Power Systems Modelling and Fault Analysis : Theory and Practice

Power Systems Modelling and Fault Analysis: Theory and Practice, Second Edition, focuses on the important core areas and technical skills required for practicing electrical power engineers. Providing a comprehensive and practical treatment of the modeling of electrical power systems, the book offers students and professionals the theory and practice of fault analysis of power systems, covering detailed and advanced theories and modern industry practices. The book describes relevant advances in the industry, such as international standards developments and new generation technologies, such as wind turbine generators, fault current limiters, multi-phase fault analysis, the measurement of equipment parameters, probabilistic short-circuit analysis, and more. Includes a fully up-to-date guide to the analysis and practical troubleshooting of short-circuit faults in electricity utilities and industrial power systems Presents sections on generators, transformers, substations, overhead powerlines and industrial systems Covers best-practice techniques, safety issues, power system planning and economics Cover......Page 1 Power Systems Modelling and Fault Analysis: Theory and Practice ......Page 3 Copyright......Page 4 Dedication......Page 5 List of electrical symbols......Page 6 Foreword to second edition......Page 9 Foreword to first edition......Page 12 Preface to the second edition......Page 14 Preface to first edition......Page 16 Biography......Page 20 1.1 General......Page 21 1.2 Structure of modern power systems......Page 22 1.3.2 Health and safety considerations......Page 23 1.3.4 Design of power system equipment......Page 29 1.4.2 Types of faults......Page 30 1.4.3 Causes of faults......Page 31 1.4.4 Characterisation of faults......Page 32 Three-phase short-circuit currents......Page 34 One-phase short-circuit current......Page 37 1.5.2 Terminology of short-circuit current interruption......Page 39 1.6.2 Mechanical effects......Page 42 1.7.2 Single-phase systems......Page 45 1.7.3 Change of base quantities......Page 48 1.7.4 Three-phase systems......Page 49 1.7.5 Mutually coupled systems having different operating voltages......Page 50 Base and per-unit values of mutual inductive impedance......Page 51 Base and per-unit values of mutual capacitive admittance......Page 53 1.7.6 Examples......Page 56 Further reading......Page 59 Chapter Outline......Page 60 2.1 General......Page 61 2.2.1 Symmetrical components of balanced three-phase voltage and current phasors......Page 62 2.2.2 Symmetrical components of unbalanced voltage and current phasors......Page 64 2.2.4 Definition of phase sequence component networks of a three-phase power system containing balanced voltage sources......Page 67 2.2.5 Sequence impedances of coupled unbalanced three-phase impedances......Page 70 2.2.6 Sequence impedances of coupled balanced three-phase impedances......Page 73 2.2.8 Examples......Page 74 2.3.2 Balanced three-phase to earth short-circuit faults......Page 77 2.3.3 Balanced three-phase clear of earth short-circuit faults......Page 79 2.3.4 Unbalanced one-phase to earth short-circuit faults......Page 81 2.3.5 Unbalanced phase-to-phase or two-phase short-circuit faults......Page 83 2.3.6 Unbalanced two-phase to earth short-circuit faults......Page 85 2.3.7 Unbalanced one-phase open-circuit faults......Page 88 2.3.8 Unbalanced two-phase open-circuit faults......Page 90 2.3.9 Example......Page 92 2.4.2 One-phase to earth short-circuit faults......Page 94 2.4.3 Two-phase to earth short-circuit faults......Page 95 2.5.2 Simultaneous short-circuit faults at the same location......Page 97 2.5.3 Cross-country faults or simultaneous faults at different locations......Page 100 2.5.4 Simultaneous open-circuit and short-circuit faults at the same location......Page 101 2.5.5 Simultaneous faults caused by broken and fallen to earth conductors......Page 102 2.5.6 Simultaneous short-circuit and open-circuit faults on distribution transformers......Page 103 2.6.1 General......Page 107 2.6.2 Symmetrical components of voltage and current sources......Page 108 2.6.3 Balanced three-phase to earth short-circuit faults......Page 109 Current sources produce positive-sequence current only......Page 110 