Download The Influence of the inhomogenuity of the field, the Ground Effect

The Influence of the Inhomogeneity of the Field, the Effect of Grounding and the
Corona Current to the Dielectric Behaviour of Small Air Gaps
Athanasios Maglaras
Electrical Engineering Department
Technological Educational Institute of Larissa
T.E.I. of Larissa
Larissa, 41110, Greece
Frangiskos V. Topalis
School of Electrical and Computer Engineering
National Technical University of Athens
Iroon Politechniou 9, Athens, 15780, Greece
+306936858768, +302410610803. maglaras@teilar,gr
ABSTRACT: The influence of the inhomogeneity of
electric field, the effect of grounding, and the corona
current to the dielectric behaviour of the rod-plate air gaps
is investigated in the present paper. The ground effect
occurs due to the fact that in the air gap arrangements one
electrode is usually grounded. The maximum and the
average value of the field strength and the field factor of
the gap were resulted by simulation. The corona onset
voltage, the corona current and the breakdown voltage of
correspondent experimental arrangements were measured.
It is resulted that (a) the effect of grounding has a
significant influence to the electric field distribution, and
hence to the corona onset and the breakdown voltage of
small air gaps and is valid for both polarities of the applied
voltage, and (b) the inhomogeneity of the field determines
the evolution of the dielectric behaviour of the gap.
Keywords: Air Gap, Field Strength, Breakdown, Corona, Ground
Effect, Polarity Effect.
I. INTRODUCTION
Small air gaps are widely used in several applications
like ozone production and chip construction, in electrostatic
filters, electrostatic painting, loudspeakers, etc. The
dielectric behaviour of these arrangements and especially
the corona onset and the breakdown voltage, as well as the
corona current is of great importance.
The mostly used air gaps are the rod-plate (or the pointplate), and the rod-rod (or point-point) air gaps, [1] - [9].
The corona effects and the polarity effect are well known
phenomena and thoroughly studied, while their influence to
the dielectric behaviour of air gaps has been investigated
for many applications [1] – [12]
The most determinant factor for the dielectric
behaviour and especially for the dielectric strength of an air
gap is the inhomogeniety of the electric field, and
especially the maximum value of the field strength in the
gap, which usually appears on the sharper edge of the
electrodes, mostly on the tip of a rod, and the field factor
across the axis of the gap. Other factors are the polarity and
the form of the applied voltage as well as the corona
effects, which take place when the field strength exceeds
some specific value [6] - [14].
In less homogenous electric fields like the small air gaps
with relatively big diameters of the electrodes, the corona
effects do not appear before breakdown. The values of the
breakdown voltage depend on the grade of the field’s
inhomogeneity. The more inhomogeneous the field is the
lower the breakdown voltage becomes [15[, [16].
In longer air gaps the field is more inhomogeneous and
corona effects and hence a corona current through the gap
occur before breakdown. The intensity of the corona effects
depend on the grade of the field’s inhomogeneity. The
more inhomogeneous the field is the higher the corona
current becomes. The corona current influences the
breakdown voltage positively [16]-[19].
It is well known that the grounding of one of the
electrodes influences the values of the breakdown voltage
of the spark gaps, especially in the vertical arrangements
(Fig. 1). This is due to the fact that the distribution of the
electric field is influenced by the parasite capacitances
between the electrodes and the grounded surroundings [1] –
[3].
In a rod-plate gap the influence also depends on the
electrode chosen to be grounded [18] – [19].
It is also well known that on the tip of a stressed rod the
corona effects start when the value of the field strength at
the tip exceeds some specific value, given by empirical
equations. The value depends on the radius of the rod’s tip
and the polarity of the applied voltage. In rod-plate air gaps
it also depends on the gap length, and the plate’s diameter
[1] – [4].
( x, y)   2 : rr  y  rr ,
 ,
R1  

2
2
2
2
 a  rr  G 2  rr  y  x  rr  G 2  rr  y 
G


2 G
( x, y)   : 2  x  2  b,
.


P
2
2
2
2
 r  b   b    x  G  b   y  r  b   b    x  G  b  
p
 p 2 2 
2 2
2 2 
2 2  

(7)
(8)
y
Shield
R
Figure 1. Spark gaps
Plate
2rr
Rod
rpl
a
rpl
x
II. THEORETICAL
In the present paper the influence of the grounding of one
of the electrodes to the field distribution and the dielectric
behaviour of horizontal rod-plate air gaps has been
analytically and experimentally investigated.
