Unified Selective Harmonic Elimination for Power Converters

About the Authors xi Preface xiii Acknowledgments xv 1 Power Converters and Selective Harmonic Elimination 1 1.1 Introduction to Power Converters 1 1.1.1 Topologies of Voltage–Source Converters 1 1.1.2 Topologies of Current–Source Converters 3 1.2 Modulation Strategies for Power Converters 4 1.2.1 PWM of Voltage–Source Converters 4 1.2.2 PWM of Current–Source Converters 7 1.3 Overview of Selective Harmonic Elimination PWM 7 1.3.1 Basic Knowledge of SHE and Its Formulation 8 1.3.2 Overview of SHE Solving Algorithms 10 1.3.3 Overview of Control Methods with SHE-PWM 13 1.3.4 Overall SHE-PWM Implementation Procedure 14 1.3.5 Real-World Implementation Cases of SHE-PWM 16 1.3.5.1 SHE-PWM in Commercialized Products 16 1.3.5.2 SHE-PWM in Traction Motor Drives 16 1.3.5.3 SHE-PWM in High-Power Rectifiers 17 1.4 Technical Challenges with SHE-PWM 18 1.4.1 Technical Challenges in SHE Formulation 18 1.4.2 Technical Challenges in SHE Solving Algorithms 18 1.4.3 Technical Challenges in SHE Applications 19 1.5 Outline of the Book 19 1.5.1 Part 1: Formulation 19 1.5.2 Part 2: Solving Algorithm 20 1.5.3 Part 3: Application 21 References 21 Part I Formulation 29 2 Principle of SHE 31 2.1 Fourier Series of Periodic Functions 31 2.1.1 Half-Wave Symmetric 32 2.1.2 Quarter-Wave Symmetric 33 2.2 Principle of SHE Formulations 33 2.2.1 Fourier Series of SquareWaveform 35 2.2.2 Three-Level SHE Formulation 35 2.2.3 Multilevel SHE Formulation 37 2.2.4 Generalized Odd-Level SHE Formulation 38 2.2.5 Even-Level SHE Formulation 40 2.2.5.1 Two-Level SHE Formulation with Three Switching Angles 41 2.2.5.2 Generalized Even-Level SHE Formulation 42 2.2.6 SHE Formulation for Asymmetric Multilevel Converters 44 2.2.7 SHE Formulation with Half-Wave Symmetric 48 2.3 Summary 51 References 51 3 Unified SHE Formula 53 3.1 Unified SHE Formulas for Multilevel Converters 53 3.1.1 Problem with Conventional Multilevel SHE Formula 53 3.1.2 Unified SHE Formula 54 3.1.3 Example with Seven Switching Angles 57 3.1.4 Experimental Results 59 3.2 Unified SHE Formulas for Asymmetric Multilevel Converters 62 3.2.1 Asymmetric Multilevel Converters 62 3.2.2 Unified SHE Formula for Asymmetric Multilevel Converters 62 3.2.2.1 Unified Asymmetric SHE Models with Fundamental Frequency Modulation 62 3.2.2.2 Asymmetric SHE Models with High-Frequency Modulation 65 3.2.3 Example with Distribution Ratio 4:2 68 3.2.4 Experimental Results 71 3.3 Optimal Implementation of Unified SHE Formula 72 3.4 Summary 77 References 77 4 SHE Formulations in Specific Applications 79 4.1 SHE Formulation with CMV Reduction Ability 79 4.1.1 Common Mode Voltage 79 4.1.2 CMV Modeling Based on SHE 79 4.1.3 SHE Formula with CMV Reduction Ability 81 4.1.4 Experimental Results 83 4.2 SHE Formulation for Parallel Converters 86 4.2.1 Operation Principles of Parallel Converters 86 4.2.2 SHE Formulation for Parallel Converters 87 4.2.2.1 SHE Formulation of Individual Converter 87 4.2.2.2 Combined Formulation of Parallel Converter 87 4.2.3 Improved Formulation with ZSCC Reduction Ability 89 4.2.4 Simulation Results 90 4.3 SHE Formulation for Current Source Converters 92 4.3.1 Operation Principles of Current Source Converters 92 4.3.2 SHE Formulations for Current Source Converters 93 4.3.3 Experimental Results 95 4.4 Selective Harmonic Mitigation for Grid-Connected Scenarios 97 4.4.1 Principles of SHM-PWM 97 4.4.2 Simulation Results 99 4.5 Summary 100 References 101 Part II Algorithm 103 5 Resultant Elimination Method 105 5.1 Introduction 105 5.2 Resultant Elimination Theory 105 5.3 Solving Procedure for SHE Equations 109 5.4 Parallel Resultant Elimination Method 111 5.4.1 Principle of Polynomial Interpolation 111 5.4.2 Algorithm Description and Its Parallelization 112 5.5 Results and Discussions 114 5.5.1 Computational Results 114 5.5.2 Optimal Solutions Versus Modulation Index in Full Range 117 5.5.3 Experimental Results 119 5.6 Summary 123 References 124 6 Groebner Basis-Based Method 125 6.1 Groebner Basis Theory 125 6.1.1 Concept of Ideal and Basis 125 6.1.2 Concept of Groebner Basis 127 6.2 Solving Procedure of SHE Equations 128 6.3 Computation Results and Verifications 131 