.4.3 RESISTANCE OF THE WINDING 51
3.5 RELAXATION TESTS 53
3.5.1 EFFECT OF TERMINALS 54
3.5.2 EFFECT OF PERTURBING VOLTAGE 55
3.6 PROCEDURE TO PERFORM OFFLINE RELAXATION TESTS 55
3.7 SUMMARY 55
CHAPTER 4: EXPERIMENTAL RESULTS 56
4.1 MEASUREMENTS 56
4.2 SIGNAL CONDITIONING 57
4.3 TPICAL RESULTS 58
4.4 CONSOLIDATED RESULTS 62
4.4.1 VARIATION OF PEAK CURRENT MAGNITUDE WITH
FREQUENCY 62
4.4.2 VARIATION OF LEADING PHASE SHIFT WITH
FREQUENCY 64
4.5 SUMMARY 67
CHAPTER 5: ANALYSIS 68
5.1 THEORY OF RELAXATION PHENOMENA 68
5.2 VARIATION OF IR(f) AND IC(f) WITH FREQUENCY 70
5.3 VARIATION OF ADMITTANCE WITH FREQUENCY 73
5.4 VARIATION OF TAN (δ) WITH FREQUENCY 75
5.5 EFFECT OF VOLTAGE ON LOSS FACTOR 77
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5.6 EFFECT OF VOLTAGE ON REAL AND IMAGINARY
ADMITTANCE 79
5.7 SUMMARY 82
CHAPTER 6: DISCUSSION 85
6.1 TEST ARRANGEMENT 86
6.1.1 DEVELOPED DIELECTROMETRY INSTRUMENTATION 86
6.1.2 THE TESTED TRANSFORMERS 87
6.1.3 COMPUTER INTERFACE 87
6.2 RATIO OF SINE WAVE RESPONSE CURRENT AT TWO
EXTREME FREQUENCY RANGE LIMITS 88
6.3 TREND OF CURRENT VARIATION WITH FREQUENCY 89
6.4 TREND OF LEADING PHASE SHIFT VARIATION WITH
FREQUENCY 90
6.5 TREND OF RESISTIVE AND CAPACITIVE CURRENT VARIATION
WITH FREQUENCY 91
6.6 TREND OF REAL AND IMAGINARY ADMITTANCE VARIATION
WITH FREQUENCY 92
6.7 TREND OF TANδ VARIATION WITH FREQUENCY 93
6.8 EFFECT OF VOLTAGE ON TANδ AND ADMITTANCE 94
6.9 SUMMARY 94
CHAPTER 7: CONCLUSIONS AND SCOPE OF FUTURE WORK 96
7.1 CONCLUSION 96
7.2 SCOPE OF FUTURE WORK 99
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REFFERENCES 101
APPENDIX-A 109
APPENDIX-B 112
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LIST OF FIGURES
Figure Title Page
Fig 1.1 An ideal Power transformer 17
Fig 2.1 Life prediction using Condition monitoring data 26
Fig 3.1 Developed Lab view graphical program 47
Fig 3.2 Typical screen control, generated and captured outputs as seen in
Computer screen front panel 48
Fig 3.3 Flow diagram 48
Fig 3.4 Developed Sine wave Relaxation Instrument 49
Fig 3.5 General Layout of Connections (A, B and G are the three terminals) 50
Fig 3.6 Tested Transformers T1, T2 and T3 52
Fig 4.1 Test on T1 in 2 second period with tank grounded. Perturbation
voltage in blue is to be multiplied by 352 and the response
current in red is to be multiplied by 6.14µA. 57
Fig 4.2 Relaxation response of T1 in periods of 0.67s and 66.7s with
141VpSine 58
Fig 4.3 Relaxation response of T1 in periods of 0.67s and 66.7s with 176VpSine 58
Fig 4.4 Relaxation response of T1 in periods of 0.67s and 66.7s with 195VpSine 59
Fig 4.5 Relaxation response of T2 in periods of 0.67s and 66.7s with 195VpSine 59
Fig 4.6 Relaxation response of T2 in periods of 0.67s and 66.7s with 195VpSine 60
Fig 4.7 Relaxation response of T2 in periods of 0.67s and 66.7s with 195VpSine 60
Fig 4.8 Relaxation response of T3 in periods of 0.67s and 66.7s with 195VpSine 61
Fig 4.9 Relaxation response of T3 in periods of 0.67s and 66.7s with 195VpSine 61
Fig 4.10 Relaxation response of T3 in periods of 0.67s and 66.7s with 195VpSine 61
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Fig 4.11 Relaxation current response of T1 at different voltages 63
Fig 4.12 Relaxation current response of T2 at different voltages 63
Fig 4.13 Relaxation current response of T3 at different voltages 64
Fig 4.14 Relaxation leading phase shift response of T1 at different voltages 65
Fig 4.15 Relaxation leading phase shift response of T2 at different voltages 65
Fig 4.16 elaxation leading phase shift response of T3 at different voltages 66
Fig 5.1 Relaxation IR and IC current response of T1 at different voltages 71
Fig 5.2 Relaxation IR and IC current response of T2 at different voltages 72
Fig 5.3 Relaxation IR and IC current response of T3 at different voltages 72
Fig 5.4 Real and imaginary admittance response of T1 at different voltages 73
Fig 5.5 Real and imaginary admittance response of T2 at different voltages 74
Fig 5.6 Real and imaginary admittance response of T3 at different voltages 75
Fig 5.7 Variation of loss Factor with frequency at different voltages in T1 76
Fig 5.8 Variation of loss Factor with frequency at different voltages in T2 76
Fig 5.9 Variation of loss Factor with frequency at different voltages in T3 77
Fig 5.10 Variation of loss Factor with reference to 176V level 79
Fig 5.11 Variation of Real admittance with reference to 176V level 81
Fig 5.12 Variation of Real admittance with reference to 176V level 82
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LIST OF TABLES
Table 2.1 Condition monitoring techniques for oil filled transformer 27
Table 2.2 Common In-service Oil Diagnostics 34
Table 3.2 Name plate details of SWER Transformers 53
Table 3.3 Terminals Connections 54
Table 4.1 Multiplication Factors 57
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NOMENCLATURE AND ACRONYMS
Symbol Notation
SWER Single Wire Earth Return
SMPS Switch Mode Power Supply
TBM Time-Based Maintenance
CBM Condition-Based Maintenance
DLF Dielectric Loss Factor
PD Partial Discharge
DGA Dissolved Gas Analysis
DC Direct Current
AC Alternate Current
HV High Voltage
LV Low Voltage
CM Condition Monitoring
RVM Recovery Voltage Method
FRA Frequency Response Analysis
PI Polarisation Index
IR Insulation Resistance
CT Current Transformer
OLCM On Load Current Method
Hz Hertz
V Volt
A Ampere
F Farad
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CHAPTER 1
INTRODUCTION 1.1 Motivation
The restructuring of the electric energy business toward competition, is being of great
concern throughout the world. It moves electrical energy business towards a
deregulated global electricity market and posing new scenarios in power systems
planning and operation through a deregulated global electricity market. In a typical
deregulated environment, energy is going to be considered as a ―product‖ and its
delivery to the users as a separate ―service‖. Hence the service provided should ensure
that the electric energy providers will maintain a standard level of security, reliability
and power quality to the users. This puts the electric utilities under severe stress to
reduce operating costs, enhance the availability of the generation, transmission and
distribution equipment and improve the supply of power and service to customers.
The most important risk experienced in the power distribution is a catastrophic failure
which may result in outages for longer period of time [1]. Hence one of the easiest
ways to improve the reliability and avoid catastrophic failure is to detect incipient
faults in the electrical equipment, which can predict failures ahead of time and suggest
necessary corrective actions to be taken to prevent outages and reduce down times.
With modern educational platform of management combined with basic engineering
qualifications, asset management programs based on scientific principles are getting
into the industry [1].
Transformer is a device which converts one form of energy to another form of energy.
Transformers are one of the most important pieces of costly equipment in power
systems. Transformers represent a high capital investment in any substations at the
same time as being a key element determining the loading capability of the station
within the network. With appropriate maintenance, including insulation
reconditioning at the appropriate time, the technical life of a transformer can be in
excess of 60 years [2]. The end of life, however, can be strategic or economic.
Quantitative risk based approach can be used to aid costly investment decisions
involving transformer life, otherwise made from a subjective viewpoint [3]. Ever
since commercialization of electrical transmission began, number of transformers has
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been installed and a great percentage of them are in constant service delivering
electrical power to big cities and rural areas throughout the world for more than 40
years. A constant threat which prevails with these old transformers operating in the
deregulated power systems is the risk of experiencing a catastrophic failure ultimately
which is associated with considerable costs. Also under deregulated competitive
energy market most of the transformers are operating close to or over their operating
limits, it further increases their chances of imminent failure due to poor operational
practices. Economics and concern for the environment (as new transformers mean use
of additional environmental resources, capital, and problem with the recycling of old
transformers) no longer permit the easy replacement of transformers. Hence by
detecting the developing faults in transformers, a catastrophic future failure can be
avoided by good maintenance techniques [4]. Thus, incipient fault detection and
proper maintenance in transformers will increase asset value, prevent forced outages
with related consequential unexpected legal costs, and make existing transformers
work longer. The diagnosis should provide the following asset management
information: (i) Information on the condition of the insulation, (ii) the limits on
further use in present condition, (iii) the necessary measures to improve the condition,
(iv) the aging rate under current loading conditions and (v) life expectancy of
transformer. All these factors are predominantly dependent on the physical behaviour
of the insulation, winding and core materials, the quality of design and manufacture
and the conditions of use [4].
The different types of industrial transformers are as follows [5].
(i) Power transformer
(ii) Instrument transformer
(iii) Pulse transformer
(iv) RF transformer
(v) Audio transformer
The different types of materials used in the transformer are as follows [5].
(i) Laminated core
(ii) Toroidal
(iii) windings
(iv) Oil /air/gas cooled transformer
(v) Copper
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(vi) Paper and other insulating materials
Fig 1.1 Example of a typical Power transformer
Fig 1.2 Example of a typical Power transformer
A typical 3φ power transformer is shown in Fig.1.1 with core and windings immersed
in oil kept in a sealed tank, its HV bushings and external oil drum showing oil level
and operating temperature. Fig. 1.2 shows the operational layout in substation. The
power transformer is a static power transfer apparatus, involving no continuously
moving parts except for cooling motors and tap changers, used in electric power
systems to transfer power between circuits through the use of electromagnetic
induction. The word, power transformer is used to those transformers used between
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
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the generator and the transmission & distribution circuits and are usually rated at
500kVA and above [7]. The purpose of a power transformer in converter mode
Power Supplies is to transfer power at HV DC efficiently. In doing so, the
transformer also provides important additional capabilities [8].
• The primary to secondary turn‘s ratio can be established to efficiently
accommodate widely different input/output voltage levels.
• Multiple secondaries with different numbers of turns can be used to achieve
multiple outputs at different voltage levels.
• Separate primary and secondary windings facilitate high voltage input/output
isolation, especially important for safety in off-line applications
Oil/paper structure is the typical configuration of transformer insulation and they
undergo long term aging due to gradual physical and chemical degradation subjected
to electrical and thermal stresses in-service. The decomposed products from insulation
aging are solid, liquid and gaseous impurity species [9]. Moisture and ageing strongly
influence the dielectric properties of oil/paper insulation system of power transformer.
To assess the reliability of insulation it is necessary to know the conditions of the oil
and the paper. In recent years, new methods to assess insulation systems have been
suggested in addition to the classical insulation resistance and Power frequency loss
factor measurements [10]. Dielectric diagnostic measurements based on polarisation
and depolarisation current measurements [65] and return voltage measurements [62]
have gained significant importance over the last ten years [10]. Large number of
power transformers around the world is approaching towards the end of their design
life [11]. They are very expensive to replace especially in the existing city
environments; however, most of these installed transformers are still in good
condition and could be used for many more years. Clearly determining their reliable
operational conditions would be of tremendous importance to the electricity industry.
Well-established time-based maintenance (TBM) by experienced staff as well as
conservative replacement planning is not feasible in the current competitive market
oriented electricity industry. Condition based maintenance (CBM) and online
monitoring are gaining importance now [13]. A variety of electrical, mechanical and
chemical techniques are currently available for insulation testing of power
transformers [3]. Most of these techniques have been in use for many years, such as
the measurement of insulation resistance (IR), dielectric loss factor (DLF), partial
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discharges (PD), interfacial polarization (IP). Sampling a small quantum of oil from
operating transformer, conditional indicators like oil insulation quality, moisture
content, and dissolved gas analysis (DGA) are estimated [3].
In the relaxation test technique with DC and AC voltages, different voltage levels in
the range from 50V to 10 kV are being used in the industry to identify different
developing faults [51][60-67]. No industrial standard has come up until this stage.
There are many industrial test methods used to identify aging in oil filled transformer
and those methods are reviewed in chapter 2. In this research, I used ‗dielectrometry‘
relaxation technique which can be carried at the University research environment with
the available facilities. It is more reliable, economical and less cost effective
technique and it can provide a lot of research data for processing and scientific
interpretation. The technical details on the developed instrumentation are explained in
the chapter 3 and the analyses are presented in the rest of the chapters.
1.2 Objectives
To develop an industrial technique for testing and identifying the sensitive aging
conditional parameters in different types of field oil filled transformers. With that
points in view, the four identified objectives are listed below:
1. Develop the instrumentation for industrial use
2. Test at QUT HV laboratory with three known aged transformers and collect
the relaxation responses.
3. Analyse the data to identify aging and extract conditional aging parameters for
future industrial transformer degradation model development.
4. Identify the sensitive parameters of aging with voltage, frequency and tested
terminals.
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1.3 Overview of the Thesis
This thesis is divided into 7 chapters to present the contributions with clarity as
follows:
Chapter 1: Introduction
The chapter details the motivation to take up this research work, the identified
objectives after the literature survey, the overview of different chapters‘ content and
summary.
Chapter 2: Literature Review on Relaxation Phenomena
Critical review on oil-filled transformer, different observed failures, and different
condition monitoring methods, procedure to predict the remaining life, different
international standards for testing, relaxation phenomena, and the existing commercial
instrumentation for such relaxation studies is presented. This survey enabled to
formulate the research plan and plan on some novelty on testing procedures to identify
aging in oil-filled transformers.
Chapter 3: Developed Instrumentation and test arrangements
In this chapter, I present the hardware and software details on the developed
dielectrometry instrumentation for relaxation studies on oil-filled power transformers.
The existing details on commercial relaxation techniques, details of test transformers,
the test layout to interface the transformer and instrument and the operational
procedure to get reproducible test data are briefed. It summarizes the technical
specifications of the developed instrumentation, initial characterisation of aged
transformers and the planned tests.
Chapter 4: Experimental Results
This chapter reports the typical measured results on three aged transformers. The
study is carried by varying (i) the voltage magnitude of exciting sine polarisation
wave, (ii) the frequency of the repetitive sine wave, and (iii) the test terminals. It
briefs the calibration procedure in using the instrument, signal conditioning methods
for relaxation data extraction, typical extracted sinusoidal relaxation responses,
consolidated current magnitude and phase shift in the tested frequency range and the
summary.
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Chapter 5: Analysis
This chapter briefs the basic theory needed for the analysis. Various analysed results
with a view to identify aging in oil filled transformers are presented. It analyses the
trend of different analysed parameters with aging. The effect of polarising voltage
magnitude on changing tanδ and real and imaginary admittances is presented.
Chapter 6: Discussion
This chapter discusses the outcomes of this project with reference to different
objectives. It discusses on the developed instrumentation and the trends of different
parameters with aging, voltage and the tested terminals of transformer.
Chapter 7: Conclusions and scope of Future Work
This chapter concludes with the summary of findings with respect to the identified
objectives and lists the topics of future research areas which can be carried further.
1.4 Summary
This chapter 1 presents the motivation to take up this project, the identified objectives
of this research problem, and the overview of presented seven chapters.
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CHAPTER 2
LITERATURE REVIEW ON RELAXATION PHENOMENA
This research on relaxation phenomenon of oil filled transformers deals with the study
of dielectric insulation characteristics. A literature survey on oil-filled transformer,
various causes of transformer failure, different condition monitoring methods and the
available relaxation measuring instruments is presented in this chapter 2.
