Electrical Machines and Drives (eBook)

Foreword 7
Preface 8
Acknowledgements 11
Contents 12
Symbols and Conventions 24
General 24
Symbols 24
Greek symbols 25
Subscripts 26
Part I Transformers and Electrical Machines 27
1 Transformers 28
1.1 Introduction 28
1.2 Transformer Equations 29
1.2.1 Basic Electromagnetic Description and Equations 29
1.2.2 Phasor Equations and Equivalent Circuit for Sinusoidal Supply 33
1.3 Referred Values: Equations and Equivalent Circuit 35
1.4 Per-Unit Description 36
1.5 Construction and Scaling Laws 36
1.5.1 Specific Rated Quantities 37
1.5.2 Rated Per-Unit Impedances 38
1.6 Alternative and Simplified Equivalent Circuits 44
1.7 No-Load Operation 46
1.8 Short-Circuit Operation 47
1.8.1 Short-Circuit Impedance 47
1.8.2 Procentual Short-Circuit Voltage 48
1.8.3 Remarks 48
1.9 Voltage Variation with Load 49
1.10 Parallel Operation of Transformers 51
1.11 Construction of Single-Phase and Three-Phase Transformers 54
1.11.1 Single-Phase Transformers 54
1.11.2 Three-Phase Transformers 54
1.12 Connection and Vector Group of a Three-Phase Transformer 58
1.12.1 Winding and Terminal Markings 58
1.12.2 Modelling of a Three-Phase Transformer 58
1.12.3 Connections and Vector Groups 59
1.12.4 Asymmetrical Operation of 3-Phase Transformers 60
1.13 Autotransformer 64
1.14 Phase-Number Transformation 66
1.14.1 Three to Six or Twelve Phases 66
1.14.2 Three to Two Phases 67
1.15 Voltage Regulation Transformers 68
1.16 Measurement Transformers 69
1.16.1 Current Transformers 69
1.16.2 Voltage Transformers 71
2 Direct Current Commutator Machines 73
2.1 Introduction 73
2.2 Construction of the DC Machine 74
2.2.1 Basic Construction - Operating Principle 74
2.2.2 Excitation 77
2.2.3 Armature 80
2.3 Electrical Power Conversion in a DC Machine 82
2.3.1 Voltage Induction (emf) 82
2.3.2 Torque 83
2.3.3 Electrical Power Conversion 84
2.4 Armature Reaction and the Compensation Winding 87
2.5 Commutation and the Commutation Poles 90
2.6 Steady-State Characteristics 94
2.6.1 Introduction - Per-Unit 94
2.6.2 Basic Characteristics and Derivation Methods 94
2.6.3 Generator Characteristics 97
2.6.4 Motor Characteristics 102
3 Rotating Field Machines: mmf, emf and Torque 109
3.1 Generation of a Rotating Field 109
3.1.1 Magnetic Field by (stator) Salient Poles with Concentrated Windings 109
3.1.2 Magnetic Field by Rotating Salient Poles with Concentrated Windings 111
3.1.3 Magnetic Field by a Distributed AC Winding 114
3.1.4 Magnetic Field by a Multiphase AC Winding 118
3.1.5 Current Layer - Linear Current Density 122
3.1.6 Discussion and Conclusions 126
3.2 Induced Voltage (Electromagnetic Force or emf) 128
3.2.1 Sinusoidal Rotating Field 128
3.2.2 Alternating Field 131
3.2.3 Non-sinusoidal Field 132
3.3 Magnetising Inductance of an Armature Winding 133
3.3.1 Single-Phase Winding 133
3.3.2 Multiphase Winding 134
3.4 Torque 135
3.4.1 General 135
3.4.2 Alternating Field and Alternating Current Layer 136
3.4.3 Rotating Field and Rotating Current Layer 137
4 The Induction Machine 140
4.1 Construction 140
4.2 Transformer Properties of the Induction Machine at Standstill 141
4.2.1 The Axes of Stator and Rotor Windings Are Co-linear 141
4.2.2 The Axes of Stator and Rotor Windings Are Displaced 145
4.2.3 Energy Conversion and Forces for an Induction Machine at Standstill 149
4.2.4 Applications of the Rotating Field Transformer 150
4.3 The Rotating Induction Machine: Operating Principle 150
4.3.1 Motoring 151
4.3.2 Generating 152
4.3.3 Frequency Converter 152
4.4 Equations and Equivalent Circuit of an Induction Machine 153
4.5 Energy Conversion and Torque 157
4.6 Torque and Torque-Slip Characteristic 160
