Download Inception Voltage of Corona Discharge from Suspended, Grounded

Abdel-Salam et al.
1
Inception Voltage of Corona Discharge from Suspended, Grounded and
Stressed Particles in Uniform-Field Gas-Insulated-Gaps at Varying Pressures
M. Abdel-Salam1, A. Ahmed2, and A. Nasr EL-deen2
1
Electrical Engineering Department, Assiut University, Egypt
2
Upper Egypt Electricity Production Company, Egypt
Abstract—In this paper, a criterion is developed for computing the inception voltage of negative corona from a
particle irrespective of its position in a uniform field gap between two parallel plates. The gap is positioned in air or SF6 at
varying pressure. The particle takes different positions in the gap; in touch with the stressed plate, suspended in the gap,
and near to the ground plate. The criterion is a formulation of the condition necessary for the recurrence of electron
avalanches growing in the vicinity of the particle. This calls for a method to be proposed based on the charge simulation
technique for evaluating the electric field in the vicinity of spherical and wire particles where avalanches grow. An
experimental step-up has been built up to measure corona inception voltage in air. The computed inception voltage values
agreed reasonably with those measured experimentally in air and SF6 for spherical and wire particles, irrespective of their
positions in the gap. The increase of the computed inception voltage with the increase of gas pressure agreed reasonably
with that obtained experimentally.
Keywords—Corona discharge, inception voltage, electron avalanche, gas-insulated gaps, gas pressure, spherical
particles, wire particles
I. INTRODUCTION
The development of gas-insulated systems (GIS) has
made rapid progress in the last few years. Practically,
GIS is normally operated at pressures above 1atm and the
breakdown phenomenon depends on gas pressure. Free
conducting particles could reduce drastically the
insulation strength in such systems. Intensive
experimental studies have been made to determine the
effects of particle size, shape and position in the gap on
the breakdown voltage [1]. A criterion was developed for
computing the discharge inception voltage in threeelectrode systems, i.e. inception voltage from free
particles existing in a uniform field gap [2]. The particles
pick up a potential depending on its position within the
electrode spacing.
A conducting particle situated on an electrode in a
uniform field gap acquires a charge which is a function
of the applied electric field and the size, shape and
orientation of the particle. When the electrostatic force
on the particle exceeds the gravitational force, the
particle will lift [3]. Once the particle is lifted, the
attraction force on the particle due to the image charge
further promotes the lifting effect.
It is well known that free conducting particles in gas
insulated power apparatus can cause a serious reduction
of the insulations strength. In practical systems, it is very
difficult to avoid metallic particle contamination due to
imperfection in fabrication and maintenance, mechanical
abrasions, deterioration of spacers, movement of
conductors under load cycling and vibrations during
shipment. Such particles are known to reduce drastically
the corona inception and breakdown voltages as a result
Corresponding author: Mazen Abdel-Salam
e-mail address: [email protected]
Received; September 16, 2009
of their movement in the electric field [4]. In a uniform
field gap, an infinite mathematical series was proposed
[4] to express the ratio of the electric field value at the
particle surface to that of the uniform field.
Experiments under particle conditions in SF6
revealed that the breakdown voltage was decreased due
to mutual interference of corona discharges from both
particle tips. However, the reduction in breakdown
voltage by the particle was small compared with that one
in the air gap [5]. Particle-triggered corona phenomena in
SF6 gas due to its electro negativity are complicated and
the influence of mutual interference of corona from both
tips of particle on the corona activity is small as
compared to those in air gap.
This paper presents a mathematical modeling of the
inception voltage of corona discharge from a particle in
uniform field gaps between two parallel plates. The
inception voltage in air and SF6 is obtained by
formulating the conditions necessary for the discharge to
be self sustained. The model takes into account all the
individual processes and events, e.g. gas ionization,
attachment, photo-ionization, etc, thought to be effective
in the discharge process. As these events are field
dependent, the accurate charge simulation technique [6]
and the method of images are used for field calculation.
The inception voltage is computed and measured in air in
the laboratory. The computed inception voltages agreed
well with those measured experimentally by the authors
in air and by others [5] in SF6 for spherical and wire
particles whose major axis extends along the gap axis.
First, the method of computing the applied field
between the two parallel plates and its distortion by the
particle is explained. Then, the mathematical modeling of
the discharge inception is presented. Finally, the results
obtained are discussed and compared with the
corresponding measured values.
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International Journal of Plasma Environmental Science & Technology, Vol.4, No.1, MARCH 2010
Z
ZZ
r(j)
r(j)
Negatively stressed plate
Negatively stressed plate
(rp (j), zp(j) )
Θ(j)
(j)
z(j)
HH
HH
L
Conducting particle
hp
S
2r
Conducting particle
R
Ground plate
(rp (j), zp(j) )
2r
z(j)
R
S
Ground plate
(a) Spherical particle
(b) Wire particle
Fig. 1. Simulation charges for the stressed plate and the particle.
Simulation ring charges,
Boundary points
II. ELECTRIC FIELD CALCULATION
A.1 Electric Potential
Fig. 1 shows a two parallel plate electrode system
with free spherical and wire conducting particles located
in the gap between the plates. The gap spacing is H. The
spherical particle has radius r and spaced S from the
ground plate. Therefore, the particle height hp above the
ground plate is equal to S + r, Fig. 1-a. The wire particle
has radius r and length L and spaced S from the ground
plate, Fig. 1-b. The particle picks up a potential VP
depending on the applied voltage V and the particle
position with respect to the stressed plate.
