Power Transformers - Principles and Applications

286 Pages·2006·2.02 MB·English

Power
Transformers
Principles and Applications
John J. Winders, Jr.
PPL Electric Utilities
Allentown, Pennsylvania
Marcel Dekker, Inc. New York • Basel
TM
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
ISBN: 0-8247-0766-4
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Copyright  2002 by Marcel Dekker, Inc. All Rights Reserved.
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Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
Series Introduction
Power engineering is the oldest and most traditional of the various areas within
electrical engineering, yet no other facet of modern technology is currently
experiencing a greater transformation or seeing more attention and interest
from the public and government. But while public concern and political deci-
sions about de-regulation and energy trading may reshape the electric utility
industry’s manner of doing business, its future like its past rests on the capabil-
ity of its transmission and distribution systems to convey safe, reliable, and
economical electric power to homes, businesses, and factories. Nothing is
more essential to this performance than the transformer, which enables modern
power and industrial systems to function.
I am particularly delighted to see this latest addition to Marcel Dekker’s
Power Engineering series. Power Transformers: Principles and Applications
is a comprehensive compendium of theory and practices for electric power
transformers. This book provides a concise but thorough treatment of basic
transformer theory, its application to various types of transformer designs and
their application in utility and industrial power systems. Its easy to read style
and linear organization make it particularly suitable as a tutorial for those who
need to learn the material independently, outside of the classroom, or as a text
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
for formal courses. This book also makes a very good practical reference for
utility and industrial power engineers.
In addition to having concise summaries of all the basics, the text pro-
vides an excellent description of the various ancillary equipment and systems,
which are often the most difficult to precisely engineer and fit into the system.
John Winders has also provided excellent coverage of how to read, interpret,
and apply a power transformer’s nameplate data, not always a straightforward
or unambiguous task and one where a surprising number of mistakes are made
by inexperienced engineers. Chapter 8 will be particularly useful to practicing
engineers and power system operators, covering maintenance needs, testing
options, and troubleshooting techniques and their use, and discussing reliabil-
ity of transformers.
As the editor of the Power Engineering series, I am proud to include
Power Transformers: Principles and Applications among this important group
of books. Like all the books in Marcel Dekker’s Power Engineering series,
this book provides modern power technology in a context of proven, practical
application, useful as a reference book as well as for self-study and advanced
classroom use. Marcel Dekker’s Power Engineering series includes books cov-
ering the entire field of power engineering, in all of its specialties and sub-
genres, each aimed at providing practicing power engineers with the knowl-
edge and techniques they need to meet the electric industry’s challenges in
the 21st century.
H. Lee Willis
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
Preface
This book is based on notes for the Transformer Applications Course offered
by the Center for Power System Study at Lehigh University. The key word
in both the title of that course and the title of this book is applications. The
material presented in the following chapters was obtained from various
sources: textbooks, industry standards, and established utility practices and
procedures. Much of this material also comes from my personal files relating
to actual events and case studies that were observed during my career in the
utility industry spanning 30 years.
There are many kinds of transformers, and all share the same set of
fundamental operating principles. Since this book focuses on power transform-
ers, it is fair to ask, ‘‘What exactly is a power transformer?’’ By definition,
a power transformer is a transformer which transfers electric energy in any
part of the circuit between the generator and the distribution primary circuits.*
This definition of power transformer in the IEEE standard appears under the
* IEEE Std. C57.12.80-1978. IEEE Standard Terminology for Power and Distribution Transform-
ers. Institute of Electrical and Electronics Engineers, Inc., 1978, New York, p. 8.
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
heading of ‘‘Size’’ and does not indicate how the transformer is used in the
power system. Thus, this book uses this definition in the broadest sense to
include discussions of specialty applications such as step voltage regulators,
phase shifters, and grounding transformers, as well as the usual step-up and
step-down applications. Since the line between power transformers and distri-
bution transformers is somewhat blurry, many of the basic principles presented
can be applied to distribution transformers as well.
The first several chapters build a solid theoretical foundation by describ-
ing the underlying physics behind transformer operation. A theoretical founda-
tion is absolutely necessary in order to understand what is going on inside a
transformer and why. The magnetic properties of materials, a review of mag-
netic units, and analysis of magnetic circuits are discussed with enough mathe-
matical rigor for the interested reader to gain full comprehension of the physics
involved. Whenever a detailed mathematical treatment is presented, it is al-
ways done with a practical objective in mind. Each chapter includes a number
of practice problems to clearly illustrate how the theory is applied in everyday
situations. Many of these practice problems are based on actual events.
Several things set this book apart from other transformer reference
books. First, this book emphasizes the importance of magnetic properties and
how the choice of a core design can affect the transformer’s electrical proper-
ties, especially during faults and unbalanced operations. Many reference books
overlook this critical aspect of transformer applications.
Next, this book discusses special types of transformer connections, such
as the zigzag, Scott, and tee connections, as well as the more common wye
and delta types. The Scott and tee connections, which transform three-phase
voltages into two-phase voltages, are seldom covered in modern transformer
reference books even though two-phase systems still exist today. Tap changing
under load and variable phase shifting transformers are covered. Different
types of transformer coil and coil construction are compared, with discussion
of the particular advantages and disadvantages of each with respect to the
various transformer connections. The reader will also gain insight into some
of the economic trade-offs of different transformer design options.
