Ferranti effect and measures to limit it

The Ferranti effect is the rise of voltage at the receiving end of a long transmission line (or cable) above the sending-end voltage when the line is on open circuit or very light load.

Cause

At light load, the line's shunt capacitance draws a charging current $I_C$ that leads $V_R$ by 90°. This current flows through the series inductance, and the drop $jI_CX$ is 180° out of phase with $V_R$ (since $j\cdot j = -1$). So $V_S = V_R + jXI_C = V_R - XI_C$, which is smaller than $V_R$: the receiving voltage is higher than the sending voltage.

                       IC ^ (leads VR by 90 deg)
                          |
   O---------------------->-----> VR
   O------------------->  VS      |
                     VS = VR - IC.X  (VS < VR)

Using the nominal-Π model at no load:

$$V_S = \left(1 + \frac{ZY}{2}\right)V_R \approx \left(1 - \frac{\omega^2LCl^2}{2}\right)V_R$$ $$V_R - V_S \approx \frac{\omega^2LCl^2}{2}V_R$$

So the rise grows with the square of line length and the square of frequency. It is significant for EHV lines above about 200–300 km and for cables (high C).

Effects

• Overvoltage stresses the insulation of the line, transformers and equipment.
• Problems when energising long lines or after sudden load rejection.

Measures to tackle the Ferranti effect

1. Shunt reactors at the receiving end (and often both ends) of long EHV lines. They absorb the charging Mvar and are the most common method. They may be switched in at light load and out at heavy load.
2. Controlled reactive devices: SVCs (thyristor-controlled reactors) and STATCOMs absorb variable reactive power quickly.
3. Synchronous condensers run under-excited at the receiving end to absorb Mvar.
4. Generator under-excitation at the sending end and coordinated voltage control.
5. Switching out shunt capacitors, and charging the line from the stronger end with a lower initial voltage.
6. Keeping a minimum load on the line, or splitting very long lines with intermediate substations and reactors.
7. On-load tap changers on transformers to bring the receiving voltage back to normal.