Electric field at sharp edge as a criterion for dimensioning condenser-type insulation systems

Abstract

Inside the oil-paper insulation of high voltage condenser-type bushings and instrument transformers, conducting surfaces or capacitive shields have been in use for many years to control electric field distribution. Traditional insulation design methods take into consideration dielectric stresses in axial and radial directions, but experience shows that partial discharges occur in the vicinity of capacitive shield edges and can severely affect the expected life of oil-paper insulation. In this paper, a criterion for dimen-sioning condenser-type insulation systems is presented, based on maximum electric field at sharp edge of capacitive shield. Maximum permitted value of the electric field at the shield's edge was obtained through numerous experimental tests and numerical field calculations based on the finite element method (FEM).

Full text

This is the author’s version of a work that was submitted/accepted for publication in the Electric
Power Systems Research journal in the following source:
Dalibor Filipović-Grčić, Božidar Filipović-Grčić, Miroslav Poljak, “Electric field at sharp
edge as a criterion for dimensioning condenser-type insulation systems”, Electric Power
Systems Research, Volume 152, 2017, Pages 485-492, ISSN 0378-7796,
https://doi.org/10.1016/j.epsr.2017.08.006.
Changes resulting from the publishing process, such as peer review, editing, corrections,
structural formatting, and other quality control mechanisms may not be reflected in this
document. Changes may have been made to this work since it was submitted for publication. A
definitive version was subsequently published in Electric Power Systems Research journal.
Notice: Changes introduced as a result of publishing processes such as copy-editing,
formatting and technical enhancement may not be reflected in this document. For a final
version of this work, please refer to the published source:
URL: http://www.sciencedirect.com/science/article/pii/S0378779617303243

Corresponding author e-mail: bozidar.filipovic-grcic@fer.hr
Electric field at sharp edge as a criterion for dimensioning
condenser-type insulation systems
Dalibor Filipović-Grčić
Končar - Electrical Engineering Institute
Fallerovo šetalište 22, 10000 Zagreb, Croatia; e-mail: dfilipovic@koncar-institut.hr
Božidar Filipović-Grčić
University of Zagreb, Faculty of Electrical Engineering and Computing
Department of Energy and Power Systems
Unska 3, 10000 Zagreb, Croatia; e-mail: bozidar.filipovic-grcic@fer.hr
Miroslav Poljak
Končar - Electrical Industry Inc.
Fallerovo šetalište 22, 10000 Zagreb, Croatia; e-mail: poljak.dd@koncar.hr
ABSTRACT
Inside the oil-paper insulation of high voltage condenser-type bushings and instrument
transformers, conducting surfaces or capacitive shields have been in use for many years
to control electric field distribution. Traditional insulation design methods take into
consideration dielectric stresses in axial and radial directions, but experience shows
that partial discharges occur in the vicinity of capacitive shield edges and can severely
affect the expected life of oil-paper insulation. In this paper, a criterion for
dimensioning condenser-type insulation systems is presented, based on maximum
electric field at sharp edge of capacitive shield. Maximum permitted value of the
electric field at the shield's edge was obtained through numerous experimental tests and
numerical field calculations based on the finite element method (FEM).
Keywords — oil-paper condenser-type insulation; electric field; dielectric stresses;
power transformer bushing; instrument transformers; partial discharges.
1 INTRODUCTION
The most frequent sources of power transformer failures are
attributed to tap changers, bushings, and oil-paper insulation
system which deteriorates mainly due to heat, oxidation, acidity,
and moisture. Bushings are one of the major components causing
forced outages of power transformers [1-2]. According to analyses
in which individual transformer components are ranked with
respect to the number of transformer failures they cause, bushings
are placed at one of the top positions [3]. This clearly shows that
there is a need for improvement of the existing criteria for the
dimensioning of insulation systems, especially in condenser-type
transformer bushings.
Modern high-voltage bushings with oil-paper insulation for
system voltages higher than 52 kV are condenser-type. The
condenser core of a bushing is built up around a central tube that
may or may not be in the current-carrying path. It is wound from
paper and impregnated with transformer oil. Capacitive shields
within oil-paper insulation take the form of coaxial cylinders and
constitute a system of cylindrical capacitors, arranged in such a
way that the electric stress in both radial and axial directions does
not exceed certain critical values. The capacitance between any
adjacent pair of capacitive shields is known as a partial
capacitance and the bushing insulation is made up of a large
number of partial condensers in series. An optimal number of
shields and each shield's dimensions lead to acceptable dielectric
stresses and the most economical design of insulation system [4-5].
In the traditional design, the maximum axial and radial electric
fields in the condenser body should not exceed certain permitted
values [6-9]. This approach does not take into account the
maximum value of electric field at the shield's edge. However, a
real operation experience and laboratory tests indicate that damage
caused by partial discharges frequently occurs at the edges of
capacitive shields [10-13]. Although the amplitudes of such partial
discharges are initially low, their occurrence causes deterioration
of insulation properties, premature aging and finally insulation
breakdown. The reason why electric field at the shield’s edge was
not taken into account, as a criterion for sizing the insulation
system, lies in the fact that it is very difficult to calculate it
accurately, even with the latest software tools, due to unfavourable
ratios between minimum and maximum dimensions of the
simulation model [14]. The ratio of model height to shield