2.1 Oil Filled Transformer
Transformers are costly essential elements of electrical power systems. In a given
electrical system, transformers are commonly used to change the voltage and current
levels, to establish electrical isolation and impedance matching and to interface the
different measuring instruments. In particular, power and distribution transformers
form a vital link between power generation, transmission and distribution of different
electrical system. In the power system applications, the single-phase and three-phase
transformers with ratings up to 5OOkVA are defined as distribution transformers,
whereas those transformers with ratings over 500kVA at voltage levels of 69 kV and
above are defined as power transformers [15].
A transformer is a static electromagnetic machine. It consists of a primary winding
and a secondary winding linked by a mutual magnetic field [16]. Ferromagnetic cores
built from insulated silicon steel laminations are employed to develop tight magnetic
coupling and high coupling flux densities. The complete transformer assembly is
surrounded by a suitable electrical insulating medium. The oil filled transformer
insulation is made of pressboard insulation immersed in transformer oil. The studied
single wire earth return (SWER) transformers had one/two low voltage (LV)
winding/s with two/ four insulated terminals, one high voltage winding (HV) with two
insulated terminals, one 11 kV rated porcelain bushing connected to the high voltage
terminal, and a sealed metal tank housing all the windings, core, oil and bushings.
Both LV and HV windings with the respective solid insulation are kept immersed in
transformer oil within the tank. It should be noted that the press-board solid insulation
is impregnated with transformer oil under vacuum condition. New transformer oil
and paper insulation will have a minimum quantum of water content. As the
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
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transformer is put into operation, the loading heats up the insulation and unloading
tracks back the insulation to lower operating temperature. In general, the transformer
is operated with a temperature rise of about 60ºC from the ambient temperature. The
paper and oil have different moisture content at different temperatures. The different
types of cooling used in power transformer are (i) air cooled, (ii) oil filled, (iii) fan
cooled and (iv) water cooled. The life expectancy of transformers, regulators, and
reactors at various operating temperatures is not accurately known, but the procedure
to determine loss of life is considered to be conservative [16]. Aging or deterioration
of insulation is a function of time and temperature. Since in most apparatus the
temperature distribution is not uniform, that part which is operating at the highest
temperature will ordinarily undergo the greatest deterioration. Therefore, it is usual to
consider the effects produced by the highest temperature "hottest spot‖ [14]. The
insulation system of a power transformer is understood as the complete internal
assembly of different dielectric insulating materials. This includes the different
insulating parts and supporting structures that cover the winding wires and also the
insulation from the core, winding and tank. Such insulation systems are fabricated
following different basic principles [17]. The TrafoStar class of ABB power
transformers used in high and extra high system voltages use oil- and cellulose
insulation, mainly arranged in a barrier-type structure [17].
2.2 Transformer Failure
As mentioned above, the transformer is a complex arrangement of coils around a steel
core with the primary purpose of utilizing magnetic induction to change voltage
levels. Components such as magnetic core, primary and secondary windings, cooling
oil and paper insulation are liable to failure.
The transformer failures that most frequently arise in practice are [16]:
1. Failures in the magnetic circuits, i.e. core, yokes, and adjacent clamping
structure;
2. Failures in the windings;
3. Failures in the dielectric circuit, i.e. in the oil and major insulation;
4. Structural failures like clamping of windings and core laminations.
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Most transformer failures occur due to faulty manufacture, short circuit faults, and
abnormal transient or sustained over load operating conditions, premature insulation
failure, and accelerated aging [16]. These transformer faults can be divided into two
main classes:
1. Internal faults, and
2. Overloads and other externally occurring different stress conditions.
Internal faults are faults between adjacent turns or parts of coils, or faults to ground on
terminal or on parts of windings. Overloads and externally applied operating
conditions include over-current, over-voltage, external short circuits and reduced
system frequency [20]. A study of the breakdown records of modem transformer
which occurred over a period of years shows that between 70-80% of the number of
failures are caused internal winding faults [21]. These winding faults are due to the
degradation of the insulation system. The purpose of electrical insulating materials is
to insulate components of a transformer from each other and from ground, and at the
same time providing mechanical support for the components. Degradation means a
reduced insulation quality, which tends to cause a breakdown in the dielectric strength
of the insulation.
During the operation of the transformer, a strong electric field is applied to the
dielectric material. It can result in the aging and deterioration of the insulation. The
relevant factors generally recognized as causing the aging and deterioration of an
insulation include thermal stresses, electrical stresses, mechanical stresses, moisture
and so on [22]. Thermal stresses are caused by the internal heating due to current
overloads combined with rise in ambient temperatures. Under the normal operating
conditions, high voltage gradients will be below the breakdown voltage that does not
cause the detectable aging. However, at elevated temperatures electrical stresses may
act to further accelerate material degradation. Mechanical stresses are caused by
wrong assembly configurations, bad manufacturing techniques and vibration
generated due to short-circuit or over-voltage phenomena in power network. Moisture
is another major cause for the dielectric breakdown properties. It can form a
conductive path on the surfaces of material or react with the material to cause
chemical degradation.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
25
The structure of a dielectric may be altered significantly during the aging process, and
these changes will affect the electrical properties of the dielectric even before
insulation failure occurs. The relaxation processes within the dielectrics change with
aging to create characteristic dielectric losses. As the structure of the dielectric
molecules alters during aging, the dielectric characteristics and electrical properties
change. Eventually, the aging and degradation process of a dielectric may lead to a
complete dielectric failure [20]. For a transformer, the deterioration of the insulation
between turns results in the dielectric breakdown resulting an internal short-circuit
fault. The period before the short-circuit but with the dielectric in a degraded state is
referred to as incipient fault.
To avoid this failure in transformers, the dielectric conditions should be monitored.
Apart from that, mechanical conditions are also monitored and the entire process of
checking the various conditional trends is called ‗condition monitoring‘ [20].
2.3 Condition Monitoring
Condition monitoring is the process of monitoring a single parameter or many
parameters of degrading conditions in machinery. It is a major part of predictive
maintenance. The use of conditional monitoring allows maintenance to be scheduled,
or other actions to be taken to avoid the consequences of major failure. Predictive
Maintenance helps to predict the possible time of failure. CM systems can only
measure the deterioration level. It is typically much more cost effective than allowing
the machinery to fail [23]. Industry uses different types of CM techniques like
Recovery voltage method (RVM) [62], Frequency response analysis (FRA) [21],
Dielectrometry [60] [64], and Partial discharge (PD) etc [22]. Fig.2.1 shows the life
prediction of transformer through oil and paper degradation data, relaxation
measurement using RVM technique and from historical failure rate data. The Table2.1
lists the different condition monitoring techniques and the best method suitable for
diagnosing different classified known faults within the transformer.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
26
Fig 2.1 Life prediction using Condition monitoring data [24]
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
27
Table 2.1 Condition monitoring techniques for oil filled transformer [24]
There are a number of different techniques available to identify the developing faults
in the transformer by external measurements. Some of them are as follows: (i)
Frequency response analysis (FRA) (ii) Recovery voltage method (RVM) (iii) Partial
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
28
discharge monitoring (iv) Temperature monitoring (v) Vibration monitoring (vi)
Current monitoring and (vii) Bushing and CT monitoring.
2.3.1 Frequency Response Analysis (FRA)
Information about transformer mechanical condition can be extracted from the
transformer winding frequency responses on individual winding or between coupled
windings[21][23]. The winding behaves as a complex RLC network and its transfer
function represents according to the system theory the characteristic behaviour of a
linear shift invariant system. Aging or deformation will cause small changes in the
geometry of the winding leading to changes of the corresponding localized
capacitances and inductances and consequently to a change in the FRA result.
Different methods exist in order to determine the transfer function of a transformer
winding [25].
High Voltage Impulse (HVI) – time domain method
Low Voltage Impulse (LVI) – time domain method
Frequency Sweep Analysis – frequency domain method
Both HVI and LVI techniques are based upon application of an impulse voltage
across the transformer terminals and measurement of current across output terminals.
The transfer function between different terminals namely input and output windings
and windings on the limb can be calculated to know the information about the
transformer impulse response distribution. High Voltage impulse as the name
suggests relies on application of a few single high voltage impulses in the range of kV
[26] across the winding.
While the LVI method relies on application of low voltage impulses with the
magnitude in the range of 100 mV to 10 V peak of either polarity in a cyclic way
across the winding. HVI method suffers from poor frequency spectrum of the input
signal and is unable to detect minor changes in the winding. The advantage of LVI is
that it allows the adjustment of steepness of the applied impulse in order to obtain a
wider frequency band [27].
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
29
FRA measures the impedance or transferred impedance of the transformer winding. It
is measured as a function of the frequency by applying a low-voltage sinusoidal test
signal with variable frequency in the range from 100 Hz to 10 MHz. The signals are
measured at discrete frequencies to determine amplitude and phase of the transfer
function for the desired full frequency range. Final aging or degradation assessment of
the test is based on verification of repeated recorded signals with original recorded
signals during installation. FRA is free from superimposed environmental noises,
however relatively longer duration of time is required to finish all the frequency
segmented measurements in different windings of the transformer [27]. Frequency
response analyser detects mechanical and electrical changes of the core and the
winding assembly of power transformers by using the SFRA method without de-
tanking the structure. SFRA stands for Sweep Frequency Response Analysis.
Winding or core defects can be identified after faults, mechanical shocks or
transportation using this external measurement. It offers a valuable opportunity to
improve the reliability of transformers, to reduce maintenance costs and, most of all,
to avoid expensive unexpected outages [36].
2.3.2 Recovery Voltage Method
Moisture gets formed due to degradation of paper insulation. Moisture gets distributed
between paper and oil insulation. Due to ageing and thermal loading, the distribution
of moisture content varies [29]. Chemical technique – Karl Fischer technique may
lead to many inaccuracies in determining moisture content in oil and then predicting
proportional moisture content in paper at that temperature. Polarisation technique
using relaxation characteristics of polar components like water is being used in the
industry as they are non-invasive [28]. To detect ageing or moisture content it is
necessary to analyse low frequency part of polarisation spectrum of dissipation factor.
A tanδ measurement using frequency domain technique known as low frequency
dielectrometry can identify the degradation. But finding a sinusoidal high voltage
source in the frequency range of 0.001 Hz is very difficult and the instrumentation is
expensive [28] [64] [66]. Industry uses the simple time domain method known as the
recovery voltage measurement (RVM) [24] [62] [65].
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
30
It was found that dc measurement of insulation resistance (IR) and the estimation of
Polarisation index (PI) do not provide the complete information on polarisation
process [29] [61] [63]. Cases were reported where electrical motors having good PI
were found to have contaminated windings and also motors having poor PI had no
problems in the winding insulation [29]. To resolve this, dc absorption technique with
one thousand seconds charging time followed by discharging test was developed to
identify the degradation [30]. Recovery Voltage Method for transformer seems to be
developed from this test. In RVM, insulation is charged for a number of known time
intervals and then shorted to ground for pre-decided short time interval. The charging
voltage varies from 50 V to 2000 V. Then the shorting is removed and the recovered
voltage is then measured using high impedance circuit across the insulation after
open-circuiting all the connected terminals. The dominant polarisation time constant
is estimated from RVM time domain spectra which are related to degradation [62].
The diagnosis is done by comparing the initial slope, the maximum of the return
voltage and the time at which the maximum of the return voltage occurs in the
complete spectrum of measurements. Good correlation has been reported with
moisture content [52].
Charging current is given as the sum of the polarisation current and the conduction
current. Polarising current is dependent on material property and state of ageing. The
polarisation of dielectric can be expressed as sum of various slow polarisation
phenomena like ion migration, slow relaxation and interfacial polarisation. Care must
be taken in the interpretation of results of RVM, in particular the relative effects of
moisture, ageing and temperature [32].
This RVM technique is known as time domain based dielectric relaxation technique
and a costly microprocessor based commercial portable instrument is released into the
market around 1995 [62]. Until today, no standard is brought in to use this method in
fixing the voltage level and in the interpretation of the results. Since it involves with
high impedance voltage measurement, this test is done on a clear day with proper
good quality cables. It is learnt that time domain industrial recovery voltage
measuring unit (RVM) takes about 5 hours of test time for one set of measurements
[32].
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
31
2.3.3 Partial Discharge Monitoring
Partial discharge measurement is the most effective method to detect developing
incipient faults in the electrical system [31]. As the electrical insulation in a
transformer begins to degrade and breakdown, there are localized discharges within
the electrical insulation. Each discharge deteriorates the insulation material by the
impact of high-energy electrons, thus causing chemical reactions. During these
discharges, ultrahigh frequency waves are emitted. Most incipient dielectric failures
will generate numerous partial discharges before the catastrophic electrical failure.
Partial discharges may occur only before failure but may also be present for years
before any type of failure. A high occurrence of partial discharges can indicate voids,
cracking, contamination, or abnormal electrical stress in the insulation. Because of
this importance, the on-line partial discharge measurements are used in diagnosing
potential catastrophic failures in an operating transformer.
PD couplers/sensors to detect frequencies in the range of 1 to 1500 MHz are used in
the industry [31]. Also UHF waves produced by the partial discharge in oil/paper
insulation generate pressure waves that are transmitted through the oil medium. Low
frequency piezoelectric sensors can also be used to detect these waves [32]. These
sensors can be placed on the outside of the tank to detect the acoustic wave impinging
on the tank. The advantage of partial discharge sensors is the ability to estimate the
actual location of insulation deterioration using multi sensors. By placing several
partial discharge sensors around the transformer tank, it becomes possible to pinpoint
the exact location of the discharges [32]. Most often the deterioration occurs at the
start of the coils near the high voltage side of the transformer. The disadvantage to
partial discharge sensors is that they are greatly affected by the electromagnetic
interference in the substation environment. Therefore, signal processing techniques
are often used to improve the signal to noise ratio in order to make the measurements
effective [33].
Recently on-line partial discharge detection technique based on a fibre optic sensor
has been developed. In this technique, a laser diode transmits light into a fibre optic
coupler that has the light propagated across an air gap inside a self-contained
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
32
diaphragm, lined with reflective gold. The reflected light combines with the small,
reflected wave inside the fibre optic coupler to produce an interference pattern that
differs as the air gap changes. In this way, the acoustic waves produced by partial
discharges can be detected [31].
2.3.4 Temperature Monitoring
Thermography is effective for checking many different transformers quickly to see if
there is any outstanding hot spot problem externally [36]. Excessive generated heat
due to different faults results in rise in temperature in oil, the bushings, pumps and
fans which is an indicator of developing faults in the transformer. Also high surface
temperature distribution at the top of main tank has been known to indicate oil
deterioration, insulation degradation, and water formation [36]. Increase in operating
temperature deteriorates the winding insulation and the dielectric properties of the
mineral oil and other insulation begins to degrade increased rate. The accelerated
chemical reactions deteriorate the insulation at much faster rate. Most common sites
of temperature monitoring on transformer are on the top end of windings and core of a
transformer as the heated oil tries to move up. Thermal sensors mounted on the top
end of core are used for protection and monitoring purposes. The advantages of
temperature sensors are that they are simple, cheap and reliable.
Focused infrared based camera is used to measure the external hot-spot temperature
and its distribution from a very safe distance. They are able to detect temperature
gradients on external surfaces of the transformer and can locate easily the overheating
of bushing or fan bank or tank surface heated area. On-line monitoring of temperature
can be achieved with thermocouples placed externally on the transformer and
windings, and can provide real-time temperature variations with load at various
locations on the transformer. Expensive distributed fibre optic temperature sensor for
power transformer condition monitoring is available in the market [31].
Transformer models for predicting temperature of the oil and winding have been
developed to identify hot-spot location [33]. Accurate complex temperature
distribution models using Kalman filters and adaptive Hopfield networks have been
developed which need input from external thermal detectors [33, 34]. The models are
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
33
found to be pretty accurate in predicting thermal state of a tested known transformer
after some training with known data.
2.3.5 Vibration monitoring
Vibration monitoring deals with the mechanical malfunctions in a transformer and it
senses the emitted frequency spectrum in the range from 10Hz to 3 kHz. Most
mechanical failures associated with insulation structure clamping are identified. In
transformer, cellulose insulation on the coils of the transformer shrinks with aging.
The shrinkage causes loosening of the clamping pressure on the coils and can lead to
short-circuit between turns [35] [37]. Short circuits often can lead to the catastrophic
failure of the transformer and is the most common cause of transformer breakdowns.
Recently, demand has increased for low-noise power transformers as well as large-
capacity and small-size power transformers. To reduce transformer noise, it is
necessary to reduce vibration of their iron cores, which is caused by magnetostrictive
forces of silicon iron insulated laminations. The vibration measurement is used to
diagnose loose structure within power transformers and the test is called the on load
current method (OLCM). It can acquire the fundamental frequency component of the
core vibration signal without testing the transformer at the open-circuited condition
[37].
