Cable Sizing With Derating and Voltage-Drop Check
A 250 kW, 400 V, three-phase feeder has a power factor of 0.85 and a route length of 150 m. The cable is copper XLPE in a ventilated tray, ambient temperature 40 deg C, with four loaded circuits bunched together. Free-air ampacities at 30 deg C are: 185 mm2 = 420 A, 240 mm2 = 495 A, 300 mm2 = 560 A, 400 mm2 = 650 A, 500 mm2 = 740 A. Derating factors are 0.87 for 40 deg C and 0.80 for four circuits. The conductor resistance at operating temperature is 0.0438 ohm/km for 400 mm2 and 0.0583 ohm/km for 300 mm2; reactance is 0.08 ohm/km. The allowable voltage drop is 5%.
1. Compute the design current and the minimum derated ampacity required.
Read the worked answer
Design current = 250,000/(sqrt3 x 400 x 0.85) = 424.5 A.
Combined derating = 0.87 x 0.80 = 0.696.
The selected cable's tabulated ampacity must satisfy I_tab x 0.696 >= 424.5, so I_tab >= 424.5/0.696 = 610 A.
2. Select the minimum standard cable size from the table and verify the derated ampacity.
Read the worked answer
Check each size with the 0.696 factor:
- 240 mm2: 495 x 0.696 = 345 A -- insufficient
- 300 mm2: 560 x 0.696 = 390 A -- insufficient
- 400 mm2: 650 x 0.696 = 452 A -- sufficient (452 > 424.5)
Minimum size is 400 mm2. The 500 mm2 cable also works but is not the minimum.
3. Verify the voltage drop for the 400 mm2 cable and state whether 300 mm2 would pass if the ambient were 30 deg C.
Read the worked answer
For 400 mm2 over 150 m: R = 0.0438 x 0.15 = 0.00657 ohm; X = 0.08 x 0.15 = 0.012 ohm; sin(phi) = 0.527.
V_phase drop = 424.5(0.00657 x 0.85 + 0.012 x 0.527) = 424.5(0.005585 + 0.006324) = 5.05 V.
Line-to-line drop = sqrt3 x 5.05 = 8.75 V, or 8.75/400 = 2.19%, which is below 5%. The 400 mm2 selection is adequate for both ampacity and voltage drop.
At 30 deg C the 40 deg C factor becomes 1.0: 300 mm2 derated = 560 x 0.80 = 448 A > 424.5 A, so it would pass thermally. Its drop would be about 6.6 V per phase (2.9% line-to-line), also within 5%. The judgment is that the cable size is driven by the 40 deg C ambient derating, not by voltage drop.