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Influence of Insulating Barrier on the Electric Field Distribution in a Point-Plane
Air Gap using COMSOL Multiphysics
Conference Paper · December 2018
DOI: 10.1109/CISTEM.2018.8613566
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Influence of Insulating Barrier on the Electric Field
Distribution in a Point-Plane Air Gap using
COMSOL Multiphysics
M.A.Benziada, A.Boubakeur, A.Mekhaldi
Laboratoire de Recherche en Electrotechnique, Ecole Nationale Polytechnique
B.P 182 El-Harrach 16200 Algiers, Algeria
mohamed_abdelghani.benziada@g.enp.edu.dz, ahmed.boubakeur@g.enp.edu.dz and abdelouahab.mekhaldi@g.enp.edu.dz
www.enp.edu.dz
Abstract— The aim of this paper is to calculate the electric
field intensity at the plane surface in a point-plane arrangement
with the introduction of an insulating barrier between electrodes.
We carried out a simulation of a point-barrier-plane
arrangement with a point-plane distance of 100 cm. The point is
subjected to DC high voltage of positive polarity. Using the
numeric finite element method, the geometric model has been
implemented in COMSOL Multiphysics® software. This method
is used to solve the partial differential equations that describe the
field distribution with the presence of space charge. We studied
the influence of several parameters of the barrier such as its
shape and its number in the interval. To show the effect of the
space charge, we considered also a barrier perforated in its
middle. We finish by representing the electric field lines and
comparing between different arrangements.
Keywords - Electric field, point-plane arrangement, finite
element method, barrier, space charge.
I. INTRODUCTION
The improvement of the dielectric strength of a point-plane air
gap by insertion of an insulating barrier is an important fact
already verified [1,2].
The distribution of the electric field undergoes a deformation
by causing a significant increase in the breakdown voltage of
the system. The increase was explained by the uniformity of the
field in the barrier-plane gap in the case of the positive point
[3,4].
In recent decades, many experimental studies have been carried
out [5]. They enabled to acquire knowledge for the elaboration
of models to reproduce the development of the discharge.
Numerical simulation studies can help in the study of electrical
discharges and reduce the costs of experimental tests [6].
L.Mokhnache and al [6-8] have used the finite element method
to calculate the electric field due to positive ions and electrons
created at the head of the avalanches in a point-plane air gap.
Their modelling was based on the formulation of the resulting
field obtained by the vector summation of the applied electric
field E0, the space charge field and the polarization field of an
insulating barrier introduced into the air gap. The resulting field
is obtained by the resolution of Maxwell's equations. Their
model took into account the influence of few parameters such
as the applied voltage level, the width of the barrier, its nature
and permittivity, and the curvature radius of the pointed
electrode.
We propose in this paper to continue the work not carried out
by L.Mokhnache on the effect of other parameters namely: the
shape of the barrier, the number of used barriers and the
perforated barriers. In our study, the electric field distribution
was determined in the point-barrier-plane configuration with
positive applied voltage. The field is calculated on the grounded
electrode using the COMSOL Multiphysics software based on
the finite element method.
II. SIMULATION MODEL
The hydrodynamic approach is the most used to model the
physical processes in non-thermal gas discharges and is
therefore presented in detail below.
A. Governing Equations
To simulate the electric field in the air, a drift-diffusion
model is used. This model describes the generation, the
annihilation and the movement of three species (electrons,
positive ions, and negative ions) [9]. It includes a set of mass
conservation equations for the charge carriers in the gas coupled
with the Poisson’s equation for the calculation of the electric
field and is described by the equations (1) to (4) [9]:
−
=
+ ∇. −
−
∇
+ ∇. −
−
∇
=
(2)
+ ∇. −
−
∇
=
(3)
∇
=
−
−
(1)
,
= −∇
(4)
+
+
−
+
−
−
−
−
−
(5)
Point
10
°
Where
represents the rate of background ionization in zero
field limit; R = αN W is the rate of electron impact
ionization ( stands for Townsend’s ionization coefficient,
m-1);
=
is the rate of electron attachment to
electronegative molecules ( is attachment coefficient, m-1);
and
=
is the rate of detachment of electron
from negative ions (
is detachment coefficient, m3/s). Two
types of recombination are considered, electron-ion and ionion, with the rates
=
and
=
,
respectively (
stands for corresponding recombination
coefficient, m3/s).
