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HANDBOOK OF LARGE HYDRO GENERATORS Operation and Maintenance
GLENN MOTTERSHEAD
STEFANO BOMBEN
ISIDOR KERSZENBAUM
GEOFF KLEMPNER
© 2021 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Names: Mottershead, Glenn, author. | Bomben, Stefano, author. | Kerszenbaum, Isidor, author. | Klempner, Geoff, author. Title: Handbook of large hydro generators : operation and maintenance / Glenn Mottershead, Stefano Bomben, Isidor Kerszenbaum, Geoff Klempner.
Other titles: Operation and maintenance of large turbo generators Description: Eleventh edition. | Hoboken, New Jersey : Wiley, [2020] | Series: IEEE press series on power engineering | Original edition published under title: Operation and maintenance of large turbo generators / Geoff Klempner, Isidor Kerszenbaum. | Includes bibliographical references and index.
Identifiers: LCCN 2020035414 (print) | LCCN 2020035415 (ebook) | ISBN 9780470947579 (hardback) | ISBN 9781119524182 (adobe pdf) | ISBN 9781119524168 (epub)
Subjects: LCSH: Turbogenerators. | Turbogenerators–Maintenance and repair. Classification: LCC TK2765 .K58 2020 (print) | LCC TK2765 (ebook) | DDC 621.31/3–dc23
LC record available at https://lccn.loc.gov/2020035414 LC ebook record available at https://lccn.loc.gov/2020035415
Set in 10/12pt Times by SPi Global, Pondicherry, India
10 9 8 7 6 5 4 3 2 1
families Victoria, Kristina, and Kayla Bomben
Susan Klempner Jackie, Livnat, and Yigal Kerszenbaum,
and To the operators, technicians, and engineers in the power stations around the world who keep the lights on and the power flowing around the clock through adverse conditions for the benefit of
everyone.
CONTENTS
1.2 Electrical–Mechanical Equivalence 6
1.3 Alternating Current (AC) 6
1.4 Three-Phase Circuits 13
1.6 The Synchronous Machine 18
1.7 Synchronous Machine: Basic Operation 23
CHAPTER 2 GENERATOR DESIGN AND CONSTRUCTION 35
2.1 Stator Core 36
2.2 Stator Frame 50
2.6 Stator Core and Frame Forces 64
2.7 Stator Windings 65
2.12 Rotor Rim 91
2.13 Rotor Spider/Drum 103
2.15 Rotor Winding and Insulation 110
2.16 Amortisseur Winding 116
2.18 Cooling Air 122
2.19 Rotor Fans/Blower 124
2.21 Thrust and Guide Bearings 128
vii
3.1 Oil Systems 157
3.3 Bearing Cooling Coils and Water Supply 165
3.4 Stator Winding Direct Cooling Water System 167
3.5 Excitation Systems 171
4.1 Basic Operating Parameters 177
4.2 Operating Modes 188
4.3 Machine Curves 190
4.6 System Considerations 225
4.8 Excitation and Voltage Regulation 237
CHAPTER 5 MONITORING AND DIAGNOSTICS 241
5.1 Generator Monitoring Philosophies 242
5.2 Simple Monitoring with Static High-Level Alarm Limits 243
5.3 Dynamic Monitoring with Load Varying Alarm Limits 244
5.4 Artificial Intelligence (AI) Diagnostic Systems 247
5.5 Monitored Parameters 250
5.7 Capacitive Coupling 274
5.9 Rotor 278
6.3 Brief Description of Protective Functions 296
6.4 Tripping and Alarming Methods 307
CHAPTER 7 INSPECTION PRACTICES AND METHODOLOGY 311
7.1 Site Preparation 311
7.3 Inspection Frequency 317
7.4 Generator Accessibility 318
7.5 Inspection Tools 319
7.6 Inspection Forms 321
8.3 Stator Core Air Ducts 354
8.4 Stator Core Laminations 356
8.5 Stator Core Clamping System 378
8.6 Stator Coils/Bars 389
8.8 Stator Wedging System 398
8.9 Stator Endwinding 405
8.10 Main and Neutral End Leads, Cables, VTs, CTs, and Insulators 411
CHAPTER 9 ROTOR INSPECTION 417
9.1 Rotor Spider with Shrunk Laminated Rims 419
9.2 Rotor Rim 430
9.3 Rotor Poles 436
9.4 Rotor Brakes 458
10.2 Excitation: Static Exciter Components 470
10.3 Brushless Exciter 470
10.6 Excitation: Sliprings, Commutator, and Brushes 481
10.7 Surface Air Coolers 499
10.8 Fire Protection 502
10.9 General Items 504
10.11 Miscellaneous Auxiliaries 510
11.1 Stator Core Mechanical 513
11.2 Stator Core Electrical Tests 518
11.3 Stator Winding Mechanical Tests 531
11.4 Stator Winding Electrical Tests 534
11.5 Rotor Mechanical Testing 568
11.6 Rotor Electrical Testing 583
