Model Predictive Control of High Power Converters and Industrial Drives

Preface xvii Acknowledgments xix List of Abbreviations xxi About the Companion Website xxvii Part I INTRODUCTION 1 Introduction 3 1.1 Industrial Power Electronics 3 1.1.1 Medium-Voltage, Variable-Speed Drives 3 1.1.2 Market Trends 5 1.1.3 Technology Trends 6 1.2 Control and Modulation Schemes 7 1.2.1 Requirements 7 1.2.2 State-of-the-Art Schemes 8 1.2.3 Challenges 9 1.3 Model Predictive Control 11 1.3.1 Control Problem 11 1.3.2 Control Principle 12 1.3.3 Advantages and Challenges 16 1.4 Research Vision and Motivation 19 1.5 Main Results 19 1.6 Summary of this Book 21 1.7 Prerequisites 25 References 26 2 Industrial Power Electronics 29 2.1 Preliminaries 29 2.1.1 Three-Phase Systems 29 2.1.2 Per Unit System 31 2.1.3 Stationary Reference Frame 33 2.1.4 Rotating Reference Frame 36 2.1.5 Space Vectors 40 2.2 Induction Machines 42 2.2.1 Machine Model in Space Vector Notation 42 2.2.2 Machine Model in Matrix Notation 44 2.2.3 Machine Model in the Per Unit System 45 2.2.4 Machine Model in State-Space Representation 48 2.2.5 Harmonic Model of the Machine 50 2.3 Power Semiconductor Devices 51 2.3.1 Integrated-Gate-Commutated Thyristors 51 2.3.2 Power Diodes 53 2.4 Multilevel Voltage Source Inverters 54 2.4.1 NPC Inverter 54 2.4.2 Five-Level ANPC Inverter 62 2.5 Case Studies 68 2.5.1 NPC Inverter Drive System 68 2.5.2 NPC Inverter Drive System with Snubber Restrictions 70 2.5.3 Five-Level ANPC Inverter Drive System 71 2.5.4 Grid-Connected NPC Converter System 72 References 75 3 Classic Control and Modulation Schemes 77 3.1 Requirements of Control and Modulation Schemes 77 3.1.1 Requirements Relating to the Electrical Machine 77 3.1.2 Requirements Relating to the Grid 80 3.1.3 Requirements Relating to the Converter 83 3.1.4 Summary 83 3.2 Structure of Control and Modulation Schemes 84 3.3 Carrier-Based Pulse Width Modulation 85 3.3.1 Single-Phase Carrier-Based Pulse Width Modulation 86 3.3.2 Three-Phase Carrier-Based Pulse Width Modulation 94 3.3.3 Summary and Properties 101 3.4 Optimized Pulse Patterns 103 3.4.1 Pulse Pattern and Harmonic Analysis 104 3.4.2 Optimization Problem for Three-Level Converters 107 3.4.3 Optimization Problem for Five-Level Converters 112 3.4.4 Summary and Properties 117 3.5 Performance Trade-Off for Pulse Width Modulation 117 3.5.1 Current TDD versus Switching Losses 118 3.5.2 Torque TDD versus Switching Losses 120 3.6 Control Schemes for Induction Machine Drives 121 3.6.1 Scalar Control 122 3.6.2 Field-Oriented Control 123 3.6.3 Direct Torque Control 130 Appendix 3.A: Harmonic Analysis of Single-Phase Optimized Pulse Patterns 139 Appendix 3.B: Mathematical Optimization 141 3.B.1 General Optimization Problems 142 3.B.2 Mixed-Integer Optimization Problems 142 3.B.3 Convex Optimization Problems 143 References 145 Part II DIRECT MODEL PREDICTIVE CONTROL WITH REFERENCE TRACKING 4 Predictive Control with Short Horizons 153 4.1 Predictive Current Control of a Single-Phase RL Load 153 4.1.1 Control Problem 153 4.1.2 Prediction of Current Trajectories 154 4.1.3 Optimization Problem 156 4.1.4 Control Algorithm 156 4.1.5 