Barrier
d
=
=
=
The model is implemented in COMSOL Multiphysics
package. The package’s “Convection and diffusion” of the
drift-diffusion (dd) interface, “transient analyzes” and
“Electrostatics” application modes are used to implement the
system of Equations (1)-(4) together with boundary conditions
shown in figure 2. The choice of boundary conditions for the
charge carriers is obvious in this case: since corona electrode
surface (point) is set to the positive potential, convective fluxes
for electrons and negative ions and zero concentration for
positive ions are specified here. The negative charges are
repelled from the surface of the grounded electrode (hence,
, = 0) and the current flow is due to positive ions only
(convective flux condition). A user-controlled mesh is applied;
the meshes dimension varies by adapting to the geometry of the
arrangement.
a
The terms R, [m-3 s-1], on the right hand side of equations
(1)-(3) represent net rates of generation/loss of species of
particular type. In the present study, the rates are [9]:
In our investigations, a positive DC voltage has been applied to
the high-voltage electrode (point) and the plane is grounded.
The atmospheric conditions are considered normal.
e = 5mm
Here, subscripts e, p, and n indicate the quantities related to
electrons, positive ions, and negative ions, respectively. N
stands for the charge carrier density, [m-3]; D is the diffusion
coefficient, [m2 s-1]; μ is the mobility, [m2V-1s-1]; E is the vector
of electric field, [Vm-1]; V is the electric potential, [V]. t stands
for time, [s]; q = 1.6·10-19 [C] is the elementary charge, and
εo = 8.854·10-12 [Fm-1] is the permittivity of vacuum.
2L=1m
[m2/V s]
[m2/V s]
[m2/s]
[m2/s]
[m3/s]
[m3/s]
[m3/s]
[1/m3 s]
Plane
4m
(6)
Drift velocity and diffusion coefficient of electrons as a
function of the electric field are approximated as:
With
= 2,5.10
.
∇
The geometry of the used point-plane electrode system with
an insulating barrier is presented in figure 1.
=0
open
boundaries
Barrier
=0
The equations of the model have been complemented with
boundary conditions and initial conditions given in [9] and are
implemented in the COMSOL Multiphysics software.
B. Implementation
,
=0
(8)
[1/m3] is the gas density.
=0
=
. −
(7)
.
, ,
=
a
= 0.07 + 8
Surface
of the
point
z
d
= 3200
.
Fig.1 Point-barrier-plane configuration.
Symmetric axis
= 2. 10
= 2.2. 10
= 5.05. 10
= 5.56. 10
= 5. 10
= 2.07. 10
= 10
= 1.7.10
x
The model parameters used in the present study are adopted
from [9,10] and are:
Air
, ,
=0,
=0,
,
=0
=0
r
Plane
Fig.2 Computational domain, n is the unit vector normal to the boundary.
To validate our model (using COMSOL Multiphysics), we
made our simulations with the electrode system used by
L.Mokhnache et al [6-8] using a MATLAB program to
calculate the electric field by the finite element method.
The model is composed of a point, a barrier, and a plane. The
various elements of this arrangement are described below. The
used point electrode has a hyperboloid form (alpha=10°). The
grounded electrode consists of a 4m wide plane. The used
insulating barrier of square form is made of Vinyl (plastic) with
relative permittivity εr = 4, width 2L = 1m and thickness e =
5mm and is placed at a distance of 20 cm from the point, i.e. a/d
= 20%, with: ‘a’ the point-barrier distance and, ‘d’ the pointplane distance [6-8]. The second type of barrier used is of
hemispherical shape with radius R = 50cm and thickness e =
5mm.
III. RESULTS AND DISCUSSIONS
We have determined the distribution of the electric field in the
point-barrier-plane air gaps taking into account the presence of
a space charge in the medium having a density ρ varying
between [1, 10]x10 C/m . We have considered several
parameters, such as the shape of the barrier, the number, and the
perforated barrier. Note that the applied voltage is implemented
as a linearly increasing function of time rising from 0 to 100 kV
within 100 s with the ramping rate of 1 kV/s and in our
simulation, we present the electric field distribution
corresponding to 100 kV.
