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Cover image for Power system analysis : short-circuit load flow and harmonics
Title:
Power system analysis : short-circuit load flow and harmonics
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Publication Information:
New York : Marcel Dekker, 2002
ISBN:
9780824707378

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30000010018787 TK1005 D37 2002 Open Access Book Book
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Summary

Summary

Featuring extensive calculations and examples, this reference discusses theoretical and practical aspects of short-circuit currents in ac and dc systems, load flow, and harmonic analyses to provide a sound knowledge base for modern computer-based studies that can be utilized in real-world applications. Presenting more than 2300 figures, tables, and equations, the author explores matrix methods for network solutions and includes load flow and optimization techniques. He discusses ac and dc short-circuit systems calculations in accordance with standards set by the American National Standards Institute (ANSI) and the International Electrotechnical Commission (IEC) .


Author Notes

J. C. Das is a Staff Consultant, Electrical Power Systems, for Amec, Inc., Atlanta, Georgia


Table of Contents

Series Introductionp. iii
Prefacep. v
1. Short-Circuit Currents and Symmetrical Componentsp. 1
1.1 Nature of Short-Circuit Currentsp. 2
1.2 Symmetrical Componentsp. 5
1.3 Eigenvalues and Eigenvectorsp. 8
1.4 Symmetrical Component Transformationp. 9
1.5 Clarke Component Transformationp. 15
1.6 Characteristics of Symmetrical Componentsp. 16
1.7 Sequence Impedance of Network Componentsp. 20
1.8 Computer Models of Sequence Networksp. 35
2. Unsymmetrical Fault Calculationsp. 39
2.1 Line-to-Ground Faultp. 40
2.2 Line-to-Line Faultp. 42
2.3 Double Line-to-Ground Faultp. 43
2.4 Three-Phase Faultp. 45
2.5 Phase Shift in Three-Phase Transformersp. 46
2.6 Unsymmetrical Fault Calculationsp. 53
2.7 System Grounding and Sequence Componentsp. 61
2.8 Open Conductor Faultsp. 64
3. Matrix Methods for Network Solutionsp. 72
3.1 Network Modelsp. 73
3.2 Bus Admittance Matrixp. 73
3.3 Bus Impedance Matrixp. 78
3.4 Loop Admittance and Impedance Matricesp. 81
3.5 Graph Theoryp. 82
3.6 Bus Admittance and Impedance Matrices by Graph Approachp. 86
3.7 Algorithms for Construction of Bus Impedance Matrixp. 89
3.8 Short-Circuit Calculations with Bus Impedance Matrixp. 103
3.9 Solution of Large Network Equationsp. 113
4. Current Interruption in AC Networksp. 116
4.1 Rheostatic Breakerp. 117
4.2 Current-Zero Breakerp. 118
4.3 Transient Recovery Voltagep. 120
4.4 The Terminal Faultp. 125
4.5 The Short-Line Faultp. 127
4.6 Interruption of Low Inductive Currentsp. 127
4.7 Interruption of Capacitive Currentsp. 130
4.8 Prestrikes in Breakersp. 133
4.9 Overvoltages on Energizing High-Voltage Linesp. 134
4.10 Out-of-Phase Closingp. 136
4.11 Resistance Switchingp. 137
4.12 Failure Modes of Circuit Breakersp. 139
5. Application and Ratings of Circuit Breakers and Fuses According to ANSI Standardsp. 145
5.1 Total and Symmetrical Current Rating Basisp. 145