Performance Evaluation 158 4.1.6 Prediction Horizons of more than 1 Step 161 4.1.7 Summary 163 4.2 Predictive Current Control of a Three-Phase Induction Machine 164 4.2.1 Case Study 164 4.2.2 Control Problem 165 4.2.3 Controller Model 166 4.2.4 Optimization Problem 167 4.2.5 Control Algorithm 168 4.2.6 Performance Evaluation 170 4.2.7 About the Choice of Norms 175 4.2.8 Delay Compensation 178 4.3 Predictive Torque Control of a Three-Phase Induction Machine 183 4.3.1 Case Study 183 4.3.2 Control Problem 184 4.3.3 Controller Model 184 4.3.4 Optimization Problem 185 4.3.5 Control Algorithm 186 4.3.6 Analysis of the Cost Function 187 4.3.7 Comparison of the Cost Functions for the Torque and Current Controllers 188 4.3.8 Performance Evaluation 191 4.4 Summary 193 References 194 5 Predictive Control with Long Horizons 195 5.1 Preliminaries 196 5.1.1 Case Study 196 5.1.2 Controller Model 197 5.1.3 Cost Function 197 5.1.4 Optimization Problem 198 5.1.5 Control Algorithm based on Exhaustive Search 200 5.2 Integer Quadratic Programming Formulation 201 5.2.1 Optimization Problem in Vector Form 201 5.2.2 Solution in Terms of the Unconstrained Minimum 202 5.2.3 Integer Quadratic Program 202 5.2.4 Direct MPC with a Prediction Horizon of 1 203 5.3 An Efficient Method for Solving the Optimization Problem 204 5.3.1 Preliminaries and Key Properties 205 5.3.2 Modified Sphere Decoding Algorithm 205 5.3.3 Illustrative Example with a Prediction Horizon of 1 207 5.3.4 Illustrative Example with a Prediction Horizon of 2 209 5.4 Computational Burden 211 5.4.1 Offline Computations 211 5.4.2 Online Preprocessing 211 5.4.3 Sphere Decoding 212 Appendix 5.A: State-Space Model 213 Appendix 5.B: Derivation of the Cost Function in Vector Form 214 References 216 6 Performance Evaluation of Predictive Control with Long Horizons 217 6.1 Performance Evaluation for the NPC Inverter Drive System 218 6.1.1 Framework for Performance Evaluation 218 6.1.2 Comparison at the Switching Frequency 250 Hz 220 6.1.3 Closed-Loop Cost 223 6.1.4 Relative Current TDD 225 6.1.5 Operation during Transients 231 6.2 Suboptimal MPC via Direct Rounding 232 6.3 Performance Evaluation for the NPC Inverter Drive System with an LC Filter 234 6.3.1 Case Study 235 6.3.2 Controller Model 237 6.3.3 Optimization Problem 237 6.3.4 Steady-State Operation 239 6.3.5 Operation during Transients 243 6.4 Summary and Discussion 245 6.4.1 Performance at Steady-State Operating Conditions 245 6.4.2 Performance during Transients 246 6.4.3 Cost Function 246 6.4.4 Control Objectives 247 6.4.5 Computational Complexity 247 Appendix 6.A: State-Space Model 248 Appendix 6.B: Computation of the Output Reference Vector 248 6.B.1 Step 1: Stator Frequency 248 6.B.2 Step 2: Inverter Voltage 249 6.B.3 Step 3: Output Reference Vector 250 References 251 Part III DIRECT MODEL PREDICTIVE CONTROL WITH BOUNDS 7 Model Predictive Direct Torque Control 255 7.1 Introduction 255 7.2 Preliminaries 257 7.2.1 Case Study 257 7.2.2 Control Problem 259 7.2.3 Controller Model 259 7.2.4 Switching Effort 262 7.3 Control Problem Formulation 263 7.3.1 Naive Optimization Problem 263 7.3.2 Constraints 264 7.3.3 Cost Function 