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Electrical Machines, Drives and Power Systems
Instructor’s Solution Manual
Sixth Edition
Theodore Wildi
Professor Emeritus, Laval University
Department of Electrical Engineering
و المحتوى كما يلي :
Preface iii
CONTENTS
Brief Overview of Chapters 1
Solution to Problems Including
Solution to Industrial Application Problems 9
Figures for overhead projection 100BRIEF OVERVIEW OF CHAPTERS
CHAPTER 1 Units
This chapter gives the essentials of SI units and their use
in the textbook. It also shows a graphical method of
making conversions between English units, U.S.
Customary Units and the SI. The important topic of per
unit notation is also discussed. The per unit methodology
is widely used in describing the magnitude of
electromechanical quantities.
CHAPTER 2 Fundamentals of Electricity
and Magnetism
This chapter gives a brief review of electrical and magnetic
fundamentals. It also includes a simple way of writing
circuit equations that many students and instructors will
find interesting and pleasing to use. It can be employed
in ac or de circuits using either double subscript or sign
notation.
CHAPTER 3 Fundamentals of Mechanics
and Heat
The performance and service life of electrical machines,
transformers and transmission lines are affected by their
mechanical and thermal properties. Consequently, this
chapter covers the fundamental elements of mechanics
and heat. Mechanical energy and inertia are discussed as
well as the dynamic relationship between torque, speed
and acceleration of electrical machines. The section on
heat shows the basic methods of cooling electrical ma¬
chines and some practical thermal equations.
CHAPTER 4 Direct-current Generators
This chapter on de generators is simultaneously an intro¬
duction to demotors. It reveals the method whereby a de
voltage is produced, together with the process of com¬
mutation and the problem of sparking at the brushes.
CHAPTER 5 Direct-current Motors
Here are discussed the various types of de motors and
their behavior when they accelerate, run at constant load,
and how inertia comes into play when they are brought
to a halt by dynamic braking
CHAPTER 6 Efficiency and Heating of
Electrical Machines
The physical elements that cause a machine to heat up
are covered here. The impact on the power rating of the
machine is revealed. A particularly useful section explains
the relationship between temperature rise and the ser¬
vice life of electrical equipment. It is directly related to
insulation classifications that are part of national and in¬
ternational standards (Sections 6.5 to 6.8).
CHAPTER 7 Active and Reactive Power
In electric power technology, the terms active, reactive
and apparent power constantly crop up. The reason is
that they facilitate the understanding of power flow in ac
machines, transformers, transmission lines, and electronic
converters. The ingenious power triangle method of
solving ac circuits is also revealed (Section 7.11). At an
intermediate level, the notion of conjugate current is used
to determine the active and reactivecomponents of power
by vector algebra (Section 7.15).
CHAPTER 8 Three-Phase Circuits
The chapter begins with a user-friendly introduction to
3-phase circuits and a simple method of solving them.
The treatment of industrial loads is then explored
together with the notion of power factor correction. The
important topic of phase sequence is also discussed, to
prepare the student for an understanding of the direc¬
tion of rotation of motors and the synchronization of ac
1generators. As another aspect of phase sequence and
phasor relationships, Section 8.21 shows how a single¬
phase load can be made to appear as a perfectly balanced
load on a three-phase line.
CHAPTER 9 The Ideal Transformer
This introductory chapter highlights the basic principles
of transformers in general. In addition to the usual vol¬
tage and current transformations, the chapter goes on to
show the meaning of polarity and how impedances can
be shifted from primary to secondary and vice versa. The
study of the ideal transformer also paves the way for
developing the equivalent circuit and phasor diagrams of
practical industrial transformers.
CHAPTER 10 Practical Transformers
The factors that cause a practical transformer to diverge
from the ideal are explained. A particularly easy way of
understanding leakage reactance is developed and
incorporated into the equivalent circuit diagram. It is well
known that the notion of leakage reactance is fundamental
to an understanding of transformers and all rotating ac
machines. Also, an interesting table makes use of per unit
values to describe the properties of transformers over a
tremendous power range (Section 10.15).
CHAPTER 11 Special Transformers
Autotransformers, current transformers, voltage
transformers and high leakage reactance transformers are
discussed in this chapter to give the student an idea of the
many industrial applications of transformers. The dozens
of photographs and technical details provide a visual
appreciation of these important devices.
