Analysis of Electric Machinery and Drive Systems E-Book

Paul C. Krause

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: IEEE Press Series on Power Engineering
• Sprache: Englisch
• Veröffentlichungsjahr: 2013

Seitenzahl: 808

Beschreibung

Introducing a new edition of the popular reference on machine analysis Now in a fully revised and expanded edition, this widely used reference on machine analysis boasts many changes designed to address the varied needs of engineers in the electric machinery, electric drives, and electric power industries. The authors draw on their own extensive research efforts, bringing all topics up to date and outlining a variety of new approaches they have developed over the past decade. Focusing on reference frame theory that has been at the core of this work since the first edition, this volume goes a step further, introducing new material relevant to machine design along with numerous techniques for making the derivation of equations more direct and easy to use. Coverage includes: * Completely new chapters on winding functions and machine design that add a significant dimension not found in any other text * A new formulation of machine equations for improving analysis and modeling of machines coupled to power electronic circuits * Simplified techniques throughout, from the derivation of torque equations and synchronous machine analysis to the analysis of unbalanced operation * A unique generalized approach to machine parameters identification A first-rate resource for engineers wishing to master cutting-edge techniques for machine analysis, Analysis of Electric Machinery and Drive Systems is also a highly useful guide for students in the field.

Leseprobe

Table of Contents

IEEE Press

Title page

Copyright page

Preface

1: Theory of Electromechanical Energy Conversion

1.1. Introduction

1.2. Magnetically Coupled Circuits

1.3. Electromechanical Energy Conversion

1.4. Elementary ac Machines

2: Distributed Windings in ac Machinery

2.1. Introduction

2.2. Describing Distributed Windings

2.3. Winding Functions

2.4. Air-Gap Magnetomotive Force

2.5. Rotating MMF

2.6. Flux Linkage and Inductance

2.7. Resistance

2.8. Voltage and Flux Linkage Equations for Distributed Winding Machines

3: Reference-Frame Theory

3.1. Introduction

3.2. Background

3.3. Equations of Transformation: Change of Variables

3.4. Stationary Circuit Variables Transformed to the Arbitrary Reference Frame

3.5. Commonly Used Reference Frames

3.6. Transformation of a Balanced Set

3.7. Balanced Steady-State Phasor Relationships

3.8. Balanced Steady-State Voltage Equations

3.9. Variables Observed from Several Frames of Reference

3.10. Transformation Between Reference Frames

3.11. Specialty Transformations

3.12. Space-Phasor Notation

4: Permanent-Magnet ac Machines

4.1. Introduction

4.2. Voltage and Torque Equations in Machine Variables

4.3. Voltage and Torque Equations in Rotor Reference-Frame Variables

4.4. Analysis of Steady-State Operation

4.5. Brushless dc Motor

4.6. Phase Shifting of Applied Voltages of a Permanent-Magnet ac Machine

4.7. Control of Stator Currents

5: Synchronous Machines

5.1. Introduction

5.2. Voltage Equations in Machine Variables

5.3. Torque Equation in Machine Variables

5.4. Stator Voltage Equations in Arbitrary Reference-Frame Variables

5.5. Voltage Equations in Rotor Reference-Frame Variables

5.6. Torque Equations in Substitute Variables

5.7. Rotor Angle and Angle Between Rotors

5.8. Per Unit System

5.9. Analysis of Steady-State Operation

5.10. Stator Currents Positive Out of Machine: Synchronous Generator Operation

5.11. Computer Simulation

6: Symmetrical Induction Machines

6.1. Introduction

6.2. Voltage Equations in Machine Variables

6.3. Torque Equation in Machine Variables

6.4. Equations of Transformation for Rotor Circuits

6.5. Voltage Equations in Arbitrary Reference-Frame Variables

6.6. Torque Equation in Arbitrary Reference-Frame Variables

6.7. Commonly Used Reference Frames

6.8. Per Unit System

6.9. Analysis of Steady-State Operation

6.10. Free Acceleration Characteristics

6.11. Free Acceleration Characteristics Viewed from Various Reference Frames

6.12. Dynamic Performance During Sudden Changes in Load Torque

6.13. Dynamic Performance During a Three-Phase Fault at the Machine Terminals

