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  • ICC C35D: Sheath Bonding of Multi-Conductor / Parallel Circuits

    Cigr references with induced voltages, IEC 60287-3-1 Standard calculations, and EMF considerations Frdric LESUR

    ICC Spring Meeting Seattle, March 2012

  • Cigr Electra 128 Publication:

    "Guide to the protection of specially bonded cable systems against sheath overvoltages"

    Cigr WG B21.07, 1990 Revision of two previous Electra

    publications (#28,1973 and #47, 1976) Main contents Types of sheath voltage limiter (SVL) in use Use of SVL Qualification tests for SVL Selection of SVL Insulation coordination + Appendix 2: Calculation of 50 Hz sheath

    overvoltages due to system faults in a specially bonded cable system

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 2

  • Cigr Technical Brochure 283

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 3

    "Special bonding of high voltage power cables"

    Cigr WG B1.18, 2005 Convener: Ray Awad (Canada) US Member: Mike Buckweitz

    Main contents (106 pages) Power frequency applications

    o 3.1.3 (power frequency impedance model) with methodology, structure of equation system, complex impedance matrix

    Transient overvoltage applications Special considerations Recommendations

    Can be downloaded at www.e-cigre.org (for free for Cigr members)

  • Cigr Technical Brochure 347

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 4

    "Earth potential rises in specially bonded screen systems"

    Cigr TF B1.26, 2008 Convener: Eric Dorison (France) Canada Member: Yves Rajotte

    Increasing number of configurations with underground cables inserted in overhead line systems (siphons) Assumption of low earth resistance at both

    ends is no longer valid Earth potential rises in case of single-phase

    fault cannot be neglected Main contents (98 pages) Calculation methods Typical situations Internal faults Worked examples

  • IEC 60287-1-3 Standard

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 5

    "Current sharing between parallel single-core cables and calculation of circulating current losses"

    IEC, 2005 Main contents (49 pages) Scope Normative references Description of method Example calculations

  • IEEE P575/D Draft Guide

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 6

    "Draft guide for bonding shields and sheaths of single-conductor power cables rated 5 kV through 500 kV"

    ICC C02W, work in progress Chair: Mike Buckweitz Annex F: Mohamed Chaaban

    Main contents (80 pages) Shield optimization Special bonding techniques Sheath voltage limiters Effect on parallel communication and control

    cables Current practice for shield/sheath standing

    voltages Calculation of induced voltages Current and voltage distribution on cable

    shields/sheaths with multiple cables per phase

  • Cigr work in progress

    WG B1.30 "Cable characteristics" Technical brochure will be published in 2012 Convener: Christian Royer (Canada) Canada Members: Yves Rajotte, Deepak Parmar (corresponding) US Member: Thomas Wilki

    Main contents Definition of cable systems electrical characteristics Cable system types Formulae for cable systems electrical characteristics Measurement techniques Case studies

    WG C4.502 "Power system technical performance issues related to the application of long HVAC cables"

    Adequate modelling of AC cable lines, more focused on transients

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 7

  • Double cable system model: IEEE P575/D11 figures

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 8

    Figure F.1 - Example of 6 parallel cables; 2 cables per phase

    Figure F.2Loops formed by the shields/sheaths of the installation

    shown in figure F.1

  • Equations and Kirchhoff's law

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 9

    Phase R Phase S Phase T Sheaths Ground conductors

    Voltages 1 p p+1 2p 2p+1 3p 3p+1 6p 6p+1 6p+q

    Ph R V1 Z1,1 I1 Z1,2 I2 Z1,3 I3 Z1,4 I4 Z1,5 I5 Z1,6 I6 Z1,7 I7 Z1,8 I8 Z1,9 I9 Z1,10 I10 Z1,11 I11 Z1,12 I12 Z1,13 I13 Z1,14 I14

    V2 Z2,1 I1 Z2,2 I2 Z2,3 I3 Z2,4 I4 Z2,5 I5 Z2,6 I6 Z2,7 I7 Z2,8 I8 Z2,9 I9 Z2,10 I10 Z2,11 I11 Z2,12 I12 Z2,13 I13 Z2,14 I14

    Ph S V3 Z3,1 I1 Z3,2 I2 Z3,3 I3 Z3,4 I4 Z3,5 I5 Z3,6 I6 Z3,7 I7 Z3,8 I8 Z3,9 I9 Z3,10 I10 Z3,11 I11 Z3,12 I12 Z3,13 I13 Z3,14 I14

    V4 Z4,1 I1 Z4,2 I2 Z4,3 I3 Z4,4 I4 Z4,5 I5 Z4,6 I6 Z4,7 I7 Z4,8 I8 Z4,9 I9 Z4,10 I10 Z4,11 I11 Z4,12 I12 Z4,13 I13 Z4,14 I14

    Ph T V5 Z5,1 I1 Z5,2 I2 Z5,3 I3 Z5,4 I4 Z5,5 I5 Z5,6 I6 Z5,7 I7 Z5,8 I8 Z5,9 I9 Z5,10 I10 Z5,11 I11 Z5,12 I12 Z5,13 I13 Z5,14 I14

    V6 Z6,1 I1 Z6,2 I2 Z6,3 I3 Z6,4 I4 Z6,5 I5 Z6,6 I6 Z6,7 I7 Z6,8 I8 Z6,9 I9 Z6,10 I10 Z6,11 I11 Z6,12 I12 Z6,13 I13 Z6,14 I14