2.3.6 Current Monitoring
Load current on the primary, secondary, and tertiary coils can be used to access the
state of the transformer. Imbalance current in the transformer is an indicator of
developing problem or impending failure [36]. Consumption of additional current by
cooling system or drop in current levels of cooling systems is an indication of fan
bank failure. Similar monitoring is done on tap-changer drive motor current.
2.3.7 Bushing and CT Monitoring
Other accessories in the transformer are bushings, load tap changers (LTC), and
cooling system. Any faults in insulation accessories will lead to catastrophic failure of
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
34
insulation [42]. Similar to the insulation around the transformer coils, there are also
layers of foil and oil impregnated insulation that surrounds the transformer oil-filled
bushings and current transformers (CTs). There is a small amount of charging current
that flows when the system is in operation. Changes in this charging current can
indicate degradation in the geometrical structure of the insulation. As the insulation
degrades, carbon deposits can short circuit some of the layers and increase the stress
on the remaining layers. This leads to a decrease in the capacitance and the charging
current changes. Eventually, the remaining layers of insulation cannot take the
increased voltage stress and the system fails, often catastrophically [32]. Some of the
causes of bushing failures include changing dielectric properties with age, oil leaks,
design or manufacturing flaws, or the presence of moisture in oil. Sensors have now
been used to monitor the health of bushings. The InsAlert monitoring probe from
Square D Co, the Intelligent Diagnostic Device (IDD) for bushings [32] and current
transformers from Doble [32] have the ability to detect abnormalities and possible
failure conditions in the bushings and CTs.
2.4 Online Oil Monitoring
Experience has shown that most internal transformer condition problems can be
detected through oil analysis [1]. There are a number of diagnostics standards that are
commonly applied to in-service transformer oil samples (Table 2.2). Of these, a few
tests are carried continuously by online oil monitors [14]. These monitors can be
roughly grouped into three categories: 1. Combustible Gas Monitoring, 2. Complete
Multi-Gas Monitoring, and 3. Oil Quality Monitoring.
Table 2.2: Common In-service Oil Diagnostics [22]
Test ASTM
Designation
Comments
Colour
D1500 Increase in colour indicates
deterioration or contamination
Visual Examination D1524 Cloudiness or sludge should be
investigated
Dielectric Breakdown
Strength
D877
D1816
Measure oil‘s ability to insulate.
Sensitive to contaminants, moisture
Power Factor
D924 Detects polar contaminants
Dissolved Gas Analysis
D3612 Detects and identifies incipient faults
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
35
Interfacial Tension D971 Detects polar contaminants and
oxidization
Neutralization Number D974 Measures acidity of oil indicator of
deterioration
Specific Gravity
D1298 Can detect contamination
Moisture Content
D1533 Moisture can damage insulation
2.4.1 Combustible Gas Monitoring
Some of the commercially available combustible gas monitors are as follows: GE
Hydran [40] and Morgan Schaffer Calisto [14]. The GE Hydran method passes the
transformer oil over a special membrane, and hydrogen and other combustible gasses
permeate through the membrane to be sensed by selective gas sensors. It is calibrated
to the proportional dissolved gas content of the oil. Hydran method is sensitive to
nature of combustible gas and the method is not capable of distinguishing different
types of gases. In the absence of ability to distinguish, it‘s difficult to know exactly
the concentration of different individual gases and the exact cause of defect. In fact
it‘s possible that different combination of individual gases might result in same value
of the current. The only way to overcome this problem is whenever reading on oil-gas
monitor changes, extract an oil sample and send it to the chemical laboratory for
immediate quantitative gas distribution analysis using costly gas chromatography
techniques [40].
Morgan Schaffer Calisto method [14] was developed in early 1980‘s. This method
extracts hydrogen using capillary tube probe from the transformer oil after diffusing it
through polymer baffles. The advantage (or disadvantage) of this method is that it‘s
insensitive to other combustible gasses. The concentration of extracted hydrogen is
measured using a thermal conductivity detector which relies on the thermal
conductivity of hydrogen gas volume.
2.4.2 Multi Gas Monitoring
Multi gas monitoring relies upon the use of different integrated circuits (ICs) that have
been developed to measure the concentration of dissolved gases and moisture content
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
36
in the transformer oil. Some of the examples of commercially available combustible
gas monitors are Serveron Online Transformer Monitor [56].
Serveron Online Transformer Monitor is one of the most sophisticated measurement
techniques and is commonly used instrument for online monitoring of multiple gases.
It is capable of recreating the laboratory gas chromatograph in real time [58]. It can
monitor and measure eight gases simultaneously and is also capable of measuring
moisture concentration [22]. The advantages of Serveron monitor are that it can
replace manual sampling, off-site laboratory analysis and capable of detecting sudden
changes with load. The accuracy of the gas estimation is better than the laboratory
dissolved gas analysis [42]. The disadvantage of Severon monitor is that it is costly
method for diagnosis. Kehnan Transfix Monitor [20] uses photo acoustic
spectroscopy (PAS) to measure concentrations of different gases and moisture. The
principle of operation of Kehan Transfix Monitor relies on absorption of infra red
light by gas, which heats the gas. The sudden heating makes the gas to expand
suddenly producing a sound wave (or thunder). Different dissolved gasses absorb
different wavelengths of the electromagnetic radiation which can be used to identify
different gases. The intensity of the sound is proportional to the concentration of the
gas. The advantages of this method lie in PAS technique, which unlike gas
chromatography, does not require any carrier gas or calibration. Once again the
disadvantage of Kehan Transfix Monitor is the higher price of the monitor [20].
2.4.3 Oil Quality Monitoring
Dissolved gas analysis (DGA) is performed in the industry for more than 60 years as
the method is non-invasive and it can be carried in on-line mode by sampling the oil.
Most of the incipient faults at high stressed area generate 9 different gases which get
dissolved partly in oil and also diffuse to the sampling location. By proper sampling,
most of the incipient faults in the oil may be detected by gas component analysis [22].
This method monitors the dissolved gases in the transformer oil in on-line mode to
assess the condition of the transformer.
Oil Quality Monitoring is an inexpensive method of monitoring quality or purity of
the oil based on its dielectric strength. A Dielectric breakdown strength test
electrically stresses the oil to the point of failure. This can be the most accurate
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
37
measure of the quality or purity of the oil and its ability to perform the job of
electrical insulation in the transformer [44]. However, destructive nature of these tests
makes it unsuitable for repeated testing and online analysis. Most common method of
online Oil Quality Monitor is the Weidmann Centurion [42]. This method uses special
high speed technology to limit any breakdown energy from damaging the oil. The
advantage of Online Quality Monitoring test is that it‘s an inexpensive method and
can be easily deployed on any transformer equipment. However, the disadvantage of
Online Quality Monitoring test is that it is sensitive to moisture, carbon and metallic
particulates, fibrous and other impurities, and any burning or degradation of the oil in
the tested localised oil volume. Moisture content in oil and paper at an operating
temperature is a very strong indicator of the health of paper insulation in a
transformer. Moisture in oil is measured by a specialized integrated circuit(IC) which
is in contact with the oil. The IC heats the oil to a constant known temperature [20]
and senses the moisture content.
Other non-destructive techniques [48] such as time-domain dielectric spectroscopy,
laser intensity modulation method and pulsed electro acoustic method are used for
research and diagnosis of insulation degradation but these popular techniques have no
practicality as engineering tools to manage the aging apparatus. A number of these
space charge ‗‗dielectric response‘‘ measuring techniques have been reviewed by
Ahmed [49].
2.5 Relaxation Phenomena
Since it is planned to research the relaxation phenomena in oil filled transformers,
literature survey is carried on this relaxation phenomena. In the study of dielectric
systems, the analysis of the dielectric losses associated with relaxation phenomena
can identify the aging effects [44] [45]. Non-destructive relaxation phenomenon in
power equipment was studied to extract the condition indicators [46-48]. The basic
theory is that when dielectric material is subjected to low electric perturbation, E (t)
thereby avoiding any destructive or non-linear effects, dipoles in the dielectrics
becomes excited. It induces new delayed response polarization, P (t) due to electronic,
ionic, dipolar and interfacial polarization processes [45] [46]. The change in
polarisation and the resistive leakage currents with E (t) is effectively used to
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
38
diagnose the aging in power apparatus. There are costly commercial relaxation
instruments which are being used to estimate the degradation and moisture content in
oil-filled insulation without opening the tank of transformer[52][60][62][64]. They
evaluate the condition of transformer from the external measurements after isolating
all the terminals.
2.5.1 Insulation Resistance Measurement
The classical insulation resistance measurement with time is used to test the
degradation. On application of DC voltage, the dielectric gets polarised and the
current supplied by the source to the dielectric reduces gradually. In simple terms, the
insulation resistance increases slowly depending on the dielectric relaxation
behaviour. Industry uses the variation of insulation resistance with time to identify the
degradation [63]. It estimates the ratio of insulation resistance measured at 10 minutes
to the insulation resistance measured at 1 minute after the application of DC voltage.
This ratio is called polarisation index (PI) and the status of insulation is classified into
four levels. A ratio around 1 or less than 1 needs immediate attention for servicing the
insulation. A dc voltage level from 100 V to 10 kV is used to different HV insulation
systems. A number of different commercial instruments are available for use [61].
Before the application of dc voltage, the terminals are shorted for more than 15
minutes to drain any trapped embedded charges in the insulation. This is a time
domain method of measurement for a period of about 10 minutes.
2.5.2 Polarisation and depolarisation current measurement (PDC)
The polarisation and depolarisation current measurement is used to detect aging of the
insulation in a non-destructive manner [2] [4] [9] [41] [48] [51] [65]. The PDC
measurement is a transient current measurement technique. It is simple, but current
varies significantly depending on the condition of insulation. The order of current
magnitude and the rate of change in current with time are different for different
insulation systems. The accuracy of the measurement of current magnitudes and times
is important for signal processing as it contains relaxation information. In PDC, the
measured current due to polarization and depolarization will be comparable to
background noise, especially in a generating station.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
39
A voltage in the order of 100 V to 2000 V is applied to the insulation and the
dielectric will be polarised. A decreasing polarising current with time is recorded and
the system will be polarised until there is not a significant change of polarising current
with time. This time may be from 1s to a few hours depending on the condition of
insulation and the change of current will be from a few amps to pico amps. Once a
steady state is reached, the power supply will be removed and the terminals will be
shorted to record the depolarisation current. Commercial instrument based on [51] is
released into the market around 2000 and a number of companies offer this
technology now at a competitive price. It is mathematically proved; the depolarisation
response behaviour will be the dielectric response function [46].
The advantage of PDC is that its test procedure is simple and the measurement
duration is considerably shorter than RVM. The interpretation of the measured results
in both RVM and PDC is very difficult as the measured dielectric response contains
much information pertaining to the interfacial and dipolar relaxation mechanisms.
This technique is also not standardised due to many uncertainties in measurement and
the level of voltage to be used even though, the technique is available from 2000. One
PDC measurement takes about three hours of test time. This method is in use in the
industry to identify the degradation trend.
Detailed presentation on RVM technique is presented in section 2.3.2. All these dc
time domain methods are simple to use but an extensive care must be made during the
measurements to get reproducible results in such a long period of measurements.
In next section, the literature survey on relaxation measurement in frequency domain
is presented.
2.5.3 Dielectrometry methods
The relaxation measurement is done in frequency domain extensively. The historical
condition monitoring technique uses 50 Hz high voltage testing using Schering bridge
[46]. The insulation is tested at rated voltage by including the apparatus in a Schering
bridge loop which measures the ratio of in-phase 50 Hz current to quadrature
capacitive 50 Hz current. That ratio is known as loss factor or tanδ. A factor of 0.001
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
40
is considered as good insulator. It is an expensive test and it needs very good
technical expertise in HV testing.
Low voltage and low frequency domain measurements are used by different dielectric
scientists [12] [54] to characterise the insulation. The team from ABB Sweden and
Swiss Federal Institute of Technology used this technique to characterise the
transformer insulation [67]. The outcome of this student project is converted into a
commercial dielectrometry instrument IDA202 around 2000 by Programma [64].
Even though this instrument is expensive and it is able to characterize the insulation
from a frequency of 1 µHz to 1000 Hz automatically with a sinusoidal voltage source
of peak magnitude around 150 V. A few other companies like GE and Omicron [60]
started manufacturing this type of dielectrometry commercial instrument with an
extensive software support. This is now being used in the industry widely. HV
versions of this technique are also in the market [66]. It can generate very low
sinusoidal frequency in the range of 0.1 to 0.01 Hz from 25 kVac to 200 kVac. It is
normally used to test the polymer HV cable.
This technique is used to determine the moisture content in oil-paper insulations of
power transformers, CT's and VT's, bushings and power cables by analysing the
dielectric response. This method can be applied to low and high frequencies, but it
needs a lot of measuring time for very low frequencies [60].
After the literature survey, it is understood that aging can be identified using the
relaxation instrument. It is found that all the existing instruments can be used only in
‗Off-line‘ mode of testing. QUT is interested in coming up with ‗On-line‘
monitoring techniques for power transformers. It is planned to develop our own
instrumentation, as the ultimate objective of the QUT condition monitoring projects is
to come up with on-line relaxation measuring technique for power transformers. The
initial development is concentrated on developing a reliable and portable ‗Off-line‘
relaxation measurement unit to identify aging with known transformers. For industrial
site measurements with a number of field transformers, the period for testing is
planned to be about 5 to 10 minutes for one set of measurement. Digital
instrumentation is planned to generate drift-free controllable low frequency signals
and to record data for further analysis. Reported analysis will be carried out with the
test data to identify the aging parameters.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
41
2.6 Summary
In this second chapter, the existing knowledge for this relaxation study on
transformers is reviewed. As a new entrant to this research field, literature survey is
made on oil-filled transformer, possible developing faults, different condition
monitoring techniques and relaxation phenomena in transformer insulation. In section
2.5, a survey of existing commercial relaxation instrumentation is made and the
research plan is formulated. The novel contribution of this work is to investigations
on relaxation measurement by varying polarising voltage level and by changing
terminals of the transformer terminals to identify the aging trend on three known
power transformers are planned.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
42
CHAPTER 3
DEVELOPED INSTRUMENTATION AND TEST
ARRANGEMENTS
As the main objective of this study is to identify relaxation phenomena with aging in
oil filled transformers, it is planned to develop relaxation instrumentation in low
sinusoidal frequency domain for such studies. Once the test arrangement is developed,
it is planned to carry a series of relaxation measurements on oil-filled transformers for
different analysis. This chapter reports on the developed relaxation instrumentation,
its specifications for use, the test layout and the details of the tested transformers.
3.1 Relaxation Instrumentation
Literature studied the relaxation phenomena with DC and AC voltages at different
voltage levels. No industrial standard has come up until this stage in fixing the
frequency range and magnitude of polarisation voltage. The relaxation measurement
as described in section 2.5 can be carried in time or frequency domains.
Time domain methods:
DC: With DC voltage, age old ‗megger test‘ is in use [19] [61] [63]. DC voltage
levels up to 5 kV of either polarity are being used depending on the voltage rating of
the tested apparatus. Any insulation resistance (IR) value greater than 100 M is
accepted for safe operation. An improvement in this technique is the measurement of
variation of IR with time. Depending on the polarisation behaviour of insulation, IR
will vary with time. Insulation quality factor known as ‗Polarisation Index‘ (PI) is
defined as the ratio of IR measured at 10 minutes and IR measured at 1 minute time
after the DC voltage energisation. A four level deciding factors like : >3 – very good;
>2 – good; >1 – ok; < 1 – immediate attention. It is widely in use as it is a simple test
and it needs less costly instrumentation. The procedure to carry the test is not
particularly complicated. The only requirement is that the injected charge should be
discharged completely before and after carrying of the test. The safety procedure
should be followed during HV application.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
43
An improvement in this technique is called the polarisation and depolarisation current
measurements (PDC) [51]. In this test, the insulation will be energised for a period
until the variation in current (known as polarisation current) is negligible with time.
After that, the DC source is isolated and the insulation will be shorted through an
ammeter and the current known as ‗depolarisation current‘ will be recorded with time.
