Melkebeek Electrical Machines and Drives

Fundamentals and Advanced Modelling
1. Auflage 2018
ISBN: 978-3-319-72730-1
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 740 Seiten

Reihe: Power Systems

This book aims to offer a thorough study and reference textbook on electrical machines and drives. The basic idea is to start from the pure electromagnetic principles to derive the equivalent circuits and steady-state equations of the most common electrical machines (in the first parts). Although the book mainly concentrates on rotating field machines, the first two chapters are devoted to transformers and DC commutator machines. The chapter on transformers is included as an introduction to induction and synchronous machines, their electromagnetics and equivalent circuits. Chapters three and four offer an in-depth study of induction and synchronous machines, respectively. Starting from their electromagnetics, steady-state equations and equivalent circuits are derived, from which their basic properties can be deduced. The second part discusses the main power-electronic supplies for electrical drives, for example rectifiers, choppers, cycloconverters and inverters. Much attention is paid to PWM techniques for inverters and the resulting harmonic content in the output waveform. In the third part, electrical drives are discussed, combining the traditional (rotating field and DC commutator) electrical machines treated in the first part and the power electronics of part two. Field orientation of induction and synchronous machines are discussed in detail, as well as direct torque control. In addition, also switched reluctance machines and stepping motors are discussed in the last chapters. Finally, part 4 is devoted to the dynamics of traditional electrical machines. Also for the dynamics of induction and synchronous machine drives, the electromagnetics are used as the starting point to derive the dynamic models. Throughout part 4, much attention is paid to the derivation of analytical models. But, of course, the basic dynamic properties and probable causes of instability of induction and synchronous machine drives are discussed in detail as well, with the derived models for stability in the small as starting point. In addition to the study of the stability in the small, a chapter is devoted to large-scale dynamics as well (e.g. sudden short-circuit of synchronous machines). The textbook is used as the course text for the Bachelor's and Master's programme in electrical and mechanical engineering at the Faculty of Engineering and Architecture of Ghent University. Parts 1 and 2 are taught in the basic course 'Fundamentals of Electric Drives' in the third bachelor. Part 3 is used for the course 'Controlled Electrical Drives' in the first master, while Part 4 is used in the specialised master on electrical energy.

Autoren/Hrsg.

Melkebeek, Jan A.

Inhaltsverzeichnis

1;Foreword;7
2;Preface;8
3;Acknowledgements;11
4;Contents;12
5;Symbols and Conventions;24
5.1;General;24
5.2;Symbols;24
5.3;Greek symbols;25
5.4;Subscripts;26
6;Part I Transformers and Electrical Machines;27
7;1 Transformers;28
7.1;1.1 Introduction;28
7.2;1.2 Transformer Equations;29
7.2.1;1.2.1 Basic Electromagnetic Description and Equations;29
7.2.2;1.2.2 Phasor Equations and Equivalent Circuit for Sinusoidal Supply;33