CHAPTER 12 Three-Phase Transformers
Three-phase transformers are the workhorses of trans¬
mission and distribution systems, and of industrial and
commercial installations. Of particular interest is how
these transformers can generate phase shifts and
multiphase outputs, in addition to the usual voltage and
current transformations.
CHAPTER 13 Three-Phase Induction Motors
This introductory chapter lays the groundwork for an
understanding of the widely-used induction motor. The
process whereby torque is developed and the relationship
between frequency and speed are clearly explained. The
construction of the motor, and a detailed description of
the windings offer a practical view of the machine, to
supplement the theory. The linear motor is also discussed,
together with its practical application in linear drives. The
principle of magnetic levitation is shown to be a useful
attribute of the linear induction motor.
CHAPTER 14 Selection and Application of
3-Phase Induction Motors
The practical aspects of induction motors is the object of
this chapter. It first describes industrial standards and goes
on to explain the behavior of the motor under plugging,
braking, single-phasing, overload, and other abnormal
conditions.The use of a wound-rotor motor as a frequency
converter alerts the student to other features that can be
exploited.
CHAPTER 15 Equivalent Circuit of the
Induction Motor
This special chapter is intended for students that want to
enlarge their understanding of the induction motor. The
theory is presented in a particularly simple way, using the
prior knowledge of the properties of a conventional trans¬
former. A comparison is made of the performance of a
5 hp versus a 5000 hp motor, particularly as regards the
torque-speed curve. The circuit diagram is then used to
illustrate (and calculate) how an induction motor can be
made to behave as a generator (Section 15.8).
CHAPTER 16 Synchronous Generators
Synchronous generators are the source of 99 percent of
all the electrical energy that is consumed; consequently,
they deserve an important place in power technology. The
different types of generators are shown in photographs,
accompanied by valuable technical data. The synchro¬
nization of alternators is explained as well as the impor¬
tant concept of the infinite bus.
2One surprising feature of a synchronous generator is its
very high internal impedance. Indeed, the impedance of
some alternators is so high that theshort circuit current is
only slightly larger than the rated current. However, be¬
cause the impedance is mainly reactive, the internal power
loss is relatively low. Particular attention should be paid
to Section 16.7 which discusses the reasons why large
alternators are preferred over smaller ones. As in every
design problem, the trade-off is that the higher efficiency
of larger machines demands increasingly complex cooling
systems.
We also want to emphasize the importance of Section 16.23
which develops an equation for the active power trans¬
ferred between two ac sources. This equation P = E\ E^
sin 8/Xs is encountered again and again in subsequent
chapters, including those dealing with transmission lines
and electronic converters.
CHAPTER 17 Synchronous Motors
The synchronous motor ranges from the millihorsepower
mite in electricclocks to the gigantic 200 000 hp machines
used in pumped storage installations. The distinguishing
feature of synchronous motors is their ability to operate
at unity and leading power factors. Indeed, some of these
machines operate at no load, their only purpose being to
generate or absorb reactive power. The astounding thing
is that these machines, having only magnetic fields, can
function as if they were capacitors.
The equivalent circuit of a synchronous motor is simpler
than that of an induction motor. It offers a fine opportunity
to use phasors in describing machine behavior.
CHAPTER 18 Single-Phase Motors
Single-phase motors are manufactured by the millions
every year and so a knowledge of the more important ty¬
pes is useful. Surprisingly, a single-phase motor is more
complex than a three-phase motor. In this chapter, we offer
the cross-field theory and the revolving field theory to
explain its performance. The revolving field theory is then
used to develop, in a simple understandable way, the
equivalent circuit of the single-phase motor (Sections
18.17 to 18.19). To our knowledge, this constitutes a first
in this category of textbook.
The inherent noisiness of standard single-phase motors
(Section 18.9) should be brought to the student’s atten¬
tion.
Another topic describes a servo system to remotely
actuate a a distant object. The principle is based on two
3-phase wound-rotor motors powered by a single-phase
source (Section 18.16).
CHAPTER 19 Stepper Motors
This chapter describes the principle of stepper motors.
They are unique in the sense that the number of rotor
poles is always different from the number of stator poles.
The big advantage of stepper motors is that the number
of revolutions is directly related to the number of pulses
applied to the stator. Consequently, these machines can
be used to precisely control the position of an object
without requiring feedback. However, the motor is always
combined with a power supply that can generate and count
the number of pulses applied to the stator. Most stepper
motors are rated at less than 50 watts. It is shown that
inertia plays an important role in the behavior of these
machines.