265 7.4 Model Predictive Direct Torque Control 266 7.4.1 Definitions 267 7.4.2 Simplified Optimization Problem 268 7.4.3 Concept of the Switching Horizon 268 7.4.4 Search Tree 274 7.4.5 MPDTC Algorithm with Full Enumeration 275 7.5 Extension Methods 277 7.5.1 Analysis of the State and Output Trajectories 278 7.5.2 Linear Extrapolation 279 7.5.3 Quadratic Extrapolation 280 7.5.4 Quadratic Interpolation 282 7.6 Summary and Discussion 284 Appendix 7.A: Controller Model of the NPC Inverter Drive System 286 References 287 8 Performance Evaluation of Model Predictive Direct Torque Control 289 8.1 Performance Evaluation for the NPC Inverter Drive System 289 8.1.1 Simulation Setup 290 8.1.2 Steady-State Operation 290 8.1.3 Operation during Transients 298 8.2 Performance Evaluation for the ANPC Inverter Drive System 300 8.2.1 Controller Model 301 8.2.2 Modified MPDTC Algorithm 303 8.2.3 Simulation Setup 304 8.2.4 Steady-State Operation 305 8.2.5 Operation during Transients 312 8.3 Summary and Discussion 314 Appendix 8.A: Controller Model of the ANPC Inverter Drive System 315 References 316 9 Analysis and Feasibility of Model Predictive Direct Torque Control 318 9.1 Target Set 319 9.2 The State-Feedback Control Law 320 9.2.1 Preliminaries 321 9.2.2 Control Law for a Given Rotor Flux Vector 322 9.2.3 Control Law along an Edge of the Target Set 331 9.3 Analysis of the Deadlock Phenomena 331 9.3.1 Root Cause Analysis of Deadlocks 332 9.3.2 Location of Deadlocks 335 9.4 Deadlock Resolution 337 9.5 Deadlock Avoidance 340 9.5.1 Deadlock Avoidance Strategies 340 9.5.2 Performance Evaluation 343 9.6 Summary and Discussion 347 9.6.1 Derivation and Analysis of the State-Feedback Control Law 347 9.6.2 Deadlock Analysis, Resolution, and Avoidance 347 References 348 10 Computationally Efficient Model Predictive Direct Torque Control 350 10.1 Preliminaries 351 10.2 MPDTC with Branch-and-Bound 352 10.2.1 Principle and Concept 352 10.2.2 Properties of Branch-and-Bound 354 10.2.3 Limiting the Maximum Number of Computations 356 10.2.4 Computationally Efficient MPDTC Algorithm 357 10.3 Performance Evaluation 359 10.3.1 Case Study 359 10.3.2 Performance Metrics during Steady-State Operation 359 10.3.3 Computational Metrics during Steady-State Operation 363 10.4 Summary and Discussion 367 References 368 11 Derivatives of Model Predictive Direct Torque Control 369 11.1 Model Predictive Direct Current Control 370 11.1.1 Case Study 370 11.1.2 Control Problem 372 11.1.3 Formulation of the Stator Current Bounds 373 11.1.4 Controller Model 376 11.1.5 Control Problem Formulation 378 11.1.6 MPDCC Algorithm 379 11.1.7 Performance Evaluation 380 11.1.8 Tuning 388 11.2 Model Predictive Direct Power Control 389 11.2.1 Case Study 391 11.2.2 Control Problem 392 11.2.3 Controller Model 393 11.2.4 Control Problem Formulation 394 11.2.5 Performance Evaluation 395 11.3 Summary and Discussion 401 11.3.1 Model Predictive Direct Current Control 401 11.3.2 Model Predictive Direct Power Control 403 11.3.3 Target Sets 403 Appendix 11.A: Controller Model used in MPDCC 405 Appendix 11.B: Real and Reactive Power 407 Appendix 11.C: Controller Model used in