11.7 Bearings 590
12.1 General Maintenance Philosophies 595
12.2 Operational and Maintenance History 597
12.3 Maintenance Intervals/Frequency 598
12.4 Planned Outages 599
12.6 Excitation System Upgrades 611
12.7 Workforce 627
12.10 Required Information, Tests and Inspection Prior to Uprating/Upgrading 631
12.11 Maintenance Schedule After Uprating 632
INDEX 633
x CONTENTS
PREFACE
Hydro generators in different plants are rarely identical, and it is not uncommon for small, medium, or large utilities to have a significant variety of unit sizes, origins, and vintage in their fleet of generators. Among these generators, there might be units 60 or more years old with all original components including stator windings due to the robust nature of this class of machinery. Somemight still have a pilot and main rotating exciter or a static pilot with a main rotating exciter, or have full static excitation. Additionally, there may be units operating over a wide range of rotating speeds in 50 and 60 Hz power grids with a few still operating at 25 Hz or other frequencies. All are designed and built by a long list of manufacturers from around the globe using a variety of materials and methods governed by different standards. These generators are still owned by traditional utilities and also owned by new deregulated independent power producers (IPPs) that acquire traditional utilities from all over the world. There are new large hydro plants still being built for tra- ditional utilities and IPPs to the most modern design standards and manufacturing methods. The owners of all types are called upon to operate and maintain an incred- ibly wide variety of machines.
The reasons why one may find so many “old” units still in operation is not difficult to determine. First of all, historically generators have been designed and manufactured with the intent to be robust enough to last typically 50 years or more. Second, replacing operating units is very capital-intensive and done only when a catastrophic failure has occurred or some significant economic benefit is possible only with complete replacement. Third, although typically designed to last many years, large hydro generators are known to be capable of having their lives extended far beyond 50 years if well maintained and operated. There are some gen- erators in operation today that were placed in service in 1896, an example is the Dominion Power and Transmission Company’s units in Decew Falls, Ontario, Canada, now operated by Ontario Power Generation. To continue to operate reli- ably older generators require replacement of at least some major components, such as the armature winding, rotor winding insulation, or replacing the entire stator frame and core or rotor spider. Managing the scope and timing of major mainte- nance is always a challenge.
There are copious amounts of information about the operation, maintenance, and troubleshooting of large hydro generators in many publications and online communities. All vendors at one stage or another have produced and published interesting literature about the operation of their generators. Institutions such as EPRI, CIGRE, IEC, IEEE, CEATI, and other organizations cover various aspects of the operation and maintenance of generators in general, but often have difficulty
xi
providing specific information that may help troubleshoot a particular generator design or operating problem. It is no wonder then that with somany dissimilar units in operation having different operating conditions, we are often forced to call the “experts,” who tend to be folks almost as old as the oldest units in operation. These are individuals who have crawled around, inspected, tested, and maintained many diverse generators over the years. In doing so, they have retained knowledge about the different designs, materials, and manufacturing characteristics, typical problems, and workable solutions. This type of expertise cannot easily be learned in a classroom.
