Preface ...................................................... xiii
Acknowledgments ................................................ xv
Author ....................................................... xvii
Chapter 1 General Considerations ............................... 1
1.1 Introduction ............................................... 1
1.2 Power System Planning ...................................... 5
References ..................................................... 10
General References ............................................. 11
Chapter 2 Basic Concepts ...................................... 13
2.1 Introduction .............................................. 13
2.2 Complex Power in Balanced Transmission Lines .............. 13
2.3 One-Line Diagram .......................................... 16
2.4 Per-Unit System ........................................... 19
2.4.1 Single-Phase System ................................ 20
2.4.2 Converting from Per-Unit Values to Physical
Values ............................................. 24
2.4.3 Change of Base ..................................... 24
2.4.4 Three-Phase Systems ................................ 25
2.5 Constant Impedance Representation of Loads ................ 38
2.6 Three-Winding Transformers ................................ 40
2.7 Autotransformers .......................................... 41
2.8 Delta-Wye and Wye-Delta Transformations ................... 43
2.9 Short-Circuit MVA and Equivalent Impedance ................ 44
2.9.1 Three-Phase Short-Circuit MVA ...................... 45
2.9.1.1 If Three-Phase Short-Circuit MVA Is
Already Known ............................. 45
2.9.2 Single-Phase-to-Ground Short-Circuit MVA ........... 46
2.9.2.1 If Single-Phase Short-Circuit MVA Is
Already Known ............................. 46
References ..................................................... 48
General References ............................................. 48
Chapter 3 Steady-State Performance of Transmission Lines ...... 51
3.1 Introduction .............................................. 51
3.2 Conductor Size ............................................ 51
3.3 Transmission Line Constants ............................... 58
3.4 Resistance ................................................ 58
3.5 Inductance and Inductive Reactance ........................ 59
3.5.1 Single-Phase Overhead Lines ........................ 59
3.5.2 Three-Phase Overhead Lines ......................... 60
3.6 Capacitance and Capacitive Reactance ...................... 61
3.6.1 Single-Phase Overhead Lines ........................ 61
3.6.2 Three-Phase Overhead Lines ......................... 64
3.6.1 Tables of Line Constants ........................... 65
3.8 Equivalent Circuits for Transmission Lines ................ 68
3.9 Transmission Lines ........................................ 68
3.9.1 Short Transmission Lines (up to 50 mi or 80 km) .... 68
3.9.2 Steady-State Power Limit ........................... 71
3.9.3 Percent Voltage Regulation ......................... 73
3.9.4 Representation of Mutual Impedance of Short Lines .. 79
3.10 Medium-Length Transmission Lines (up to 150 mi or
240 km) ................................................... 80
3.11 Long Transmission Lines (above 150 mi or 240 km) .......... 90
3.11.1 Equivalent Circuit of Long Transmission Line ...... 100
3.11.2 Incident and Reflected Voltages of Long
Transmission Line ................................. 103
3.11.3 Surge Impedance Loading of Transmission Line ...... 107
3.12 General Circuit Constants ................................ 110
3.12.1 Determination of А, В, C, and D Constants ........ 111
3.12.2 Measurement of ABCD Parameters by Test ........... 112
3.12.3 А, В, C, and D Constants of Transformer .......... 116
3.12.4 Asymmetrical π and T Networks .................... 117
3.12.5 Networks Connected in Series ..................... 119
3.12.6 Networks Connected in Parallel ................... 121
3.12.7 Terminated Transmission Line ..................... 123
3.12.8 Power Relations Using А, В, C, and D Line
Constants ........................................ 127
3.13 EHV Underground Cable Transmission ....................... 134
3.14 Gas-Insulated Transmission Lines ......................... 142
3.15 Bundled Conductors ....................................... 147
3.16 Effect of Ground on Capacitance of Three-Phase Lines ..... 151
3.17 Environmental Effects of Overhead Transmission Lines ..... 152
References ............................................... 153
General References ....................................... 153
Chapter 4 Disturbance of Normal Operating Conditions and
Other Problems ................................................ 159
4.1 Introduction ............................................. 159
4.2 Fault Analysis and Fault Types ........................... 161
4.3 Balanced Three-Phase Faults at No Load ................... 164
4.4 Fault Interruption ....................................... 168
4.5 Balanced Three-Phase Faults at Full Load ................. 175
4.6 Application of Current-Limiting Reactors ................. 181