A. Charge Simulation Technique
The charge simulation method [6] is used to compute
the potential and the electric field in the space
surrounding the particle between the two parallel plates.
The simulation charges are rings for the stressed plate
and the particle. Image charges with respect to the
ground plate are considered. This ensures that the ground
plate is kept at zero potential.
The stressed plate is simulated by a set of N1 ring
charges. Each ring has a coordinate z (j) related to its
radius r (j) as expressed by equation (1):
z (j) = H + r (j) j = 1, 2, … , Nl
(1)
The value of the r (j) extends along the radial direction at
gradually increasing displacements as shown in Fig. 1.
Either the spherical or wire particle is simulated by a
set of N2 ring charges inside the particle. The radius r (j)
of the ring charges is chosen equal to a fraction  from
the particle radius at the same z level. The rings are
uniformly distributed along the particle height as shown
in Fig 1.
The potential at any point G (r, z) is the algebraic
sum of the potential due the unknown simulation charges
and their images;
VG (r , z ) 
N1  N 2
 Q( j )  P( j )
(2)
j 1
where,
P (j) is the potential coefficient of the јth ring
charge [6]
K (k 2 ) 
1
2  K (k1 )
 

Pj 
4     1
 2 
where,
1  ( r  r j ) 2  ( z  z j ) 2
 2  ( r  rj ) 2  ( z  z j ) 2
k1 
2  rj  r
1
k2 
2  rj  r
2
and K (k) is the complete elliptic integral of the first kind.
A.2 Boundary conditions
The first boundary condition is that the potential at
any boundary point (rp, zp) on the stressed plate electrode
–being of equipotential surface- must be equal to the
known applied negative voltage Va, i.e.
V (rp , zp ) = Va
(3)
The second boundary condition is that the potential at
any boundary point (rp, zp) on the particle -being of
equipotential surface- is equal to the unknown potential
VP picked up by the particle, i.e.
V (rp , zp ) = Vp
(4)
Abdel-Salam et al.
3
The potential at any point on the ground plate
electrode is zero and is automatically satisfied by
considering the image charges which are symmetrical
located with respect to that plate.
For floating particles between the gap plates, the sum
of the charges simulating the particle must be equal to
zero, i.e.
N N
(5)
Q( j )  0
1

the stressed plate. The check points were located mid
way between the boundary points. The deviation of the
computed potential at these check points from the applied
voltage is a measure of the accuracy of proposed
simulation method. The rms value of the potential
deviation ∆V averaged over the stressed plate should not
exceed a prescribed value; ± 0.01 % in the present work.
2
j N 1 1
A.3 Boundary points
(1) To satisfy the boundary conditions (3) and (4),
boundary points are chosen on both the stressed plate
electrode and the particle. Corresponding to each
simulation charge of stressed plate, a boundary point is
chosen at the same r-coordinate of the ring as shown in
Fig. 1. The z-coordinate of the boundary points z (j), j =
1,2,3,……,N1 is equal to the gap spacing H.
(2) On the spherical particle surface, the angle  (j),
Fig. 1, defines the coordinates rp (j) and zp (j) of the jth
boundary point, j = N1+1, N1+2,…, N1+N2 as given by
Subsequently, the coordinates of the boundary points are
expressed as:
(6)
On the wire particle surface, the coordinates rp (j) and zp
(j) of the jth boundary points, j = N1+1, N1+2,…, N1+N2
are expressed as:
rp (j) = r
zp (j) = S + [L/(N2+1)] · (j − N1)
With the knowledge of the unknowns, the potential
VP picked up by the particle - being an unknown - is now
defined and the components Er and Ez of the electric field
in the vicinity of the particle are computed using the
following expressions [5].
N1N2
Q
rj2r2 zzj 2  E K1  12  K K1 rj2r2 zzj 2  EK2  22  K K2 
Er  4j  1r 


2
2
1  1
2  2
j1


E
z
1 
 (j) = (j − N1)  / (N2+1)
rp (j) = r sin (j)
zp (j) = (S + r) − r cos (j)
B. Electric field
(7)
The number of boundary points is equal to the number of
the unknown ring charges (i.e. N1+N2). However, the
total number of unknown is (N1+N2+1), as the potential
VP picked up by the particle is also an unknown. If the
particle is not floating, the number of the unknowns is
(N1+N2).
A.4 Determination of the unknowns
Equation (2) for the potential written at each
boundary point defined above using the conditions (3)
and (4) plus the supplementary condition (5) (for floating
particle) form a set of linear algebraic equations whose
number equals N1+N2+1, i.e. the number of unknowns.
The values of these unknowns are determined by solving
simultaneously these equations using the Gauss
eliminations method [7].
