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ENGINEERING © 2004 by CRC Press LLC © 2004 by CRC Press LLC Library of Congress Cataloging-in-Publication Data
Electric power transformer engineering / edited by James H. Harlow.
p. cm. — (The Electric Power Engineering Series ; 9)
Includes bibliographical references and index.
ISBN 0-8493-1704-5 (alk. paper)
1. Electric transformers. I. Harlow, James H. II. title. III. Series.
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Printed on acid-free paper © 2004 by CRC Press LLC Preface Transformer engineering is one of the earliest sciences within the ﬁeld of electric power engineering, and
power is the earliest discipline within the ﬁeld of electrical engineering. To some, this means that
transformer technology is a fully mature and staid industry, with little opportunity for innovation or
ingenuity by those practicing in the ﬁeld.
Of course, we in the industry ﬁnd that premise to be erroneous. One need only scan the technical
literature to recognize that leading-edge suppliers, users, and academics involved with power transformers
are continually reporting novelties and advancements that would have been totally insensible to engineers
of even the recent past. I contend that there are three basic levels of understanding, any of which may
be appropriate for persons engaged with transformers in the electric power industry. Depending on dayto-day involvement, the individual’s posture in the ﬁeld can be described as:
• Curious — those with only peripheral involvement with transformers, or a nonprofessional lacking
relevant academic background or any particular need to delve into the intricacies of the science
• Professional — an engineer or senior-level technical person who has made a career around electric
power transformers, probably including other heavy electric-power apparatus and the associated
power-system transmission and distribution operations
• Expert — those highly trained in the ﬁeld (either practically or analytically) to the extent that
they are recognized in the industry as experts. These are the people who are studying and publishing the innovations that continue to prove that the ﬁeld is nowhere near reaching a technological culmination.
So, to whom is this book directed? It will truly be of use to any of those described in the previous
The curious person will ﬁnd the material needed to advance toward the level of professional. This
reader can use the book to obtain a deeper understanding of many topics.
The professional, deeply involved with the overall subject matter of this book, may smugly grin with
the self-satisfying attitude of, “I know all that!” This person, like myself, must recognize that there are
many transformer topics. There is always room to learn. We believe that this book can also be a valuable
resource to professionals.
The expert may be so immersed in one or a few very narrow specialties within the ﬁeld that he also
may beneﬁt greatly from the knowledge imparted in the peripheral specialties.
The book is divided into three fundamental groupings: The ﬁrst stand-alone chapter is devoted to
Theory and Principles. The second chapter, Equipment Types, contains nine sections that individually treat
major transformer types. The third chapter, which contains 14 sections, addresses Ancillary Topics associated with power transformers. Anyone with an interest in transformers will ﬁnd a great deal of useful
information. © 2004 by CRC Press LLC I wish to recognize the interest of CRC Press and the personnel who have encouraged and supported
the preparation of this book. Most notable in this regard are Nora Konopka, Helena Redshaw, and
Gail Renard. I also want to acknowledge Professor Leo Grigsby of Auburn University for selecting me to
edit the “Transformer” portion of his The Electric Power Engineering Handbook (CRC Press, 2001), which
forms the basis of this handbook. Indeed, this handbook is derived from that earlier work, with the
addition of four wholly new chapters and the very signiﬁcant expansion and updating of much of the
other earlier work. But most of all, appreciation is extended to each writer of the 24 sections that
comprise this handbook. The authors’ diligence, devotion, and expertise will be evident to the reader. James H. Harlow
Editor © 2004 by CRC Press LLC Editor James H. Harlow has been self-employed as a principal of Harlow Engineering Associates, consulting to
the electric power industry, since 1996. Before that, he had 34 years of industry experience with Siemens
Energy and Automation (and its predecessor Allis-Chalmers Co.) and Beckwith Electric Co., where he
was engaged in engineering design and management. While at these ﬁrms, he managed groundbreaking
projects that blended electronics into power transformer applications. Two such projects (employing
microprocessors) led to the introduction of the ﬁrst intelligent-electronic-device control product used
in quantity in utility substations and a power-thyristor application for load tap changing in a step-voltage
Harlow received the BSEE degree from Lafayette College, an MBA (statistics) from Jacksonville State
University, and an MS (electric power) from Mississippi State University. He joined the PES Transformers
Committee in 1982, serving as chair of a working group and a subcommittee before becoming an ofﬁcer
and assuming the chairmanship of the PES Transformers Committee for 1994–95. During this period,
he served on the IEEE delegation to the ANSI C57 Main Committee (Transformers). His continued
service to IEEE led to a position as chair of the PES Technical Council, the assemblage of leaders of the
17 technical committees that comprise the IEEE Power Engineering Society. He recently completed a
2-year term as PES vice president of technical activities.
