A comprehensive text, combining all important concepts and topics of Electrical Machines and featuring exhaustive simulation models based on MATLAB/Simulink

Electrical Machine Fundamentals with Numerical Simulation using MATLAB/Simulink provides readers with a basic understanding of all key concepts related to electrical machines (including working principles, equivalent circuit, and analysis). It elaborates the fundamentals and offers numerical problems for students to work through. Uniquely, this text includes simulation models of every type of machine described in the book, enabling students to design and analyse machines on their own.

Unlike other books on the subject, this book meets all the needs of students in electrical machine courses. It balances analytical treatment, physical explanation, and hands-on examples and models with a range of difficulty levels. The authors present complex ideas in simple, easy-to-understand language, allowing students in all engineering disciplines to build a solid foundation in the principles of electrical machines. This book:

Includes clear elaboration of fundamental concepts in the area of electrical machines, using simple language for optimal and enhanced learning
Provides wide coverage of topics, aligning with the electrical machines syllabi of most international universities
Contains extensive numerical problems and offers MATLAB/Simulink simulation models for the covered machine types
Describes MATLAB/Simulink modelling procedure and introduces the modelling environment to novices
Covers magnetic circuits, transformers, rotating machines, DC machines, electric vehicle motors, multiphase machine concept, winding design and details, finite element analysis, and more

Electrical Machine Fundamentals with Numerical Simulation using MATLAB/Simulink is a well-balanced textbook perfect for undergraduate students in all engineering majors. Additionally, its comprehensive treatment of electrical machines makes it suitable as a reference for researchers in the field.

Dr. Atif Iqbal is a Professor in the Department of Electrical Engineering, Qatar University. He is an IET Fellow (UK), IE Fellow (India), and Senior Member of the IEEE, as well as Associate Editor, IEEE Trans.

Dr. Shaikh Moinoddin is a Senior Member of the IEEE, India. He is former Assistant Professor in the Electrical Engineering Section, University Polytechnic, Aligarh Muslim University, Aligarh, India.

Dr. B. Prathap Reddy is currently working as a Post-doc at the Department of Electrical Engineering, Qatar University and is a member of the IEEE.

