Ferranti Effect

Ferranti Effect

It can be seen that for a long transmission line under no load conditions, the voltage at receiving end is more than that at sending end because of the effect of the line capacitance. This is called Ferranti effect. This can be explained by various ways.

In case of long transmission line, we have studied the equation for V_S given by,

A general expression for V_S is obtained by considering I_R = 0 as the line is at no load.

From the above expression it can be seen that there are two components of voltages. One is increasing exponentially while the other is decreasing exponentially. At l = 0 both the components reduce to V_R / 2 so the total voltage is V_R. The variation of these components is shown in Fig. 2.21.1.

As the length I increases component V_R / 2 e^αl 1 increases exponentially and subtends an angle of βl and is represented by phasor OC. The other component V_R / 2 e^-αl decreases exponentially and phasor rotates through a negative angle of βl as given by phasor OD. The phasor sum of this two components is V_S which can be seen to be less than V_R from geometry from magnitude point of view.

Another simpler explaination can be given on the basis of approximation of transmission line model by lumping its inductance and capacitance and neglecting resistance as shown in Fig. 2.21.2.

From the network we have

Here L and C are inductance and capacitance of line per unit length and I is total length of the line.

Normally capacitance of line is small compared to inductance. Hence X_C is more than X_L. So neglecting X_L we get

The Ferranti effect can also be explained on the basis of net reactive power flow in the line. If a reactive power generated at a point is more than the reactive power absorbed the voltage at that point becomes higher than its normal value. The inductive reactance absorbs the reactive power whereas the capacitances generate reactive power. Under light load conditions or no load conditions the capacitance associated with the line generate more reactive power than the reactive power which is absorbed hence the voltage at the receiving end is found to be greater than that at sending end.

Review Question

1. Explain the ferranti effect with a phasor diagrams and its causes.