Especially investigated is the way in which the
inhomogeneity of the field influences the appearance of the
corona or the breakdown in a rod-plate air gap. What need
to be clarified is if it is possible, using exclusively
simulation analysis, and not experiments, to predict
whether in a gap stressed by high voltage corona effects or
breakdown is expected.
Special models of rod-plate and rod-rod air gaps have
been analyzed with the Finite Element Method. All the
analyzed models are axisymetric, with a spherical boundary
shield big enough in diameter. The influence of the
grounding to the electric field distribution in air gaps has
been investigated.
Special software has been used for the simulation
analysis of the air gap models. It is based on the Finite
Element Method with the use of Poisson’s equation
 2V    
,
(1)
and the Dirichlet boundary conditions V=0, in order to
solve two-dimensional problems of axisymetric models.
The initial conditions of a rod-plate air gap are given by
the following equations (Fig. 2)
a) For the arrangements with the rod grounded, while the
plate is stressed by 1V:
V ( x, y)  0, if ( x, y)  R1   ,
(2)
V ( x, y )  2, if ( x, y )  P
(3)
b) For the arrangements with the plate grounded, while
the rod is stressed by 1V:
V ( x, y )  0, if ( x, y )  P  
,
(4)
V ( x, y)  1, if ( x, y)  R1
,
(5)
where
  ( x, y)   2 : x 2  y 2  R 2 ,
(6)
G/2
G/2
b
Figure 2. The rod-plate model. One electrode is stressed,
whereas the other is grounded. R>>G.
III INVESTIGATION PROCEDURE
The differences between equations (2), (3), and (4), (5),
for the initial conditions, are significant, and lead to
differences in the electric field distribution.
The maximum value of the field strength in the gap, and
the average value of the field strength and the field factor
along the axis of the gap have been resulted from analysis,
listed and analyzed.
The corona onset, the corona current and the breakdown
voltage of correspondent experimental horizontal
laboratory arrangements have been measured. The
influence of the ground effect to the corona onset and the
breakdown voltage of small air gaps have been
investigated.
Special attention has been given to the investigation of
the way in which the average value of the field strength and
the field factor across the axis of the gap influence the
phenomena of corona and breakdown.
The arrangements, which have been modeled, analyzed,
and experimentally studied, are typical rod-plate air gap
arrangements of different electrode geometry. The rod
electrode is a cylinder long enough, with a relatively small
diameter (4-14 mm) and a hemisphere tip, and the plate
electrode is a disk up to 150 mm in diameter. High DC
voltage of negative or positive polarity is applied to one
electrode while the other is at earth potential (grounded), or
both electrodes are symmetrically charged with opposite
190
Field strength on the rod
(V/m).
and equal voltages. A.C. and lightning Impulse voltage
have also been used.
The influence of the surrounding is minimized, by
keeping relatively big distances between the models and
the boundary shielding, as well as between the
experimental arrangements and the grounded elements of
the laboratory. All the analyzed models are axisymetric
with a spherical boundary shield big enough in diameter (at
least 200 times bigger than the gap’s length) at earth
potential (Fig. 2). In the experimental models the grounded
surroundings are at a distance of at least 20 times longer
than the gap’s length.
The average value of the field strength, along the axis of
an air gap (Fig. 2 ) is defined by equation:
av  V G
(9)
Rod 10 mm
Plate 100 mm
1V
150
110
70
30
1
2
3
4
5
6
7
8
Gap length (cm)
The field factor (or efficiency factor) n is a net number,
which defines the inhomogeneity of the field in the gap and
is expressed by equation:
nE
E
max av ,
(10)
where V is the applied voltage, G is the gap length, Emax
is the maximum value of the field strength (on the tip of the
rod), and Eav is the average value of the field strength
along the axis of the gap.
For a rod-plate air gap, with a very big plate, the field
factor is given by equation [1,2]:
2G
, if G>>rr,
(11)
n
r  ln( G r )
r
r
where and rr is the radius of the rod. The plate’s diameter is
big enough.
The polarity of the applied voltage affects the maximum
values of the field strength at corona onset and breakdown,
the influence depending on the rod’s and the plate’s
diameter (polarity effect) [1] – [4].
IV. THE SIMULATION RESULTS
The simulation analysis with the Finite Element Method
has shown a significant influence of the ground effect to
the field distribution in rod-plate air gaps. The differences
between the arrangements with the rod or the plate
grounded, or with symmetrically charged electrodes are
obvious as shown in Figures 3, and 4.