Preface

Acknowledgments

Chapter.1 Fundamental of Electrical Machines 1

1.1 Preliminary Remarks 1

1.2 Basic Laws of Electrical Engineering 1

1.2.1 Ohm’s Law 1

1.2.2 Generalization of Ohm’s law 2

1.2.3 Ohm’s Law for magnetic circuits 3

1.2.4 Kirchhoff’s Laws for magnetic circuits 3

1.2.5 Lorentz Force Law 5

1.2.6 Biot-Savart Law 7

1.2.7 Ampere Circuital Law 18

1.2.8 Faraday's law 22

1.2.8.1 Motional emf 27

1.2.9 Flux Linkages and Induced Voltages 32

1.2.10 Induced Voltages 33

1.2.11 Induced Electric Fields 34

1.2.12 Reformulation of Faraday’s law 35

1.3 Inductance 44

1.3.1 Application of Ampere’s law to find B in a solenoid: 44

1.3.2 Magnetic Field of a Toroid 45

1.3.3 The inductance of circular air-cored toroid 46

1.3.4 Mutual Inductance 50

1.4 Energy 53

1.5 Overview of Electric Machines 55

1.6 Summary 66

1.7 Problems 66

1.8 References 76

Chapter.2 Magnetic Circuits 77

2.1 Preliminary Remarks 77

2.2 Permeability 77

2.3 Classification of Magnetic Materials 78

2.3.1 Uniform Magnetic Field [1] 80

2.3.2 Magnetic-Field Intensity [2] 80

2.4 Hysteresis Loop 82

2.5 Eddy-Current and Core Losses 86

2.6 Magnetic Circuits 90

2.6.1 The Magnetic Circuit Concept 90

2.6.2 Magnetic Circuits Terminology 91

2.6.3 Effect of Air Gaps 95

2.6.3.1 MAGNETIC CIRCUIT WITH AN AIR GAP [5] 95

2.6.3.2 Magnetic Forces Exerted By Electromagnets [5] 98

2.7 Field Energy 110

2.7.1 Energy Stored In A Magnetic Field [ 7] 110

2.7.1.1 The Magnetic Energy in Terms of the Magnetic Induction B 112

2.7.1.2 The magnetic Energy in Terms of the Current Density J and the Vector Potential A 113

2.7.1.3 The Magnetic Energy in Terms of the Current I and of the Flux Ψm 114

2.7.1.4 The Magnetic Energy in Terms of the Currents and Inductances 114

2.8 The Magnetic Energy for a Solenoid Carrying a Current I 115

2.9 Energy flow diagram 117

2.9.1 Power Flow Diagram of DC Generator and DC Motor 117

2.10 Multiple excited systems [9] 121

2.10.1 Torque developed [11] 126

2.11 Concept of Rotating Magnetic Field 136

2.11.1 Rotating Magnetic Field Due to 3-Phase Currents [12] 137

2.11.1.1 Speed of rotating magnetic field 142

2.11.1.2 Direction of rotating magnetic field 143

2.11.2 Alternate Mathematical Analysis for Rotating Magnetic Field [3] 143

2.12 Summary 147

2.13 Problems 147

2.14 References 156

Chapter.3 Single-phase and Three-phase Transformers 158

3.1 Preliminary Remarks 158

3.2 Classification of Transformers 160

3.2.1 Classification Based on Number of Phases 160

3.2.2 Classification based on Operation 162

3.2.3 Classification Based on Construction 163

3.2.4 Classification Based on Number of Windings 165

3.2.5 Classification based on the use 166

3.3 Principle of operation of transformer: 167

3.3.1 Ideal Transformer 167

3.4 Impedance Transformation 170

3.5 DOT Convention 171

3.6 Real/Practical Transformer 172

3.7 Equivalent Circuit of a Single-phase Transformer 174

3.8 Phasor Diagrams Under Load Condition 183

3.9 Testing of Transformer 190

3.9.1 Open-Circuit Test 190

3.9.2 Short-Circuit Test 192

3.10 Performance measures of a Transformer 196

3.10.1 Voltage Regulation 197

3.10.1.1 Condition for Maximum Voltage Regulation 199

3.10.1.2 Condition for Zero Voltage Regulation 200

3.10.2 Maximum Efficiency Condition 204

3.11 Auto-Transformer 210

3.12 Three-phase Transformer 216

3.13 Single-phase Equivalent Circuit of three-phase transformer 226

3.14 Open-delta connection or V connection 230

3.15 Harmonics in a single-phase Transformer 236

3.15.1 Excitation Phenomena in a single-phase Transformer 241

3.15.2 Harmonics in three-phase Transformer 245

3.16 Disadvantages of Harmonics in Transformer 250

3.16.1 Oscillating Neutral Phenomena 252

