Faculty of electrical and computer engineering
POWER SYSTEM I
EEng-3132
Corona
Compiled by: Biniyam Z.
1 4/9/2019
Chapter Six
Corona
Outline
Introduction
Corona phenomenon
Disruptive critical voltage
Visual critical voltage
Corona power loss
Factors affecting corona
Line design based on corona
Advantages and disadvantages of corona
Methods of reducing corona Effect
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INTRODUCTION
The use of high voltage is extremely important in order to meet the rapidly
increasing power demand
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 violet glow, hissing noise and production of ozone gas
in an overhead transmission line is known as corona
The corona characteristic of transmission lines having voltage level 220 kV
or above assumed greater importance
Investigations on the basis of experiments reveals that it is possible to
predict corona performance of transmission line under various operating
conditions
Corona has associated power loss, radio and TV interference and audible
noise
Corona influences the line losses and design of overhead transmission line
conductors, accessories, hardware and insulators, etc
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PHENOMENON OF CORONA
Air is not a perfect insulator and even under normal condition, the air
contains a number of free electrons and ions
Consider two large parallel conducting planes. When an electric gradient
is setup between them, the electrons and ions acquire motion by this
electric field and they maintain a very small current between the
conducting planes. This current is negligible, when the electric field
intensity is less than 30 kV/cm
But when the electric field intensity or potential gradient reaches the
critical value of about 30 kV/cm, the air in the immediate vicinity of
conductors no more remains a dielectric and at this intensity, the ions
attain high velocity and on striking another neutral molecule dislodge one
or more electrons from the neutral molecule. This produces a new
electron and a positive ion which in turn are accelerated and collide with
other air molecules to ionize them further
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Thus the number of charged particles goes on increasing rapidly.
If a uniform field intensity is assumed between the electrodes such
conditions are produced everywhere in the gap. As a result of this, the
saturation is reached. Therefore, the air becomes conducting, hence a
complete electric breakdown occurs and arc is established between the
two electrodes
When an alternating potential difference is applied across two
conductors whose spacing is large in comparison with the diameter, then
the air surrounding the conductor is subjected to electro-static stresses.
This stress or intensity is maximum at the surface of the conductor and
then decreases in reverse proportion to the distance from the center of
the conductor
If this potential difference is gradually increased, a point will be reached
when a faint luminous glow of violet color will make its appearance, and
at the same time a hissing noise will be heard. This phenomenon is called
corona and is accompanied by the formation of ozone, as indicated by
5 the characteristic odor of this gas. 4/9/2019
This luminous glow is due to the fact that the atmospheric air around the
conductor becomes conducting due to electrostatic stress.
If the potential difference is raised still further, the glow and the noise
will increase in intensity until eventually a spark-over will take place.
If the conductors are perfectly uniform and smooth, the glow will be
uniform along their length, otherwise the rough points of the conductor
will appear brighter
The effects of corona can be summarized as
It is accompanied by power loss
A luminous violet glow is observed around the conductor
This glow is much brighter over rough and dirty surfaces of the conductor
It produces a hissing noise
It produces ozone gas which can be readily detected by its characteristic
odour
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CRITICAL DISRUPTIVE VOLTAGE
The minimum phase-neutral voltage at which complete disruption of
air occurs and corona starts is called the disruptive critical voltage.
The potential gradient corresponding to this value of the voltage is
called disruptive critical voltage gradient
Consider a single phase transmission line of figure below. Let r be the
radius of each conductor and D the distance of separation such that
D>>r.
Since it is a single phase transmission line, let q be the charge per unit
length on one of the conductors and hence –q on the other.
If the operating voltage is V, the potential of conductor A with respect to
neutral plane N will beV/2 and that of B will be –V/2
Consider a point p at a distance x where we want to find the electric
field intensity, Bringing a unit positive charge at P.