The effect of grounding is intense when the gap length is
relatively big and the plate’s and rod’s diameters are
relatively small. In the air gaps with the rod-grounded (rgr) the field is less inhomogeneous than in the plategrounded (pl-gr) arrangement, (Figure 4). The maximum
values of the field strength on the rod and the values of the
field factor along the axis are relatively lower in the
arrangements with the rod grounded (r-gr), and higher in
the arrangements with the plate grounded. In the
arrangements with symmetrically charged electrodes the
values are somewhere in between, (Figure 3)
Figure 3. The maximum values of the field strength on
the rod and the field factor along the axis of rod-plate air
gaps, for the different arrangements with the rod (r-gr),
or the plate grounded (pl-gr), either with symmetrically
charged electrodes (symm.).
Plate-grounded. Symm. charged
Rod-grounded
Figure 4 Field strength distribution in rod-plate air
gap models for the different arrangements.
V. THE EXPERIMENTAL RESULTS
The grounding of one electrode influences the corona
onset and the breakdown voltage of the rod-plate air gaps
greatly.
The corona onset voltage is higher in the less
inhomogeneous arrangement with the rod grounded and
lower in the arrangement with the plate grounded. The
grade of the differences depends on the gap length, as well
as the rod’s and the plate’s diameter.
When the applied voltage is negative the effect of
grounding to the corona onset voltage is intense, as shown
in Figure 5. In the rod-grounded arrangement the field is
less inhomogeneous and there are no corona effects before
the breakdown, and thus the breakdown voltage is
80
70
60
50
40
30
20
10
0
overlapped. This is the effect of the corona current to the
breakdown voltage [19].
100
Vbr, r-gr
Corona onset voltage (KV)
Volta ge (KV)
compared to the corona onset voltage of the plate-grounded
arrangement.
Vc , pl-gr
1
2
3
4
5
6
7
8
9
10
80
R-gr, Vbr, DC(-)
Rod (+)
60
40
Pl-gr, Vc, DC(+)
20
0
G a p le ngth (c m )
1
2
3
4
45
40
35
30
r-gr
25
pl-gr
20
15
10
1
2
Ga p le ngth, c m
3
Corona Ons et Voltage
(KV)
70
60
50
40
30
20
10
0
r-gr
pl-gr
1
2
3
4
5
6
7
8
9
Gap length (cm)
6
7
8
9
10
11
60
50
40
V, r-gr, DC (-)
Rod (-)
30
V, pl-gr, DC
(+)
20
10
0
1
(b) Breakdown voltage
Figure 5. The effect of grounding to the corona onset
and the breakdown voltage of rod-plate air gaps
stressed by DC negative voltage.
5
Gap length (cm)
Breakdown voltage (KV)
Bre akdown voltage, KV
(a) Corona onset and breakdown voltage
2
3
4
5
Gap length (cm)
Figure 7. The effect of grounding to the corona onset and
the breakdown voltage, when the polarity of the rod is the
same (positive or negative) compared to the plate.
The effect of grounding is also valid when the applied
voltage is DC of positive polarity, (Figure 6).
The effect of grounding is clearer for the cases in which
the rod has the same polarity (positive or negative)
compared to the plate. The corona onset and the breakdown
voltage are analogically higher in the arrangement with the
rod grounded than in the arrangement with the plate
grounded in small and longer air gaps (Figure 7), as it is
expected from Figure 3. In these arrangements there is no
polarity effect.
(a) Corona onset voltage
Breakdown Voltage (KV)
80
70
60
Rod-plate
10-100 mm
DC(+)
r-gr
VI. THE INFLUENCE OF THE AVERAGE
VALUE OF THE FIELD STRENGTH
50
40
30
pl-gr
20
10
0
1
2
3
4
5
Gap length, (cm)
(b) Breakdown voltage
Figure 6. The effect of grounding to the corona onset
and the breakdown voltage of rod-plate air gaps stressed
by DC positive voltage.
The corona current minimizes the effect of grounding to
the breakdown voltage. The corona current, appears earlier
in the plate-grounded arrangement, than in the arrangement
with the rod-grounded, and changes the field distribution,
making it less inhomogeneous. The maximum value of the
field strength decreases and the breakdown voltage
increases, (Figure 5). The effect of grounding is
The average value of the field strength across the axis of
a rod-plate air gap at corona onset or breakdown, given by
equation (9), decreases as the gap length increases, the
value also depending on the gap’s geometry.
From figure 9 it can be resulted that breakdown occurs
without corona when the average value of the field strength
across the gap is higher than a specific value Eav1>11
KV/cm. Otherwise, and under the circumstance that the
maximum value of the field strength is higher than the
appropriate value Ec, corona appears before breakdown. It
can also be resulted that the breakdown occurs before
corona when the gap’s length is smaller than 2 - 4 cm, the
value depending on the rod’s diameter also.