6.3.1 Computation Results for Single-Phase Converters 132 6.3.2 Computation Results for Three-Phase Converters 135 6.3.3 Experimental Verifications 138 6.4 Comparative Analysis 139 6.4.1 Comparison with Resultant Elimination Method 140 6.4.2 Comparison with Numerical and Intelligent Methods 142 6.5 Summary 143 References 144 7 Degree Reduction of SHE Equations 147 7.1 Symmetric Polynomials 147 7.1.1 Concept of Elementary Symmetric Polynomials 147 7.1.2 Solving Procedure of SHE Equations Based on Symmetric Polynomials 149 7.1.3 Computation Results 153 7.1.4 Experimental Results 158 7.2 Newton’s Identities 159 7.2.1 Definitions of Newton’s Identities 159 7.2.2 Solving Procedure of SHE Equations Based on Newton Identities 160 7.2.3 Computation Results 164 7.2.4 Experimental Results 164 7.2.5 Performance Evaluations and Comparative Analysis 166 7.3 Summary 171 References 172 8 Online Implementation of SHE 173 8.1 Introduction 173 8.2 Algebraic-Numerical Hybrid Algorithm 173 8.2.1 Offline Transformation of SHE Equations 174 8.2.2 Online Implementation Stage 176 8.2.2.1 Online Solving Procedure 177 8.2.2.2 Case Study 178 8.2.3 Algorithm Evaluations and Verifications 179 8.2.3.1 Computing Results 180 8.2.3.2 Online Calculation Performance on MCUs 181 8.2.3.3 Algorithm Comparison with Other Solving Methods 182 8.2.3.4 Experimental Verifications 184 8.3 Summary 187 References 187 Part III Application 189 9 Selective Harmonic Elimination PWM in Multilevel Converters 191 9.1 General Requirements of Multilevel Converters 191 9.2 Overview of Existing Capacitor Voltage Balancing Methods Under SHE-PWM 193 9.3 Capacitor Voltage Balancing Control Methods for Multilevel Converters Under SHE-PWM 194 9.3.1 Self-Balancing Control 194 9.3.1.1 Operation Principles 194 9.3.1.2 Results and Discussions 196 9.3.2 Charge Amount Regulation 197 9.3.2.1 Operation Principles 197 9.3.2.2 Results and Discussions 201 9.3.3 Switching Angle Modifications 202 9.3.3.1 Operation Principles 202 9.3.3.2 Results and Discussions 204 9.3.4 Redundant State Adjustment 204 9.3.4.1 Operation Principles 204 9.3.4.2 Results and Discussions 208 9.3.5 Space Voltage Vector Adjustment 210 9.3.5.1 Operation Principles 210 9.3.5.2 Results and Discussions 211 9.3.6 Composite SHE-MPC Method 214 9.3.6.1 Operation Principles 214 9.3.6.2 Results and Discussions 217 9.4 Summary 218 References 219 10 SHE-Based Closed-Loop Controller Design 223 10.1 Controller Design for PMSM Drives Under SHE-PWM 223 10.1.1 Mathematical Model of PMSMs 223 10.1.2 Classical Control Strategies of PMSM 226 10.1.2.1 Field-Oriented Control 226 10.1.2.2 Direct Torque Control 227 10.1.3 Control Strategies Based on SHE-PWM 228 10.1.3.1 Inner Current Loop 229 10.1.3.2 Outer Speed Loop 230 10.1.3.3 SHE-PWM Modulation 230 10.2 Advanced Closed-Loop Controller Design Under SHE-PWM 231 10.2.1 Analysis of SHE-PWM Field-Oriented Control Issues 231 10.2.2 Improved SHE-PWM Field-Oriented Control Method Based on Dead Zone 233 10.2.2.1 Principle of Dead Zone-Based SHE-PWM Field-Oriented Control 233 10.2.2.2 Dead Zone Threshold Configuration Based on Current Ripple Model 234 10.3 Simulation Results 237 10.4 Summary 240 References 241 11 Model Predictive Control with SHE-PWM 243 11.1 Hybrid Predictive Control with SHE-PWM 243 11.1.1 Principle of FCS-MPC 244 11.1.2 Implementation of the Switching Strategy 245 11.1.2.1 Initialization of the PI controller for Voltage Estimation Based on SOGI 245 11.1.2.2 The Impact of SOGI Filtering on the Stability of the Modulationb Index 247 11.1.2.3 Analysis of the Control Loop Model Based on SOGI 248 11.1.2.4 System Switching Criteria 250 11.2 Model Predictive Pulse Pattern Control 251 11.2.1 Relation Between Modulation Index and Flux Amplitude 252 11.2.2 Reference Trajectory of Stator Flux 253 11.2.3 Speed and Torque Outer-Loop Control 254 11.2.4 Flux Inner-Loop Control 254 11.3 Model Predictive SHE Control 258 11.3.1 Standard of Choosing SHE Optimal Solutions 258 11.3.2 Revision Limitations of SHE-PWM Switching Angles 262 11.4 Simulation and Experimental Results 265 11.4.1 Simulation Results 265 11.4.2 Speed Variation Simulation 273 11.4.3 Experimental Results 274 11.5 Summary 282 References 282 Index 285