| Preface |
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xiii | |
| Acknowledgments |
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xiv | |
| Nomenclature |
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xv | |
| Chapter 1 Introduction to Power Electronic Converters |
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1 | (56) |
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1.1 Basic Converter Topologies |
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2 | (5) |
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2 | (2) |
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1.1.2 Bidirectional Chopper |
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4 | (1) |
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1.1.3 Single-Phase Full-Bridge (H-Bridge) Inverter |
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5 | (2) |
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1.2 Voltage Source/Stiff Inverters |
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7 | (7) |
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1.2.1 Two-Phase Inverter Structure |
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7 | (1) |
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1.2.2 Three-Phase Inverter Structure |
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8 | (1) |
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1.2.3 Voltage and Current Waveforms in Square-Wave Mode |
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9 | (5) |
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1.3 Switching Function Representation of Three-Phase Converters |
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14 | (3) |
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1.4 Output Voltage Control |
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17 | (4) |
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1.4.1 Volts/Hertz Criterion |
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17 | (1) |
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1.4.2 Phase Shift Modulation for Single-Phase Inverter |
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17 | (2) |
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1.4.3 Voltage Control with a Double Bridge |
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19 | (2) |
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1.5 Current Source/Stiff Inverters |
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21 | (3) |
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1.6 Concept of a Space Vector |
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24 | (14) |
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1.6.1 d-q-0 Components for Three-Phase Sine Wave Source/Load |
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27 | (3) |
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1.6.2 d-q-0 Components for Voltage Source Inverter Operated in Square-Wave Mode |
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30 | (5) |
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1.6.3 Synchronously Rotating Reference Frame |
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35 | (3) |
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1.7 Three-Level Inverters |
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38 | (4) |
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1.8 Multilevel Inverter Topologies |
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42 | (13) |
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1.8.1 Diode-Clamped Multilevel Inverter |
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42 | (7) |
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1.8.2 Capacitor-Clamped Multilevel Inverter |
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49 | (2) |
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1.8.3 Cascaded Voltage Source Multilevel Inverter |
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51 | (3) |
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1.8.4 Hybrid Voltage Source Inverter |
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54 | (1) |
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55 | (2) |
| Chapter 2 Harmonic Distortion |
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57 | (38) |
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2.1 Harmonic Voltage Distortion Factor |
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57 | (4) |
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2.2 Harmonic Current Distortion Factor |
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61 | (3) |
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2.3 Harmonic Distortion Factors for Three-Phase Inverters |
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64 | (3) |
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2.4 Choice of Performance Indicator |
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67 | (3) |
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2.5 WTHD of Three-Level Inverter |
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70 | (3) |
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2.6 The Induction Motor Load |
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73 | (9) |
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2.6.1 Rectangular Squirrel Cage Bars |
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73 | (5) |
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2.6.2 Nonrectangular Rotor Bars |
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78 | (1) |
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2.6.3 Per-Phase Equivalent Circuit |
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79 | (3) |
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2.7 Harmonic Distortion Weighting Factors for Induction Motor Load |
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82 | (8) |
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2.7.1 WTHD for Frequency-Dependent Rotor Resistance |
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82 | (2) |
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2.7.2 WTHD Also Including Effect of Frequency-Dependent Rotor Leakage Inductance |
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84 | (4) |
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2.7.3 WTHD for Stator Copper Losses |
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88 | (2) |
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2.8 Example Calculation of Harmonic Losses |
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90 | (1) |
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2.9 WTHD Normalization for PWM Inverter Supply |
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91 | (2) |
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93 | (2) |
| Chapter 3 Modulation of One Inverter Phase Leg |
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95 | (60) |
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3.1 Fundamental Concepts of PWM |
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96 | (1) |
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3.2 Evaluation of PWM Schemes |
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97 | (2) |
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3.3 Double Fourier Integral Analysis of a Two-Level Pulse Width Modulated Waveform |
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99 | (6) |
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3.4 Naturally Sampled Pulse Width Modulation |
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105 | (15) |
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3.4.1 Sine-Sawtooth Modulation |
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105 | (9) |
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3.4.2 Sine-Triangle Modulation |
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114 | (6) |
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3.5 PWM Analysis by Duty Cycle Variation |
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120 | (5) |
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3.5.1 Sine-Sawtooth Modulation |
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120 | (3) |