Harlow has authored more than 30 technical articles and papers, most recently serving as editor of
the transformer section of The Electric Power Engineering Handbook, CRC Press, 2001. His editorial
contribution within this handbook includes the section on his specialty, LTC Control and Transformer
Paralleling. A holder of ﬁve U.S. patents, Harlow is a registered professional engineer and a senior member
of IEEE. © 2004 by CRC Press LLC Contributors Dennis Allan Scott H. Digby James H. Harlow MerlinDesign
Stafford, England Waukesha Electric Systems
Goldsboro, North Carolina Harlow Engineering Associates
Mentone, Alabama Dieter Dohnal Ted Haupert Hector J. Altuve
Monterrey, Mexico Maschinenfabrik Reinhausen
Regensburg, Germany Gabriel Benmouyal Douglas Dorr Schweitzer Engineering
Longueuil, Quebec, Canada Behdad Biglar
Canada Wallace Binder
New Castle, Pennsylvania EPRI PEAC Corporation
Knoxville, Tennessee Richard F. Dudley
Scarborough, Ontario, Canada Ralph Ferraro
Ferraro, Oliver & Associates, Inc.
Knoxville, Tennessee Dudley L. Galloway
Jefferson City, Missouri TJ/H2b Analytical Services
Sacramento, California William R. Henning
Waukesha Electric Systems
Waukesha, Wisconsin Philip J. Hopkinson
Charlotte, North Carolina Sheldon P. Kennedy
Buffalo, New York Andre Lux
KEMA T&D Consulting
Raleigh, North Carolina Antonio Castanheira
Trench Brasil Ltda.
Contegem, Minas Gelais, Brazil Anish Gaikwad Arindam Maitra EPRI PEAC Corporation
Knoxville, Tennessee EPRI PEAC Corporation
Knoxville, Tennessee Armando Guzmán Arshad Mansoor Craig A. Colopy
Cooper Power Systems
Waukesha, Wisconsin Robert C. Degeneff
Rensselaer Polytechnic Institute
Troy, New York © 2004 by CRC Press LLC Schweitzer Engineering
Pullman, Washington EPRI PEAC Corporation
Knoxville, Tennessee Shirish P. Mehta Paulette A. Payne Leo J. Savio Waukesha Electric Systems
Waukesha, Wisconsin Potomac Electric Power
Washington, DC ADAPT Corporation
Kennett Square, Pennsylvania Harold Moore
H. Moore & Associates
Niceville, Florida Michael Sharp
Dan D. Perco
Perco Transformer Engineering
Stoney Creek, Ontario, Canada Dan Mulkey
Paciﬁc Gas & Electric Co.
Petaluma, California H. Jin Sim
Graz, Austria Randy Mullikin
Kuhlman Electric Corp.
Versailles, Kentucky Trench Ltd.
Scarborough, Ontario, Canada Waukesha Electric Systems
Goldsboro, North Carolina Robert F. Tillman, Jr.
Matthews, North Carolina Alabama Power Company
Birmingham, Alabama Alan Oswalt Loren B. Wagenaar Consultant
Big Bend, Wisconsin America Electric Power
Pickerington, Ohio © 2004 by CRC Press LLC Contents Chapter 1 Theory and Principles Dennis Allan and Harold Moore Chapter 2 Equipment Types
2.9 Chapter 3 Power Transformers H. Jin Sim and Scott H. Digby
Distribution Transformers Dudley L. Galloway and Dan Mulkey
Phase-Shifting Transformers Gustav Preininger
Rectiﬁer Transformers Sheldon P. Kennedy
Dry-Type Transformers Paulette A. Payne
Instrument Transformers Randy Mullikin
Step-Voltage Regulators Craig A. Colopy
Constant-Voltage Transformers Arindam Maitra, Anish Gaikwad,
Ralph Ferraro, Douglas Dorr, and Arshad Mansoor
Reactors Richard F. Dudley, Michael Sharp, Antonio Castanheira,
and Behdad Biglar Ancillary Topics
3.14 © 2004 by CRC Press LLC Insulating Media Leo J. Savio and Ted Haupert
Electrical Bushings Loren B. Wagenaar
Load Tap Changers Dieter Dohnal
Loading and Thermal Performance Robert F. Tillman, Jr.
