Contents

Preface xiii

1 INTRODUCTION 1

1.1 On Modeling in General 11.2 Modeling Power Components 31.3 Tools for Dynamic Simulation 4

- 2 INTRODUCTION TO MATLAB/SIMULlNK 6

2.1 Introd uction 62.2 CD-ROM Files 72.3 Getting to SIMULlNK 72.4 Creating a SIMULlNK Simulation 72.5 Choosing an Integration Method 92.6 Starting and Running a Simulation 12

2.6.1 Viewing Variables During a Run 122.7 Printing 13

2.7.1 Printing a Figure 132.7.2 Saving Data 13

v

2.82.92.102.11

2.7.3 PlottingExercise 1: Variable-frequency OscillatorExercise 2: Parallel RLC CircuitExercise 3: ac Energization of an RL CircuitExercise 4: Series RLC Resonant Circuit

3.1 Introduction3.2 Magnetic Materials

3.2.1 BH Characteristics 01Ferromagnetic Materials3.2.2 Magnetic Circuits

3.3 Energy Conversion3.3.1 ac Excitations

3.4 Permanent Magnets3.4.1 Permanent Magnet Materials3.4.2 Equivalent Magnetic Circuits

3.5 Line Parameters3.5.1 Resistance3.5.2 1nductance3.5.3 Self- and Mutual1nductances 01 Circuits with Ground3.5.4 Geometric Mean Radius and Distance3.5.5 Transposition 01Line Conductors3.5.6 Capacitance3.5.7 Self- and Mutual Capacitance 01 a Conductor Group3.5.8 The Presence 01 Ground

3.6 Lumped Parameter Circuit Models3.6.1 Series RL and Nominal1T Circuit Models3.6.2 ABCD Transmission Matrix

3.7 Distributed Parameter Model3.7.1 The Bewley Lattice Diagram3.7.2 Equivalent 1TModel3.7.3 Terminations and Junctions

3.8 Simulation of a Single-phase Line3.9 Projects

3.9.1 Project 1: Line Parameters and Circuit Models3.9.2 Project 2: Switching Transients in a Single-phase Line

4.14.24.3

IntroductionIdeal TransformerModel of a Two-winding Transformer4.3.1 Flux Linkage Equations4.3.2 Voltage Equations4.3.3 Equivalent Circuit Representation

4.4 Simulation of a Two-winding Transformer4.5 Terminal Conditions4.6 Incorporating Core Saturation into Simulation

4.6.1 1nstantaneous Value Saturatíon Curve4.7 Three-phase Connections

4.7.1 Wye-Wye Connectíon4.7.2 Delta- Wye Connectíon

4.8 Projects4.8.1 Project 1: Short-círcuít and RL Load Termínatíons4.8.2 Project 2: Open-círcuít Termínatíon, 1n-rush Current.

and dc Bías Core Saturatíon4.8.3 Projeet 3: Autotransformer Connectíon4.8.4 Projeet 4: Delta- Wye Transformer

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5.1 Introduction5.2 Electrical Radians and Synchronous Speed5.3 Flux Per Pole and Induced Voltage

5.3.1 RMS Value ofthe Induced Voltage5.3.2 Dístríbutíon Factor5.3.3 Pítch Factor

5.4 Spatial mmf Distribution of a Winding5.4.1 The Effect of Dístríbutíng the Phase Coils5.4.2 The Effect of Short-pitchíng

5.5 Winding Inductances5.6 Rotating Fields5.7 Developed Torque of a Uniform Airgap Machine5.8 Three-phase Transformations

5.8.1 Clarke's Transformatíon5.8.2 Park's Transformatíon

5.9 qdO Transformation Applied to Line Elements5.9.1 qdO Transformatíon to Se ríes RL5.9.2 qdO Transformatíon to Shunt Capacitances

5.10 Space Vectors and Transformations5.10.1 Transformatíon between abc and Statíonary qdO5.10.2 Transformatíon between abc and Rotatíng qdO

5.11 Projects5.ll.1 Projeet 1: qdO Transformatíon ofNetwork Components5.11.2 Project 2: Space Vectors5.ll.3 Project 3: Sínusoídal and Complex Quantítíes ín qdO

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Introduction6.1.1 Constructíon ofThree-phase Inductíon Machínes

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viii Contents

6.2 Rotating Magnetic Field and Slip 1696.3 Circuit Model of a Three-phase Induction Machine 170

6.3.1 Voltage Equations 1706.4 Machine Model in Arbitrary qdO Reference Frame 172

6.4.1 qdO Voltage Equations 1746.4.2 qdO Flux Linkage Relation 1756.4.3 qdO Torque Equation 177

6.5 qdO Stationary and Synchronous Reference Frames 1806.6 Steady-State Model 1836.7 Transient Model 1926.8 Simulation of an Induction Machine in the Stationary

Reference Frame 1966.8.1 Saturation of Mutual Flux 202

6.9 Linearized Model 2046.10 Single-phase Induction Motor 2146.11 Projects 224

6.11.1 Project 1.; Operating Characteristics 2246.11.2 Project 2: Starting Methods 2296.11.3 Project 3: Open-circuit Conditions 2336.]].4 Project 4: Linearized Analysis 2366.11.5 Project 5: Some Non-zero vsg Conditions 2396.11.6 Project 6: Single-phase 1nduction Motor 243

7 SYNCHRONOUS MACHINES 2597.1 Introduction 2597.2 Mathematical Model 262

7.2.1 Transformation to the Rotor's qdO Reference Frame 2647.2.2 Flux Linkages in Terms ofWinding Currents 2667.2.3 Referring Rotor Quantities to the Stator 2677.2.4 Voltage Equations in the Rotor's qdO Reference Frame 2697.2.5 Electromagnetic Torque 270

