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 ixList of Symbols xiList of Abbreviations xv1. Introduction to Power Inverters 11.1 Fundamental Inverter Topologies 11.1.1 Single-Phase (1φ) Inverters 21.1.2 Three-Phase (3φ) Inverters 41.2 Multilevel Inverter Topologies 61.2.1 Neutral-Point Clamped Multilevel Inverter 71.2.2 Diode-Clamped Multilevel Inverter 81.2.3 Capacitor-Clamped Multilevel Inverter 81.2.4 Cascaded H-Bridge Multilevel Inverter 91.3 Fundamental Inverter Switching 111.4 Harmonic Distortion 151.5 Summary 172. Wavelets and the Sampling Theorem 192.1 Introduction 192.2 Wavelet Basis Functions 212.2.1 Orthogonal Wavelet Basis Functions 232.2.2 Semi-Orthogonal Wavelet Basis Functions 252.2.3 Bi-Orthogonal Wavelet Basis Functions 272.2.4 Shift-Orthogonal Wavelet Basis Functions 282.3 Sampling Process as a Multiresolution Analysis (MRA) 292.4 Sampling Forms 332.4.1 Uniform Sampling 332.4.2 Nonuniform Sampling 352.4.3 Nonuniform Recurrent Sampling 362.5 Wavelet Sampling Theory 372.6 Summary 393. Modeling of Power Inverters 413.1 Introduction 413.2 Sampling-Based Modeling of Single-Phase Inverters 433.2.1 Nonuniform Sampling-Based Representation 443.2.2 Reconstructing the Reference-Modulating Signal from Nonuniform Samples 463.3 Testing the Nonuniform Recurrent Sampling-Based Model of Inverters 513.3.1 PWM Inverter Output Voltage for Two Carrier Frequencies 523.4 Sampling-Based Modeling of Three-Phase Inverters 533.5 Summary 624. Scale-Based Linearly Combined Wavelets 654.1 Introduction 654.2 Scale-Based Linearly Combined Wavelet Basis Functions 664.2.1 Balancing the Order of the Scale-Based Linearly Combined Scaling Function ϕ(t) 704.2.2 Scale-Based Linearly Combined Wavelet Function ψϕ(t) 724.2.3 Construction of Scale-Based Linearly Combined Synthesis Scaling Functions ϕ(t) 744.3 Nondyadic MRA Structure 764.3.1 MRA for Nonuniform Recurrent Sampling 764.4 Scale-Based Linearly Combined Scaling Functions for Three-Phase Inverters 794.5 Summary 835. Single-Phase Wavelet Modulated Inverters 855.1 Introduction 855.2 Implementing the Wavelet Modulation Technique 855.3 Simulated Performance of a Wavelet Modulated Inverter 885.4 Experimental Performance of a Wavelet Modulated Inverter 955.5 The Scale-Time Interval Factor γ 1015.6 Summary 1066. Three-Phase Wavelet Modulated Inverters 1076.1 Introduction 1076.2 Implementing the Wavelet Modulation Technique for a Three-Phase Inverter 1086.3 Simulated Performance of a Three-Phase Wavelet Modulated Inverter 1116.4 Experimental Performance of a Three-Phase Wavelet Modulated Inverter 1196.5 Summary 127Appendix A Nondyadic MRA for 3φ WM Inverters 131A.1 Preliminary Derivations 131A.2 Time and Scale Localization of MRA Spaces 132Bibliography 135Index 143