A.5 Accuracy of solution and check points
To check the accuracy of the obtained simulation
charges, check points have been chosen of the surface of

N 1N 2

j 1
Q j
4

2

  z  z j   E  K 1   z  z j   E  K 2   (8)



2
2
2  2
 1  1

 r  rj   z  z j 
2
2
, 2 
r  rj   z  z j 
2
2
(9)
III. CALICULATION OF CORONA INCEPTION VOLTAGE
A. Criterion
When the electric field strength at the particle
surface reaches the threshold value for ionization by
electron collision, an electron avalanche starts to develop
along the direction away from the particle as shown in
Fig. 2. With the growth of the avalanche within the
ionization zone of thickness ri, more electrons are
developed at its head, more photons are emitted in all
directions and more positive ions are left in the avalanche
wake.
The number of electrons Ne (z) at a distance z from
the starting point (z = 0) is given by:
z

N e ( z )  exp    ( z )   ( z )  dz 
0

(10)
The ionization and attachment coefficients depend
on the electric field [8]. The electric field E is the
resultant of the space-charge-free field due to the applied
voltage V and the space charge field of the avalanche
itself.
For a successor avalanche to be started, the
preceding avalanche should somehow provide an
initiating electron at the particle surface, possibly by
photoemission, positive-ion impact, metastable action, or
field emission, Fig. 2. Field emission is possible only at
field strengths exceeding 5 × 107 V/m [9]. Electron
emission by positive-ion impact is more than two orders
of magnitude less probable than photoemission [9].
Metastables have been reported to have an effect
approximately equal to that of positive-ion impact [8].
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International Journal of Plasma Environmental Science & Technology, Vol.4, No.1, MARCH 2010
Fig. 2. (a) Development of an avalanche in the vicinity of a spherical particle in touch with the stressed plate.
(b) Development of an avalanche in the vicinity of a spherical particle suspended between the two parallel plates.
(c) Development of an avalanche in the vicinity of a wire particle suspended between the two parallel plates.
Therefore, only the first mechanism (electron emission
by photons) was considered in determining the inception
voltage V0 [10].
The number of electrons photo-emitted from the
particle surface is
ri
Ne( ph)   ph   ( z )Ne ( z ) g ( z ) exp(  z )dz
(11)
close to the ground plate, suspended or in touch with the
stressed plate. This calls for accurate determination of the
different discharge parameters in air and SF6 in terms of
the electric field [12, 13]. Appendix I reports the
equations defining the discharge parameters in air and
SF6.
0
where ri, the ionization-zone thickness, is the limiting
value of z at which  = . ph is Townsend’s second
coefficient due to the action of photons. g (z) is a
geometry factor to account for the fact that some photons
are not received by the particle [11].
The condition for a new (successor) avalanche to
develop is
Ne (ph) ≥ 1
(12)
The inception voltage does not appear explicitly in the
relation (12). However, the applied voltage affects the
values of  (z),  (z),  and hence, Ne (z). The inception
voltage V0 is the critical value which fulfills the equality
(12).
B. Numerical Data
The inception voltage of corona in air and SF6 from
the spherical and wire particles positioned between the
two parallel plates is computed wherever the particle is
IV. EXPERIMNTAL SETUP AND TECHNIQUE
A. Setup
Two brass disc electrodes of 50 mm diameter and 18
mm thickness forming a parallel-plate electrode system
were installed inside a pressure vessel to vary the gap
spacing over the range 10-20 mm. The edges of the
electrodes were rounded to avoid edge flashover, Fig. 3.
The vessel is designed to withstand air pressures up to 5
atmospheres.
Two shapes of particles, spherical and wire particles,
were tested in the pressure vessel. The spherical particles
were made of silver with radii 1.175 and 1.825 mm. The
wire particles were cut from a copper wire of radius
(0.125 mm) with length 4 and 6mm. The particles were
positioned between the two brass electrodes by a thin
plastic rope (radius = 0.05 mm) extending parallel to
electrodes as shown in Fig. 3.
A negative high D.C voltage, obtained from a halfwave rectifier circuit, was applied to the upper electrode
through a limiting resistance to prevent any damage of
Abdel-Salam et al.
5
Fig. 3. (a) Parallel plate electrode system for observing the corona discharge occurring from a spherical particle.
(b) Parallel plate electrode system for observing the corona discharge occurring from a wire particle.
(c) A particle suspended between the two parallel plates by a plastic rope.
the instruments when flashover occurs between the
electrodes. The lower electrode was grounded through a
sensitive micro ammeter for measuring the corona
inception voltage in air at varying pressure.
B. Electric field
The inception voltage is the applied voltage when the
micro ammeter starts to record a reading. The inception
voltage in air was measured for spherical and wire
particles with different dimensions when they were near
to the ground plate, suspended in the gap and in touch
with the stressed plate.
V. RESULTS AND DISCUSSION
A. Accuracy of proposed charge simulation technique
For a unit applied voltage, Fig. 4 shows the
computed potential with respect to the applied value
along the surface of the stressed plate –being an
equipotential- for spherical (r = 0.5 mm, S = 10-3 mm, H
= 15 mm) and wire (r = 0.125 mm, L = 4 mm, S = 10-3
mm, H = 15 mm) particles positioned in the gap. The
simulation charges of the stressed plate N1 and the
particle N2 were 115, 90 for spherical particle and 201,
150 for wire particle. The potential-deviation of the
computed potential from the applied voltage value along
the stressed plate did not exceed 0.4 %, which confirms
the accuracy of the proposed simulation of surface
charges on the stressed plate and the particle.