7.3 Currents in Terms of Flux Linkages 2727.4 Steady-state Operation 273

7.4.1 Steady-state Equations of the Stator 2747.4.2 Locating the Rotor's q,-axis 2757.4.3 Time Phasors and Space Vectors 2767.4.4 Steady-state Torque Expression 2777.4.5 Phasor and Space Vector Diagrams 278

7.5 Simulation of Three-phase Synchronous Machines 2787.5.1 Torque Expression 2837.5.2 Equation of Motion ofthe Rotor Assembly 2837.5.3 Per-unit Expressions for Torque and the Equation of Motion 284

7.6 Machine Parameters 2937.6.1 Synchronous 1nductances 2947.6.2 Transient Inductances 296

7.6.3 Transient Flux Linkages and Voltages behind the TransientInductances

7.6.4 Sub-transient Inductances7.6.5 Sub-transient Flux Linkages and Voltages Behind

the Sub-transient Inductances7.6.6 Transient Time Constants7.6.7 Sub-transient Time ConstantsCalculating Machine Parameters7.7.1 Sample CalculationHigher-order Models7.8.1 Equations lor SimulationPermanent Magnet Synchronous MotorsSynchronous Machine Projects7.10.1 Project 1: Operating Characteristics and Parameter Variations7.10.2 Project 2: Terminal Faults on a Synchronous Generator7.10.3 Project 3: Linearized Analysis 01a Synchronous Generator7.10.4 Project 4: Permanent Magnet Synchronous Motor7.10.5 Project 5: Simulation 01 Synchronous Machine Model with

Unequal Stator and Rotar Mutual and Coupling 01Rotor Circuits7.10.6 Project 6: Six-phase Synchronous Machine

7.97.10

Introd uctionArmature Windings8.2.1 Lap Windings8.2.2 Wave Windings8.2.3 Equipotential ConnectorsField ExcitationInduced Voltage of the Armature WindingElectromagnetic TorqueArmature ReactionCommutation8.7.1 Interpoles8.7.2 Compensating WindingsModes of Operation8.8.1 Motoring8.8.2 GeneratingFeasible Torque-speed RegionBrakingSpeed Control8.11.1 Speed Control by Varying Circuit Resistance8.11.2 Speed Control by Varying Excitation Flux8.11.3 Speed Control by Varying Applied VoltageFour-quadrant OperationStarting a Shunt dc Generator

8.38.48.58.68.7

8.98.108.11

8.128.13

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8.14 Starting a Shunt dc Motor8.14.1 Direct-on-line Starting8.14.2 Resistance Starting

8.15 Projects8.15.1 Project 1: Startup and Loading of a Shunt dc Generator8.15.2 Project 2: Resistance Starting of a dc Shunt Motor8.15.3 Project 3: Methods of Braking8.15.4 Project 4: Universal Motor8.15.5 Project 5: Series dc Machine Hoist

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9.1 Introduction9.1.1 Basics of Multi-quadrant Operation9.1.2 Operating Region Limited by Equipment Ratings

9.2 Speed Control9.2.1 Reducing Applied Voltage Magnitude9.2.2 Adjusting Rotor Circuit Resistance9.2.3 Adjusting Stator Voltage and Frequency

9.3 Constant Airgap Flux Operation9.4 Constant Volts/Hertz Operation9.5 Induction Machine Drives

9.5.1 Operating Strategies9.5.2 Scalar Control

9.6 Field-oriented Control9.6.1 Direct Field-oriented Current Control9.6.2 Direct Field-oriented Voltage Control

9.7 Indirect Field Orientation Methods9.8 Projects

9.8.1 Project 1: Closed-loop Speed Using Scalar Control9.8.2 Project 2: Six-step /nverterl/nduction Motor Drive9.8.3 Project 3: Field·Oriented Control

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10 SVNCHRONOUS MACHINES IN POWER SVSTEMSANO ORIVES

10.110.210.310.410.5

IntroductionSynchronous Generators in Power SystemsTransient Model With d and q Field WindingsSub-transient Model With Field and Damper WindingsSpecific Cases10.5.1 Salient-pole Machines10.5.2 Neglecting the dÁq/dt and dÁd/dt Terms10.5.3 Neglecting Sub-transient and Transient SaliencyExcitation Systems10.6.1 Voltage Transducer and Load Compensation Circuir

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10.6.2 Regulator10.6.3 dc Exciter10.6.4 Stabilizer10.6.5 Diode Bridge Operating Characteristic10.6.6 Power System Stabilizer

10.7 Shaft Torsional10. 7.1 Simulation10. 7.2 Computing Q and Scaling

10.8 Synchronous Motor Drives10.9 Projects

10.9.1 Project 1: Transient Models10.9.2 Project 2: Multi-machines System10.9.3 Project 3: Subsynchronous Resonance10.9.4 Project 4: Power System Stabilizer10.9.5 Project 5: Self-controlled Permanent Magnet Motor Drive

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A.1A.2A.3A.4A.5A.6A.7A.8

I ntroductionEuler MethodsTrapezoidal RuleRunge-Kutta MethodsLinear Multi-step MethodsAdams MethodsGear's Backward Difference FormulasSolving the Resulting Algebraic EquationsA.8.1 PivotingStep Size ControlChanging Order of IntegrationHandling of Conditional Discrete EventsA.11.1 Locating Discontinuities

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A.9A.10A.11