Skin effect and proximity effect

Skin effect

Skin effect is the tendency of alternating current to crowd towards the outer surface of a conductor. The current density is highest at the surface and lowest at the centre.

Cause: Imagine the conductor as many thin filaments. A filament at the centre is linked by the flux inside the conductor and also by the flux outside, while a filament at the surface is linked only by the outside flux. So the central filaments have more inductance and a higher reactance $\omega L$. The AC current takes the easier, low-reactance path near the surface.

  DC: uniform           AC: crowded at surface
    .-------.               .-------.
   / . . . . \             / ####### \
  | . . . . . |           | ##     ## |
  | . . . . . |           | #  low  # |
   \ . . . . /             \ ####### /
    '-------'               '-------'

Effects:

• The effective area is reduced, so $R_{ac} > R_{dc}$. This increases $I^2R$ loss.
• Internal inductance is slightly reduced.

Factors: the effect increases with frequency, conductor diameter, permeability and conductivity. The depth of current flow is $\delta = \sqrt{\frac{2\rho}{\omega\mu}}$; for copper at 50 Hz, $\delta \approx 9.3$ mm.

Remedies: stranded and ACSR conductors (the steel core carries little current), hollow or tubular conductors, and bundled conductors. There is no skin effect with DC.

Proximity effect

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

• When two nearby conductors carry current in the same direction, current crowds to their far sides.
• When they carry current in opposite directions (go and return), current crowds to the sides facing each other.

 Same direction        Opposite directions
 (#  )   (  #)          (  #) (#  )
 crowd outward          crowd towards each other

Effects: the effective resistance rises further, and the inductance changes slightly.

Where it matters: in cables and closely spaced conductors (bus-bars, cable cores, transformer windings). It is negligible in overhead lines, where the conductors are metres apart.