Transformer
Engineering
Copyright © 2004 by Marcel Dekker, Inc.
POWER ENGINEERING
1. Power Distribution Planning Reference Book,
H.Lee Willis
2. Transmission Network Protection: Theory and Practice,
Y.G.Paithankar
3. Electrical Insulation in Power Systems,
N.H.Malik, A.A.Al-Arainy, and
M.I.Qureshi
4. Electrical Power Equipment Maintenance and Testing,
Paul Gill
5. Protective Relaying: Principles and Applications, Second Edition,
J.
Lewis Blackburn
6. Understanding Electric Utilities and De-Regulation,
Lorrin Philipson and
H.Lee Willis
7. Electrical Power Cable Engineering,
William A.Thue
8. Electric Systems, Dynamics, and Stability with Artificial Intelligence
Applications,
James A.Momoh and Mohamed E.El-Hawary
9. Insulation Coordination for Power Systems,
Andrew R.Hileman
10. Distributed Power Generation: Planning and Evaluation,
H.Lee Willis and
Walter G.Scott
11. Electric Power System Applications of Optimization, James A.Momoh

Ali Abur
and Antonio Gómez Expósito
25. Transformer Engineering: Design and Practice,
S.V.Kulkarni and
S.A.Khaparde
ADDITIONAL VOLUMES IN PREPARATION
Copyright © 2004 by Marcel Dekker, Inc.
Transformer
Engineering
Design and Practice
S.V.Kulkarni
S.A.Khaparde
Indian Institute of Technology, Bombay
Mumbai, India
NEW Y ORK • BASELMARCEL DEKKER, INC.
Copyright © 2004 by Marcel Dekker, Inc.
Transferred to Digital Printing 2005
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and are used only for identification and explanation without intent to infringe.
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transformers. The transformer as a system consists of several components and it is
absolutely essential that the integrity of all these components individually and as
a system is ensured. A transformer is a complex three-dimensional
electromagnetic structure, and it is subjected to variety of stresses, viz. dielectric,
thermal, electrodynamic, etc. In-depth understanding of various phenomena
occurring inside the transformer is necessary. Most of these can now be simulated
on computers so that suitable changes can be made at the design stage to eliminate
potential problems.
I find that many of these challenges in the design and manufacture of
transformers, to be met in fast changing market conditions and technological
options, are elaborated in this book. There is a nice blend of theory and practice in
almost every topic discussed in the text. The academic background of the authors
has ensured that a thorough theoretical treatment is given to important topics. A
number of landmark references are cited at appropriate places. The previous
industry experience of S.V.Kulkarni is reflected in many discussions in the book.
The various theories have been supported in the text by reference to actual
practices. For example, while deliberating on various issues of stray loss
estimation and control, the relevant theory of eddy currents has been first
explained. This theoretical basis is then used to explain various design and
iii
Copyright © 2004 by Marcel Dekker, Inc.
manufacturing practices established in the industry to analyze and minimize the
stray losses in the windings and structural components. The design and
manufacturing practices and processes have significant impact on the
performance parameters of the transformers, and the same have been identified in
the text while discussing various topics.
Wherever required, a number of examples and case studies are given which are
of great practical value. The knowledge of zero-sequence characteristics of
transformers is very important for utilities. It is essential to understand the
difference between magnetizing and leakage zero-sequence reactances of the

Past Chairman, IEEE Transformers Committee
iv Foreword
Copyright © 2004 by Marcel Dekker, Inc.
Preface
In the last decade, rapid advancements and developments have taken place in the
design, analysis, manufacturing and condition-monitoring technologies of
transformers. The technological progress will continue in the forthcoming years.
The phenomenal growth of power systems has put tremendous responsibilities on
the transformer industry to supply reliable and cost-effective transformers.
There is a continuous increase in ratings of generator transformers and
autotransformers. Further, the ongoing trend to go for higher system voltages for
transmission increases the voltage rating of transformers. The increase in current
and voltage ratings calls for special design and manufacturing considerations.
Advanced computational techniques have to be used that should be backed up by
experimental verification to ensure quality of design and manufacturing
processes. Some of the vital design challenges are: stray loss control, accurate
prediction of winding hot spots, short-circuit withstand capability and reliable
insulation design. With the increase in MVA ratings, the weight and size of large
transformers approach or exceed transport and manufacturing capability limits.
Also, due to the ever-increasing competition in the global market, there are
continual efforts to optimize the material content in transformers. Therefore, the
difference between withstand levels (e.g., short circuit, dielectric) and
corresponding operating stress levels is diminishing. Similarly, the guaranteed
performance figures and actual test values are now very close. All these factors
demand greater efforts from researchers and designers for accurate calculation of
various stress levels and performance figures for the transformers. In addition,
strict control of manufacturing processes is required. Manufacturing variations of
components should be monitored and controlled.
Many of the standard books on transformers are now more than 10 years old.
Some of these books are still relevant and widely referred for understanding the