Current sources produce positive- and negative-sequence currents......Page 112 Current sources produce positive-sequence current only......Page 114 Current sources produce positive- and negative-sequence currents......Page 116 Books......Page 117 Paper......Page 118 Chapter Outline......Page 119 3.2.1 Background......Page 120 General......Page 122 Potential coefficients, shunt capacitances and susceptances......Page 124 Self impedance......Page 125 Earth return path impedances......Page 128 Summary of self and mutual impedances......Page 130 Stranded conductors......Page 132 Bundled phase conductors......Page 134 Average height of conductor above earth......Page 136 Phase and sequence series impedance matrices......Page 137 Phase and sequence shunt susceptance matrices......Page 142 3.2.4 Transposition of single-circuit three-phase overhead lines......Page 145 Phase and sequence series impedance matrices......Page 151 Phase and sequence shunt susceptance matrices......Page 154 3.2.6 Transposition of double-circuit overhead lines......Page 156 3.2.7 Phase and sequence parameter matrices of untransposed and transposed multiple-circuit lines......Page 172 Lines with three coupled circuits......Page 173 Lines with four coupled circuits......Page 174 3.2.8 Examples......Page 176 Potential coefficients, capacitance, phase and sequence susceptance matrices......Page 179 Phase and sequence impedance matrices......Page 182 Potential coefficients, capacitance, phase and sequence susceptance matrices......Page 185 Phase and sequence impedance matrices......Page 187 3.3.1 Background......Page 190 Single-point bonded cables......Page 192 Cross-bonded cables......Page 193 General......Page 194 Shunt capacitances and susceptances......Page 195 Single-core underground cables......Page 198 Single-core submarine cables......Page 202 Three-core armoured cables and pipe-type cables......Page 203 Power frequency impedance equations......Page 205 ac resistance at power frequency......Page 207 General......Page 209 Three-core cables, three single-core cables in touching trefoil and three single-core cables in equilateral layout......Page 210 Single-core cables in a flat layout......Page 212 Single-core armoured cables......Page 215 Three-core armoured cables and pipe-type cables......Page 218 Screened cables with no armour......Page 219 Unscreened or belted cables......Page 221 3.3.6 Impedance matrix of three-phase double-circuit cables......Page 223 3.3.7 Examples......Page 225 Cable impedances......Page 226 3.4.1 Background......Page 228 Core dc resistance is available......Page 229 Insulation, semiconductive screens and bedding tape......Page 230 Metallic sheath made of copper wire screen only......Page 232 Stranded copper core......Page 233 Composite sheath......Page 234 3.5.1 Background......Page 235 Overhead lines......Page 237 Cables......Page 238 3.5.3 Sequence π models of double-circuit overhead lines......Page 239 3.5.4 Sequence π models of double-circuit cables......Page 242 3.6 Sequence π models of three-circuit overhead lines......Page 243 3.7.2 Single-circuit overhead lines and cables......Page 245 3.7.3 Double-circuit overhead lines and cables......Page 246 General......Page 249 Single-circuit overhead lines with one earth wire......Page 250 Errors between model lumped parameters and measured distributed parameters......Page 253 Double-circuit overhead lines......Page 254 Measurement of cable dc resistances......Page 256 Measurement of cable positive-sequence/negative-sequence impedance......Page 257 Measurement of positive-/negative-/zero-sequence susceptance of a three-core belted cable......Page 259 3.9.1 Overhead lines......Page 260 Papers......Page 261 Chapter Outline......Page 263 4.2.1 Background......Page 264 Transformer core construction and general equivalent circuit......Page 267 Transformer equivalent circuit in actual physical units......Page 269 Transformer equivalent circuit in per unit......Page 271 Transformer equivalent circuit in per unit based on nominal impedance......Page 274 Interpreting transformer equivalent circuit and off-nominal tap ratio......Page 275 π equivalent circuit model......Page 278 4.2.3 Three-phase two-winding transformers......Page 280 Positive-phase sequence and negative-phase sequence equivalent