7.3;1.3 Referred Values: Equations and Equivalent Circuit;35
7.4;1.4 Per-Unit Description;36
7.5;1.5 Construction and Scaling Laws;36
7.5.1;1.5.1 Specific Rated Quantities;37
7.5.2;1.5.2 Rated Per-Unit Impedances;38
7.6;1.6 Alternative and Simplified Equivalent Circuits;44
7.7;1.7 No-Load Operation;46
7.8;1.8 Short-Circuit Operation;47
7.8.1;1.8.1 Short-Circuit Impedance;47
7.8.2;1.8.2 Procentual Short-Circuit Voltage;48
7.8.3;1.8.3 Remarks;48
7.9;1.9 Voltage Variation with Load;49
7.10;1.10 Parallel Operation of Transformers;51
7.11;1.11 Construction of Single-Phase and Three-Phase Transformers;54
7.11.1;1.11.1 Single-Phase Transformers;54
7.11.2;1.11.2 Three-Phase Transformers;54
7.12;1.12 Connection and Vector Group of a Three-Phase Transformer;58
7.12.1;1.12.1 Winding and Terminal Markings;58
7.12.2;1.12.2 Modelling of a Three-Phase Transformer;58
7.12.3;1.12.3 Connections and Vector Groups;59
7.12.4;1.12.4 Asymmetrical Operation of 3-Phase Transformers;60
7.13;1.13 Autotransformer;64
7.14;1.14 Phase-Number Transformation;66
7.14.1;1.14.1 Three to Six or Twelve Phases;66
7.14.2;1.14.2 Three to Two Phases;67
7.15;1.15 Voltage Regulation Transformers;68
7.16;1.16 Measurement Transformers;69
7.16.1;1.16.1 Current Transformers;69
7.16.2;1.16.2 Voltage Transformers;71
8;2 Direct Current Commutator Machines;73
8.1;2.1 Introduction;73
8.2;2.2 Construction of the DC Machine;74
8.2.1;2.2.1 Basic Construction - Operating Principle;74
8.2.2;2.2.2 Excitation;77
8.2.3;2.2.3 Armature;80
8.3;2.3 Electrical Power Conversion in a DC Machine;82
8.3.1;2.3.1 Voltage Induction (emf);82
8.3.2;2.3.2 Torque;83
8.3.3;2.3.3 Electrical Power Conversion;84
8.4;2.4 Armature Reaction and the Compensation Winding;87
8.5;2.5 Commutation and the Commutation Poles;90
8.6;2.6 Steady-State Characteristics;94
8.6.1;2.6.1 Introduction - Per-Unit;94
8.6.2;2.6.2 Basic Characteristics and Derivation Methods;94
8.6.3;2.6.3 Generator Characteristics;97
8.6.4;2.6.4 Motor Characteristics;102
9;3 Rotating Field Machines: mmf, emf and Torque;109
9.1;3.1 Generation of a Rotating Field;109
9.1.1;3.1.1 Magnetic Field by (stator) Salient Poles with Concentrated Windings;109
9.1.2;3.1.2 Magnetic Field by Rotating Salient Poles with Concentrated Windings;111
9.1.3;3.1.3 Magnetic Field by a Distributed AC Winding;114
9.1.4;3.1.4 Magnetic Field by a Multiphase AC Winding;118
9.1.5;3.1.5 Current Layer - Linear Current Density;122
9.1.6;3.1.6 Discussion and Conclusions;126
9.2;3.2 Induced Voltage (Electromagnetic Force or emf);128
9.2.1;3.2.1 Sinusoidal Rotating Field;128
9.2.2;3.2.2 Alternating Field;131
9.2.3;3.2.3 Non-sinusoidal Field;132
9.3;3.3 Magnetising Inductance of an Armature Winding;133
9.3.1;3.3.1 Single-Phase Winding;133
9.3.2;3.3.2 Multiphase Winding;134
9.4;3.4 Torque;135
9.4.1;3.4.1 General;135
9.4.2;3.4.2 Alternating Field and Alternating Current Layer;136
9.4.3;3.4.3 Rotating Field and Rotating Current Layer;137
10;4 The Induction Machine;140
10.1;4.1 Construction;140
10.2;4.2 Transformer Properties of the Induction Machine at Standstill;141
10.2.1;4.2.1 The Axes of Stator and Rotor Windings Are Co-linear;141
10.2.2;4.2.2 The Axes of Stator and Rotor Windings Are Displaced;145
10.2.3;4.2.3 Energy Conversion and Forces for an Induction Machine at Standstill;149
10.2.4;4.2.4 Applications of the Rotating Field Transformer;150