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3.5.2 Sine-Triangle Modulation |
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123 | (2) |
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3.6 Regular Sampled Pulse Width Modulation |
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125 | (21) |
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3.6.1 Sawtooth Carrier Regular Sampled PWM |
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130 | (4) |
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3.6.2 Symmetrical Regular Sampled PWM |
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134 | (5) |
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3.6.3 Asymmetrical Regular Sampled PWM |
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139 | (7) |
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146 | (2) |
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3.8 Integer versus Non-Integer Frequency Ratios |
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148 | (2) |
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3.9 Review of PWM Variations |
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150 | (2) |
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152 | (3) |
| Chapter 4 Modulation of Single-Phase Voltage Source Inverters |
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155 | (60) |
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4.1 Topology of a Single-Phase Inverter |
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156 | (1) |
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4.2 Three-Level Modulation of a Single-Phase Inverter |
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157 | (12) |
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4.3 Analytic Calculation of Harmonic Losses |
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169 | (8) |
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177 | (6) |
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4.5 Switched Pulse Position |
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183 | (17) |
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4.5.1 Continuous Modulation |
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184 | (2) |
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4.5.2 Discontinuous Modulation |
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186 | (14) |
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4.6 Switched Pulse Sequence |
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200 | (11) |
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4.6.1 Discontinuous PWM - Single-Phase Leg Switched |
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200 | (7) |
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4.6.2 Two-Level Single-Phase PWM |
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207 | (4) |
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211 | (4) |
| Chapter 5 Modulation of Three-Phase Voltage Source Inverters |
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215 | (44) |
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5.1 Topology of a Three-Phase Inverter (VSI) |
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215 | (1) |
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5.2 Three-Phase Modulation with Sinusoidal References |
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216 | (10) |
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5.3 Third-Harmonic Reference Injection |
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226 | (15) |
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5.3.1 Optimum Injection Level |
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226 | (4) |
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5.3.2 Analytical Solution for Third-Harmonic Injection |
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230 | (11) |
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5.4 Analytic Calculation of Harmonic Losses |
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241 | (9) |
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5.5 Discontinuous Modulation Strategies |
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250 | (1) |
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5.6 Triplen Carrier Ratios and Subharmonics |
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251 | (6) |
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5.6.1 Triplen Carrier Ratios |
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251 | (2) |
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253 | (4) |
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257 | (2) |
| Chapter 6 Zero Space Vector Placement Modulation Strategies |
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259 | (78) |
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6.1 Space Vector Modulation |
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259 | (8) |
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6.1.1 Principles of Space Vector Modulation |
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259 | (6) |
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6.1.2 SVM Compared to Regular Sampled PWM |
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265 | (2) |
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6.2 Phase Leg References for Space Vector Modulation |
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267 | (3) |
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6.3 Naturally Sampled SVM |
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270 | (2) |
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6.4 Analytical Solution for SVM |
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272 | (19) |
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6.5 Harmonic Losses for SVM |
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291 | (3) |
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6.6 Placement of the Zero Space Vector |
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294 | (5) |
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6.7 Discontinuous Modulation |
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299 | (8) |
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6.7.1 120° Discontinuous Modulation |
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299 | (3) |
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6.7.2 60° and 30° Discontinuous Modulation |
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302 | (5) |
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6.8 Phase Leg References for Discontinuous PWM |
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307 | (4) |
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6.9 Analytical Solutions for Discontinuous PWM |
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311 | (11) |
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6.10 Comparison of Harmonic Performance |
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322 | (4) |
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6.11 Harmonic Losses for Discontinuous PWM |
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326 | (4) |
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330 | (1) |
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6.13 Switched Pulse Sequence |
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331 | (2) |
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333 | (4) |
| Chapter 7 Modulation of Current Source Inverters |
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337 | (12) |
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7.1 Three-Phase Modulators as State Machines |
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338 | (5) |
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7.2 Naturally Sampled CSI Space Vector Modulator |
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343 | (1) |
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7.3 Experimental Confirmation |
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343 | (2) |
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345 | (4) |
| Chapter 8 Overmodulation of an Inverter |