Air gaps with two different rod’s diameter of 4 and 12
mm, and a plate diameter of 100 mm, have been chosen.
The results of gaps with bigger diameter of plate, or with
rod’s diameter between 4 and 12, are somewhere between.
In the graphs of Figure 9, two different areas can be
clearly separated: the left area, in which breakdown occurs
without corona, and the right area, where corona appears
(right bottom area) before breakdown (top right area).
Average field strength (KV/cm)
20
18
R-gr, (+)
16
14
12
Breakdown
after corona
Brekdown
without corona
pl-gr, (-)
10
R-gr, (+)
8
pl-gr, (-)
6
Corona
4
2
r(-)
It can be generally concluded from Figures 9 and 10 that
in rod-plate air gaps stressed by high voltage: a) The gap is
led to breakdown without corona when the average value
of the field strength along the axis of the gap is higher than
11 KV/cm, and the value of the field factor is lower than
3.5, b) the gap is led to breakdown after corona when the
average value of the field strength along the axis of the gap
is higher than 11 KV/cm, and the value of the field factor is
higher than 3.5, and c) corona occurs when the average
value of the field strength along the axis of the gap is lower
than 11 KV/cm, and the value of the field factor along the
axis is higher than 4.5. These results are valid for air gaps
with a rod’s diameter between 4 and 12 mm.
0
1
2
3
4
5
18
6
16
Gap length (cm)
Corona and
breakdown
14
Field factor
25
20
15
Breakdown
after corona
Brekdown
without corona
Average field strength (KV/cm)
(a) Negative rod 4 mm, plate 100 mm
12
10
R-gr
8
6
4
Brekdown without
corona
2
pl-gr, (-)
0
R-gr, (+)
1
10
2
3
4
5
6
7
8
R-gr, (+)
Gap length (cm)
pl-gr, (-)
5
pl-gr
r(-)
Corona
(a) Rod 4 mm, plate 100 mm
0
7
1
2
3
4
5
6
6
Gap length (cm)
The dashed lines of the graphs show the values of
average value of the field strength, for which breakdown
occurs before corona effects.
The polarity of the applied voltage influences the results
greatly.
VII. THE INFLUENCE OF THE FIELD
FACTOR
The value of the field factor across the axis of a rod-plate
air gap at corona onset or breakdown, given by equation
(10), increases as the gap length increases, the value also
depending on the gap’s geometry.
From Figure 9 it can be resulted that breakdown occurs
without corona when the value of the field factor across the
axis is lower than a specific value FF1<3,5 or 4,5, the value
depending on the rod’s diameter. Otherwise, and under the
circumstance that the maximum value of the field strength
is higher than the appropriate value Ec, corona appears
before breakdown. The influence of the polarity of the
applied voltage is not significant.
In figure 10, two areas can be clearly separated. In the
bottom area the gap is led to breakdown without corona,
though in the top area corona effects are followed by
breakdown.
Field factor
(b) Negative rod 12 mm, plate 100 mm
Figure 9. The average value of the field strength at corona
and breakdown.
Pl-gr
Corona and
breakdown
5
4
3
Brekdown without
corona
2
r-gr
1
0
1
2
3
4
5
6
7
8
Gap length (cm)
(b) Rod 12, plate 100 mm
Figure 10. The values of the field factor at corona and
breakdown..
VIII. CONCLUSIONS
1) The grounding of one of the electrodes has a significant
influence to the electric field distribution, the maximum
value of the field strength in the gap, as well as the average
value of the field strength and the value of the field factor
across the axis of the gap.
2) The ground effect also influences the corona onset and
the breakdown voltage of relatively small air gaps and is
valid for both polarities of DC applied voltage (positive or
negative).
3) The average value of the field strength and the field
factor across the axis of the gap are determinant factors for the
corona and the breakdown of the gaps.
4) When the average value of the field strength is lower than
11 KV/cm and the field factor is higher than 4.5 corona
appears before breakdown.
5) When the average value of the field strength is higher
than 11 KV/cm and the field factor is lower than 3.5 the gap is
led to breakdown without corona.
VIII. ACKNOWLEDGMENT
The project is co-funded by the European Social Fund and
& National Resources.
IX. REFERENCES
E. Kuffel, W. Z. Zaengl, J. Kuffel, High voltage
engineering. Fundamentals, Newnes Oxford, 2000 .
[2] M. Khalifa, High voltage engineering, Theory and
practice, Marcel Dekker inc., New York, 1990
[3] M. S. Naidu, V. Kamaraju, High voltage engineering,
Mc Graw Hill, New York, 1996.
