Model Predictive Control of High Power Converters and Industrial DrivesISBN: 9781119010906
576 pages
November 2016

Description
In this original book on model predictive control (MPC) for power electronics, the focus is put on highpower applications with multilevel converters operating at switching frequencies well below 1 kHz, such as mediumvoltage drives and modular multilevel converters.
Consisting of two main parts, the first offers a detailed review of threephase power electronics, electrical machines, carrierbased pulse width modulation, optimized pulse patterns, stateofthe art converter control methods and the principle of MPC. The second part is an indepth treatment of MPC methods that fully exploit the performance potential of highpower converters. These control methods combine the fast control responses of deadbeat control with the optimal steadystate 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 controlrelated 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 highperformance MPC schemes.
Table of 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 MediumVoltage, VariableSpeed 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 StateoftheArt 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 ThreePhase 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 StateSpace Representation 48
2.2.5 Harmonic Model of the Machine 50
2.3 Power Semiconductor Devices 51
2.3.1 IntegratedGateCommutated Thyristors 51
2.3.2 Power Diodes 53
2.4 Multilevel Voltage Source Inverters 54
2.4.1 NPC Inverter 54
2.4.2 FiveLevel 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 FiveLevel ANPC Inverter Drive System 71
2.5.4 GridConnected 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 CarrierBased Pulse Width Modulation 85
3.3.1 SinglePhase CarrierBased Pulse Width Modulation 86
3.3.2 ThreePhase CarrierBased 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 ThreeLevel Converters 107
3.4.3 Optimization Problem for FiveLevel Converters 112
3.4.4 Summary and Properties 117
3.5 Performance TradeOff 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 FieldOriented Control 123
3.6.3 Direct Torque Control 130
Appendix 3.A: Harmonic Analysis of SinglePhase Optimized Pulse Patterns 139
Appendix 3.B: Mathematical Optimization 141
3.B.1 General Optimization Problems 142
3.B.2 MixedInteger 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 SinglePhase 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 ThreePhase 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 ThreePhase 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: StateSpace 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 ClosedLoop 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 SteadyState Operation 239
6.3.5 Operation during Transients 243
6.4 Summary and Discussion 245
6.4.1 Performance at SteadyState 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: StateSpace 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 SteadyState 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 SteadyState 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 StateFeedback 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 StateFeedback 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 BranchandBound 352
10.2.1 Principle and Concept 352
10.2.2 Properties of BranchandBound 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 SteadyState Operation 359
10.3.3 Computational Metrics during SteadyState 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 StateoftheArt 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 LookUp 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 SteadyState 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 SteadyState 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 CarrierBased 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 SteadyState Operation 488
14.4.3 Operation during Transients 491
14.5 Design Parameters 496
14.5.1 OpenLoop Prediction Errors 496
14.5.2 ClosedLoop 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 TradeOff 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
Author Information
Tobias Geyer joined ABB's Corporate Research Center as a deputy group leader and principal scientist in 2012. In this role, he is building up a dedicated research team focusing on Model predictive control (MPC) for power electronic systems. After obtaining his PhD at ETH Zurich, he spent three years in GE's Corporate Research Center in Munich as a project leader for highpower electronics and drives. He subsequently worked at the intersection of academia and industrial research, fully funded by ABB and part of an ABB research team, whilst being employed by the University of Auckland as a Research Fellow. During this time, his focus was on the development of a new generation of drive control schemes that is intended to replace ABB's currently used schemes in their mediumvoltage drive portfolio. Tobias Geyer has been working on MPC for power electronics since 2002, and was one of the first researchers who began working in this field. During the past 12 years he has written approximately 100 peerreviewed journal and conference publications and patent applications. He is also an Associate Editor of Transactions on Power Electronics and Transactions on Industry Applications.