Model Predictive Control of High Power Converters and Industrial Drives

In this original book on model predictive control (MPC) for power electronics, the focus is put on high-power applications with multilevel converters operating at switching frequencies well below 1 kHz, such as medium-voltage drives and modular multi-level converters.

Consisting of two main parts, the first offers a detailed review of three-phase power electronics, electrical machines, carrier-based pulse width modulation, optimized pulse patterns, state-of-the art converter control methods and the principle of MPC. The second part is an in-depth treatment of MPC methods that fully exploit the performance potential of high-power converters. These control methods combine the fast control responses of deadbeat control with the optimal steady-state performance of optimized pulse patterns by resolving the antagonism between the two.

MPC is expected to evolve into the control method of choice for power electronic systems operating at low pulse numbers with multiple coupled variables and tight operating constraints it. Model Predictive Control of High Power Converters and Industrial Drives will enable to reader to learn how to increase the power capability of the converter, lower the current distortions, reduce the filter size, achieve very fast transient responses and ensure the reliable operation within safe operating area constraints.

Targeted at power electronic practitioners working on control-related aspects as well as control engineers, the material is intuitively accessible, and the mathematical formulations are augmented by illustrations, simple examples and a book companion website featuring animations. Readers benefit from a concise and comprehensive treatment of MPC for industrial power electronics, enabling them to understand, implement and advance the field of high-performance MPC schemes.

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

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.