Introduction to Electric Power and Drive Systems (eBook)

Paul C. Krause, Oleg Wasynczuk, Timothy O'Connell, Maher Hasan (Autoren)

eBook Download: EPUB

2017
John Wiley & Sons (Verlag)
978-1-119-21427-4 (ISBN)

Infos

An introduction to the analysis of electric machines, power electronic circuits, electric drive performance, and power systems

This book provides students with the basic physical concepts and analysis tools needed for subsequent coursework in electric power and drive systems with a focus on Tesla's rotating magnetic field. Organized in a flexible format, it allows instructors to select material as needed to fit their school's power program. The first chapter covers the fundamental concepts and analytical methods that are common to power and electric drive systems. The subsequent chapters offer introductory analyses specific to electric machines, power electronic circuits, drive system performance and simulation, and power systems. In addition, this book:

• Provides students with an analytical base on which to build in advanced follow-on courses
• Examines fundamental power conversions (dc-dc, ac-dc and dc-ac), harmonics, and distortion
• Describes the dynamic computer simulation of a brushless dc drive to illustrate its performance with both a sinusoidal inverter voltage approximation and more realistic stator six-step drive  applied voltages
• Includes in-chapter short problems, numerous worked examples, and end-of-chapter problems to help readers review and more fully understand each topic

Paul C. Krause is Board Chairman of PC Krause and Associates Inc. (PCKA), and a retired Professor of Electrical and Computer Engineering at Purdue University. He has authored or co-authored more than 100 technical papers and is the co-author of Analysis of Electric Machinery and Drive Systems, Third Edition (Wiley-IEEE Press), and Electromechanical Motion Devices, Second Edition (Wiley-IEEE Press).  He is a Life Fellow of the IEEE and was the 2010 recipient of the IEEE Nikola Tesla Award.

Oleg Wasynczuk is Professor of Electrical and Computer Engineering at Purdue University and Chief Technical Officer of PCKA. He has authored or co-authored more than 100 technical papers and is the co-author of Analysis of Electric Machinery and Drive Systems, Third Edition (Wiley-IEEE Press), and Electromechanical Motion Devices, Second Edition (Wiley-IEEE Press). He is a Fellow of the IEEE and was the 2008 recipient of the IEEE PES Cyril Veinott Electromechanical Energy Conversion Award.

Timothy O'Connell is a Senior Lead Engineer at PCKA, where he leads a multi-member industry modeling and simulation team supporting the design and analysis of more electric aircraft. He has authored or co-authored over 20 technical papers on electric machine analysis and design, aerospace power systems, and modeling and simulation. He is a Senior Member of IEEE.

Maher Hasan is a Senior Lead Engineer at PCKA, where he has led several software development efforts for the simulation of circuits and electromechanical and power systems, and is involved in modeling and simulation in support of multiple efforts. He has authored or co-authored several technical papers in the fields of dynamic simulation and numerical methods.

