Shielded Cable Parameters Equations

3Ampacity

Conductor @ 90°C @ 105°C 4Insulation Thickness (in)

kcmil 1mm2 2Diameter (in) Cu Al Cu Al 34.5 kV 69 KV 115 kV 138 kV 230 kV 345 kV
500 253.4 0.740 557 436 600 470 0.345 0.354 0.512 0.591 0.906 1.140
750 380.0 0.910 695 547 749 590 0.224 0.354 0.512 0.591 0.906 1.140
1000 506.7 1.060 807 641 870 691 0.224 0.354 0.512 0.591 0.906 1.140
1250 633.4 1.190 902 723 972 779 0.224 0.354 0.512 0.591 0.906 1.140
1500 760.1 1.320 981 795 1058 857 0.224 0.354 0.512 0.591 0.906 1.140
1750 886.7 1.430 1051 859 1133 926 0.224 0.354 0.512 0.591 0.906 1.140
2000 1013.4 1.500 1109 917 1196 989 0.224 0.354 0.512 0.591 0.906 1.140
2500 1266.8 1.730 1260 1043 1358 1124 0.224 0.354 0.512 0.591 0.906 1.140
3000 1520.1 1.890 1379 1150 1488 1240 0.224 0.354 0.512 0.591 0.906 1.140
3500 1773.5 2.070 1490 1249 1607 1347 0.224 0.354 0.512 0.591 0.906 1.140
4000 2026.8 2.170 1592 1342 1717 1447 0.224 0.354 0.512 0.591 0.906 1.140
5000 2533.5 2.480 1779 1513 1919 1632 0.224 0.354 0.512 0.591 0.906 1.140
6000 3040.2 2.670 1948 1669 2102 1799 0.224 0.354 0.512 0.591 0.906 1.140

(1) Cross-Sectional area calculated: 1.0 kcmil = 0.5067 mm2

(2) Conductor diameters from Southwire XLPE cable data Relative Insulation
Permittivity
(3) Ampacities from Okonite Handbook (>= 2500 kcm exptrapolated)
(4) Insulation thickness from Southwire XLPE cable data (34.5 kV extrapolated) Type eR
XLPE 2.3
EPR 3.0
𝐷𝑒𝑓𝑎𝑢𝑙𝑡 𝑠ℎ𝑖𝑒𝑙𝑑 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑖𝑠 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑎𝑠 0.081 𝑖𝑛𝑐ℎ𝑒𝑠 (𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 12 𝐴𝑊𝐺)
PVC 5.0
3
𝐷𝑒𝑓𝑎𝑢𝑙𝑡 𝑗𝑎𝑐𝑘𝑒𝑡 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑖𝑠 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑎𝑠 = 0.18750 𝑖𝑛𝑐ℎ𝑒𝑠
16
 Shielded Cable Parameters Equations (cont.)
all calculations use SI system
conductor diameter, insulation thickness and shield thickness must be converted to meters
1 𝑚𝑒𝑡𝑒𝑟 = 39.3701 𝑖𝑛𝑐ℎ𝑒𝑠
Positive Sequence 1 𝑚𝑒𝑡𝑒𝑟 = 3.28084 𝑓𝑒𝑒𝑡
Resistance at 20C conductor temperature
DC resistance of conductor (per-meter) AC resistance of conductor (per-meter)
𝜌 ′
𝑅𝐴𝐶 = 𝑅𝐷𝐶 1 + 𝜆𝑠 + 𝜆𝑝
𝑅𝐷𝐶 =
𝐴 𝜆𝑠 = 𝑠𝑘𝑖𝑛 𝑒𝑓𝑓𝑒𝑐𝑡 𝑓𝑎𝑐𝑡𝑜𝑟
Ω𝑚𝑚2
𝜌𝐶𝑜𝑝𝑝𝑒𝑟 = 0.017240 𝜆𝑝 = 𝑝𝑟𝑜𝑥𝑖𝑚𝑖𝑡𝑦 𝑒𝑓𝑓𝑒𝑐𝑡 𝑓𝑎𝑐𝑡𝑜𝑟
𝑚 𝜆𝑝 ≈ 0 (𝑖𝑛𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑐𝑜𝑚𝑝𝑎𝑟𝑒𝑑 𝑡𝑜 𝑠𝑘𝑖𝑛 𝑒𝑓𝑓𝑒𝑐𝑡)
Ω𝑚𝑚2
𝜌𝐴𝑙𝑢𝑚𝑖𝑛𝑢𝑚 = 0.028264 2𝑓𝜇0
𝑚 𝑋𝑠 = 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
𝐴 = 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑎𝑟𝑒𝑎 𝑚𝑚 2 𝑅𝐷𝐶
𝑓 = 𝑠𝑦𝑠𝑡𝑒𝑚 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝐻𝑧
𝐻
𝜇0 = 4𝜋 ∗ 10−7
𝑚
𝑋𝑠4
𝜆𝑠 =
192.0 + 0.8𝑋𝑠4
′
𝑅𝐴𝐶 ≈ 𝑅𝐷𝐶 1 + 𝜆𝑠