10.3;4.3 The Rotating Induction Machine: Operating Principle;150
10.3.1;4.3.1 Motoring;151
10.3.2;4.3.2 Generating;152
10.3.3;4.3.3 Frequency Converter;152
10.4;4.4 Equations and Equivalent Circuit of an Induction Machine;153
10.5;4.5 Energy Conversion and Torque;157
10.6;4.6 Torque and Torque-Slip Characteristic;160
10.7;4.7 The Current Locus of an Induction Machine;163
10.8;4.8 Per-Unit Description;168
10.9;4.9 Effect of s/r, x? and xm on Current and Torque;170
10.10;4.10 Scaling Laws - Rated Specific Values;175
10.11;4.11 Single-Phase and Two-Phase Induction Machines;176
10.11.1;4.11.1 Two-Phase Induction Machines;176
10.11.2;4.11.2 Single-Phase Induction Machines;177
11;5 The Synchronous Machine;187
11.1;5.1 Introduction - Construction;187
11.2;5.2 Smooth Rotor Synchronous Machines;190
11.2.1;5.2.1 Field Curve and No-Load Characteristic;190
11.2.2;5.2.2 Armature Reaction;192
11.2.3;5.2.3 Phasor Diagram of Voltages and Currents;196
11.2.4;5.2.4 Linearised Equivalent Circuit of a Smooth Rotor Synchronous Machine;199
11.2.5;5.2.5 Torque - Power - Energy Flow;203
11.2.6;5.2.6 Per-Unit Values;206
11.2.7;5.2.7 The Current Locus for Constant Excitation;207
11.2.8;5.2.8 Characteristics of Synchronous Machines;209
11.3;5.3 Salient-Pole Synchronous Machines;215
11.3.1;5.3.1 Emf Induced by a Salient-Pole Rotor with Concentrated DC Winding;215
11.3.2;5.3.2 Armature Reaction;217
11.3.3;5.3.3 Equations and Phasor Diagram of the Salient Pole Synchronous Machine;220
11.3.4;5.3.4 Equivalent Circuits for a Salient Pole Synchronous Machine;222
11.3.5;5.3.5 Torque, Power and Energy;224
11.3.6;5.3.6 Current Diagram;226
11.4;5.4 Synchronous Machines Connected to a Power Grid;227
11.5;5.5 Synchronous Motors;229
12;Part II Basics of Power Electronics;230
13;6 Power Electronic Components;231
13.1;6.1 Introduction;231
13.2;6.2 The Diode;232
13.3;6.3 The Thyristor;233
13.4;6.4 The Triac;236
13.5;6.5 The GTO;236
13.6;6.6 The IGCT;238
13.7;6.7 The BJT;238
13.8;6.8 The Mosfet;240
13.9;6.9 The IGBT;241
13.10;6.10 SiC and GaN Devices;242
13.11;6.11 Other Power Electronic Devices;244
13.12;6.12 Concluding Remarks;246
14;7 Rectifier;253
14.1;7.1 Introduction;253
14.2;7.2 Basic Theory of the Rectifier;253
14.2.1;7.2.1 Uncontrolled Diode Rectifier;253
14.2.2;7.2.2 Phase-Controlled Rectifier;259
14.2.3;7.2.3 Discontinuous Conduction Mode;261
14.2.4;7.2.4 Rectifier with a Capacitive Load;262
14.2.5;7.2.5 Non-ideal AC Source: Finite Commutation Duration;264
14.2.6;7.2.6 Power Exchange Between Rectifier and Grid;267
14.3;7.3 Rectifier Supply of DC Machines;279
14.3.1;7.3.1 Anti-parallel Connection;279
14.3.2;7.3.2 Cross Connection;281
15;8 DC Chopper;282
15.1;8.1 Basic Chopper Circuits;282
15.1.1;8.1.1 Step-Down Chopper (Buck Chopper);282
15.1.2;8.1.2 Step-Up Chopper (Boost Chopper);285
15.1.3;8.1.3 Mixed Step-Down and Step-Up Chopper Circuits;286
15.1.4;8.1.4 Resistance Chopping;286
15.2;8.2 Practical Switches for Choppers;287
15.3;8.3 Buffer Capacitor and Multiphase Chopping in Traction Applications;288
15.4;8.4 Chopper Supply of DC Machines;288
15.4.1;8.4.1 Motoring;288
15.4.2;8.4.2 Two-Quadrant Operation;289
15.5;8.5 Resonant Circuits for DC-DC Converters;290
15.5.1;8.5.1 Series-Loaded Half Bridge;290
15.5.2;8.5.2 Parallel-Loaded Resonant Converter;294
16;9 AC Chopper;295
16.1;9.1 Basic Principle;295
16.2;9.2 Phase Control of a Single-Phase Inductance;296