6.14. Computer Simulation in the Arbitrary Reference Frame

7: Machine Equations in Operational Impedances and Time Constants

7.1. Introduction

7.2. Park's Equations in Operational Form

7.3. Operational Impedances and G(p) for a Synchronous Machine with Four Rotor Windings

7.4. Standard Synchronous Machine Reactances

7.5. Standard Synchronous Machine Time Constants

7.6. Derived Synchronous Machine Time Constants

7.7. Parameters from Short-Circuit Characteristics

7.8. Parameters from Frequency-Response Characteristics

8: Alternative Forms of Machine Equations

8.1. Introduction

8.2. Machine Equations to Be Linearized

8.3. Linearization of Machine Equations

8.4. Small-Displacement Stability: Eigenvalues

8.5. Eigenvalues of Typical Induction Machines

8.6. Eigenvalues of Typical Synchronous Machines

8.7. Neglecting Electric Transients of Stator Voltage Equations

8.8. Induction Machine Performance Predicted with Stator Electric Transients Neglected

8.9. Synchronous Machine Performance Predicted with Stator Electric Transients Neglected

8.10. Detailed Voltage Behind Reactance Model

8.11. Reduced Order Voltage Behind Reactance Model

9: Unbalanced Operation and Single-Phase Induction Machines

9.1. Introduction

9.2. Symmetrical Component Theory

9.3. Symmetrical Component Analysis of Induction Machines

9.4. Unbalanced Stator Conditions of Induction Machines: Reference-Frame Analysis

9.5. Typical Unbalanced Stator Conditions of Induction Machines

9.6. Unbalanced Rotor Conditions of Induction Machines

9.7. Unbalanced Rotor Resistors

9.8. Single-Phase Induction Machines

9.9. Asynchronous and Unbalanced Operation of Synchronous Machines

10: dc Machines and Drives

10.1. Introduction

10.2. Elementary dc Machine

10.3. Voltage and Torque Equations

10.4. Basic Types of dc Machines

10.5. Time-Domain Block Diagrams and State Equations

10.6. Solid-State Converters for dc Drive Systems

10.7. One-Quadrant dc/dc Converter Drive

10.8. Two-Quadrant dc/dc Converter Drive

10.9. Four-Quadrant dc/dc Converter Drive

10.10. Machine Control with Voltage-Controlled dc/dc Converter

10.11. Machine Control with Current-Controlled dc/dc Converter

11: Semi-Controlled Bridge Converters

11.1. Introduction

11.2. Single-Phase Load Commutated Converter

11.3. Three-Phase Load Commutated Converter

11.4. Conclusions and Extensions

12: Fully Controlled Three-Phase Bridge Converters

12.1. Introduction

12.2. The Three-Phase Bridge Converter

12.3. Six-Step Operation

12.4. Six-Step Modulation

12.5. Sine-Triangle Modulation

12.6. Extended Sine-Triangle Modulation

12.7. Space-Vector Modulation

12.8. Hysteresis Modulation

12.9. Delta Modulation

12.10. Open-Loop Voltage and Current Regulation

12.11. Closed-Loop Voltage and Current Regulation

13: Induction Motor Drives

13.1. Introduction

13.2. Volts-per-Hertz Control

13.3. Constant Slip Current Control

13.4. Field-Oriented Control

13.5. Direct Field-Oriented Control

13.6. Robust Direct Field-Oriented Control

13.7. Indirect Rotor Field-Oriented Control

13.8. Direct Torque Control

13.9. Slip Energy Recovery Drives

13.10. Conclusions

14: Permanent-Magnet ac Motor Drives

14.1. Introduction

14.2. Voltage-Source Inverter Drives

14.3. Equivalence of Voltage-Source Inverters to an Idealized Source

14.4. Average-Value Analysis of Voltage-Source Inverter Drives

14.5. Steady-State Performance of Voltage-Source Inverter Drives

14.6. Transient and Dynamic Performance of Voltage-Source Inverter Drives

14.7. Case Study: Voltage-Source Inverter-Based Speed Control

14.8. Current-Regulated Inverter Drives

14.9. Voltage Limitations of Current-Regulated Inverter Drives

14.10. Current Command Synthesis

14.11. Average-Value Modeling of Current-Regulated Inverter Drives

14.12. Case Study: Current-Regulated Inverter-Based Speed Controller

15: Introduction to the Design of Electric Machinery

15.1. Introduction

15.2. Machine Geometry

15.3. Stator Windings

15.4. Material Parameters

15.5. Stator Currents and Control Philosophy

15.6. Radial Field Analysis

15.7. Lumped Parameters

15.8. Ferromagnetic Field Analysis

15.9. Formulation of Design Problem

15.10. Case Study

15.11. Extensions

Acknowledgments

Appendix A: Trigonometric Relations, Constants and Conversion Factors, and Abbreviations