interaction aspects of transformers in an interconnected power
system to improve on specifications and employ diagnostic tools
for condition monitoring
(3) Undergraduate and postgraduate students who wish to integrate
traditional transformer theory with modern computing practices
In Chapter 1, in addition to the transformer fundamentals, various types of
transformers in a typical power system are explained along with their features.
There is a trend to use better materials to reduce core losses. Often the expected
loss reduction is not obtained with these better grades. The design and
manufacturing practices and processes that have significant impact on the core
performance are highlighted in Chapter 2. The three-phase three-limb core has
inherent magnetizing asymmetry that sometimes results in widely different no-
load current and losses in three phases of the transformer during the no-load loss
measurement by the three-wattmeter method. It is shown that one of the three
wattmeters can have a negative reading depending on the magnitude of
asymmetry between phases and the level of excitation. Although the inrush
current phenomenon is well understood, the sympathetic inrush phenomenon—
in which the magnetization level of a transformer is affected by energization of
vi Preface
Copyright © 2004 by Marcel Dekker, Inc.
another interconnected transformer—is not well known. The factors influencing
the phenomenon are elucidated in the chapter. The phenomenon was investigated
by the first author in 1993 based on switching tests conducted at a site.
Chapter 3 is devoted to reactance of transformers, which can be calculated by
either analytical or numerical methods. Procedures for the calculation of
reactance of various types and configurations of windings, including zigzag and
sandwich windings, are illustrated. The reactance for complex winding
configurations can be easily calculated by the finite element method (FEM),
which is the most widely used numerical method. The chapter gives exhaustive
treatment of zero-sequence characteristics of the transformers. Procedures for

7. The results of three different methods are presented for a typical winding.
Methods for avoiding winding resonances are also explained.
Chapter 8 examines in detail the insulation design philosophy. Various factors
that affect insulation strength are summarized. The formulae given for bulk oil
Preface vii
Copyright © 2004 by Marcel Dekker, Inc.
and creepage withstand are very useful to designers. Procedures for the design of
major and minor insulation systems are presented.
Chapter 9 deals with the thermal aspects of transformer design. After a
description of the modes of heat transfer, various cooling systems are described.
The insulation aging phenomenon and life expectancy are also discussed. A
number of recent failures of large transformers have been attributed to the static
electrification phenomenon, which is explained at the end of the chapter.
Various types of loads and tests that determine aspects of structural design are
discussed in Chapter 10. Tank-stiffening arrangements are elaborated. This
material has been scarce in the available literature. Because of increasing
environmental concerns, many users are specifying transformers with lower noise
levels. Different noise level reduction techniques are discussed and compared.
Chapter 11 is devoted to four special transformers: rectifier transformers,
HVDC converter transformers, furnace transformers and phase-shifting
transformers. Their design aspects and features, different from those of
conventional distribution and power transformers, are enumerated.
The text concludes by identifying current research and development trends.
The last chapter is intended to give pointers to readers desirous of pursuing
research in transformers.
Even though the transformer is a mature product, there are still a number of
design, manufacturing and power system interaction issues that continue to
attract the attention of researchers. This book addresses many of these issues and
provides leads to most of the remaining ones. It encompasses all the important
aspects of transformer engineering including the recent advances in research and