A. Electric field with and without barrier
The influence of the insertion of an insulating barrier in the
point-plane gap on the electric field at the plane is given in
figure 3.
Figure 4 shows the influence of the shape of the barrier on the
distribution of the electric field at the plane.
The results show that the electric field decreases by 30% for a
hemispherical barrier and whose cavity is in front of the point
with respect to the planar barrier.
For the hemispherical barrier whose cavity is facing the plane,
the value of the electric field is slightly elevated with respect to
the planar barrier and decreases away from the axis of the highvoltage electrode.
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-200 -150 -100 -50 0
50
100 150 200
Position on the plane (cm)
Without barrier
Hemispherical barrier facing the point
Hemispherical barrier facing the plane
Fig.4 Electric field depending on the shape of the barrier.
(V=100kV, alpha = 10°, d= 1m, Ɛr= 4)
C. Influence of the number of barrier
50 100 150 200
Position on the plane (cm)
Without barrier
B. Influence of the shape of the barrier
Planar barrier
E (kV/cm)
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-200 -150 -100 -50 0
In both cases, with and without barrier, we observe that the
electric field is more important at the center of the plane, and
then decreases as it moves away from this axis. We also notice
that the electric field at the plane is reduced with the inserting
of the insulating barrier in the interval.
E (kV/cm)
C. Validation of the model
With barrier
Fig.3 Electric field with and without barrier.
(V=100 kV, alpha = 10°, d= 1m, 2L= 1m, a/d = 20%, Ɛr= 4)
In figure 5, we show the results of the electric field distribution
at the plane as a function of the number of barriers and their
position in the air gaps.
We note that the insertion of a second barrier in the air gap
increases the dielectric strength [11] especially if it is located
near the grounded plane. We also observe that the decreases of
the electric field at the plane between a system with a single
barrier and a system with two barriers increases as it moves
away from the axis of the point.
When the barrier is perforated, The electric field of the pointbarrier-plane arrangement tends to increase as the diameter of
the hole increases. At the limit, it becomes equal to that of the
point-plane arrangement for holes larger than 30 mm in
diameter (figure 6).
One barrier
Two barriers
E (kV/cm)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-200 -150 -100 -50 0
E. Representation of electric field lines
We have made a representation of the electric field lines for the
following four cases:
50
100 150 200
System point-plane with a planar barrier, system point-plane
with hemispherical barrier facing the point, system point-plane
with hemispherical barrier facing the plane and finally system
point-plane with two planar barriers (figure 7).
Position on the plane (cm)
a/d=40%
a/d=60%
a/d=80%
Fig.5 Electric field depending on the number of barriers.
(V=100kV, alpha = 10°, d= 1m, 2L= 1m, Ɛr= 4)
D. Influence of the perforated barrier
The majority of the studies carried out on the influence of the
insulating barrier have shown that this barrier mainly plays the
role of a geometric obstacle to the direct development of the
disruptive discharge [5].
The influence of the perforated barrier at the center on the
electric field is given in figure 6.
(a)
2
E (kV/cm)
1.5
1
0.5
(b)
0
-200 -150 -100 -50
0
50
100
150
200
Position on the plane (cm)
Without barrier
Unperforated barrier
Dt=2mm
Dt=6mm
Dt=10mm
Dt=20mm
Dt=30mm
Fig.6 Influence of a perforated barrier on the electric field.
( V= 100kV, d= 1m, 2L= 1m, a/d = 20%, Ɛr= 4)
(c)
axis of the point. From the results obtained in the case of the
perforated barrier, it has been found that electric field increases
with the increase in the diameter of the holes of the barrier. The
representation of the electric field lines allows better
understanding the influence of different parameters on the
dielectric strength of the point-barrier-plane arrangement. The
results leading to the conclusion that numerical simulation with
finite element method can help in the study of electric field
distribution and reduce the costs of experimental tests.
REFERENCES
[1]
(d)
Fig.7 Electric field lines representation.