circuits......Page 281 Zero-sequence equivalent circuits......Page 283 Effect of winding connection phase shifts on sequence voltages and currents......Page 287 4.2.4 Three-phase three-winding transformers......Page 292 Positive-phase sequence and negative-phase sequence equivalent circuits in actual physical units......Page 293 Positive-phase sequence and negative-phase sequence equivalent circuits in per unit......Page 296 Transformer equivalent circuit in per unit based on nominal impedance......Page 298 4.2.5 Three-phase autotransformers with and without tertiary windings......Page 301 Positive-sequence and negative-sequence equivalent circuits in physical units......Page 303 Positive-sequence and negative-sequence equivalent circuits in per unit......Page 308 Zero-sequence equivalent circuit in physical units and in per unit......Page 311 Zero-sequence equivalent circuit of an autotransformer with an isolated neutral......Page 314 General......Page 317 Positive-sequence equivalent circuit of a four-winding transformer......Page 318 4.2.7 Three-phase earthing or zigzag transformers......Page 320 4.2.8 Single-phase traction transformers connected to three-phase systems......Page 322 4.2.9 Variation of transformer’s positive-sequence leakage impedance with tap position......Page 323 4.2.10 Practical aspects of zero-sequence impedances of three-phase transformers and effect of core construction......Page 324 Three-phase transformers made up of three single-phase banks......Page 325 Three-phase transformers of five-limb core-form construction and shell-type core construction including seven-limb shell-form......Page 326 Three-phase transformers of three-limb core-form construction......Page 328 4.2.11 Measurement of sequence impedances of three-phase transformers......Page 329 Positive-sequence and zero-sequence impedance tests on two-winding transformers......Page 332 Positive-sequence and zero-sequence impedance tests on three-winding transformers......Page 333 4.2.12 Examples......Page 335 4.3.1 Background......Page 343 Positive-sequence equivalent circuit model......Page 345 Negative-sequence equivalent circuit model......Page 348 4.3.3 Measurement of sequence impedances of QB and PS transformer......Page 350 4.3.4 Examples......Page 352 4.4.2 Modelling of series reactors......Page 355 4.4.3 Modelling of shunt reactors and capacitors......Page 358 General modelling aspects of series capacitors......Page 361 Modelling of series capacitors for short-circuit analysis......Page 363 4.5.1 Background......Page 367 4.6.1 Background......Page 368 4.7.2 Three-phase modelling of reactors and capacitors......Page 370 Single-phase two-winding transformers......Page 371 Three-phase banks two-winding Ynd connected transformers with no interphase mutual couplings......Page 376 Three-phase common-core two-winding Ynd connected transformers with interphase mutual coupling......Page 379 4.7.4 Three-phase modelling of QB and PS transformers......Page 384 Books......Page 386 Papers......Page 387 Chapter Outline......Page 388 5.2 Overview of synchronous machine modelling in the phase frame of reference......Page 389 5.3.1 Transformation from ryb reference to dq0 reference......Page 392 5.3.2 Machine dq0 equations in per unit......Page 394 q-Axis operator reactance......Page 396 d-Axis operator reactance......Page 397 q-Axis parameters......Page 398 d-Axis parameters......Page 401 5.4.1 Synchronous machine sequence equivalent circuits......Page 403 Short-circuit currents......Page 404 Positive-sequence reactance and resistance......Page 408 Short-circuit fault through an external impedance......Page 412 Simplified machine short-circuit current equations......Page 414 5.4.3 Unbalanced two-phase (phase-to-phase) short-circuit faults......Page 415 Negative-sequence reactance and resistance......Page 418 Simplified machine short-circuit current equations......Page 419 5.4.4 Unbalanced single-phase to earth short-circuit faults......Page 420 Zero-sequence reactance and resistance......Page 422 Simplified machine short-circuit current equations......Page 423 5.4.5 Unbalanced two-phase to earth short-circuit faults......Page 424 Machine internal voltages......Page 429 One-phase to earth short circuit......Page 430 5.4.7 Effect of automatic voltage