The measured current will be very low in the range of µA to pA, and it will be
changing very fast with sampling time. With industrial ambient noise, the
measurement to a period up to 1 hour or more requires a good knowledge of leakage
current measurement. No standard is set so far on the applied DC voltage level and
polarity of the applied voltage. The commercial instruments provide a voltage level up
to 2 kV [65]. The variation of depolarisation current with time is analysed and the
trend is fitted to electrical RC equivalent circuits to identify the degradation. It should
be noticed that the injected DC polarisation current should be completely discharged
before and after the test as the trapped charge may induce degradation. The technique
is a time consuming test and it requires good skills to identify the defects.
For high rating apparatus especially on polymer cables, another DC voltage technique
known as recovery voltage method (RVM) is in use [50][62]. The details on this
technique are described in section 2.3.2. In this the insulation of the apparatus is
charged for a certain period, shorted for nearly half of the charging period and then
the terminals will be completely open-circuited. The injected charge with slow
relaxation time will relax slowly and charge the geometrical capacitance of the
terminals slowly. This rises the voltage at the terminals and is known as ‗recovery
voltage‘ (RV) and then it decays slowly. This test will be repeated with various
charging times. By measuring the peak of RV and the initial slope of rise with
different charging time, various degradation factors are identified. It is time
consuming test with the requirement of very high input impedance to measure RV.
Charging, discharging and open-circuited timings are to be controlled. The
interpretation of the responses and the evaluation procedures are a bit complicated. A
properly trained person alone can carry this relaxation measurement.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
44
In all the DC tests, ambient conditions play a major role by introducing the leakage
phenomena externally. Also, the injected charge due to uni-polar voltage should be
completely discharged.
Frequency domain methods:
AC: AC test is the more preferred test in the industry as it polarises and depolarises in
the repeated cyclic periods. HV Schering bridge test at 50 Hz is used to identify the
development of loss mechanism for more than 70 years [46]. It estimates the loss
angle – tan which is nothing but the ratio of in-phase to quadrature current
components of AC insulation current. It is normally tested at the rated voltage of the
apparatus or as specified by the user.
An extension of that principle is known as ‗dielectrometry‘ which is widely used by
material scientists to characterize the dielectric materials. It used a voltage in the
range of 10 V with frequency range from 1 Hz to 1 MHz [12]. ABB group used this
idea to identify the degradation in oil-filled transformers. They used a voltage level
around 110 Vac with a frequency range from 1 µHz to 1000 Hz to suit the industrial
test time requirement [67]. The instrument is very expensive but it is bipolar
measurement.
It is planned to use that technique as this may be extended for future ‗on-line
relaxation measurement‘. With the limited budget, an attempt is made to develop in-
house QUT relaxation instrumentation to generate low frequency drift-free AC sine
waves and measure the response relaxation currents in the order of a few nA.
3.2 Developed Relaxation Instrument
After a series of planning, a drift free high voltage amplifier with a gain of 20 to
generate AC voltage in the range of 200 V with a frequency response from 0.001 Hz
to 10 Hz is designed and tested for use. The designed HV amplifier is tested with
normal analog function generator and digital oscilloscope. It is found that many of the
analog function generators were drifting with varying asymmetrical characteristics in
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
45
the tested low frequency ranges. Hence, (i) A low frequency function generator to
generate distortion free programmable sine wave shape, (ii) a low leakage response
current measuring system and (iii) simultaneous digital data acquisition and storage of
function generator sine wave form and the corresponding leakage response current are
designed and tested for use. The details are presented below:
3.2.1 Function generator
Controllable waveform is generated using the hardware NI6009 [68] which are
interfaced with bench or lap-top computer using the USB interface. Necessary lab
view control software is developed.
Hardware – NI 6009 and HV amplifier:
The hardware NI 6009 can interface with eight analog input channels (AI), two analog
output channels (AO) and twelve digital input/ output channels (DIO). It contains a
32-bit counter for any timing applications. Other technical features are listed in Table
3.1. The generated waveform from one of the analog output channel is interfaced to
the buffer electronics and HV amplifier to generate sine wave with a peak magnitude
in the range from 90V to 200 V. The generated control low voltage waveform is
interfaced to one of the analog input channel to record the control waveform.
Software:
A lab view graphical program shown in Fig. 3.1 is developed to generate sine wave.
Desired frequencies and the magnitude of control voltage can be keyed in the control
panel shown in Fig. 3.2. By activating the lab view buttons, the control waveforms
can be generated in sequence. Screen1 at the top in Figure 3.2 shows the input control
sine wave and left side panels show the keyed in frequencies, evaluated peak values
and input control voltage level.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
46
3.2.2 Leakage Current response measuring System
Using current to voltage converter, leakage current response from transformer is
converted to measurable voltage level. Another analog input channel is used to record
the proportional response current simultaneously with control voltage waveform
sampling. A manually controlled 3 range amplification is used to record a current
level from 1A to 100 µA with a maximum resolution of 30 nA without noise.
Screen 2 at the bottom in Figure 3.2 shows the control sine voltage wave form in
white and the corresponding leakage current response in red.
3.2.3 Data acquisition and storage
The developed software can record the proportional perturbation sine wave voltage
and the corresponding proportional response current waveform digitally. The control
flow is shown in Fig. 3.3. Depending on the keyed in frequency value, the sampling
internal clock rate is set. The control panel can be used to generate continuous sine
wave or single burst of 3 sine waves with the same frequency. The 3 sine waves are
generated to identify any initial transients in the measured initial relaxation responses
for analysis. The digital control signal and the corresponding response are
continuously recorded and stored as per the set control panel frequencies in a loop.
The execution can be terminated at any time using the stop button shown in the
control panel.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
47
Fig 3.1 Developed Lab view graphical program
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
48
Fig 3.2 Typical screen control, generated and captured outputs as seen in computer
screen front panel
Fig 3.3 Control flow diagram
NI USB-6009 card, interfacing electronics, HV amplifier and leakage current
measuring system are housed in an earthed instrument box shown in Figure 3.4. A
three terminals measurement is done to eliminate the leakage current through the
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
49
grounded paths as shown in Fig. 3.5. The HV transformer in the cage is connected
with two long shielded coaxial XLPE insulated leads to the interfacing instrument box
kept on the work table. The developed instrument can be interfaced with the
computer through USB connection. The applied HV level can be monitored using a
DMM. The instrument is calibrated for current ranges and phase shifts using known
resistive loads. Using a manually controlled knob, the desired current amplification is
selected.
Fig 3.4 Developed Sine wave Relaxation Instrument
3.3 Developed Relaxation Instrument Specifications
• Controllable HV output to transformer test terminals: +/-90V to +/-200V.
• Measured leakage current in 3 ranges: R1—0 to 100µA
(6 digit accuracy in 5V range) R2– 0 to 10µA
R3– 0 to 1µA
Frequency range: 0.001Hz to 10Hz
Frequency steps: Five steps or desired number of steps for a sweep.
Waveforms: Sinusoidal, triangular and square
Operation: Continuous or discrete with 3 sine waves of 3000 sampled points
Requirement of Lab view Development System for field testing: No
Requirement of laptop or bench top computer: Yes
Approximate storage area for one sampling: 50kB
Power Consumption: less than 10 W
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
50
Size of the instrument without computer: 30x20x10 (in cms)
Weight: < 500 gm
Fig 3.5 General Layout of Connections (A, B and G are the three terminals)
3.4 Tested HV Transformers
Since the study is connected with relaxation measurement on the oil-filled
transformers, a sincere attempt is made to collect a few transformers of similar
construction and rating so that the relaxation characteristics can be compared with
aging. It is found that Queensland utilities use a significant number of single wire
earth return transformers (SWER) and they have to be evaluated at the field at a later
date. With that objectives in mind, a brand new SWER transformer T2 is purchased.
The local utilities provided other two aged transformers (T1 and T3) with name plate
age of 30 years and 15 years respectively. The details of those tested transformers are
provided in Table 3.2 and the photograph in Fig.3.6 shows the tested three
transformers. All the transformers are SWER type and they had three terminals. The
high voltage winding is abbreviated as ‗H‘, the low voltage winding is abbreviated as
‗L‘ and the tank is abbreviated as ‗T‘. To evaluate aging and degradation, it is planned
to study the effects of terminals and the effects of perturbing voltage levels. Before
starting the experiments, a preliminary analysis is made on the existing conditions of
the tested transformers.
3.4.1 Polarisation Index
Using Hioki insulation tester [61], PI is determined across the low and high voltage
windings of the transformers. The measured indexes are listed below:
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
51
[T1]: 1.28
[T2]: 3.49
[T3]: 1.34
From the readings, it is estimated the transformer, T1 is aged more than T3. New
transformer, T2 is fairly in good condition with a value of 3.49 and it is significantly
more than PI readings of T1 and T3.
3.4.2 Oil/( Insulation+ core + winding) weight ratio
[T1]: 19.08/86.92 kg
[T2]: 42.24/97.76 kg
[T3]: 33.18/106.32 kg
The ratio of oil to other components weight ratio varied as 20% for [T1], 30% for [T2]
and 20% for [T3]. It should be noted the new transformer [T2] is rated for 10 kVA
while the other two are rated for 5 kVA only. It clearly suggests that oil plays a
significant role in controlling the polarisation and heat transfer characteristics.
3.4.3 Resistance of the windings
[T1]: HV/LV - 425/1.2 ohms
[T2]: HV/LV - 165/0.5 ohms
[T3]: HV/LV - 1120/1.5 ohms
The above readings suggest that the operating temperature of the winding and oil in
loaded conditions can be estimated using the variation of HV winding resistance. The
change in LV winding resistance with temperature will be significantly low.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
52
Fig 3.6 Tested Transformers T1, T2 and T3
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
53
Table 3.2 Name plate details of tested SWER Transformers
Terms
Transformer 1(T1) Transformer 2(T2) Transformer 3(T3)
Age
30 years old New transformer 15 years old
KVA
5 10 5
Volts HT
12,700 19,100
Volts LT
250 250
Amps HT
0.394 0.262
Amps LT
20 20
IMP 3.5% 3.3% 4.12%
Temp rise 60Deg 65Deg 55Deg
Cooling ON ON ON
Frequency 50Hz 50Hz 50Hz
Resistance HT/LT
425/1.2Ohms 165/0.5 Ohms 1120/1.5 Ohms
Height/Width
55.5/106 cms 55/130 cms 61/105 cms
Oil
21.68 L 48 L 37.7 L
Total wt
106 Kg 140 kg 139.5 Kg
Manufacture
PWA Electrical Industries
ABB Transformer PWA Electrical Industries
3.5 Relaxation Tests
The HV laboratory test floor is a grounded metal sheet.
Test objects:
The test transformers kept in the HV laboratory are insulated from ground so that
floating or insulated H, L and T terminals are available for independent tests. The
transformer terminals are grounded for an hour before starting the relaxation
measurement. Safety procedure is followed by keeping the test transformer in the
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
54
grounded faraday cage. The test transformer terminals are connected to the relaxation
instrument by two long shielded cables.
Relaxation Instrument:
The instrument is kept on the external work bench and is interfaced with a computer.
Five discrete frequencies are used to scan the desired frequency range.
Three voltage levels are used to understand the role of voltage magnitude on the
relaxation behaviour.
The instrument is calibrated with known resistance loads to estimate the phase errors
in the tested frequency range and to determine the conversion factors on voltage level
(V) and the three current (I) ranges.
Two sets of tests are planned as indicated below:
3.5.1 Effect of terminals
The transformer had three metal terminals to connect. The used abbreviations
are as follows: T- Tank; L – Low voltage winding; H – High voltage winding;
A – High voltage output from the instrument; B – High voltage return terminal
to the instrument and G – system ground.
Table 3.3 lists the connected terminals in Test1, Test2 and Test3.
Table 3.3 Terminals Connections
HV Unit output A B G
Test 1 /Transformer L H T
Test 2 /Transformer T H L
Test 3 /Transformer L T H
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
55
3.5.2 Effect of perturbing voltage
The effects of voltage on relaxation responses are evaluated by varying voltage level
in the range from +/-141V to+/-195V. Three voltage levels: +/-141V, +/-176V, +/-
195V are selected for the relaxation measurements.
3.6 Procedure to Perform Offline Relaxation Testing
All the transformer terminals are short-circuited and grounded for a minimum
period of 60 minutes before starting the measurements.
The transformer terminals are connected as per Table 3.3.
By selecting the lowest frequency measurement, the current range is set.
The data is collected at the selected five frequencies for each transformer
under three different voltages (+/-141V, +/-176V, +/-195V).
After the test, all the three transformer terminals are shorted to ground after
removing the connections to the instrument.
All the recorded readings are converted by using multiplication conversion
factors. Conditioning of data in the form of noise removal, single sine wave
extraction, and phase correction is carried as post data conditioning, and the
cleaned data is stored for further analysis.
3.7 Summary
With the above procedure and experimental layouts, reproducible relaxation results on
oil filled transformers are obtained in QUT high voltage laboratory. Since the aging
status is approximately known, the relaxation responses can be compared with aging.
No published relaxation papers are available by varying the terminals and perturbation
voltage levels. Novelty of testing by varying the terminals and voltage levels to link
with aging phenomena is introduced in this program. All the results are analysed
further for identifying sensitive parameters with aging on oil-filled transformers. The
developed instrument is also tested for reliable field operation without having lab
view software platform.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
56
CHAPTER 4
EXPERIMENTAL RESULTS
In this chapter, the relaxation results obtained on three oil-filled power transformers
are reported. The oil filled transformer consists of low voltage winding and high
voltage winding mounted on iron core, and the entire structure is kept immersed in oil
kept in a sealed metal tank. The windings are insulated from core and tank with oil
immersed paper insulation. The external metallic contact terminals available for
electrical measurements are low voltage winding, high voltage winding and metallic
tank. The insulation gets deteriorated due to thermally induced electrical loading and
ageing. The status of aging in insulation is evaluated by means of dielectrometry
condition monitoring technique using the developed sine wave relaxation
instrumentation.
4.1 Measurements
Since three contact terminals are available for insulation measurements in the tested
transformers, three terminals measurement is carried out by connecting two terminals
to the instrument with other terminal shorted to system ground. Three sets of results
are obtained in the tested frequency range. Since the developed instrument can vary
the voltage level, the measurements are also carried by varying the voltage in 3 levels.
As a result, nine measurements are made. Since the test will introduce transients, the
measurement at each frequency is carried for 3 continuous cycles. At each frequency,
the total number of sampled digital points for the measured 3 continuous cycles is
3000. Five frequencies in the range of 15 MHz to 1.5 Hz are selected for the
measurements. The test periods are as follows: 2, 10, and 20, 100 and 200 seconds for
3 cycles. Hence each set of measurement will take (2+10+20+100+200 = 332
seconds) about 5 to 6 minutes of test duration. Each set of measurement will record
proportional perturbation sine voltage, response current and time of each of 3000
sampled points in separate data files. The stored data are analysed using the developed
Mat lab programs.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
57
4.2 Signal conditioning
A typical recorded result is shown below in Figure 4.1. The used abbreviations are as
follows: ‗TG‘ means tank grounded and the insulation measurements are made across
low voltage winding (L) and high voltage winding (H). The distortion of the current
response (TG) shown in red in the first cycle can be seen. The recorded last cycle of
measurement with 1000 sampled points is taken for analysis. The multiplication
factors for current range are tabulated in Table 4.1. Occasional transients are recorded
and it is eliminated using signal processing. The magnitudes of voltage and current,
and phase shift between them are preciously measured. A leading phase angle on the
response current with respect to perturbation voltage is obtained in all the cases.
Table 4.1 Multiplication Factors
Range 1 Range 2 Range 3
Current 61.4 µA 6.14 µA 0.614 µA
0 0.5 1 1.5 2-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Time in seconds
Vo
ltag
e in
V;C
urr
en
t in
A
T1 176
TG
V
Fig 4.1 Test on T1 in 2 second period with tank grounded. Perturbation voltage in
blue is to be multiplied by 352 and the response current in red is to be multiplied by
6.14µA.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
58
4.3 Typical results
By extracting single sine wave, the relaxation characteristics are analysed and
compared. The low and high voltage windings are abbreviated as ‗L‘ and ‗H‘
respectively while the tank is abbreviated as ‗T‘. TG means with the tank grounded
the insulation current response measurements across ‗L‘ and ‗H‘ with perturbation
sine voltage is measured. The three peak sine voltage levels 141V, 176V and 195 V
are used for the studies. The recorded measurements on the tested three transformers
at the two extreme periods 0.67s and 66.7s are presented below in Figures 4.2 to 4.10.
