Ferranti effect is prominent in medium or long transmission lines. When these lines are open-circuited at the receiving end or are under lightly loaded conditions then the receiving end voltage is found to be greater than the sending end voltage. This phenomenon of rising in voltage at the receiving end is known as the Ferranti effect.
The effect is due to voltage drops in the inductance of the line and due to the charging currents. The charging current is in phase with the applied voltage at the sending end side. Hence, both capacitance and inductance of the line are responsible for this effect.
Why Ferranti effect does not occur in short transmission lines?
The effect of capacitance in a short transmission line is negligible. Capacitance being negligible, charging current is also negligible. Both capacitance and inductance are necessary for the Ferranti effect to take place. So, the Ferranti effect does not occur in short transmission lines.
For a transmission line of length 300 km operating at 50 Hz frequency. When its receiving end is open-circuited the rise in voltage at the receiving end is found to be around 5% than the sending end voltage. [How 5%? This will be discussed below.]
Voltage Rise Due to Ferranti Effect
The figure below represents the phasor diagram for the Ferranti effect.
For receiving end voltage VR being taken as reference phasor represented by OA.
Charging current IC is represented by phasor OD.
The sending end voltage VS is represented by phasor OC. VS is the phasor sum of VR, resistive drop (ICR represented by phasor AB) in the line, and reactive drop (jICX represented by phasor BC) in the line.
For an overhead transmission line of long length, the reactance of the line is very high compared to the resistance of the line. So by neglecting the resistive drop (ICR) in the line for simple approximation.
The rise in voltage is given by AC= OA – OC
Consider C0 and L0 are the capacitance and inductance of the line per km and ‘l’ be the length of the line.
The capacitive reactance of line XC is given by
The capacitance of the line is uniformly distributed throughout the line. So the average charging current flowing throughout the line is
The reactance of the transmission line is
The rise in voltage is
is the velocity of propagation of light and is constant for all overhead transmission lines. Its value is 3 x 105 km/s.
So the expression for rising in voltage is
Equation (i) is the expression for the rise in voltage at the receiving end due to the Ferranti effect. From the above expression, we can conclude that:
- The rise in voltage at receiving end is proportional to the square of the length of the transmission line.
For a transmission line of length 300 km and operating at 50 Hz frequency, the percentage rise in voltage is around 5%. This can be calculated by the above expression.
Reducing Ferranti Effect
Due to the Ferranti effect, the voltage at the receiving end increases for medium or long transmission lines at low or no-load conditions.
This effect can be reduced by placing a shunt reactor at the receiving side of the transmission line. For long transmission lines of high and extra-high voltages, these shunt capacitors are placed at the receiving end side. The shunt capacitors absorb the part of the charging current or shunt capacitive VA of the line during no load or light load to prevent the overvoltages on the line.
Reference: “A Course in Power Systems”, J.B. Gupta
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