5.2 Asymmetrical Ratingsp. 147
5.3 Voltage Range Factor Kp. 148
5.4 Capabilities for Ground Faultsp. 148
5.5 Closing-Latching-Carrying Interrupting Capabilitiesp. 149
5.6 Short-Time Current Carrying Capabilityp. 153
5.7 Service Capability Duty Requirements and Reclosing Capabilityp. 153
5.8 Capacitance Current Switchingp. 155
5.9 Line Closing Switching Surge Factorp. 160
5.10 Out-of-Phase Switching Current Ratingp. 162
5.11 Transient Recovery Voltagep. 163
5.12 Low-Voltage Circuit Breakersp. 168
5.13 Fusesp. 173
6. Short-Circuit of Synchronous and Induction Machinesp. 179
6.1 Reactances of a Synchronous Machinep. 180
6.2 Saturation of Reactancesp. 182
6.3 Time Constants of Synchronous Machinesp. 183
6.4 Synchronous Machine Behavior on Terminal Short-Circuitp. 183
6.5 Circuit Equations of Unit Machinesp. 194
6.6 Park's Transformationp. 198
6.7 Park's Voltage Equationp. 202
6.8 Circuit Model of Synchronous Machinesp. 203
6.9 Calculation Procedure and Examplesp. 204
6.10 Short-Circuit of an Induction Motorp. 214
7. Short-Circuit Calculations According to ANSI Standardsp. 219
7.1 Types of Calculationsp. 219
7.2 Impedance Multiplying Factorsp. 220
7.3 Rotating Machines Modelp. 222
7.4 Types and Severity of System Short-Circuitsp. 222
7.5 Calculation Methodsp. 223
7.6 Network Reductionp. 231
7.7 Breaker Duty Calculationsp. 233
7.8 High X/R Ratios (DC Time Constant Greater than 45ms)p. 233
7.9 Calculation Procedurep. 235
7.10 Examples of Calculationsp. 236
7.11 Thirty-Cycle Short-Circuit Currentsp. 261
7.12 Dynamic Simulationp. 262
8. Short-Circuit Calculations According to IEC Standardsp. 267
8.1 Conceptual and Analytical Differencesp. 267
8.2 Prefault Voltagep. 271
8.3 Far-From-Generator Faultsp. 271
8.4 Near-to-Generator Faultsp. 275
8.5 Influence of Motorsp. 281
8.6 Comparison with ANSI Calculation Proceduresp. 283
8.7 Examples of Calculations and Comparison with ANSI Methodsp. 285
9. Calculations of Short-Circuit Currents in DC Systemsp. 302
9.1 DC Short-Circuit Current Sourcesp. 303
9.2 Calculation Proceduresp. 304
9.3 Short-Circuit of a Lead Acid Batteryp. 306
9.4 DC Motor and Generatorsp. 312
9.5 Short-Circuit Current of a Rectifierp. 318
9.6 Short-Circuit of a Charged Capacitorp. 324
9.7 Total Short-Circuit Currentp. 325
9.8 DC Circuit Breakersp. 326
10. Load Flow Over Power Transmission Linesp. 328
10.1 Power in AC Circuitsp. 329
10.2 Power Flow in a Nodal Branchp. 331
10.3 ABCD Constantsp. 334
10.4 Transmission Line Modelsp. 336
10.5 Tuned Power Linep. 345
10.6 Ferranti Effectp. 346
10.7 Symmetrical Line at No Loadp. 347
10.8 Illustrative Examplesp. 349
10.9 Circle Diagramsp. 352
10.10 System Variables in Load Flowp. 356
11. Load Flow Methodsp. 360
11.1 Modeling a Two-Winding Transformerp. 361
11.2 Load Flow, Bus Typesp. 366
11.3 Gauss and Gauss-Seidel Y-Matrix Methodsp. 367
11.4 Convergence in Jacobi-Type Methodsp. 377
11.5 Gauss-Seidel Z-Matrix Methodp. 383
11.6 Conversion of Y to Z Matrixp. 384
12. Load Flow Methods: Part IIp. 391
12.1 Function with One Variablep. 391
12.2 Simultaneous Equationsp. 393
12.3 Rectangular Form of Newton-Raphson Method of Load Flowp. 395