Transformer 1 (T1)
0 0.1 0.2 0.3 0.4 0.5 0.6-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T1 141
TG
LG
HG
V
0 10 20 30 40 50 60-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T1 141
TG
LG
HG
V
Fig 4.2 Relaxation response of T1 in periods of 0.67s(Vx705;Ix1.25e-5) and
66.7s(Vx14100;Ix1.25e-5) with 141VpSine
0 0.1 0.2 0.3 0.4 0.5 0.6-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T1 176V
TG
LG
HG
V
0 10 20 30 40 50 60-0.03
-0.02
-0.01
0
0.01
0.02
0.03
Time in seconds
Vo
ltag
e i
n V
; C
urr
en
t in
A
T1 176V
TG
LG
HG
V
Fig 4.3 Relaxation response of T1 in periods of 0.67s(Vx440;Ix1.2e-5) and
66.7s(Vx8800;Ix1.2e-5) with 176VpSine
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
59
0 0.1 0.2 0.3 0.4 0.5 0.6
-1
-0.5
0
0.5
1
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T1 195
TG
LG
HG
V
0 10 20 30 40 50 60-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T1 195
TG
LG
HG
V
Fig 4.4 Relaxation response of T1 in periods of 0.67s(Vx279;Ix1.2e-5) and
66.7s(Vx4875;Ix1.2e-5) with 195VpSine
With T1, as the period of sine wave is increased the peak magnitude decreases
significantly. At 141V, the ratio with HG is : 0.38/0.014=27; with TG is:
0.37/0.008=46; with LG is 0.16/0.005=32. The leakage current is minimum with LG.
As the voltage is increased, the peak current magnitude increases.
At 176V, the ratio with HG is : 0.78/0.022=35; with TG is: 0.76/0.018=42; with LG is
0.32/0.015=21. The leakage current is minimum with LG.
At 195V, the ratio with HG is : 1.2/0.05=24; with TG is: 1.1/0.02=55; with LG is
0.45/0.015=30. The leakage current is minimum with LG.
The ratio indirectly indicates approximately the ratio of capacitive to resistive
leakage current responses. It is maximum with TG configuration at all voltage levels.
T1 is 30 years old transformer as per the name plate details.
Transformer 2 (T2)
0 0.1 0.2 0.3 0.4 0.5 0.6
-1
-0.5
0
0.5
1
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T2 141
TG
LG
HG
V
0 10 20 30 40 50 60-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Time in seconds
Vo
ltag
e i
n V
; C
urr
en
t in
A
T2 141
TG
LG
HG
V
Fig 4.5 Relaxation response of T2 in periods of 0.67s(Vx201;Ix1.15e-5) and
66.7s(Vx14100;Ix1.15e-5) with 141VpSine
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
60
0 0.1 0.2 0.3 0.4 0.5 0.6
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T2 176
TG
LG
HG
V
0 10 20 30 40 50 60-0.03
-0.02
-0.01
0
0.01
0.02
0.03
Time in seconds
Vo
ltag
e i
n V
; C
urr
en
t in
A
T2 176
TG
LG
HG
V
Fig 4.6 Relaxation response of T2 in periods of 0.67s(Vx117;Ix1.18e-5) and
66.7s(Vx8800;Ix1.18e-5) with 176VpSine
0 0.1 0.2 0.3 0.4 0.5 0.6-3
-2
-1
0
1
2
3
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T2 195
TG
LG
HG
V
0 10 20 30 40 50 60-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
Time in seconds
Vo
ltag
e i
n V
; C
urr
en
t in
A
T2 195
TG
LG
HG
V
Fig 4.7 Relaxation response of T2 in periods of 0.67s(Vx97.5;Ix1.22e-5) and
66.7s(Vx6500;Ix1.22e-5) with 195VpSine
T2 is fairly NEW transformer. As the period of sine wave is increased the peak
magnitude decreases significantly. At 141V, the ratio with HG is : 0.05/0.004=12;
with TG is: 1.05/0.012=87; with LG is 0.2/0.006=33. The leakage current is minimum
with HG.
As the voltage is increased, the peak current magnitude increases.
At 176V, the ratio with HG is : 0.3/0.009=33; with TG is: 2.1/0.022=95; with LG is
0.5/0.012=42. The leakage current is minimum with HG.
At 195V, the ratio with HG is : 0.4/0.01=40; with TG is: 3/0.031=97; with LG is
0.7/0.018=39. The leakage current is minimum with HG.
The ratio was maximum with TG configuration at all voltage levels.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
61
Transformer 3 (T3)
0 0.1 0.2 0.3 0.4 0.5 0.6
-1
-0.5
0
0.5
1
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T3 141
TG
LG
HG
V
0 10 20 30 40 50 60
-0.5
0
0.5
Time in seconds
Vo
ltag
e i
n V
; C
urr
en
t in
A
T3 141
TG
LG
HG
V
Fig 4.8 Relaxation response of T3 in periods of 0.67s(Vx141;Ix1.33e-5) and
66.7s(Vx564;Ix1.33e-5) with 141VpSine
0 0.1 0.2 0.3 0.4 0.5 0.6
-2
-1
0
1
2
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T3 176
TG
LG
HG
V
0 10 20 30 40 50 60
-1
-0.5
0
0.5
1
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T3 176
TG
LG
HG
V
Fig 4.9 Relaxation response of T3 in periods of 0.67s(Vx88;Ix1.24e-5) and
66.7s(Vx220;Ix1.24e-5) with 176VpSine
0 0.1 0.2 0.3 0.4 0.5 0.6-3
-2
-1
0
1
2
3
Time in seconds
Vo
ltag
e in
V;
Cu
rren
t in
A
T3 195
TG
LG
HG
V
0 10 20 30 40 50 60
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Time in seconds
Vo
ltag
e i
n V
; C
urr
en
t in
A
T3 195
TG
LG
HG
V
Fig 4.10 Relaxation response of T3 in periods of 0.67s(Vx97.5;Ix1.23e-5) and
66.7s(Vx325;Ix1.23e-5 ) with 195VpSine
T3 is 15 years old transformer and it was used extensively used for continuous HV
testing. As the period of sine wave is increased the peak magnitude decreases by half.
At 141V, the ratio with HG is : 1.2/0.45=2.7; with TG is: 0.7/0.15=4.6; with LG is
0.35/0.1=3.5. The leakage current is minimum with LG.
As the voltage is increased, the peak current magnitude increases.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
62
At 176V, the ratio with HG is : 2.49/0.9=2.7; with TG is: 1.56/0.28=5.5; with LG is
0.8/0.22=3.6. The leakage current is minimum with LG.
At 195V, the ratio with HG is : 2.95/0.82=3.6; with TG is: 2.1/0.42=5; with LG is
1/0.25=4. The leakage current is minimum with LG.
It is maximum with HG configuration at all voltage levels.
The responses clearly suggest that the current responses retain the wave shape but it
leads with respect to voltage. The current peak magnitude decreases if the test sine
wave period is increased. With respect to terminals of test, the patterns of responses
vary. More leakage current is obtained with HG on T1 and T3. With T2, high leakage
current is obtained with TG.
4.4 Consolidated results
The measurements are done at 5 selected frequencies by varying voltage level and
terminals. Since the significant changes occur in the peak sine wave magnitudes and
the phase shift, they are extracted and plotted in the following figures from Figure
4.11 to Fig.4.16.
4.4.1 Variation of peak current magnitude with frequency
Figure 4.11 shows the variation of peak current magnitude with frequency on T1. It
increases with increase in frequency and applied peak voltage magnitude. With LG
configuration, minimum leakage current is obtained.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
63
10-2
100
0
0.2
0.6
1
1.4
x 10-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
AT1 141V
TG
LG
HG
10-2
100
0
0.2
0.6
1
1.4x 10
-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
A
T1 176V
TG
LG
HG
10-2
100
0
0.2
0.6
1
1.4x 10
-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
A
T1 195V
TG
LG
HG
Fig 4.11 Relaxation current response of T1 at different voltages
10-2
100
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
A
T2 141V
TG
LG
HG
10-2
100
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
A
T2 176V
TG
LG
HG
10-2
100
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
A
T2 195V
TG
LG
HG
Fig 4.12 Relaxation current response of T2 at different voltages
Figure 4.12 shows the variation of peak current magnitude with frequency on T2. It
increases with increase in frequency and applied peak voltage magnitude. With HG
configuration, minimum leakage current is obtained. More current magnitude is
recorded in T2 in comparison with T1.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
64
10-2
100
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
A
T3 141V
TG
LG
HG
10-2
100
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
A
T3 176V
TG
LG
HG
10-2
100
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-5
Frequency in Hz
Resp
on
se s
ine p
eak C
urr
en
t in
A
T3 195V
TG
LG
HG
Fig 4.13 Relaxation current response of T3 at different voltages
Figure 4.13 shows the variation of peak current magnitude with frequency on T3. The
current increases with increase in frequency and applied peak voltage magnitude.
With LG configuration, minimum leakage current is obtained. More current
magnitude is recorded in T3 in comparison with T1.
4.4.2 Variation of leading phase shift with frequency
Figure 4.14 shows the variation of leading phase shift between the perturbation
voltage and the measured response current. With T1, the phase shift increases with
increase in frequency. At high frequency, it tends to be more capacitive and at low
frequency, it is more ohmic. A variation of 22º to 89º is obtained. More ohmic
behaviour is observed with HG configuration. The effect of voltage magnitude is
significant in the lowest frequency range. The voltage magnitude increases the phase
shift suggesting the increase in capacitive current in relation to resistive current.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
65
10-2
100
20
30
40
50
60
70
80
90
Frequency in Hz
Ph
ase
Sh
ift
in d
eg
ree
s
T1 141V
TG
LG
HG
10-2
100
20
30
40
50
60
70
80
90
Frequency in Hz
Ph
ase
Sh
ift
in d
eg
ree
s
T1 176V
TG
LG
HG
10-2
100
20
30
40
50
60
70
80
90
Frequency in Hz
Ph
ase
Sh
ift
in d
eg
ree
s
T1 195V
TG
LG
HG
Fig 4.14 Relaxation leading phase shift response of T1 at different voltages
10-2
100
10
20
30
40
50
60
70
80
90
Frequency in Hz
Ph
ase S
hif
t in
deg
rees
T2 141V
TG
LG
HG
10-2
100
10
20
30
40
50
60
70
80
90
Frequency in Hz
Ph
ase S
hif
t in
deg
rees
T2 176V
TG
LG
HG
10-2
100
10
20
30
40
50
60
70
80
90
Frequency in Hz
Ph
ase S
hif
t in
deg
rees
T2 195V
TG
LG
HG
Fig 4.15 Relaxation leading phase shift response of T2 at different voltages
Figure 4.15 shows the variation of leading phase shift between the perturbation
voltage and the measured response current on NEW transformer T2. With T2, the
phase shift increases with increase in frequency. At high frequency, it tends to be
more capacitive and at low frequency, it is modulated with capacitive and ohmic
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
66
current responses. A variation of 50º to 89º is obtained. More ohmic behaviour is
observed with HG configuration. The effect of voltage magnitude is significant in the
lowest frequency range and the effect of change is less than observed in T1. The
voltage magnitude increases the phase shift suggesting the increase in capacitive
current with voltage in relation to resistive current.
10-2
100
10
20
40
60
80
Frequency in Hz
Ph
ase S
hif
t in
deg
rees
T3 141V
10-2
100
10
20
40
60
80
Frequency in Hz
Ph
ase S
hif
t in
deg
rees
T3 176V
10-2
100
10
20
40
60
80
Frequency in Hz
Ph
ase S
hif
t in
deg
rees
T3 195V
TG
LG
HG
TG
LG
HG
TG
LG
HG
Fig 4.16 Relaxation leading phase shift response of T3 at different voltages
Figure 4.16 shows the variation of leading phase shift between the perturbation
voltage and the measured response current on 15 years old transformer T3. With T3,
the phase shift increases with increase in frequency. At high frequency, it is
modulated with capacitive and ohmic current responses. At low frequency, it is more
ohmic. A variation of 8º to 70º is obtained. More ohmic behaviour is observed with
HG configuration. The effect of voltage magnitude is significant in the lowest
frequency range and the effect of change is less than observed in T1. The voltage
magnitude increases the phase shift suggesting the increase in capacitive current with
voltage in relation to resistive current.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
67
4.5 Summary
Relaxation current responses are recorded on three oil-filled transformers with sine
wave perturbation peak voltage magnitudes in the range from 145V to 195V. A
frequency range from 15 MHz to 1.5 Hz is selected so that each set of measurements
will take about 5 to 6 minutes. The tested transformers had three external terminals
for the measurements: (i) high voltage winding (H), (ii) low voltage winding (L), and
(iii) metallic tank (T). Three terminals measurements are undertaken to evaluate
insulation across selected two terminals at a time. The current magnitudes from new
T2 and old T3 are significantly more in comparison with old T1.
In all the cases, the increase in frequency increases the current magnitude. The
increase in voltage also increases the current magnitude. The current magnitude with
low voltage winding grounded (LG) is less than the values obtained on grounding the
high voltage winding (HG) and tank (TG) in T1 and T3; In the case of T2, HG current
is less. The change in phase shift with frequency is significant in T1 and T2 in all the
terminals configurations and changes in applied sine wave voltages. Further analysis
is carried out to quantify the parameters to relate with ageing in the next chapter.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
68
CHAPTER 5
ANALYSIS
In this chapter, the relaxation results obtained on three oil-filled power transformers
are analysed to extract sensitive parameters of aging. The section 5.1 presents the
theoretical basis for the requirement of analysis connected with the relaxation
phenomena. The section 5.2 presents the variation of extracted in phase current (IR)
component and 90º phase shifted capacitive response current (IC) component with
reference to frequency, voltage and terminal connections. The section 5.3 analyses
the variation of real and imaginary admittance components with reference to
frequency, voltage and terminal connections. The section 5.4 evaluates the variation
of tanδ with reference to frequency, voltage and terminal connections. After knowing
the trend of aging on all the three transformers, the effect of polarisation voltage
magnitude is studied. The section 5.5 reports the effect of voltage drop from 176V to
141V, and also the effect of voltage rise from 176 V to 195V on loss factor variation
with reference to 176V record. The section 5.6 evaluates the effect of similar voltage
change on percentage change of real and imaginary admittances.
5.1 Theory of Relaxation Phenomena
The basic theory of relaxation phenomena is that when dielectric material is subjected
to low electric voltage, E (t) thereby avoiding any destructive or non-linear effects,
dipoles becomes excited. It induces new delayed response polarisation, P (t) due to
electronic, ionic, dipolar and interfacial polarization processes [12] [45-46]. The net
induced dielectric flux density, D (t) can be expressed by (1).
tPtEtD 0 (1)
The time dependency of P (t) and D (t), however, will not be the same as that of E (t),
as the different polarization processes will have delays. P (t) is the increase in
polarisation due to the polarisation characteristics of the insulation and it varies as a
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
69
product of the susceptibility (χ) of the material and the applied voltage, E (t). The
equation (1) is rewritten as (2).
tEttEttEtD r 000 ) (2)
The factor, r is known as the dielectric constant. The measured r for transformer oil
is around 2.2 [48] while for composite insulation as around 3.5 [48]. The dielectric
constant of water is around 80.
On applying electric field E (t), both free and bonded charges will give rise to a
current flow, I (t). The movement of the free charges leads to a leakage current in
phase with the voltage, and the magnitude relies on dielectric conductivity 0 and
electrical stress E (t).
The electric displacement D (t) represents the (positive and negative) electric charges
(Q) per unit area as deposited at the outer surface of the electrodes which are the
origin of all electric field lines from sources and sinks. The so-called ‗displacement
current‘,ID(t) released from the voltage source as necessary to maintain the area
charge density at the electrodes is then only governed by ID(t) = dQ/dt, if Q is the sum
or integral of all charges deposited on each of the electrodes [44][46] [54]. Hence the
bonded charges contribute to the displacement current being a sum of the vacuum or
geometry based displacement current and polarisation current due to dielectrics.
The response current, I (t) is a sum of conduction and total displacement currents
shown in (3).
dt
tdDtEtI 0 = IR(t) + jxIC(t) (3)
By applying sinusoidal voltage, E(t), the response current can be measured. The in
phase component of the current, IR(t) represents the leakage or resistive or energy
dissipating component. While, the quadrature component, IC(t) represents the
capacitive or energy storing component. High quality dielectric materials do not have
any leakage component and the ratio of IR(t) with IC(t) is known as loss factor. It is
expressed in terms of phase shift as per equation (4).
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
70
Loss Factor = tan (δ) = tan (90º-Φ) = tI
tI
C
R (4)
For very good dielectrics, tan (δ) will be less than 0.001.
