Proximity effect in overhead lines

Proximity effect is the non-uniform distribution of current in a conductor caused by the alternating magnetic field of a nearby current-carrying conductor. It increases the effective AC resistance of the conductor.

How it occurs

• The alternating flux of conductor B links parts of conductor A unequally: the side of A nearer to B is linked by more (or less) flux than the far side.
• This produces unequal inductive reactance across the cross-section of A, so current crowds to one side.
• For opposite currents (go and return of a circuit), current crowds on the adjacent (near) faces; for currents in the same direction, it crowds on the far faces.

 Opposite currents       Same direction
   [   ##][##   ]        [##   ][   ##]
    A  ->  <- B           A ->    B ->
  (## = higher current density)

Effects

• The effective current-carrying area is reduced, so AC resistance rises and $I^2R$ loss increases.
• It adds to the skin effect; both are included in the AC resistance of a line.

Factors

Proximity effect increases with:

• Frequency (larger flux variation),
• Conductor size (diameter),
• Closeness of conductors (smaller spacing),
• Conductivity and permeability of the material.

In practice

In overhead lines the spacing between phases is several metres, so the proximity effect is negligible. In underground cables, conductors are only a few centimetres apart, so the proximity effect is significant and must be considered in the cable's AC resistance.