3.17 Open circuit and Short Circuit Conditions in Three-phase Transformer 254

3.18 Matlab/Simulink Model of a 1-phase Transformer 256

3.19 Matlab/Simulink Model of Testing of Transformer 259

3.20 Matlab/Simulink Model of Auto-Transformer 260

3.21 Matlab/Simulink Model of Three-phase Transformer 262

3.22 Supplementary Solved Problems 267

3.23 Summary 289

3.24 Problems 289

3.25 References 298

Chapter.4 Fundamental of Rotating Electrical Machines and Machine Windings 300

4.1 Preliminary Remarks 300

4.1.1 Generator Principle 300

4.1.2 Simple Loop Generator 301

4.1.3 Action of Commutator 302

4.1.4 Force on a Conductor 303

4.1.4.1 D.C. Motor Principle 303

4.1.4.2 Motor Action 303

4.1.4.3 Working of D.C. Motor 303

4.2 Machine Windings 304

4.2.1 Coil construction 304

4.2.1.1 Coil Construction: Distributed Winding[2] 304

4.2.1.2 Coil Construction: Concentrated Winding[2] 305

4.2.1.3 Coil Construction: Conductor Bar[2] 305

4.2.1.4 Coil pitch or Coil span (Ycs) 306

4.2.1.5 Back pitch (Yb) 306

4.2.1.6 Front pitch (Yf) 307

4.2.1.7 Resultant pitch (Y) 307

4.2.2 Lap winding 308

4.2.2.1 LAP MULTIPLE OR PARALLEL WINDINGS [3] 309

4.2.2.2 Formulas for Lap Winding: 309

4.2.2.3 Multiplex, Single, Double and Triple Windings: 311

4.2.2.4 Meaning of the Term Reentrant: 311

4.2.2.5 Multiplex Lap Windings: 312

4.2.3 Wave winding 323

4.2.3.1 Formulas for Wave Winding: 324

4.2.3.2 Multiplex Wave or Series-Parallel Winding: 326

4.2.3.3 Formulas for Series-Parallel Winding: 326

4.2.4 Symmetrical Windings: 327

4.2.4.1 Possible Symmetrical Windings for D.C. Machines of Different Number of Poles: 327

4.2.5 Equipotential Connectors (Equalizing Rings): 328

4.2.6 Applications of Lap and Wave Windings[1] 330

4.2.7 Dummy or Idle Coils 361

4.2.8 Whole coil winding and Half coil winding[3] 362

4.2.9 Concentrated winding 363

4.2.10 Distributed winding 363

4.3 Electromotive Force (EMF) Equation 363

4.3.1 E.M.F. Equation of an Alternator [1] 363

4.3.2 Winding Factors 364

4.3.2.1 Pitch Factor or Coil Pitch (pitch factor (Kp)or coil span factor (Kc)) 364

4.4 Magnetomotive Force (mmf) of AC Windings 367

4.4.1 Magneto-motive force and flux in rotating machine 367

4.4.2 Main air-gap flux (Field Flux) 367

4.4.2.1 Magneto-motive force 368

4.4.2.2 M.m.f of distributed windings 368

4.4.2.3 MMF Space Wave of a Single Coil 369

4.4.2.4 MMF Space Wave of One Phase of a Distributed Winding [4] 370

4.5 Harmonic Effect [6] 374

4.5.1 The Form Factor and the E.M.F. per Conductor. 374

4.5.2 The Wave Form. 374

4.5.3 Problem due to Harmonics. 375

4.5.4 Elimination or Suppression of Harmonics 376

4.5.4.1 Shape of Pole Face. 376

4.5.4.2 Use of Several Slots per Phase per Pole. 376

4.5.4.3 Use of Short-pitch Windings. 377

4.5.4.4 Effect of the Y- and Δ -Connection on Harmonics. 379

4.5.4.5 Harmonics Produced by Armature Slots. 381

4.6 Basic Principles of Electric Machines 382

4.6.1 AC Rotating Machines[7] 383

4.6.1.1 The Rotating Magnetic Field 383

4.6.1.2 The Relationship between Electrical Frequency and the Speed of Magnetic Field Rotation 385

4.6.1.3 Reversing the Direction of the Magnetic Field Rotation 387

4.6.1.4 The Induced Voltage in AC Machines 388

4.6.1.5 The Induced Voltage in a Coil on a Two-Pole Stator 388

4.6.1.6 The Induced Voltage in a Three-Phase Set of Coils 390

4.6.1.7 The RMS Voltage in a Three-Phase Stator 390

4.6.2 The Induced Torque in an AC Machine 391

4.7 Summary 392

4.8 Problems 392

4.9 References 393

Chapter.5 DC Machines 394

5.1 Preliminary Remarks 394

5.2 Construction and types of DC generator 395

5.2.1 Construction of DC machine 395

5.2.2 Types of DC generator 396

5.3 Principle of operation of DC generator 398