In this study, the instrumentation measures the response current in the sinusoidal
frequency (f) plane with period from 0.67s to 66.7s. The next section determines the
corresponding IR(f) and IC(f) in the frequency range down from 1.5Hz to 15 MHz.
Then corresponding admittance can be estimated for different applied voltages. The
variation of admittance and loss-factor with frequency can be related with aging on
each tested transformer.
5.2 Variation of IR(f) and IC(f) with frequency
The polarisation response current followed the sinusoidal perturbation voltage wave
shape with leading phase shift in all the cases. It suggests that the polarisation
response depends on resistive and capacitive components of current which follows the
theoretical equation (3). The variation of peak current magnitude with frequency is
shown in Figures 4.11 to 4.13. As the frequency is increased, the current magnitude
increases significantly. The corresponding phase shifts are shown in Figures 4.14 to
4.16. As the frequency is increased, the phase shift tends to move towards 90º. The in
phase resistive (IR) component is the current component multiplied by the cosine of
measured phase shift angle. The capacitive (IC) component is the current component
multiplied by the sine of measured phase shift angle. By separating each component
of the current, the trend of aging behaviour can be identified with its physical
reasoning. The used abbreviation is as follows: ‗TGIR‘ means tank grounded
configuration in phase (iR) current component. Similar abbreviation is followed on
LG, HG, IC, 141V, 176V, and 195V, T1, T2 and T3.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
71
10-2
100
10-8
10-7
10-6
10-5
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T1 141V
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
10-2
100
10-8
10-7
10-6
10-5
10-4
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T1 176V
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
10-2
100
10-7
10-6
10-5
10-4
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T1 195V
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
Fig 5.1 Relaxation IR and IC current responses of T1 at different voltages
Figure 5.1 presents the estimated the current magnitudes on old transformer T1. In
most of the cases, both current components increase with increase in frequency. As
the voltage is increased, the current magnitude increases. In general, capacitive
component is found to be more than the resistive component. The capacitive current is
maximum under TG and HG configurations. The resistive current is maximum under
HG configuration.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
72
10-2
100
10-8
10-7
10-6
10-5
10-4
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T2 141V
10-2
100
10-8
10-7
10-6
10-5
10-4
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T2 176V
10-2
100
10-8
10-7
10-6
10-5
10-4
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T2 195V
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
Fig 5.2 Relaxation IR and IC current responses of T2 at different voltages
Figure 5.2 presents the estimated the current magnitudes on new transformer T2.
Both the current components increase with increase in frequency. As the voltage is
increased, the current magnitude increases. In general, capacitive component is found
to be more than the resistive component. The capacitive and resistive current
components are maximum under TG configuration.
10-2
100
10-7
10-6
10-5
10-4
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T3 141V
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
10-2
100
10-7
10-6
10-5
10-4
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T3 176V
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
10-2
100
10-6
10-5
10-4
Frequency in Hz
Resp
on
se p
eak IR
an
d IC
in
A
T3 195V
TGIR
TGIC
LGIR
LGIC
HGIR
HGIC
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
73
Fig 5.3 Relaxation IR and IC current responses of T3 at different voltages
Figure 5.3 presents the estimated the current magnitudes on old transformer T3.
Both current components,IR and IC increase with increase in frequency. Fast rate of
change is observed with the capacitive component. As the voltage is increased, the
current magnitude increases. In general, IC is found to be less than IR in the low
frequency range. In the high frequency range, IC is more than IR. The capacitive
current is maximum under TG and HG configurations. The resistive current is
maximum under HG configuration. It follows the response of old transformer T1.
5.3 Variation of admittance with frequency
The admittance can be computed by dividing IR and IC by the applied voltage, E(t).
Real part of the admittance (AR) represents the conductance or reciprocal of
resistance. Imaginary part of the admittance (AC) represents the reciprocal of
capacitive impedance. AC is proportional to the product of capacitance and frequency.
10-2
100
10-10
10-9
10-8
10-7
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T1 141V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
10-2
100
10-11
10-10
10-9
10-8
10-7
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T1 176V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
10-2
100
10-10
10-9
10-8
10-7
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T1 195V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
Fig 5.4 Real and imaginary admittance responses of T1 at different voltages
Figure 5.4 presents the trend of admittance on old transformer T1. AR and AC
increase with increase in frequency and applied voltage level. The effect of voltage is
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
74
significant in the lowest tested frequency range. Reactive admittance is more than the
conductive admittance. The capacitive admittance is maximum under TG and HG
configurations. The conductive admittance is maximum under HG configuration.
10-2
100
10-10
10-9
10-8
10-7
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T2 141V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
10-2
100
10-10
10-9
10-8
10-7
10-6
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T2 176V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
10-2
100
10-10
10-9
10-8
10-7
10-6
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T2 195V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
Fig 5.5 Real and imaginary admittance responses of T2 at different voltages
Figure 5.5 presents the trend of admittance on new transformer T2. AR and AC
increase with increase in frequency and applied voltage level. A marginal increase is
observed with increase in voltage. Reactive admittance is significantly more than the
conductive admittance. The capacitive admittance is maximum under TG
configuration. The conductive admittance is also maximum under TG configuration.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
75
10-2
100
10-9
10-8
10-7
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T3 141V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
10-2
100
10-9
10-8
10-7
10-6
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T3 176V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
10-2
100
10-9
10-8
10-7
10-6
Frequency in Hz
Resp
on
se A
R a
nd
AC
in
Mh
os
T3 195V
TGAR
TGAC
LGAR
LGAC
HGAR
HGAC
Fig 5.6 Real and imaginary admittance responses of T3 at different voltages
Figure 5.6 presents the trend of admittance on old transformer T3. AR and AC
increase with increase in frequency. The effect of applied voltage level is more in the
low frequency range. Variation of reactive admittance with frequency is significantly
more than the conductive admittance. The capacitive admittance is maximum under
TG and HG configurations. The conductive admittance is more than the capacitive
admittance in the low frequency range. Maximum resistive conductance is obtained in
HG configuration.
5.4 Variation of tan(δ) with frequency
Loss factor, tan(δ) can be computed using equation 4 in the frequency plane. The
computed tan (δ) variations with frequency for three tested transformers are shown in
Figures 5.7 to 5.9 respectively.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
76
10-2
100
0
0.5
1
1.5
2
2.5
Frequency in Hz
Lo
ss F
acto
r
T1 141V
10-2
100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Frequency in Hz
Lo
ss F
acto
r
T1 176V
10-2
100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Frequency in Hz
Lo
ss F
acto
r
T1 195V
TG
LG
HG
TG
LG
HG
TG
LG
HG
Fig 5.7 Variation of loss Factor with frequency at different voltages in T1
For the old transformer T1, the loss factor decreases with increase in frequency and
perturbation voltage level. Maximum tanδ is obtained in HG configuration.
10-2
100
0
0.2
0.4
0.6
0.8
Frequency in Hz
Lo
ss
Fac
tor
T2 141V
10-2
100
0
0.2
0.4
0.6
0.8
Frequency in Hz
Lo
ss
Fac
tor
T2 176V
10-2
100
0
0.2
0.4
0.6
0.8
Frequency in Hz
Lo
ss
Fac
tor
T2 195V
TG
LG
HG
TG
LG
HG
TG
LG
HG
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
77
Fig 5.8 Variation of loss Factor with frequency at different voltages in T2
For the new transformer T2 also, the loss factor decreases with increase in
frequency. The decrease of loss factor with perturbation voltage level is less than T1.
The maximum loss factor is obtained with 141 V at the lowest tested frequency.
Maximum tanδ is obtained in HG and LG configurations.
10-2
100
0
2
4
6
8
Frequency in Hz
Lo
ss
Fac
tor
T3 141V
TG
LG
HG
10-2
100
0
2
4
6
Frequency in Hz
Lo
ss
Fac
tor
T3 176V
TG
LG
HG
10-2
100
0
1
2
3
4
Frequency in Hz
Lo
ss
Fac
tor
T3 195V
TG
LG
HG
Fig 5.9 Variation of loss Factor with frequency at different voltages in T3
The maximum loss factor of about 8 is obtained with 141 V at the lowest tested
frequency in old transformer T3. The loss factor decreases with increase in
frequency like all the tested transformers. The decrease of loss factor with
perturbation voltage level is more significant at the lowest tested frequency.
Maximum tanδ is obtained in HG configuration.
5.5 Effect of voltage on loss factor
Since perturbation voltage level is found to alter admittance and loss factor, the
percentage variation of those parameters is estimated with reference to 176 V level
measurements. Figure 5.10 presents the percentage variation from 176V level due to
141 V and 195 V readings on three transformers. The loss factor increases if the
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
78
perturbation voltage level is decreased as can be seen by the dotted lines. The loss
factor decreases if the perturbation voltage level is increased.
T1 – With the old tranformer T1, the loss factor is maximum around 2.4 at the lowest
test frequency in Fig. 5.7. The percentage change due to 176V to 141V change
(shown as dotted lines in Fig.5.10) is around 12 to 25%. The configurations HG and
LG resulted in more changes at the lowest test frequency. While the percentage
change due to 176V to 195V change (shown as solid lines in Fig.5.10) is less than
10% at the lowest test frequency. The change is almost same in all the three
configurations.
T2 – With the new tranformer T2, the loss factor is maximum around 0.85 at the
lowest test frequency in Fig.5.8. The percentage change due to 176V to 141V change
(shown as dotted lines in Fig.5.10) is around 10%. The configurations TG and LG
resulted in more changes at the lowest test frequency. While the percentage change
due to 176V to 195V change (shown as solid lines in Fig. 5.10) is less than 40% at
the lowest test frequency. The change is more with TG configuration.
T3 – With the old tranformer T3, the loss factor is maximum around 8 at the lowest
test frequency in Fig. 5.9. The percentage change due to 176V to 141V change
(shown as dotted lines in Fig.5.10) is around 55%. The configurations HG and LG
resulted in more changes at the lowest test frequency. While the percentage change
due to 176V to 195V change (shown as solid lines in Fig. 5.10) is less than 38% at
the lowest test frequency. The change is more with TG and LG configurations. With
increase in frequency, the percentage change decreases.
On comparing the three transformers, T3 is found to have significant change at the
lowest test frequency. Maximum change in LG and HG configurations suggest that
both low and high voltage windings may be undergoing severe degradation in T3.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
79
10-2
100
-50
0
50
100
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f L
F w
.r.t
176
V
T1 Loss Factor/Voltage
TG141
TG195
LG141
LG195
HG141
HG195
10-2
100
-50
0
50
100
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f L
F w
.r.t
176
V
T2 Loss Factor/Voltage
TG141
TG195
LG141
LG195
HG141
HG195
10-2
100
-60
-40
-20
0
20
40
60
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f L
F w
.r.t
176
V
T3 Loss Factor/Voltage
TG141
TG195
LG141
LG195
HG141
HG195
Fig 5.10 Variation of loss Factor with reference to 176V level
5.6 Effect of voltage on real and imagninary admittance
Variation of real and imaginary admittance with voltage is analysed in this section
5.6. By taking the response at 176V as base, the changes due to 141V and 195V are
analysed.
T1- Real (AR) and imaginary admittance(AC) variation for old transformer T1 is
shown in Fig.5.4. With increase in voltage and frequency, both components of
admittance increase. By changing the voltage from 176V to 141V, percentage
decrease in real admittance (shown as dotted lines in Fig.5.11) is around 52%. The
configuration LG resulted in more changes at the lowest test frequency. While the
percentage change of real admittance due to 195V to 176V change (shown as solid
lines in Fig. 5.11) is less than 80% at the lowest test frequency. The change is more
with HG configuration. With increase in frequency, in many cases the percentage
change decreases.
The behaviour of imaginary admittance is interesting. It increases significantly with
voltage at the lowest tested frequency in Fig. 5.4. By changing the voltage from 176V
to 141V, percentage decrease in imaginary admittance (shown as dotted lines in
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
80
Fig.5.12) is around 64%. The configuration LG resulted in more changes at the lowest
test frequency. While the percentage change of imaginary admittance due to 195V to
176V change (shown as solid lines in Fig. 5.12) is less than 90% at the lowest test
frequency. The change is more with HG configuration. With increase in frequency,
the percentage change decreases.
T2- Real (AR) and imaginary admittance(AC) variation for new transformer,T2 is
shown in Fig.5.5. With increase in voltage and frequency, both components of
admittance increase. By changing the voltage from 176V to 141V, percentage
decrease in real admittance (shown as dotted lines in Fig.5.11) is around 52%. The
configuration HG resulted in more changes. While the percentage change of real
admittance due to 195V to 176V change (shown as solid lines in Fig. 5.11) is less
than 85% at the lowest test frequency. The change is more with LG configuration.
With increase in frequency, in many cases the percentage change increases.
The behaviour of imaginary admittance is interesting. It increases significantly with
voltage at the lowest tested frequency in Fig. 5.5. By changing the voltage from 176V
to 141V, percentage decrease in imaginary admittance (shown as dotted lines in
Fig.5.12) is around 60%. The configuration HG resulted in more changes at the lowest
test frequency. While the percentage change of imaginary admittance due to 195V to
176V change (shown as solid lines in Fig. 5.12) is less than 75% at the lowest test
frequency. The change is more with TG configuration. With increase in frequency, in
many cases the percentage change decreases.
T3- Real (AR) and imaginary admittance(AC) variation for old transformer,T3 is
shown in Fig.5.6. With increase in voltage and frequency, both components of
admittance increase. By changing the voltage from 176V to 141V, percentage
decrease in real admittance (shown as dotted lines in Fig.5.11) is around 44%. All the
configurations resulted in more changes. While the percentage change of real
admittance due to 195V to 176V change (shown as solid lines in Fig. 5.11) is less
than 61% at the lowest test frequency. The change is more with HG configuration.
With increase in frequency, in many cases the percentage change decreases.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
81
The behaviour of imaginary admittance is interesting. It increases significantly with
voltage at the lowest tested frequency in Fig. 5.6. By changing the voltage from 176V
to 141V, percentage decrease in imaginary admittance (shown as dotted lines in
Fig.5.12) is around 62%. The configurations HG and LG resulted in more changes at
the lowest test frequency. While the percentage change of imaginary admittance due
to 195V to 176V change (shown as solid lines in Fig. 5.12) is less than 120% at the
lowest test frequency. The change is more with HG configuration. With increase in
frequency, in many cases the percentage change decreases.
With all the three transformers, the change in real admittance with T3 is less. The
change in imaginary admittance on voltage with old transformers T1 and T3 is more.
10-2
100
-200
-150
-100
-50
0
50
100
150
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f re
al
A w
.r.t
. 17
6V
T2 Admittance/Voltage
10-2
100
-100
-80
-60
-40
-20
0
20
40
60
80
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f re
al
A w
.r.t
. 17
6V
T3 Admittance/Voltage
10-2
100
-100
-50
0
50
100
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f re
al
A w
.r.t
. 17
6V
T1 Admittance/Voltage
TGR141
TGR195
LGR141
LGR195
HGR141
HGR195
TGR141
TGR195
LGR141
LGR195
HGR141
HGR195
TGR141
TGR195
LGR141
LGR195
HGR141
HGR195
Fig 5.11 Variation of Real admittance with reference to 176V level
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
82
10-2
100
-80
-60
-40
-20
0
20
40
60
80
100
120
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f Im
ag
. A
w.r
.t.
17
6V
T1 Admittance/Voltage
10-2
100
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
80
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f Im
ag
. A
w.r
.t.
17
6V
T2 Admittance/Voltage
10-2
100
-80
-60
-40
-20
0
20
40
60
80
100
120
Frequency in Hz
Perc
en
tag
e c
ha
ng
e o
f Im
ag
. A
w.r
.t.