Transformer Connections Dan D. Perco
Transformer Testing Shirish P. Mehta and William R. Henning
Load-Tap-Change Control and Transformer Paralleling
James H. Harlow
Power Transformer Protection Armando Guzmán, Hector J. Altuve,
and Gabriel Benmouyal
Causes and Effects of Transformer Sound Levels Jeewan Puri
Transient-Voltage Response Robert C. Degeneff
Transformer Installation and Maintenance Alan Oswalt
Problem and Failure Investigation Wallace Binder
and Harold Moore
On-Line Monitoring of Liquid-Immersed Transformers Andre Lux
U.S. Power Transformer Equipment Standards and Processes
Philip J. Hopkinson 1
Theory and Principles Dennis Allan 1.1
1.4 Magnetic Circuit • Leakage Reactance • Load Losses • ShortCircuit Forces • Thermal Considerations • Voltage
Considerations MerlinDesign Harold Moore
H. Moore and Associates Air Core Transformer
Iron or Steel Core Transformer
Equivalent Circuit of an Iron-Core Transformer
The Practical Transformer References Transformers are devices that transfer energy from one circuit to another by means of a common magnetic
ﬁeld. In all cases except autotransformers, there is no direct electrical connection from one circuit to the
When an alternating current ﬂows in a conductor, a magnetic ﬁeld exists around the conductor,
as illustrated in Figure 1.1. If another conductor is placed in the ﬁeld created by the ﬁrst conductor such
that the ﬂux lines link the second conductor, as shown in Figure 1.2, then a voltage is induced into the
second conductor. The use of a magnetic ﬁeld from one coil to induce a voltage into a second coil is the
principle on which transformer theory and application is based. 1.1 Air Core Transformer
Some small transformers for low-power applications are constructed with air between the two coils. Such
transformers are inefﬁcient because the percentage of the ﬂux from the ﬁrst coil that links the second
coil is small. The voltage induced in the second coil is determined as follows.
E = N dJ/dt 108 (1.1) where N is the number of turns in the coil, dJ/dt is the time rate of change of ﬂux linking the coil, and J
is the ﬂux in lines.
At a time when the applied voltage to the coil is E and the ﬂux linking the coils is J lines, the
instantaneous voltage of the supply is:
e = 2 E cos [t = N dJ/dt 108 (1.2) dJ/dt = (2 cos [t 108)/N (1.3) The maximum value of J is given by:
J = (2 E 108)/(2 T f N)
Using the MKS (metric) system, where J is the ﬂux in webers, © 2004 by CRC Press LLC (1.4) Current carrying
conductor Flux lines FIGURE 1.1 Magnetic ﬁeld around conductor. Flux lines Second conductor
in flux lines FIGURE 1.2 Magnetic ﬁeld around conductor induces voltage in second conductor. E = N dJ/dt (1.5) J = (2E)/(2 T f N) (1.6) and Since the amount of ﬂux J linking the second coil is a small percentage of the ﬂux from the ﬁrst coil,
the voltage induced into the second coil is small. The number of turns can be increased to increase the voltage
output, but this will increase costs. The need then is to increase the amount of ﬂux from the ﬁrst coil
that links the second coil. 1.2 Iron or Steel Core Transformer
The ability of iron or steel to carry magnetic ﬂux is much greater than air. This ability to carry ﬂux is
called permeability. Modern electrical steels have permeabilities in the order of 1500 compared with 1.0 for
air. This means that the ability of a steel core to carry magnetic ﬂux is 1500 times that of air. Steel cores
were used in power transformers when alternating current circuits for distribution of electrical energy
were ﬁrst introduced. When two coils are applied on a steel core, as illustrated in Figure 1.3, almost
100% of the ﬂux from coil 1 circulates in the iron core so that the voltage induced into coil 2 is equal
to the coil 1 voltage if the number of turns in the two coils are equal.