A.1. Basic Trigonometric Relations

A.2. Three-Phase Trigonometric Relations

A.3. Constants and Conversion Factors

A.4. Abbreviations

Appendix B: Carter's Coefficient

Appendix C: Leakage Inductance

Index

IEEE Press

445 Hoes Lane

Piscataway, NJ 08854

IEEE Press Editorial Board 2013

John Anderson, Editor in Chief

Linda ShaferSaeid NahavandiGeorge ZobristGeorge W. ArnoldDavid JacobsonTariq SamadEkram HossainMary LanzerottiDmitry GoldgofOm P. Malik

Kenneth Moore, Director of IEEE Book and Information Services (BIS)

Copyright © 2013 by Institute of Electrical and Electronics Engineers, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone], or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, [phone], fax [phone], or online at http://www.wiley.com/go/permissions.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at [phone], outside the United States at [phone] or fax [phone].

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Krause, Paul C.

Analysis of electric machinery and drive systems / Paul Krause, Oleg Wasynczuk, Scott Sudhoff, Steven Pekarek. – Third edition.

pages cm

“Institute of Electrical and Electronics Engineers.”

Includes bibliographical references and index.

ISBN 978-1-118-02429-4 (cloth)

1. Electric machinery. 2. Electric driving. I. Wasynczuk, Oleg. II. Sudhoff, Scott D. III. Pekarek, Steven. IV. Institute of Electrical and Electronics Engineers. V. Title.

TK2181.K72 2013

621.31'042–dc23

2012050394

Preface

Those familiar with previous editions of this book will find that this edition has been expanded and modified to help meet the needs of the electric machinery, electric drives, and electric power industries.

Like previous editions, reference-frame theory is at the core of this book. However, new material has been introduced that sets the stage for machine design. In particular, in Chapter 2, the winding function approach is used to establish the rotating air-gap magnetomotive force and machine inductances, including end-turn winding effects. In addition, an introduction to machine design is set forth in Chapter 15. These two new chapters, combined with reference-frame theory-based machine analysis, add a significant dimension not found in other texts.

Another major change is set forth in Chapter 8, wherein the standard linear and reduced-order machine equations are derived and a section has been added on the method of analysis referred to as voltage behind reactance. This new formulation of the machine equations is especially useful in the analysis and modeling of electric machines that are coupled to power electronic circuits. Consequently, this technique has become a useful tool in the electric power and electric drives industries.

There are other, less major, changes and additions in this edition that warrant mentioning. In Chapter 1, the electromagnetic force (torque) equations are derived without the need of numerous, involved summations that have plagued the previous approach. This straightforward approach is made possible by the identification of a second energy balance relationship. Also, the chapter on reference-frame theory has been augmented with transformations that apply when the three-phase currents, currents, and flux linkages sum to zero. Although this is not the case if a third harmonic is present, it is quite common, and the transformations are helpful in cases where the neutral is not accessible, and only the line-to-line voltages are available.

Calculation of operational impedances is given in Chapter 7. Added to this material is a generalized approach of determining machine parameters from machine measurements. An interesting combination of Park's approach to the derivation of the torque relationship and reference-frame theory is set forth in Chapter 6.

In the previous editions the synchronous machine was analyzed assuming positive current out of the machine, convenient for the power system engineer. Unfortunately, this approach is somewhat frustrating to the electric drives engineer. The chapter on synchronous machines has been modified in an attempt to accommodate both drive and power system engineers. In particular, the analysis is first carried out with positive currents into the machine and then with the current direction reversed. However, whenever power system operation or system fault studies are considered, positive current is assumed out of the machine consistent with power system convention. The remaining chapters, including the chapters on electric drives, as well as the chapters on converters, have been updated to include recent advances in analysis and converter control. Also, the analysis of unbalanced operation covered in the first edition but not in the second, has been simplified and is presented in Chapter 9.

We have spent a major part of our professional careers dealing with electric machines and drives. We are not only coauthors but colleagues and good friends. With the close working relationship that existed during the preparation of this manuscript, an ordering of the coauthors based on contribution would be difficult if not impossible; instead, the ordering is by age only.