4.7 The Current Locus of an Induction Machine 163
4.8 Per-Unit Description 168
4.9 Effect of s/r, x? and xm on Current and Torque 170
4.10 Scaling Laws - Rated Specific Values 175
4.11 Single-Phase and Two-Phase Induction Machines 176
4.11.1 Two-Phase Induction Machines 176
4.11.2 Single-Phase Induction Machines 177
5 The Synchronous Machine 187
5.1 Introduction - Construction 187
5.2 Smooth Rotor Synchronous Machines 190
5.2.1 Field Curve and No-Load Characteristic 190
5.2.2 Armature Reaction 192
5.2.3 Phasor Diagram of Voltages and Currents 196
5.2.4 Linearised Equivalent Circuit of a Smooth Rotor Synchronous Machine 199
5.2.5 Torque - Power - Energy Flow 203
5.2.6 Per-Unit Values 206
5.2.7 The Current Locus for Constant Excitation 207
5.2.8 Characteristics of Synchronous Machines 209
5.3 Salient-Pole Synchronous Machines 215
5.3.1 Emf Induced by a Salient-Pole Rotor with Concentrated DC Winding 215
5.3.2 Armature Reaction 217
5.3.3 Equations and Phasor Diagram of the Salient Pole Synchronous Machine 220
5.3.4 Equivalent Circuits for a Salient Pole Synchronous Machine 222
5.3.5 Torque, Power and Energy 224
5.3.6 Current Diagram 226
5.4 Synchronous Machines Connected to a Power Grid 227
5.5 Synchronous Motors 229
Part II Basics of Power Electronics 230
6 Power Electronic Components 231
6.1 Introduction 231
6.2 The Diode 232
6.3 The Thyristor 233
6.4 The Triac 236
6.5 The GTO 236
6.6 The IGCT 238
6.7 The BJT 238
6.8 The Mosfet 240
6.9 The IGBT 241
6.10 SiC and GaN Devices 242
6.11 Other Power Electronic Devices 244
6.12 Concluding Remarks 246
7 Rectifier 253
7.1 Introduction 253
7.2 Basic Theory of the Rectifier 253
7.2.1 Uncontrolled Diode Rectifier 253
7.2.2 Phase-Controlled Rectifier 259
7.2.3 Discontinuous Conduction Mode 261
7.2.4 Rectifier with a Capacitive Load 262
7.2.5 Non-ideal AC Source: Finite Commutation Duration 264
7.2.6 Power Exchange Between Rectifier and Grid 267
7.3 Rectifier Supply of DC Machines 279
7.3.1 Anti-parallel Connection 279
7.3.2 Cross Connection 281
8 DC Chopper 282
8.1 Basic Chopper Circuits 282
8.1.1 Step-Down Chopper (Buck Chopper) 282
8.1.2 Step-Up Chopper (Boost Chopper) 285
8.1.3 Mixed Step-Down and Step-Up Chopper Circuits 286
8.1.4 Resistance Chopping 286
8.2 Practical Switches for Choppers 287
8.3 Buffer Capacitor and Multiphase Chopping in Traction Applications 288
8.4 Chopper Supply of DC Machines 288
8.4.1 Motoring 288
8.4.2 Two-Quadrant Operation 289
8.5 Resonant Circuits for DC-DC Converters 290
8.5.1 Series-Loaded Half Bridge 290
8.5.2 Parallel-Loaded Resonant Converter 294
9 AC Chopper 295
9.1 Basic Principle 295
9.2 Phase Control of a Single-Phase Inductance 296
9.3 Phase Control of a Three-Phase Inductance 298
9.4 Phase Control of a General Load 303
10 Cycloconverter 304
10.1 Introduction 304
10.2 Operating Principle 305
10.3 Examples of Some Practical Cycloconverter Circuits 306
10.4 Control Methods 308
10.4.1 Sinusoidal Modulation (Open Loop) 308
10.4.2 Trapezoidal Modulation (Open Loop) 310
10.4.3 Closed-Loop Control 312
10.5 Cycloconverter Circuits with or Without Circulating Current 314
10.5.1 Cycloconverters with Free Circulating Current 314
10.5.2 Cycloconverters Without Circulating Current 315
10.6 Output Voltage Harmonic Content 317
10.7 Input Current Power Factor and Harmonic Content 319
11 Inverter 323
11.1 Single-Phase Inverter 323
11.2 Three-Phase Six-Step Inverters 325
11.2.1 The 120° Switching Sequence 325
11.2.2 The 180° Switching Sequence 327
11.2.3 The Six-Step Voltage Source Inverter (VSI) 328
11.2.4 The Six-Step Current Source Inverter (CSI) 332
11.3 PWM Inverters 335
11.3.1 Principle: Single-Phase PWM Inverters 335
