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Impedance

Cable impedance can be calculated in accordance with IEC 60909-2 'Short-circuit currents in three-phase a.c. systems - Part 2: data of electrical equipment for short-circuit current calculations' table 7.  This table gives appropriate formulae for single and multi-core cables with or without metallic sheaths or shields. 

Cables without metallic sheaths or shields

For three single core cables, in either trefoil or flat formation, the positive and negative sequence impedance is given by:

Z 1 =R+jω μ 0 2π ( 1 4 +ln d r L )                (1)
 
where:
R - conductor resistance (see Conductor Resistance), Ω
μ0 - permeability of free space (= 4π × 10−7), H.m−1
rL - radius of the conductor, m
 

with:  d= d L1L2 d L1L3 d L2L3 3

where: dL1L2, dL1L3, dL2l3 are the axial distance between conductors, m

  Z 0 =R+3ω μ 0 8 +jω μ 0 2π ( 1 4 +3ln δ r L d 2 3 )                 (2)

with:  δ= 1.851 ω μ 0 ρ

where:
δ - equivalent soil penetration depth, m
ρ - soil resitivity, Ωm

For four single core cables (L1, L2, L3 and N)  the positive sequence impedance is given by:

  Z 1 =R+jω μ 0 2π ( 1 4 +ln d r L )                (3)

and with the return current through the neutral:

  Z 0 =4R+j4ω μ 0 2π ( 1 4 +ln d LN 3 r L d )                 (4)

and the return current through both the neutral and earth, with Zo(2) being the impedance calculated from equation (2) :

  Z 0 = Z 0(2) 3 ( ω μ 0 8 +jω μ 0 2π ln δ d LN ) 2 R+ω μ 0 8 +jω μ 0 2π ( 1 4 +ln δ r L )                 (5)

with:  d LN = d L1N d L2N d L3N 3

where: dL1N, dL2N, dL3N are the axial distances between each conductor and neutral, m

Cables with metallic sheaths or shields

For three single core cables, with a metallic sheath or shield, in either trefoil or flat formation, the positive and negative sequence impedance is given by:

  Z 1 = Z 1(1) + ( ω μ 0 2π ln d r Sm ) 2 R s +jω μ 0 2π ln d r Sm                 (6)

  Z 0 = Z 0(2) ( 3ω μ 0 8 +j3ω μ 0 2π ln δ r Sm d 2 3 ) 2 R s +3ω μ 0 8 +j3ω μ 0 2π ln δ r Sm d 2 3                 (7)

where:
Rs - metallic sheath or screen resistances, Ωm
rSm - mean radius of the sheath or shield, m
Z1(1) and Z0(2) are the impedances given by equations (1) and (2)

 

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