Paul Krause

Oleg Wasynczuk

Scott Sudhoff

Steven Pekarek

West Lafayette, Indiana

May 2013

1

Theory of Electromechanical Energy Conversion

1.1. Introduction

The theory of electromechanical energy conversion allows us to establish expressions for torque in terms of machine electrical variables, generally the currents, and the displacement of the mechanical system. This theory, as well as the derivation of equivalent circuit representations of magnetically coupled circuits, is established in this chapter. In Chapter 2, we will discover that some of the inductances of the electric machine are functions of the rotor position. This establishes an awareness of the complexity of these voltage equations and sets the stage for the change of variables (Chapter 3) that reduces the complexity of the voltage equations by eliminating the rotor position dependent inductances and provides a more direct approach to establishing the expression for torque when we consider the individual electric machines.

1.2. Magnetically Coupled Circuits

Magnetically coupled electric circuits are central to the operation of transformers and electric machines. In the case of transformers, stationary circuits are magnetically coupled for the purpose of changing the voltage and current levels. In the case of electric machines, circuits in relative motion are magnetically coupled for the purpose of transferring energy between mechanical and electrical systems. Since magnetically coupled circuits play such an important role in power transmission and conversion, it is important to establish the equations that describe their behavior and to express these equations in a form convenient for analysis. These goals may be achieved by starting with two stationary electric circuits that are magnetically coupled as shown in Figure 1.2-1. The two coils consist of turns N1 and N2, respectively, and they are wound on a common core that is generally a ferromagnetic material with permeability large relative to that of air. The permeability of free space, μ0, is 4π × 10−7 H/m. The permeability of other materials is expressed as μμrμ0, where μr is the relative permeability. In the case of transformer steel, the relative permeability may be as high as 2000–4000.

Figure 1.2-1. Magnetically coupled circuits.

In general, the flux produced by each coil can be separated into two components. A leakage component is denoted with an l subscript and a magnetizing component is denoted by an m subscript. Each of these components is depicted by a single streamline with the positive direction determined by applying the right-hand rule to the direction of current flow in the coil. Often, in transformer analysis, i2 is selected positive out of the top of coil 2 and a dot placed at that terminal.

The flux linking each coil may be expressed

(1.2-1)

(1.2-2)

The leakage flux Φl1 is produced by current flowing in coil 1, and it links only the turns of coil 1. Likewise, the leakage flux Φl2 is produced by current flowing in coil 2, and it links only the turns of coil 2. The magnetizing flux Φm1 is produced by current flowing in coil 1, and it links all turns of coils 1 and 2. Similarly, the magnetizing flux Φm2 is produced by current flowing in coil 2, and it also links all turns of coils 1 and 2. With the selected positive direction of current flow and the manner in that the coils are wound (Fig. 1.2-1), magnetizing flux produced by positive current in one coil adds to the magnetizing flux produced by positive current in the other coil. In other words, if both currents are flowing in the same direction, the magnetizing fluxes produced by each coil are in the same direction, making the total magnetizing flux or the total core flux the sum of the instantaneous magnitudes of the individual magnetizing fluxes. If the currents are in opposite directions, the magnetizing fluxes are in opposite directions. In this case, one coil is said to be magnetizing the core, the other demagnetizing.

Before proceeding, it is appropriate to point out that this is an idealization of the actual magnetic system. Clearly, all of the leakage flux may not link all the turns of the coil producing it. Likewise, all of the magnetizing flux of one coil may not link all of the turns of the other coil. To acknowledge this practical aspect of the magnetic system, the number of turns is considered to be an equivalent number rather than the actual number. This fact should cause us little concern since the inductances of the electric circuit resulting from the magnetic coupling are generally determined from tests.

The voltage equations may be expressed in matrix form as

(1.2-3)

where r = diag[r1r2], is a diagonal matrix and

(1.2-4)

where f represents voltage, current, or flux linkage. The resistances r1 and r2 and the flux linkages λ1 and λ2 are related to coils 1 and 2, respectively. Since it is assumed that Φ1 links the equivalent turns of coil 1 and Φ2 links the equivalent turns of coil 2, the flux linkages may be written

(1.2-5)

(1.2-6)

where Φ1 and Φ2 are given by (1.2-1) and (1.2-2), respectively.

Linear Magnetic System

If saturation is neglected, the system is linear and the fluxes may be expressed as

(1.2-7)

(1.2-8)

(1.2-9)

(1.2-10)

where and are the reluctances of the leakage paths and is the reluctance of the path of the magnetizing fluxes. The product of N times i (ampere-turns) is the magnetomotive force (MMF), which is determined by the application of Ampere's law. The reluctance of the leakage paths is difficult to express and measure. A unique determination of the inductances associated with the leakage flux is typically either calculated or approximated from design considerations. The reluctance of the magnetizing path of the core shown in may be computed with sufficient accuracy from the well-known relationship