CHAPTER 20 Basics of Industrial Motor Control
Many industrial components that control electric motors
are simple, non-electronic devices. They are described in
this chapter, together with the conventional circuit
diagrams and symbols encountered in industry. The
student will discover how motors arestarted,stopped, and
reversed by usingsimple switches.Section 20.17 then gives
an introduction to electric drives, including the notion of
quadrants, followed by a brief view of variable frequency
control of an induction motor.
3CHAPTER 21 Fundamental Elements of
Power Electronics
This chapter covers such a broad range that it is impossi¬
ble to sum it up in a few words. Rather, we suggest a quick
glance through the Section headings to become familiar
with the contents. The user-friendly presentation is
arranged so that even the non-initiated will be able to
understand the meaning and thrust of power electronics.
No complicated mathematics, no nitty-gritty detail to
mask the basic principles.
Distortion power factor, displacement power factor and
total harmonic distortion are introduced in Sections 21.12
to 21.14. These terms have become important in today’s
power electronic environment.
The application of thyristors has been grouped into six
fundamental circuits that describe the majority of all
industrial applications (Sections 21.20 to21.25).They give
the student a broad understanding of how linecommutated converters are used in industry. (The term
naturally-commutated is sometimes used instead of linecommutated).
The development of GTOs and IGBTs has permitted the
development of self-commutated converters that can
initiate and terminate conduction at will. (The term forcecommutated is sometimes used instead of self¬
commutated). Section 21.36 begins with a brief descrip¬
tion of these switching converters. The text then goes on
to analyze the operation of a dc-to-dc converter,
sometimes called a chopper. Particular attention
should be paid to Sections 21.41 and 21.42 because the 2-
quadrant and 4-quadrant converters are fundamental to
a large number of electronic devices and drives. It is
recognized that in this emerging world of megawatt
electronic power, switching converters have become just
as important as induction motors and transformers.
The transformation of a dc-to-dc converter into a dc-toac converter is explained in Section 21.44. The really
exciting part then begins with Section 21.45 where the
notion of pulse width modulation (PWM) is introduced.
The PWM converter is probably one of the most useful
converters that was ever invented. It permits the conver¬
sion of a de voltage into a voltage of any frequency, ma¬
gnitude and phase angle by simply modifying the signals
applied to the semiconductor gates. Indeed, even the
waveshape of the output can be modeled to anything we
please. The beauty of the situation is that power can flow
in either direction (de side to ac side and vice versa) with¬
out changing connections. Furthermore, the output impe¬
dances on both the ac and de sides are inherently low.
CHAPTER 22 Electronic Control of DirectCurrent Motors
The speed and torque control of de motors is first
described by using thyristors that convert ac power into
de. Section 22.7 is worth examining in detail because it
gives a systematic way of determining whether a converter
is operating in the rectifier or inverter mode.
Sections 22.8 and 22.9 cover two special versions of thy¬
ristor rectifiers. Although quite popular in industry, their
behavior is somewhat more complex and a summary
treatment in class is usually sufficient. On the other hand,
Sections 22.10 and 22.11 are very pertinent to de motor
drives because they make use of the 4-quadrant dc-to-dc
self-commutated converter. Instructors will find the
detailed description of instantaneous current flow through
the motor and converter of particular interest because it
removes all ambiguity as to what goes on during the
switching process.
Finally, the literature often makes reference to the
brushless de machine. Sections 22.12 through 22.16
describe in a novel and interesting way how this motor
evolved, together with its practical application.
CHAPTER 23 Electronic Control of
Alternating Current Motors
Many electronic drives involve synchronous motors and
induction motors. We have segregated the drives into
seven distinct types which account for at least 90 % of all
industrial ac drives. Sections 23.2 to 23.6 cover drives that
use thyristors. They include cycloconverters used in ocean
liners and cement-mills to back-to-back drives for small
fans. Section 23.7 then describes solid-state induction
motor starters that have found an enormous market in
new installations and retrofitting applications. Section 23.7
is therefore a must assignment.
4Section 23.12covers an interesting application of a wound¬
rotor motor for variable speed control.The energy usually
lost in external resistors is recovered by using a linecommutated thyristor inverter in the rotor circuit.
Self-commutated switching converters that generate
rectangular voltages and currents (Sections 23.8 to 23.11)
are often employed to drive induction motors. Today, they
involve IGBTs and GTOs, but many older installations
used thyristors that were specially configured to operate
as if they were GTOs. Consequently, in these four Sec¬
tions the actual circuit configuration of the semiconductors
is not shown.
