Proximity effect in cables vs overhead lines

Proximity effect is the crowding of current in a conductor caused by the alternating magnetic field of a nearby current-carrying conductor. Its size depends mainly on how close the conductors are compared with their size.

Overhead lines: negligible

• Phase conductors are spaced several metres apart (e.g. 4–10 m at 132–400 kV) for insulation in air.
• At such distances, the flux from one conductor is almost the same over the whole cross-section of the other (conductor diameter ≈ 2–3 cm, so $d/D$ is tiny).
• So the current distribution is hardly disturbed, and the rise in AC resistance is negligible.

Underground cables: significant

• Cable cores are separated only by thin solid insulation, a few mm to a few cm, so cores are almost touching ($D$ close to $d$).
• The field of a neighbouring core changes strongly across the cross-section, so current crowds to one side of each core.
• Cable conductors are also large in cross-section (to carry high current with limited cooling), which strengthens the effect.
• This noticeably increases $R_{ac}$ and $I^2R$ losses, so it must be included in cable ratings.