Capacitive-resistive Field Calculation on HV Bushings using BEM

IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 5 No. 2, April 1998
237
Capacitive-resistive Field Calculation on HV
Bushings using the Boundary-element
Method
S. Chakravorti,
Electrical Engineering Department, Jadavpur University, Calcutta, India
and
H. Steinbigler
Institute of High Voltage Engineering
and Electric
Power Transmission, Technical University, Munich, Germany
ABSTRACT
Capacitive-resistive field distributions including surface and volume resistivities have been
computed
in and around HV porcelain and capacitor bushings. The boundary element method
has been applied
for field computation in two axi-symmetric bushing configurations including
four dielectrics. Effects of uniform and non-uniform distributions
of surface resistivity and vol-
ume resistivities of different dielectric media are studied in detail. Special emphasis has been
given to the stress distributions along the various dielectric-dielectric boundaries. Further, the
values and locations of maximum stresses in different dielectrics are determined and reported
in this paper. The plots
of equipotential lines for a few typical cases of field distributions are
also presented here for both bushings.
1 INTRODUCTION
V bushings are integral components of very important electric
H power system equipment such as transformers, shunt reactors
etc. Depending upon the operating voltage of the bushing, it may occur
that an electrical discharge is initiated at
a certain point in or around the
bushing surface because the local electric field at that point has reached
the critical value. Once initiated, the discharge will
in general grow
rapidly and unless interrupted by local conditions elsewhere, such as
much lower electric field at some other location, the discharge may
quickly develop into
a complete breakdown. Thus the knowledge of
electric field distribution in and around
HV bushings are of great im-
portance for reliable operation
of major HV equipment.
The distribution of electric field in and around an outdoor
HV bush-
ing is governed mainly by the bushing geometry, permittivity and vol-
ume resistivity of the insulating materials and the surface resistivity due
to surface contamination
[l]. Of all these factors, the surface resistiv-
ity is the most variable parameter
as a result of the ambient environ-
mental conditions. The well-known combination
of surface pollution
deposit and wetting by fog or condensation is considered to be
a major
factor responsible for failures of outdoor
HV bushings [2]. However for
HVDC wall bushings it has been suggested that uneven wetting from
rain is also
a decisive triggering mechanism for most of the observed
flashovers
[24]. Hence, the determination of capacitive-resistive field
distributions in and around outdoor
HV bushings including volume and
surface resistivities is of significant practical importance.
Electric field calculations in and around
HV bushings with the help
of numerical methods are reported in the literature. Mukherjee and Roy
carried out capacitive field calculation in a capacitor bushing
[5] as well
as in a porcelain bushing [6] by the charge simulation method [7]. Okubo
et al. [8] reported capacitive field analysis of HV bushings by a combi-
nation method, involving charge simulation and finite element method.
Capacitive-resistive field calculation including surface resistance for
a
simple bushing configuration by finite element method was done by An-
dersen
[9]. Applications of finite element method for electric field mod-
eling of
HVDC wall bushings including surface resistance are also pre-
sented
[lo-111.
In recent years the BEM (boundary element method) has evolved into
a powerful tool for electric field calculation
[12-131. In this work BEM
has been applied for capacitive-resistive field calculation including vol-
ume and surface resistance in axi-symmetric systems. As case studies,
two multi-dielectric examples are taken
viz. a porcelain bushing and a
capacitor bushing. In addition to uniform surface resistance, the effects
of non-uniform surface resistance without and
also with volume resis-
tance are studied. The results of these investigations are presented in
this paper.
2 CAPACITIVE-RESISTIVE FIELD
CALCULATION BY BEM
For electric field calculations, it is very important to simulate the
boundaries accurately. The basic idea of the boundary element method
1070-9878/98/ $3.00 0 1998 IEEE

238
Chakravorfi et al.: Capacitive-resistive Fields on HV Bushings
is to divide the electrode or insulator surfaces into a large number of sur-
face elements. On each of these elements, a specific distribution function
for charge is considered, which is calculated by imposing appropriate
boundary conditions.
For capacitive-resistive field calculation the system of equations ob-
tained for both known and floating potential conductor boundaries is
the same as those for capacitive field calculation
[14] with the only differ-
ence that in this case the potentials and charges are complex quantities.
However the system of equations
as obtained for dielectric-dielectric
boundaries is to be modified suitably
to take into account the volume
and surface resistivities, as detailed below.
Ir I I I I I I I1
Porcelain Bushing Configuration
( 4-Dielectric Arrangement )
1 -_ HV Conductor
2 -- Earthed Metal Tank
3 -- Bakelite Insulation -
d 4 -- Transformer Oil
5 -- Porcelain Outer Cover
6 -- Air
All dimensions in meters -
9
I
06 - 6
02p 4
1
OL 1 I I ILJIlJ
0 005 01 015 02 025 03 035 0.4
Figure 1 A typical porcelain bushing configuration.