Inhalt

ABOUT THE AUTHORS ix

PREFACE AND ACKNOWLEDGMENT xi

CHAPTER 1 BASIC CONCEPTS 1

1.1 Introduction 1

1.2 Phasor Analysis and Power Calculations 1

Power and Reactive Power 5

1.3 Elementary Magnetic Circuits 8

Field Energy and Coenergy 13

1.4 Stationary Coupled Circuits 16

Magnetically Linear Transformer 16

Field Energy 20

1.5 Coupled Circuits in Relative Motion 22

Field Energy 25

1.6 Electromagnetic Force and Torque 26

1.7 Elementary Electromechanical Device 32

1.8 Two- and Three-Phase Systems 35

Two-Phase Systems 35

Three-Phase Systems 37

References 40

Problems 40

CHAPTER 2 ELECTRIC MACHINES 43

2.1 Introduction 43

2.2 Fundamentals of Electric Machine Analysis 44

Concentrated Winding 44

Distributed Windings 47

Rotating Air-Gap MMF - Tesla's Rotating Magnetic Field 52

Two-Pole Two-Phase Stator 52

Three-Phase Stator 56

P-Pole Machines 58

Machine Inductances 62

2.3 Two-Phase Permanent-Magnet AC Machine 63

2.4 Analysis of a Two-Phase Permanent-Magnet AC Machine 69

Transformation 70

Steady-State Analysis 77

2.5 Three-Phase Permanent-Magnet AC Machine 81

Voltage Equations and Winding Inductances 82

Torque 83

The qsr-, dsr-, and 0s- Equations 84

References 89

Problems 89

CHAPTER 3 POWER ELECTRONICS 91

3.1 Introduction 91

3.2 Switching-Circuit Fundamentals 91

Power Conversion Principles 92

Fourier Analysis 95

Switches and Switching Functions 97

Energy Storage Elements 101

3.3 DC-DC Conversion 103

Buck Converter 104

Boost Converter 113

Advanced Circuit Topologies 118

3.4 AC-DC Conversion 118

Half-Wave Rectifier 118

Full-Wave Rectifier 125

3.5 DC-AC Conversion 133

Single-Phase Inverter 133

Three-Phase Inverter 136

3.6 Harmonics and Distortion 144

References 147

Problems 147

CHAPTER 4 PERFORMANCE AND SIMULATION OF AN ELECTRIC DRIVE 149

4.1 Introduction 149

4.2 Operating Modes of a Brushless DC Motor 149

Brushless DC Motor Operation with = 0 150

Maximum Torque Per Volt Operation of a Brushless DC Motor ( = MT?MV ) 155

Maximum Torque Per Ampere Operation of a Brushless DC Motor ( = MT?MA) 160

4.3 Operation of a Brushless DC Drive 164

Operation of Brushless DC Drive with = 0 166

Operation of Brushless DC Drive with = MT?MV 170

Operation of Brushless DC Drive with = MT?MA 172

Modes of Control of a Brushless DC Drive 174

4.4 Simulation of a Brushless DC Drive 180

Simulation of Coupled Circuits 180

Simulation of Drive Inverter and Transformation 181

Simulation of Permanent-Magnet AC Machine 183

References 186

Problems 186

CHAPTER 5 POWER SYSTEMS 187

5.1 Introduction 187

5.2 Three-Phase Transformer Connections 187

Wye-Wye Connection 188

Delta-Delta Connection 190

Wye-Delta or Delta-Wye Connection 191

Ideal Transformers 192

5.3 Synchronous Generator 193

Damper Windings 198

Torque 198

Steady-State Operation and Rotor Angle 198

5.4 Reactive Power and Power Factor Correction 204

5.5 Per Unit System 209

Per Unitizing the Synchronous Generator 210

5.6 Discussion of Transient Stability 215

Three-Phase Fault 215

References 220

Problems 220

APPENDIXA TRIGONOMETRIC RELATIONS, CONSTANTS AND CONVERSION FACTORS, AND ABBREVIATIONS 221

APPENDIX B WINDING INDUCTANCES 225

APPENDIXC ANIMATIONS 229

INDEX 231

Textauszug

CHAPTER 1
Basic Concepts

1.1 Introduction

The twentieth century began with the electric power industry in its infancy; Thomas Edison and Nikola Tesla were locked in battle with Edison advocating direct current (dc) and Tesla alternating current (ac). The century ended with the electric power industry expanding rapidly from the traditional power generation, transmission, and utilization into propulsion of air, ground, and sea transportation. The advent of the computer and the silicon-controlled rectifier in the mid-1900s brought about an expansion of the power area to include the smart grid, microgrids, efficient and robust electric drives, more-electric aircraft, ships, and land vehicles. This growth is likely to continue into the foreseeable future.

Before the advent of the computer, engineers were essentially limited to steady-state analysis and therefore unable to conveniently deal with the analytical challenges of the expanding power industry. This chapter sets forth some of the basic concepts and analysis tools that are part of the present-day power and electric drives area. Although not inclusive, the material covered in this chapter is representative and common to all disciplines of the power area.

1.2 Phasor Analysis and Power Calculations

Since the early twentieth century, we have lived in an alternating current (ac) world. Thanks to George Westinghouse and Nikola Tesla, power systems are predominately ac; power is generated by large ac generators, transmitted by high voltage transmission lines, and transformed to a low voltage and distributed to homes and factories. The evolution of the ac power system brought about many engineering challenges and, as we look back, it is difficult to comprehend how these problems were solved without a computer. Even steady-state ac-circuit analysis posed a problem until the early 1900s when Charles Stienmetz, who was a less flamboyant colleague of Edison and Tesla, came up with the concept of what is now known as phasors. Some may consider the phasor a casualty of the computer age along with the slide rule. It is, however, still a very useful means for understanding and portraying the steady-state performance of electric machines, power systems, and electric drives. Moreover, the phasor concept provides a means of visualizing sinusoidal variations from different frames of reference and in Chapter 2 we will find that the voltage and current phasors combined with Tesla's rotating magnetic field provides a straightforward means of analyzing and portraying the steady-state operation of ac machines.

The phasor can be established by expressing a steady-state sinusoidal variable as

(1.2-1)

where the a subscript is used here to denote sinusoidal quantities. The sinusoidal variations are expressed as cosines, capital letters are used to denote steady-state quantities, and Fp is the peak value of the sinusoidal variation. Generally, F or f represents voltage (V or v) or current (I or i) in circuit analysis, but it could be any sinusoidal variable. For steady-state conditions, θef may be written as

(1.2-2)

where ωe is the electrical angular velocity in radians/second (2π times the frequency) and θef(0) is the time-zero position of the electrical variable. Substituting (1.2-2) into (1.2-1) yields

(1.2-3)

Now, Euler's Identity is

(1.2-4)

and since we are expressing the sinusoidal variation as a cosine, (1.2-3) may be written as