The integral of the computed electric field along the
gap axis excluding the space occupied by the particle (=
diameter 2r for spherical particle and length L for wire
particle) is equal to the applied voltage with a deviation
less than 2 %. This is another measure of the accuracy of
the proposed charge simulation technique.
B. Normalized particle-surface electric field Emax/E0
In the absence of the particle, the electric field
between the plates is uniform and equal to E0. With the
presence of the particle, the field is distorted in the
vicinity of the particle with a value Emax at the particle
surface. It is worthy to mention that the field pattern
around the particle depends on the particle position in the
gap; in touch with the stressed plate or suspended in the
gap or near to the ground plate.
The present computed values of the normalized
surface electric field Emax/E0 for a spherical particle at
variable spacing S from the ground plate, agreed
reasonably with those reported before [4, 14] with a
deviation not exceeding 0.001 %, Fig. 5. The normalized
field Emax/E0 decreases with the increase of the ratio S/r,
Fig. 5.
Fig. 6 shows that the normalized surface electric
field Emax/E0 for a spherical particle depends only on the
ratio of S/r irrespective of the value of particle radius r in
International Journal of Plasma Environmental Science & Technology, Vol.4, No.1, MARCH 2010
Normalized surface field, Emax/Eo
6
Fig. 4. Computed potential versus distance measured from the gap
axis along the stressed plate compared with the unit applied voltage
for spherical (r = 0.5 mm, S = 10-3 mm, H = 15 mm) and wire (L =
4 mm, r = 0.125 mm, S = 10-3 mm, H = 15 mm) particles.
Fig. 6. Normalized surface electric field Emax/E0 as a function of the
ratio S/r for a different spherical particle of radius r = 0.5, 1, 1.5 mm,
H = 15 mm.
Fig. 7. Normalized surface electric field Emax/E0 as a function of the
distance S for a spherical particle of radius r = 0.5 mm, H = 15 mm.
Fig. 5. Normalized surface electric field Emax/E0 as a function of the
ratio S/r for a spherical particle of radius r = 0.5 mm, H = 15 mm.
conformity to previous findings [4].
Fig. 7 shows the normalized surface electric field
Emax/E0 for a spherical particle of radius r = 0.5 mm
positioned in a gap with spacing H = 15 mm. The surface
electric field Emax is more than four times that of the
uniform-field value E0 when the particle is very near to
the ground plate, three times E0 for suspended particle
close to the middle of the gap and 3.4 times E0 when the
particle touches the stressed plate. All these values are
close to those obtained before [2, 4].
Fig. 8 shows the normalized surface electric field
Emax/E0 for a wire particle of length L = 4 mm, radius
0.125 mm positioned vertically in a gap with spacing H =
15 mm. The electric field value is more than 7.2 times
that of the uniform-field value E0 when the particle is
very near to the ground plate, 6.3 times E0 value for
suspended particle close to the middle of the gap and 6.8
times E0 value when the particle touches the stressed
plate.
Fig. 8. Normalized surface electric field Emax/E0 as a function of the
distance S for a wire particle of radius r = 0.5 mm, H = 15 mm.
C. Normalized electric field E/E0 in particle vicinity
Fig. 9 shows the normalized electric field E/E0 along
the gap axis for a spherical particle of radius r = 0.5 mm,
positioned in a gap with spacing H = 15 mm. When the
Abdel-Salam et al.
7
Fig. 9. (a) Normalized electric field along the gap axis for a spherical particle near the ground plate (r = 0.5 mm, H = 15 mm).
(b) Normalized electric field along the gap axis for a spherical particle near the ground plate and in touch with the stressed plate (r = 0.5 mm, H
=15 mm).
Fig. 10. (a) Normalized electric field along the gap axis for a wire particle near the ground plate (L = 4 mm, r = 0.125 mm, H = 15 mm).
(b) Normalized electric field along the gap axis for a wire particle near the ground plate and in touch with stressed plate (L = 4 mm, r =
0.125 mm, H = 15 mm).
particle is positioned near the ground plate, the surface
electric field value is more than 3 and 5.5 times that of
the uniform field value. The normalized field E/E0
decreases from its surface value and approaches the
uniform-field value toward the negatively stressed plate.
Fig. 10 shows the normalized electric field E/E0
along the gap axis in the vicinity of a wire particle
(length L = 4 mm, radius r = 0.125 mm) positioned in a
gap with spacing H = 15 mm. When the particle is
positioned near the ground plate, the surface electric field
value is more than 6 and 9.3 times that of the uniform
field value. The normalized field E/E0 decreases from its
surface value and approaches the uniform-field value, the
same as the case for spherical particle, Fig. 9.
D. Particle pick-up voltage
Fig. 11 shows the calculated space potential Vp
picked-up by a spherical particle of radius 0.5 mm
positioned in a gap of spacing H = 15 mm and unit
applied voltage. When the particle moves along the gap
axis, the space potential picked-up by the particle
increases almost linearly as the particle approaches the
stressed plate.
Fig. 12 shows the calculated space potential Vp
picked-up by a wire particle (length L = 4 mm, radius r =
0.125 mm) positioned in a gap of spacing H = 15 mm
and unit applied voltage. When the particle moves along
the gap axis, the space potential picked-up by the particle
increases almost linearly as the particle approaches the
stressed plate, the same as the case for spherical particle,
Fig. 11.