At any node i on the dielectric-dielectric boundary,
E1Qi) - E&2n(i) = ZS(i)
(1)
where E is the permittivity and ZS (i) is found from the general condi-
tion of the current density vector at the node
i [15] as follows
where
pu is volume resistivity and suffixes 1 and 2 denote dielectrics 1
and 2 respectively
The surface current density term in Equation
(3) may be expanded as
follows
(4)
f
@(i) - @(i - 1) - @(i + 1) - @(2)]
AJs(i) = -
R(i + 1)
where @(i) is the potential of node i, S(i) a small area and R(i) and
R(i + 1) are surface resistances around node i. The method of calcu-
lation of
S(i), R(i), and R(i + 1) are described in [16].
Combining Equations
(l), (3) and (4), they can be written as
a(.; -52) + 2i
(E; +&) En(i) - wS(i)(E; +;)x
1 @(i + 1) cp’(i - 1)
Z(i)
+-=o
EO
I
z = 1, 2 (5)
+
Ex = EOETx - ~
w Pux
where w = a~f, f is the frequency & (i) is the normal component of
electric field intensity at the node
i by charge densities at all the nodes
[12,14], and
Z(i) is the charge density at the node i.
200 1
150
100
50
0
Case-I -
Case-ll -----
Case-Ill
Case-IV
-
Case-VI ...
Case-VI1 ---...
Case-VIII ..-- ...
W X Y
z
Along the specified line wxyz
Figure 2. Stresses along a predetermined line in the critical zone of the
porcelain bushing.
In this paper, axi-symmetric field calculation is done with the help of
two types
of elements, viz. straight line and elliptic arc element, and a
linear basis function is assumed
for the description of charge distribu-
tion along the elements between the nodes.
A complete program based
on the formulations described above has been developed in
C and the
case studies reported here have been carried out using this program.
3 FIELD DISTRIBUTION IN AND
AROUND
A PORCELAIN
BUSHING
Porcelain bushings used in transformers generally consist of four di-
electrics with transformer oil, porcelain and atmospheric air common
to all bushings. The fourth dielectric used
is either bakelite tube or
PVC /paper tape. Figure 1 shows the arrangement of an outdoor porce-
lain bushing fitted with grounded metal tank, which has been analyzed
for capacitive-resistive field distribution in this paper. In this bushing,
bakelite
has been considered as the fourth dielectric. The relative per-
mittivities of bakelite, transformer oil and porcelain have been taken
as 5.5, 2.5 and
6.0, respectively. The metal tank with associated fix-
ing arrangement is assumed to be cylindrical,
so that the whole sys-
tem can be taken as axi-symmetric. For the bushing shown in Figure
1,

IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 5 No. 2, April 1998
ab Porcelain Bushing Configuration
0.8 -
d
Surface
B : A- I-
Surface C : a - o
ky-j
0,3-+y++B 0.2 - I All dimensions in m -
I I I I I
0 002 004 0.06 0.08 0.1 0.12 0 14
120
100
z .
>
: 80
P
- r
2 60
2
z
.- 40
c
a
m UI
- 2
m
tc
20
n
Case1 -
Case II ---
Case Ill
Case VI
CaseVII - -
M N 0 P Q
Along the Bakelite-Oil Boundary
Figure 3. (a) Detailed description of the dielectric surfaces of porcelain
bushing. (b) Stresses along the bakelite-oil boundary
of the porcelain bush-
ing.
the surface lengths are as follows: Surface
A, i.e. bakelite-oil interface is
0.526 m, Surface
B, i.e. porcelain-oil interface 0.609 m and surface C, i.e.
porcelain-air interface - 0.659 m.
In the present work both uniform and non-uniform distributions of
psc, i.e. surface resistivity along the surface C, are considered, while
ps~ and ps~, i.e. surface resistivities along the surfaces A and B,
are considered to be uniform. Volume resistivity is considered only
for transformer oil and is denoted by
pvo. For uniform contamina-
tion of any surface,
ps is taken to be constant along that surface. For
non-uniform contamination of surface
C, pSc is taken to be constant
along the contaminated sections, while
psc = 00 are taken for the
contamination-free sections. Lower values of
psc are considered to be
due to atmospheric and industrial pollution, while lower values of
ps~
and ps~ are considered to be due to deposition of impurities present
and/or produced in transformer oil during use. Lower values of
pvo are
also due to the presence of impurities in the transformer oil. The poten-
tial of the central conductor varies sinusoidally with time at
a frequency
of 50
Hz. The electric stresses are presented in a normalized format, i.e.