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349 | (34) |
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8.1 The Overmodulation Region |
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350 | (1) |
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8.2 Naturally Sampled Overmodulation of One Phase Leg of an Inverter |
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351 | (5) |
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8.3 Regular Sampled Overmodulation of One Phase Leg of an Inverter |
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356 | (4) |
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8.4 Naturally Sampled Overmodulation of Single- and Three-Phase Inverters |
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360 | (4) |
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8.5 PWM Controller Gain during Overmodulation |
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364 | (12) |
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8.5.1 Gain with Sinusoidal Reference |
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364 | (3) |
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8.5.2 Gain with Space Vector Reference |
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367 | (4) |
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8.5.3 Gain with 60° Discontinuous Reference |
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371 | (2) |
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8.5.4 Compensated Modulation |
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373 | (3) |
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8.6 Space Vector Approach to Overmodulation |
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376 | (6) |
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382 | (1) |
| Chapter 9 Programmed Modulation Strategies |
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383 | (50) |
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9.1 Optimized Space Vector Modulation |
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384 | (12) |
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9.2 Harmonic Elimination PWM |
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396 | (15) |
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9.3 Performance Index for Optimality |
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411 | (5) |
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416 | (5) |
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421 | (9) |
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430 | (3) |
| Chapter 10 Programmed Modulation of Multilevel Converters |
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433 | (20) |
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10.1 Multilevel Converter Alternatives |
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433 | (3) |
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10.2 Block Switching Approaches to Voltage Control |
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436 | (4) |
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10.3 Harmonic Elimination Applied to Multilevel Inverters |
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440 | (7) |
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10.3.1 Switching Angles for Harmonic Elimination Assuming Equal Voltage Levels |
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440 | (1) |
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10.3.2 Equalization of Voltage and Current Stresses |
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441 | (2) |
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10.3.3 Switching Angles for Harmonic Elimination Assuming Unequal Voltage Levels |
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443 | (4) |
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10.4 Minimum Harmonic Distortion |
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447 | (2) |
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449 | (4) |
| Chapter 11 Carrier-Based PWM of Multilevel Inverters |
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453 | (78) |
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11.1 PWM of Cascaded Single-Phase H-Bridges |
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453 | (12) |
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11.2 Overmodulation of Cascaded H-Bridges |
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465 | (2) |
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11.3 PWM Alternatives for Diode-Clamped Multilevel Inverters |
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467 | (2) |
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11.4 Three-Level Naturally Sampled PD PWM |
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469 | (12) |
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11.4.1 Contour Plot for Three-Level PD PWM |
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469 | (4) |
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11.4.2 Double Fourier Series Harmonic Coefficients |
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473 | (2) |
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11.4.3 Evaluation of the Harmonic Coefficients |
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475 | (4) |
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11.4.4 Spectral Performance of Three-Level PD PWM |
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479 | (2) |
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11.5 Three-Level Naturally Sampled APOD or POD PWM |
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481 | (3) |
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11.6 Overmodulation of Three-Level Inverters |
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484 | (5) |
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11.7 Five-Level PWM for Diode-Clamped Inverters |
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489 | (10) |
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11.7.1 Five-level Naturally Sampled PD PWM |
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489 | (3) |
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11.7.2 Five-Level Naturally Sampled APOD PWM |
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492 | (5) |
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11.7.3 Five-Level POD PWM |
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497 | (2) |
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11.8 PWM of Higher Level Inverters |
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499 | (5) |
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11.9 Equivalent PD PWM for Cascaded Inverters |
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504 | (3) |
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11.10 Hybrid Multilevel Inverter |
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507 | (10) |
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11.11 Equivalent PD PWM for a Hybrid Inverter |
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517 | (2) |
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11.12 Third-Harmonic Injection for Multilevel Inverters |
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519 | (7) |
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11.13 Operation of a Multilevel Inverter with a Variable Modulation Index |
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526 | (2) |
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528 | (3) |
| Chapter 12 Space Vector PWM for Multilevel Converters |
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531 | (24) |
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12.1 Optimized Space Vector Sequences |
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531 | (3) |
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12.2 Modulator for Selecting Switching States |
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534 | (1) |
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12.3 Decomposition Method |
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535 | (3) |