Continuing in the MKS system, the fundamental relationship between magnetic ﬂux density (B) and
magnetic ﬁeld intensity (H) is: © 2004 by CRC Press LLC Flux in core Steel core Exciting winding Second winding FIGURE 1.3 Two coils applied on a steel core. B = Q0 H (1.7) where Q0 is the permeability of free space | 4T v 10–7 Wb A–1 m–1.
Replacing B by J/A and H by (I N)/d, where
J = core ﬂux in lines
N = number of turns in the coil
I = maximum current in amperes
A = core cross-section area
the relationship can be rewritten as:
J = (Q N A I)/d (1.8) where
d = mean length of the coil in meters
A = area of the core in square meters
Then, the equation for the ﬂux in the steel core is:
J = (Q0 Qr N A I)/d (1.9) whereQr = relative permeability of steel } 1500.
Since the permeability of the steel is very high compared with air, all of the ﬂux can be considered as
ﬂowing in the steel and is essentially of equal magnitude in all parts of the core. The equation for the
ﬂux in the core can be written as follows:
J = 0.225 E/fN (1.10) where
E = applied alternating voltage
f = frequency in hertz
N = number of turns in the winding
In transformer design, it is useful to use ﬂux density, and Equation 1.10 can be rewritten as:
B = J/A = 0.225 E/(f A N)
where B = ﬂux density in tesla (webers/square meter). © 2004 by CRC Press LLC (1.11) 1.3 Equivalent Circuit of an Iron-Core Transformer
When voltage is applied to the exciting or primary winding of the transformer, a magnetizing current
ﬂows in the primary winding. This current produces the ﬂux in the core. The ﬂow of ﬂux in magnetic
circuits is analogous to the ﬂow of current in electrical circuits.
When ﬂux ﬂows in the steel core, losses occur in the steel. There are two components of this loss, which
are termed “eddy” and “hysteresis” losses. An explanation of these losses would require a full chapter.
For the purpose of this text, it can be stated that the hysteresis loss is caused by the cyclic reversal of
ﬂux in the magnetic circuit and can be reduced by metallurgical control of the steel. Eddy loss is
caused by eddy currents circulating within the steel induced by the ﬂow of magnetic ﬂux normal to the
width of the core, and it can be controlled by reducing the thickness of the steel lamination or by applying
a thin insulating coating.
Eddy loss can be expressed as follows:
W = K[w]2[B]2 watts (1.12) where
K = constant
w = width of the core lamination material normal to the ﬂux
B = ﬂux density
If a solid core were used in a power transformer, the losses would be very high and the temperature
would be excessive. For this reason, cores are laminated from very thin sheets, such as 0.23 mm and 0.28
mm, to reduce the thickness of the individual sheets of steel normal to the ﬂux and thereby reducing the
losses. Each sheet is coated with a very thin material to prevent shorts between the laminations. Improvements made in electrical steels over the past 50 years have been the major contributor to smaller and
more efﬁcient transformers. Some of the more dramatic improvements include:
• Development of cold-rolled grain-oriented (CGO) electrical steels in the mid 1940s
Introduction of thin coatings with good mechanical properties
Improved chemistry of the steels, e.g., Hi-B steels
Further improvement in the orientation of the grains
Introduction of laser-scribed and plasma-irradiated steels
Continued reduction in the thickness of the laminations to reduce the eddy-loss component of
the core loss
• Introduction of amorphous ribbon (with no crystalline structure) — manufactured using rapidcooling technology — for use with distribution and small power transformers
The combination of these improvements has resulted in electrical steels having less than 40% of the noload loss and 30% of the exciting (magnetizing) current that was possible in the late 1940s.
The effect of the cold-rolling process on the grain formation is to align magnetic domains in the
direction of rolling so that the magnetic properties in the rolling direction are far superior to those in
other directions. A heat-resistant insulation coating is applied by thermochemical treatment to both sides
of the steel during the ﬁnal stage of processing. The coating is approximately 1-Qm thick and has only
a marginal effect on the stacking factor. Traditionally, a thin coat of varnish had been applied by the
transformer manufacturer after co...
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