Fundamentals of Electric Power Engineering

MASSIMO CERAOLO received his MSc degree in Electrical Engineering from the University of Pisa, with honors, in 1985. He has been Full Professor of Electric Power Systems since 2002. He has taught Networks, Components and Electric Systems at the University of Pisa, where he currently teaches Electric and Hybrid Vehicles. He has authored over one hundred scientific papers in several fields of electrical engineering. DAVIDE POLI received his MSc degree, with honors, and his PhD in Electrical Engineering from the University of Pisa, in 1997 and in 2001. He has been Assistant Professor of Electric Power Systems since 2001. Currently, he teaches Power Quality and Power System Reliability at the University of Pisa. He has authored eighty scientific papers in the field of power systems.

PREFACE xv

ABOUT THE AUTHORS xix

PART I PRELIMINARY MATERIAL 1

1 Introduction 3

1.1 The Scope of Electrical Engineering, 3

1.2 This Book’s Scope and Organization, 7

1.3 International Standards and Their Usage in This Book, 8

1.3.1 International Standardization Bodies, 8

1.3.2 The International System of Units (SI), 9

1.3.3 Graphic Symbols for Circuit Drawings, 11

1.3.4 Names, Symbols, and Units, 13

1.3.5 Other Conventions, 15

1.4 Specific Conventions and Symbols in This Book, 15

1.4.1 Boxes Around Text, 16

1.4.2 Grayed Boxes, 16

1.4.3 Terminology, 17

1.4.4 Acronyms, 17

1.4.5 Reference Designations, 18

2 The Fundamental Laws of Electromagnetism 19

2.1 Vector Fields, 20

2.2 Definition of E and B; Lorentz’s Force Law, 22

2.3 Gauss’s Law, 25

2.4 Ampère’s Law and Charge Conservation, 26

2.4.1 Magnetic Field and Matter, 31

2.5 Faraday’s Law, 32

2.6 Gauss’s Law for Magnetism, 35

2.7 Constitutive Equations of Matter, 36

2.7.1 General Considerations, 36

2.7.2 Continuous Charge Flow Across Conductors, 36

2.8 Maxwell’s Equations and Electromagnetic Waves, 38

2.9 Historical Notes, 40

2.9.1 Short Biography of Faraday, 40

2.9.2 Short Biography of Gauss, 40

2.9.3 Short Biography of Maxwell, 41

2.9.4 Short Biography of Ampère, 41

2.9.5 Short Biography of Lorentz, 41

PART II ELECTRIC CIRCUIT CONCEPT AND ANALYSIS 43

3 Circuits as Modelling Tools 45

3.1 Introduction, 46

3.2 Definitions, 48

3.3 Charge Conservation and Kirchhoff’s Current Law, 50

3.3.1 The Charge Conservation Law, 50

3.3.2 Charge Conservation and Circuits, 51

3.3.3 The Electric Current, 53

3.3.4 Formulations of Kirchhoff’s Current Law, 55

3.4 Circuit Potentials and Kirchhoff’s Voltage Law, 60

3.4.1 The Electric Field Inside Conductors, 60

3.4.2 Formulations of Kirchhoff’s Voltage Law, 64

3.5 Solution of a Circuit, 65

3.5.1 Determining Linearly Independent Kirchhoff Equations (Loop-Cuts Method), 66

3.5.2 Constitutive Equations, 68

3.5.3 Number of Variables and Equations, 70

3.6 The Substitution Principle, 73

3.7 Kirchhoff’s Laws in Comparison with Electromagnetism Laws, 75

3.8 Power in Circuits, 76

3.8.1 Tellegen’s Theorem and Energy Conservation Law in Circuits, 78

3.9 Historical Notes, 80

3.9.1 Short Biography of Kirchhoff, 80

3.9.2 Short Biography of Tellegen, 80

4 Techniques for Solving DC Circuits 83

4.1 Introduction, 84

4.2 Modelling Circuital Systems with Constant Quantities as Circuits, 84

4.2.1 The Basic Rule, 84

4.2.2 Resistors: Ohm’s Law, 87

4.2.3 Ideal and “Real” Voltage and Current Sources, 89

4.3 Solving Techniques, 91

4.3.1 Basic Usage of Combined Kirchhoff-Constitutive Equations, 92

4.3.2 Nodal Analysis, 95

4.3.3 Mesh Analysis, 98

4.3.4 Series and Parallel Resistors; Star/Delta Conversion, 99

4.3.5 Voltage and Current Division, 103

4.3.6 Linearity and Superposition, 105

4.3.7 Thévenin’s Theorem, 107

4.4 Power and Energy and Joule’s Law, 112

4.5 More Examples, 114