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The field due to A will be repulsive and that
due to B will be attractive; thereby the
electric field intensity at p due to both the
line charges will be additive and it will be
q q 1 q 1
Ex + =
x D x
2 0 x 2 0 D x 2 0
The potential diffrence between the conductors
Dr D r q 1 1
V Ex dx dx
r r 2 0 x D x
q Dr
= ln x ln D x r
2 0
q Dr q Dr
= .2 ln ln (6.1)
2 0 r 0 r
Since r is very small as compared to D, D-r D
q D
V= ln (6.2)
8 0 r 4/9/2019
Now gradient at any point x from the center of the conductor A is given by
q 1 1
Ex
2 0 x D x
q D
= .
2 0 x D x
Substituting for q from the above equation,
oV
q
D
ln
r
V 1 D
Ex o . .
D 2 o x D x
ln
r
V D
= .
D x D x
2 ln
r
V 'D
= (6.3)
D
x D x ln
r
Here V ' is the line to neutral voltage of the system. In case of 3-phase system
VL
V'
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From the expression for the gradient it is clear that for a given
transmission system the gradient increases as x decreases i.e., the
gradient is maximum when x = r, the surface of the conductor, and this
value is given by
V 'D
g max Er Emax
D
r ( D r ) ln
r
V'
=
D
r ln
r
or
D
V ' rg max ln (6.4)
r
Critical disruptive voltage is defined as the voltage at which complete
disruptive of dielectric occurs.
This voltage corresponds to the gradient at the surface equal to the
breakdown strength of air
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This dielectric strength is normally denoted by g o and is equal to 30
kV/cm peak at NTP i.e, 250 C and 76 cm Hg
At any other temperature and pressure
g o' g o . (6.5)
Where is the air density correction factor and is given by
3.92b
(6.6)
273 t
Where b is the barometeric pressure in cm of Hg and t the temperature in oC
Therefore, the critical distruptive voltage is given by
D
V ' rg o ln kV (6.7)
r
In driving the above expression, an assumption is made that the
conductor is solid and the surface is smooth.
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The irregularities on the surface of such a conductor are increased further
because of the deposition of dust and dirty on its surface and the
breakdown voltage is further reduced
An average value for the ratio of breakdown voltage for such a conductor
and smooth conductor lies between 0.85 to unity and is denoted by mo
Suitable values of mo are given below
Polished wires 1.0
Roughened or weathered wires 0.98 to 0.93
Seven strand cable 0.87 to 0.83
Large cables with more then seven strands 0.90 approx.
The final expression for critical disruptive voltage after taking into account
the atmospheric conditions and the surface of the conductor is given by
D
V ' rgo mo ln kV (6.8)
r
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VISUAL CRITICAL VOLTAGE
Visual luminous glow of corona generally occurs at a voltage higher than
the disruptive critical voltage. Actual visual corona does not start at the
disruptive critical voltage
The voltage at which corona glow appears all along the line conductor is
called visual critical voltage
If Vv is the critical visual voltage, then
D
Vv g v r ln
r
for visual distruptive, the voltage gradient is
0.3
g v g o 1
r
Then
0.3 D
Vv rg o 1 ln r kV
r
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In case the irregularity factor is taken into account
0.3 D
Vv g o mv r 1 ln r kV
r
0.3 D
21.1mv r 1 ln r kV (r.m.s)
r
Wher r is the radius in cms. the irregularity factor mv has the following values
mv 1.0 for polished wires
= 0.98 to 0.93 for rough conductor exposed to atmospheric severity
= 0.72 for local corona on stranded conductors
Since the surface of the conductor is irregular, the corona does not start
simultaneously on the whole surface but it takes place at different points
of the conductor which are pointed and this is known as local corona.
For local corona mv = 0.72 and for decided corona or general corona mv =
0.82
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Example
Find the critical disruptive voltage and visual critical voltages for local and
general corona on a 3-phase overhead transmission line, consisting of three
stranded copper conductors spaced 2.5 m apart at the corners of an
equilateral triangle. Air temperature and pressure are 21°c and 73.6 cm
Hg respectively. The conductor diameter, irregularity factor and surface
factor are 10.4 mm, 0.85, 0.7 and 0.8 respectively.
