Analysis of Faulted Power Systems Paul Anderson

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Front Cover
	Table of Contents
	Preface to the IEEE Reissued Edition 
	Preface 
	List of Symbols 
	Chapter 1. General Considerations 
	1.1 Per Unit Calculations 5
	1.2 Change of Base 
	1.3 Base Value Charts
	1.4 Three-Phase Systems
	1.5 Converting from Per Unit Values to System Values 10
	1.6 Examples of Per Unit Calculations 10
	1.7 Phasor Notation 15
	1.8 The Phasor a or a-Operator 16
	Problems 17
	Chapter 2. Symmetrical Components
	2.1 Symmetrical Components of an n-Phase system 19
	2.2 Symmetrical Components of a Three-Phase System 23
	2.3 Symmetrical Components of Current Phasors 25
	2.4 Computing Power of Symmetrical Components 25
	2.5 Sequence Components of Unbalanced Network Impedances 27
	2.6 Sequence Components of Machine Impedances 30
	2.7 Definition of Sequence Networks 31
	Problems 33
	Chapter 3. Analysis of Unsymmetrical Faults: Three-Component Method 
	I. Shunt Faults 
	3.1 The Single-Line-to-Ground (SLG) Fault 37
	3.2 The Line-to-Line (LL) Fault 42
	3.3 The Double Line-to-Ground (2LG) Fault 44
	3.4 The Three-Phase (3Ø) Fault 49
	3.5 Other Types of Shunt Faults 52
	3.6 Comments on Shunt Fault Calculation 53
	II. Series Faults 53
	3.7 Sequence Network Equivalents for Series Faults 55
	3.8 Unequal Series Impedances 61
	3.9 One Line Open (1LO) 63
	3.10 Two Lines Open (2LO) 64
	3.11 Other Series Faults 66
	Problems 66
	Chapter 4. Sequence Impedance of Transmission Lines
	4.1 Positive and Negative. Sequence Impedances of Lines 71
	4.2 Mutual Coupling 73
	4.3 Self and Mutual Inductances of Parallel Cylindrical Wires 75
	4.4 Carson’s Line 78
	4.5 Three-Phase Line Impedances 81
	4.6 Transpositions and Twists of Line Conductors 84
	4.7 Completely Transposed Lines 98
	4.8 Circuit Unbalance Due to Incomplete Transposition 102
	4.9 Sequence Impedance of Lines with Bundled Conductors 106
	4.10 Sequence Impedance of Lines with One Ground Wire 112
	4.11 Sequence Impedance of Lines with Two Ground Wires 123
	4.12 Sequence Impedance of Lines with n Ground Wires 128
	4.13 Zero Sequence Impedance of Transposed Lines with Ground Wires 129
	4.14 Computations Involving Steel Conductors 133
	4.15 Parallel Transposed and Untransposed Multicircuit Lines 137
	4.16 Optimizing a Parallel Circuit for Minimum Unbalance 143
	Problems 145
	Chapter 5. Sequence Capacitance of Transmission Lines
	5.1 Positive and Negative Sequence Capacitance of Transposed Lines 152
	5.2 Zero Sequence Capacitance of Transposed Lines 156
	5.3 Mutual Capacitance of Transmission Lines 158
	5.4 Mutual Capacitance of Three-Phase Lines without ground Wires 163
	5.5 Sequence Capacitance of a Transposed Line without Ground Wires 166
	5.6 Mutual Capacitance of Three-Phase Lines with Ground Wires 168
	5.7 Capacitance of Double Circuit Lines 172
	5.8 Electrostatic Unbalance of Untransposed Lines 177
	Problems 181
	Chapter 6. Sequence Impedance of Machines
	I. Synchronous Machine Impedances 183
	6.1 General Considerations 183
	6.2 Positive Sequence Impedance 189
	6.3 Negative Sequence Impedance 199
	6.4 Zero Sequence Impedance 201
	6.5 Time Constants 203
	6.6 Synchronous Generator Equivalent Circuits 205
	6.7 Phasor Diagram of a Synchronous Generator 207
	6.8 Subtransient Phasor Diagram and Equivalent Circuit 214
	6.9 Armature Current Envelope 219
	6.10 Momentary Currents 221
	II. Induction Motor Impedances 222
	6.11 General Considerations 222
	6.12 Induction Motor Equivalent Circuit 222
	6.13 Induction Motor Subtransient Fault Contribution 226
	6.14 Operation with One Phase Open 227
	Problems 228
	Chapter 7. Sequence Impedance of Transformers 