Unfortunately, not every company retains an individual with the breadth and depth of expertise required for troubleshooting the generators. In fact, with the advent of deregulation, many small nonutility (third-party) power producers operate small fleets of generators without the benefit of in-house expertise. In lieu of that, they depend heavily on OEMs and independent consultants. Large utilities in many places have also seen their expertise dissipate, not to a small extent because of a refocusing of management priorities. All these developments are occurring at the same time that these aging units are called to operate in a deregulated or semideregulated world which typically results in an increase in load-cycling.
Some effort has been made over the years to capture the experts’ knowledge and make it readily available to any operator as a computer-based expert system. However, difficulty with adaptation of the associated computer programs to the many different types of generators and related equipment in existence has proved to be the Achilles heel of this technology. There is just no substitute for someone who understands machine design and has the required experience to recognize the significance of visual indications while crawling through a machine on a regu- lar basis.
This book is designed to partially fill the gap by offering a comprehensive view of many issues related to the operation, inspection, maintenance, and trouble- shooting of large hydro generators. All of the information in the book is the result of many years of combined hands-on experience of the authors, which at the time of this writing, amounts to 157 years. It was written with the machine’s oper- ator and inspector in mind, as well as providing a guide to uprating and life enhancement of large hydro generators. Although not designed to provide a step-by-step guide for the troubleshooting of large hydro generators, it serves as a valuable source of information that may prove to be useful during troubleshoot- ing activities. The topics covered are also cross-referenced to other sources. Many such references are included to facilitate those readers interested in enlarging their knowledge of a specific issue under discussion. For the most part, theoretical equa- tions have been left out, as there are several exceptionally good books on the theory of operation of synchronous machines. Those readers who so desire can readily access those books, several references are cited. This book, however, is about the practical aspects that characterize the design, operation, and maintenance of large hydro generators, and a number of practical calculations used commonly in maintenance and testing situations have been added.
xii PREFACE
Chapter 1 (Principles of Operation of Synchronous Machines) provides a basis of theory for electricity and electromagnetism upon which the machines cov- ered in this book are based. As well, the fundamentals of synchronous machine construction and operation are also discussed. This is for the benefit of generator operators who have a mechanics background and are inclined to attain a modicum of proficiency in understanding the basic principles of operation of the generator. It also comes in handy for those professors who would like to adopt this book as a reference for a course on large rotating electric machinery.
Chapters 2 and 3 (Generator Design and Construction and Generator Aux- iliary Systems) contain a very detailed and informative description of all the com- ponents found in a typical generator and its associated auxiliary systems. Described therein are the functions that the components perform, as well as all relevant design and operational constrains. Some additional insight into design methods and cal- culations are also provided.
Chapter 4 (Operation and Control) introduces the layperson to the many operational variables that describe a generator. Most generator–grid interaction issues and their effect on machine components and operation are covered in great detail.
Chapter 5 (Monitoring and Diagnostics) and Chapter 6 (Generator Protec- tion) serve to introduce all aspects related to the online and offline monitoring and protection of a large hydro generator. Although not intended to serve as a guideline for designing and setting up the protection systems of a generator, they provide a wealth of background information and pointers to additional literature.
Chapters 7 (Inspection Practices and Methodology), leads off the second part of the book with a look at preparing for a hands-on inspection of large hydro generators. The chapter discusses the issues of concern for both safety of personnel and the equipment as well as the types of tools and approaches used in inspecting large hydro generators. This chapter also contains a collection of inspection forms that can be used for inspecting large hydro generators. These forms are very useful and can be readily adapted to any machine and plant.
Chapter 8 (Stator Inspection), Chapter 9 (Rotor Inspection), and Chapter 10 (Auxilliaries Inspection) constitute the core of this book. They describe all compo- nents presented in Chapters 2 and 3, but within the context of their behavior under real operational constraints, modes of failure, and typical troubleshooting activ- ities. These chapters provide detailed information on what to look for, and how to recognize problems in the machine during inspection. Chapters 8 and 9 also con- tain hundreds of pictures to assist in the inspection process in a methodical step-by- step crawl through of the machine.