17
6V
T3 Admittance/Voltage
TGC141
TGC195
LGC141
LGC195
HGC141
HGC195
TGC141
TGC195
LGC141
LGC195
HGC141
HGC195
TGC141
TGC195
LGC141
LGC195
HGC141
HGC195
Fig 5.12 Variation of Imaginary admittance with reference to 176V level
5.7 Summary
In Fig. 5.1, (T1) the variation of IC : (a) with frequency is around 50 to 90;
(b) with voltage is around 4
(c) with terminals is around 2
the variation of IR : (a) with frequency is around 4 to 9;
(b) with voltage is around 3
(c) with terminals is around 10
In Fig. 5.2,(T2) the variation of IC : (a) with frequency is around 15 to 100;
(b) with voltage is around 3
(c) with terminals is around 10
the variation of IR : (a) with frequency is around 4 to 12;
(b) with voltage is around 5
(c) with terminals is around 3 to 6
In Fig. 5.3, (T3) the variation of IC : (a) with frequency is around 80 to 110;
(b) with voltage is around 3
(c) with terminals is around 2
the variation of IR : (a) with frequency is around 3 to 5;
(b) with voltage is around 2
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
83
(c) with terminals is around 3 to 5
In Fig. 5.4, (T1) the variation of AC : (a) with frequency is around 47 to 100;
(b) with voltage is around 4
(c) with terminals is around 2
the variation of AR : (a) with frequency is around 2 to 8;
(b) with voltage is around 3
(c) with terminals is around 10
In Fig. 5.5, (T2) the variation of AC : (a) with frequency is around 17.5 to 167;
(b) with voltage is around 3
(c) with terminals is around 10
the variation of AR : (a) with frequency is around 2.8 to 23.3;
(b) with voltage is around 5
(c) with terminals is around 3 to 6
In Fig. 5.6, (T3) the variation of AC : (a) with frequency is around 16.7 to 40;
(b) with voltage is around 3
(c) with terminals is around 2
the variation of AR : (a) with frequency is around 1.1 to 5;
(b) with voltage is around 2
(c) with terminals is around 3 to 5
In Fig. 5.7, (T1) the variation of LF : (a) with frequency is around 8 to 24;
(b) with voltage is around 1.7 to 2.4
(c) with terminals is around 1.2 to 2.4
In Fig. 5.8, (T2) the variation of LF : (a) with frequency is around 4.35 to 12
(b) with voltage is around 0.7 to 0.85
(c) with terminals is around 0.3 to 0.85
In Fig. 5.9, (T3) the variation of LF : (a) with frequency is around 5.8 to 17;
(b) with voltage is around 4 to 8
(c) with terminals is around 2.5 to 8
In Fig. 5.10, the variation of LF: (a) with frequency is around -40 to 100;
(w.r.t. 176V to 141V &
w.r.t. 176V to 195V) (b) with voltage is around 50 to 100
(c) with terminals is around -40 to 100
In Fig. 5.11, the variation of AR: (a) with frequency is around 150 to -50
(w.r.t. 176V to 141V &
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
84
w.r.t. 176V to 195V) (b) with voltage is around 50
(c) with terminals is around 60 to -50
In Fig. 5.12, the variation of AC: (a) with frequency is around 120 to -60;
(w.r.t. 176V to 141V &
w.r.t. 176V to 195V) (b) with voltage is around 60
(c) with terminals is around 40 to -60
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
85
CHAPTER 6
DISCUSSION
In this chapter, the measured relaxation phenomena in oil filled transformers are
discussed with a view to identify ageing tendency. The oil filled transformer
insulation is made of pressboard insulation immersed in transformer oil. The studied
single wire earth return (SWER) transformers had one/two low voltage (LV)
winding/s with two/ four insulated terminals, one high voltage winding (HV) with two
insulated terminals, one 11 kV rated porcelain bushing connected to the high voltage
terminal, and a sealed metal tank housing all the windings, core and bushings. Both
LV and HV windings with the respective solid insulation are kept immersed in
transformer oil within the tank. From the name plate details, the weight of oil
insulation varied from 20% to 30% of total weight of the transformer. It should be
noted that the press-board solid insulation is impregnated with transformer oil under
vacuum condition. New transformer oil and paper insulation will have a minimum
quantum of water content. As the transformer is put into operation, the loading heats
up the insulation and unloading tracks back the insulation to lower operating
temperature. In general, the transformer may be operated with a temperature rise of
about 60ºC (as per name plate details) from the ambient. The paper and oil have
different moisture content at different temperatures [52]. Because of that, moisture
migration occurs between the insulation due to fluctuating operating temperatures and
degrades the oil. In addition, moisture may leak through weak transformer sealing
arrangements. Localised high electrical stresses may create hot-spots leading to
partial discharges [32] [55]. Because of all the different phenomena, it is found that
the acidity level and oxidation rate within the insulation increased [22] [60] and the
paper polymer strength, and oil breakdown strength would be reduced. The leakage
current normally increases leading to more heating of transformer [65].
In this study, dielectric relaxation measurements are carried out to identify ageing of
three known transformers of more or less similar rating and construction. Since the
objective of this study is related with the industrial asset management of oil filled
transformers, an industrial grade dielectric instrumentation is designed and tested for
use.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
86
6.1 Test arrangement
The test arrangement consists of the developed dielectrometry instrumentation, the
test objects of three ‗SWER‘ transformers with known aging level and a lab-top based
controller to generate the control waveform, to store the current response and to
analyse the relaxation characteristics of insulation.
6.1.1 Developed dielectrometry instrumentation
From the literature survey [60][64], dielectric sine wave measurements in the
frequency range from 1 µHz to 1000 Hz with a perturbation peak sine wave
magnitude of 141V are used to diagnose the degradation or moisture content in
different oil filled power apparatus. Also, it is learnt that time domain industrial
recovery voltage measuring unit (RVM) takes about 3 hours of test time for one set of
measurements [50][62]. It is found that all the existing instruments can be used only
in ‗Off-line‘ mode of testing. QUT is interested in coming up with ‗On-line‘
relaxation measurement unit. My initial development is concentrated on developing a
reliable and portable ‗Off-line‘ relaxation measurement unit to identify aging with
known transformers. For industrial site measurements, the period for testing is limited
to about 5 to 6 minutes. Since it is a digital instrumentation, the output is drift-free to
any lowest frequency level of measurement. The data can be stored with the desired
number of sampled points, and the number and desired number of frequencies can be
programmed in. Chapter 3 briefs the developed hardware and controlling software.
Two coaxial shielded cables with Teflon insulation are used to connect the
transformer.
The developed instrumentation can generate bipolar sine or any other programmed
wave with a peak voltage magnitude in the range from ±50 V to ±200 V. The
maximum current output from the unit can be 1 mA and the response current can be
recorded in 3 ranges with 6 digits resolution with multiplication factors of 1, 10 and
100. A current level of 30 nA can be recorded. The instrument is calibrated with the
known resistive load. The respective multiplication factors to convert recorded
voltage signals to the real applied HV and the response currents are tabulated in Table
(4.1). The high voltage generator introduced a phase shift error and the instrument is
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
87
calibrated to determine the introduced phase error with frequency in all the current
ranges.
After checking the reproducibility of the results, the measurement procedure is
standardised. A frequency range of 15 MHz to 1.5 Hz is selected so that one set of 5
discrete frequency measurements in that frequency range can be completed in 5 to 6
minutes by using the program. At each selected frequency, three consecutive cycles of
same period are recorded. The first and second cycles are found to have distorted
current responses. The last third cycle of measurement is taken for the analysis.
6.1.2 The test transformers
The tested ‗SWER‘ transformer has three metallic terminals. The insulation between
low voltages winding (L), high voltage winding (H) and tank (T) are tested by taking
two terminals at a time with other terminal grounded. Normally, the high voltage
winding gets degraded due to significant stresses.
Before taking any relaxation measurement, the terminals L, H and T of the
transformers are shorted to ground for about 15 to 30 minutes so that any residual
trapped charge across the insulation can be drained significantly. The trapped charge
can degrade the insulation and may not result in reproducible current response for any
voltage perturbation. T1 and T3 are aged as per the name plate details for 30 years
and 15 years respectively. T1 insulating oil was replaced about 3 years back. T3 was
used extensively for continuous HV testing. T2 is aged only for about six months and
is fairly new transformer. The dc test measurement between low and high voltage
windings indicated the polarisation index of T1, T2 and T3 as 1.28, 3.49 and 1.34. As
per the maintenance rules, T1 and T3 should be inspected for any degradation. The
transformers are kept on the insulated platform so that the tank is not grounded by the
supporting structure.
6.1.3 Computer interface
A lab-top computer loaded with control software communicates with dielectrometry
instrumentation to generate the desired sine waveform, and to store the proportional
HV perturbation voltage signal and response current signal with time of sampling.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
88
Mat lab software routines are used to extract single voltage wave and the
corresponding response current wave shown in Figures 4.1 to 4.10. The various
analysis routines to extract aging tendency are developed.
The relaxation measurements are carried by varying the peak voltage magnitude of
sine wave and by varying the metallic terminals, L, H and T of the ‗SWER‘
transformers.
6.2 Ratio of sine wave response currents at two extreme frequency range limits
All the current responses lead the perturbation sine wave voltage suggesting that the
dielectric media behaves like an RC element. Figures 4.2 to 4.10 show the
proportional voltage and current responses with TG, LG and HG configurations. As
the frequency is reduced, the response current magnitude decreases. A frequency
change of 100 times (1.5 Hz to 15 MHz) results in current reduction of 42 to 55, 21to
32, 24 to 35 in TG, LG and HG configurations respectively with T1. With the new
transformer, T2 the corresponding current reductions are 87 to 97, 33 to 42, 12 to 40
in TG,LG and HG configurations respectively. The changes are more on TG
configuration. The corresponding current reductions with T3 are 4.6 to 5.5, 3.5 to 4,
2.7 to 3.6 in TG, LG and HG configurations respectively.
The change in current magnitude with change in frequency is more with new
transformer, T1. It is significantly less with transformer, T3. It suggests that T3 is
aged more than T2 and T1 across low and high voltage insulation.
Following the same reasoning, the insulation of low and high voltage windings with
respect to tank of T3 is in very bad condition.
In T2, new transformer‘s low voltage winding insulation with reference to tank is in
bad condition compared to T1. High voltage winding insulation with reference to
tank of T2 is better than the corresponding high voltage winding insulation to ground
of T1.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
89
As the perturbation voltage magnitude is increased, the response current magnitude
also increases.
6.3 Trend of current variation with frequency
Figures 4.11 to 4.13 show the trend of current variation with frequency. In all the
transformers, the current increased with increase in frequency and applied
perturbation voltage.
In the old transformer T1, the observed peak current variation with voltage lied in the
range (0.18-0.58) x10-5
A with a ratio of 3.2; (0.45-1.3) x 10-5
A with a ratio of 2.9;
and (0.45-1.3) x 10-5
A with a ratio of 2.9 with the tested configurations of LG, TG
and HG respectively. The observed ratio of variation at the two extreme frequencies is
discussed in section 6.2.
In the new transformer T2, the observed peak current variation with voltage lied in the
range (0.3-0.8) x10-5
A with a ratio of 2.7; (1.25-3.7) x 10-5
A with a ratio of 3; and
(0.1-0.55) x 10-5
A with a ratio of 5.5 with the tested configurations of LG, TG and
HG respectively.
In the old transformer T3, the observed peak current variation with voltage lied in the
range (0.5-1.25) x10-5
A with a ratio of 2.5; (0.9-2.6) x 10-5
A with a ratio of 2.9; and
(1.4-3.55) x 10-5
A with a ratio of 2.5 with the tested configurations of LG, TG and
HG respectively.
New transformer showed a maximum current variation in the range of (0.55 to 3.7) x
10-5
A with a good sensitivity to voltage in the ratio of 2.7 to 5.5. The old transformer
T3 showed a maximum current variation of (1.25 to 3.55) x 10-5
A with a voltage
variation ratio of 2.5 to 2.9. The transformer T1 followed the characteristic of T3.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
90
6.4 Trend of leading phase angle variation with frequency
Figures 4.14 to 4.16 show the variation of phase shift with frequency, voltage and
tested terminals. Monotonically increasing phase shift with increase in frequency and
voltage is seen in all the tested cases.
At 141V, old transformer, T1 had the phase variation of 56º(32º to 88º), 55º (27º to
82º) and 56º (23º to 79º ) with TG, LG and HG configurations for a frequency
increase of 100 times. At 195V, for the same frequency change, the phase variation
reduced to 49º (40º to 89º), 47º (34º to 81º) and 49º (30.5º to 79.5º) with TG, LG and
HG. With an increase in voltage, more polarisations are observed in all the tested
configurations.
At 141V, new transformer, T2 had the phase variation of 25º (62º to 87º), 38º (49º to
87º) and 31º (50º to 81º) for a frequency increase of 100 times with TG, LG and HG
configurations. At 195V, for the same frequency change, the phase variation reduced
to 14º (75º to 89º), 32º (54º to 86º ) and 26º (54º to 80º) with TG, LG and HG
configurations. With increase in voltage, more polarisations are observed in all the
tested configurations.
At 141V, old transformer, T3 had the phase variation of 50º (13º to 63º), 49º (9º to
58º) and 40º (8º to 48º ) for a frequency increase of 100 times with TG, LG and HG
configurations. At 195V, for the same frequency change, the phase variation reduced
to 50º (21º to 71º), 42º (18º to 60º) and 38º (15º to 53º) with TG, LG and HG
configurations. With increase in voltage, more polarisations are observed in all the
tested configurations.
The new transformer, T2 had phase variation in the range of 25º to 38º at 141V which
reduced to 14º to 32º at 195V.
The old transformer T3 had phase variation in the range of 40º to 50º at 141V which
reduced to 38º to 50º at 195V. T1 had phase variation in the range of 55º to 56º at
141V which reduced to 47º to 49º at 195V. With ageing, the range swings to more
phase shift with reduced variation with increase in voltage.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
91
6.5 Trend of resistive and capacitive currents variation with frequency
Section 5.2 analyses the variation of in-phase resistive (IR) current and 90º phase
shifted capacitive (IC) current with frequency. Both the currents increase as the
frequency and applied perturbation magnitude are increased.
In old transformer T1, the rate of increase in IC with frequency is slightly more than
the rate of increase in IR with frequency. A frequency change of 100 resulted in
increased change of IC by 80 to125, 50 to 100, 43 to111 under TG, LG, and HG
configurations. The corresponding changes with IR are 1.88 to 2.7, 5 to 6.7 and 5 to
7.5. The increase in voltage resulted in more current for all the cases in the entire
frequency range. More polarisation current is recorded in TG and HG configurations.
More leakage current response is observed in HG configuration.
In new transformer T2, the rate of monotonic increase in IC with frequency is more
than the rate of increase in IR with frequency. A frequency change of 100 resulted in
increased change of IC by 105 to 133, 43 to 50, and 60 to 62 under TG, LG, and HG
configurations. The corresponding changes with IR are 7 to 20, 2 to 5, and 2.3 to12.5.
The effect of voltage is significant at the lowest tested frequency. With TG
configuration, more polarisation (IC) and leakage (IR) behaviour are observed across
low and high voltage winding insulation.
In old transformer T3 also, monotonically increasing current response is seen with
increase in frequency. The rate of change in IC with frequency follows the pattern of
T1. It is less than the resistive current component in the low frequency range. A
frequency change of 100 resulted in increased change of IC by 15.8 to 22, 15 to 25,
and 14.5 to 50 under TG, LG, and HG configurations. The corresponding changes
with IR are 1.89 to 2.2, 1.43 to 2 and 2.22 to 5. The effect of voltage in increasing the
current is seen in the entire frequency range. With HG and TG configurations, more
polarisation current (IC) trend is seen while increased leakage current (IR) behaviour is
seen with HG configuration.
Good new transformer, T2 resulted in increase IC current ratio in the range of 43 to
133 with increase in frequency. Similar range of variation is observed with T1. Bad
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
92
transformer, T3 resulted in IC current ratio in the range of 14.5 to 50 with increase in
frequency.
Good new transformer, T2 resulted in increase in IR current ratio in the range of 2 to
20 with increase in frequency. The corresponding range of variation with old
transformer T1 is 1.88 to 7.5. Bad transformer, T3 results are like T1 with IR current
ratio in the range of 1.43 to 5 with increase in frequency.
Following that logic in T2, the insulation between low voltage and high voltage
winding is in good condition.
6.6 Trend of real and imaginary admittance variation with frequency
Figures 5.4 to 5.6 present the variation of admittance with frequency and voltage. The
real (AR) and imaginary (AC) admittances in general increase monotonically with
increase in frequency and voltage.
In old transformer T1, the rate of increase in AC with frequency is slightly more than
the rate of increase in AR with frequency. A frequency change of 100 resulted in
increased change of AC by 87.5 to100, 50 to 100, and 47 to 75 under TG, LG, and HG
configurations. The corresponding changes with IR are 2 to 2.1, 5.14 to 7.7 and 6 to 8.
The increase in voltage resulted in more admittance for all the cases in the entire
frequency range. More polarisation admittance (AC) is recorded in TG and HG
configurations. More leakage current response is observed in HG configuration.