E. Experimental validation of results
E.1
Inception voltage for spherical particles at
atmospheric pressure
Tables I and II give the computed and measured
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International Journal of Plasma Environmental Science & Technology, Vol.4, No.1, MARCH 2010
TABLE I
COMPUTED AND MEASURED INCEPTION VOLTAGES OF CORONA
FROM A SPHERICAL PARTICLE OF RADIUS r ＝ 1.175 MM
POSITIONED IN ATMOSPHERIC AIR BETWEEN PLATES SPACED H
＝ 10 MM.
Position of
Computed V0
Measured V0
Deviation (%)
particle
[kV]
[kV]
Near to
ground
plate
16.6
17.6
6
(S = 10-3
mm
spacing)
Fig. 11. Potential picked-up by a spherical particle versus the
distance S (r = 0.5 mm, H = 15 mm) for a unit applied voltage.
suspended
(at the
middle of
gap)
23.1
22.7
1.7
In touch
with
stressed
plate
17.94
18.6
3.6
TABLE II
COMPUTED AND MEASURED INCEPTION VOLTAGES OF CORONA
FROM A SPHERICAL PARTICLE OF RADIUS r ＝ 1.825 MM
POSITIONED IN ATMOSPHERIC AIR BETWEEN PLATES SPACED H
＝ 10 MM.
Position of
Computed V0
Measured V0
Deviation (%)
particle
[kV]
[kV]
Near to
ground
plate
14.75
15.1
2.3
(S = 10-3
mm
spacing)
Normalized electric field, E/Eo
Fig. 12. Potential picked-up by a spherical particle versus the
distance S (L = 4 mm, r = 0.125 mm, H = 15 mm) for a unit applied
voltage.
Fig. 13. Normalized electric field along the gap axis for a spherical
particle near the ground plate of radii r = 1.175, 1.825 mm, H = 15
mm.
corona inception voltages V0 for spherical particles of
radii 1.175 and 1.825 mm positioned in atmospheric air
between the two parallel plate electrodes with spacing H
= 10 mm. It is satisfactory that the computed inception
voltages agreed reasonably with those measured
experimentally with a deviation not exceeding 8.5 %.
suspended
(at the
middle of
gap)
20.4
21.45
5.1
In touch
with
stressed
plate
16.45
17.85
8.5
TABLE III
COMPUTED INCEPTION VOLTAGES OF CORONA FROM A
SPHERICAL PARTICLE POSITIONED IN SF6 AT 1 ATM BETWEEN
PLATES SPACED H ＝ 10 MM.
Position of
V0 [kV]
V0 [kV]
particle
at r = 1.175 mm
at r = 1.825 mm
Near to
ground
plate
32.9
30.75
(S = 10-3
mm
spacing)
suspended
(at the
middle of
gap)
42.1
38.8
In touch
with
stressed
plate
35.8
32.6
Tables I and II show that the inception voltage of
corona from suspended particles is the highest where the
electric field at particle surface is the lowest as depicted
in Fig. 9. Not only the surface field but also the field in
Abdel-Salam et al.
9
TABLE IV
COMPUTED AND MEASURED INCEPTION VOLTAGES OF CORONA FROM A WIRE PARTICLE (L = 4 MM, r = 0.125 MM) POSITIONED IN
ATMOSPHERIC AIR BETWEEN PLATES SPACED H ＝15 MM AND H = 20 MM.
gap spacing H = 15 mm
gap spacing H = 20 mm
Measured V0
Computed V0
Measured V0
Computed V0
Deviation (%)
Deviation (%)
Position of particle
[kV]
[kV]
[kV]
[kV]
Near to ground plate
16.100
17.248
7
17.65
19.10
8
(S = 10-3 mm spacing)
suspended
(at the middle of gap)
18.800
21.000
11.7
24.06
25.760
7
In touch with stressed plate
16.400
18.100
10.3
18.00
20.00
11
TABLE V
COMPUTED AND MEASURED INCEPTION VOLTAGES OF CORONA FROM A WIRE PARTICLE (L = 6 MM, r = 0.125 MM) POSITIONED IN
ATMOSPHERIC AIR BETWEEN PLATES SPACED H ＝15 MM AND H = 20 MM.
gap spacing H = 15 mm
gap spacing H = 20 mm
Computed V0
Measured V0
Computed V0
Measured V0
Position of particle
Deviation (%)
Deviation (%)
[kV]
[kV]
[kV]
[kV]
Near to ground plate
12.810
13.400
4.6
17.00
15.50
8.8
(S = 10-3 mm spacing)
suspended
(at the middle of gap)
15.10
14.500
3.9
20.225
20.00
1.1
In touch with stressed plate
13.210
14.00
5
17.810
16.20
9
TABLE VI
COMPUTED INCEPTION VOLTAGES OF CORONA FROM A WIRE PARTICLE (L = 4, 6 MM, r = 0.125 MM) POSITIONED IN SF6 AT 1 ATM
BETWEEN PLATES SPACED H ＝15 MM AND H = 20 MM.
gap spacing H = 15 mm
Position of particle
gap spacing H = 20 mm
V0 [kV] at L = 4 mm
V0 [kV] at L = 6 mm
V0 [kV] at L = 6 mm
V0 [kV] at L = 6 mm
Near to ground plate
(S = 10-3 mm spacing)
12.81
13.4
4.6
17
Suspended
(at the middle of gap)
15.1
14.5
3.9
20.225
In touch with stressed plate
13.21
14
5
17.81
the vicinity of the suspended particle is also the lowest
when compared with the other positions of the particle in
the gap.
