Pulse Width Modulation for Power Converters Principles and Practice

, by Holmes, D. Grahame; Lipo, Thomas A.

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ISBN: 9780471208143 | 0471208140
Cover: Hardcover
Copyright: 10/3/2003

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* The first single volume resource for researchers in the field who previously had to depend on separate papers and conference records to attain a working knowledge of the subject. * Brings together the field's diverse approaches into an integrated and comprehensive theory of PWM

Preface

xiii

Acknowledgments

xiv

Nomenclature

Chapter 1 Introduction to Power Electronic Converters

(56)

1.1 Basic Converter Topologies

(5)

1.1.1 Switch Constraints

(2)

1.1.2 Bidirectional Chopper

(1)

1.1.3 Single-Phase Full-Bridge (H-Bridge) Inverter

(2)

1.2 Voltage Source/Stiff Inverters

(7)

1.2.1 Two-Phase Inverter Structure

(1)

1.2.2 Three-Phase Inverter Structure

(1)

1.2.3 Voltage and Current Waveforms in Square-Wave Mode

(5)

1.3 Switching Function Representation of Three-Phase Converters

(3)

1.4 Output Voltage Control

(4)

1.4.1 Volts/Hertz Criterion

(1)

1.4.2 Phase Shift Modulation for Single-Phase Inverter

(2)

1.4.3 Voltage Control with a Double Bridge

(2)

1.5 Current Source/Stiff Inverters

(3)

1.6 Concept of a Space Vector

(14)

1.6.1 d-q-0 Components for Three-Phase Sine Wave Source/Load

(3)

1.6.2 d-q-0 Components for Voltage Source Inverter Operated in Square-Wave Mode

(5)

1.6.3 Synchronously Rotating Reference Frame

(3)

1.7 Three-Level Inverters

(4)

1.8 Multilevel Inverter Topologies

(13)

1.8.1 Diode-Clamped Multilevel Inverter

(7)

1.8.2 Capacitor-Clamped Multilevel Inverter

(2)

1.8.3 Cascaded Voltage Source Multilevel Inverter

(3)

1.8.4 Hybrid Voltage Source Inverter

(1)

1.9 Summary

(2)

Chapter 2 Harmonic Distortion

(38)

2.1 Harmonic Voltage Distortion Factor

(4)

2.2 Harmonic Current Distortion Factor

(3)

2.3 Harmonic Distortion Factors for Three-Phase Inverters

(3)

2.4 Choice of Performance Indicator

(3)

2.5 WTHD of Three-Level Inverter

(3)

2.6 The Induction Motor Load

(9)

2.6.1 Rectangular Squirrel Cage Bars

(5)

2.6.2 Nonrectangular Rotor Bars

(1)

2.6.3 Per-Phase Equivalent Circuit

(3)

2.7 Harmonic Distortion Weighting Factors for Induction Motor Load

(8)

2.7.1 WTHD for Frequency-Dependent Rotor Resistance

(2)

2.7.2 WTHD Also Including Effect of Frequency-Dependent Rotor Leakage Inductance

(4)

2.7.3 WTHD for Stator Copper Losses

(2)

2.8 Example Calculation of Harmonic Losses

(1)

2.9 WTHD Normalization for PWM Inverter Supply

(2)

2.10 Summary

(2)

Chapter 3 Modulation of One Inverter Phase Leg

(60)

3.1 Fundamental Concepts of PWM

(1)

3.2 Evaluation of PWM Schemes

(2)

3.3 Double Fourier Integral Analysis of a Two-Level Pulse Width Modulated Waveform

(6)

3.4 Naturally Sampled Pulse Width Modulation

105

(15)

3.4.1 Sine-Sawtooth Modulation

105

(9)

3.4.2 Sine-Triangle Modulation

114

(6)

3.5 PWM Analysis by Duty Cycle Variation

120

(5)

3.5.1 Sine-Sawtooth Modulation

120

(3)

3.5.2 Sine-Triangle Modulation

123

(2)

3.6 Regular Sampled Pulse Width Modulation

125

(21)

3.6.1 Sawtooth Carrier Regular Sampled PWM

130

(4)

3.6.2 Symmetrical Regular Sampled PWM

134

(5)

3.6.3 Asymmetrical Regular Sampled PWM

139

(7)

3.7 "Direct" Modulation

146

(2)

3.8 Integer versus Non-Integer Frequency Ratios

148

(2)

3.9 Review of PWM Variations

150

(2)

3.10 Summary

152

(3)

Chapter 4 Modulation of Single-Phase Voltage Source Inverters

155

(60)

4.1 Topology of a Single-Phase Inverter

156

(1)

4.2 Three-Level Modulation of a Single-Phase Inverter

157

(12)

4.3 Analytic Calculation of Harmonic Losses

169

(8)

4.4 Sideband Modulation

177

(6)

4.5 Switched Pulse Position

183

(17)

4.5.1 Continuous Modulation

184

(2)

4.5.2 Discontinuous Modulation

186

(14)

4.6 Switched Pulse Sequence

200

(11)

4.6.1 Discontinuous PWM - Single-Phase Leg Switched

200

(7)