In new transformer T2, the rate of increase in AC with frequency is more than the rate
of increase in AR with frequency. A frequency change of 100 resulted in increased
change of AC by 133 to 167, 56 to 67, and 17.5 to 20 under TG, LG, and HG
configurations. The corresponding changes with IR are 5.8 to 23.3, 4.3 to 5 and 2.8 to
10. The increase in voltage resulted in more admittance for all the cases in the entire
frequency range. More polarisation admittance (AC) is recorded in TG configuration.
More leakage current response is observed in HG configuration.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
93
In old transformer T3, the rate of increase in AC with frequency is more than the rate
of increase in AR with frequency. A frequency change of 100 resulted in increased
change of AC by 16.7 to 20, 13.3 to 30, and 15 to 40 under TG, LG, and HG
configurations. The corresponding changes with IR are 1.1 to 2.14, 2.57 to 2.67 and
2.2 to 5. The increase in voltage resulted in more admittance for all the cases in the
entire frequency range. More polarisation admittance (AC) is recorded in TG and HG
configurations. More leakage current response is observed in HG configuration.
Good new transformer, T2 resulted an increase in AC current ratio in the range of 17.5
to 167 with increase in frequency. Similar range of variation is observed with T1. Bad
transformer, T3 resulted in AC current ratio in the range of 13.3 to 40 with increase in
frequency.
Good new transformer, T2 resulted an increase in AR current ratio in the range of 2.8
to 23.3 with increase in frequency. The corresponding range of variation with old
transformer T1 is 2 to 8. Results on bad transformer, T3 are like T1 with AR current
ratio lying in the range of 1.1 to 5 with increase in frequency.
Following that logic in T2, the insulation between low voltage and high voltage
winding is in good condition.
6.7 Trend of tanδ variation with frequency
Figures 5.7 to 5.9 show the variation of sensitive parameter tanδ with frequency and
voltage. The loss factor, tanδ decreases in all the cases with the increase in frequency
and perturbation voltage level.
In old transformer T1, for a frequency change of 100, the observed changes are 16 to
24, 8 to 11 and 8.5 to 11.8 under TG, LG, and HG configurations. The loss factor was
maximum under HG configuration indicating the weak low voltage winding
insulation with respect to tank.
In new transformer T2, the estimated loss factor is minimum. For a frequency change
of 100, the observed changes are 6.88 to 14, 11 to 12 and 4.35 to 5.5 under TG, LG,
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
94
and HG configurations. The loss factor was maximum under LG and HG
configuration.
In old transformer T3, maximum loss factor is observed. For a frequency change of
100, the observed changes are 8.7 to14, 8 to17 and 5.8 to 13.3 under TG, LG, and HG
configurations. The loss factor was maximum under HG configuration indicating the
weak low voltage winding insulation with respect to tank.
New transformer T2 had minimum loss factors and the variation with frequency and
voltage is minimum.
6.8 Effect of voltage on tanδ and admittance
Figure 5.10 shows the percentage variation of loss factor with voltage. With new
transformer, the change was maximum at the highest tested frequency. Increasing
trend of change is observed with increase in frequency.
Fig. 5.11 shows the percentage variation of real admittance with voltage. With new
transformer, more changes are observed. While Fig. 5.12 shows the variation of
imaginary admittance with voltage. The change is comparatively less on new
transformer.
6.9 Summary
This chapter discusses about the observed results under this research program. Section
6.1 presents in detail the developed new industrial relaxation instrumentation and the
test program. Section 6.2 analyses and discusses the results on response currents with
reference to aging indicators. Sections 6.3 and 6.4 discuss the trend of current and
phase shift to identify the aging tendency. Section 6.5 discusses the trend of resistive
and capacitive components of current with three transformers. While section 6.6
discusses on the estimated real and imaginary admittances. The section 6.7 analyses
the sensitive parameter of aging, tan δ variation with aging. The last section 6.8
discusses on the effect of perturbation voltage level on tanδ and admittance variation
on three transformers.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
95
In simple terms, the study suggests that the aged insulation can be identified with
different analyses discussed in chapters 5 and 6. It can be quantified to relate with the
traditional aging rate measurements by fitting the trend of current, phase, admittance
and tanδ parameters with equations. The future field measurements with a number of
transformers may push the direction of this promising relaxation measurement to
identify aging tendency, aging level and aging rate.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
96
CHAPTER 7
CONCLUSIONS AND SCOPE OF FUTURE WORK
This chapter summarizes the findings of this investigation and presents the possible
future work which may be undertaken further.
The main objectives of the research as stated in Chapter 1 are:
1. To develop and evaluate the specifications of a portable relaxation
instrumentation for industrial use.
2. To test the instrument and collect relaxation responses on known three aged
oil-filled transformers.
3. To analyse the data and identify aging conditional indicators.
4. Study the variation of aging indicators by varying the frequency range,
perturbation voltage level and terminals of test.
To the best of my abilities, the research tasks have been completed. The task will be
complete if the software and hardware is tested at any substation site transformer
away from controlled and protected QUT environment.
7.1 Conclusion
Objective 1:
The developed lab view software (i) to generate the digital control waveform, (ii) to
convert that data to suitable analog level signal to amplify, (iii) to store the
proportional high voltage polarisation and response relaxation current signal. The
developed software can run with lab view software platform. With the converted
*.exe module, it can be loaded to any computer – bench-top or lab top to interface
with the instrument. The communication is done through USB cable. The instrument
is calibrated with a known resistive load and the conversion factors are provided in
Table 4.1. It is found that HV amplifier generated phase shift error above 1.5Hz in
three current ranges.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
97
In the appendix, the developed *.exe software to generate sine wave, triangular wave
and square wave is loaded in CD. The corresponding source programs *.vi are also
included. In this project, the testing is done with sine wave only. Most of the
measurements are carried only in the middle range of the incorporated 3 amplifier
ranges. The instrument is able to provide a maximum of 1 mA at a maximum voltage
level of ± 200 Vdc. In the conducted experiments, a frequency range from 15 mHz to
1.5Hz is selected. The limitation on that range is due to modulated noise current level
from the transformers in the lowest frequency level of 15 mHz. The software and
hardware are tested in lap-top as well as bench-top. It is also tested by other fellow
research students.
It is to be tested for use of substation site transformer.
Objective 2:
The instrument is tested with three known ‗SWER‘ oil filled transformers of different
aged levels. T2 is a new transformer. T1 is 30 years old transformer as per name plate
details. This transformer T1 is a reconditioned one after decommissioning after 25
years of service. The transformer oil was replaced with fresh oil and the utility
donated to QUT. T3 is another used transformer but it was used in a continuous mode
in utility and at QUT for pollution testing work. All the transformers had metallic
terminals from the low voltage winding, high voltage winding and tank. All the
shorting links were removed for the measurements and the tank was mounted on an
insulated platform for carrying the required tests. The available terminals were
shorted to ground before and after the relaxation measurements.
Three terminals insulation measurement is carried out to identify the degradation
between (i) low voltage winding and tank by grounding the high voltage winding, (ii)
high voltage winding and tank by grounding the low voltage winding,(iii) low voltage
winding and high voltage winding by grounding the tank. This way, the insulation
status of the windings can be evaluated in a better way. The relaxation sine wave
measurements in the selected frequency range were carried on a transformer with
three different configurations.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
98
From the theory, it is learnt that the insulation will have two components of current. It
was planned to investigate the role of applied polarisation voltage level on the
relaxation current components. Using the instrument, it is found that the transformers
can be tested in a frequency range from 15 mHz to 1.5 Hz without much modulated
noise. Five set frequencies: 15 mHz, 30 mHz, 150 mHz, 300 mHz, and 1.5 Hz are
used for the test to get a frequency spectrum. Each set of measurement in that
frequency range took about 5 to 6 minutes. It is found that the initial perturbation
generated some distortion in the periodic response and the third consecutive cycle is
used for analysis.
The number of sampled points for each cycle was 1000 points for any frequency
range. A minimum current level of about 30 nA can be recorded with this unit and
the maximum perturbation voltage can be ± 200 V. Reproducible results are obtained
with the unit. Teflon coated shielded cables are used to connect the instrument to the
test transformer.
Objective 3:
The data are stored as *.txt files. Using the developed Matlab routines, the data are
analysed. Identification of aging condition indicators is made by the trend of data with
frequency, perturbation voltage level and terminals of test. All the relaxation current
responses are found to retain the sine wave shape and they are found to have leading
phase shift with reference to applied perturbation sine wave voltage.
Initial analysis is made on variation of current magnitude and phase shift with
frequency, perturbation voltage level and three test terminals configurations.
Then the derived analysis is made.
The variation of real/in phase /resistive current component and imaginary/90º phase
shifted/capacitive component with frequency, perturbation voltage level and three
test configurations are studied with three transformers. The loss factor or tanδ is
computed as a ratio of resistive current component to capacitive current component.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
99
After that, admittance with real and imaginary admittance components is analysed.
The effect of perturbation voltage on tanδ and admittance responses is analysed. It is
found that the current and phase shift changed with increase in voltage. The
measurements are done at 141V, 176V and 195V. By taking 176V reading as
reference, the upward and downward voltage variation effects are analysed.
The ageing indicators tanδ, admittance and its changes with voltage in the lowest test
frequency can be effectively used as ageing predictors. At this stage, a correct
relationship could not be established as the method is not tested on many transformers
and also, the degree of polymerisation data to quantify aging using traditional method
is not available.
Objective 4:
It is found that the response relaxation current increases with increase in frequency
and perturbation voltage level. Chapter 6 provides the trend in some quantitative way.
It is found that T2 is in very good condition followed by T1 and then last more aged
as T3.
7.2 Scope of future work
The scope of this condition monitoring work appears to be enormous.
(i) This technique has to be validated in the substation test site oil filled
transformers of different rating and some valid data base to relate with
aging must be developed along with other condition indicators.
(ii) The instrumentation must be tested and improved for ‗On-line
measurement‘, and in that square wave or single pulse perturbation modes
may be of great use.
(iii) It seems that more curve fitting and extensive time and frequency domain
analysis can be made to identify the most sensitive conditional parameters
with aging.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
100
(iv) This method may be extended to other electrical power apparatus for
ageing identification.
(v) ‗Effect of operation Temperature‘ and ‗Wave shape of perturbation
signal‘ to identify aging on transformers will be good area for the applied
research.
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
101
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APPENDIX A
1 Lab view software:
The one objective of this thesis is to develop the lab view software program for
(i) To generate the digital control waveform.
(ii) To convert that data to suitable analog level signal to amplify.
(iii) To store the proportional high voltage polarisation and response relaxation
current signal.
Three transformers are tested using this lab view software. This software is used to
collect the relaxation data for each of the transformer. The lab view software is used
under three different voltages ± 141V, ± 176V, and ± 195V and the each voltage is
operated under five frequency range of 15MHz to 1.5Hz. The each transformer is
tested under three conditions as shown in the chapter 3 in table 3.3. The relaxation
data is collected using this lab view software and plotted in the chapter 4 in fig 4.2 to
4.10. The graphical software code is shown in Fig.3.1.
2 Mat lab Program for Results:
In the chapter 4, the results are shown.
(i) The relaxation current response, from the data collected using lab view
software; the results are extracted using the Mat lab software. The M-file
for the fig 4.11, 4.12 and 4.13. The same M-file is used for the figures
4.11, 4.12 and 4.13. Just the values, magnitude and transformers are
changed in the program.
clear; F=[0.015 0.03 0.15 0.3 1.5]; TG=[[0.02+0.005 0.025+0.01 0.075+0.055 0.13+0.115
0.6+0.59]*3.9542*10-6]; LG=[[0.01+0.005 0.01+0.01 0.035+0.03 0.06+0.055 0.25+0.25]*3.9542*10-
6]; HG=[[0.02+0.02 0.03+0.02 0.08+0.07 0.14+0.13 0.61+0.61]*3.9542*10-6]; plot(F,TG,F,LG,F,HG); grid; legend('TG','LG','HG'); xlabel('Frequency in Hz'); ylabel('Response Sine Peak Current in A'); title('T1 141V');
Investigation of ‗Off-Line‘ Relaxation Phenomena in Oil Filled Transformers
110
(ii) The relaxation leading phase shift, from the data collected using lab view
software; the results are extracted using the Mat lab software. The M-file
for the fig 4.14, 4.15 and 4.16. The same M-file is used for the figures
4.14, 4.15 and 4.16. Just the values, phase and transformers are changed in
the program.
clear; F=[0.015 0.03 0.15 0.3 1.5]; TG=[32.4 57.6 75.6 77.4 66.6+21.49]; LG=[27 50.4 60.12 68.4 61.2+21.49]; HG=[23.4 43.2 51.12 64.8 57.96+21.49]; plot(F,TG,F,LG,F,HG); grid; legend('TG','LG','HG'); xlabel('Frequency in Hz'); ylabel('Leading phase shift in degrees'); title('T1 141V');
(iii) Program to find Phase and Admittance
clear; k=3.1236e-6 load a20_01.txt; a1=a20_01(:,1); a2=a20_01(:,2); a4=a20_01(:,4);%4.5 to 0.5 i=1:3002; V1=max(a4); V2=min(a4); V3=(V1-V2)*0.5; V4=a4-V3-V2; plot(V4); V5=V4./(max(V4)); V6=V5*195; plot(V6);%***********voltage I1=a2; I2=I1*k; plot(a1,I2); V=V6(1250:length(V6)-10); I=I2(1250:length(V6)-10); T=a1(1250:length(V6)-10); save ND20_01 T V I; clear; load ND20_01;%T V I; plot(T,V); MV=max(V); MI=max(I); Adm=MI/MV %**********Phase NV=V./max(V);
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NI=I./max(I); t=1:length(NV); plot(t,NV,t,NI); grid;
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APPENDIX B
The analysis is done using the equations 1, 2, 3 and 4 in chapter 5, to find the
resistive current, capacitive current, resistive admittance, capacitive admittance
and loss factor. The mat lab program is done to show the plots plotted in the
chapter 5.
(i) Relaxation IR and IC current response for the fig 5.1, 5.2 and 5.3:
clear; F=[0.015 0.03 0.15 0.3 1.5]; TGIC=[1.79E-9 2.49E-9 2E-9 1.93E-9 2.02E-9]; LGIC=[2.33e-9 2.27e-9 1.04e-9 9.17e-10 8.57e-10]; HGIC=[3.42e-9 3.21e-9 1.94e-9 3.9e-9 2.03e-9]; TGIR=[0.113E11 0.1E11 0.621E10 0.370E10 0.168E10]; LGIR=[0.704E10 0.840E10 0.535E10 0.439E10 0.29E10]; HGIR=[0.408E10 0.465E10 0.204E10 0.869E9 0.84E9]; plot(F,TGIR,F,TGIC,F,LGIR,F,LGIC,F,HGIR,F,HGIC); legend('TGIR','TGIC','LGIR','LGIC','HGIR','HGIC'); xlabel('Frequency in Hz'); ylabel('Response peak IR and IC in A'); title('T1 141V');
(ii) Real and imaginary admittance response for the fig 5.4, 5.5 and 5.6:
clear; F=[0.015 0.03 0.15 0.3 1.5]; TGAR=[2.46E-9 3.97E-9 3.03E-9 3E-9 3.12E-9]; LGAR=[1.7e-9 1.71e-9 1.52e-9 1.39e-9 1.33e-9]; HGAR=[4.13e-9 4.17e-9 3.18e-9 3.28e-9 3.15e-9]; TGAC=[3.45E-8 2.27E-8 7.74E-9 6.58E-9 6.02E-9]; LGAC=[1.72E-8 1.08E-8 3.31E-9 3.2E-9 2.84E-9]; HGAC=[7.19E-8 4.21E-8 1.31E-8 1.05E-8 7.89E-9]; plot(F,TGAR,F,TGAC,F,LGAR,F,LGAC,F,HGAR,F,HGAC); legend('TGAR','TGAC','LGAR','LGAC','HGAR','HGAC'); xlabel('Frequency in Hz'); ylabel('Response AR and AC in Mhos'); title('T1 141V');
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(iii) Variation of loss factor for the fig 5.7, 5.8 and 5.9:
clear; F=[0.015 0.03 0.15 0.3 1.5]; TG=[1.57 0.63 0.26 0.22 0.03]; LG=[1.97 0.83 0.57 0.39 0.13]; HG=[2.31 1.06 0.8 0.47 0.19]; plot(F,TG,F,LG,F,HG); legend('TG','LG','HG'); xlabel('Frequency in Hz'); ylabel('Loss factor'); title('T1 141V');