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

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

ICC Spring Meeting Seattle, March 2012

Cigré Electra 128 Publication:

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

• Cigré 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): Cigré, IEC and general practices 2

Cigré Technical Brochure 283


"Special bonding of high voltage power cables"

• Cigré 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 Cigré members)

http://www.e-cigre.org/

Cigré Technical Brochure 347


"Earth potential rises in specially bonded screen systems"

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ends is no longer valid Earth potential rises in case of single-phase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


"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


"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

Cigré 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


Double cable system model: IEEE P575/D11 figures


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

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

shown in figure F.1

Equations and Kirchhoff's law


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 ΔV1 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

ΔV2 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 ΔV3 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


Ph T ΔV5 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


Sheaths







Ground conductors



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 ΣZi,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 ΣZi,jIj - ΣZi+1,jIj = 0

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

Write equation of currents of sheaths and grounded conductors • ΣIk = 0

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


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

ω : angular frequency of system (2πf), [s-1] μ0 : magnetic permeability of free space = 4π.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 (i≠j)

Subtraction of two adjacent rows • D is eliminated


πω

+ω

+=+ω

+=ji,

00ji,ji,

0ji,ji, d

Dln2μj

8μRXj

8μRZ

ω=

πω

−

πω

=− +

++

ji,

j1,i7-

j1,i

0

ji,

0j1,iji, d

dln10.2

dDln

2μ

dDln

2μXX

Calculation of inductances

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

dc : diameter of the conductor [mm] α : 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


α

πω

=

+

πω

=c

0

c

0c d

Dln2μ

d2D

41ln

2μX

π

ω=

s

0s d

Dln2μX s(outer)s(inner)s .ddd =

Calculation of loss factor

IEC 60287-1-3 Standard


IEC 60287-1-3 example 1

More digits to check your own calculation tool… • Results: magnitude (A) and angle of currents I, and sheath loss factor λ'p


1) (x,y) = 0.0000 ; -1.0000 ; Icalc -> 50.0000 (A) / 0.00° ph[0] Icalc -> 28.7177 (A) / -138.79° lambda1 = 2.0362 2) (x,y) = 0.2000 ; -1.0000 ; Icalc -> 50.0000 (A) / -120.00° ph[1] Icalc -> 25.2974 (A) / 121.16° lambda1 = 1.5800 3) (x,y) = 0.4000 ; -1.0000 ; Icalc -> 50.0000 (A) / 120.00° ph[2] Icalc -> 34.8026 (A) / -4.50° lambda1 = 2.9905 4) (x,y) = 0.6000 ; -1.0000 ; Icalc -> 50.0000 (A) / 120.00° ph[2] Icalc -> 34.8026 (A) / -4.50° lambda1 = 2.9905 5) (x,y) = 0.8000 ; -1.0000 ; Icalc -> 50.0000 (A) / -120.00° ph[1] Icalc -> 25.2974 (A) / 121.16° lambda1 = 1.5800 6) (x,y) = 1.0000 ; -1.0000 ; Icalc -> 50.0000 (A) / 0.00° ph[0] Icalc -> 28.7177 (A) / -138.79° lambda1 = 2.0362

IEC 60287-1-3 Results

-1 0 1 2 3

-1,00

1,00

Laying depth = 1.0 m Axial distance between conductors = 0.20 m



T1,T2

T1s, T2s

S1, S2

S1s, S2s

R1, R2

R1s, R2s

-50

-40

-30

-20

-10

0

10

20

30

40

50

-50 -40 -30 -20 -10 0 10 20 30 40 50-1 0 1 2 3

-1,00

1,00


Influence of phase rotation (example 1 rotation reversed) • Results: magnitude (A) and angle of currents I, and sheath loss factor λ'p



1) (x,y) = 0,0000 ; -1,0000 ; Icalc -> 50,0000 (A) / 0,00° ph[0] Icalc -> 34,3695 (A) / -122,59° lambda1 = 2,9165 2) (x,y) = 0,2000 ; -1,0000 ; Icalc -> 50,0000 (A) / 120,00° ph[2] Icalc -> 24,4600 (A) / -0,91° lambda1 = 1,4772 3) (x,y) = 0,4000 ; -1,0000 ; Icalc -> 50,0000 (A) / -120,00° ph[1] Icalc -> 29,9388 (A) / 101,45° lambda1 = 2,2130 4) (x,y) = 0,6000 ; -1,0000 ; Icalc -> 50,0000 (A) / -120,00° ph[1] Icalc -> 29,9388 (A) / 101,45° lambda1 = 2,2130 5) (x,y) = 0,8000 ; -1,0000 ; Icalc -> 50,0000 (A) / 120,00° ph[2] Icalc -> 24,4600 (A) / -0,91° lambda1 = 1,4772 6) (x,y) = 1,0000 ; -1,0000 ; Icalc -> 50,0000 (A) / 0,00° ph[0] Icalc -> 34,3695 (A) / -122,59° lambda1 = 2,9165


-1 0 1 2 3

-1,00

1,00


Same data as example 1, phase rotation has been reversed

T1,T2

T1s, T2s

S1, S2

S1s, S2s

R1, R2

R1s, R2s

-50

-40

-30

-20

-10

0

10

20

30

40

50

-50 -40 -30 -20 -10 0 10 20 30 40 50



-1 0 1 2 3

-1,00

1,00


Same data as example 1, phase rotation has been reversed


Trefoil formation leads to balanced currents • Results: magnitude (A) and angle of currents I, and sheath loss factor λ'p