On the other hand, the inception voltage for the
particle in touch with the stressed plate is higher than that
of the particle near to the ground plate, Tables I and II.
This is because the electric field is not symmetrical along
the gap axis, i.e., the field values near the stressed plate
are different from those near the ground plate. Therefore,
the electric field at particle surface and in its vicinity is
lower for the particle in touch with the stressed plate as
compared with that for the particle near the ground
electrode, Fig. 9-b.
For the tested spherical particles, the inception
voltage was close to the pre-breakdown voltage in
agreement with previous findings [15].
Table III gives the computed corona inception
voltages V0 for spherical particles of radii 1.175 and
1.825 mm positioned in SF6 gas between the two parallel
plate electrodes with spacing H = 10 mm. The table gives
that the inception voltage of corona in SF6 from
suspended particles is the highest in agreement with
Tables I and II for air. On the other hand, the inception
voltage for the particle in touch with the stressed plate is
higher than that of the particle near to the ground plate,
Table III, the same as in air as depicted in Tables I and II.
Of course, all the inception voltages values in SF6 (Table
III) are higher than those in air (Tables I and II) because
of the high electron affinity of SF6 compared to air.
The inception voltage values in air and SF6 for the
spherical particle with radius r = 1.825 mm are smaller
than those for the particle with radius r = 1.175 mm
irrespective of the position of the particle in the gap with
spacing H. This is simply attributed to smaller net gap
spacing (H − 2r) between the gap plates and
subsequently higher electric field values for the particle
with r = 1.825 mm when compared with the other
particle. It is quite clear that the larger the radius of the
sphere, the lower is the electric field at sphere surface at
constant gap sacing for the same applied voltage. In Fig.
13, the net gap spacing (H − 2r) is different as r is
changing from 1.175 to 1.825 mm. It worthy to mention
that the field values in the spacing between particle and
ground plate for r = 1.825 mm are higher than for r =
International Journal of Plasma Environmental Science & Technology, Vol.4, No.1, MARCH 2010
E.2 Inception voltage for wire particles at atmospheric
pressure
Tables IV and V give the computed and measured
corona inception voltages V0 for wire particles (r = 0.125
mm, L = 4 mm and 6 mm) positioned in atmospheric air
between the two parallel plate electrodes with spacing H
= 15 and 20 mm. It is satisfactory that the computed
inception voltages agreed reasonably with those
measured experimentally, with a deviation not exceeding
11.7 %.
Tables IV and V indicate that the inception voltage
of corona from suspended particles is the highest where
the electric field at particle surface is the lowest as
depicted in Fig. 10. Also, the inception voltage when the
particle in touch with the stressed plate is higher than that
of the particle near the ground plate, Tables III and IV.
This is because the electric field at particle surface and in
its vicinity is lower for the particle in touch with the
stressed plate as compared with that for the particle near
to the ground plate, Fig. 10-b, the same as for spherical
particles, Tables I and II.
Table VI gives the computed corona inception
voltages V0 for wire particles (r = 0.125 mm, L = 4 mm
and 6 mm) positioned in SF6 gas between the two parallel
electrodes with spacing H = 15 and 20 mm. The table
gives that the inception voltage of corona from
suspended particles is the highest in agreement with
tables IV and V for air. On the other hand, the inception
voltage for the particle in touch with the stressed plate is
higher than that of the particle near to the ground plate,
Table VI, the same as in air as depicted in tables IV and
V. A gain, the inception voltage values in SF6 (table VI)
are higher than those in air (Tables IV and V).
The inception voltage values in air and SF6 for wire
particle with length L = 6 mm are smaller than those for
the particle with length L = 4 mm irrespective of the
position of the particle in the gap with spacing H. This is
simply attributed to smaller gas spacing (H − L) between
the gap plates, and subsequently higher electric field
values for the particle with L = 6 mm when compared
with the other particle.
The inception voltage values in air and SF6 for the
same wire particle at gap spacing H = 20 mm are higher
than those for gap spacing H = 15 mm irrespective of the
position of the particle in the gap. This is simply
attributed to the increase the gas spacing (H − L) between
the gap plates with a subsequent decrease of electric field
in the vicinity of the particle.
(a) 70
65
cal. (near to ground plate)
60
exp. (near to ground plate).
cal. (suspended in gap)
55
exp.(suspended in gap)
50
Inception voltage [V]
1.175 mm. This is true in order to achieve that the
integral of the electric field along the net gap spacing is
constant and equal to the unit applied voltage. A smaller
gas spacing corresponds to a lower pre-breakdown
voltage or inception voltage.
45
40
35
30
25
20
15
10
5
0
0
1
2
(b) 70
3
Air pressure [atm]
4
5
6
cal.(in touch w ith stressed plate)
exp.(in touch w ith stressed plate)
65
60
55
50
Inception voltage [V]
10
45
40
35
30
25
20
15
10
5
0
0
1
2
3
Air pressure [atm]
4
5
6
Fig. 14. (a) Corona inception voltage V0 versus pressure for a wire
particle (L = 6 mm, r = 0.125 mm) suspended, near to the ground
plate at gap spacing H = 20 mm.