11.3.2 Three-Phase PWM Inverters 337
11.3.3 PWM Modulation Principles 338
11.4 Space Vector Modulation 355
Part III Electrical Drives and Special Electric Machines 359
12 DC Commutator Motor Drives 360
12.1 Basic Characteristics of DC Motors 360
12.2 Torque-Speed Characteristics of Separately Excited or Shunt-Excited DC Motors 361
12.2.1 Basic Characteristics 361
12.2.2 Ward-Leonard Drive 362
12.3 Characteristics of Series-Excited DC Motors 364
12.3.1 Speed Control 364
12.3.2 Braking 365
12.3.3 Power-Electronic Supply of Series-Excited DC Motors 368
13 Constant Frequency Voltage Supply of Rotating Field Machines 370
13.1 Start-Up, Accelerating and Braking of Squirrel-Cage Induction Machines 370
13.1.1 Accelerating Time and Power Loss 370
13.1.2 Traditional Starting Methods for Cage Induction Machines 374
13.1.3 Braking of Induction Machines 376
13.2 Slip-Ring Induction Machines: Start-Up, Speed Control and Energy Recuperation 383
13.2.1 Start-Up of Slip-Ring Induction Machines 384
13.2.2 Speed Control of Slip-Ring Induction Machines Using Secondary Resistances 387
13.2.3 Speed Control of Slip-Ring Induction Machines by Means of Cascade Connections 389
13.3 Behaviour of Rotating Field Machines at Voltage Variations 395
13.3.1 Introduction 395
13.3.2 Induction Machines at Voltage Variations 396
13.3.3 Synchronous Machines at Voltage Variations 399
13.4 Power Electronic Starting and Voltage Adjustment of Rotating Field Machines to the Load 401
13.4.1 Introduction 401
13.4.2 Power Electronic Starting of Induction Machines 402
13.4.3 Power Electronic Voltage Adjustment to the Load 403
14 Ideal Current Supply of Rotating Field Machines 405
14.1 Current Supply of DC Commutator Machines 405
14.1.1 Individual Current Supply 405
14.1.2 Group Current Supply 406
14.2 Ideal Current Supply of Induction Machines 406
14.2.1 Current, Voltage and Torque Relations 406
14.2.2 Behaviour of the Induction Machine Neglecting Main Field Saturation 407
14.2.3 Behaviour of the Induction Machine Including Main Field Saturation 408
14.3 Ideal Current Supply of Synchronous Machines 412
14.3.1 Current, Voltage and Torque Relations 412
14.3.2 Behaviour of the Synchronous Machine Neglecting Main Field Saturation 416
14.3.3 Behaviour of the Synchronous Machine Including Main Field Saturation 417
15 Variable Frequency Voltage Supply of Rotating Field Machines 419
15.1 Introduction 419
15.2 Variable Frequency Supply of Induction Machines 420
15.3 Variable Frequency Supply of Synchronous Machines 424
16 Modelling of Inverter Supplied Rotating Field Machines 427
16.1 Fundamental Harmonic Models of VSI and CSI 427
16.1.1 Review of the Basic Inverter Schemes 427
16.1.2 Idealised Output Waveforms 430
16.1.3 Secondary Quantities 432
16.1.4 Fundamental Harmonic Equivalent Circuits 433
16.1.5 Discussion of the Equivalent Circuits 436
16.2 Inverter Supply of Induction Machines (Open Loop) 437
16.2.1 Induction Motor Supplied by a VSI or PWM-VSI 437
16.2.2 Induction Motor Fed by a CSI 439
16.3 Inverter Supply of Synchronous Machines 445
16.3.1 Introduction 445
16.3.2 CSI-Fed Synchronous Machine with Smooth Rotor 445
16.3.3 CSI-Fed Salient-Pole Synchronous Machines 451
16.4 Effect of the Commutation Delay 454
17 Basics of Controlled Electrical Drives 457
17.1 Introduction: DC Machine Analogy 457
17.2 V/f Control of Rotating Field Machines 458
17.2.1 Introduction 458
17.2.2 V/f Control of Induction Machines 458
17.2.3 V/f Control of Synchronous Machines 459
17.3 Vector Control of Rotating Field Machines 459
17.3.1 Principle 459
17.3.2 Vector Control and Field Orientation of Synchronous Machines 461