5.3.1 Voltage Build-up in a DC generator 400

5.3.2 Function of commutator 401

5.4 Commutation problem and solution 403

5.4.1 Brush shifting 404

5.4.2 Commutating poles 404

5.4.3 Compensating windings 404

5.5 Types of windings 405

5.6 EMF equations in a DC generator 407

5.7 Brush placement in a DC machine 408

5.8 Equivalent circuit of DC generator 408

5.9 Losses of DC Generator 409

5.10 Armature reaction 415

5.11 Principle of operation of a DC motor 418

5.11.1 Equivalent circuit of DC motor 419

5.12 Emf and torque equations of DC motor 420

5.13 Types of DC motor 420

5.13.1 Separately excited DC motor 420

5.13.2 Self excited DC motor 422

5.13.2.1 Shunt DC motor: 422

5.13.2.2 Series DC motor 423

5.14 Characteristics of DC motors 425

5.14.1 Separately excited and DC shunt motor 425

5.14.2 DC series motor 427

5.14.3 Compound motor 428

5.15 Starting of DC motor 429

5.15.1 Design of a Starter for DC motor: 429

5.15.2 Types of Starters 431

5.15.2.1 Three-point starter 432

5.15.2.2 Four-point starter 432

5.16 Speed control of DC motor 433

5.16.1 Separately excited and DC shunt motor 433

5.16.2 DC series motor 435

5.17 Solved examples 437

5.18 Matlab/Simulink model of DC machine 446

5.18.1 Matlab/Simulink model of separately/ shunt DC motor 446

5.18.2 Matlab/Simulink model of DC series motor 449

5.18.3 Matlab/Simulink model of Compound DC motor 451

5.19 Summary 453

5.20 Problems 454

5.21 References 459

Chapter.6 Three-phase Induction Machine 460

6.1 Preliminary Remarks 460

6.2 Construction of a three-phase induction machine 460

6.2.1 Stator 461

6.2.2 Stator Frame 461

6.2.3 Rotor 462

6.3 Principle operation of three-phase induction motor 463

6.3.1 Slip in induction motor 465

6.3.2 Frequency of Rotor Voltage and Current 466

6.3.3 Induction machine and Transformer 467

6.4 Per-phase Equivalent circuit of a three-phase induction machine 467

6.5 Power Flow diagram in a three-phase induction motor 475

6.6 Power relations in a three-phase induction motor 477

6.7 Steps to find different powers and efficiency 478

6.8 Per-phase Equivalent circuit considering stray load losses 481

6.9 Torque and Power Using Thevenin's Equivalent circuit 482

6.10 Torque-Speed Characteristics 486

6.10.1 Condition for Maximum Torque 489

6.10.2 Condition for Maximum torque at Starting 491

6.10.3 Approximate Equations 492

6.11 Losses in a three-phase induction machine 496

6.11.1 Copper losses or resistive losses 496

6.11.2 Magnetic Losses 497

6.11.3 Mechanical Losses: 497

6.11.4 Stray-Load Losses: 498

6.12 Testing of three-phase induction motor 498

6.12.1 No-load Test 498

6.12.2 Blocked rotor test 500

6.12.3 DC Test 502

6.12.4 Load test 502

6.12.5 International Standards for Efficiency of Induction machines 506

6.12.6 International Standards for the Evaluation of Induction Motor Efficiency: 507

6.13 Starting of a three-phase induction motor 508

6.13.1 Direct-on-line start 511

6.13.2 Line Resistance Start 513

6.13.3 Star-delta Starter 513

6.13.4 Auto-transformer Starter 515

6.14 Speed Control of Induction Machine 517

6.14.1 By varying the frequency of the Supply: 517

6.14.2 Pole Changing Method: 519

6.14.2.1 Multiple Numbers of Windings: 519

6.14.2.2 Consequent Pole Method: 520

6.14.3 Stator Voltage Control: 520

6.14.3.1 Voltage/frequency = constant control 522

6.14.3.2 Rotor resistance Variation: 524

6.14.3.3 Rotor Voltage Injection Method: 524

6.14.3.4 Cascade Connection of Induction Machines: 524

6.14.3.5 Pole Phase Modulation for Speed Control 526

6.15 Matlab/Simulink Modeling of three-phase Induction Motor 530

6.15.1 Plotting Torque-Speed Curve Under Steady-State Condition 530

