Cable Charging Current Formulas

Cable charging current formulas: the capacitance of a length of cable, the charging current per phase and the reactive power the cable produces.

The formulas

c is the capacitance per kilometre from the cable data sheet, L the length in kilometres, f the frequency in hertz and VL the line-to-line voltage in volts. C is in farads and Q in VAR for a three-phase circuit. The cable produces reactive power that the supply does not need to give, and on a long cable with a light load this can raise the voltage at the far end. The capacitance of 0.3 µF/km is an example for a medium-voltage cable, so use the data sheet. The current is that of a cable with no load, and it adds to the load current in the supply end of the cable.

Worked example: 20 km of 11 kV cable

c = 0.3 µF/km at 50 Hz.

1. C = 0.3 × 20 = 6 µF
2. Ic = 2π × 50 × 6e-6 × (11,000 / √3) = 11.97 A
3. Q = 2π × 50 × 6e-6 × 11,000² = 228.1 kVAR

Charging current by length (0.3 µF/km, 11 kV)

Frequently asked questions

What is the charging current?

The current that flows into the capacitance between the conductors and the screen or earth. It flows even when the cable carries no load.

Why does it matter for long cables?

It grows with the length and the voltage. On a long lightly loaded cable it can reach a large part of the cable rating and it raises the voltage at the end.

Does it matter for low-voltage cables?

Rarely. The charging current falls with the square of the voltage for a given power, so it is small on low-voltage cables.

How is the voltage rise controlled?

By a shunt reactor, which takes the reactive power that the cable makes. It is used on long high-voltage and medium-voltage cables.

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