Resistance at 90C conductor temperature

′
𝑅𝐴𝐶 = 𝑅𝐴𝐶 1 + 𝛼 𝑇 − 20
𝑇 = 90 °𝐶 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒
𝛼 = 0.00393 𝑐𝑜𝑝𝑝𝑒𝑟 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 @ 20°𝐶
𝛼 = 0.00403 𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 @ 20°𝐶
′
𝑅𝐴𝐶 = 𝑅𝐴𝐶 1 + 70𝛼
 Shielded Cable Parameters Equations (cont.)
Positive Sequence
Shunt Capacitance (per-meter)
2𝜋𝜀𝑅 𝜀0 𝐹
𝐶=
𝑟 𝑚
ln 𝑠
𝑟𝑐
𝜀𝑅 = 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑝𝑒𝑟𝑚𝑖𝑡𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝐹
𝜀0 = 8.854 ∗ 10−12
𝑚
𝑠ℎ𝑖𝑒𝑙𝑑 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠
𝑟𝑠 = 𝑠ℎ𝑖𝑒𝑙𝑑 𝑟𝑎𝑑𝑖𝑢𝑠 = 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 +
2
𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟
𝑟𝑐 = 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 =
2

Shunt Susceptance (per-meter)

𝑚ℎ𝑜
𝐵 = ω𝐶
𝑚
𝑟𝑎𝑑
𝜔 = 2𝜋𝑓
𝑠𝑒𝑐

Shunt Susceptance per-unit (per-meter)

𝐵𝑝𝑢 = 𝐵𝑍𝐵𝑎𝑠𝑒 (𝑛𝑜 𝑢𝑛𝑖𝑡𝑠)
𝑘𝑉 2
𝑍𝐵𝑎𝑠𝑒 = Ω
100
 Shielded Cable Parameters Equations (cont.)
Positive Sequence
Impedance (per-meter)
ω𝜇0 𝐺𝑀𝐷 2
ω𝜇0 1 𝐺𝑀𝐷 ln
2𝜋 𝑟𝑠ℎ
𝑍 = 𝑅𝐴𝐶 + 𝑗 + ln +
2𝜋 4 𝑟𝑐 ω𝜇 𝐺𝑀𝐷
𝑅𝑠ℎ + 𝑗 0 ln
2𝜋 𝑟𝑠ℎ
𝑟𝑎𝑑
𝜔 = 2𝜋𝑓
𝑠𝑒𝑐
𝐻
𝜇0 = 4𝜋 ∗ 10−7
𝑚
3
𝐺𝑀𝐷 = 𝐴𝐵𝐶 𝑚 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑚𝑒𝑎𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟𝑠
𝑟𝑐 = 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 (𝑚)
𝑟𝑠ℎ = 𝑠ℎ𝑖𝑒𝑙𝑑 𝑟𝑎𝑑𝑖𝑢𝑠 (𝑚)
1
𝑅𝑠ℎ = 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑠ℎ𝑖𝑒𝑙𝑑 Ω 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑖𝑠 3𝑅𝐴𝐶 𝑜𝑟 𝑛𝑒𝑢𝑡𝑟𝑎𝑙
3