17.3.3 Vector Control and Field Orientation of Induction Machines 464
17.4 Other Torque Control Methods for Rotating Field Machines 467
18 Small Electric Machines and Their Power Electronic Control 473
18.1 Small DC Commutator Machines 473
18.1.1 Introduction 473
18.1.2 Series-Excited DC Machine 474
18.1.3 Permanent-Magnet Excited DC Machine 474
18.1.4 Power Electronic Supply of (Small) DC Machines 476
18.2 Small Induction Machines 478
18.2.1 Three- and Two-Phase Induction Machines 478
18.2.2 Single-Phase Induction Motors 478
18.2.3 Power-Electronic Supply of Small Induction Motors 479
18.3 Small Synchronous Machines and Their Power-Electronic Control 482
19 Single-Phase AC Commutator machines 486
19.1 Introduction 486
19.2 Motional EMF, Transformer EMF and Torque 486
19.2.1 Motional EMF 486
19.2.2 Transformer EMF 488
19.2.3 Torque 488
19.2.4 Commutation 490
19.3 The Single-Phase AC Commutator Motor (Universal Motor) 492
19.3.1 Introduction 492
19.3.2 Operating Characteristics 492
19.3.3 Remarks 495
19.4 Special Single-Phase Commutator Machines 496
19.4.1 The Repulsion Motor 496
19.4.2 The Déri Motor 499
20 Small Synchronous Motors 501
20.1 Synchronous Machines with Excitation by Permanent Magnets 501
20.1.1 Permanent Magnet Material 501
20.1.2 Rotor Configurations 504
20.1.3 Electromagnetic Behaviour and Torque of PM Motors 506
20.1.4 Axial Flux Permanent Magnet Motors 510
20.2 Reluctance Motors 514
20.2.1 Introduction 514
20.2.2 Current and Torque: Effect of the Stator Resistance 514
20.2.3 Design and Construction 515
20.3 Hysteresis Motors 520
20.3.1 Construction 520
20.3.2 Principle 521
20.3.3 Properties 525
20.3.4 Final Remarks 526
20.4 Small Motors for Special Applications 526
20.4.1 Impulse-Field Motor (Not Self Starting) 526
20.4.2 Self-starting Impulse-Field Motor 528
20.4.3 Other Single-Phase Synchronous Motors 528
20.5 Electrostatic Motors 529
20.5.1 Electrostatic Stepping Motor 530
20.5.2 Piezo-Electric Actuators 531
20.5.3 Ultrasonic Actuators and Motors 531
21 Stepping Motors 535
21.1 Introduction: Stepping Motion Versus Continuous Motion 535
21.2 Characteristic Quantities and Properties 536
21.2.1 Static Characteristics 536
21.2.2 Dynamic Characteristics 537
21.2.3 Eigen Frequency, Damping, Resonance 538
21.3 The Permanent Magnet Stepping Motor 539
21.4 The Variable-Reluctance Stepping Motor 540
21.5 Multi-stack Stepping Motors 543
21.6 Hybrid Stepping Motors 544
22 Switched Reluctance Machines 548
22.1 Operation Principle 548
22.2 Electromagnetic and Electrical Analysis 550
22.3 Converters for Switched Reluctance Machines 555
22.4 Control of an SRM 558
22.5 SRM Types and Applications 559
Part IV Dynamics of Electrical Machines and Drives 562
23 Stability and Dynamics 563
23.1 Introduction: Definition of Stability 563
23.2 Classifications of Stability 563
23.2.1 Stability of an Equilibrium Point 563
23.2.2 Input--Output Stability 564
23.3 Mathematical Tools to Explore the Stability of a System 565
24 Transient Phenomena in Simple Electrical Circuits 566
24.1 Switching On or Off a Resistive-Inductive Circuit 566
24.2 Single-Phase Transformer 568
24.3 Coil with Massive Iron Core 573
24.4 Quasi-stationary Modelling of Rotating Machines 577
25 Induction Machines with Pulsating Loads 578
25.1 Introduction 578
25.2 Quasi-stationary Analysis 579
25.3 Drive Dimensioning 583
26 Modelling and Dynamic Behaviour of DC Machines 586
26.1 Standard Dynamic Model of the DC Machine 586
26.1.1 Basic Assumptions and Equations 586
26.1.2 Per-Unit (pu) or Relative Description 588
26.1.3 Modelling of Saturation and Armature Reaction 588
26.2 Characteristic Dynamic Behaviour According to the Standard Model 591
