Model Predictive Control of High Power Converters and Industrial Drives By Tobias Geyer

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Model Predictive Control of High Power Converters and Industrial Drives By Tobias Geyer

Contents

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
viii Contents
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
Contents ix
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
x Contents
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
Contents xi
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
xii Contents
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
Contents xiii
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
xiv Contents
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
Contents xv
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

 

Preface

This book focuses on model predictive control (MPC) schemes for industrial power electronics.
The emphasis is on three-phase ac–dc and dc–ac power conversion systems for high-power
applications of 1 MVA and above. These systems are predominantly based on multilevel voltage
source converters that operate at switching frequencies well below 1 kHz. The book mostly
considers medium-voltage (MV), variable-speed drive systems and, to a lesser extent, MV
grid-connected converters. The proposed control techniques can also be applied to low-voltage
power converters when operated at low pulse number, that is, at small ratios between the
switching frequency and the fundamental frequency.
For high-power converters, the pulse number typically ranges between 5 and 15. As a result,
the concept of averaging, which is commonly applied to power electronic systems to conceal
the switching aspect from the control problem, leads to performance deterioration. In general,
to achieve the highest possible performance for a high-power converter, averaging is to be
avoided, and the traditionally used current control loop and modulator should be replaced by
one single control entity.
This book proposes and reviews controlmethods that fully exploit the performance potential
of high-power converters, by ensuring fast control at very low switching frequencies and low
harmonic distortions. To achieve this, the control and modulation problem is addressed in one
computational stage. Long prediction horizons are required for theMPC controllers to achieve
excellent steady-state performance. The resulting optimization problem is computationally
challenging, but can be solved in real time by branch-and-bound methods. Alternatively, the
optimal switching sequence to be applied during steady-state operation—the so-called optimized
pulse pattern (OPP)—can be precomputed offline and refined online to achieve fast
closed-loop control.
To this end, the research vision is to combine the benefits of deadbeat control methods (such
as direct torque control) with the optimal steady-state performance of OPPs, by resolving the
antagonism between the two. Three such MPC methods are presented in detail.