# Ferranti Effect Calculations

The Ferranti effect is observed as an increase in voltage at the receiving end of an energised transmission line. The capacitive charging current of the line produces a voltage drop across the line inductance which is in-phase with the sending end voltage. For this reason, the line inductance and capacitance are primarily responsible for the voltage rise. Interestingly, the Ferranti effect is much more pronounced in underground cables because of the capacitance, which is represented by the susceptance B in the following diagram (the susceptance is the capacitive admittance).

The temporary over-voltages at the remote end of a line need to be considered as they can affect auto-reclosure settings, corona designs and the insulation coordination. Here the voltage rise along the energised transmission line is given by:

Where VA is the sending-end voltage, VB is the remote-end voltage, XL is the positive sequence line reactance in % on 100MVA base, and B is the line charging in MVAr at nominal voltage.

This temporary over-voltage can be increased further if the three-phase fault level at the sending-end busbar is relatively low. Without any loading, the line behaves as a capacitor and increases the voltage of the sending end busbar. The voltage step change at the sending-end busbar can be defined by:

The following approximation can be derived by ignoring the small phase angle differences between the source voltage and the voltage at busbar A.

For a small change in the voltage VA, Id or Iq, the following equations holds:

Where FL is the three-phase fault level at the sending-end busbar.
Therefore the remote-end voltage VB can also be defined as a function of the sending-end voltage VA before the line is energised