regulators on short-circuit currents......Page 431 5.4.8 Modelling of synchronous motors/compensators/condensers......Page 434 Three-phase short-circuit fault......Page 435 One-phase short-circuit fault......Page 436 Three-phase short-circuit fault......Page 439 One-phase to earth short-circuit fault......Page 440 Measurement and separation of ac and dc current components......Page 441 Transient reactance and transient short-circuit time constant......Page 443 Subtransient reactance and subtransient short-circuit time constant......Page 444 5.5.2 Measurement of negative-sequence impedance......Page 445 5.5.3 Measurement of zero-sequence impedance......Page 446 5.5.4 Example......Page 448 Direct axis transient reactance and time constant......Page 449 Transient reactance at the end of the subtransient period......Page 450 Negative-sequence impedance......Page 451 5.6.1 General......Page 452 5.6.2 Overview of induction motor modelling in the phase frame of reference......Page 453 5.7.1 Transformation to Park dq axes......Page 457 5.7.3 Operator reactance and parameters of a single-winding rotor......Page 459 5.7.4 Operator reactance and parameters of double-cage or deep-bar rotor......Page 461 Total short-circuit current contribution from a motor on no load......Page 465 Simplified motor short-circuit current equations......Page 469 Positive-sequence reactance and resistance......Page 470 Effect of short-circuit fault through an external impedance......Page 472 Short-circuit current equations......Page 474 Negative-sequence reactance and resistance......Page 475 5.8.3 Modelling the effect of initial motor loading......Page 476 Steady-state equivalent circuit: stator resistance test......Page 477 Steady-state equivalent circuit: locked rotor test......Page 478 Steady-state equivalent circuit: no-load test......Page 480 Transient parameters from a sudden three-phase short-circuit immediately after motor disconnection......Page 481 5.8.5 Examples......Page 482 Papers......Page 485 Chapter Outline......Page 486 6.1 General......Page 488 6.2.1 Basic operation of voltage-source converters......Page 489 6.3 Types of wind turbine generator technologies......Page 494 6.4.1 Modelling and analysis of short-circuit current contribution......Page 495 6.4.2 Example......Page 496 6.5.1 Modelling and analysis of short-circuit current contribution......Page 497 6.5.2 Example......Page 500 6.6.1 Background......Page 501 6.6.2 Basic operation principle......Page 502 6.6.3 Rotor protection......Page 503 6.6.4 Passive and active crowbar protection......Page 504 6.6.5 dc chopper protection......Page 506 6.6.7 DFIG steady-state equivalent circuit......Page 507 6.6.8 DFIG natural stator and rotor short-circuit currents under constant ac excitation......Page 508 6.6.9 DFIG stator and rotor short-circuit currents under crowbar action......Page 514 6.6.10 DFIG short-circuit currents with dc chopper control......Page 522 6.6.11 DFIG short-circuit currents with rotor converter control......Page 523 6.6.12 Examples......Page 524 6.8 Type 5 variable-speed wind turbine synchronous generators......Page 528 6.9.2 Solar PV generator components......Page 529 6.9.3 Solar PV voltage-source inverters......Page 530 6.9.4 Grid connection of solar PV power plant......Page 531 6.10 Technologies interfaced to the ac grid through voltage-source inverters......Page 533 6.11.1 General inverter model......Page 534 6.11.2 Phase-locked loop......Page 537 6.11.3 Inverter inner current control loop......Page 538 6.11.4 Inverter outer control loops......Page 542 6.11.5 Short-circuit current contribution of voltage-source inverters with frozen controls......Page 544 6.12 Grid code requirements for dynamic reactive current injection from inverters......Page 547 6.13.1 Dynamic reactive current control......Page 550 6.13.2 Examples of inverter positive-sequence short-circuit current contribution......Page 551 6.14.1 Inverter model in positive- and negative-sequence synchronous reference frames......Page 554 6.14.2 Examples of inverter positive- and negative-sequence short-circuit current contributions......Page 556 6.15 Sequence network representation of voltage-source inverters during balanced and unbalanced short-circuit faults......Page 559 6.16.1 General......Page 560 6.16.2 