4.6 Resistive Circuits Operating with Variable Quantities, 120

4.7 Historical Notes, 121

4.7.1 Short Biography of Ohm, 121

4.7.2 Short Biography of Thévenin, 121

4.7.3 Short Biography of Joule, 122

4.8 Proposed Exercises, 122

5 Techniques for Solving AC Circuits 131

5.1 Introduction, 132

5.2 Energy Storage Elements, 132

5.2.1 Power in Time-Varying Circuits, 133

5.2.2 The Capacitor, 133

5.2.3 Inductors and Magnetic Circuits, 136

5.3 Modelling Time-Varying Circuital Systems as Circuits, 140

5.3.1 The Basic Rule, 140

5.3.2 Modelling Circuital Systems When Induced EMFs Between Wires Cannot Be Neglected, 145

5.3.3 Mutual Inductors and the Ideal Transformer, 146

5.3.4 Systems Containing Ideal Transformers: Magnetically Coupled Circuits, 150

5.4 Simple R–L and R–C Transients, 152

5.5 AC Circuit Analysis, 155

5.5.1 Sinusoidal Functions, 155

5.5.2 Steady-State Behaviour of Linear Circuits Using Phasors, 156

5.5.3 AC Circuit Passive Parameters, 163

5.5.4 The Phasor Circuit, 164

5.5.5 Circuits Containing Sources with Different Frequencies, 169

5.6 Power in AC Circuits, 171

5.6.1 Instantaneous, Active, Reactive, and Complex Powers, 171

5.6.2 Circuits Containing Sources Having Different Frequencies, 177

5.6.3 Conservation of Complex, Active, and Reactive Powers, 178

5.6.4 Power Factor Correction, 180

5.7 Historical Notes, 184

5.7.1 Short Biography of Boucherot, 184

5.8 Proposed Exercises, 184

6 Three-Phase Circuits 191

6.1 Introduction, 191

6.2 From Single-Phase to Three-Phase Systems, 192

6.2.1 Modelling Three-Phase Lines When Induced EMFs Between Wires Are Not Negligible, 198

6.3 The Single-Phase Equivalent of the Three-Phase Circuit, 200

6.4 Power in Three-Phase Systems, 202

6.5 Single-Phase Feeding from Three-Phase Systems, 206

6.6 Historical Notes, 209

6.6.1 Short Biography of Tesla, 209

6.7 Proposed Exercises, 209

PART III ELECTRIC MACHINES AND STATIC CONVERTERS 213

7 Magnetic Circuits and Transformers 215

7.1 Introduction, 215

7.2 Magnetic Circuits and Single-Phase Transformers, 215

7.3 Three-Phase Transformers, 225

7.4 Magnetic Hysteresis and Core Losses, 227

7.5 Open-Circuit and Short-Circuit Tests, 230

7.6 Permanent Magnets, 233

7.7 Proposed Exercises, 235

8 Fundamentals of Electronic Power Conversion 239

8.1 Introduction, 239

8.2 Power Electronic Devices, 240

8.2.1 Diodes, Thyristors, Controllable Switches, 240

8.2.2 The Branch Approximation of Thyristors and Controllable Switches, 242

8.2.3 Diodes, 243

8.2.4 Thyristors, 246

8.2.5 Insulated-Gate Bipolar Transistors (IGBTs), 248

8.2.6 Summary of Power Electronic Devices, 250

8.3 Power Electronic Converters, 251

8.3.1 Rectifiers, 251

8.3.2 DC–DC Converters, 257

8.3.3 Inverters, 264

8.4 Analysis of Periodic Quantities, 276

8.4.1 Introduction, 276

8.4.2 Periodic Quantities and Fourier’s Series, 276

8.4.3 Properties of Periodic Quantities and Examples, 279

8.4.4 Frequency Spectrum of Periodic Signals, 280

8.5 Filtering Basics, 283

8.5.1 The Basic Principle, 283

8.6 Summary, 289

9 Principles of Electromechanical Conversion 291

9.1 Introduction, 292

9.2 Electromechanical Conversion in a Translating Bar, 292

9.3 Basic Electromechanics in Rotating Machines, 297

9.3.1 Rotating Electrical Machines and Faraday’s Law, 297

9.3.2 Generation of Torques in Rotating Machines, 301

9.3.3 Electromotive Force and Torque in Distributed Coils, 302

9.3.4 The Uniform Magnetic Field Equivalent, 304

9.4 Reluctance-Based Electromechanical Conversion, 305

10 DC Machines and Drives and Universal Motors 309

10.1 Introduction, 310

10.2 The Basic Idea and Generation of Quasi-Constant Voltage, 310

10.3 Operation of a DC Generator Under Load, 315

10.4 Different Types of DC Machines, 318

10.4.1 Generators and Motors, 318