The subdivision dealing with speed control by pulse width
modulation is particularly adapted to modern drives. It
begins with a brief review of PWM (Sections 23.13 and
23.14). The harmonic frequencies in PWM are much
higher than the fundamental frequency and so they are
easy to filter out. Consequently, the fundamental
frequencies that are generated by a PWM converter can
range from 400 Hz to zero, which opens the way to vector
control of induction motors. Because of the resulting wide
speed range, it is necessary to cover the behavior of the
induction motor in greater detail. Thus, Section 23.15
introduces the notion of flux orientation in a de motor
with a view to comparing it to the flux orientation in an
induction motor.Sections 23.16 to 23.19 then go on to show
how the rotor voltages, currents, torques and slip speeds
are related to each other. This is an in-depth look at basic
principles that are really an extension of Chapters 14 and
15. It is interesting to note that slip speed is a more useful
concept than slip when discussing variable speed control.
Sections 23.20 to 23.22 make use of the equivalent circuit
diagram of the induction motor to understand the
problems that arise when the speed is very low. It is seen
that the constant volts per hertz rule produces a drastic
reduction in torque when the speed is less than about10%
of rated synchronous speed. To compensate for this, the
volts per hertz must be raised as the speed approaches
zero.
A word about the equivalent circuit diagram (Sections
23.20 and 23.21) to is in order. The circuit is essentially
similar to that of a transformer. It is therefore simple and
easy to solve, particularly when using a computer program.
Sections 23.23 to 23.26 explain the basic principles of
vector control. It is seen that the magnetomotive forces
of the currents flowing in a three-phase stator can be
combined vectorially to produce a resultant mmf having
a specific magnitude and direction. Similarly, the
magnetomotive forces of the currents flowing in the ro¬
tor can be combined vectorially to produce a resultant
mmf having another specificmagnitude and direction. The
vector sum of these resultant rotor and stator mmfs
produces a third mmf which gives rise to the mutual flux
in the machine. The rotor current corresponding to the
resultant rotor mmf interacts with the mutual flux to
produce the torque.
But that is only part of the story. It is the presence of the
high-speed computer, incorporated in the vector drive,
that makes it possible to ensure that during transient con¬
ditions the mutual flux is always oriented correctly with
respect to the currents flowing in the rotor.
Another feature that deserves particular attention is the
electric traction drive described in Sections 23.27 to 23.30.
It shows how the voltage and phase shift of a PWM
converter can be controlled so as to force the required
active and reactive power to flow between the overhead
line and the electric train. In particular, the power is made
to flow at unity power factor. Furthermore, because of
the PWM mode of operation, the fundamental voltage
generated on the ac side of the converter is inherently
sinusoidal and only the high frequency harmonics need
to be filtered out. This is a remarkable example of how a
5switching converter can resolve several problems
simultaneously. On account of the wide applicability of
this principle, the study of Sections 23.27 to 23.30 is highly
recommended.
CHAPTER 24 Generation of Electrical Energy
This chapter is particularly interesting because it gives in
a nutshell all the essential elements concerning the
generation of electric power. The purpose of pumped
storage systems, the reason for cooling towers, the dis¬
tinction between light-water and heavy-water nuclear
reactors, are some of the many points that are explained
in a simple way. Even if time does not permit class study
of this subject, it should be given as a reading assignment
to every student of electric power. The same remark
applies to Chapters 25 and 26.
CHAPTER 25 Transmission of Electrical Energy
Transmission is the term used whenever electric power is
carried over high-voltage (HV) and extra-high-voltage
(EHV) lines. In the same style as the previous chapter on
generation, this chapter highlights the essential features
of transmission, using simple mathematics. A transmis¬
sion line is composed of a string of L, R, C components
that determine its power-handling capacity and voltage
regulation. The effect of these components is explained
in simple terms by making use of phasor diagrams.
Another topic of interest is the so-called BIL of electrical
apparatus, a term that describes its tolerance level to
lightning strokes and switching transients (Sections 25.10
to 25.12).
CHAPTER 26 Distribution of Electrical Energy
The distribution of electric power covers all systems
operating roughly between120 V single-phase, and 69 kV,
3-phase. This chapter describes the equipment used to
transport, regulate, protect, interrupt and transform
electric power for use by the ultimate consumer. Also
covered are the important questions of grounding and the
safety measures needed to prevent electric shocks (Sec¬
tions 26.18 to 26.22).
