Circuit
Cable Impedance
Reactance from geometry
Centre to centre; the cable overall diameter if touching.
Sets X from X = ω·2×10-7·ln(2S/d). Leave alone if volt drop is resistance-dominated, or switch to datasheet values above.
Volt Drop Against Route Length
The 3 % and 5 % guides are the BS 7671 figures for lighting and for other uses at low voltage, and are hidden when they coincide with your own limit. On an HV connection the limit comes from the network operator and the design case.
Calculation Method
Voltage drop
Three-phase: ΔU = √3 · I · L · (R cosφ + X sinφ)
Single-phase: ΔU = 2 · I · L · (R cosφ + X sinφ)
d.c.: ΔU = 2 · I · L · R
The three-phase result is the line-to-line drop, so the percentage is taken against the line-to-line nominal voltage. The single-phase result is the drop in the loop, taken against the phase-to-neutral voltage.
Conductor resistance
R20 = ρ20 / A
Rθ = R20 [1 + α20(θ - 20)]
With the IEC 60287-1-1 values ρ20 = 1.7241×10-8 Ωm and α20 = 3.93×10-3 /K for copper, 2.8264×10-8 Ωm and 4.03×10-3 /K for aluminium.
Reactance
X = ω · 2×10-7 · ln(2S / d)
Where S is the axial spacing and d the conductor diameter.
Read this before you size a cable on it
- · The estimated resistance is the ideal value for the stated area. IEC 60228 maximum values for stranded conductors run several percent higher, and a.c. resistance adds skin and proximity effects that matter above roughly 300 mm². For a design calculation, enter the datasheet a.c. resistance.
- · Volt drop is only one of the checks. A cable also has to pass steady-state ampacity to IEC 60287, cyclic and emergency ratings to IEC 60853, and short-circuit withstand to IEC 60949. Passing volt drop proves nothing about any of those.
- · The load is taken as a single lump at the far end, at constant power factor. A distributed load gives a lower drop, and a leading power factor can give a rise rather than a drop.
- · Cables per phase divides both R and X, which assumes equal current sharing. Unequal formation or lengths break that assumption.
Frequently Asked Questions
How do you calculate voltage drop in a three-phase cable?
The line-to-line drop is √3 × I × L × (R cosφ + X sinφ). For a single-phase circuit the factor is 2 rather than √3, because the current flows out and back.
What is the maximum permissible voltage drop?
At low voltage in the UK, BS 7671 gives 3 % of nominal for lighting and 5 % for other uses, from the origin of the installation. On an HV connection the limit is set by the network operator and the design case, and 3 % across the private network is common. Confirm the figure that applies before fixing a size.
Why does reactance matter?
Resistance falls with conductor area but reactance does not, so above roughly 95 to 120 mm² the reactive term becomes significant, and at a poor power factor it can dominate. Sizing a large cable on resistance alone understates the drop.
At 20 °C or at operating temperature?
Operating temperature. Copper at 90 °C has about 27 % more resistance than at 20 °C, so the 20 °C figure understates the drop. This tool corrects for temperature.