Case I -
Case II ---
Case ill
Case VI
Case VI1 - -
60
50
40
30
20
10
0
239
A BC DE F G HI
Along the Porcelain-Oil Boundary
Figure 4. Stresses along the porcelain-oil boundary of the porcelain
bushing.
50
45
40
35
30
25
20
15
10
5
0
on m Ik J ih g fe d c ba
Along the Porcelain-Air
Boundary
Figure 5. Stresses along the porcelain-air boundary of the porcelain
bushing.
Field calculations have been carried out for various combinations
of
surface resistivity distribution along the different surfaces with the vol-
ume resistivity
of transformer oil. Furthermore, these studies have been
carried out
for varying values of surface and volume resistivities. How-
ever only those cases, as detailed below, are reported here for which the
results have been found to be interesting.
1. With infinite surface and volume resistivities, i.e. purely capacitive field
2. pvo = 10' R.m with infinite surface resistivities,
3. uniform pSc = lo7 62 and ps~ = ps~ = pv, = 00,
4. uniform pSc = lo7 0, psa = ps~ = 00 and p,, = lo6 R m,
5. psc = lo7 R in section a to d of Figure 1, while psc = m along the
6. p,c = w, uniform psa = ps~ = lo7 Cl and p,, = 00,
distribution,
rest
of the surface C and p.,~. = ps~ = p,, = 00,

240
Chakravorti et al.: Capacitive-resistive Fields on HV Bushings
7. psc = -,uniformps~ = ps~ = lo7 Rand p,, = lo6 Rmand
8. p,~ = lo7 R in sections a to d, e tog, h to j and k to m of Figure 1, while
p,~ = - along the remaining parts of surface C, ps~ = P,B = 00 and
p,, = lo6 Qm.
Figure
6. Equipotential lines for capacitive field distribution in the case
of porcelain bushing.
Figure
7. Equipotential lines for uniform pollution of porcelain cover
outer surface in the case of porcelain bushing.
4 RESULTS AND DISCUSSION
A line wxyz as specified in Figure 1, is considered for electric stress
calculation, because in this zone the distance between the central con-
ductor and the grounded metal tank is minimum and
also because
three different dielectrics are
in series in this zone between the live and
grounded electrodes. Figure
2 shows the resultant stress E,,, along this
line for different cases
as mentioned earlier. It can be seen that E,,, in
bakelite at the location w
of Figure 1 becomes very high for the cases
2,4 and 8, the highest being for case 8. This abnormal rise in E,,, can
thus be attributed to lower value of
puo. However lower value of pvo
reduces the stresses in transformer oil in this zone. E,,, is maximum
in transformer oil at the location x
of Figure 1 for case 6. As the lower
values of
p,~ and p,~ for case 6 are due to impurities of transformer
oil, a lower value
of pvo may also be taken together with the parame-
ters
of case 6, which then corresponds to case 7. Figure 2 shows that for
case
7 E,,, values are small in transformer oil and the same in bakelite
are much lower
as compared to the cases 2,4 and 8. However there is a
significant rise in
E,,, at the location z of Figure 1, i.e. in the vicinity of
the grounded metal tank, for case
7, the amount of increase being nearly
100% in comparison to E,,, at z for case 6.
Electric stresses also are calculated along all the three surfaces, i.e.
surfaces A, B and C. The detailed description of the dielectric-dielectric
interfaces are shown in Figure 3
(a). Figure 3(b) shows Ere, along the
surface
A, the stresses being calculated on the oil-side of the surface, for
a few significant cases. As in Figure 2, Figure 3(b) also shows that the
maximum
ETes on this surface occurs near the location x of Figure 1 in
section
NO of Figure 3(a) for case 6 Stresses at the location M of Fig-
ure 3(a),
i.e. very close to the central conductor, is maximum for case 2.
For lower values of pvo, ETes values are found to be small in section
NQ of Figure 3(a) of surface A.
E,,, along the surface B for some of the notable cases are shown in
Figure 4, where the stresses are calculated on the oil-side of the surface.
Figure
4 shows that the stresses are higher on this surface in section CG
of Figure
3(a). The maximum stresses are within the range 35 to 45 for
the cases
1 and 3 occurring near location F and also for case 7 occur-
ring near location
D. However the worst E,,, occurs near location E
for case 6. Comparison of stresses for cases 6 and 7 shows that a lower
value of
pvo moderates the stresses along the surface B significantly It
also shows that uniform pollution of surface C causes the highest Eres
on surface B, increasing by -30% in comparison to the corresponding
value for
a purely capacitive field.