Solution
The critical disruptive voltage is given by
D
Vd 21.1m r ln
r
3.92b 3.92 x73.6
where = 0.9813
273+t 273 21
250
Vd 21.1x0.85 x0.9813 x0.52 ln 56.5 kV
0.52
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or the critical disruptive line to line voltage 56.5 x 3 97.89 kV
The visual critical voltage is given by
0.3 D
Vv 21.1m r 1 ln r
r
Here m 0.7 for local corona
0.8 for decided corona or general corona
Now r 0.52 x0.9813 0.71433
D
Vv for local corona 21.1x0.7 x0.9813 x0.52 1 0.42 ln
r
10.7 x6.175
66.0725 kV
The line to line voltage will be 66.0725 x 3 114.44 kV
The visual critical voltage for general corona will be
0.8
114.44 x 130.78 kV
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0.7 4/9/2019
CORONA POWER LOSS
Formation of corona is always accompanied by energy loss which is
dissipated in the form of light, heat, sound and chemical action
The power dissipated in the transmission line due to corona discharge is
called corona loss.
Estimation of accurate corona loss is very difficult because of its extremely
variable nature.
It has been found that corona loss under fair weather conditions is very
small as compared to the losses found under foul weather conditions
According to F.W. Peek, the corona loss under fair weather conditions is
given by the formula:
f 25 r
Pc 244 x10 5 Vn V0
2
kW/km/phase
D
Where Pc corona power loss
f supply frequency (Hz)
air density factor
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Vn rms phase-voltage (Line to neutral voltage) in kV
V0 rms value of disruptive critical voltage per phase in kV
r radius of the conductor (meters)
D spacing (or equivalent spacing) between conductors (meters)
It is also to be noted that for a single phase line
1
Vn x line voltage
2
and for a three phase line
line voltage
Vn
3
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peek's formula for corona loss is valid when corona losses are predominant and
Vn Vn
the ratio is greater than 1.8. when 1.8, the following formula known as
Vo Vo
Peterson's formula, gives better results:
2
Vn
Pc 2.1 f x10 5 xF kW/phase/km
log D
10 r
Where Pc corona loss
f supply frequency
Vn rms phase voltage (line to neutral) in kV
r radius of conductor (meters)
D spacing (or equivalent spacing) between conductors (meters)
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The factor F is called the corona loss function. it varies with
Vn
the ration and is given below in tabular form:
V0
Vn 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Vo
F 0.012 0.018 0.05 0.08 0.30 1.0 3.5 6.0 8.0
FACTORS AFFECTING CORONA
The phenomenon of corona is affected by the physical state of the
atmosphere as well as by the condition of the line
The following are the factors upon which corona depends:
(i).Atmosphere
As corona is formed due to ionization of air surrounding the conductors,
therefore, it is affected by physical state of atmosphere.
In the stormy weather, the number of ions is more than normal as such
20 corona occurs at much less voltage as compared with fair weather 4/9/2019
(ii). 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
stress at the conductor surface, thus avoiding corona formation
(iii). 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
(iv). Conductor shape
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 irregular surface and hence gives rise to more
corona than a solid conductor
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(v). Frequency
Corona loss is directly proportional to system frequency
(vi). Dust and dirt
In the presence of dust and dirt, required voltage gradient is less for
maintaining sustained discharge.
Disruptive critical voltage is reduced due to dust and dirt and hence corona loss
is more
(vii). Conductor configuration
Conductors of three phase overhead transmission lines can be placed in either
horizontal or vertical configuration.
The electric field intensity at the surface of middle conductor is higher than the
outer conductors. Therefore, the disruptive critical voltage for middle conductor
will be less than the two other outer conductors and hence there will be more
corona loss in the middle conductor.