10.4.2 Starting a DC Motor with Constant Field Current, 320

10.4.3 Independent, Shunt, PM, and Series Excitation Motors, 326

10.5 Universal Motors, 329

10.6 DC Electric Drives, 331

10.7 Proposed Exercises, 335

11 Synchronous Machines and Drives 337

11.1 The Basic Idea and Generation of EMF, 338

11.2 Operation Under Load, 345

11.2.1 The Rotating Magnetic Field, 345

11.2.2 Stator–Rotor Interaction, 348

11.2.3 The Phasor Diagram and the Single-Phase Equivalent Circuit, 350

11.3 Practical Considerations, 353

11.3.1 Power Exchanges, 353

11.3.2 Generators and Motors, 357

11.4 Permanent-Magnet Synchronous Machines, 359

11.5 Synchronous Electric Drives, 360

11.5.1 Introduction, 360

11.5.2 PM, Inverter-Fed, Synchronous Motor Drives, 361

11.5.3 Control Implementation, 366

11.6 Historical Notes, 370

11.6.1 Short Biography of Ferraris and Behn-Eschemburg, 370

11.7 Proposed Exercises, 371

12 Induction Machines and Drives 373

12.1 Induction Machine Basics, 374

12.2 Machine Model and Analysis, 378

12.3 No-Load and Blocked-Rotor Tests, 391

12.4 Induction Machine Motor Drives, 394

12.5 Single-Phase Induction Motors, 399

12.5.1 Introduction, 399

12.5.2 Different Motor Types, 402

12.6 Proposed Exercises, 404

PART IV POWER SYSTEMS BASICS 409

13 Low-Voltage Electrical Installations 411

13.1 Another Look at the Concept of the Electric Power System, 411

13.2 Electrical Installations: A Basic Introduction, 413

13.3 Loads, 418

13.4 Cables, 422

13.4.1 Maximum Permissible Current and Choice of the Cross-Sectional Area, 422

13.5 Determining Voltage Drop, 427

13.6 Overcurrents and Overcurrent Protection, 429

13.6.1 Overloads, 429

13.6.2 Short Circuits, 430

13.6.3 Breaker Characteristics and Protection Against Overcurrents, 432

13.7 Protection in Installations: A Long List, 437

14 Electric Shock and Protective Measures 439

14.1 Introduction, 439

14.2 Electricity and the Human Body, 440

14.2.1 Effects of Current on Human Beings, 440

14.2.2 The Mechanism of Current Dispersion in the Earth, 443

14.2.3 A Circuital Model for the Human Body, 444

14.2.4 The Human Body in a Live Circuit, 446

14.2.5 System Earthing: TT, TN, and IT, 448

14.3 Protection Against Electric Shock, 450

14.3.1 Direct and Indirect Contacts, 450

14.3.2 Basic Protection (Protection Against Direct Contact), 451

14.3.3 Fault Protection (Protection Against Indirect Contact), 453

14.3.4 SELV Protection System, 458

14.4 The Residual Current Device (RCD) Principle of Operation, 459

14.5 What Else?, 462

References, 462

15 Large Power Systems: Structure and Operation 465

15.1 Aggregation of Loads and Installations: The Power System, 465

15.2 Toward AC Three-Phase Systems, 466

15.3 Electricity Distribution Networks, 468

15.4 Transmission and Interconnection Grids, 470

15.5 Modern Structure of Power Systems and Distributed Generation, 473

15.6 Basics of Power System Operation, 475

15.6.1 Frequency Regulation, 478

15.6.2 Voltage Regulation, 480

15.7 Vertically Integrated Utilities and Deregulated Power Systems, 482

15.8 Recent Challenges and Smart Grids, 484

15.9 Renewable Energy Sources and Energy Storage, 486

15.9.1 Photovoltaic Plants, 486

15.9.2 Wind Power Plants, 490

15.9.3 Energy Storage, 494

Appendix: Transmission Line Modelling and Port-Based Circuits 501

A.1 Modelling Transmission Lines Through Circuits, 501

A.1.1 Issues and Solutions When Displacement Currents are Neglected, 502

A.1.2 Steady-State Analysis Considering Displacement Currents, 506

A.1.3 Practical Considerations, 509

A.2 Modelling Lines as Two-Port Components, 510

A.2.1 Port-Based Circuits, 510

A.2.2 Port-Based Circuit and Transmission Lines, 511

A.2.3 A Sample Application, 512

A.3 Final Comments, 513

SELECTED REFERENCES 515

ANSWERS TO THE PROPOSED EXERCISES 519

INDEX 529