Chapter 11 (Maintenance and Testing) contains a comprehensive summary of the many techniques used to test the many components and systems comprising a generator. The purpose of the descriptions is not to serve as a guide to performing the tests as there are well established guides and standards for this purpose. Rather, they are intended to illustrate the palette of possible tests to choose from. Provided as well is a succinct explanation of the character of each test and explanations of how they are carried out.
PREFACE xiii
Chapter 12 (Maintenance Philosophies, Upgrades and Uprates) is included to provide some perspective to the reader on the many choices and approaches that can be taken in generator and auxiliary systems maintenance, as well as upgrading equipment and uprating of the machine. Often, there are difficult decisions on how far to take maintenance. In some cases, only basic maintenance may be required, and on other occasions, it may be appropriate to carry out extensive rehabilitation of existing equipment or even replacement of components that can yield a higher efficiency or higher rating for the machine. This chapter discusses some of the issues that need to be considered when deciding on what, how much, and where to do it.
We hope that this book will be not only useful to the operator in the power plant but also to the design engineer and the generator operations engineer. We have provided a wealth of information obtained in the field about the behavior of such machines, including typical problems and conditions of operation. The book should also be useful to the student of electrical rotating machines as a com- plementary reference to the books on machine theory. When read in its entirety, this book will assist the user in performing a complete machine inspection and understand with reasonable clarity, what they are observing, if there is a problem, and how to go about finding a solution to fix it.
Although we have tried our best to cover each topic as comprehensively as possible, the book should not be seen as a guide to troubleshooting. In each case in which a real problem is approached, a whole number of very specific issues only relevant to that very unique machine come into play. These can never be antici- pated or known and thus described in a book. Thus, we recommend the use of this book as a general reference source, but that the reader should always obtain ade- quate on-the-spot expertise when approaching a particular problem.
Glenn Mottershead Stefano Bomben
Isidor Kerszenbaum Geoff Klempner
Toronto, Ontario, Canada Irvine, California
xiv PREFACE
ABOUT THE AUTHORS
Mr. Mottershead has worked or consulted on rotating apparatus for over 45 years with 33 of these years as an engineer at Westinghouse, where he was mentored by a select group of electrical and mechanical generator design and manufacturing engineers. These mentors had lineage that reached back to Nikola Tesla, George Westinghouse, and other key pioneers of the early power generation industry. His objective in writing this book with the other expert authors is to pass on lessons he was fortunate to receive to those working at all levels of hydro power generation. Mr. Mottershead is an IEEE Life Member and a Principle Consultant at HDR.
Mr. Bomben is a Sr. Engineer at Ontario Power Generation (formerly Ontario Hydro) with over 29 years of experience inspecting large hydro generators, provid- ing oversight on rewinds, overhauls, new machines, failure investigations, repairs and testing, and writing technical specifications. He is a senior member of the IEEE with many contributions to the development of generator operation, maintenance, and insulation standards. The inspiration for this book was to produce a comprehen- sive written knowledge base for use by any power engineer interested in large hydro generators, informed by theory, operational history and physical inspection.
Mr. Klempner is an IEEE Fellow and large rotating electrical machines spe- cialist in the power industry for over 43 years. He provides electrical machine technical services on a global basis, regarding large generators and motors. This includes inspection, testing, design evaluation, failure analysis, life assessment, preparation of technical specifications, and test procedures. Previously, he worked with Ontario Hydro (now Ontario Power Generation) for over 25 years, and then NSS (Nuclear Safety Solutions) and Kinectrics Inc. He has authored or coauthored 65 papers and articles, and 4 textbooks. He also has an extensive background of professional activities, with IEEE, EPRI, and CIGRE.