(b) Corona inception voltage V0 versus pressure for a wire
particle (L = 6 mm, r = 0.125 mm) in touch with the stressed plate at
gap spacing H = 20 mm. : Experimental scatter of V0.
E.3 Inception voltage as influenced by air pressure
The effect of pressure on the corona inception
voltage from a wire particle (r = 0.125 mm and L = 6
mm) is studied by increasing the air pressure inside the
vessel using a compressor.
Fig. 14 shows the increase of the computed and
measured inception voltages with the increase the
pressure when the particle is in touch with the stressed
plate, suspended at the middle of the gap and near to the
ground plate. It is satisfactory that the computed values
agreed reasonably with those measured experimentally
with a deviation less than 11.7 %.
E.4 Inception voltage as influenced by SF6 pressure
The corona inception voltage in SF6 from a wire
particle (r = 0.5 mm and L = 10 mm) is also computed at
varying gas pressure.
Fig. 15 shows the increase of the computed inception
voltages with the increase the SF6 pressure when the
particle is near to the ground plate. It is satisfactory that
the computed values agreed reasonably with those
measured experimentally [5] with a deviation less than
9.33 %.
Abdel-Salam et al.
11
inception voltages with the increase of particle length L
positioned in SF6 at varying pressure when the particle
near to the ground plate. This is simply attributed to the
increase of the electric field in the vicinity of the particle
because of the decrease of gas spacing (H − L), where H
is the gap spacing.
60
computed
Exp. finding
inception voltage [kV]
50
40
30
E.6 Inception voltage as influenced by radius of a
particle positioned in SF6 at varying pressure
20
10
0
30
35
40
45
SF6 pressure [kPa]
50
Fig. 15. Inception voltage versus pressure of SF6 gas for the particle
length 10 mm, r = 0.5 mm near to the ground plate with gap spacing
H = 40 mm between two parallel plate. : Experimental scatter of
V0.
60
Inception v oltage at P=30 kPa
Inception v oltage at P=40 kPa
Inception v oltage at P=50 kPa
The effect of particle radius on the corona inception
voltage from a wire particle (length L = 10 mm) is
computed at varying SF6 pressure.
Fig. 17 shows the increase of the computed inception
voltages with the increase of particle radius r positioned
in SF6 at varying pressure when the particle near to the
ground plate. This is simply attributed to the decrease of
the electric field in the vicinity of the particle with the
increase of its radius.
Inception voltage [kV]
50
VI. CONCLUSION
40
30
P=50 kPa
20
P=40 kPa
P=30 kPa
10
0
0
5
10
15
Particle length [mm]
20
25
Fig. 16. Inception voltage versus particle length, at constant r = 0.5
mm near to the ground plate with gap spacing H = 40 mm between
two parallel plate positioned in SF6 at varying pressure.
60
Inception voltage at P=30 kPa
55
Inception voltage at P=40 kPa
50
Inception voltage at P=50 kPa
Inception voltage [kV]
45
P=50 kPa
40
35
P=40 kPa
30
P=30 kPa
25
20
15
10
5
0
0
0.2
0.4
0.6
0.8
1
1.2
Particle radius [mm]
Fig. 17. Inception voltage versus particle radius, at constant L = 10
mm near to the ground plate with gap spacing H = 40 mm between
two parallel plate positioned in SF6 at varying pressure.
E.5 Inception voltage as influenced by length of a
particle positioned in SF6 at varying pressure
The effect of particle length on the corona inception
voltage from a wire particle (radius r = 0.5 mm) is
computed at varying SF6 pressure.
Fig. 16 shows the decrease of the computed
From the present analysis one can conclude the
following.
(1) A method is proposed based on the charge
simulation technique for evaluating the electric field in
the vicinity of spherical and wire particles positioned in a
uniform field gap (i) in touch with the stressed plate, (ii)
suspended in the gap, and (iii) near to the ground plate.
(2) A method is described for computing the
inception voltage of negative corona from the particle
irrespective of its position in the gap. The method is
based on a criterion for the recurrence of electric
avalanches growing in the vicinity of the particle. The
electron emission by photons was considered the
effective mechanism for triggering the successor
avalanches.
(3) Surface electric field changes from 6.3 to 7.2
times of uniform field for wire particles (of radius 0.125
mm with length 4 and 6mm) and changes from 3 to 4.2
times of uniform field for spherical particles (of radius
1.175 and 1.825 mm) in gaps with spacing in the rang
10-20 mm.
(4) The corona inception voltage was very close to
pre-breakdown voltage in agreement with previous
findings for spherical particles.
(5) The corona inception voltage is the highest for
suspended spherical and wire particles when compared
with their positions in touch with stressed plate and near
to the ground plate.
(6) The voltage picked-up by the suspended
spherical and wire particles increases almost linearly
with the distance of the particle from the ground plate.
(7) The computed inception voltage values agreed
reasonably (within 10 %) with those measured
experimentally for spherical and wire particles,
irrespective of their positions in the gap.