0.6r1 I I I I I I I I-,
0.5
0.4
0.3
10
7
Condenser Bushing Configuration
4-Dielectric Arrap ement
with
3 Floating potent^$ Electrodes
1
-*
2 --
3 --
4 -_
5 --
6 --
7 --
8 -_
il
8
. Air
11 AH dimensions in meters
01 -
OLI I I I
0 0 05 0 1 0 15 0.2 0.25 0 3 035 04 0.45 0.5
Figure 8. A typical capacitor bushing configuration
Figure
5 shows the distribution of E,,, along the surface C for the
cases for which the results are
of significance. The stresses as depicted
in Figure
5 are calculated on the air side of the surface. Figure 5 shows
that for capacitive field distribution
Ere3 is maximum at the location o

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 5 No. 2, April 1998 241
of Figure 1 and in the vicinity of the grounded metal tank the stresses
are higher than the other sections of surface
C. For case 3, i.e. with uni-
form pollution of surface
C, the stresses at the tip of the top two insulator
sheds,
viz. locations d and g of Figure 1, get enhanced, the stress at the
tip of the third shed,
viz. location j of Figure 1, remains more or less un-
changed and the stress at the tip of the bottommost shed,
viz. location m
of Figure 1, gets reduced. Further the stresses in section k to
o of surface
C near the grounded metal tank are lower for case 3 compared to case 1.
For case 5, i.e. when the surface C is partially polluted in section a to d
of Figure
1, the stress at the tip of the topmost shed is increased greatly,
but the stresses in section g to
o are nearly the same as those for case
1. However the highest stress occurs for case 8, i.e. when the surface C
is partially polluted in different sections, viz. a to d, e to g, h to j and k
to m of Figure 1. For case 8 very high stresses occur near the locations
e and h, the highest being near the location h, but the stresses near the
grounded metal tank are lower than those for case
1. Analysis of the
results obtained for case 3 and case 4 shows that the stresses along sur-
face
C are not much affected by low volume resistivity of transformer
oil, when surface
C is uniformly polluted. Results are also obtained for
a case when surface C is partially polluted as in case 8, but considering
pvo to be infinite. These results show that the maximum stress of 35.85
occurs near location
m for this case, while the maximum stress for case
8 is 45.1 near location e. In other words, a lower value of pno increases
the stresses on surface
C in the case of partial pollution. A similar effect
has been found also but to
a lesser extent, when surface C is partially
polluted
as in case 5. In such cases, the stress near location d is 30.53 for
pvo = 00 and is 31.45 for pvo = lo6 0.m.
Case-1 -
Case-6 -----
90 *I Case-3 Case-5 ---
85
55 I
50
I I I
k I m n 0
Along the specified line k-o
Figure 9. Stresses along a predetermined line in the critical zone of the
capacitor bushing.
0.55 r I I I , I-
Condenser Bushing Configuration
0.5 -7
045 -
04 -
035 -
0.3 -
025- pw
SurfaceB: A-E
SurfaceG: a-j
0.2 ;J
All Dimensions in meters
015L ' I_
(a) 0 002 004 0.06 008 01 012 014
50 , I
0' 1
U V w XY
(b) Along the Paper-Oil Boundaty
Figure 10. (a) Detailed description of the dielectric surfaces of capacitor
bushing.
@) Stresses along the paper-oil boundary of the capacitor bush-
ing.
around the porcelain bushing.
Two representative field distributions
are shown in Figures 6 and
7. Figure 6 shows the equipotential lines
for purely capacitive field, while Figure 7 shows the same for uniform
pollution of surface
C. The concentration of equipotential lines in Fig-
ure 6 near the bottommost shed of the porcelain cover indicates higher
stresses
in that region for case 1, while similar concentration of equipo-
tential lines in Figure
7 near the top two sheds indicates higher stresses
in the upper section of surface
C for case 3. These observations can be
duly corroborated from Figure
5, where stress distributions along the
surface
C are presented. From Figures 6 and 7, it is also evident that
the pollution of surface
C has very little effect on the field distribution
within the metal tank.
The maximum stresses within each of the four dielectrics are also cal-
culated, the values of which are
as detailed below. Within bakelite, 195.8
at location
w for case 8, within transformer oil 112.1 at location 0 for
case 6, within porcelain 62.63
at location z for case 7 and in air 45.10 at
location e for case
8.
5 FIELD DISTRIBUTION IN AND
AROUND A CAPACITOR
BUSHING
Studies have been carried out also to determine the equipotential
lines for getting
a visual idea about the nature of field distribution in and
A major disadvantage of porcelain bushing is the high degree of
nonlinearity in potential distribution, which gives rise to high electric