12.4 Polar Form of Jacobian Matrixp. 397
12.5 Simplifications of Newton-Raphson Methodp. 405
12.6 Decoupled Newton-Raphson Methodp. 408
12.7 Fast Decoupled Load Flowp. 408
12.8 Model of a Phase-Shifting Transformerp. 411
12.9 DC Modelsp. 413
12.10 Load Modelsp. 415
12.11 Impact Loads and Motor Startingp. 422
12.12 Practical Load Flow Studiesp. 424
13. Reactive Power Flow and Controlp. 435
13.1 Voltage Instabilityp. 436
13.2 Reactive Power Compensationp. 442
13.3 Reactive Power Control Devicesp. 447
13.4 Some Examples of Reactive Power Flowp. 460
13.5 FACTSp. 467
14. Three-Phase and Distribution System Load Flowp. 478
14.1 Phase Co-Ordinate Methodp. 479
14.2 Three-Phase Modelsp. 481
14.3 Distribution System Load Flowp. 491
15. Optimization Techniquesp. 500
15.1 Functions of One Variablep. 501
15.2 Concave and Convex Functionsp. 502
15.3 Taylor's Theoremp. 503
15.4 Lagrangian Method, Constrained Optimizationp. 505
15.5 Multiple Equality Constraintsp. 507
15.6 Optimal Load Sharing Between Generatorsp. 508
15.7 Inequality Constraintsp. 510
15.8 Kuhn-Tucker Theoremp. 511
15.9 Search Methodsp. 512
15.10 Gradient Methodsp. 514
15.11 Linear Programming--Simplex Methodp. 516
15.12 Quadratic Programmingp. 521
15.13 Dynamic Programmingp. 521
15.14 Integer Programmingp. 523
16. Optimal Power Flowp. 525
16.1 Optimal Power Flowp. 525
16.2 Decoupling Real and Reactive OPFp. 527
16.3 Solution Methods of OPFp. 528
16.4 Generation Scheduling Considering Transmission Lossesp. 528
16.5 Steepest Gradient Methodp. 536
16.6 OPF Using Newton's Methodp. 539
16.7 Successive Quadratic Programmingp. 545
16.8 Successive Linear Programmingp. 545
16.9 Interior Point Methods and Variantsp. 547
16.10 Security and Environmental Constrained OPFp. 551
17. Harmonics Generationp. 554
17.1 Harmonics and Sequence Componentsp. 556
17.2 Increase in Nonlinear Loadsp. 557
17.3 Harmonic Factorp. 557
17.4 Three-Phase Windings in Electrical Machinesp. 557
17.5 Tooth Ripples in Electrical Machinesp. 559
17.6 Synchronous Generatorsp. 560
17.7 Transformersp. 560
17.8 Saturation of Current Transformersp. 564
17.9 Shunt Capacitorsp. 565
17.10 Subharmonic Frequenciesp. 565
17.11 Static Power Convertersp. 566
17.12 Switch-Mode Power (SMP) Suppliesp. 581
17.13 Arc Furnacesp. 582
17.14 Cycloconvertersp. 584
17.15 Thyristor-Controlled Factorp. 586
17.16 Thyristor-Switched Capacitorsp. 588
17.17 Pulse Width Modulationp. 588
17.18 Adjustable Speed Drivesp. 591
17.19 Pulse burst Modulationp. 591
17.20 Chopper Circuits and Electric Tractionp. 592
17.21 Slip Frequency Recovery Schemesp. 594
17.22 Lighting Ballastsp. 594
17.23 Interharmonicsp. 595
18. Effects of Harmonicsp. 597
18.1 Rotating Machinesp. 598
18.2 Transformersp. 603
18.3 Cablesp. 607
18.4 Capacitorsp. 608
18.5 Harmonic Resonancep. 609
18.6 Voltage Notchingp. 613
18.7 EMI (Electromagnetic Interference)p. 613
18.8 Overloading of Neutralp. 614
18.9 Protective Relays and Metersp. 615
18.10 Circuit Breakers and Fusesp. 615
18.11 Telephone Influence Factorp. 616
19. Harmonic Analysisp. 619
19.1 Harmonic Analysis Methodsp. 620
19.2 Harmonic Modeling of System Componentsp. 626