CHAPTER 27 The Cost of Electricity
Everyone is interested in the cost of electricity. The basic
elements that make up an electricity bill are presented
here, together with the reasons that justify the various
tariff structures.
CHAPTER 28 Direct-current Transmission
Direct current transmission has become a viable alterna¬
tive to high-voltage ac transmission and is being exploited
throughout the world. This chapter makes use of
knowledge previously gained in Chapter 21 concerning
line-commutated thyristor converters, harmonics and
reactive power. It gives an overview of existing de trans¬
mission lines, including back-to-back converters (Section
28.19). The latter are used whenever power has to be
exchanged between two large ac systems whose
frequencies are not synchronized.
CHAPTER 29 Transmission and Distribu¬
tion Solid-State Controllers
This pioneering chapter discusses the current state of the
electronic control of large blocks of ac power. This has
been made possible by the development of IGBTs and
GTOs that can switch large currents at high voltages. The
chapter reveals how the reactance of a line can be reduced
by series compensation and how this enables the control
of power flow (Section 29.1 and 29.2). It also shows how
capacitors and inductors can be replaced by electronic
converters that create either lagging or leading reactive
power by switching alone. This remarkable achievement
is having repercussions throughout the power industry
(Section 29.3).
As an example of what is happening, you are invited to
read Section 29.6 that describes a 20 MW frequency
converter that has absolutely no moving parts.Then read
on in Section 29.5 that discusses a unified power flow
controller (UPFC) that can electronically modify the
phase-shift and magnitude of an injected voltage and
thereby control the magnitude and direction of active and
reactive power flow between two interconnected regions.
6CHAPTER 30 Harmonics
Industrial and commercial enterprises, govern-ment and
private institutions, as well as electrical utilities are
becoming increasingly aware of distortion and the quality
of electric power. The main problem is the effect of
harmonics on electrical equipment and distribution
systems. Harmonics are becoming very important because
they are generated by electronic drives, computers and
other switching devices that are being installed
everywhere.
This important chapter explains the origin of harmonics
and their effects. It shows that harmonics are always
created by non-linear loads. Thus, when a perfect sine
wave of voltage or current is applied to a load that contains
linear and non-linear elements, the latter will always
generate harmonic voltages and currents.
In effect, a non-linear load behaves like a frequency
converter. It converts a portion of the fundamental power
it absorbs into harmonic power. One striking example of
a non-linear load is a simple switch that opens and closes
periodically. The switch absorbs power at the fundamental
frequency and converts it into harmonic power of many
different frequencies.
Another important feature is that a periodic switch can
either absorb or deliver reactive power at the fundamental
frequency. This makes it possible to simulate the
properties of capacitors and inductors by using an
appropriate switching procedure.
The book reveals a simple method of analyzing a distorted
wave. It helps the student get a better grasp of the meaning
of harmonics. The method is based on Fourier series, but
in a very user-friendly way. Software on harmonic analysis
is available that yields an immediate solution. However,
students find it more interesting when they actively
participate in the harmonic-solving procedure. In this re¬
gard, a spreadsheet is easy to set up and the computation
is straightforward. Problems toward the end of the chapter
were solved this way.
Although this chapter appears at the end of the book, it
may be referred to whenever the need arises.
The chapter also discusses electronic converters that are
being developed to meet Power Quality requirements at
the distribution level. Some of these devices behave like
active filters capable of neutralizing harmonics at the con¬
sumer premises.
It is important to note that the material covered in this
chapter rests upon concepts developed in previous
chapters. Consequently, although the applications are new,
the underlying knowledge is the same.
With power regulation becoming an important issue, the
development of these electronic power devices will have
a profound impact on the transmission and distribution
of electric power.
Chapter 31 Programmable Logic
Controllers
Programmable logic controllers (PLCs) have been in ser¬
vice for the past thirty years. During that time, the trans¬
mission of information, including automatic controls, has
grown enormously. In consequence, it is now possible to
control not only the operation of specific machines or
processes, but the entire operation of a business including
shipping, inventory, sales and finance.
This chapter explains the basic principles of PLCs. The
many examples make it easy to understand how hardware
devices can be converted into virtual items that are easily
manipulated and interconnected.
A final broad section on the Modernization Of An
Industry offers the student an opportunity to see how a
business gradually moves from older to more modern concepts.
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