S T U D I E S IN E L E C T R I C A L A N D

E L E C T R O N I C E N G I N E E R I N G 4 6

AUTOMATIC CONTROL OF CONVERTER-FED DRIVES

MARIAN P. KAZMIERKOWSKI

and

HENRYK TUNIA

Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw, Poland

ELSEVIER Amsterdam-London-New York-Tokyo

PWN—POLISH SCIENTIFIC PUBLISHERS Warszawa

1994

Contents

Introduction 1

Chapter 1 Mathematical models of electric motors 4

1.1 Introduction 4 1.2 Voltage and flux-current equations 5 1.3 Space vectors and their representations in coordinate

systems 11 1.3.1 Physical basis 11 1.3.2 Definitions and basic properties 13 1.3.3 Space vectors in coordinate systems 17

1.4 Voltage and flux-current equations written in terms of space vectors 19

1.5 Transformation of vector equations into a common rota­ting coordinate system 22

1.6 Referring rotor quantities to the stator circuit . . . . 24 1.7 Instantaneous power and electromagnetic torque . . . 27 1.8 Mechanical motion equation 29 1.9 Complete set of equilibrium equations 30

1.10 Park's transformation 32 1.11 Relationship between equations based on complex space

vectors and the unified theory of electric motors . . . 33 1.12 Linearization of equilibrium equations. State equations

and transfer functions 34 1.13 Per unit system 36

Chapter 2 Three-phase induction motor 37

2.1 Design and basic types 37 2.2 Vector equilibrium equations in per unit system . . . . 38

VI CONTENTS

2.3 Block diagrams 43 2.3.1 Stator-fixed system of coordinates (a, ß, 0) . . . 43 2.3.2 Rotor-fixed system of coordinates (d, q,0) . . . 46 2.3.3 Synchronous-rotating system of coordinates (x, y, 0) 48

2.4 State equations 52 2.4.1 State equations in nonlinear form 52 2.4.2 State equations in linearized form 54

2.5 Properties of induction motors in steady states . . . . 55 2.5.1 Equivalent circuits and phasor diagrams . . . . 56 2.5.2 Steady-state characteristics 62

2.6 Speed control by changing the supply frequency . . . . 68

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Chapter 3 Three-phase ac synchronous motor 70

3.1 Design and major types 70 3.2 Equilibrium equations in per unit system 73 3.3 Block diagrams 76 3.4 Properties of synchronous motors in steady states . . . 79

3.4.1 Equivalent circuits and phasor diagrams . . . . 79 3.4.2 Steady-state characteristics 83

3.5 Speed control 85

Chapter 4 Separately excited dc motor 87

4.1 Design and major parameters 87 4.2 Equilibrium equations and equivalent circuits 89 4.3 Block diagrams and operator transfer functions . . . . 92

4.3.1 Per unit equations 92 4.3.2 General block diagram 94 4.3.3 Transfer functions with constant flux operation . 95 4.3.4 Transfer functions with variable flux operation . 96 4.3.5 State equations 98

4.4 Steady-state characteristics 101 4.5 Speed control methods 102

4.5.1 Control by changing armature voltage 103 4.5.2 Control by flux weakening 104 4.5.3 Two-zone control 106

CONTENTS VII

Chapter 5 Power converters for motor control 108

5.1 Introduction 108 5.2 Line-commutated rectifiers and inverters 112

5.2.1 Rectifier operation 112 5.2.2 Commutation 115 5.2.3 Inverter operation 121 5.2.4 Converter systems 124 5.2.5 Dual converters 128 5.2.6 Mathematical model 133 5.2.7 Unwanted output voltage components 136 5.2.8 Input power factor 140

5.3 Frequency changers 144 5.3.1 Modulation function 144 5.3.2 Natural commutation converters 146 5.3.3 Frequency changers with forced commutation . . 156 5.3.4 Input power factor 164 5.3.5 Equivalent circuit for frequency changer . . . . 166

5.4 Current-sourced inverters 167 5.4.1 Principle of operation 167 5.4.2 Analysis of the commutation process 172 5.4.3 System start-up 179 5.4.4 Neutralization of selected unwanted components of

output current waveform 180 5.5 Voltage-sourced inverters 184

5.5.1 Principle of operation 184 5.5.2 Output voltage control and reduction of unwanted

components 188 5.5.3 Impulse-commutated thyristor circuits 191 5.5.4 Neutral-point-clamped PWM inverter 203

5.6 Dc-to-dc converters 207 5.6.1 One-quadrant voltage-sourced converter . . . . 207 5.6.2 One-quadrant current-sourced converter . . . . 210 5.6.3 Buck-boost converter 212 5.6.4 Neutralization of unwanted components . . . . 214

