Ferranti effect and skin effect

Ferranti effect

The Ferranti effect is the rise of receiving-end voltage above the sending-end voltage when a long or medium line is on no load or very light load.

• At light load, the line's shunt capacitance draws a charging current $I_C$ that leads the voltage by $90^\circ$.
• This current flows through the series inductance and produces a drop $jX_L I_C$, which points opposite to $V_R$ (since $jX_L \cdot jI = -X_L I$), so $V_S = V_R - X_L I_C$ is smaller than $V_R$.
• For a nominal-$\pi$ line at no load (neglecting $R$, with $L$ and $C$ the total line values), $V_S = A V_R$ with $A = 1 - \omega^2 LC/2$, so $V_R = V_S/(1-\omega^2LC/2) > V_S$.
• The rise is roughly proportional to the square of the line length and is large for EHV lines (about 5–10 % at 400 km).

        jXL*Ic
   Vr --------> Vs  (Vs shorter than Vr)
   ^
   | Ic (leads Vr by 90 deg)

Remedy: shunt reactors at the receiving end, or keeping some load connected.

Skin effect

The skin effect is the tendency of alternating current to crowd towards the outer surface of a conductor instead of spreading uniformly over its cross-section.

• The inner filaments of a conductor link more flux than the outer ones, so they have higher inductive reactance. Current therefore takes the outer, lower-reactance path.
• The effective area carrying current falls, so the AC resistance is greater than the DC resistance.
• It increases with frequency, conductor diameter, permeability and conductivity. At 50 Hz it is small for normal conductors (a few percent) but is not negligible for large conductors.
• It is absent for DC.

Reduction: use stranded conductors (ACSR) or hollow/tubular conductors; in ACSR the steel core sits at the centre, where little current flows anyway.