    Sheaths

    V7 Z7,1 I1 Z7,2 I2 Z7,3 I3 Z7,4 I4 Z7,5 I5 Z7,6 I6 Z7,7 I7 Z7,8 I8 Z7,9 I9 Z7,10 I10 Z7,11 I11 Z7,12 I12 Z7,13 I13 Z7,14 I14

    V8 Z8,1 I1 Z8,2 I2 Z8,2 I2 Z8,4 I4 Z8,5 I5 Z8,6 I6 Z8,7 I7 Z8,8 I8 Z8,9 I9 Z8,10 I10 Z8,11 I11 Z8,12 I12 Z8,13 I13 Z8,14 I14

    V9 Z9,1 I1 Z9,2 I2 Z9,3 I3 Z9,4 I4 Z9,5 I5 Z9,6 I6 Z9,7 I7 Z9,8 I8 Z9,9 I9 Z9,10 I10 Z9,11 I11 Z9,12 I12 Z9,13 I13 Z9,14 I14

    V10 Z10,1 I1 Z10,2 I2 Z10,3 I3 Z10,4 I4 Z10,5 I5 Z10,6 I6 Z10,7 I7 Z10,8 I8 Z10,9 I9 Z10,10 I10 Z10,11 I11 Z10,12 I12 Z10,13 I13 Z10,14 I14

    V11 Z11,1 I1 Z11,2 I2 Z11,3 I3 Z11,4 I4 Z11,5 I5 Z11,6 I6 Z11,7 I7 Z11,8 I8 Z11,9 I9 Z11,10 I10 Z11,11 I11 Z11,12 I12 Z11,13 I13 Z11,14 I14

    V12 Z12,1 I1 Z12,2 I2 Z12,3 I3 Z12,4 I4 Z12,5 I5 Z12,6 I6 Z12,7 I7 Z12,8 I8 Z12,9 I9 Z12,10 I10 Z12,11 I11 Z12,12 I12 Z12,13 I13 Z12,14 I14

    Ground conductors

    V13 Z13,1 I1 Z13,2 I2 Z13,3 I3 Z13,4 I4 Z13,5 I5 Z13,6 I6 Z13,7 I7 Z13,8 I8 Z13,9 I9 Z13,10 I10 Z13,11 I11 Z13,12 I12 Z13,13 I13 Z13,14 I14

    V14 Z14,1 I1 Z14,2 I2 Z14,3 I3 Z14,4 I4 Z14,5 I5 Z14,6 I6 Z14,7 I7 Z14,8 I8 Z14,9 I9 Z14,10 I10 Z14,11 I11 Z14,12 I12 Z14,13 I13 Z14,14 I14

    Currents

    IR [ ] I1 I2

    IS [ ] I3 I4

    IT [ ] I5 I6

    [ ] I7 I8 I9 I10 I11 I12 I13 I14

    Example of 6 parallel cables (2 cables per phase, p = 2) and 2 ground continuity conductors (q = 2)

  • Methodology

    Prepare the symmetric matrix Sort the Zi,jIj for conductors connected to the same phase (RST or ABC),

    sheaths and ground continuity conductors Calculate the impedances Zi,jIj Matrix is symmetric (mutual influence of metallic conductors, value linked to the axial

    distance between metallic conductors di,j = dj,i)

    Subtract two adjacent rows of same voltage drop V Leading to Zi,jIj - Zi+1,jIj = 0

    Write equations of currents of conductor loops Ik = IR, respectively Is and IT

    Write equation of currents of sheaths and grounded conductors Ik = 0

    Solve the equation system [Q]=[Z][I] With classical matrix algebra [I]=[Z]-1[Q] Unique solution, no iterative converging process

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 10

  • Calculation of impedances

    General formula of mutual impedance between two metallic conductors (i,j)

    Applied to cores, shields/sheaths, ground continuity conductors, per unit length

    : angular frequency of system (2f), [s-1] 0 : magnetic permeability of free space = 4.10-7, [H/m] D : distance to earth return fictitious path by an equivalent conductor

    o No need to be calculated, is eliminated by the subtraction of two adjacent rows Self resistance Ri,i= AC resistance of conductor (i=j) Mutual resistance Ri,j= 0 (ij)

    Subtraction of two adjacent rows D is eliminated

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 11

    +

    +=+

    +=ji,

    00ji,ji,

    0ji,ji, d

    Dln

    2

    j8

    RXj8

    RZ

    =

    = +

    ++

    ji,

    j1,i7-

    j1,i

    0

    ji,

    0j1,iji, d

    dln10.2

    dD

    ln2

    dD

    ln2

    XX

  • Calculation of inductances

    Special cases (on the matrix diagonal) Self inductance of the conductor

    dc : diameter of the conductor [mm] : coefficient depending on the construction of the conductor, to represent the mean

    radius of the core (see Table 1 in IEC 60287-1-3 + annex for hollow cores) Self inductance of the sheath

    ds : mean diameter of the shield/sheath [mm]

    Self inductance of the ground continuity conductor Same expression for Xg than for Xc with dg instead of dc

    Mutual impedance between conductor and shield of the same cable Involves mean distance between core and sheath Same expression for Xi,j than for Xs with mean diameter of sheath ds

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 12

    =

    +

    =c

    0

    c

    0c d

    Dln

    2

    d2D

    41

    ln2

    X

    =s

    0s d

    Dln

    2

    X s(outer)s(inner)s .ddd =

  • Calculation of loss factor

    IEC 60287-1-3 Standard

    C35D (Sheath Bonding of Multi-Conductor / Parallel Circuits): Cigr, IEC and general practices 13

  • IEC 60287-1-3 example 1

    More digits to check your own calculation tool Results: magnitude (A) and angle of

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