5.7 Minimization of the losses of high-frequency power elec­tronic switches 217

VII I CONTENTS

5.7.1 Turn-on process 218 5.7.2 Turn-off process 220 5.7.3 Snubber circuits 222 5.7.4 Resonant dc-link converter 224 5.7.5 Modulation strategies 228

Chapter 6 Principles of control system synthesis 230

6.1 Introduction 230 6.2 Dynamic optimization of continuous-time closed-loop

systems 232 6.2.1 Synthesis of conventional control systems . . . 232

6.2.1.1 Criteria of optimal linear regulator set­tings 232

6.2.1.2 Control system structures 242 6.2.2 State space synthesis of control systems . . . . 244

6.2.2.1 Controllability and observability of con­trol processes 245

6.2.2.2 State feedback control 246 6.2.2.3 Observer technique 250 6.2.2.4 Structure of optimal state control sys­

tems for reference and disturbance signals 252 6.2.2.5 Cascade state control 253

6.3 Digital control systems 254 6.3.1 Introduction 254 6.3.2 Mathematical representation: Use of Z trans­

formation 259 6.3.3 Design rules for digital controllers 268

6.4 Adaptive control systems 269

Chapter 7 Control systems for dc motor drives 273

7.1 Dynamic properties of speed control systems 273 7.1.1 Cascade speed control 273

7.1.1.1 Synthesis of armature current control loop 274 7.1.1.2 Synthesis of angular speed control loop 279

7.1.2 Direct speed control 284

CONTENTS IX

7.1.3 Comparison of cascade speed control with direct speed control structure 286

7.1.4 State feedback speed control 289 7.1.4.1 State equations for control system . . . 290 7.1.4.2 Calculation of state vector feedback coef­

ficients 292 7.1.4.3 Operator transfer functions 295 7.1.4.4 Selection of pole placement 295

7.1.5 Concluding remarks 297 7.2 Dc drive with line-commutated converter 297

7.2.1 Two-quadrant drive with two-zone speed control 297 7.2.2 Reverse drive with double converter supplying dc

motor armature 300 7.2.3 Reverse drive with armature circuit switch . . . 304

7.3 Dc drive with dc-to-dc converter 306 7.4 Digital-analogue speed control systems 309 7.5 Adaptive speed control system 313

Chapter 8 Control systems for the wound rotor induction motors 319

8.1 Speed control by supply voltage variation 319 8.2 Speed control by varying rotor circuit resistance . . . 322 8.3 Double-fed induction motor drives 324

8.3.1 Subsynchronous converter cascade 324 8.3.2 One-quadrant drive in subsynchronous cascade

configuration 326 8.3.3 Subsynchronous-supersynchronous drive system . 327

8.3.3.1 Mathematical description 329 8.3.3.2 The effect of dc link current control . . 330 8.3.3.3 Field-oriented and voltage-oriented con­

trol 332

Chapter 9 Frequency-controlled induction motor drive systems . 339

9.1 Introduction 339 9.2 Conditions of static optimization of control 340

9.2.1 Indirect flux stabilization 340

CONTENTS

9.2.1.1 Indirect flux stabilization by voltage con­trol 340

9.2.1.2 Indirect flux stabilization by current con­trol 342

9.2.2 Direct flux stabilization 343 9.2.3 Minimum reactive power consumption 344 9.2.4 Part-load performance optimization 346

9.3 Induction motor operation with non-sinusoidal supply waveforms 348 9.3.1 Operation under voltage-sourced inverter supply 348

9.3.1.1 Space vector representation of inverter output voltage 349

9.3.1.2 Harmonic equivalent circuits and har­monic currents 351

9.3.1.3 Electromagnetic torque waveform . . . 355 9.3.1.4 Waveforms under six-step VSI supply . 359 9.3.1.5 Waveforms under voltage-sourced PWM

inverter supply 360 9.3.2 Operation under current-sourced inverter supply 367

9.3.2.1 Space-vector representation of inverter output current 367

9.3.2.2 Harmonic currents 369 9.3.2.3 Waveforms of flux linkages and the stator

voltage . 370 9.3.2.4 Electromagnetic torque waveform . . . 372 9.3.2.5 Waveforms under six-step CSI supply . 375 9.3.2.6 Waveforms under a current-sourced PWM

inverter supply 380 9.4 Dynamic behaviour of frequency converter-fed induc­

tion motors under different modes of control 382 9.4.1 Current-controlled frequency converter 382 9.4.2 Block diagram of current-controlled frequency con­

verter-fed induction motor 384 9.4.3 Torque control methods 388 9.4.4 Torque control under constant flux 389