1) (x,y) = 0,0000 ; -1,0000 ; Icalc -> 50,0000 (A) / -120,00° ph[1] Icalc -> 13,7617 (A) / 134,48° lambda1 = 0,4676 2) (x,y) = 0,0300 ; -0,9480 ; Icalc -> 50,0000 (A) / 0,00° ph[0] Icalc -> 13,8587 (A) / -107,03° lambda1 = 0,4742 3) (x,y) = 0,0600 ; -1,0000 ; Icalc -> 50,0000 (A) / 120,00° ph[2] Icalc -> 14,1229 (A) / 14,06° lambda1 = 0,4925 4) (x,y) = 0,2000 ; -1,0000 ; Icalc -> 50,0000 (A) / 120,00° ph[2] Icalc -> 14,1229 (A) / 14,06° lambda1 = 0,4925 5) (x,y) = 0,2300 ; -0,9480 ; Icalc -> 50,0000 (A) / 0,00° ph[0] Icalc -> 13,8587 (A) / -107,03° lambda1 = 0,4742 6) (x,y) = 0,2600 ; -1,0000 ; Icalc -> 50,0000 (A) / -120,00° ph[1] Icalc -> 13,7617 (A) / 134,48° lambda1 = 0,4676


-1 0 1 2 3

-0,98

1,00

Bottom trench laying depth = 1.0 m Axial distance between conductors = 0.06 m

Trefoil formation

-1 0 1 2 3

-0,98

1,00

Bottom trench laying depth = 1.0 mAxial distance between conductors = 0.06 m

Trefoil formation

T1,T2

T1s, T2s

S1, S2

S1s, S2s

R1, R2

R1s, R2s

-50

-40

-30

-20

-10

0

10

20

30

40

50

-50 -40 -30 -20 -10 0 10 20 30 40 50



Conductors of one phase placed together (flat as example 1) • Results: magnitude (A) and angle of currents I, and sheath loss factor λ'p



1) (x,y) = 0,0000 ; -1,0000 ; Icalc -> 46,3082 (A) / 1,13° ph[0] Icalc -> 38,3598 (A) / -149,88° lambda1 = 4,2354 2) (x,y) = 0,8000 ; -1,0000 ; Icalc -> 44,5950 (A) / -124,53° ph[1] Icalc -> 37,4186 (A) / 105,13° lambda1 = 4,3457 3) (x,y) = 1,6000 ; -1,0000 ; Icalc -> 50,7573 (A) / 115,11° ph[2] Icalc -> 43,7042 (A) / -20,53° lambda1 = 4,5762 4) (x,y) = 0,4000 ; -1,0000 ; Icalc -> 53,7086 (A) / -0,98° ph[0] Icalc -> 36,4617 (A) / -150,17° lambda1 = 2,8448 5) (x,y) = 1,2000 ; -1,0000 ; Icalc -> 55,6564 (A) / -116,37° ph[1] Icalc -> 34,8476 (A) / 101,88° lambda1 = 2,4198 6) (x,y) = 2,0000 ; -1,0000 ; Icalc -> 49,6166 (A) / 125,00° ph[2] Icalc -> 44,4178 (A) / -23,21° lambda1 = 4,9468


0 1 2 3 4

-1,00

1,00


Same geometry as example 1, Conductors of one phase placed together

current sharing between phase

conductors is not equal,

sheath losses for this cable arrangement are

very high,

This arrangement must be avoided

R1

R1s

S1

S1s

T1

T1s

T2

T2s

S2

S2s

R2

R2s

-60

-40

-20

0

20

40

60

-40 -30 -20 -10 0 10 20 30 40 50 60



0 1 2 3 4

-1,00

1,00

Laying depth = 1.0 mAxial distance between conductors = 0.40 m

Same geometry as example 1,Conductors of one phase placed together

current sharing between phase

conductors is not equal,

sheath losses for this cable arrangement are

very high,

This arrangement must be avoided

Electromagnetic Field 50 Hz

x-distance from axis power line (m)11109876543210-1-2-3-4-5-6-7-8-9

Max

Fie

ld rm

s (µ

T)

0,5

0,45

0,4

0,35

0,3

0,25

0,2

0,15

0,1

0,05

0

EMF mitigation technique: shields/sheaths make a passive loop to compensate the magnetic field

Example 1 of IEC 60287-1-3 • Shielding factor SF = 1.44


Laying depth = 1.0 m Axial distance between conductors = 0.20 m MF calculated 1 m above ground surface, with (red) and without (blue) solid bonding,

I = 50 A in each cable

Work in progress


Features IEC 60287-1-3 Current tool

number of circuits in parallel 2 n ≥ 1

number of phases 3 (RST or ABC) multiple of 3 (possibility of

independent circuits)

number of ground continuity conductors 0 q ≥ 0

3 and 2-phase circuits mixed in parallel no

other grounding mode than solid bonding no

single bonding (calculation of induced

voltages)

coupling with EMF calculations no yes

Further work for next ICC Meeting

ICC Fall Meeting in Saint Pete (FL), November 2012 • Presentation of new case studies Parallel independent circuits (connected to different busbars with different current

ratings) Single bonded circuits and calculation of induced voltages

• Call for worked examples! Send to [email protected]

Future prospects • Transposed conductors • Crossbonded shields/sheaths • Transposed ground continuity conductors


mailto:[email protected]

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Documents

cigr electra

conductor power cables

phase cigr work

bonded cable systems

bonding shields

general practices

parallel communication

icc c35d