Corona Effect in Power Transmission Lines

A corona discharge is ionization of air surrounding a power conductor or it is a luminous, audible electrical discharge that develop due to high electric field on the surface of the conductor.

When an alternating potential difference is applied across two conductors whose spacing is large as compared to their diameters, there is no apparent change in the condition of atmospheric air surrounding the wires if the applied voltage is low.
However, when the applied voltage exceeds a certain value, called critical disruptive voltage, the conductors are surrounded by a faint violet glow called corona.
The phenomenon of corona is accompanied by a hissing sound, production of ozone, power loss and radio interference.
The higher the voltage is raised, the larger and higher the luminous envelope becomes, and greater are the sound, the power loss and the radio noise.

If the applied voltage is increased to breakdown value, a flash-over will occur between the conductors due to the breakdown of air insulation.
The phenomenon of violet glow hissing noise and production of ozone gas in an overhead transmission line is known as corona.
If the conductors are polished and smooth, the corona glow will be uniform throughout the length of the conductors, otherwise the rough points will appear brighter.
With d.c. voltage, there is difference in the appearance of the two wires.
The positive wire has uniform glow about it, while the negative conductor has spotty glow.

Some ionisation is always present in air due to cosmic rays, ultra- violet radiations and radioactivity.
Therefore, under normal conditions, the air around the conductors contains some ionised particles (i.e. free electrons, and +ve ions) and neutral molecules.
When p.d. is applied between the conductors, potential gradient is set up in the air which will have maximum value at the conductor surfaces.
Under the influence of potential gradient, the existing free electrons acquire greater velocities.
The greater the applied voltage, the greater the potential gradient and more is the velocity of free electrons.
When the potential gradient at the conductor surface reaches about 30 \(\mathrm{kV/cm}\) (max. value), the velocity acquired by the free electrons is sufficient to strike a neutral molecule with enough force to dislodge one or more electrons from it.
This produces another ion and one or more free electrons, which is turn are accelerated until they collide with other neutral molecules, thus producing other ions.
Thus, the process of ionisation is cumulative.
The result of this ionisation is that either corona is formed or spark takes place between the conductors.

The phenomenon of corona is affected by the physical state of the atmosphere as well as by the conditions of the line.
Factors upon which corona depends:
- Atmosphere
  - As corona is formed due to ionisation of air surrounding the conductors, therefore, it is affected by the physical state of atmosphere.
  - In the stormy weather, the number of ions is more than normal and as such corona occurs at much less voltage as compared with fair weather.

Conductor size
- The corona effect depends upon the shape and conditions of the conductors.
- The rough and irregular surface will give rise to more corona because unevenness of the surface decreases the value of breakdown voltage.
- Thus a stranded conductor has ir- regular surface and hence gives rise to more corona that a solid conductor.
Spacing between conductors
- If the spacing between the conductors is made very large as compared to their diameters, there may not be any corona effect.
- It is because larger distance between conductors reduces the electro-static stresses at the conductor surface, thus avoiding corona formation.

Line voltage
- The line voltage greatly affects corona.
- If it is low, there is no change in the condition of air surrounding the conductors and hence no corona is formed.
- However, if the line voltage has such a value that electrostatic stresses developed at the conductor surface make the air around the conductor conducting, then corona is formed.

It is the minimum phase-neutral voltage at which corona occurs.
Consider two conductors of radii \(r\) cm and spaced \(d\) cm apart.
If \(V\) is the phase-neutral potential, then potential gradient at the conductor surface is given by: \[\boxed{g=\dfrac{V}{r \log _{e} \dfrac{d}{r}} }~\text { volts } / \mathrm{cm}\]
In order that corona is formed, the value of \(g\) must be made equal to the breakdown strength of air.
The breakdown strength of air at \(76~ \mathrm{cm}\) pressure and temperature of \(25^{\circ} \mathrm{C}\) is \(30 ~\mathrm{kV} / \mathrm{cm}(\mathrm{max})\) or \(21 \cdot 2 \mathrm{kV} / \mathrm{cm}(\mathrm{r} \cdot \mathrm{m} \cdot \mathrm{s} .)\) and is denoted by \(\mathrm{g}_{0}\).

If \(V_{c}\) is the phase-neutral potential required under these conditions, then, \[\boxed{g_{0}=\dfrac{V_{c}}{r \log _{e} \left(\dfrac{d}{r}\right)}}\] where \(g_{0}=\) breakdown strength of air at \(76\) cm of mercury and \(25^{\circ} \mathrm{C}\) \[=30 \mathrm{kV} / \mathrm{cm}(\mathrm{max}) \text { or } 21 \cdot 2 \mathrm{kV} / \mathrm{cm}(\mathrm{r}. \mathrm{m} . \mathrm{s} .)\]
Critical disruptive voltage, \(V_{c}=g_{0} r \log _{e} \left(\dfrac{d}{r}\right)\)
The above expression for disruptive voltage is under standard conditions i.e., at \(76 \mathrm{cm}\) of \(\mathrm{Hg}\) and \(25^{\circ} \mathrm{C} .\)
However, if these conditions vary, the air density also changes, thus altering the value of \(g_{o}\)

The value of \(g_{o}\) is directly proportional to air density.
Thus the breakdown strength of air at a barometric pressure of \(b\) cm of mercury and temperature of \(t^{\circ} \mathrm{C}\) becomes \(\delta g_{o}\) where \[\boxed{\delta=\text { air density factor }=\frac{3 \cdot 92 b}{273+t}}\]
Under standard conditions, the value of \(\delta=1\) \[\therefore \quad \text { Critical disruptive voltage, } \boxed{V_{c}=g_{o} \delta r \log _{e} \frac{d}{r}}\]
Correction must also be made for the surface condition of the conductor.
This is accounted for by multiplying the above expression by irregularity factor \(m_{o}\)

Critical disruptive voltage, \[V_{c}=m_{o} g_{o} \delta r \log _{e} \left(\dfrac{d}{r}\right)~ \mathrm{kV/phase}\] where \(m_{o}\) for

\[\begin{aligned} \text{polished conductors} & = 1 \\ \text{dirty conductors} & = 0.98-0.92\\ \text{stranded conductors} & = 0.87- 0.8 \end{aligned}\]

It is the minimum phase-neutral voltage at which corona glow appears all along the line conductors.
It has been seen that in case of parallel conductors, the corona glow does not begin at the disruptive voltage \(V_{c}\) but at a higher voltage \(V_{v}\) called visual voltage.
The phase-neutral effective value of visual critical voltage is given by the following empirical formula:

\[\boxed{V_{v}=m_{v} g_{o} \delta r\left(1+\frac{0 \cdot 3}{\sqrt{\delta r}}\right) \log _{e} \frac{d}{r}}~ \mathrm{kV} / \text { phase }\]

where \(m_{v}\) is another irregularity factor having a value of 1.0 for polished conductors and \(0\cdot 72\) to \(0\cdot 82\) for rough conductors.