16.3;9.3 Phase Control of a Three-Phase Inductance;298
16.4;9.4 Phase Control of a General Load;303
17;10 Cycloconverter;304
17.1;10.1 Introduction;304
17.2;10.2 Operating Principle;305
17.3;10.3 Examples of Some Practical Cycloconverter Circuits;306
17.4;10.4 Control Methods;308
17.4.1;10.4.1 Sinusoidal Modulation (Open Loop);308
17.4.2;10.4.2 Trapezoidal Modulation (Open Loop);310
17.4.3;10.4.3 Closed-Loop Control;312
17.5;10.5 Cycloconverter Circuits with or Without Circulating Current;314
17.5.1;10.5.1 Cycloconverters with Free Circulating Current;314
17.5.2;10.5.2 Cycloconverters Without Circulating Current;315
17.6;10.6 Output Voltage Harmonic Content;317
17.7;10.7 Input Current Power Factor and Harmonic Content;319
18;11 Inverter;323
18.1;11.1 Single-Phase Inverter;323
18.2;11.2 Three-Phase Six-Step Inverters;325
18.2.1;11.2.1 The 120° Switching Sequence;325
18.2.2;11.2.2 The 180° Switching Sequence;327
18.2.3;11.2.3 The Six-Step Voltage Source Inverter (VSI);328
18.2.4;11.2.4 The Six-Step Current Source Inverter (CSI);332
18.3;11.3 PWM Inverters;335
18.3.1;11.3.1 Principle: Single-Phase PWM Inverters;335
18.3.2;11.3.2 Three-Phase PWM Inverters;337
18.3.3;11.3.3 PWM Modulation Principles;338
18.4;11.4 Space Vector Modulation;355
19;Part III Electrical Drives and Special Electric Machines;359
20;12 DC Commutator Motor Drives;360
20.1;12.1 Basic Characteristics of DC Motors;360
20.2;12.2 Torque-Speed Characteristics of Separately Excited or Shunt-Excited DC Motors;361
20.2.1;12.2.1 Basic Characteristics;361
20.2.2;12.2.2 Ward-Leonard Drive;362
20.3;12.3 Characteristics of Series-Excited DC Motors;364
20.3.1;12.3.1 Speed Control;364
20.3.2;12.3.2 Braking;365
20.3.3;12.3.3 Power-Electronic Supply of Series-Excited DC Motors;368
21;13 Constant Frequency Voltage Supply of Rotating Field Machines;370
21.1;13.1 Start-Up, Accelerating and Braking of Squirrel-Cage Induction Machines;370
21.1.1;13.1.1 Accelerating Time and Power Loss;370
21.1.2;13.1.2 Traditional Starting Methods for Cage Induction Machines;374
21.1.3;13.1.3 Braking of Induction Machines;376
21.2;13.2 Slip-Ring Induction Machines: Start-Up, Speed Control and Energy Recuperation;383
21.2.1;13.2.1 Start-Up of Slip-Ring Induction Machines;384
21.2.2;13.2.2 Speed Control of Slip-Ring Induction Machines Using Secondary Resistances;387
21.2.3;13.2.3 Speed Control of Slip-Ring Induction Machines by Means of Cascade Connections;389
21.3;13.3 Behaviour of Rotating Field Machines at Voltage Variations;395
21.3.1;13.3.1 Introduction;395
21.3.2;13.3.2 Induction Machines at Voltage Variations;396
21.3.3;13.3.3 Synchronous Machines at Voltage Variations;399
21.4;13.4 Power Electronic Starting and Voltage Adjustment of Rotating Field Machines to the Load;401
21.4.1;13.4.1 Introduction;401
21.4.2;13.4.2 Power Electronic Starting of Induction Machines;402
21.4.3;13.4.3 Power Electronic Voltage Adjustment to the Load;403
22;14 Ideal Current Supply of Rotating Field Machines;405
22.1;14.1 Current Supply of DC Commutator Machines;405
22.1.1;14.1.1 Individual Current Supply;405
22.1.2;14.1.2 Group Current Supply;406
22.2;14.2 Ideal Current Supply of Induction Machines;406
22.2.1;14.2.1 Current, Voltage and Torque Relations;406
22.2.2;14.2.2 Behaviour of the Induction Machine Neglecting Main Field Saturation;407
22.2.3;14.2.3 Behaviour of the Induction Machine Including Main Field Saturation;408
