An Introduction to Wavelet Modulated Inverters

S. A. SALEH, PHD, IEEE Member, is a faculty member at the School of Ocean Technology, Marine Institute, Memorial University of Newfoundland, Canada. He has published more than ten IEEE Transactions and holds two patents. Dr. Saleh’s research interests include wavelets, wavelet transforms, power system protection and control, power electronic converters, modulation techniques, digital signal processing and its applications in power systems, and power electronics. M. AZIZUR RAHMAN, PHD, IEEE Life Fellow, is Professor and University Research Professor at Memorial University of Newfoundland, Canada. He has forty-eight years of teaching experience. Rahman has published more than 650 papers and holds eleven patents. He is the recipient of numerous awards.

Preface ix

List of Symbols xi

List of Abbreviations xv

1. Introduction to Power Inverters 1

1.1 Fundamental Inverter Topologies 1

1.1.1 Single-Phase (1φ) Inverters 2

1.1.2 Three-Phase (3φ) Inverters 4

1.2 Multilevel Inverter Topologies 6

1.2.1 Neutral-Point Clamped Multilevel Inverter 7

1.2.2 Diode-Clamped Multilevel Inverter 8

1.2.3 Capacitor-Clamped Multilevel Inverter 8

1.2.4 Cascaded H-Bridge Multilevel Inverter 9

1.3 Fundamental Inverter Switching 11

1.4 Harmonic Distortion 15

1.5 Summary 17

2. Wavelets and the Sampling Theorem 19

2.1 Introduction 19

2.2 Wavelet Basis Functions 21

2.2.1 Orthogonal Wavelet Basis Functions 23

2.2.2 Semi-Orthogonal Wavelet Basis Functions 25

2.2.3 Bi-Orthogonal Wavelet Basis Functions 27

2.2.4 Shift-Orthogonal Wavelet Basis Functions 28

2.3 Sampling Process as a Multiresolution Analysis (MRA) 29

2.4 Sampling Forms 33

2.4.1 Uniform Sampling 33

2.4.2 Nonuniform Sampling 35

2.4.3 Nonuniform Recurrent Sampling 36

2.5 Wavelet Sampling Theory 37

2.6 Summary 39

3. Modeling of Power Inverters 41

3.1 Introduction 41

3.2 Sampling-Based Modeling of Single-Phase Inverters 43

3.2.1 Nonuniform Sampling-Based Representation 44

3.2.2 Reconstructing the Reference-Modulating Signal from Nonuniform Samples 46

3.3 Testing the Nonuniform Recurrent Sampling-Based Model of Inverters 51

3.3.1 PWM Inverter Output Voltage for Two Carrier Frequencies 52

3.4 Sampling-Based Modeling of Three-Phase Inverters 53

3.5 Summary 62

4. Scale-Based Linearly Combined Wavelets 65

4.1 Introduction 65

4.2 Scale-Based Linearly Combined Wavelet Basis Functions 66

4.2.1 Balancing the Order of the Scale-Based Linearly Combined Scaling Function ϕ(t) 70

4.2.2 Scale-Based Linearly Combined Wavelet Function ψϕ(t) 72

4.2.3 Construction of Scale-Based Linearly Combined Synthesis Scaling Functions ϕ(t) 74

4.3 Nondyadic MRA Structure 76

4.3.1 MRA for Nonuniform Recurrent Sampling 76

4.4 Scale-Based Linearly Combined Scaling Functions for Three-Phase Inverters 79

4.5 Summary 83

5. Single-Phase Wavelet Modulated Inverters 85

5.1 Introduction 85

5.2 Implementing the Wavelet Modulation Technique 85

5.3 Simulated Performance of a Wavelet Modulated Inverter 88

5.4 Experimental Performance of a Wavelet Modulated Inverter 95

5.5 The Scale-Time Interval Factor γ 101

5.6 Summary 106

6. Three-Phase Wavelet Modulated Inverters 107

6.1 Introduction 107

6.2 Implementing the Wavelet Modulation Technique for a Three-Phase Inverter 108

6.3 Simulated Performance of a Three-Phase Wavelet Modulated Inverter 111

6.4 Experimental Performance of a Three-Phase Wavelet Modulated Inverter 119

6.5 Summary 127

Appendix A Nondyadic MRA for 3φ WM Inverters 131

A.1 Preliminary Derivations 131

A.2 Time and Scale Localization of MRA Spaces 132

Bibliography 135

Index 143