( V= 100kV, d= 1m, a/d = 20%, Ɛr= 4, alpha = 10°)
(a) point-plane with planar barrier
(b) point-plane with hemispherical barrier facing the point
(c) point-plane with hemispherical barrier facing the plane
(d) point-plane with two planar barriers
In the presence of an insulating barrier (figure 7a), the electric
field lines deviate as they approach the barrier and follow a path
from the point to the edge of the barrier and from that edge to
the grounded plane.
In figures 7b and 7c, the electric field lines represent the most
frequent paths taken by the discharge in the case of a clean
barrier with its cavity oriented towards the point and towards
the grounded plane respectively. The elongation of the
discharge is noted, especially when the concavity of the barrier
is directed towards the point.
The results of figure 7d confirm that the insertion of a second
barrier into the air gap increases the dielectric strength of the
system by increasing the length of the discharge.
From the obtained numerical results, we can conclude that the
shape of the curves is in general coherent with the theoretical
and experimental knowledge.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
IV. CONCLUSION
In the present study, simulation of electric field distribution for
a non-uniform configuration has been carried out with finite
element method using COMSOL Multiphysics software. The
point-barrier-plane configuration has been used in our
investigation. The dielectric strength of the system increases by
using a hemispherical barrier with respect to the planar barrier.
The insertion of a second barrier into the air gap reduces the
electric field at the plane especially by moving away from the
View publication stats
[10]
[11]
E. Marx, “Der Durchschlag der Luft im unhomogenen elektrischen
Felde bei verschiedenen Spannungsarten,” E.T.Z., vol. A33, pp.
1161–1165, 1930.
H. Roser, Schirme zur Erhöhung der Durchschlagsspannung in
Luft, E.T.Z., Vol. B17, 1932, pp. 411-412.
A.Boubakeur, "Influence des barrières sur l'amorçage des moyens
intervalles d'air pointe-plan", Rozprawy Elektrotechniczne (Polish
Academy of Sciences), Vol.27, N°3, 1981, pp.729-744.
A. Beroual and A. Boubakeur, “Influence of Barriers on the
Lightning and Switching Impulse Strength of Mean Air Gap in
Point/Plane Arrangements”, IEEE Trans. on Dielectrics and
Electrical Insulation, Vol. 26, No. 6, pp. 1130-1139, 1991.
A. Boubakeur, “ Influence des barrières sur la tension de décharge
disruptive des moyens intervalles d’air pointe-plan “, Thèse de
Doctorat, E.P .Varsovie, Pologne, 1979.
L. Mokhnache, “ Contribution à l’étude de l’influence des barrières
dans les intervalles d’air pointe-plan par le calcul numérique du
champ à l’aide de la méthode des éléments finis avec et sans charge
d’espace ”, Thèse de magister, ENP d’Alger 1997.
A.Boubakeur, L.Mokhnache, S.Boukhtache, “ Numerical model
describing the effect(s) of a barrier and the space charge fields on
the electrical strength of a point-plane air gap using the finite
elements ”, Conference on Electrical. Insulation and Dielectric
Phenomena CEIDP 2000, Vol.2, pp.466-469, Victoria (Canada),
2000.
A.Boubakeur,
L.Mokhnache,
S.Boukhtache,
A.Felliachi,
“Theoretical investigation on barrier effect on point-plane air gap
breakdown voltage based on streamers criterion”, IEE. Science,
Measurement and Technology. Vol.151, pp.167-174, 2004.
Y. V. Serdyuk, “Numerical simulations of non-thermal electrical
discharges in air: Lightning electromagnetics”, IET power and
energy series, pp. 87-138, 2012.
S. Singh, Y. Serdyuk, R. Summer, "Streamer Propagation in Hybrid
Gas-Solid Insulation". IEEE Conference on Electric Insulation and
Dielectric Phenomena, CEIDP 2015, pp. 387-390, Ann Arbor,
United States, 2015.
S. Merabet, R. Boudissa, S. Slimani and A. Bayadi, “Optimisation
of the dielectric strength of a non-uniform electric field electrode
system under positive DC voltage by insertion of multiple barriers,”
IEEE Transactions on Dielectrics and Electrical Insulation, vol. 21,
pp. 74-79, February 2014.