(1.2-5)

where Re is the shorthand for “real part of.” Equations (1.2-3) and (1.2-5) are equivalent. Let us rewrite (1.2-5) as

(1.2-6)

We need to take a moment to define what is referred to as the root-mean-square (rms) of a sinusoidal variation. In particular, the rms value is defined as

(1.2-7)

where F is the rms value of Fa(t) and T is the period of the sinusoidal variation. It is left to the reader to show that the rms value of (1.2-3) is . Therefore, we can express (1.2-6) as

(1.2-8)

By definition, the phasor representing Fa(t), which is denoted with a raised tilde, is

(1.2-9)

which is a complex number. The reason for using the rms value as the magnitude of the phasor will be addressed later in this section. Equation (1.2-6) may now be written as

(1.2-10)

A shorthand notation for (1.2-9) is

(1.2-11)

Equation (1.2-11) is commonly referred to as the polar form of the phasor. The Cartesian form is

(1.2-12)

When using phasors to calculate steady-state voltages and currents, we think of the phasors as being stationary at t = 0; however, we know that a phasor is related to the instantaneous value of the sinusoidal quantity it represents. Let us take a moment to consider this aspect of the phasor and thereby, give some physical meaning to it. From (1.2-4), we realize that is a line of unity length rotating counterclockwise at an angular velocity of ωe. Therefore, backing up for a minute

(1.2-13)

is a line with a constant amplitude of rotating counterclockwise in the real-imaginary plane at an angular velocity of ωe with a time-zero displacement from the positive real axis of θef(0). Since is the peak value of the sinusoidal variation, the instantaneous value of Fa(t) expressed as a cosine is the real part of (1.2-13). In other words, the real projection of the phasor rotating counterclockwise at ωe is the instantaneous value of . Thus, with θef(0) = 0 in (1.2-3)

(1.2-14)

the phasor representing (1.2-14) is

(1.2-15)

For

         (1.2-16)

the phasor is

(1.2-17)

We will use degrees and radians interchangeably when expressing phasors. Although there are several ways to arrive at (1.2-17) from (1.2-16), it is helpful to ask yourself where the rotating phasor must be positioned at time-zero so that, when it rotates counterclockwise at ωe, its real projection is . It follows that a phasor of amplitude F positioned at 90° represents .

In other words, we are viewing a sinusoidal variation as the real projection in the real-imaginary plane of a rotating line equal in magnitude to the positive peak value of the variation and rotating at the electrical angular velocity of the sinusoidal variation. Since we are dealing with a steady-state variation, we can stop the rotation at any time and view it as a fixed line, but knowing full well that it, in fact, represents a sinusoidal variation and to represent the sinusoidal variation we must rotate it counterclockwise at ωe and take the real projection. Please understand that if we ran at ωe in unison with the rotating line it would appear as a constant to us; therefore, in viewing a sinusoidal variation in this manner it would appear to us as a constant. This is no different than stopping the phasor at some arbitrary time-zero; but realizing that it actually represents a sinusoidal variation. We will talk more about this important aspect as we go along; in particular, see Example 1A.

In order to show the facility of the phasor in the analysis of steady-state performance of ac circuits and devices, it is useful to consider a series circuit consisting of a resistance, an inductance L, and a capacitance C. Thus, using uppercase letters to indicate steady-state variables

(1.2-18)

Throughout the text, we will use either R or r to represent resistance. For steady-state operation, let

(1.2-19)

(1.2-20)

where we have dropped the functional notation and the subscript a helps to distinguish the instantaneous value from the rms value of the steady-state variables. The steady-state voltage equation may be obtained by substituting (1.2-19) and (1.2-20) into (1.2-18), whereupon we can write

(1.2-21)

The second term on the right-hand side of (1.2-21), which is , can be written

(1.2-22)

Since , from (1.2-21), we can write

(1.2-23)

Since , (1.2-23) may be written

(1.2-24)

If we follow a similar procedure, we can show that

(1.2-25)

Differentiation of a steady-state sinusoidal variable rotates the phasor counterclockwise by or j; integration rotates the phasor clockwise by or − j.

The steady-state voltage equation given by (1.2-21) can now be written in phasor form as

(1.2-26)

We can express (1.2-26) compactly as

(1.2-27)

where the impedance, Z, is a complex number; it is not a phasor. It may be expressed...

Produkt-Details

• Erscheint lt. Verlag: 8.2.2017
• Reihe/Serie: IEEE Press Series on Power and Energy Systems
• Reihe/Serie: IEEE Press Series on Power Engineering
• Reihe/Serie: IEEE Press Series on Power Engineering
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Electrical & Electronics Engineering • electric drives • Electric Power Electronics • electric power systems • Elektrische Energietechnik • Elektrotechnik u. Elektronik • Energie • Energy • Leistungselektronik • Machine Design • Power Electronics • Simulations • winding inductances
• ISBN-10: 1-119-21427-0 / 1119214270
• ISBN-13: 978-1-119-21427-4 / 9781119214274