	I. Single-Phase Transformers 231
	7.1 Single-Phase Transformer Equivalents 231
	7.2 Transformer Impedances 233
	7.3 Transformer Polarity and Terminal Markings 234
	7.4 Three-Winding Transformers 236
	7.5 Autotransformer Equivalents 239
	7.6 Three-Phase Banks of Single-Phase Units 243 
	II. Three-Phase Transformers 247 
	7.7 Three-Phase Transformer Terminal Markings 247
	7.8 Phase Shift in Y-∆ Transformers 248
	7.9 Zero Sequence Impedance of Three-Phase Transformers 251
	7.10 Grounding Transformers 255
	7.11 The Zigzag - ∆ Power Transformer 257
	III. Transformers in System Studies 260
	7.12 Off-Nominal Turns Ratios 260
	7.13 Three-Winding Off-Nominal Transformers 265 
	Problems 265 
	Chapter 8. Changes in Symmetry
	8.1 Creating Symmetry by Labeling 273
	8.2 Generalized Fault Diagrams for Shunt (Transverse) Faults 273
	8.3 Generalized Fault Diagrams for Series (Longitudinal) Faults 278
	8.4 Computation of Fault Cun’ents and Voltages 280
	8.5 A Fundamental Result: The Invariance of Power 284
	8.6 Constraint Matrix K 286
	8.7 Kron’s Primitive Network 288
	8.8 Other Useful Transformations 291
	8.9 Shunt Fault Transformations 294
	8.10 Transformations for Shunt Faults with Impedance 298
	8.11 Series Fault Transformations 304
	8.12 Summary 304
	Problems 305
	Chapter 9. Simultaneous Faults
	I. Simultaneous Faults by Two-Port Network Theory 308
	9.1 Two-Port Networks 308
	9.2 Interconnection of Two-Port Networks 319
	9.3 Simultaneous Fault Connection of Sequence Networks 323
	9.4 Series-Series Connection (Z-Type Faults) 325
	9.5 Parallel-Parallel Connection (Y-Type Faults) 330
	9.6 Series-Parallel Connection (H-Type Faults) 334
	II. Simultaneous Faults by Matrix Transformations 336
	9.7 Constraint Matrix for Z-Type Faults 337
	9.8 Constraint Matrix for Y-Type and H-Type Faults 339
	Problems 341 
	Chapter 10. Analytical Simplifications 
	10.1 Two-Component Method 345
	I. Shunt Faults 347
	10.2 Single-Line-to-Ground Fault 347
	10.3 Line-to-Line Fault 349
	10.4 Double Line-to-Ground Fault 350 
	10.5 Three-Phase Fault 352
	II. Series Faults 353
	10.6 Two Lines Open (2LO) 353
	10.7 One Line Open (1LO) 354
	III. Changes in Symmetry with Two-Component Calculations 355
	10.8 Phase Shifting Transformer Relations 356 
	10.9 SLG Faults with Arbitrary Symmetry 357 
	10.10 2LG Faults with Arbitrary Symmetry 358
	10.11 Series Faults with Arbitrary Symmetry 360
	IV. Solution of the Generalized Fault Diagrams 362
	10.12 Series Network Connection—SLG and 2LO Faults 362
	10.13 Parallel Network Connection - 2LG and 1LO Faults 363
	Problems 363
	Chapter 11. Computer Solution Methods Using the Admittance Matrix 
	11.1 Primitive Matrix 366
	11.2 Node Incidence Matrix 369
	11.3 Node Admittance and Impedance Matrices 373
	11.4 Indefinite Admittance Matrix 375
	11.5 Definite Admittance Matrix 386
	Problems 389
	Chapter 12. Computer Solution Methods Using the Impedance Matrix 
	12.1 Impedance Matrix in Shunt Fault Computations 393
	12.2 An Impedance Matrix Algorithm 401
	12.3 Adding a Radial Impedance to the Reference 401
	12.4 Adding a Radial Branch to a New Node 402 
	12.5 Closing a Loop to the Reference 403 
	12.6 Closing a Loop Not Involving the Reference 404 
	12.7 Adding a Mutually Coupled Radial Element 408 
	12.8 Adding a Group of Mutually Coupled Lines 415
	12.9 Comparison of Admittance and Impedance Matrix Techniques 418
	Problems 419
	Appendix A. Matrix Algebra 421
	Appendix B. Line Impedance Tables 436 
	Appendix C. Trigonometric Identities for Three-Phase Systems 467 
	Appendix D. Self Inductance of a Straight Finite Cylindrical Wire 470
	Appendix E. Solved Examples 474
	Appendix F. ∆ -Y Transformations 502
	Bibliography 503 
	Index 507