If conductors are placed equilaterally, the average electric field intensity at each
conductor will be same. Since the ground is an equipotential surface, the electric
field distribution is affected by the presence of earth.
Corona loss will be less, if conductors are placed at more height
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LINE DESIGN BASED ON CORONA
Transmission lines are designed in such a fashion that the corona loss is
small enough in fair weather condition because corona loss reduces the
efficiency of the lines.
If the disruptive critical voltage of about 10% more than the operating
voltage, then it is acceptable even though some corona loss will take
place under foul weather condition.
Generally, corona loss under foul weather condition will be 10 time
higher than the fair weather condition
An increased in Deq and r increase the disruptive critical voltage, thus
reduces the corona loss but increases the cost
A typical transmission line may have a fair weather loss of 1 kW per 3-
phase mile and foul weather loss of 20 kW per three phase mile
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Example 1:
Conductor of a three phase transmission line are equilaterally spaced 6m
apart. The radius of each conductor is 1cm. The air temperature is 30 °C
and pressure is 740 mm of Hg. If surface factor is 0.83 and irregularity
factor is 0.92, calculate the disruptive critical voltage and visual critical
voltage
Solution:
The air density factor,
0.392 P
273 t
0.392 x740
0.957
273 30
Distruptive critical voltage,
3 x106 Deq
Vo r mo ln volts
2 r
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Given that mo 0.92, 0.957, r 1cm 0.01m, Deq 6 m
3 x106 6
Vo x 0.01x 0.957 x 0.92 x ln volts
2 0.01
V0 119.475 kV (rms)
The visual critical voltage
3 x106 0.0301 Deq
VV mv r 1 ln r volts
2 r
3 x106 0.0301 6
VV 0.83x 0.01x 0.957 x 1 ln 0.01 volts
2 0.01x0.957
VV 140.95 kV (rms)
Exercise
1. Determine the corona characteristics of a three phase line 160 km long,
conductor diameter 1.036 cm, 2.44 m delta spacing, air temperature
26.67°C, altitude 2440 m, corresponding to an approximate barometric
pressure of 73.15 cm, operating voltage 110 kV at 50 Hz
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ADVANTAGES AND DISADVANTAGES OF CORONA
Corona has many advantages and disadvantages
In the correct design of a high voltage overhead line, a balance should be
struck between the advantages and disadvantages
Advantages
i. Due to corona formation, the air surrounding the conductor becomes
conducting and hence virtual diameter of the conductor increased. The
increases diameter reduces the electrostatic stresses between the
conductors
ii. Corona reduces the effects of transients produced by surges
Disadvantages
(i). Corona is accompanied by loss of energy. This effects the
transmission efficiency of the line
(ii). Ozone is produced by corona and may cause corrosion of the
conductor due to chemical action
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(iii). The current drawn by the line due to corona is non-sinusoidal and hence
non-sinusoidal voltage drop occurs in the line. This may cause inductive
interference with neighboring communication lines
METHODS OF REDUCING CORONA EFFECT
It has been seen that intense corona effects are observed at a working
voltage of 33 kV or above
Therefore, careful design should be made to avoid corona on the sub-
stations or bus-bars rated for 33 kV and higher voltages otherwise highly
ionized air may cause flash-over in the insulators or between the phases,
causing considerable damage to equipment. The corona effects can be
reduced by the following methods:
(i). By increasing conductor size
By increasing conductor size, the voltage at which corona occurs is raised
and hence effects are considerably reduced
This is one of the reasons that ACSR conductors which have a larger cross-
27
sectional area are used in transmission lines 4/9/2019
(ii). By increasing conductor spacing
By increasing the spacing between conductors, the voltage at which
corona occurs is raised and hence corona effects can be eliminated
However, spacing cannot be increased too much otherwise the cost of
supporting structure ( e.g., bigger cross arms and supports) may increase
to a considerable extent
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Q?
Thank you
Next
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