Resistance (per-meter) Reactance (per-meter) Inductance (per-meter)

𝑋
𝑅 = ℛ𝑒(𝑍) 𝑋 = 𝑖𝑚(𝑍) 𝐿=
𝜔
 Shielded Cable Parameters Equations (cont.)
Zero Sequence
Shunt Capacitance, Susceptance (per-meter)
Zero Sequence = Positive Sequence
𝐶0 = 𝐶
𝐵0 = 𝐵
0
𝐵𝑝𝑢 = 𝐵𝑝𝑢

Impedance (per-meter)
1.851
𝛿=
𝜔𝜇0 𝜌𝑒𝑎𝑟𝑡ℎ
𝜌𝑒𝑎𝑟𝑡ℎ = 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑒𝑎𝑟𝑡ℎ Ω𝑚 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 = 100
2
3𝜔𝜇0 3𝜔𝜇0 𝛿
+𝑗 ln
3𝜔𝜇0 ω𝜇0 1 𝛿 8 2𝜋 3
𝑟𝑠ℎ 𝐺𝑀𝐷2
0
𝑍 = 𝑅𝐴𝐶 + +𝑗 + 3 ln −
8 2𝜋 4 3
𝑟𝑐 𝐺𝑀𝐷2 3𝜔𝜇0 3𝜔𝜇0 𝛿
𝑅𝑠ℎ + 8 + 𝑗 2𝜋 ln 3
𝑟𝑠ℎ 𝐺𝑀𝐷2
𝑟𝑐 = 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 (𝑚)
𝑟𝑠ℎ = 𝑠ℎ𝑖𝑒𝑙𝑑 𝑟𝑎𝑑𝑖𝑢𝑠 (𝑚)
1
𝑅𝑠ℎ = 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑠ℎ𝑖𝑒𝑙𝑑 Ω 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑖𝑠 3𝑅𝐴𝐶 𝑜𝑟 𝑛𝑒𝑢𝑡𝑟𝑎𝑙
3

Resistance (per-meter) Reactance (per-meter) Inductance (per-meter)

0
𝑅 = ℛ𝑒(𝑍 )0 0
𝑋 = 𝑖𝑚(𝑍 )0 𝑋0
𝐿=
𝜔
 Shielded Cable Parameters Equations (cont.)
convert to US units
𝑅 Ω
𝑅𝑓𝑡 =
3.28084 𝑓𝑡
𝐿 𝐻
𝐿𝑓𝑡 =
3.28084 𝑓𝑡
𝐶 𝐹
𝐶𝑓𝑡 =
3.28084 𝑓𝑡
𝑋 Ω
𝑋𝑓𝑡 =
3.28084 𝑓𝑡
𝐵 𝑚ℎ𝑜
𝐵𝑓𝑡 =
3.28084 𝑓𝑡

calculate total R,X,B

𝑅 = 𝑙𝑒𝑛𝑔𝑡ℎ ∗ 𝑅𝑓𝑡 Ω
𝑋 = 𝑙𝑒𝑛𝑔𝑡ℎ ∗ 𝑋𝑓𝑡 Ω
𝐵 = 𝑙𝑒𝑛𝑔𝑡ℎ ∗ 𝐵𝑓𝑡 𝑚ℎ𝑜

convert to per-unit
𝑅
𝑅𝑝𝑢 = 𝑛𝑜 𝑢𝑛𝑖𝑡𝑠
𝑍𝐵𝑎𝑠𝑒
𝑋
𝑋𝑝𝑢 = 𝑛𝑜 𝑢𝑛𝑖𝑡𝑠
𝑍𝐵𝑎𝑠𝑒
𝐵𝑝𝑢 = 𝐵𝑍𝐵𝑎𝑠𝑒 𝑛𝑜 𝑢𝑛𝑖𝑡𝑠

thanks to myCableEngineering, NEPSI, for guidance

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