4.7 Insulators ............................................... 185
4.7.1 Types of Insulators ............................... 185
4.7.2 Testing of Insulators ............................. 187
4.7.3 Voltage Distribution over a String of Suspension
Insulators ........................................ 189
4.7.4 Insulator Flashover due to Contamination .......... 194
4.7.5 Insulator Flashover on Overhead High-Voltage DC
Lines ............................................. 196
4.8 Grounding ................................................ 197
4.8.1 Electric Shock and Its Effects on Humans .......... 197
4.8.2 Reduction of Factor C8 ............................ 204
4.8.3 GPR and Ground Resistance ......................... 206
4.8.4 Ground Resistance ................................. 207
4.8.5 Soil Resistivity Measurements ..................... 209
4.8.5.1 Wenner Four-Pin Method ................... 209
4.8.5.2 Three-Pin or Driven-Ground Rod Method .... 213
4.8.5.1 Substation Grounding ..................... 214
4.10 Ground Conductor Sizing Factors .......................... 218
4.11 Mesh Voltage Design Calculations ......................... 221
4.12 Step Voltage Design Calculations ......................... 223
4.13 Types of Ground Faults ................................... 223
4.13.1 Line-to-Line-to-Ground Fault ...................... 223
4.13.2 Single-Line-to-Ground Fault ....................... 224
4.14 Ground Potential Rise .................................... 224
4.15 Transmission Line Grounds ................................ 233
4.16 Types of Grounding ....................................... 235
References ............................................... 238
General References ....................................... 239
Chapter 5 Symmetrical Components and Sequence Impedances ..... 245
5.1 Introduction ............................................. 245
5.2 Symmetrical Components ................................... 245
5.3 Operator a ............................................... 247
5.4 Resolution of Three-Phase Unbalanced System of Phasors
into Its Symmetrical Components .......................... 248
5.5 Power in Symmetrical Components .......................... 252
5.6 Sequence Impedances of Transmission Lines ................ 255
5.6.1 Sequence Impedances of Untransposed Lines ......... 255
5.6.2 Sequence Impedances of Transposed Lines ........... 257
5.6.3 Electromagnetic Unbalances due to Untransposed
Lines ............................................. 260
5.6.4 Sequence Impedances of Untransposed Line with
Overhead Ground Wire .............................. 267
5.7 Sequence Capacitances of Transmission Line ............... 268
5.7.1 Three-Phase Transmission Line without Overhead
Ground Wire ....................................... 268
5.7.2 Three-Phase Transmission Line with Overhead
Ground Wire ....................................... 271
5.8 Sequence Impedances of Synchronous Machines .............. 275
5.9 Zero-Sequence Networks ................................... 280
5.10 Sequence Impedances of Transformers ...................... 281
References ............................................... 288
General References ....................................... 288
Chapter 6 Analysis of Unbalanced Faults ...................... 293
6.1 Introduction ............................................. 293
6.2 Shunt Faults ............................................. 293
6.2.1 SLG Fault ......................................... 293
6.2.2 Line-to-Line Fault ................................ 302
6.2.3 DLG Fault ......................................... 307
6.2.4 Symmetrical Three-Phase Faults .................... 312
6.2.5 Unsymmetrical Three-Phase Faults .................. 317
6.3 Generalized Fault Diagrams for Shunt Faults .............. 323
6.4 Series Faults ............................................ 329
6.4.1 One Line Open ..................................... 330
6.4.2 Two Lines Open .................................... 330
6.5 Determination of Sequence Network Equivalents for Series
Faults ................................................... 332
6.5.1 Brief Review of Two-Port Theory ................... 332
6.5.2 Equivalent Zero-Sequence Networks ................. 333
6.5.3 Equivalent Positive- and Negative-Sequence
Networks .......................................... 334
6.6 Generalized Fault Diagram for Series Faults .............. 339
6.7 System Grounding ......................................... 343
6.8 Elimination of SLG Fault Current by Using Peterson
Coils .................................................... 349
6.9 Six-Phase Systems ........................................ 352
6.9.1 Application of Symmetrical Components ............. 353
6.9.2 Transformations ................................... 353
6.9.3 Electromagnetic Unbalance Factors ................. 355
6.9.4 Transposition on the Six-Phase Lines .............. 357
6.9.5 Phase Arrangements ................................ 358
6.9.6 Overhead Ground Wires ............................. 358
6.9.7 Double-Circuit Transmission Lines ................. 358