Steady-state and transient characteristics of inverter short-circuit reactive currents......Page 561 6.16.3 Analysis of three-phase short-circuit fault currents......Page 562 Inverters do not contribute a fault current......Page 563 Inverter current source is open-circuited......Page 564 Inverters do not contribute a fault current......Page 565 ac grid voltage source is short-circuited......Page 566 Inverters contribute positive- and negative-sequence currents......Page 569 ac grid voltage source is short-circuited......Page 570 Inverters contribute positive-sequence current only......Page 571 ac grid voltage source is short-circuited......Page 572 ac grid voltage source is short-circuited......Page 574 6.16.6 Examples......Page 576 6.17.2 Emerging challenges in power systems dominated by grid-following voltage-source inverters......Page 585 6.17.3 Control structure of grid-forming inverters......Page 586 6.18.1 Possible VSM inverter features of real synchronous machines......Page 587 6.18.2 A model of grid-forming VSM inverters......Page 588 VSM inverter's virtual rotor model with inertia and damping......Page 590 6.19 Grid-forming voltage-source inverters using droop control......Page 592 6.20.1 Natural three-phase short-circuit current of grid-forming inverters......Page 596 6.20.2 Natural two-phase short-circuit current of grid-forming inverters......Page 597 6.21.1 General......Page 598 Strategy 1: Clipping PWM voltage reference......Page 599 Strategy 3: Static virtual resistor......Page 600 Strategy 4: Transient virtual resistor......Page 601 Strategy 1: Saturation of individual current references......Page 603 Strategy 2: Saturation of magnitude of current reference......Page 604 6.22 Symmetrical components sequence equivalent circuits of ‘grid-forming’ inverters......Page 606 6.23 Examples......Page 608 Papers......Page 612 Chapter Outline......Page 614 7.2.1 Simulation of short-circuit faults in networks containing active voltage sources only......Page 615 7.2.2 Simulation of short-circuit faults in networks containing mixed active voltage and current sources......Page 618 7.2.3 Simulation of open-circuit faults in networks containing active voltage sources only......Page 619 7.2.4 Simulation of open-circuit faults in networks containing active voltage and current sources......Page 621 7.3.1 Background......Page 622 7.3.3 The ac short-circuit analysis technique......Page 623 7.3.5 Estimation of ac short-circuit current component variation with time......Page 624 7.4 Time domain short-circuit analysis techniques in large-scale power systems......Page 625 7.5.1 Single voltage source connected by a radial network......Page 626 Three-phase short-circuit fault......Page 627 7.5.2 Parallel independent voltage sources connected by radial networks......Page 629 Network ac time constant......Page 630 Network dc time constant......Page 631 7.5.3 Multiple voltage sources in interconnected meshed networks......Page 633 Network ac time constant......Page 634 Network dc time constant......Page 637 Thévenin’s and Norton’s positive-sequence equivalent models of machines......Page 639 Positive-sequence admittance and impedance matrix equations......Page 640 General analysis of three-phase short-circuit faults......Page 643 Three-phase short-circuit fault at one location......Page 644 Simultaneous three-phase short-circuit faults at two different locations......Page 647 Three-phase short-circuit fault between two nodes......Page 649 Nodal sequence impedance matrices......Page 651 General mathematical analysis......Page 652 One-phase open-circuit faults......Page 656 General analysis of three-phase short-circuit faults......Page 660 Step 1: Fault current due to conventional machines in the network and all inverter current sources are open-circuited......Page 661 Step 2: Fault current due to inverter current sources in the network and all conventional machines' voltage sources are sho.........Page 664 7.7.1 Background......Page 665 Synchronous machines......Page 666 Induction machines......Page 669 7.7.3 Three-phase analysis of ac short-circuit current in the phase frame of reference......Page 670 Two-phase fault through a fault impedance ZF......Page 673 Two-phase to earth fault through a fault impedance ZF......Page 674 One-phase to