Power System Dynamics with Computer-Based Modeling and Analysis

Yoshihide Hase is a power systems engineering consultant in Japan. Tanuj Khandelwal is CTO and Senior Principal Electrical Engineer at ETAP - Operation Technology, Inc. in the USA. Kazuyuki Kameda provides engineering and consulting services for Electrical and Control Systems at Eltechs Engineering & Consulting Co., Ltd, in Japan.

About the Authors xxix

Preface xxxi

Acknowledgments xxxiii

Part A Power Systems Theories and Practices 1

1 Essentials of Electromagnetism 3

1.1 Overview 3

1.2 Voltage, Current, Electric Power, and Resistance 3

1.3 Electromagnetic Induction (Faraday’s Law) 4

1.4 Self Inductance and Mutual Inductance 6

1.5 Mutual Capacitance 7

2 Complex Number Notation (Symbolic Method) and the Laplace Transform 11

2.1 Euler’s Formula 11

2.2 Complex Number Notation of Electricity Based on Euler’s Formula 12

2.3 LR Circuit Transient Calculation Using Complex Number Notation and the Laplace Transform 14

2.4 LCR Circuit Transient Calculation 16

2.5 Resistive, Inductive, and Capacitive Load, and Phasor Expressions 21

3 Transmission Line Matrices and Symmetrical Components 25

3.1 Overhead Transmission Lines with Inductive LR Constants 25

3.2 Overhead Transmission Lines with Capacitive C Constants 30

3.3 Symmetrical Coordinate Method (Symmetrical Components) 32

3.4 Conversion of a Three-Phase Circuit into a Symmetrical Coordinated Circuit 39

3.5 Transmission Lines by Symmetrical Components 39

3.6 Generator by Symmetrical Components (Simplified Description) 47

3.7 Description of a Three-Phase Load Circuit by Symmetrical Components 49

4 Physics of Transmission Lines and Line Constants 51

4.1 Inductance 51

4.2 Capacitance and Leakage Current 59

4.3 Actual Configuration of Overhead Transmission Lines 66

4.4 Special Properties of Working Inductance and Working Capacitance 68

4.5 MKS Rational Unit System 71

5 The Per-Unit Method 77

5.1 Fundamental Concepts of the PU Method 77

5.2 PU Method for a Single-Phase Circuit 77

5.3 PU Method for Three-Phase Circuits 79

5.4 Base Quantity Modification of Unitized Impedance 80

5.5 Unitized Symmetrical Circuit: Numerical Example 81

6 Transformer Modeling 91

6.1 Single-Phase Three-Winding Transformer 91

6.2 − − Δ-Connected Three-Phase, Three-Winding Transformer 95

6.3 Three-Phase Transformers with Various Winding Connections 101

6.4 Autotransformers 105

6.5 On-Load Tap-Changing Transformer (LTC Transformer) 107

6.6 Phase-Shifting Transformer 109

6.7 Woodbridge Transformers and Scott Transformers 113

6.8 Neutral Grounding Transformer 116

6.9 Transformer Magnetic Characteristics and Inrush Current Phenomena 118

7 Fault Analysis Based on Symmetrical Components 127

7.1 Fundamental Concepts of Fault Analysis Based on the Symmetrical Coordinate Method 127

7.2 Line-to-Ground Fault (Phase-a to Ground Fault: 1ϕG) 127

7.3 Fault Analysis at Various Fault Modes 132

7.4 Conductor Opening 137

7.5 Visual Vector Diagrams of Voltages and Currents under Fault Conditions 139