refining Chapter 8. He also gave useful comments on Chapter 9. We thank Mr.
G.S.Gulwadi for reviewing Chapters 1 and 8. Mr. V.D.Deodhar helped to improve
Chapter 10.
We are also thankful to Dr. B.N.Jayaram for reviewing Chapter 7. The efforts of
Dr. G.Bhat in improving Chapter 9 are greatly appreciated. Mr. V.K. Reddy
contributed significantly to Chapter 10. Mr. M.W.Ranadive gave useful
suggestions on some topics. We are grateful to Prof. J.Turowski, Mr. P.
Ramachandran and Prof. L.Satish for constructive comments.
Ms. Rita Lazazzaro and Ms. Dana Bigelow of Marcel Dekker, Inc., constantly
supported us and gave good editorial input.
Finally, the overwhelming support and encouragement of our family members
is admirable. S.V.Kulkarni would like to particularly mention the sacrifice made
and moral support given by his wife, Sushama.
ix
Copyright © 2004 by Marcel Dekker, Inc.
Contents
Foreword Jin Sim iii
Preface v
Acknowledgements ix
1 Transformer Fundamentals 1
1.1 Perspective 1
1.2 Applications and Types of Transformers 5
1.3 Principles and Equivalent Circuit of a Transformer 11
1.4 Representation of Transformer in Power System 20
1.5 Open-Circuit and Short-Circuit Tests 23
1.6 Voltage Regulation and Efficiency 25
1.7 Parallel Operation of Transformers 33
References 34
2 Magnetic Characteristics 35
2.1 Construction 36

5 Stray Losses in Structural Components 169
5.1 Factors Influencing Stray Losses 171
5.2 Overview of Methods for Stray Loss Estimation 182
5.3 Core Edge Loss 184
5.4 Stray Loss in Frames 185
5.5 Stray Loss in Flitch Plates 187
5.6 Stray Loss in Tank 192
5.7 Stray Loss in Bushing Mounting Plates 197
5.8 Evaluation of Stray Loss Due to High Current Leads 199
5.9 Measures for Stray Loss Control 206
5.10 Methods for Experimental Verification 214
5.11 Estimation of Stray Losses in Overexcitation Condition 216
5.12 Load Loss Measurement 218
References 224
6 Short Circuit Stresses and Strength 231
6.1 Short Circuit Currents 232
6.2 Thermal Capability at Short Circuit 239
6.3 Short Circuit Forces 240
6.4 Dynamic Behavior Under Short Circuits 247
6.5 Failure Modes Due to Radial Forces 251
6.6 Failure Modes Due to Axial Forces 254
xii Contents
Copyright © 2004 by Marcel Dekker, Inc.
6.7 Effect of Pre-Stress 260
6.8 Short Circuit Test 260
6.9 Effect of Inrush Current 261
6.10 Split-Winding Transformers 262
6.11 Short Circuit Withstand 264
6.12 Calculation of Electrodynamic Force Between
Parallel Conductors 268

9.6 Direct Hot Spot Measurement 384
9.7 Static Electrification Phenomenon 385
References 387
Contents xiii
Copyright © 2004 by Marcel Dekker, Inc.
10 Structural Design 389
10.1 Importance of Structural Design 389
10.2 Different Types of Loads and Tests 390
10.3 Classification of Transformer Tanks 392
10.4 Tank Design 395
10.5 Methods of Analysis 397
10.6 Overpressure Phenomenon in Transformers 401
10.7 Seismic Analysis 403
10.8 Transformer Noise: Characteristics and Reduction 404
References 409
11 Special Transformers 411
11.1 Rectifier Transformers 411
11.2 Converter Transformers for HVDC 417
11.3 Furnace Transformers 424
11.4 Phase Shifting Transformers 428
References 433
12 Recent Trends in Transformer Technology 437
12.1 Magnetic Circuit 437
12.2 Windings 438
12.3 Insulation 440
12.4 Challenges in Design and Manufacture of Transformers 441
12.5 Computer-Aided Design and Analysis 443
12.6 Monitoring and Diagnostics 445
12.7 Life Assessment and Refurbishment 449
References 449