[4] P. N. Nikolopoulos, High voltages, National Technical
University of Athens, 1990.
[5] “Der
elektrische
durchshlag
von
luft
im
unhomogenen feid“, E. Marx, Arch. F. El., vol. 24,
1930, pp. 61f.
[6] “Point to plane corona in dry air”, H. Bandel,
Physical Review, 1951.
[7] “From the glow corona into the breakdown”, K. Feser,
H. Singer, ETZ-A Bd 93, H 1, p 36-39, 1972.
[8] “Negative corona in air using a point/cup electrode
system, IEEE Transactions on Dielectrics and
Electrical Insulation”, Er-ning Li, J. M. K. MacAlpine,
Vol. 7 No 6., December 2000.
[9] “A comment on the methods of calculation of corona
onset voltage”, M. Salama, H. Parekh, K. Srivastava,
1976.
[10] M. Abdel-Salam, N. Allen, “Onset voltage of positive
glow corona in rod-plane gaps as influenced by
temperature”,
IEEE
Proceedings
Science,
Measurement and Technology, 2005.
[11] “Application of a corona onset criterion to calculation
of corona onset voltage of stranded conductors”,
Kenichi Yamazaki, Robert G. Olsen, IEEE
Transactions on Dielectrics and Electrical Insulation,
Vol. 11, No 4, 2004
[12] “Computing the corona onset and the utilization factor
of rod-plane electrode by using charge simulation
method, Ozcan Kalenderli, Emel Onal, Ozkan Altay,
IEEE, 2001
[13] “Method for measuring field in space charge by
means of Pockel’s device”, K. Hidaka, T. Kouno, J.
Electrostatics vol. 11,1982, pp. 195-211, (1982)
[14] “Negative Corona in Air Using a Point/Cup Electrode
System”, Er-ning Li, J. M. K. MacAlpine, IEEE
Transactions on Dielectrics and Electrical Insulation,
Vol. 7, No 6, 2000.
[15] Li Ming, Mats Leijon and Tord Bengtsson, “Factors
influencing barrier effects in air gaps”, Ninth
International
Symposium
on
High
Voltage
Engineering, Graz, Austria, 1995.
[16] A. Maglaras, “Numerical analysis of electric field in
air gaps, related to the Barrier Effect”, 1st IC-SCCE
Athens, 2004.
[17] A. Maglaras, L. Maglaras, “Numerical Modeling and
Analysis of electric field distribution in rod – plate air
gaps, with or without barrier, stressed by breakdown
voltages”, 1st IC-EpsMsO, Athens, 2005.
[18] A. Maglaras, L. Maglaras, J. Drigojias, “ Modeling
and analysis along with experimental investigation of
the Ground Effect in rod-plate air gaps with or without
barrier”, 5th WSEAS/ IASME International Conference
on Electric Power Systems, High Voltages, Electric
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[19] A. Maglaras, L. Maglaras, “The ground effect, the
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Symposium of ISH, Ljubljana, Slovenia, 2007
[1]
IV. BIOGRAPHIES
Athanasios
Maglaras
(M’85-93,
M’06) was born in Greece in 1948. He
received the Electrical and Mechanical
Engineering degree from the National
Technical University of Athens, in
Greece, in 1971, the M.Sc. degree in
1985, and he is a Ph.D. student in
National Technical University of
Athens, in Greece. Since 1980 he is an Associate Professor
of Technological Education Institute (T.E.I.) of Larissa in
Greece. He was Head of the Electrical Engineering
Department of the T.E.I. of Larissa for 6 years, and he is
the Head of the High Voltage and CAD/CAE Laboratory in
the T.E.I. of Larissa since 1990. He is a member of the
Technical Chamber of Greece, the IEEE, and the CIGRE.
The main research interests are High Voltages,
Electromagnetic Field Analysis, and CAD/CAE. He was
supervisor and partner in many European research and
educational projects. He is author of 5 books concerning
High Voltages, Electric Fields, CAD/CAE, and more than
20 papers in scientific magazines and conferences.
Frangiskos V. Topalis (M’90) received
the Diploma in Electrical and
Mechanical Engineering and the Ph.D.
from the National Technical University
of Athens (NTUA) in 1979 and in 1990
respectively. Since 2007 he is Professor
of the School of Electrical and
Computer Engineering of National
Technical University of Athens His research interests
concern high voltages, harmonics, lighting and rational use
of energy. He is a member of the Technical Chamber of
Greece and of IEEE. He is an author of 5 books and 4
technical brochures concerning high voltages, lightning and
electrical measurements and more than 100 papers in
scientific journals and conferences.