26.3 Characteristic Dynamic Behaviour Taking into Account … 594
27 Modelling and Dynamic Behaviour of Induction Machines 599
27.1 Introduction: Modelling of Rotating Field Machines Without Saliency 599
27.2 The Standard Dynamic Model of an Induction Machine 600
27.2.1 Derivation of the Dynamic Model 600
27.2.2 Equations for Steady State and for Small Deviations Around an Equilibrium State 605
27.2.3 Dynamic Model with Pu Time and Speeds 606
27.2.4 Approximation for Saturation 607
27.3 Characteristic Dynamic Behaviour of the Induction Machine 608
27.3.1 Dynamic Model in Real Matrix Form 608
27.3.2 Dimensionless Parameters for Dynamic Analysis 609
27.3.3 Scaling Laws for the Dynamical Parameters 610
27.3.4 Block Diagrams and Characteristic Equation 611
27.3.5 Eigenvalue Analysis 613
27.3.6 Typical Dynamic Behaviour 620
27.4 Conclusions 630
28 Modelling and Dynamic Behaviour of Synchronous Machines 631
28.1 Introduction: Modelling of Rotating Field Machines with Saliency 631
28.2 The Standard Dynamic Model of a Synchronous Machine 633
28.2.1 Basic Assumptions and Equations 633
28.2.2 Equations for Sinusoidal Steady State and for Small Deviations Around Steady State 639
28.2.3 Reciprocity - pu or Absolute Modelling 639
28.2.4 Approximation for Saturation in Standard Modelling 644
28.3 Characteristic Dynamic Behaviour of Synchronous Machines 645
28.3.1 Dynamic Parameters 645
28.3.2 Block Diagram and Characteristic Equation 649
28.3.3 Gain 651
28.3.4 Eigenvalue Analysis of the Synchronous Machine 653
28.3.5 Eigenvalue Analysis of the Reluctance Motor 659
28.3.6 Eigenvalue Analysis of a Symmetrical Synchronous Machine 663
28.3.7 Modelling and Stability for Current Supply 666
28.4 Conclusions and Further Remarks 667
29 Dynamics in Vector Control and Field Orientation 669
29.1 Introduction 669
29.2 Torque Control of a DC Machine 669
29.3 Vector Control of a Synchronous Machine 671
29.3.1 Steady State 671
29.3.2 Dynamical Analysis 674
29.3.3 Practical Implementations 678
29.3.4 Vector Control and Field Orientation of Synchronous Machines: Conclusions 680
29.4 Vector Control of the Induction Machine 680
29.4.1 Introduction 680
29.4.2 Torque Control Based on underlineIs? and underlineIs? 683
29.4.3 Implementation of Field Orientation for the Induction Machine 687
29.4.4 Other Field Orientation Techniques for Induction Machines 693
30 Transient Phenomena in Electrical Machines 695
30.1 Introduction 695
30.2 Transients in Synchronous Machines at Constant Speed 696
30.2.1 Direct Transients 696
30.2.2 Zero-Sequence and Negative Sequence Transients 705
31 Voltage Surge Phenomena in Electrical Machines 709
31.1 Introduction 709
31.2 Voltage Surge Waves in a Single-Layer Coil 711
31.2.1 Simplified Theory Disregarding Mutual Coupling 711
31.2.2 Effect of the Mutual Coupling 717
31.2.3 Discussion of the Models 720
31.3 Surge Phenomena in Real Machines and Transformers 720
31.4 Protection Against Voltage Surges 721
Appendix A Terminal Markings and Markings of Windings 724
A.1 Markings for Three-Phase Transformers 724
A.2 Markings for Single-Phase Transformers 726
A.3 Markings and Rotation Direction of Rotating Electrical Machines 726
A.3.1 General Rules 726
A.3.2 Terminal Markings of Electric Machines 727
A.3.2.1 Markings for AC Machines (Except AC Commutator Machines) 727
A.3.2.2 DC Commutator Machines 728
A.3.3 Rotation Direction 729
A.3.4 Relation Between the Markings and the Rotation Direction 730
A.3.4.1 AC Machines 730
A.3.4.2 DC Commutator Machines 731
Appendix B Static Stability of a Drive 732
Appendix C Phasors and Space Vectors 734
C.1 General: Basic Definitions 734
C.2 Mathematical Extension 735
References 739