7.6 Three-Phase-Order Misconnections 151

8 Fault Analysis with the αβ0-Method 155

8.1 αβ0-Method (Clarke-Components) 155

8.2 Fault Analysis with αβ0-Components 166

8.3 Advantages of the αβ0-Method 171

8.4 Fault-Transient Analysis with Symmetrical Components and the αβ0-Method 171

9 Power Cables 175

9.1 Structural Features of Power Cables 175

9.2 Circuit Constants of Power Cables 183

9.3 Metallic Sheaths and Outer Coverings 190

10 Synchronous Generators, Part 1: Circuit Theory 195

10.1 Generator Model in a Phase abc-Domain 195

10.2 dq0 Method (dq0 Components) 203

10.3 Transformation of Generator Equations from the abc-Domain to the dq0-Domain 206

10.4 Physical Meanings of Generator Equations in the dq0-Domain 210

10.5 Generator dq0-Domain Equations 213

10.6 Generator dq0-Domain Equivalent Circuit 218

10.7 Generator Operating Characteristics and Vector Diagram on the d- and q-Axes Plane 220

10.8 Generator Transient Reactance 223

10.9 Symmetrical Equivalent Circuits of Generators 225

10.10 Laplace-Transformed Generator Equations and Time Constants 231

10.12 Relations Between the dq0-Domain and αβ0-Domain 239

10.13 Calculating Generator Short-Circuit Transient Current Under Load 239

11 Synchronous Generators, Part 2: Characteristics of Machinery 251

11.1 Apparent Power P + jQ in the abc-, 012-, dq0-Domains 251

11.2 Mechanical (Kinetic) Power and Generating (Electrical) Power 257

11.3 Kinetic Equation for Generators 259

11.4 Generator Operating Characteristics with P-Q (or p-q) Coordinates 269

11.5 Generator Ratings and Capability Curves 271

11.6 Generator’s Locus in the pq-Coordinate Plane under Various Operating Conditions 275

11.7 Leading Power-Factor (Under-Excitation Domain) Operation, and UEL Function by AVR 277

11.8 Operation at Over-Excitation (Lagging Power-Factor Operation) 282

11.9 Thermal Generators’ Weak Points (Negative-Sequence Current, Higher Harmonic Current, Shaft-Torsional Distortion) 282

11.10 Transient Torsional Twisting Torque of a TG Coupled Shaft 287

11.11 General Description of Modern Thermal/Nuclear TG Units 290

12 Steady-State, Transient, and Dynamic Stability 297

12.1 P-δ Curves and Q-δ Curves 297

12.2 Power Transfer Limits of Grid-Connected Generators (Steady-State Stability) 299

12.3 Transient Stability 306

12.4 Dynamic Stability 309

12.5 Four-Terminal Circuit and the P − δ Curve under Fault Conditions 310

12.6 P-δ Curve under Various Fault-Mode Conditions 312

12.7 PQV Characteristics and Voltage Instability (Voltage Avalanche) 313

12.8 Generator Characteristics with an AVR 319

12.9 Generator Operation Limit With and Without an AVR in PQ Coordinates 330

12.10 VQ (Voltage and Reactive Power) Control with an AVR 332

13 Induction Generators and Motors (Induction Machines) 337

13.1 Introduction to Induction Motors and Generators 337

13.2 Doubly Fed Induction Generators and Motors 337

13.3 Squirrel-Cage Induction Motors 355

13.4 Proportional Relations of Mechanical Quantities and Electrical Quantities as a Basis of Power-Electronic Control 367