References ............................................... 361
General References ....................................... 361
Chapter 7 System Protection .................................. 373
7.1 Introduction ............................................. 373
7.2 Basic Definitions and Standard Device Numbers ............ 377
7.3 Factors Affecting Protective System Design ............... 380
7.4 Design Criteria for Protective Systems ................... 380
7.5 Primary and Backup Protection ............................ 382
7.6 Relays ................................................... 385
7.7 Sequence Filters ......................................... 394
7.8 Instrument Transformers .................................. 396
7.8.1 Current Transformers .............................. 397
7.8.1.1 Method 1. The Formula Method ............. 400
7.8.1.2 Method 2. The Saturation Curve Method .... 401
7.8.2 Voltage Transformers .............................. 402
7.9 R-X Diagram .............................................. 403
7.10 Relays as Comparators .................................... 409
7.11 Duality between Phase and Amplitude Comparators .......... 409
7.12 Complex Planes ........................................... 410
7.13 General Equation of Comparators .......................... 412
7.14 Amplitude Comparator ..................................... 413
7.15 Phase Comparator ......................................... 414
7.16 General Equation of Relays ............................... 418
7.17 Distance Relays .......................................... 419
7.17.1 Impedance Relay ................................... 422
7.17.2 Reactance Relay ................................... 427
7.17.3 Admittance (Mho) Relay ............................ 429
7.17.4 Offset Mho (Modified Impedance) Relay ............. 431
7.17.5 Ohm Relay ......................................... 433
7.18 Overcurrent Relays ....................................... 439
7.19 Differential Protection .................................. 450
7.20 Pilot Relaying ........................................... 459
7.21 Computer Applications in Protective Relaying ............. 462
7.21.1 Computer Applications in Relay Settings and
Coordination ...................................... 462
7.21.2 Computer Relaying ................................. 462
7.21.1 References ........................................ 464
General References ....................................... 465
Chapter 8 Power Flow Analysis ................................ 471
8.1 Introduction ............................................. 471
8.2 Power Flow Problem ....................................... 473
8.3 Sign of Real and Reactive Powers .................... 475
8.4 Gauss Iterative Method ................................... 476
8.5 Gauss-Seidel Iterative Method ............................ 477
8.6 Application of Gauss-Seidel Method: Ybus ................. 478
8.7 Application of Acceleration Factors ...................... 482
8.8 Special Features ......................................... 482
8.8.1 LTC Transformers .................................. 483
8.8.2 Phase-Shifting Transformers ....................... 483
8.8.3 Area Power Interchange Control .................... 484
8.9 Application of Gauss-Seidel Method: Zbus ................. 488
8.10 Newton-Raphson Method .................................... 489
8.11 Application of Newton-Raphson Method ..................... 493
8.11.1 Application of Newton-Raphson Method to Load
Flow Equations in Rectangular Coordinates ......... 493
8.11.2 Application of Newton-Raphson Method to Load
Flow Equations in Polar Coordinates ............... 504
8.11.2.1 Method 1. First Type of Formulation of
Jacobian Matrix ......................... 505
8.11.2.2 Method 2. Second Type of Formulation
of Jacobian Matrix ...................... 509
8.12 Decoupled Power Flow Method .............................. 510
8.13 Fast Decoupled Power Flow Method ......................... 511
8.14 The DC Power Flow Method ................................. 513
References .................................................... 525
General References ............................................ 527
Appendix A: Impedance Tables for Overhead Lines,
Transformers, and Underground Cables .............. 533
Appendix B: Standard Device Numbers Used in Protection
Systems ........................................... 621
Appendix C: Unit Conversions from English System to SI
System ............................................ 623
Appendix D: Unit Conversions from SI System to English
System ............................................ 625
Appendix E: Prefixes .......................................... 627
Appendix F: Greek Alphabet Used for Symbols ................... 629
Appendix G: Additional Solved Examples of Shunt Faults ........ 631
Appendix H: Additional Solved Examples of Shunt Faults Using
MATLAB ............................................ 655
Appendix I: Glossary for Modern Power System Analysis
Terminology ....................................... 683
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