connected electrically, but coupled magnetically. A transformer is termed as either
a step-up or step-down transformer depending upon whether the secondary
voltage is higher or lower than the primary voltage, respectively. Transformers can
be used to either step-up or step-down voltage depending upon the need and
application; hence their windings are referred as high-voltage/low-voltage or
high-tension/low-tension windings in place of primary/secondary windings.
Magnetic circuit: Electrical energy transfer between two circuits takes place
through a transformer without the use of moving parts; the transformer therefore
has higher efficiency and low maintenance cost as compared to rotating electrical
Copyright © 2004 by Marcel Dekker, Inc.
Chapter 12
machines. There are continuous developments and introductions of better grades
of core material. The important stages of core material development can be
summarized as: non-oriented silicon steel, hot rolled grain oriented silicon steel,
cold rolled grain oriented (CRGO) silicon steel, Hi-B, laser scribed and
mechanically scribed. The last three materials are improved versions of CRGO.
Saturation flux density has remained more or less constant around 2.0 Tesla for
CRGO; but there is a continuous improvement in watts/kg and volt-amperes/kg
characteristics in the rolling direction. The core material developments are
spearheaded by big steel manufacturers, and the transformer designers can
optimize the performance of core by using efficient design and manufacturing
technologies. The core building technology has improved from the non-mitred to
mitred and then to the step-lap construction. A trend of reduction of transformer
core losses in the last few years is the result of a considerable increase in energy
costs. The better grades of core steel not only reduce the core loss but they also
help in reducing the noise level by few decibels. Use of amorphous steel for
transformer cores results in substantial core loss reduction (loss is about one-third
that of CRGO silicon steel). Since the manufacturing technology of handling this
brittle material is difficult, its use in transformers is not widespread.
Windings: The rectangular paper-covered copper conductor is the most

dielectric strength of oil-impregnated paper and pressboard is the main reason for
using oil as the most important constituent of the transformer insulation system.
Manufacturers have used silicon-based liquid for insulation and cooling. Due to
non-toxic dielectric and self-extinguishing properties, it is selected as a
replacement of Askarel. High cost of silicon is an inhibiting factor for its
widespread use. Super-biodegradable vegetable seed based oils are also available
for use in environmentally sensitive locations.
There is considerable advancement in the technology of gas immersed
transformers in recent years. SF6 gas has excellent dielectric strength and is non-
flammable. Hence, SF6 transformers find their application in the areas where fire-
hazard prevention is of paramount importance. Due to lower specific gravity of
SF6 gas, the gas insulated transformer is usually lighter than the oil insulated
transformer. The dielectric strength of SF6 gas is a function of the operating
pressure; the higher the pressure, the higher the dielectric strength. However, the
heat capacity and thermal time constant of SF6 gas are smaller than that of oil,
resulting in reduced overload capacity of SF6 transformers as compared to oil-
immersed transformers. Environmental concerns, sealing problems, lower
cooling capability and present high cost of manufacture are the challenges which
have to be overcome for the widespread use of SF6 cooled transformers.
Dry-type resin cast and resin impregnated transformers use class F or C
insulation. High cost of resins and lower heat dissipation capability limit the use of
these transformers to small ratings. The dry-type transformers are primarily used
for the indoor application in order to minimize fire hazards. Nomex paper
insulation, which has temperature withstand capacity of 220°C, is widely used for
dry-type transformers. The initial cost of a dry-type transformer may be 60 to 70%
higher than that of an oil-cooled transformer at current prices, but its overall cost
at the present level of energy rate can be very much comparable to that of the oil-
cooled transformer.
Design: With the rapid development of digital computers, the designers are freed
from the drudgery of routine calculations. Computers are widely used for