22.3;14.3 Ideal Current Supply of Synchronous Machines;412
22.3.1;14.3.1 Current, Voltage and Torque Relations;412
22.3.2;14.3.2 Behaviour of the Synchronous Machine Neglecting Main Field Saturation;416
22.3.3;14.3.3 Behaviour of the Synchronous Machine Including Main Field Saturation;417
23;15 Variable Frequency Voltage Supply of Rotating Field Machines;419
23.1;15.1 Introduction;419
23.2;15.2 Variable Frequency Supply of Induction Machines;420
23.3;15.3 Variable Frequency Supply of Synchronous Machines;424
24;16 Modelling of Inverter Supplied Rotating Field Machines;427
24.1;16.1 Fundamental Harmonic Models of VSI and CSI;427
24.1.1;16.1.1 Review of the Basic Inverter Schemes;427
24.1.2;16.1.2 Idealised Output Waveforms;430
24.1.3;16.1.3 Secondary Quantities;432
24.1.4;16.1.4 Fundamental Harmonic Equivalent Circuits;433
24.1.5;16.1.5 Discussion of the Equivalent Circuits;436
24.2;16.2 Inverter Supply of Induction Machines (Open Loop);437
24.2.1;16.2.1 Induction Motor Supplied by a VSI or PWM-VSI;437
24.2.2;16.2.2 Induction Motor Fed by a CSI;439
24.3;16.3 Inverter Supply of Synchronous Machines;445
24.3.1;16.3.1 Introduction;445
24.3.2;16.3.2 CSI-Fed Synchronous Machine with Smooth Rotor;445
24.3.3;16.3.3 CSI-Fed Salient-Pole Synchronous Machines;451
24.4;16.4 Effect of the Commutation Delay;454
25;17 Basics of Controlled Electrical Drives;457
25.1;17.1 Introduction: DC Machine Analogy;457
25.2;17.2 V/f Control of Rotating Field Machines;458
25.2.1;17.2.1 Introduction;458
25.2.2;17.2.2 V/f Control of Induction Machines;458
25.2.3;17.2.3 V/f Control of Synchronous Machines;459
25.3;17.3 Vector Control of Rotating Field Machines;459
25.3.1;17.3.1 Principle;459
25.3.2;17.3.2 Vector Control and Field Orientation of Synchronous Machines;461
25.3.3;17.3.3 Vector Control and Field Orientation of Induction Machines;464
25.4;17.4 Other Torque Control Methods for Rotating Field Machines;467
26;18 Small Electric Machines and Their Power Electronic Control;473
26.1;18.1 Small DC Commutator Machines;473
26.1.1;18.1.1 Introduction;473
26.1.2;18.1.2 Series-Excited DC Machine;474
26.1.3;18.1.3 Permanent-Magnet Excited DC Machine;474
26.1.4;18.1.4 Power Electronic Supply of (Small) DC Machines;476
26.2;18.2 Small Induction Machines;478
26.2.1;18.2.1 Three- and Two-Phase Induction Machines;478
26.2.2;18.2.2 Single-Phase Induction Motors;478
26.2.3;18.2.3 Power-Electronic Supply of Small Induction Motors;479
26.3;18.3 Small Synchronous Machines and Their Power-Electronic Control;482
27;19 Single-Phase AC Commutator machines;486
27.1;19.1 Introduction;486
27.2;19.2 Motional EMF, Transformer EMF and Torque;486
27.2.1;19.2.1 Motional EMF;486
27.2.2;19.2.2 Transformer EMF;488
27.2.3;19.2.3 Torque;488
27.2.4;19.2.4 Commutation;490
27.3;19.3 The Single-Phase AC Commutator Motor (Universal Motor);492
27.3.1;19.3.1 Introduction;492
27.3.2;19.3.2 Operating Characteristics;492
27.3.3;19.3.3 Remarks;495
27.4;19.4 Special Single-Phase Commutator Machines;496
27.4.1;19.4.1 The Repulsion Motor;496
27.4.2;19.4.2 The Déri Motor;499
28;20 Small Synchronous Motors;501
28.1;20.1 Synchronous Machines with Excitation by Permanent Magnets;501
28.1.1;20.1.1 Permanent Magnet Material;501
28.1.2;20.1.2 Rotor Configurations;504
28.1.3;20.1.3 Electromagnetic Behaviour and Torque of PM Motors;506