A brief tutorial on symmetrical components is also included. The topic
is covered in other reference books but seldom in such a compact and straight-
forward way, enabling the reader to immediately apply the technique in practi-
cal problems.
A section of the book defines a transformer’s nameplate rating versus
its thermal capability and describes how to calculate a transformer’s rate of
loss of life. An entire chapter is devoted to describing abnormal operating
conditions that can damage power transformers, including overloads, short
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
circuits, single phasing from primary fuse operations, ferroresonance, and
voltage surges. The chapter describes ways to avoid these conditions, or at
least ways to mitigate them through proper system design and selection of
appropriate transformer designs.
The reader will learn how to interpret and use a transformer test report
as well as the information on the transformer nameplate. The book concludes
with a comprehensive discussion of preventive and predictive maintenance,
good utility practices, factory and field testing, and failure rate analysis.
This book is intended primarily for readers having an electrical engi-
neering background although training as an electrical engineer is not neces-
sary, and others will also benefit from the conclusions that can be drawn from
the practical examples. Mastery of the principles presented in this book will
provide a sound working knowledge of how to specify, operate, and maintain
power transformers in a utility or plant environment.
I wish to thank Anthony F. Sleva for his thorough review of the manu-
script and his many helpful suggestions for improving it, and for making it
possible to publish this book. I am indebted to the late Charles H. Morrison,
who patiently shared with me so much of his extensive theoretical and practi-
cal knowledge about power transformers.
John J. Winders, Jr.
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
Contents
Series Introduction H. Lee Willis
Preface
1 Basic Transformer Theory
1.1 Definition of a Transformer
1.2 Magnetic Units and Conversion Factors
1.3 Currents and Magnetic Fields
1.4 Magnetic Induction
1.5 Constructing a Simple Transformer
1.6 The Magnetic Circuit
1.7 The B-H Curve
1.8 The B-H Curve and Hysteresis
1.9 Magnetizing Currents and Harmonics
1.10 Transformer Core Design and Construction
1.11 Magnetostriction
1.12 Completing the Transformer by Adding a Second
Winding
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
1.13 Placement of the Windings
References
2 Two-Winding Transformer Connections
2.1 Introduction
2.2 The Y-Y Connection in Three-Phase Systems
2.3 Advantages of the Y-Y Connection
2.4 Disadvantages of the Y-Y Connection
2.5 The Y-∆ Connection and the ∆-Y Connection
2.6 Phase Angle Displacement and Phase Rotation
2.7 The Y-∆ Grounding Bank
2.8 The Zigzag Connection
2.9 Comparisons of Economy of the Different Winding
Configurations
2.10 Trade-Off Between Steel and Copper in the Design of a
Transformer
2.11 Connecting Three-Phase Banks Using Single-Phase
Transformers
2.12 Transforming Three-Phase Voltages into Two-Phase
Voltages
2.13 The Scott Transformer Connection
2.14 Three-Phase Transformer Designs
2.15 Standard Terminal Markings for Transformers
References
3 Transformer Impedance and Losses
3.1 Leakage Flux and Leakage Reactance
3.2 Conductor Losses
3.3 No-Load Losses
3.4 Magnetizing Reactance
3.5 Equivalent Circuit of a Two-Winding Transformer
3.6 A Brief Tutorial on Symmetrical Components
3.7 Transformer Equivalent Circuits Modeled in Zero Phase
Sequence Networks
3.8 Series Impedance and Regulation
3.9 Matching Transformers for Parallel and Bank
Operations
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
3.10 Impedance Mismatch in Three-Phase Transformer
Banks
3.11 Temperature Rise and the Thermal Capability
3.12 Interpreting Transformer Test Reports
3.13 Calculating the Hot-Spot Temperature Using the IEEE
Method
3.14 Calculating the Loss of Life
References
4 Autotransformers and Three-Winding Transformers
4.1 Autotransformer Connections
4.2 Impedance of an Autotransformer
4.3 Limitations of the Autotransformer Connection
4.4 Autotransformer Voltages with Short Circuits Applied
4.5 Impulse Voltages Applied to Autotransformers
4.6 Autotransformer Core and Coil Designs and Terminal
Configurations
4.7 Advantages and Disadvantages of the Autotransformer
Connection
4.8 Three-Winding Transformers
4.9 Modification of Transformer Laws with Three Windings
4.10 Equivalent Circuit of a Three-Winding Transformer
4.11 Core and Coil Construction of Three-Winding
Transformers
4.12 Thermal Capability of Three-Winding Transformers
4.13 The Stabilizing Effect of a ∆ Tertiary Winding
Reference
5 Short Circuits, Inrush Currents, and Other Phenomena
5.1 Effects of Short Circuits on Transformers
5.2 Comparisons of Short-Circuit Currents for Various
Faults
5.3 Mechanical Forces in Transformers
5.4 Forces between Transformer Windings
5.5 Short-Circuit Forces in Three-Winding Transformers
5.6 Exciting Current Inrush
5.7 Tank Overheating from Zero-Sequence Currents
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.