# Ferranti Effect: Detailed Explanation, Causes, Phasor Diagram

The Ferranti effect refers to the occurrence of voltage amplification at the receiving end of a lengthy transmission line in comparison to the voltage at the sending end. The occurrence of the Ferranti effect is more frequent in situations where the load is minimal or absent, such as in an open circuit.

The Ferranti effect can be expressed either as a numerical factor or as a percentage increase. For all electrical systems electric current flows from the region of higher potential to the lower potential region to compensate for the electrical potential difference that exists in the system. In all practical cases, the sending end voltage is higher than the receiving end voltage so the electric current flows from the source to the supply end of the load.

In 1980 sir S.Z Ferranti came up with a theory about the medium-distance transmission line (8 KM to 160KM) or long-distance transmission lines (more than 160 KM) suggesting that in case of light loading or no-load operation of the transmission system, the receiving end voltage increases beyond the sending end voltage leading to a phenomenon known as Ferranti effect in the power system.

In a medium or long transmission line when open circuited or lightly loaded the receiving end voltage is found more than the sending end voltage.This phenomenon of rise in voltage at the receiving end of the open circuited or lightly loaded line is called the ferranti effect.

## Causes of Ferranti Effects

This effect is due to voltage drop across the line inductance, due to the charging current, being in phase with the applied voltage at the sending end of the line. Both capacitance and inductance are necessary to cause this phenomenon. Hence the Ferranti effect is negligible in the case of short transmission lines as the inductor of such line is nearly equal to zero. For a 300km line operating at a frequency of 50Hz, the no-load receiving end voltage is found to be 5% higher than the sending end voltage.

## Detailed explanation of the Ferranti effect by considering a nominal pi (π) model

A transmission line can be considered to compose a considerably high amount of capacitance and inductance distributed across the entire length of the line. Ferranti effect occurs when current drawn by the distributed capacitance of the line itself is greater than the current associated with the load at the  receiving end of the line(during light or no load).This capacitor charging current leads to voltage drop across the line inductor of the transmission system which is in phase with the sending end voltage.This voltage drop keeps on increasing as we move towards the load end of the line and the receiving end voltage tends to get larger than applied voltage leading to the phenomenon called ferranti effects in power system.

## Phasor diagram of Ferranti effect

Taking receiving end phase voltage as reference phasor,

represented by phasor OA

charging current,

represented by phasor OD.

voltage at sending end,

Vs=VR+resistive drop in line+reactive drop in line

represented by phasor oc.

Now in the case of a long transmission line, it has been practically observed that the line electrical resistance is negligibly small compared to the line reactance, hence we can assume the length of the phasor IcR=0; we can consider the rise in voltage is only due to OA-OC=resistive drop in the line.

Now if we consider Co and Lo are the values of capacitance and inductor per km of the transmission line,where l is the length of the line.

This the capacitive reactance

As the capacitance of the line is uniformly distributed over the entire length of the line therefore the average current flowing throughout  the line

Now the inductive reactance of the line =wLol

thus the rise in voltage due to line inductor is given by,

The quantity

is constant for all overhead lines and is equal to the velocity of propagation of electromagnetic waves.And is nearly equal to 3*10^5 km/s.

so rise in voltage at the receiving end,

From the above equation it is absolutely evident,that the rise in voltage at the receiving end is directly proportional to the square of the line length,and hence in case of a long transmission line it keeps increasing with length and even goes beyond the applied sending end voltage at times,leading to the phenomena called ferranti effect in power system.

## How to reduce the Ferranti effects?

Ferranti effect on long transmission lines at low load or no load increases the receiving end voltage.This voltage can be controlled by placing the shunt reactors at the receiving end of the lines.For long high voltage and extra high voltage lines shunt reactors are provided to absorb part of charging current or shunt capacitive VA of the line on no load and light load in order to prevent over voltages on the line.The high voltage at the receiving end cause the burn of winding. When this effect occurs in long transmission lines, shunt reactors compensate the capacitive VAr of the lines and therefore the voltage is regulated within the required limit.

## References

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