12
International Journal of Plasma Environmental Science & Technology, Vol.4, No.1, MARCH 2010
(8) The computed and measured inception voltage
values increase with the increase of gas pressure in the
vessel where the test gap is positioned either in air and
SF6.
APPENDIX: THE DISCHARGE PARAMETER IN AIR AND SF6
The ionization coefficient  in air [12].
/P = 4.7786 exp (-221 P/E) [V/cm torr] 25 ≤ E/P ≤ 60
/P = 9.682 exp (-2642 P/E) [V/cm torr] 60 ≤ E/P ≤ 240
And the attachment coefficient in air is
 (cm 1.torr )  0.01298  0.541x 3( E / P)  0.87 x 5( E / P) 2
10
10
P
The ionization coefficient  in SF6 [16].
 ( m 1.kPa 1 )  0.0242 * E / P  1323.31.
P
And the attachment coefficient in SF6 is
 (m 1.kPa 1 )  9.7594  0.541x10 3 * E / P  0.1157 x10 7 ( E / P) 2
P
The photon absorption coefficient in air and SF6:
 = 0P at P ≤ 1 atm
 = 0 at P > 1 atm (1 atm = 101.3 kPa)
Where 0 is the absorption coefficient at atmospheric
pressure, 0 = 500 m-1 for air and 0 = 600 m-1 for SF6.
The Townsend's second coefficient ph due to the action
of photons is constant at its value, 3 × 10-3 for air [17]
and 8 × 10-6 for SF6 [18].
REFERENCES
C. M. Cooke, R. E. Wootton, and A. H. Cookson, "Influence of
particles on AC and DC electrical performance of gas insulated
systems at extra-high-voltage," IEEE Transactions on Power
Apparatus and Systems, vol. 96, pp. 768-777, 1977.
[2] M. Abdel-Salam, "Discharge inception in high-voltage threeelectrode systems," Journal of Physics D: Applied Physics, vol.
20, pp. 629-634, 1987.
[3] M. Abdel-Salam, "On the Computation of Lifting Voltage for
Free Conducting Particles in Compressed SF6," presented at
IEEE PES winter meeting, Paper No. A-79-0035, 1979.
[4] H. Parekh, K. D. Srivastava, and R. G. van Heeswijk, "Lifting
Field of Free Conducting Particles in Compressed SF6 with
Dielectric Coated Electrodes," IEEE Transactions on Power
Apparatus and Systems, vol. PAS-98, pp. 748-758, 1979.
[5] Y. Negara, K. Yaji, J. Suehiro, N. Hayashi, and M. Hara, "DC
corona discharge from floating particle in low pressure SF6,"
IEEE Transactions on Dielectrics and Electrical Insulation, vol.
13, pp. 1208-1216, 2006.
[6] H. Singer, H. Steinbigler, and P. Weiss, "A Charge Simulation
Method for the Calculation of High Voltage Fields," IEEE
Transactions on Power Apparatus and Systems, vol. PAS-93, pp.
1660-1668, 1974.
[7] M. L. James, G. M. Simth, and J. C. Wolford, "Applied
Numerical Methods for Digital Computation" 3rd ed (New York:
Harper and Row), 1985.
[8] F E. Nasser, "Fundamentals of Gaseous Ionization and Plasma
Electronics," J. Wiley and Sons, N.Y., USA, 1971.
[9] L. B. Loeb, "Electrical Coronas: Their Basic Physical
Mechanisms," University of California Press, Berkeley, USA,
1965.
[10] M. Khalifa, M. Abdel-Salam and M. Abou-Seada, "Calculation of
Negative Corona Onset Voltage," IEEE PES paper # C-73-160-9,
1973.
[1]
[11] G. N. Alexandrov, "Physical Conditions for The formation of an
AC Corona Discharge," J. Tech. phys. (USSR), vol. 26, pp. 17691781, 1956.
[12] M. P. Sarma and W. Janischewskyj, "D.C. corona on smooth
conductors in air. Steady-state analysis of the ionisation layer," in
Proceedings of the Institution of Electrical Engineers, vol. 116,
pp. 161-166, 1969.
[13] M. Abdel-Salam and E. K. Stanek, "On the calculation of
breakdown voltages for uniform electric fields in compressed air
and SF6," IEEE Transactions on Industry Applications, vol. 24,
pp. 1025-1030, 1988.
[14] M. Hara and M. Akazaki, "A method for prediction of gaseous
discharge threshold voltage in the presence of a conducting
particle," Journal of Electrostatics, vol. 2, pp. 223-239, 1977.
[15] S. Berger, "Onset or breakdown voltage reduction by electrode
surface roughness in air and SF6," IEEE Transactions on Power
Apparatus and Systems, vol. 95, pp. 1073-1079, 1976.
[16] M. S. Bhalla and J. D. Craggs, "Measurement of Ionization and
Attachment Coefficients in Sulphur Hexafluoride in Uniform
Fields," Proceedings of the Physical Society, vol. 80, pp. 151160, 1962.
[17] L. B. Loeb, Electrical Coronas, Their Basic Physical Mechanism
Berkely, CA: Univ. of California Press, 1965.
[18] G. N. Alexandrov, "Development of discharges in certain gases in
homogeneous fields," in proc. IEE Gas Discharge Conf., pub. 90,
pp. 398-402, 1972.