Size the three-phase 400 V supply cable for an industrial motor load of 400 A continuous rating, 50 m underground run through a concrete duct bank. The installation is in a thermal resistivity soil of 1.2 K·m/W, ambient temperature 25°C, with 4 circuits in the same duct. Select the minimum XLPE copper conductor cross-section per IEC 60287 and verify voltage drop.
| Load current | I_b = 400 A |
| Conductor material | Copper, XLPE insulation |
| Installation | Buried in concrete duct, 4 circuits |
| Run length | L = 50 m |
| Ambient temperature | θ_a = 25 °C |
| Soil thermal resistivity | ρ_s = 1.2 K·m/W |
| System voltage | 400 V, 50 Hz, 3-phase |
| Power factor | cos φ = 0.88 |
| Reactance | x = 0.08 Ω/km |
| Max permitted VD | 3% (12 V) |
| Check | Status | Util. | Value |
|---|---|---|---|
| Ampacity — derating factors | PASS |
|
I_r = 507 A (target), cable must carry ≥ 507 A |
| Conductor selected | PASS |
|
3 × 240 mm² XLPE Cu (I_r = 527 A ≥ 507 A) |
| Voltage drop — IEC 60287 | PASS |
|
ΔU = 7.3 V (1.83%) ≤ 12 V (3%) |
| Earth fault loop impedance | PASS |
|
Z_s = 0.082 Ω ≤ 0.167 Ω |
| Short-circuit thermal withstand | PASS |
|
I²t = 4.8 × 10⁶ A²s ≤ 7.2 × 10⁶ A²s limit |
| Group derating (4 circuits) | PASS |
|
k_g = 0.78 — applied to base ampacity |
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