MPDPC 409 References 410 Part IV MODEL PREDICTIVE CONTROL BASED ON PULSE WIDTH MODULATION 12 Model Predictive Pulse Pattern Control 415 12.1 State-of-the-Art Control Methods 415 12.2 Optimized Pulse Patterns 416 12.2.1 Summary, Properties, and Computation 416 12.2.2 Relationship between Flux Magnitude and Modulation Index 418 12.2.3 Relationship between Time and Angle 419 12.2.4 Stator Flux Reference Trajectory 420 12.2.5 Look-Up Table 422 12.3 Stator Flux Control 422 12.3.1 Control Objectives 422 12.3.2 Control Principle 422 12.3.3 Control Problem 423 12.3.4 Control Approach 424 12.4 MP3C Algorithm 425 12.4.1 Observer 426 12.4.2 Speed Controller 428 12.4.3 Torque Controller 428 12.4.4 Flux Controller 428 12.4.5 Pulse Pattern Loader 429 12.4.6 Flux Reference 429 12.4.7 Pulse Pattern Controller 429 12.5 Computational Variants of MP3C 433 12.5.1 MP3C based on Quadratic Program 433 12.5.2 MP3C based on Deadbeat Control 437 12.6 Pulse Insertion 438 12.6.1 Definitions 439 12.6.2 Algorithm 439 Appendix 12.A: Quadratic Program 443 Appendix 12.B: Unconstrained Solution 444 Appendix 12.C: Transformations for Deadbeat MP3C 445 References 446 13 Performance Evaluation of Model Predictive Pulse Pattern Control 447 13.1 Performance Evaluation for the NPC Inverter Drive System 447 13.1.1 Simulation Setup 447 13.1.2 Steady-State Operation 448 13.1.3 Operation during Transients 455 13.2 Experimental Results for the ANPC Inverter Drive System 462 13.2.1 Experimental Setup 462 13.2.2 Hierarchical Control Architecture 463 13.2.3 Steady-State Operation 465 13.3 Summary and Discussion 468 13.3.1 Differences to the State of the Art 469 13.3.2 Discussion 471 References 472 14 Model Predictive Control of a Modular Multilevel Converter 474 14.1 Introduction 474 14.2 Preliminaries 475 14.2.1 Topology 475 14.2.2 Nonlinear Converter Model 477 14.3 Model Predictive Control 479 14.3.1 Control Problem 479 14.3.2 Controller Structure 480 14.3.3 Linearized Prediction Model 481 14.3.4 Cost Function 481 14.3.5 Hard and Soft Constraints 483 14.3.6 Optimization Problem 484 14.3.7 Multilevel Carrier-Based Pulse Width Modulation 485 14.3.8 Balancing Control 486 14.4 Performance Evaluation 486 14.4.1 System and Control Parameters 486 14.4.2 Steady-State Operation 488 14.4.3 Operation during Transients 491 14.5 Design Parameters 496 14.5.1 Open-Loop Prediction Errors 496 14.5.2 Closed-Loop Performance 498 14.6 Summary and Discussion 499 Appendix 14.A: Dynamic Current Equations 501 Appendix 14.B: Controller Model of the Converter System 501 References 503 Part V SUMMARY 15 Summary and Conclusion 507 15.1 Performance Comparison of Direct Model Predictive Control Schemes 507 15.1.1 Case Study 508 15.1.2 Performance Trade-Off Curves 508 15.1.3 Summary and Discussion 515 15.2 Assessment of the Control and Modulation Methods 519 15.2.1 FOC and VOC with SVM 519 15.2.2 DTC and DPC 519 15.2.3 Direct MPC with Reference Tracking 520 15.2.4 Direct MPC with Bounds 521 15.2.5 MP3C based on OPPs 521 15.2.6 Indirect MPC 523 15.3 Conclusion 524 15.4 Outlook 525 References 525 Index 527

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• Engenharia electrónica