19.3 Load Modelsp. 630
19.4 System Impedancep. 630
19.5 Three-Phase Modelsp. 631
19.6 Modeling of Networksp. 633
19.7 Power Factor and Reactive Powerp. 637
19.8 Shunt Capacitor Bank Arrangementsp. 640
19.9 Study Casesp. 644
20. Harmonic Mitigation and Filtersp. 664
20.1 Mitigation of Harmonicsp. 664
20.2 Band Pass Filtersp. 665
20.3 Practical Filter Designp. 668
20.4 Relations in a ST Filterp. 678
20.5 Filters for a Furnace Installationp. 681
20.6 Filters for an Industrial Distribution Systemp. 683
20.7 Secondary Resonancep. 684
20.8 Filter Reactorsp. 686
20.9 Double-Tuned Filterp. 687
20.10 Damped Filtersp. 689
20.11 Design of a Second-Order High-Pass Filterp. 693
20.12 Zero Sequence Trapsp. 694
20.13 Limitations of Passive Filtersp. 696
20.14 Active Filtersp. 698
20.15 Corrections in Time Domainp. 701
20.16 Corrections in the Frequency Domainp. 702
20.17 Instantaneous Reactive Powerp. 704
20.18 Harmonic Mitigation at Sourcep. 706
Appendix A Matrix Methodsp. 712
A.1 Review Summaryp. 712
A.2 Characteristics Roots, Eigenvalues, and Eigenvectorsp. 716
A.3 Diagonalization of a Matrixp. 718
A.4 Linear Independence or Dependence of Vectorsp. 719
A.5 Quadratic Form Expressed as a Product of Matricesp. 719
A.6 Derivatives of Scalar and Vector Functionsp. 720
A.7 Inverse of a Matrixp. 721
A.8 Solution of Large Simultaneous Equationsp. 725
A.9 Crout's Transformationp. 727
A.10 Gaussian Eliminationp. 729
A.11 Forward-Backward Substitution Methodp. 730
A.12 LDU (Product Form, Cascade, or Choleski Form)p. 733
Appendix B Calculation of Line and Cable Constantsp. 736
B.1 AC Resistancep. 736
B.2 Inductancep. 736
B.3 Impedance Matrixp. 739
B.4 Three-Phase Line with Ground Conductorsp. 739
B.5 Bundle Conductorsp. 741
B.6 Carson's Formulap. 742
B.7 Capacitance of Linesp. 748
B.8 Cable Constantsp. 751
Appendix C Transformers and Reactorsp. 756
C.1 Model of a Two-Winding Transformerp. 756
C.2 Transformer Polarity and Terminal Connectionsp. 761
C.3 Parallel Operation of Transformersp. 763
C.4 Autotransformersp. 765
C.5 Step-Voltage Regulatorsp. 770
C.6 Extended Models of Transformersp. 770
C.7 High-Frequency Modelsp. 776
C.8 Duality Modelsp. 776
C.9 GIC Modelsp. 779
C.10 Reactorsp. 780
Appendix D Sparsity and Optimal Orderingp. 784
D.1 Optimal Orderingp. 784
D.2 Flow Graphsp. 785
D.3 Optimal Ordering Schemesp. 788
Appendix E Fourier Analysisp. 792
E.1 Periodic Functionsp. 792
E.2 Orthogonal Functionsp. 792
E.3 Fourier Series and Coefficientsp. 792
E.4 Odd Symmetryp. 795
E.5 Even Symmetryp. 795
E.6 Half-Wave Symmetryp. 796
E.7 Harmonic Spectrump. 797
E.8 Complex Form of Fourier Seriesp. 799
E.9 Fourier Transformp. 800
E.10 Sampled Waveform: Discrete Fourier Transformp. 803
E.11 Fast Fourier Transformp. 807
Appendix F Limitation of Harmonicsp. 809
F.1 Harmonic Current Limitsp. 809
F.2 Voltage Qualityp. 811
F.3 Commutation Notchesp. 813
F.4 Interharmonicsp. 816
F.5 Flickerp. 817
Appendix G Estimating Line Harmonicsp. 819
G.1 Waveform without Ripple Contentp. 819
G.2 Waveform with Ripple Contentp. 821
G.3 Phase Angle of Harmonicsp. 827
Indexp. 831
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