Sheath bonding
Standing sheath voltage, single-point bonded cables
- where
- sheath reactance (Ω/m)
- frequency (Hz)
- axial spacing between adjacent cables (mm)
- mean diameter of the screen or sheath (mm)
- mutual reactance term for the outer cables of a flat group (Ω/m)
- sheath voltage, trefoil or flat centre cable (V)
- conductor current (A)
- length of the single-point bonded section (km)
- sheath voltage, flat outer cables (V)
Explain this equation
Gives the voltage that builds up between the screen and earth at the open end of a single-point bonded cable section, for normal load or a balanced through fault.
X_s is the reactance between a conductor and the sheaths, set by the spacing s and the mean sheath diameter d_m. X_m is an extra term for the outer cables of a flat group, which sit 2s from one neighbour. I is the conductor current and l the section length.
With no sheath current, each sheath picks up the voltage induced by the flux of all three conductor currents. In trefoil and for the flat centre cable the neighbour fluxes add to I·X_s per metre; the outer flat cables have unequal spacing and the result is the vector sum shown under the root. The 10³ turns km into metres.
500 A in trefoil at 70 mm spacing and 45 mm sheath diameter gives about 36 V per km; the flat outer cables are about 40 % higher. During a 20 kA through fault the same section stands 40 times higher.
This covers balanced currents only. Earth-fault sheath voltages depend on the earth return and earth continuity conductor and need the full method.
Voltage between the sheath (screen) and earth at the free end of a single-point bonded section, under balanced load or through-fault current.
Enter your values to see the result.
Good to know
Xs = 2ω·10⁻⁷ ln(2s/dm) Ω/m is the IEC 60287-1-1 sheath reactance for trefoil. With balanced currents the induced voltage is I·Xs per metre for trefoil cables and for the centre cable of a flat group; the outer cables of a flat group see I·√(Xs² + XsXm + Xm²) with Xm = 2ω·10⁻⁷ ln 2, the published simplified form given in IEEE 575 and the Electric Cables Handbook. Enter the three-phase through-fault current to size sheath voltage limiters; for earth faults the voltage depends on the earth return path and the parallel earth continuity conductor and is not calculated here. UK practice commonly keeps standing voltage at full load within about 65 V (check your network operator's policy, e.g. ENA guidance).
Common mistake
Applying the trefoil result to the outer cables of a flat formation, which see the highest voltage, or forgetting that the voltage during an external fault scales with fault current.
Limits
Simplified formula: balanced sinusoidal currents, equal spacing, no other circuits nearby, sheath currents zero (single-point bonding). Earth-fault and cross-bonded minor-section voltages need the full IEEE 575 / CIGRE TB 283 methods.
Sources
- IEEE 575-2014 Guide for bonding shields and sheaths of single-conductor power cables rated 5 kV through 500 kV
- IEC 60287-1-1:2023 Electric cables – Calculation of the current rating – Part 1-1: Current rating equations (100 % load factor) and calculation of losses
- Moore, G.F. (ed.) Electric Cables Handbook, 3rd edn, Blackwell Science / Wiley
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.