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 corona effects:
(i) Critical disruptive voltage
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:
g =[V/ r loge (d/r)] volts / 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 cm pressure and temperature of 25ºC is 30 kV/cm (max) or 21·2 kV/cm (r.m.s.) and is denoted by go. If Vc is the phase-neutral potential required under these conditions, then,
go =[Vc/ r loge (d/r)] volts / cm
where go = breakdown strength of air at 76 cm of mercury and 25ºC = 30 kV/cm (max) or 21·2 kV/cm (r.m.s.)
∴ Critical disruptive voltage, Vc = go r loge d/r
The above expression for disruptive voltage is under standard conditions i.e., at 76 cm of Hg and 25ºC. However, if these conditions vary, the air density also changes, thus altering the value of go.
The value of go is directly proportional to air density. Thus the breakdown strength of air at a barometric pressure of b cm of mercury and temperature of tºC becomes δ go where
δ = air density factor = 3.92b / 273 + t
Under standard conditions, the value of δ = 1.
∴ Critical disruptive voltage ,V c = go δ r loge 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 mo.
∴ Critical disruptive voltage, Vc = mo go δ r loge d/r …. kV/phase
mo = 1 for polished conductors
= 0·98 to 0·92 for dirty conductors
= 0·87 to 0·8 for stranded conductors
(ii) Visual critical voltage
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 Vc but at a higher voltage Vv , called visual critical voltage. The phase-neutral effective value of visual critical voltage is given by the following empirical formula :
is another irregularity factor having a value of 1·0 for polished conductors and 0·72 to 0·82 for rough conductors.
Reference and bibliography: Power System Analysis, By VK Mehata, AK Mehta.