Dr. Kerszenbaum has been involved in design, manufacturing, maintenance, and operation of large electrical machines for about 40 years. He also has been a contributor in writing IEEE standards for this type of equipment. He authored and coauthored several books on the subject, and educated hundreds of engineers over the years.
xv
ACKNOWLEDGMENTS
The contents of this book are in part the result of personal experience accumulated over years of working with large hydro generators. It is also the result of the important long-term contribution of coworkers and associates. Each author was motivated by an important individual at an early stage of his career, and by many outstanding individuals in the profession over subsequent years. Two engineers, Frank Barnard and John F. Lyles, need to be recognized here as they had significant hydro generator mentoring roles for Mottershead and Bomben, respectively. Coau- thors Geoff Klempner and Izzy Kerszenbaum are also important mentors as they pioneered the writing of the book Operation and Maintenance of Large Turbo Generators, which was the model for this book.
The authors would like to give special recognition to Sungsoo Kim for writ- ing Chapter 6 (Generator Protection); his patience and contribution has produced a magnificent compilation of his expertise. The authors would also like to thank Tim Maricic and Wayne Martin for their gracious contributions to Chapter 2. The authors are privileged to have had two very patient technical reviewers, John Linn and Richard Huber, who painstakingly went through the manuscript and con- tributed useful ideas. The authors are also very grateful to the individuals who kindly supplied the many pictures and information that make up this handbook.
The authors wish to thank Ontario Power Generation for the incredibly large volume of pictures that form part of this book, without this support, this book would not have been possible. Unless otherwise indicated, all pictures in the book are courtesy of Ontario Power Generation.
Special thanks to Victoria Bomben and Paolo Bomben for their assistance with the design of the front cover, and to Voith for the picture.
The authors are most indebted to the IEEE Press for supporting its publication.
The authors also would like to thank the members of the editorial depart- ments of the IEEE Press and Wiley, the reviewers, and all others involved in the publication of this book for their support in making its publication possible.
Finally, but certainly most intensely, the authors wish to thank their imme- diate families for their continuous support and encouragement while we played with big machines around the world.
xvii
CHAPTER1 PRINCIPLES OF OPERATION OF SYNCHRONOUS MACHINES
The synchronous generator belongs to the family of electric rotating machines. Other members of the family are the direct-current (DC) motor or generator, the induction motor or generator, and a number of derivatives of these three. What is common to all the members of this family is the basic physical process involved in their operation, which is the conversion of electromagnetic energy to mechanical energy, and vice versa. Therefore, to gain an understanding of the physical prin- ciples governing the operation of electric rotating machines, one has to understand some rudiments of electrical and mechanical engineering.
Chapter 1 is for those who are involved in operating, maintaining, and trou- ble-shooting electrical generators. Specifically, those who want to acquire a better understanding of the principles governing the machines’ design and operation, but lack an electrical engineering background. The chapter starts by introducing the rudiments of electricity and magnetism, quickly building up to a description of the basic laws of physics governing the operation of the synchronous electric machine, which is the type of machine to which all salient pole hydro generators belong.
1.1 INTRODUCTION TO BASIC NOTIONS ON ELECTRIC POWER
1.1.1 Magnetism and Electromagnetism
Certain materials found in nature exhibit a characteristic to attract or repel each other. These materials, called magnets, are also called ferromagnetic because they include the element iron as one of their constituent elements. Magnets always have two poles: one called north, the other called south. Two north poles will repel each
Handbook of Large Hydro Generators: Operation and Maintenance, First Edition. Glenn Mottershead, Stefano Bomben, Isidor Kerszenbaum, and Geoff Klempner. © 2021 The Institute of Electrical and Electronics Engineers, Inc. Published 2021 by John Wiley & Sons, Inc.
1
other, as will two south poles. However, north and south poles will attract each other. Amagnetic field is defined as a physical field established between two poles. Its intensity and direction determine the forces of attraction or repulsion existing between the two magnets.
Figures 1.1-1 and 1.1-2 are typical representations of two interacting mag- netic poles and the magnetic field established between them.