earth short-circuit fault......Page 675 Three-phase to earth short-circuit fault......Page 677 7.7.5 Example......Page 678 Three-phase to earth fault......Page 679 Books......Page 680 Papers......Page 681 8.1 General......Page 682 8.2.2 Analysis technique and voltage source at the short-circuit location......Page 683 Directly connected synchronous generators and compensators (factor KG)......Page 685 Power station units with and without on-load tap-changers (factors KS; KG,S; KT,S; and KSO; KG,SO; KT,SO)......Page 686 Step-up transformer with an on-load tap-changer (factors KS; KG,S and KT,S)......Page 687 Asynchronous or induction motors......Page 688 Wind power station units with asynchronous generators......Page 690 Calculation of initial rms short-circuit current......Page 691 Calculation of X/R ratio......Page 692 Calculation of symmetrical rms breaking current......Page 693 Calculation of symmetrical rms steady-state current......Page 696 8.2.8 Example......Page 697 Asynchronous machines......Page 698 Small induction motors forming part of the general power system load......Page 699 General......Page 700 8.3.5 Implementation of ER G7/4 in the UK......Page 701 8.4.1 Background......Page 703 General......Page 704 E/X simplified method......Page 705 Closing and latching current......Page 706 8.4.5 Example......Page 707 8.5 Examples of calculations using IEC 60909, UK ER G7/4 and IEEE C37.010......Page 708 dc current rating......Page 715 Asymmetrical ratings......Page 716 8.6.2 Assessment of aymmetrical circuit-breaker short-circuit duty against rating......Page 718 Books......Page 720 Papers......Page 721 9.1 General......Page 722 9.2.1 Theory of static network reduction......Page 723 9.2.2 Need for power system equivalents......Page 724 Conventional bus impedance or admittance matrices......Page 726 Illustration of equivalents of one, two and three boundary nodes......Page 727 Direct derivation of admittance matrix of power system equivalents......Page 729 Generalised time-dependent power system equivalents......Page 733 9.3.1 Representation of power-generating stations......Page 734 9.3.2 Representation of transmission, distribution and industrial networks......Page 735 9.4.2 Effect of mutual coupling between overhead line circuits......Page 737 9.4.3 Severity of fault types and substation configuration......Page 739 9.5.1 Confidence in calculations......Page 742 9.5.2 Data, models and analysis techniques......Page 743 9.5.4 Quality control and precision versus accuracy......Page 744 9.6.2 Probabilistic analysis of an ac short-circuit current component......Page 745 Factors affecting dc short-circuit current magnitude......Page 747 Probabilistic analysis of dc short-circuit current magnitude......Page 750 9.6.4 Example......Page 754 9.7.1 Background......Page 755 9.7.3 Theory of quantified risk assessment......Page 756 9.7.4 Methodology of quantified risk assessment......Page 757 Papers......Page 758 Chapter Outline......Page 759 10.2.2 Recertification of existing plant short-circuit rating......Page 760 10.2.3 Substation splitting and use of circuit-breaker autoclosing......Page 761 10.2.4 Network splitting and reduced system parallelism......Page 762 10.2.5 Sequential disconnection of healthy then faulted equipment......Page 763 10.2.6 Increasing short-circuit fault clearance time......Page 764 10.2.9 Example......Page 765 10.3.2 Opening of unloaded delta-connected transformer tertiary windings......Page 767 10.3.4 Upgrading to higher nominal system voltage levels......Page 768 10.3.8 Examples......Page 769 10.4.2 Earthing resistor or reactor connected to transformer neutral......Page 771 10.4.3 Pyrotechnic-based fault current limiters......Page 772 10.4.4 Permanently inserted current-limiting series reactors......Page 773 10.4.6 Limiters using magnetically coupled circuits......Page 774 Flux-cancelling limiter with reverse parallel to series reconnection......Page 775 10.4.8 Passive damped resonant limiter......Page 776 Series resonant limiter using a thyristor protected series capacitor......Page 777 Solid-state limiter using normally conducting power electronics switches......Page 778 Background......Page 779 Saturated inductance superconducting limiter......Page 780 Air-gap superconducting limiter......Page 781 10.5.1 