14 Directional Distance Relays and R–X Diagrams 371

14.1 Overview of Protective Relays 371

14.2 Directional Distance Relays (DZ-Ry) and R–X Coordinate Plane 372

14.3 R–X Diagram Locus under Fault Conditions 375

14.4 Impedance Locus under Ordinary Load Conditions and Step-Out Conditions 381

14.5 Impedance Locus Under Faults with Load-Flow Conditions 385

14.6 Loss of Excitation Detection by Distance Relays (40-Relay) 386

15 Lightning and Switching Surge Phenomena and Breaker Switching 391

15.1 Traveling Wave on a Transmission Line, and Equations 391

15.2 Four-Terminal Network Equations between Two Arbitrary Points 398

15.3 Examination of Line Constants 399

15.4 Behavior of Traveling Waves at Transition Points 401

15.5 Surge Overvoltages and Their Three Different, Confusing Notations 404

15.6 Behavior of Traveling Waves at a Lightning-Strike Point 406

15.7 Traveling Wave Phenomena of Three-Phase Transmission Lines 408

15.8 Reflection Lattices and Transient Behavior Modes 413

15.9 Switching Surge Phenomena Caused by Breakers Tripping 415

15.10 Breaker Phase Voltages and Recovery Voltages after Fault Tripping 424

15.11 Three-Phase Breaker TRVs across Independent Poles 426

15.12 Circuit Breakers and Switching Practices 432

15.13 Switching Surge Caused by Line Switches (Disconnecting Switches) 452

15.14 Surge Phenomena Caused on Power Cable Systems 454

15.15 Lightning Surge Caused on Cable Lines 456

15.16 Switching Surge Caused on Cable Lines 458

15.17 Surge Voltages Caused on Cables and GIS Jointed Points 459

16 Overvoltage Phenomena 463

16.1 Neutral-Grounding Methods 463

16.2 Arc-Suppression Coil (Petersen Coil) Neutral-Grounded Method 467

16.3 Overvoltages Caused by a Line-to-Ground Fault 467

16.4 Other Low-Frequency Overvoltage Phenomena (Non-resonant Phenomena) 469

16.5 Lower-Frequency Resonant Overvoltages 472

16.6 Interrupted Ground Fault of a Cable Line in a Neutral-Ungrounded System 475

16.7 Switching Surge Overvoltages 475

16.8 Overvoltage Phenomena Caused by Lightning Strikes 477

17 Insulation Coordination 481

17.1 Overvoltages as Insulation Stresses 481

17.2 Classification of Overvoltages 483

17.3 Fundamental Process of Insulation Coordination 486

17.4 Countermeasures on Transmission Lines to Reduce Overvoltages and Flashover 487

17.5 Tower-Mounted Arrester Devices 489

17.6 Using Unequal Circuit Insulation (Double-Circuit Lines) 490

17.7 Using High-Speed Reclosing 490

17.8 Overvoltage Protection with Arresters at Substations 491

17.9 Station Protection Using OGWs and Reduced Grounding Resistance 499

17.10 Insulation Coordination Details 501

17.11 Transfer Surge Voltages through Transformers, and Generator Protection 509

17.12 Transformer Internal High-Frequency Voltage Oscillation Phenomena 518

17.13 Oil-Filled Transformers Versus Gas-Filled Transformers 524

18 Harmonics and Waveform Distortion Phenomena 527

18.1 Classification of Harmonics and Waveform Distortion 527

18.2 Impact of Harmonics 527

18.3 Harmonic Phenomena Caused by Power Cable Line Faults 529

19 Power Electronic Applications, Part 1: Devices 535

19.1 Fundamental Concepts of Power Electronics 535

19.2 Power Switching with Power Devices 535

19.3 Snubber Circuit 539

19.4 Voltage Conversion with Switching 540

19.5 Power Electronics Devices 542

19.6 Mathematical Background for Analyzing Power Electronics Applications 547

20 Power Electronics Applications, Part 2: Circuit Theory 553

20.1 AC-to-DC Conversion: A Rectifier with a Diode 553

20.2 AC-to-DC Controlled Conversion: Rectifier with a Thyristor 562

20.3 DC-to-DC Converters (DC-to-DC Choppers) 571

20.4 DC-to-AC Inverters 579

20.5 PWM Control of Inverters 583

20.6 AC-to-AC Converters (Cycloconverters) 587

21 Power Electronics Applications, Part 3: Control Theory 589

21.1 Introduction 589

21.2 Driving Motors 589

21.3 Static Var Compensators (SVC: A Thyristor-Based Approach) 597

21.4 Active Filters 603

21.5 Generator Excitation Systems 609

21.6 Adjustable-Speed Pumped-Storage Generator-Motor Units 610

21.7 Wind Generation 615

21.8 Small Hydro Generation 618

21.9 Solar Generation (Photovoltaic Generation) 619

21.10 High-Voltage DC Transmission (HVDC Transmission) 621

21.11 FACTS Technology 625

21.12 Railway Applications 627