6.15.2 Dynamic Simulation of Induction Machine: 532

6.16 Practice Problems 539

6.17 Summary 552

6.18 Problems 552

6.19 References 558

Chapter.7 Synchronous Machine 559

7.1 Preliminary Remarks 559

7.2 Synchronous Machine Structures 559

7.2.1 Stator and Rotor 559

7.3 Working Principle of The synchronous generator 564

7.3.1 The synchronous Generator Under No-load 566

7.3.2 The synchronous Generator Under Load 567

7.4 Working Principle of The synchronous Motor 571

7.5 Starting of The synchronous Motor 572

7.6 Armature Reaction in Motor 573

7.7 Equivalent circuit and Phasor Diagram of The synchronous Machine 577

7.8 Open circuit and short circuit characteristics 587

7.9 Voltage Regulation 594

7.9.1 Emf or The synchronous Method 595

7.9.2 The Ampere-Turn or MMF Method 597

7.9.3 Zero power factor method or Potier Triangle method 601

7.10 Efficiency of The synchronous Machine 605

7.11 Torque and Power curves 610

7.11.1 Real/Active output power of the synchronous generator 611

7.11.2 Reactive output power of the synchronous generator 612

7.11.3 Complex Input Power to the synchronous generator 613

7.11.4 Real/Active Input Power to The synchronous Generator 613

7.11.5 Reactive Input Power to The synchronous Generator 614

7.12 Maximum Power Output of the synchronous Generator 615

7.13 Capability Curve of the synchronous machine 620

7.14 Salient Pole Machine 625

7.14.1 Phasor Diagram of a salient pole the synchronous generator: 626

7.14.2 Power Delivered by a Salient Pole The synchronous Generator 634

7.14.3 Maximum Active and Reactive Power Delivered by a Salient Pole The synchronous Generator 637

7.15 Synchronization of Alternator with Bus-bar 641

7.16 Operation of The synchronous Machine Connected to an Infinite Bus-bar (Constant Vt and f) 647

7.16.1 Motor Operation of Change in Excitation at fixed Shaft power 647

7.16.2 Generator Operation for Change in Output Power at fixed Excitation 651

7.17 Hunting in The synchronous Motor 657

7.18 Parallel operation of The synchronous generators 660

7.19 Matlab/Simulink Model of a Salient Pole The synchronous Machine 671

7.20 Summary 677

7.21 Problems 677

7.22 References 682

Chapter.8 Single-phase and Special Machines 683

8.1 Preliminary Remarks 683

8.2 Single-phase Induction Machine 683

8.2.1 Field System in a Single-phase Machine 685

8.3 Equivalent Circuit of Single-phase Machines 689

8.3.1 Equivalent Circuit Analysis 691

8.3.1.1 Approximate Equivalent Circuit 692

8.3.1.2 Thevenin’s Equivalent Circuit 694

8.4 How to make single-phase induction motor self starting 695

8.5 Testing of Induction Machine 703

8.5.1 No-load test 703

8.5.2 Blocked-Rotor test 705

8.6 Types of Single-phase Induction Motors 708

8.6.1 Split phase induction motor 708

8.6.2 Capacitor start induction motor 709

8.6.3 Capacitor start capacitor run induction motor (two value capacitor method). 710

8.7 Single-Phase Induction Motor Winding Design 711

8.7.1 Split phase induction motor 713

8.7.2 Capacitor Start Motors: 714

8.8 Permanent split capacitor (PSC) motor 718

8.9 Shaded pole induction motor. 719

8.10 Universal Motor 720

8.11 Switched Reluctance Motor (SRM) 721

8.12 Permanent Magnet Synchronous Machines 723

8.13 Brushless DC Motor 723

8.14 Mathematical model of the single-phase induction motor: 725

8.15 Simulink Model of single phase Induction Motor 726

8.16 Summary 731

8.17 Problems 731

8.18 References 735

Chapter.9 Motors for Electric Vehicles and Renewable Energy System 736

9.1 Introduction 736

9.2 Components of Electric Vehicles 737

9.2.1 Types of EVs 738

9.2.1.1 Battery based Electric Vehicles: 739

9.2.1.2 Hybrid Electric Vehicles: 741

9.2.1.3 Fuel Cell Electric Vehicles 743