28.1.4;20.1.4 Axial Flux Permanent Magnet Motors;510
28.2;20.2 Reluctance Motors;514
28.2.1;20.2.1 Introduction;514
28.2.2;20.2.2 Current and Torque: Effect of the Stator Resistance;514
28.2.3;20.2.3 Design and Construction;515
28.3;20.3 Hysteresis Motors;520
28.3.1;20.3.1 Construction;520
28.3.2;20.3.2 Principle;521
28.3.3;20.3.3 Properties;525
28.3.4;20.3.4 Final Remarks;526
28.4;20.4 Small Motors for Special Applications;526
28.4.1;20.4.1 Impulse-Field Motor (Not Self Starting);526
28.4.2;20.4.2 Self-starting Impulse-Field Motor;528
28.4.3;20.4.3 Other Single-Phase Synchronous Motors;528
28.5;20.5 Electrostatic Motors;529
28.5.1;20.5.1 Electrostatic Stepping Motor;530
28.5.2;20.5.2 Piezo-Electric Actuators;531
28.5.3;20.5.3 Ultrasonic Actuators and Motors;531
29;21 Stepping Motors;535
29.1;21.1 Introduction: Stepping Motion Versus Continuous Motion;535
29.2;21.2 Characteristic Quantities and Properties;536
29.2.1;21.2.1 Static Characteristics;536
29.2.2;21.2.2 Dynamic Characteristics;537
29.2.3;21.2.3 Eigen Frequency, Damping, Resonance;538
29.3;21.3 The Permanent Magnet Stepping Motor;539
29.4;21.4 The Variable-Reluctance Stepping Motor;540
29.5;21.5 Multi-stack Stepping Motors;543
29.6;21.6 Hybrid Stepping Motors;544
30;22 Switched Reluctance Machines;548
30.1;22.1 Operation Principle;548
30.2;22.2 Electromagnetic and Electrical Analysis;550
30.3;22.3 Converters for Switched Reluctance Machines;555
30.4;22.4 Control of an SRM;558
30.5;22.5 SRM Types and Applications;559
31;Part IV Dynamics of Electrical Machines and Drives;562
32;23 Stability and Dynamics;563
32.1;23.1 Introduction: Definition of Stability;563
32.2;23.2 Classifications of Stability;563
32.2.1;23.2.1 Stability of an Equilibrium Point;563
32.2.2;23.2.2 Input--Output Stability;564
32.3;23.3 Mathematical Tools to Explore the Stability of a System;565
33;24 Transient Phenomena in Simple Electrical Circuits;566
33.1;24.1 Switching On or Off a Resistive-Inductive Circuit;566
33.2;24.2 Single-Phase Transformer;568
33.3;24.3 Coil with Massive Iron Core;573
33.4;24.4 Quasi-stationary Modelling of Rotating Machines;577
34;25 Induction Machines with Pulsating Loads;578
34.1;25.1 Introduction;578
34.2;25.2 Quasi-stationary Analysis;579
34.3;25.3 Drive Dimensioning;583
35;26 Modelling and Dynamic Behaviour of DC Machines;586
35.1;26.1 Standard Dynamic Model of the DC Machine;586
35.1.1;26.1.1 Basic Assumptions and Equations;586
35.1.2;26.1.2 Per-Unit (pu) or Relative Description;588
35.1.3;26.1.3 Modelling of Saturation and Armature Reaction;588
35.2;26.2 Characteristic Dynamic Behaviour According to the Standard Model;591
35.3;26.3 Characteristic Dynamic Behaviour Taking into Account …;594
36;27 Modelling and Dynamic Behaviour of Induction Machines;599
36.1;27.1 Introduction: Modelling of Rotating Field Machines Without Saliency;599
36.2;27.2 The Standard Dynamic Model of an Induction Machine;600
36.2.1;27.2.1 Derivation of the Dynamic Model;600
36.2.2;27.2.2 Equations for Steady State and for Small Deviations Around an Equilibrium State;605
36.2.3;27.2.3 Dynamic Model with Pu Time and Speeds;606
36.2.4;27.2.4 Approximation for Saturation;607
36.3;27.3 Characteristic Dynamic Behaviour of the Induction Machine;608
36.3.1;27.3.1 Dynamic Model in Real Matrix Form;608
36.3.2;27.3.2 Dimensionless Parameters for Dynamic Analysis;609