21.13 Uninterruptible Power Supplies 628

Appendix A Mathematical Formulae 631

Appendix B Matrix Equation Formulae 635

Part B Digital Computation Theories 639

22 Digital Computation Basics 641

22.1 Introduction 641

22.2 Network Types 642

22.3 Circuit Elements 645

22.4 Ohm’s Law 653

22.5 Kirchhoff’s Circuit Laws 655

22.6 Electrical Division Principle 656

22.7 Instantaneous, Average, and RMS Values 657

22.8 Nodal Formulation 658

22.9 Procedure for Mesh Analysis 662

22.10 Norton’s and Thévenin’s Equivalents 664

22.11 Maximum Power Transfer Theorem 668

22.13 Network Topology 675

22.14 Power System Matrices 681

22.15 Transformer Modeling 692

22.16 Transmission Line Modeling 696

23 Power-Flow Methods 701

23.1 Newton–Raphson Method 701

23.2 Gauss–Seidel Method 702

23.3 Adaptive Newton–Raphson Method 703

23.4 Fast-Decoupled Method 703

24 Short-Circuit Methods 705

24.1 ANSI/IEEE Calculation Methods 705

24.2 IEC Calculation Methods 719

25 Harmonics 729

25.1 Problem Formulation 729

25.2 Methodology and Standards 733

25.3 Harmonic Indices 735

25.4 Harmonic Component Modeling 740

25.5 Power System Components 741

25.6 System Resonance 743

25.7 Harmonic Mitigation 744

26 Reliability 749

26.1 Methodology and Standards 749

26.2 Performance Indices 752

27 Numerical Integration Methods 755

27.1 Accuracy 755

27.2 Stability 755

27.3 Stiffness 757

27.4 Predictor–Corrector 757

27.5 Runge–Kutta 758

28 Optimization 761

28.1 Power-Flow Injections 761

28.2 Voltage Magnitude Constraints 762

28.3 Line-Flow Thermal Constraints 762

28.4 Line-Flow Constraints as Current Limitations 763

28.5 Line-Flow Constraints as Voltage Angle Constraints 763

Part C Analytical Practices and Examples using ETAP 765

29 Introduction to Power System Analysis 767

29.1 Planning Studies 767

29.2 Need for Power-System Analysis 768

29.3 Computers in Power Engineering 768

29.4 Study Approach 768

29.5 Operator Training 772

29.6 System Reliability and Maintenance 772

29.7 Electrical Transient Analyzer Program (ETAP) 772

30 One-Line Diagrams 777

30.1 Introduction 777

30.2 Engineering Parameters 777

30.3 One-Line Diagram Symbols 778

30.4 Power-System Configurations 780

30.5 Network Topology Processing 787

30.6 Illustrative Example – Per-Unit and Single-Line Diagram 790

31 Load Flow 791

31.1 Introduction 791

31.2 Study Objectives 791

31.3 Problem Formulation 792

31.4 Calculation Methodology 794

31.5 Required Data for ETAP 796

31.6 Data Collection and Preparation 797

31.7 Model Validation 797

31.8 Study Scenarios 799

31.9 Contingency Analysis 800

31.10 Optimal or Optimum Power Flow 801

31.11 Illustrative Examples 803

32 Short-Circuit/Fault Analysis 841

32.1 Introduction 841

32.2 Analysis Objectives 841

32.3 Methodology and Standards 846

32.4 Study Scenarios 855

32.5 Results and Reports 856

32.6 Illustrative Examples 858

33 Motor Starting 881

33.1 Methods 881

33.2 Analysis Objectives 893

33.3 Methodology and Standards 894

33.4 Required Data 902

33.5 Illustrative Examples 903

33.6 Motor-Starting Plots and Results 913

33.7 Motor-Starting Alerts 916

34 Harmonics 917

34.1 Introduction 917

34.2 Analysis Objectives 919

34.3 Required Data 921

34.4 Harmonic Load Flow and Frequency Scan 923

34.5 Illustrative Examples 924

35 Transient Stability 939

35.1 Introduction 939

35.2 Analysis Objectives 940

35.3 Basic Concepts of Transient Stability 942

35.4 Dynamic Models 944

35.5 User-Defined Models 967

35.6 Parameter Tuning 967

35.7 Single-Generator Power System Model 971

35.8 Data Collection and Preparation 973

35.9 Study Scenarios 974

35.10 Stability Improvement 977

35.11 System Simulation 977

35.12 Illustrative Examples 979

36 Reliability Assessment 1003

36.1 Introduction 1003

36.2 Analysis Objectives 1003

36.3 Problem Formulation 1004

36.4 Required Data 1005

36.5 Illustrative Examples 1005

37 Protective Device Coordination 1019

37.1 Introduction 1019

37.2 Relays 1022

37.3 Methodology 1028

37.4 Required Data 1035

37.5 Principle of Protection 1036

37.6 Principle of Selectivity/Coordination 1037

37.7 Art of Protection and Coordination >600 V 1040

37.8 Illustrative Examples 1048

Appendix C Standards, Regulations, and Best Practice 1071

Further Reading 1083

Index 1085