9.2.2 Significant components of EVs 745

9.2.2.1 Battery Bank 745

9.2.2.2 DC-DC Converters: 756

9.2.2.3 Power Inverter: 757

9.2.2.4 Electric Motor: 757

9.2.2.5 Transmission System or Gear Box: 757

9.2.2.6 Other Components: 758

9.3 Challenges and Requirements of Electric Machines for EVs 758

9.3.1 Challenges of Electric Machines for EVs 758

9.3.2 Requirements of Electric Machines for EVs 759

9.4 Commercially Available Electric Machines for EVs 762

9.4.1 DC Motors 766

9.4.2 Induction Motor 766

9.4.3 Permanent magnet synchronous motors (PMSM): 767

9.4.4 Brushless DC Motors: 767

9.4.5 Switched Reluctance Motors (SRM): 768

9.5 Challenges and Requirements of Electric Machines for RES 768

9.6 Commercially Available Electric Machines for RES 770

9.6.1 DC Machine 771

9.6.2 Induction Machines 772

9.6.3 Synchronous Machines 774

9.6.4 Advanced Machines for Renewable Energy 777

9.7 Summary 777

9.8 References 777

Chapter.10 Multiphase (More Than 3-phase) Machines Concepts and Characteristics 780

10.1 Preliminary Remarks 780

10.2 Necessity of the Multiphase Machines 780

10.2.1 Evolution of the Multiphase Machines 781

10.2.2 Advantages of Multiphase Machines 785

10.2.2.1 Better Space Harmonics Profile 785

10.2.2.2 Better Torque Ripple Profile 787

10.2.2.3 Improved Efficiency 787

10.2.2.4 Reduced ratings of Semiconductor Switches and Better Power/Torque Distribution 791

10.2.2.5 Torque Enhancement by Injecting Lower Order Harmonics into Stator Currents 791

10.2.3 Applications of Multiphase Machines 792

10.3 Working Principle 793

10.3.1 Multiphase Induction Machine 794

10.3.2 Multiphase Synchronous Machine 794

10.4 Stator Winding Design 795

10.4.1 3-Phase Windings 798

10.4.2 5-Phase Windings 806

10.4.3 6-Phase Windings 809

10.4.4 9-Phase Windings 813

10.5 Mathematical Modelling of Multiphase Machines 816

10.5.1 Mathematical Modelling of Multiphase Induction Machines in Original Phase-Variable Domain 817

10.5.2 Transformation matrix for Multiphase Machines 820

10.5.3 Modelling of Multiphase Induction Machine in Arbitrary Reference Frame 822

10.5.4 Commonly used Reference Frames 825

10.5.5 Modelling of Multiphase Synchronous Machine 826

10.6 Vector Control Techniques for Multiphase Machines 829

10.6.1 Indirect Field Oriented Control or Vector Control Techniques for Multiphase Induction Machines 831

10.6.2 Vector Control for Multiphase Synchronous Machines 834

10.7 MATLAB/Simulink Model of Multiphase Machines 836

10.7.1 Dynamic Model of the 9-phase Induction Machine 836

10.7.2 Dynamic Model of the 9-phase Synchronous Machine 841

10.8 Summary 846

10.9 Problems 846

10.10 References 847

Chapter.11 Numerical Simulation of Electrical Machines Using Finite Element Method 849

11.1 Introduction 849

11.2 Methods of Solving Electromagnetic Analysis 850

11.2.1 Analytical Techniques 852

11.2.2 Numerical Techniques 854

11.2.2.1 Finite Difference Method: 856

11.2.2.2 Finite Element Method: 857

11.2.2.3 Solution of Laplace Equation using Finite Element Method: 858

11.3 Formulation of 2-Dimensional and 3-Dimensional Analysis 863

11.3.1 Maxwell Equations 865

11.3.1.1 Gauss Law 866

11.3.1.2 Gauss Law of Magnetism 866

11.3.1.3 Ampere’s Integral Law 866

11.3.1.4 Faraday’s integral law 867

11.3.1.5 Differential form of Maxwell Equations 867

11.3.2 FEM Adaptive Meshing 869

11.3.3 FEM Variation Principle 870

11.4 Analysis and Implementation of FEM Machine Models 871

11.4.1 RMxprt Design to Implement Maxwell Model of Machine 872

11.4.2 Power Converter Design in Simplorer 881

11.4.3 Integration of Power Converter with Maxwell Model for Testing Drive 882

11.5 Example Model of 3-phase IM in Ansys Maxwell 2D 885

11.6 Summary 889

Index