Magnets are found in nature in all sorts of shapes and chemical constitution. Magnets used in industry are artificially made. Magnets that sustain their magnet- ism for long periods of time are denominated “permanent magnets.” The magnetic field produced by the north and the south pole of a permanent magnet is directional from north to south as shown in Figure 1.1-3. These are widely used in several types of electric rotating machines, including synchronous machines. However, due to mechanical as well as operational reasons, permanent magnets in synchro- nous machines are restricted to those with ratings much lower than large hydraulic (“hydro”) turbine-driven generators, which is the subject of this book. Hydro gen- erators take advantage of the fact that magnetic fields can be created by the flow of electric currents in conductors, see Figure 1.1-4.
The direction of the lines of force is given by the “law of the screwdriver”: mentally follow the movement of a screw as it is screwed in the same direction as
N S
Lines of force
Figure 1.1-1 Representation of two magnetic poles of opposite polarity, with the magnetic field between them shown as “lines of force.”
N N
Lines of force
Figure 1.1-2 Representation of two north poles and the magnetic field between them. South poles will create similar field patterns, but the lines of force will point toward the poles.
2 CHAPTER 1 PRINCIPLES OF OPERATION OF SYNCHRONOUS MACHINES
that of the current; the lines of force will then follow the circular direction of the head of the screw. The magnetic lines of force are perpendicular to the direction of current. A very useful phenomenon is that forming the conductor into the shape of a coil can augment the intensity of the magnetic field created by the flow of current through the conductor. In this manner, as more turns are added to the coil, the same current produces larger and larger magnetic fields. For practical reasons, all mag- netic fields created by current in a machine are generated in coils as shown in Figure 1.1-5.
The use of coils to amplify the magnetic field intensity requires them to be constructed in a very specific manner so that the resulting flux is produced in an effective way. When the coil is operating in air, the magnetic field direction, shape, and intensity depends on the number of turns in the coil, the size of the coil, and the direction of electric current flow in the coil winding. The flux produced is basically divided into two types. One is the effective flux that links the entire coil and does the useful work, and the other is the leakage flux which is a more localized effect and does no useful work. In fact, the leakage flux creates additional losses that make the coil less efficient, electromagnetically speaking (see Figure 1.1-6). The
N S
Figure 1.1-3 Representa- tion of a “permanent mag- net” showing the north and south poles and the mag- netic field between them flowing from north to south outside the magnet.
Conductor
Electric current
Lines of
forceFigure 1.1-4 Representation of a magnetic field created by the flow of current in a conductor.
1.1 INTRODUCTION TO BASIC NOTIONS ON ELECTRIC POWER 3
principles illustrated here become very important later on as we discuss the mag- netic field in the generator and stray losses.
To use the flux produced in a coil as effectively as possible, highly perme- able ferromagnetic materials are used to capture and direct the flux so that the amount of leakage flux is minimized. This allows the coil to do more useful work and keeps losses to a minimum. Iron in various derivatives is by far the most widely used material because it has all the magnetic characteristics required. It is structur- ally suitable, and cost-effective. When an “iron” core is used within the coil, and current is flowing, the magnetic field produced is shaped effectively, and the iron core essentially becomes a north–south magnet in the process (see Figure 1.1-7). This is why stator cores and rotor poles of generators are made of steel, containing iron and a few small quantities of additional elements. The iron allows the princi- ples discussed above to become a reality and is one of the reasons generators can be built to at least 97.5% efficiency.
Current flow
Lines of force
Figure 1.1-5 Representa- tion of a magnetic field pro- duced by the flow of electric current in a coil-shaped conductor.
Effective flux Leakage flux
Current inCurrent out
Figure 1.1-6 Representation of a magnetic field produced by the flow of electric current in a coil-shaped conductor operating in air, showing the effective and leakage flux components of the magnetic field produced.
4 CHAPTER 1 PRINCIPLES OF OPERATION OF SYNCHRONOUS MACHINES
1.1.2 Electricity
Electricity is the flow of positive or negative charges. Electricity can flow in elec- trically conducting elements (called conductors), or it can flow as clouds of ions in space or within gases. As will be shown in later chapters, both types of electrical conduction are found in hydro generators (see Figure 1.1-8).