9.4.4.1 Dynamic behaviour under indirect flux stabilization 389

CONTENTS XI

9.4.4.2 Dynamic behaviour under direct flux sta­bilization 391

9.4.4.3 Phase relations between rotor flux and stator current vectors: synchronous con­trol method 392

9.4.4.4 Improving the dynamic properties of torque control by independent command of flux and torque current components: the field-oriented control method (is,6) 394

9.4.4.5 Concluding remarks 396 9.4.5 Torque control under variable flux 397

9.4.5.1 Dynamic behaviour under constant slip frequency control 397

9.4.5.2 Dynamic behaviour under constant torque angle control 399

9.4.5.3 Concluding remarks 400 9.4.6 Voltage-controlled frequency converter 401 9.4.7 Block diagram of voltage-controlled frequency con­

verter-fed induction motor 402 9.5 CSI-fed drive systems 405

9.5.1 Direct field-oriented control 406 9.5.1.1 Basic block scheme 406 9.5.1.2 Current amplitude control loop . . . . 407 9.5.1.3 Torque angle control loop 408

9.5.2 Indirect field-oriented control 410 9.5.3 EMF-oriented control 413 9.5.4 Indirect torque angle control 417 9.5.5 Open loop voltage/frequency control 418

9.6 Current-controlled P W M inverter-fed drive systems . . 420 9.6.1 Current control methods for voltage-sourced P W M

inverters 420 9.6.1.1 A voltage-sourced P W M inverter as a

control unit of an induction motor current loop ' 420

9.6.1.2 Three independent hysteresis controllers 422 9.6.1.3 Space vector-based hysteresis controllers 424 9.6.1.4 Fixed-frequency nonlinear controllers . 428

XII CONTENTS

9.6.1.5 Linear controllers 429 9.6.1.6 Space vector-based intelligent predictive

Controllers 431 9.6.2 Direct field-oriented control 434 9.6.3 Indirect field-oriented control 437

9.6.3.1 Basic block scheme 437 9.6.3.2 The effect of parameter changes . . . . 437 9.6.3.3 Parameter adaptation 440 9.6.3.4 Transistor PWM inverter-fed induction

motor drive with indirect field-oriented control 442

9.6.4 Induction motor servodrives 445 9.6.5 Current-controlled dc link PWM converter with bi­

directional power flow 447 9.7 VSI-fed induction motor drives 449

9.7.1 Direct field-oriented control 449 9.7.1.1 Basic block scheme 449 9.7.1.2 Voltage decoupler 451 9.7.1.3 Space vector modulator 452

9.7.2 Indirect field-oriented control 454 9.7.3 Direct flux and torque control 455

9.7.3.1 Principle of the method 455 9.7.3.2 Basic block scheme 461 9.7.3.3 Control of transistor PWM inverter-fed

drives 462 9.7.3.4 Control of thyristor PWM inverter-fed

drives 465 9.7.4 Voltage/frequency control 467

Chapter 10 Frequency-controlled synchronous motor drive systems 469

10.1 Introduction 469 10.2 Optimization conditions under steady states 469

10.2.1 Indirect flux stabilization 470 10.2.1.1 Indirect flux stabilization by excitation

current control 470

CONTENTS XII I

10.2.1.2 Indirect flux stabilization by stator volt­age control 471

10.2.2 Minimum reactive power consumption 472 10.3 Open-loop and self-controlled operation 474 10.4 Cycloconverter-fed drive systems 475

10.4.1 Rotor-oriented control 476 10.4.2 Field-oriented control 479

10.5 Load-commutated CSI-fed drive systems 485 10.5.1 Basic properties and torque production . . . . 486 10.5.2 Standard control 488 10.5.3 Constant inverter margin time control 490 10.5.4 Starting methods 492

10.6 Transistor P W M inverter-fed PM synchronous motor drive systems 494 10.6.1 Basic properties and torque production . . . . 494 10.6.2 PM synchronous motor drives with sinusoidal

current 497 10.6.3 PM synchronous motor drives with rectangular

(switched) current 500 10.7 Voltage/frequency control of VSI-fed multiple motor

drives 502

Chapter 11 Introduction to microprocessor control 504

Appendix. Signal processing for vector control systems 511

A.l Phase conversion and coordinate transformation . . . 511 A.2 Models for flux vector estimation 517 A.3 Observers for flux vector estimation 523 A.4 Torque and torque angle estimation 526 A.5 Real-time calculator for converter-fed ac motor drives

investigation and control 529

References , 530

Symbols employed 545

Index 553