When there exists a potential difference between two conductors of a transmission line, where the distance between them (spacing) is larger compared to their diameters. Then the air surrounding the conductors is subjected to electro-static stresses. If the potential difference applied reaches a value, then the air between the conductors gets ionized and hence produces ions.
The ionization of air causes an electrical discharge accomplished by a faint glow of violet color, hissing noise, and the production of ozone gas known as the corona effect. The phenomenon of corona plays an important role in the design of an overhead transmission line. Therefore, it is profitable to consider the following terms much used in the analysis of the corona effect on transmission lines.
Critical Disruptive Voltage :
Critical disruptive voltage is defined as the minimum phase-to-neutral voltage at which corona occurs. It is denoted by Vc. Consider two parallel conductors of radius r and spaced by a distance d as shown below. Let V be the phase to neutral voltage.
Now, if V is the phase to neutral potential, then potential gradient at the surface of the conductor is given by,
In order that corona to be formed, the value of potential gradient g must be made equal to the breakdown strength of air. Under normal operating conditions (i.e., at 76cm pressure and temperature of 25° C), the breakdown strength of air is 30kV/cm maximum value of 21.2kV/cm RMS value and is denoted by go.If Vc is the phase to neutral potential required under these conditions, by equating the potential gradient at the surface of the conductor to the breakdown strength of air (i.e., g = go) we get,
The above expression for disruptive voltage is under standard conditions i.e. at 76cm of Hg and 25°C. However, the above equation varies with the variation in the breakdown strength of air, further varying the air density factor. Hence, considering the air density factor at a barometric pressure of k cms mercury and temperature at t°C. The air density factor δ becomes,
Correction must also be made for the surface condition of the conductor. This is accounted for by multiplying the above expression by irregularity factor mo. Therefore, the expression for critical disruptive voltage Vc is given as,
Where,- mo = 1 for smooth and polished conductors,
- = 0.92 to 0.98 for rough conductors, and
- = 0.87 for stranded conductors.
Visual Critical Voltage :
In the case of transmission lines with parallel conductors, the corona glow does not being at the critical disruptive voltage Vc, but it begins at a higher voltage called the Visual Critical Voltage. It is denoted by Vv. Thus visual critical voltage is the minimum phase-neutral voltage at which the visual corona starts or appearance of the faint luminous glow of violet color all along the transmission line conductors.
Thus, when corona begins, the potential gradient gr at the conductor surface is higher than the disruptive gradient go. Peak states that the critical disruptive voltage must be so exceeded that the stress is greater than the breakdown value up to a distance of 0.3√δr cm from the conductor.
Thus visual corona will occur when the breakdown value is attained at a distance (r + 0.3√δr) from the axis. In order to achieve this the phase to neutral voltage should be (1 + 0.3/√δr) times the critical disruptive voltage. Therefore, the visual critical voltage Vv is given as,
Where,- mv = 1 for smooth and polished conductors,
- = 0.92 to 0.98 for rough conductors, and
- = 0.72 for stranded conductors.
- go = Breakdown strength of air at 76cm of Hg and 25°C
- δ = Air density factor
- r = Radius of the conductor
- d = Spacing between the conductors.
Factors Affecting Critical Disruptive Voltage and Visual Critical Voltage :
From the experiment of visual critical voltage, we can see that Vv also depends on the size of the conductor, spacing between the conductors, and the surface condition of conductors. The effects of various parameters on Vc and Vv can be summarized as below.
Size of Conductors :
The increase in the conductor size increases the voltage at which the corona occurs and appears to increase. Because as the size of the conductor is increased, the electric field intensity reduces. Hence, the corona will occur at a greater voltage if the size of the conductor is increased.
However, an increase in conductor size will increase the cost of conductors and the mechanical stress on the insulators. Hence, the conductor size cannot be increased to a large value, in order to avoid the early occurrence of the corona.
So, we have to make a compromise and go for a conductor size that will give a good value of critical disruptive voltage Vc and visual critical voltage Vv at the same time it does not increase the cost by much.
Spacing Between the Conductors :
As the spacing between the overhead conductors is increased, the electrostatic stress between the two conductors decreases. Hence, the air between the conductors will get ionized at a higher voltage i.e., the value of critical disruptive voltage and the visual critical voltage increases, and corona is eliminated.
Once again the spacing between the conductors cannot be increased to a very large value because we have to go for larger cross arms and long tower structures for the increased spacing. Also, we have to go for a higher right of way to install the tower structure.
Surface Condition of Conductors :
Surface condition plays an important role in the process of the corona. In order to account for the surface conditions, surface factors such as mo and mv are introduced in the expression of Vc and Vv.
If the conductor surface is smooth i.e., in the case of polished conductors, the voltage at which corona occurs and appears will be high. Hence, corona can be avoided. On the other hand, if the surface is irregular and dirty, the value of Vc and Vv will be less and corona will occur even at low voltages. The different values for mo and mv are,