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HV cables

Cable charging current and three-phase charging kvar

Ic=2πfClU0×10−3Q=3U0Ic
where
Ic
charging current per phase (A)
f
frequency (Hz)
C
capacitance per phase (µF/km)
l
route length (km)
U₀
voltage to earth (kV)
Q
three-phase charging reactive power (kvar)
Explain this equation

Gives the capacitive current each phase draws when the cable is energised with no load, and the total reactive power the cable generates. Use it to size test sets and reactors, and to check switching and earth-fault capacitive currents.

I_c is the charging current per phase, set by the capacitance C, the length l, the voltage to earth U₀ and the frequency f. Q is the three-phase reactive power, 3 × U₀ × I_c.

Each core is a capacitor of C × l to its earthed screen, so the current is ωCU₀ with ω = 2πf. The 10⁻³ combines µF to F (10⁻⁶) with kV to V (10³), so I_c comes out in amperes and Q in kvar.

An 11 kV cable at 0.3 µF/km draws about 0.6 A per km per phase, roughly 11 kvar per km. A 132 kV cable at 0.2 µF/km draws nearly 5 A per km and over 1 Mvar per km.

Use U₀, not the line voltage; using U overstates I_c by √3. For a VLF test set, put the VLF frequency in f.

Capacitive charging current drawn by an energised but unloaded cable, and the reactive power it generates. Used for test-set sizing, switching duty, earth-fault (capacitive) current and reactive compensation.

µF/km
Hz

Enter your values to see the result.

Good to know

Ic = ωCU0 per phase per unit length, multiplied by length. The three-phase reactive power is 3U0Ic = ωCU²l where U is the line voltage. For the earth-fault capacitive current of an unearthed or resonant-earthed system, the total is 3Ic (summed over all galvanically connected cable).

Common mistake

Using the line voltage U instead of U0 in Ic, which overstates the current by √3.

Limits

Distributed capacitance treated as lumped; voltage assumed uniform along the cable (Ferranti rise neglected, fine for distribution lengths). Use the operating, not the test, frequency; for VLF test sets use the VLF frequency.

Sources

For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.

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