36.3.3;27.3.3 Scaling Laws for the Dynamical Parameters;610
36.3.4;27.3.4 Block Diagrams and Characteristic Equation;611
36.3.5;27.3.5 Eigenvalue Analysis;613
36.3.6;27.3.6 Typical Dynamic Behaviour;620
36.4;27.4 Conclusions;630
37;28 Modelling and Dynamic Behaviour of Synchronous Machines;631
37.1;28.1 Introduction: Modelling of Rotating Field Machines with Saliency;631
37.2;28.2 The Standard Dynamic Model of a Synchronous Machine;633
37.2.1;28.2.1 Basic Assumptions and Equations;633
37.2.2;28.2.2 Equations for Sinusoidal Steady State and for Small Deviations Around Steady State;639
37.2.3;28.2.3 Reciprocity - pu or Absolute Modelling;639
37.2.4;28.2.4 Approximation for Saturation in Standard Modelling;644
37.3;28.3 Characteristic Dynamic Behaviour of Synchronous Machines;645
37.3.1;28.3.1 Dynamic Parameters;645
37.3.2;28.3.2 Block Diagram and Characteristic Equation;649
37.3.3;28.3.3 Gain;651
37.3.4;28.3.4 Eigenvalue Analysis of the Synchronous Machine;653
37.3.5;28.3.5 Eigenvalue Analysis of the Reluctance Motor;659
37.3.6;28.3.6 Eigenvalue Analysis of a Symmetrical Synchronous Machine;663
37.3.7;28.3.7 Modelling and Stability for Current Supply;666
37.4;28.4 Conclusions and Further Remarks;667
38;29 Dynamics in Vector Control and Field Orientation;669
38.1;29.1 Introduction;669
38.2;29.2 Torque Control of a DC Machine;669
38.3;29.3 Vector Control of a Synchronous Machine;671
38.3.1;29.3.1 Steady State;671
38.3.2;29.3.2 Dynamical Analysis;674
38.3.3;29.3.3 Practical Implementations;678
38.3.4;29.3.4 Vector Control and Field Orientation of Synchronous Machines: Conclusions;680
38.4;29.4 Vector Control of the Induction Machine;680
38.4.1;29.4.1 Introduction;680
38.4.2;29.4.2 Torque Control Based on underlineIs? and underlineIs?;683
38.4.3;29.4.3 Implementation of Field Orientation for the Induction Machine;687
38.4.4;29.4.4 Other Field Orientation Techniques for Induction Machines;693
39;30 Transient Phenomena in Electrical Machines;695
39.1;30.1 Introduction;695
39.2;30.2 Transients in Synchronous Machines at Constant Speed;696
39.2.1;30.2.1 Direct Transients;696
39.2.2;30.2.2 Zero-Sequence and Negative Sequence Transients;705
40;31 Voltage Surge Phenomena in Electrical Machines;709
40.1;31.1 Introduction;709
40.2;31.2 Voltage Surge Waves in a Single-Layer Coil;711
40.2.1;31.2.1 Simplified Theory Disregarding Mutual Coupling;711
40.2.2;31.2.2 Effect of the Mutual Coupling;717
40.2.3;31.2.3 Discussion of the Models;720
40.3;31.3 Surge Phenomena in Real Machines and Transformers;720
40.4;31.4 Protection Against Voltage Surges;721
41;Appendix A Terminal Markings and Markings of Windings;724
41.1;A.1 Markings for Three-Phase Transformers;724
41.2;A.2 Markings for Single-Phase Transformers;726
41.3;A.3 Markings and Rotation Direction of Rotating Electrical Machines;726
41.4;A.3.1 General Rules;726
41.5;A.3.2 Terminal Markings of Electric Machines;727
41.6;A.3.2.1 Markings for AC Machines (Except AC Commutator Machines);727
41.7;A.3.2.2 DC Commutator Machines;728
41.8;A.3.3 Rotation Direction;729
41.9;A.3.4 Relation Between the Markings and the Rotation Direction;730
41.10;A.3.4.1 AC Machines;730
41.11;A.3.4.2 DC Commutator Machines;731
42;Appendix B Static Stability of a Drive;732
43;Appendix C Phasors and Space Vectors;734
43.1;C.1 General: Basic Definitions;734
43.2;C.2 Mathematical Extension;735
44;References;739