bushings are also available for oil-to-air applications. Due to high elasticity and
strength of the silicon rubber material, the strength of these bushings against
mechanical stresses and shocks is higher. The oil-to-SF6 bushings are used in GIS
(gas insulated substation) applications.
The service reliability of on load tap changers is of vital importance since the
continuity of the transformer depends on the performance of tap changer for the
entire (expected) life span of 30 to 40 years. It is well known that the tap changer
failure is one of the principal causes of failure of transformers. Tap changers,
particularly on-load tap changers (OLTC), must be inspected at regular intervals
to maintain a high level of operating reliability. Particular attention must be given
for inspecting the diverter switch unit, oil, shafts and motor drive unit. The
majority of failures reported in service are due to mechanical problems related to
the drive system, for which improvements in design may be necessary. For service
reliability of OLTCs, several monitoring methods have been proposed, which
include measurement of contact resistance, monitoring of drive motor torque/
current, acoustic measurements, dissolved gas analysis and temperature rise
measurements.
Diagnostic techniques: Several on-line and off-line diagnostic tools are available
for monitoring of transformers to provide information about their operating
conditions. Cost of these tools should be lower and their performance reliability
Copyright © 2004 by Marcel Dekker, Inc.
Transformer Fundamentals 5
should be higher for their widespread use. The field experience in some of the
monitoring techniques is very much limited. A close cooperation between
manufacturers and utilities is necessary for developing good monitoring and
diagnostic systems for transformers.
Transformer technology is developing at a tremendous rate. The computerized
methods are replacing the manual working in the design. Continuous
improvements in material and manufacturing technologies along with the use of
advanced computational tools have contributed in making transformers more

station. Lower noise level is usually not essential as other equipment in the
generating station may be much noisier than the transformer.
Generator transformers are usually provided with off-circuit tap changer with a
Copyright © 2004 by Marcel Dekker, Inc.
Chapter 16
Figure 1.1 Different types of transformers in a typical power system
Copyright © 2004 by Marcel Dekker, Inc.
Transformer Fundamentals 7
small variation in voltage (e.g., ±5%) because the voltage can always be
controlled by field of the generator. Generator transformers with OLTC are also
used for reactive power control of the system. They may be provided with a
compact unit cooler arrangement for want of space in the generating stations
(transformers with unit coolers have only one rating with oil forced and air forced
cooling arrangement). Alternatively, they may also have oil to water heat
exchangers for the same reason. It may be economical to design the tap winding as
a part of main HV winding and not as a separate winding. This may be permissible
since axial short circuit forces are lower due to a small tapping range. Special care
has to be taken while designing high current LV lead termination to avoid any hot-
spot in the conducting metallic structural parts in its vicinity. The epoxy bonded
CTC conductor is commonly used for LV winding to minimize eddy losses and
provide greater short circuit strength. Severe overexcitation conditions are taken
into consideration while designing generator transformers.
b. Unit auxiliary transformers: These are step-down transformers with primary
connected to generator output directly. The secondary voltage is of the order of 6.9
kV for supplying to various auxiliary equipment in the generating station.
c. Station transformers: These transformers are required to supply auxiliary
equipment during setting up of the generating station and subsequently during
each start-up operation. The rating of these transformers is small, and their
primary is connected to a high voltage transmission line. This may result in a
smaller conductor size for HV winding, necessitating special measures for

voltage is reduced to actual utilization voltage (~415 or 460 V) for domestic/
industrial use. A great variety of transformers fall into this category due to many
different arrangements and connections. Load on these transformers varies
widely, and they are often overloaded. A lower value of no-load loss is desirable to
improve all-day efficiency. Hence, the no-load loss is usually capitalized with a
high rate at the tendering stage. Since very little supervision is possible, users
expect the least maintenance on these transformers. The cost of supplying losses
and reactive power is highest for these transformers.
Classification of transformers as above is based on their location and broad
function in the power system. Transformers can be further classified as per their
specific application as given below. In this chapter, only main features are
highlighted; details of some of them are discussed in the subsequent chapters.
g. Phase shifting transformers: These are used to control power flow over
transmission lines by varying the phase angle between input and output voltages
of the transformer. Through a proper tap change, the output voltage can be made
to either lead or lag the input voltage. The amount of phase shift required directly
affects the rating and size of the transformer. Presently, there are two types of
design: single-core and two-core design. Single-core design is used for small
phase shifts and lower MVA/voltage ratings. Two-core design is normally used for
bulk power transfer with large ratings of phase shifting transformers. It consists of
two transformers, one associated with the line terminals and other with the tap
changer.
h. Earthing or grounding transformers: These are used to get a neutral point that
facilitates grounding and detection of earth faults in an ungrounded part of a
network (e.g., the delta connected systems). The windings are usually connected
in the zigzag manner, which helps in eliminating third harmonic voltages in the
lines. These transformers have the advantage that they are not affected by a DC
magnetization.
i. Transformers for rectifier and inverter circuits: These are otherwise normal
transformers except for the special design and manufacturing features to take into