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Cable size for an allowable voltage drop

The smallest conductor size that keeps the voltage drop of a three-phase or single-phase line within the limit, and the next larger standard size — including long lines to well pads and submersible cables.

Formula
ΔU_a = δ · U / 100S = ρ_t · cos φ / (ΔU_a / (k · I · L) − x_0 · sin φ)ρ_t = ρ_20 · (1 + α · (t − 20)), k = √3 (3~), 2 (1~)

If the reactive drop k · I · x_0 · L · sin φ alone exceeds the limit, a larger conductor will not help and no result is shown: raise the voltage or run parallel lines. A size chosen for voltage drop is also checked for current-carrying capacity (IEC 60364-5-52), short-circuit withstand and protection tripping. Above 240 mm², several cables are usually run in parallel. ESP cables also come in AWG sizes: 13.3, 21.2 and 33.6 mm².

Source: IEC 60364-5-52:2009, Annex G; conductor sizes per IEC 60228

Inputs

You can change a field's unit: the value is converted to the formula's units automatically.

m
U

Line-to-line voltage for three phases, phase voltage for a single phase.

I
Calculate →
cos φ

Induction motors at rated load 0.80–0.90, lightly loaded 0.3–0.6; heaters 1.

L

Cable route length; for an ESP, from the control panel or transformer to the motor.

δ

IEC 60364-5-52: lighting 3 %, other loads 5 % (6 and 8 % when supplied from the user's own substation).

ρ_20
t

At full load: PVC insulation 70 °C, XLPE 90 °C; 20 °C for no correction. Submersible cable: the average well temperature plus heating by the current.

x_0Ω/km

Cables up to 1 kV about 0.08 Ω/km (IEC 60364-5-52), 6–10 kV 0.08–0.12, flat submersible cable about 0.1; overhead lines 0.3–0.4 Ω/km.

Unit converter for this formulaVoltage · Current · Length · Temperature · Area · Fraction and percent
  • V1
  • kV0.001
All units →
Result
S — Smallest conductor size
Fill in all fields
  • S_std — Standard size (IEC 60228)
    –mm²
  • ΔU/U — Voltage drop at the standard size
    –

More in Cables

Cable voltage drop and power loss

Voltage drop in a three-phase or single-phase cable line from the conductor resistance at the operating temperature and the reactance, the power loss in the cable and the sending-end voltage — including a long ESP submersible cable.

Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.