Ferranti Effect in PI Model
The Ferranti effect in extensive transmission line where OE-signifies the receiving end voltage, OH-signifies the flow of current in the capacitor at the receiving end. A decrease in voltage across the resistance R is indicated by the FE-phasor, and a decrease in voltage across the inductance (X) is indicated by the FG. The OG-phasor means the sending end voltage in a condition of no-load. The nominal Pi model of the transmission line at no load condition circuit is shown in below.
In the following phasor representation, OE is greater than OG(OE>OG). In different terms, the voltage at the less than receiving end is better than the voltage at the transmitting end when the transmission line is at no load condition. Here the Ferranti effect phasor diagram is shown below.
Vs = (1+ZY/2)Vr + ZIr
Where, Ir =0 at no load condition
Vs = (1+ZY/2)Vr + Z (0)
= (1+ZY/2) Vr
Vs – Vr = (1+ZY/2)Vr-Vr
Vs – Vr = Vr [1+ZY/2-1]
Vs – Vr = (ZY/2) Vr
Z= (r + jwl)S, and Y = (jwc)S
Assuming that the transmission line’s resistance is unnoticed
Vs – Vr = (ZY/2) Vr
Substitute Z= (r + jwl)S, and Y = (jwc)S in the above Vs
Vs – Vr= ½ ( jwls) (jwcs) Vr
Vs – Vr= – ½ (W2S2) lcVr
For the lines of above, 1/√LC = 3×108m/s (velocity of electromagnetic wave transmission on the transmission lines).
1/√LC = 3×108m/s
√LC = 1/3×108
LC = 1/(3×108 )2
Vs – VR = – ½ W2S2 . ( 1/(3×108 )2) Vr
W = 2πf
Vs – VR = – ((4π2/18)* 10-16) f2S2Vr
That’s what the above equation represents (Vs – Vr) is negative, that means Vr is greater than Vs This is also illustrated that this effect will also determine by the electrical period of the transmission lines and frequency.
Generally, for each line
Vs = AVr + BLr
On no load condition
Ir =0, Vr = Vrnl
Versus = AVrnl
|Vrnl| = |Vs|/|A|
For a extensive transmission line, A is<1 and it reduces with the increase in the extent of the transmission line. Hence, the voltage at no load is more greater than the voltage at the load (Vrnl > Vs) As the length of line in the voltage on the collecting end, then at no load acts as the main.
Ferranti Effect
As we know electricity is generated at power generation plants using huge electromechanical generators by conversion from different types of energy. After that, a long-distance transmission line carries this electrical energy to the end users. In order to maximize the effectiveness of the power transmission and distribution system and ensure the safety of the connected loads and personnel, the electrical power transmission lines require a variety of safety devices and components. The transmission line faces different types of losses and characteristics that influence its efficiency. The Ferranti Effect is one such phenomenon that has a significant impact on the transmission line.
For the most part, we assume that the voltage generally drops in the transmission lines because of the line losses. In a long-distance transmission line with a very low load or no load at all, the Ferranti Effect causes the receiving voltage to be higher than the sending voltage.
In this article, we will be going through the Ferranti effect, First, we will start with the basics of the Ferranti Effect, Then we will go through the Causes of the Ferranti Effect, After that we will go through the Ferranti Effect in Transmission Lines and ways to reduce Ferranti effect, At last, we will conclude our Article with Advantages, Disadvantages, and characteristics of Ferranti effect.
Table of Content
- Ferranti Effect
- Terminologies
- Causes
- Ferranti Effect in Transmission Line
- Ferranti Effect in PI model
- How to Reduce Ferranti Effect?
- Characteristics
- Advantages
- Disadvantages