Effective flux
N S
Figure 1.1-7 Representation of a magnetic field produced by the flow of electric current in a coil-shaped conductor with an “iron” core. The majority of the field produced is effective flux and the leakage field is reduced to a minimum.
(I)
Negative
charge
free electrons
Figure 1.1-8 Electricity. (I) Ionic clouds of positive and negative currents. The positive clouds are normally atoms that lost one or more electrons; the negative clouds are normally free electrons. This effect can be found inside the generator as partial discharge in the stator winding. (II) The flow of electrons inside a conductor material, for example, the copper windings of the rotor and stator.
1.1 INTRODUCTION TO BASIC NOTIONS ON ELECTRIC POWER 5
1.2 ELECTRICAL–MECHANICAL EQUIVALENCE
There is an interesting equivalence between the various parameters describing electrical and mechanical forms of energy. People with either electrical or mechan- ical backgrounds find this equivalence useful to the understanding of the physical process in either form of energy. Figure 1.2-1 describes the various forms of electrical–mechanical equivalence.
1.3 ALTERNATING CURRENT (AC)
Synchronous generators operate with both alternating-current (AC) and direct- current (DC) electric power. The DC can be considered a particular case of the general AC, with frequency equal to zero.
The frequency of an alternating circuit is a measure of the number of times the currents and/or voltages change direction (polarity) in a unit of time. The hertz (Hz) is the universally accepted unit of frequency, and measures cycles per second. One Hz equals one cycle per second. Alternating currents and voltages encoun- tered in the world of industrial electric power are for all practical purposes of con- stant frequency. This is important because periodic systems, namely systems that have constant frequency and sinusoidal signals, allow the currents and voltages to be represented by phasors.
Electrical Mechanical
Battery Pump
V
K
I
E =
V = Voltage H = Pressure head Q = Flow rate R = Resistance
ΔH = Pressure drop
ΔH
R
I
Electrostatic
storage
(inertia)
Spring
Δx
6 CHAPTER 1 PRINCIPLES OF OPERATION OF SYNCHRONOUS MACHINES
A phasor is a rotating vector. The benefit of using phasors in electrical engi- neering analysis is that it greatly simplifies the calculations required to solve circuit problems.
Figure 1.3-1 depicts a phasor of magnitude E, and its corresponding sinus- oidal trace representing the instantaneous value of the voltage quantity e. The mag- nitude E represents the maximum value of voltage (e).
The phasor is made of a vector with magnitude proportional to the magnitude of E, rotating at a constant rotational speedω. The convention is that phasors rotate counterclockwise. The vertical projection of the phasor results in a sinusoid repre- senting the instantaneous voltage (e) existing at any time. In Figure 1.3-1, α =ω × t, where t is the time elapsed from its zero crossing.
When a sinusoidal voltage is applied to a closed circuit, a current will flow in it. After a while, the current will have a sinusoidal shape (this is called the steady- state current component) and the same frequency as the voltage. An interesting phenomenon in periodic circuits is that the resulting angle between the applied voltage and the current depends on certain characteristics of the circuit. These char- acteristics combine into one representative parameter, impedance and are broken down into resistive, capacitive, and inductive. The angle between the voltage and the current in the circuit is called the power factor angle and is defined as φ. The cosine of the same angle is called the power factor of the circuit or, for short, the PF.
In the case of a circuit having only resistances, the voltages and currents are in phase, meaning that the angle between them equals zero. Figure 1.3-2 shows the various parameters encountered in a resistive circuit. This is a representation of a sinusoidal voltage of magnitude “E” applied on a circuit with a resistive load “R.” The schematics show the resultant current (i) in phase with the voltage (v). It also shows the phasor representation of the voltage and current. It is important to note that resistances have the property of generating heat when a current flows through them. The heat generated equals the square of the current times the value of the resistance. When the current is measured in amperes and the resistance
Voltage (e)
E (phasor)
α
α
ω
Figure 1.3-1 A phasor E that can represent the voltage impressed on a circuit.