4.6.2 Two-Level Single-Phase PWM

207

(4)

4.7 Summary

211

(4)

Chapter 5 Modulation of Three-Phase Voltage Source Inverters

215

(44)

5.1 Topology of a Three-Phase Inverter (VSI)

215

(1)

5.2 Three-Phase Modulation with Sinusoidal References

216

(10)

5.3 Third-Harmonic Reference Injection

226

(15)

5.3.1 Optimum Injection Level

226

(4)

5.3.2 Analytical Solution for Third-Harmonic Injection

230

(11)

5.4 Analytic Calculation of Harmonic Losses

241

(9)

5.5 Discontinuous Modulation Strategies

250

(1)

5.6 Triplen Carrier Ratios and Subharmonics

251

(6)

5.6.1 Triplen Carrier Ratios

251

(2)

5.6.2 Subharmonics

253

(4)

5.7 Summary

257

(2)

Chapter 6 Zero Space Vector Placement Modulation Strategies

259

(78)

6.1 Space Vector Modulation

259

(8)

6.1.1 Principles of Space Vector Modulation

259

(6)

6.1.2 SVM Compared to Regular Sampled PWM

265

(2)

6.2 Phase Leg References for Space Vector Modulation

267

(3)

6.3 Naturally Sampled SVM

270

(2)

6.4 Analytical Solution for SVM

272

(19)

6.5 Harmonic Losses for SVM

291

(3)

6.6 Placement of the Zero Space Vector

294

(5)

6.7 Discontinuous Modulation

299

(8)

6.7.1 120° Discontinuous Modulation

299

(3)

6.7.2 60° and 30° Discontinuous Modulation

302

(5)

6.8 Phase Leg References for Discontinuous PWM

307

(4)

6.9 Analytical Solutions for Discontinuous PWM

311

(11)

6.10 Comparison of Harmonic Performance

322

(4)

6.11 Harmonic Losses for Discontinuous PWM

326

(4)

6.12 Single-Edge SVM

330

(1)

6.13 Switched Pulse Sequence

331

(2)

6.14 Summary

333

(4)

Chapter 7 Modulation of Current Source Inverters

337

(12)

7.1 Three-Phase Modulators as State Machines

338

(5)

7.2 Naturally Sampled CSI Space Vector Modulator

343

(1)

7.3 Experimental Confirmation

343

(2)

7.4 Summary

345

(4)

Chapter 8 Overmodulation of an Inverter

349

(34)

8.1 The Overmodulation Region

350

(1)

8.2 Naturally Sampled Overmodulation of One Phase Leg of an Inverter

351

(5)

8.3 Regular Sampled Overmodulation of One Phase Leg of an Inverter

356

(4)

8.4 Naturally Sampled Overmodulation of Single- and Three-Phase Inverters

360

(4)

8.5 PWM Controller Gain during Overmodulation

364

(12)

8.5.1 Gain with Sinusoidal Reference

364

(3)

8.5.2 Gain with Space Vector Reference

367

(4)

8.5.3 Gain with 60° Discontinuous Reference

371

(2)

8.5.4 Compensated Modulation

373

(3)

8.6 Space Vector Approach to Overmodulation

376

(6)

8.7 Summary

382

(1)

Chapter 9 Programmed Modulation Strategies

383

(50)

9.1 Optimized Space Vector Modulation

384

(12)

9.2 Harmonic Elimination PWM

396

(15)

9.3 Performance Index for Optimality

411

(5)

9.4 Optimum PWM

416

(5)

9.5 Minimum-Loss PWM

421

(9)

9.6 Summary

430

(3)

Chapter 10 Programmed Modulation of Multilevel Converters

433

(20)

10.1 Multilevel Converter Alternatives

433

(3)

10.2 Block Switching Approaches to Voltage Control

436

(4)

10.3 Harmonic Elimination Applied to Multilevel Inverters

440

(7)

10.3.1 Switching Angles for Harmonic Elimination Assuming Equal Voltage Levels

440

(1)

10.3.2 Equalization of Voltage and Current Stresses

441

(2)

10.3.3 Switching Angles for Harmonic Elimination Assuming Unequal Voltage Levels

443

(4)

10.4 Minimum Harmonic Distortion

447

(2)

10.5 Summary

449

(4)

Chapter 11 Carrier-Based PWM of Multilevel Inverters

453

(78)

11.1 PWM of Cascaded Single-Phase H-Bridges

453

(12)

11.2 Overmodulation of Cascaded H-Bridges

465

(2)

11.3 PWM Alternatives for Diode-Clamped Multilevel Inverters

467

(2)

11.4 Three-Level Naturally Sampled PD PWM

469

(12)

11.4.1 Contour Plot for Three-Level PD PWM

469

(4)

11.4.2 Double Fourier Series Harmonic Coefficients

473

(2)

11.4.3 Evaluation of the Harmonic Coefficients

475

(4)

11.4.4 Spectral Performance of Three-Level PD PWM

479

(2)

11.5 Three-Level Naturally Sampled APOD or POD PWM

481

(3)