Operation principles and design of resistive superconducting fault current limiters......Page 782 10.5.2 Modelling of resistive superconducting fault current limiters for short-circuit analysis......Page 783 10.5.3 Short-circuit analysis behaviour of resistive superconducting fault current limiters......Page 785 10.5.4 Example......Page 788 10.6 Characteristics of the ideal fault current limiter......Page 789 10.7 Applications of fault current limiters......Page 790 10.8 Examples......Page 794 Papers......Page 796 Chapter Outline......Page 798 11.1 Background......Page 799 11.2.2 Electrical resistance of the human body......Page 800 11.2.3 Effects of ac current on the human body......Page 802 General......Page 804 One driven vertical rod......Page 805 Multiple driven vertical rods in a hollow square......Page 806 Buried horizontal strip or wire......Page 807 Buried vertical or horizontal flat plate......Page 808 Buried horizontal grid or mesh......Page 809 Combined horizontal mesh with driven vertical rods around periphery......Page 810 11.4.1 Earthing network of overhead line earth wire and towers......Page 811 11.4.2 Equivalent earthing network impedance of an infinite overhead line......Page 813 11.5 Analysis of earth fault zero-sequence current distribution in overhead line earth wire, towers and in earth......Page 814 11.6 Earthing system impedance of cables......Page 819 11.7 Overall substation earthing system and its equivalent impedance......Page 820 11.9 Screening factors for overhead lines......Page 821 11.10.2 Single-phase cable with metallic sheath......Page 824 11.10.3 Three-phase cable with metallic sheaths......Page 826 11.11 Analysis of earth return currents for short-circuits in substations......Page 829 11.12 Analysis of earth return currents for short circuits on overhead line towers......Page 830 11.13 Calculation of rise of earth potential in substations and at towers......Page 833 11.14 Examples......Page 834 11.15.2 Effects of environment on earth (soil) resistivity......Page 839 11.15.3 Need for measurement......Page 840 11.15.4 Wenner four-electrode method......Page 841 11.15.5 Schlumberger–Palmer four-electrode method......Page 842 11.15.6 Driven rod three-electrode fall of potential method......Page 843 11.15.7 Interpretation of apparent earth (soil) resistivity measurements and derivation of two-layer earth model......Page 844 11.15.9 Examples......Page 847 Books......Page 848 Papers......Page 849 12.1 Background......Page 850 12.2.1 General......Page 851 12.2.2 Calculation of pipeline voltage to earth and discharge currents through a person’s body......Page 852 Earthed pipelines......Page 853 Nonparallel exposure......Page 854 12.3.1 Electromagnetic coupling mechanism......Page 855 12.3.3 Mutual impedance between power line and pipeline......Page 856 12.3.4 Analysis of induced EMF on the pipeline during steady-state system conditions......Page 858 12.3.5 Analysis of induced EMF on the pipeline during a short-circuit fault in the power system......Page 859 12.4.1 Modelling and analysis of distributed parameter pipelines......Page 860 12.4.2 Calculation of pipeline voltages caused by inductive coupling......Page 863 Case 1: the pipeline continues for several kilometres beyond the parallelism at both ends A and B......Page 864 Case 2: the pipeline continues for several kilometres beyond the parallelism at end A but stops at end B where it is insula.........Page 865 Case 3: the pipeline is earthed at end A but continues for several kilometres beyond the parallelism at end B......Page 866 12.5.2 Pipeline shunt admittance......Page 867 12.6 Resistive or conductive coupling from power systems to pipelines......Page 868 12.7 Examples......Page 869 Papers......Page 876 Appendix A.1 Analysis of distributed multiconductor overhead lines and cables......Page 877 A.2.2 Induction machine model in an arbitrary reference frame......Page 881 A.2.2.2 Synchronously rotating reference frame......Page 884 A.2.3 Complex space vector representation of induction machines......Page 885 A.2.3.3 Rotor reference frame......Page 886 Appendix A.3 Root mean square value of an asymmetrical current waveform......Page 887 A.4.1.2 For transformers......Page 890 A.4.2 Data......Page 891 Index......Page 905 Back Cover......Page 915