1.3 ALTERNATING CURRENT (AC) 7
in ohms, the resulting power dissipated as heat is given in watts. In electrical machines, this heat represents a loss of energy. One of the fundamental require- ments in designing an electric machine is the efficient removal of the energy resulting from these resistive losses, with the purpose of limiting the temperature rise of the internal components of the machine. In resistive circuits, the instan- taneous power delivered by the source to the load equals the product of the instan- taneous values of the voltage and the current. When the same sinusoidal voltage is applied across the terminals of a circuit with capacitive or inductive character- istics, the steady-state current will exhibit an angular (or time) displacement in relation to the driving voltage.
The magnitude of the angle (or power factor) depends on how capacitive or inductive the load is. In a purely capacitive circuit, the current will lead the voltage by 90 , whereas in a purely inductive one, the current will lag the voltage by 90 (see Figure 1.3-3). Here, the sinusoidal voltage E is applied to a circuit comprised of resistive, capacitive, and inductive elements. The resulting angle between the current and the voltage depends on the value of the resistance, capacitance, and inductance of the load.
A circuit that has capacitive or inductive characteristics is referred to as being a reactive circuit. In such a circuit, the following parameters are defined:
I
E
E
E
X
R Δυ
i
current wave forms are in phase, i.e.
the power factor of the circuit equals 1
Figure 1.3-2 Alternating circuits (resistive).
8 CHAPTER 1 PRINCIPLES OF OPERATION OF SYNCHRONOUS MACHINES
S: The apparent power S = E × I, given in units of volt-amperes or VA. P: The active power P = E × I × cos φ, where φ is the angle between the
voltage and the current. P is given in units of watts. Q: The reactive power Q = E × I × sin φ, given in units of volt-amperes-
reactive or VAR.
The active power P of a circuit indicates a real energy flow. This is power that may be dissipated on a resistance as heat, or may be transformed into mechan- ical energy. However, the use of the word “power” in the definition of S and Q has been an unfortunate choice that has resulted in confounding most individuals with- out an electrical engineering background for many years. The fact is that apparent power and reactive power do not represent any measure of real energy. They do represent the reactive characteristic of a given load or circuit, and the resulting angle (power factor) between the current and voltage. This angle between voltage and current significantly affects the operation of an electric machine.
For the time being, let us define another element of AC circuit analysis: the power triangle. From the relationships shown above among S, P, Q, E, I, and φ, it can be readily shown that S, P, andQ form a triangle. By convention,Q is shown as positive (above the horizontal), when the circuit is inductive, and vice versa when capacitive (see Figure 1.3-4).
R
υR
S = υ•i (VA) is apparent power p = υ•i•cos φ (W) is active power q = υ•i•sin φ (volt-amperes-reactive [VAR's] is reactive power
φ
φ
φ
υ
τ
Figure 1.3-3 Alternating circuits (resistive-inductive-capacitive).
1.3 ALTERNATING CURRENT (AC) 9
To demonstrate the use of the power triangle within the context of large generators and their interaction with the power system, we need to consider a one-line schematic that includes the generator, transmission system, and the con- nected load at the end (see Figure 1.3-5).
The voltage required at the load, so that it will operate correctly, is given as 1000 V. The transmission line resistance and reactance are provided and the line impedance calculated as shown, using the power triangle approach. If we now con- sider an actual load for the simple system of Figure 1.3-5, we can calculate the cur- rent drawn by the load and the voltage required from the generator source to compensate for all the line losses and voltage drop across the line. Two cases are provided to illustrate the effect of a purely resistive load versus a load with
E υ
drop on lines and cables
Figure 1.3-4 Definition of the “power triangle” in a reactive circuit.
Line losses = I2Rline Load
Simple power system showing a generator, bus, line, and load
Line resistance (R) = 10 Ω (resistive)
Line reactance (X) = 10 Ω (inductive)
Line impedance (Z) = √(102 + 102) = 14.14 Ω
Figure 1.3-5 Schematic of a simple system in one- line form.
10 CHAPTER 1 PRINCIPLES OF OPERATION OF SYNCHRONOUS MACHINES