11.6 Overmodulation of Three-Level Inverters

484

(5)

11.7 Five-Level PWM for Diode-Clamped Inverters

489

(10)

11.7.1 Five-level Naturally Sampled PD PWM

489

(3)

11.7.2 Five-Level Naturally Sampled APOD PWM

492

(5)

11.7.3 Five-Level POD PWM

497

(2)

11.8 PWM of Higher Level Inverters

499

(5)

11.9 Equivalent PD PWM for Cascaded Inverters

504

(3)

11.10 Hybrid Multilevel Inverter

507

(10)

11.11 Equivalent PD PWM for a Hybrid Inverter

517

(2)

11.12 Third-Harmonic Injection for Multilevel Inverters

519

(7)

11.13 Operation of a Multilevel Inverter with a Variable Modulation Index

526

(2)

11.14 Summary

528

(3)

Chapter 12 Space Vector PWM for Multilevel Converters

531

(24)

12.1 Optimized Space Vector Sequences

531

(3)

12.2 Modulator for Selecting Switching States

534

(1)

12.3 Decomposition Method

535

(3)

12.4 Hexagonal Coordinate System

538

(5)

12.5 Optimal Space Vector Position within a Switching Period

543

(2)

12.6 Comparison of Space Vector PWM to Carrier-Based PWM

545

(3)

12.7 Discontinuous Modulation in Multilevel Inverters

548

(2)

12.8 Summary

550

(5)

Chapter 13 Implementation of a Modulation Controller

555

(30)

13.1 Overview of a Power Electronic Conversion System

556

(1)

13.2 Elements of a PWM Converter System

557

(15)

13.2.1 VSI Power Conversion Stage

563

(2)

13.2.2 Gate Driver Interface

565

(2)

13.2.3 Controller Power Supply

567

(1)

13.2.4 I/O Conditioning Circuitry

568

(1)

13.2.5 PWM Controller

569

(3)

13.3 Hardware Implementation of the PWM Process

572

(7)

13.3.1 Analog versus Digital Implementation

572

(2)

13.3.2 Digital Timer Logic Structures

574

(5)

13.4 PWM Software Implementation

579

(5)

13.4.1 Background Software

580

(1)

13.4.2 Calculation of the PWM Timing Intervals

581

(3)

13.5 Summary

584

(1)

Chapter 14 Continuing Developments in Modulation

585

(38)

14.1 Random Pulse Width Modulation

586

(4)

14.2 PWM Rectifier with Voltage Unbalance

590

(8)

14.3 Common Mode Elimination

598

(5)

14.4 Four Phase Leg Inverter Modulation

603

(4)

14.5 Effect of Minimum Pulse Width

607

(5)

14.6 PWM Dead-Time Compensation

612

(7)

14.7 Summary

619

(4)

Appendix 1 Fourier Series Representation of a Double Variable Controlled Waveform

623

(6)

Appendix 2 Jacobi-Anger and Bessel Function Relationships

629

(6)

A2.1 Jacobi-Anger Expansions

629

(2)

A2.2 Bessel Function Integral Relationships

631

(4)

Appendix 3 Three-Phase and Half-Cycle Symmetry Relationships

635

(2)

Appendix 4 Overmodulation of a Single-Phase Leg

637

(26)

A4.1 Naturally Sampled Double-Edge PWM

637

(12)

A4.1.1 Evaluation of Double Fourier Integral for Overmodulated Naturally Sampled PWM

638

(8)

A4.1.2 Harmonic Solution for Overmodulated Single-Phase Leg under Naturally Sampled PWM

646

(1)

A4.1.3 Linear Modulation Solution Obtained from Overmodulation Solution

647

(1)

A4.1.4 Square-Wave Solution Obtained from Overmodulation Solution

647

(2)

A4.2 Symmetric Regular Sampled Double-Edge PWM

649

(5)

A4.2.1 Evaluation of Double Fourier Integral for Overmodulated Symmetric Regular Sampled PWM

650

(2)

A4.2.2 Harmonic Solution for Overmodulated Single-Phase Leg under Symmetric Regular Sampled PWM

652

(1)

A4.2.3 Linear Modulation Solution Obtained from Overmodulation Solution

653

(1)

A4.3 Asymmetric Regular Sampled Double-Edge PWM

654

(9)

A4.3.1 Evaluation of Double Fourier Integral for Overmodulated Asymmetric Regular Sampled PWM

655

(5)

A4.3.2 Harmonic Solution for Overmodulated Single-Phase Leg under Asymmetric Regular Sampled PWM

660

(1)

A4.3.3 Linear Modulation Solution Obtained from Overmodulation Solution

661

(2)

Appendix 5 Numeric Integration of a Double Fourier Series Representation of a Switched Waveform

663

(8)

A5.1 Formulation of the Double Fourier Integral

663

(3)

A5.2 Analytical Solution of the Inner Integral

666

(2)

A5.3 Numeric Integration of the Outer Integral

668

(3)

Bibliography

671

(44)

Index

715

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Pulse Width Modulation for Power Converters Principles and Practice

Summary

Author Biography

Table of Contents

Supplemental Materials