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12.4 Hexagonal Coordinate System |
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538 | (5) |
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12.5 Optimal Space Vector Position within a Switching Period |
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543 | (2) |
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12.6 Comparison of Space Vector PWM to Carrier-Based PWM |
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545 | (3) |
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12.7 Discontinuous Modulation in Multilevel Inverters |
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548 | (2) |
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550 | (5) |
| Chapter 13 Implementation of a Modulation Controller |
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555 | (30) |
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13.1 Overview of a Power Electronic Conversion System |
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556 | (1) |
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13.2 Elements of a PWM Converter System |
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557 | (15) |
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13.2.1 VSI Power Conversion Stage |
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563 | (2) |
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13.2.2 Gate Driver Interface |
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565 | (2) |
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13.2.3 Controller Power Supply |
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567 | (1) |
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13.2.4 I/O Conditioning Circuitry |
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568 | (1) |
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569 | (3) |
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13.3 Hardware Implementation of the PWM Process |
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572 | (7) |
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13.3.1 Analog versus Digital Implementation |
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572 | (2) |
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13.3.2 Digital Timer Logic Structures |
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574 | (5) |
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13.4 PWM Software Implementation |
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579 | (5) |
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13.4.1 Background Software |
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580 | (1) |
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13.4.2 Calculation of the PWM Timing Intervals |
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581 | (3) |
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584 | (1) |
| Chapter 14 Continuing Developments in Modulation |
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585 | (38) |
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14.1 Random Pulse Width Modulation |
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586 | (4) |
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14.2 PWM Rectifier with Voltage Unbalance |
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590 | (8) |
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14.3 Common Mode Elimination |
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598 | (5) |
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14.4 Four Phase Leg Inverter Modulation |
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603 | (4) |
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14.5 Effect of Minimum Pulse Width |
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607 | (5) |
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14.6 PWM Dead-Time Compensation |
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612 | (7) |
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619 | (4) |
| Appendix 1 Fourier Series Representation of a Double Variable Controlled Waveform |
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623 | (6) |
| Appendix 2 Jacobi-Anger and Bessel Function Relationships |
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629 | (6) |
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A2.1 Jacobi-Anger Expansions |
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629 | (2) |
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A2.2 Bessel Function Integral Relationships |
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631 | (4) |
| Appendix 3 Three-Phase and Half-Cycle Symmetry Relationships |
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635 | (2) |
| Appendix 4 Overmodulation of a Single-Phase Leg |
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637 | (26) |
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A4.1 Naturally Sampled Double-Edge PWM |
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637 | (12) |
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A4.1.1 Evaluation of Double Fourier Integral for Overmodulated Naturally Sampled PWM |
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638 | (8) |
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A4.1.2 Harmonic Solution for Overmodulated Single-Phase Leg under Naturally Sampled PWM |
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646 | (1) |
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A4.1.3 Linear Modulation Solution Obtained from Overmodulation Solution |
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647 | (1) |
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A4.1.4 Square-Wave Solution Obtained from Overmodulation Solution |
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647 | (2) |
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A4.2 Symmetric Regular Sampled Double-Edge PWM |
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649 | (5) |
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A4.2.1 Evaluation of Double Fourier Integral for Overmodulated Symmetric Regular Sampled PWM |
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650 | (2) |
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A4.2.2 Harmonic Solution for Overmodulated Single-Phase Leg under Symmetric Regular Sampled PWM |
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652 | (1) |
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A4.2.3 Linear Modulation Solution Obtained from Overmodulation Solution |
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653 | (1) |
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A4.3 Asymmetric Regular Sampled Double-Edge PWM |
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654 | (9) |
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A4.3.1 Evaluation of Double Fourier Integral for Overmodulated Asymmetric Regular Sampled PWM |
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655 | (5) |
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A4.3.2 Harmonic Solution for Overmodulated Single-Phase Leg under Asymmetric Regular Sampled PWM |
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660 | (1) |
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A4.3.3 Linear Modulation Solution Obtained from Overmodulation Solution |
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661 | (2) |
| Appendix 5 Numeric Integration of a Double Fourier Series Representation of a Switched Waveform |
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663 | (8) |
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A5.1 Formulation of the Double Fourier Integral |
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663 | (3) |
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A5.2 Analytical Solution of the Inner Integral |
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666 | (2) |
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A5.3 Numeric Integration of the Outer Integral |
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668 | (3) |
| Bibliography |
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671 | (44) |
| Index |
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715 | |
