Ferranti Effect
In the Ferranti effect, the receiving end voltage of the transmission lines is more than the sending end voltage of the line. This effect occurs when the transmission line is lightly loaded or open circuit at receiving end or in no-load condition. This phenomenon of a rise in voltage at the receiving end of the open-circuited or lightly loaded line is called the Ferranti effect of the transmission line. The Ferranti effect is founded by S. Z. de Ferranti in 1890.
The charging current is responsible for the Ferranti effect in Transmission lines. The charging current increases in the transmission line when the receiving end voltage is more than the sending end voltage of the transmission line. The Ferranti effect occurs in transmission through the interaction between the capacitance and inductance of the transmission line.
The transmission line consists of inductance and capacitance. These both cause the Ferranti effect in the transmission line. The Ferranti effect is due to the voltage drop or loss in line inductance, due to the line charging current, the charging current is in phase with applied voltage at the sending of the transmission line.
The capacitance and charging current are negligible in short transmission lines. so, in short transmission lines, the Ferranti effect not occurred. In medium and long transmission lines Ferranti effect occurs. In a transmission line with a length of 300km and operates on a 50hz supply, the receiving end voltage on the open-circuited line is usually roughly 5% higher than the sending end voltage.
The main parameters are capacitance and inductance when the line length is 240km or above. When the voltage is applied at sending end of the transmission and the line is not loaded or lightly loaded, the current drawn by the line capacitor is more than the current drawn by the load.
Due to the Ferranti effect, the voltage at the user's end or receiving end is increased which causes damage to the costly equipment and windings of the motor of the user. The Ferranti effect in the transmission line is reduced by placing the shunt capacitors at the sending end of the lines. The Ferranti effect is also reduced by placing a shunt reactor in the line which compensates for the capacitive current. The shunt reactor is connected to the main and neutral lines.
What is a short, medium, and long transmission line?
When the length of the transmission line is 80km, this line is known as a short transmission line. When the length of the transmission line is between 80km to 250km, this line is known as a medium transmission line. When the length of the transmission line is greater than 250km, this line is known as a long transmission line.
Three factors, resistance, capacitance, and inductance obstruct the flow of current in the transmission line. the resistance and inductance remain in series and capacitance is in parallel with the phase conductor. These factors occur power loss in the transmission line.
Why Does Ferranti Effect occur?
When we transfer the power from generating power station to the substation, an imaginary capacitor forms between the two conductors. Two conductors and an Air gap between the two conductors behave as the dielectric medium, forming an imaginary capacitor.
The capacitors are charge-storing devices. When the current flows through the overhead transmission lines, some amount of power drops in these capacitors. Due to this current reduction in the line. when current reduces in the transmission line voltage increases at the receiving end station.
Another reason is an overhead transmission line, insulators are attached to the metallic rod at the top of the tower. The air gap between the tower and the metallic rod behaves as a capacitor. Where some amount of charge will drop and current will increase and the voltage will automatically decrease. Due to the Ferranti effect power loss increase in transmission lines.
The formula of the Ferranti Effect
The below figure shows the phase diagram of the Ferranti effect.
VR =
Receiving end voltage = OA
VS =
Sending end voltage = AC
IC =
Charging current = OD
IcX
= Reactive drop = CB
IcR
= Resistive drop = AB
VR is a receiving end voltage and VR is
taken as a reference phaser and represented by OA.
VR = VR(1+j0)
Charging
current is given by
IC
= jωCVR
Where C is
the line capacitance.
The sending
end voltage VS is the phaser sum of receiving end voltage VR,
resistive drop IcR, and reactive drop IcX.
VS
= VR + resistive drop + reactive drop
= VR
+ IcR + jIcX
= VR
+ IC(R + jX)
Put the
value of IC = jωCVR and X = jωL where L is the inductance
of the transmission line in the above equations
= VR + jωCVR(R + jωL)
= VR + jωCVRR - ω2CLVR
In a long
transmission line, reactance is very high compared to the resistance of the
line. So resistive drop ICR can be neglected.
Consider C0
and L0 are the capacitance and inductance of the transmission line
and L is the length of the line
Now Capacitive
reactance of the transmission line XC is given by
XC = 1 / ωlC0
In a long
transmission line, the capacitance of the line is uniformly distributed throughout
the line. The charging current flowing through the line is given by the
IC = 1 VR / 2XC
Now put the
value of the XC in above equations
IC = VRC0ωl
/ 2
The Inductive
reactance of the transmission line is given by
X = ωL0l
The rise in
voltage is given by
= ICX
Put the
value of Ic and X in the above equation
= VRC0ωl / 2 X ωL0l
= ω2l2VRC0L0 / 2 Volts
Where 1 / √L0C0
is the velocity of propagation of light and it is constant for all transmission
lines and its value is given by 3 X 105 km/s.
Now we put the
above value in the rising voltage equation
Rising
Voltage = ω2l2VR / 2 X (3 X 105)2
= ω2l2VR / 2 X 9 X 1010
= ω2l2VR
X 10-10 / 18 Volts
The above equation
is for the rising voltage which is occurred at receiving end voltage due to the
Ferranti effect.
Important
Points:
From the above
equation, we can conclude that the rise in voltage at the receiving end of the
line is proportional to the square of the length of the transmission line which
means if the length of the transmission line increased than the voltage at the receiving
end increases.
The Ferranti effect is more occurs in short line cables due to very high capacitance.
If the length
of the transmission line is 300km and the frequency of the supply voltage is 50
Hz then the percentage rise in voltage is calculated by
Rise in
voltage = ω2l2VR X 10-10 / 18
Percentage rise
in Voltage = ω2l2VR X 10-10 X 100 /
18 X VR
= ω2l2 X 10-8 / 18
= (2Ï€f)2 (300)2 10-8 / 18 = (2Ï€ X 50)2
X (300)2 X 10-8 / 18
= 4.93 % is equal to 5 %.
