Ferranti Effect in Transmission Line
Let’s consider the equivalent circuit diagram of a long transmission line. Since a long transmission line is made out of high capacitance and inductance distributed through the entire length of the line, this diagram addresses the parameters per kilometer of length. In this manner the capacitance and inductance are proportional to the length of the line. The inductors are connected to the power lines in series, while the shunt capacitors are connected in parallel.
Circuit-Diagram-of-Ferranti-Effect
The parameters in the given circuit diagram are :
- Vs = Sending or source Voltage
- Vr = Receiving Voltage
- Is = Sending or Source Current
- Ir = Receiving Current
- Ic = Capacitive or Charging Current
- R = Resistance of line
- Xc = Capacitive reactance of the line
- XL = inductive reactance of the line
- C = Capacitance of line
- L = inductance of the line
Phasor diagram of the given circuit is shown in below. During the Ferranti effect, there is no load subsequently
Phasor-Diagram-of-Ferranti-Effect
Receiving current Ir = 0
The receiving voltage Vr is taken as reference OA where the capacitive current Ic is addressed by opposite line OD driving the Vr by 90°. The capacitive current Ic has a voltage drop across the line resistance R and the line inductance L, as shown by the equation:
Voltage drop across the resistor = IcR = AB
Voltage drop across the inductor = IcXL = BC
The inductive voltage drop IcXL (BC) is 90 degrees higher than the resistive voltage drop IcR (AB). Where the sending voltage Vs is the amount of all voltage drops + receiving voltage represented by OC.
Vs = Vr + Resistive voltage drop + Inductive voltage drop
Vs = OA + AB + BC = OC
As shown in the phasor diagram, the receiving voltage Vr at the load side is grater than the sending voltage Vs at the source side.
Now let’s derive the equation for the Ferranti effect using the same circuit diagram of the transmission line.
Vs = Vr + resistive drop + inductive drop
Vs = Vr + IcR + IcXL
Vs = Vr + Ic (R + XL)
Since capacitive current, Ic = jwCVr
Vs = Vr + jwCVr (R + XL)
Since XL = jwL
Vs = Vr + jwCVr (R + jwL)
Vs = Vr + jwCVrR + j 2w 2CLVr
Vs = Vr + jwCVrR – w 2CLVr
Vs – Vr = jwCVrR – w 2CLVr
In long transmission lines, the line resistance is a more smaller than the line reactance. Therefore the resistance R, as well as resistive voltage drop is neglected
Vs – Vr = – w 2CLVr
Now assume the capacitance and inductance per km of the length are Co and Lo respectively and the length of the transmission line is l. The equation becomes
Vs – Vr = -w2(CO I)(LO l)Vr
Vs – Vr = -w2 l 2 CoLoVr
Since the line capacitance is distributed throughout the entire length (l) of the transmission line, the charging current as well as the voltage drop associated with it is taken as an average.
Now assume Therefore;
Vs – Vr = – (1/2) w2 l 2 CoLoVr
The voltage distinction between the sending and receiving voltage is negative which implies the voltage rises. Additionally, it is directly proportional to the squares of line length (l) and frequency (w). This condition demonstrates that the Ferranti effect increases with an expansion in the length of the transmission line and supply frequency. Consequently little transmission lines and HVDC transmission are not impacted by the Ferranti effect.
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