thickness can be several orders of magnitude. For such a model, it
is very difficult to obtain the fine mesh density of finite elements
what improves calculation accuracy.
This paper presents a criterion for dimensioning condenser-type
insulation systems. The proposed criterion is based on a method
developed for more accurate calculation of electric field at shield’s
edge. The maximum electric field at the shield's edge should not
exceed the partial discharge inception stress, which was
determined through numerous laboratory tests on samples that
represent bushing insulation [15].
2 RADIAL AND AXIAL ELECTRIC FIELDS AS
CRITERIA FOR DIMENSIONING
CONDENSER-TYPE INSULATION
In traditional approach, capacitive shields within oil-paper
insulation are arranged in such a way that the electric stress in the
radial direction does not exceed a certain permitted value E
r
(typically 13 kV/mm) and so that the axial stress does not exceed a
value E
aa
(typically 0.5 kV/mm) for the air side, and E
ao
(typically
1.3 kV/mm) for the oil side of the bushing [6]. Axial stress is given
as the voltage between adjacent shields divided by the axial
distance between the ends of the shields. Condenser bushing
details are shown in Fig. 1.
Figure 1. Condenser bushing details
The central tube on which the condenser body is wound is at
100 % of the potential, while the last outer shield is grounded.
Fig. 1 shows shields numbered from 1 to n, their lengths l, and
radiuses r at which they are inserted in the insulation. a
represents the axial spacing between the shields from the air
side of the bushing while c represents the axial spacing
between the shields from the oil side.
The number of shields, and thus of partial condensers, is
chosen in such a way that the test voltage of each condenser
does not exceed a specific value. All things considered, the
task is to determine the physical dimensions of shields which
give the most economical design. Essentially, the design of
bushings may be based upon several methods, but the most
favourable design is obtained by considering equal partial
capacitances and equal axial steps between shields, separately
for air and oil sides. This method gives a linear voltage
distribution in the axial direction and this is important since
dielectric strength in the axial direction is significantly less
than strength in the radial direction.
As the axial spacing between shields at both air and oil sides
are constant, with a linear distribution of potential, axial
stresses at the air and the oil side are uniform. However, the
distribution of radial electric field is not linear and has a saddle
shape with equal maximum radial field between the central
tube and the first shield, and also between the second last and
the last shield, while radial field between the other shields are
lower. A typical distribution of the radial field E
r
and axial
field E
ao
at the oil side is shown in Fig. 2 [15].
Figure 2. A typical distribution of the radial and axial electric field at the oil
side of the bushing
Axial distance a between the ends of adjacent shields on the
air side of the bushing is determined as:
aa
En
U
a⋅
=
, (1)
where U represents the applied voltage and n the number of
shields. Similarly, the axial distance c between the ends of
adjacent shields on the oil side of the bushing is determined as:
ao
En
U
c⋅
=
. (2)
Maximum radial field between shields i-1 and i is determined
from the expression:
1i
i
1i
i
ri
ln
−
−
=
r
r
r
U
E
, (3)
where U
i
is the voltage drop between the shields i-1 and i.
From expression (3) it follows:

1i
i
ri1i
i
ln
−−
=r
r
Er
U
. (4)
Sum of expression (4) for i=1…n-1 gives:
0
1n
1n
1i 1i
i
1n
1i ri1i
i
lnln r
r
r
r
Er
U
−
−
=−
−
=−
==
∑∑
. (5)
Expression (5) can be written as:
∑
−
=−
−
=−
1n
2i 1i
i
0
1
0
1n
lnlnln r
r
r
r
r
r
. (6)
Linear distribution of potential across the shields is obtained if
the capacitances between the shields are equal:
1n
n
n
1
2
2
0
1
1
ln
2
...
ln
2
ln
2
−
πε
==
πε
=
πε
r
r
l
r
r
l
r
r
l
. (7)
From the equality of capacitance between the first shield and
the central tube to all other capacitances it follows:
0
1
1
i
1i
i
lnln
r
r
l
l
r
r=
−
. (8)
Substituting (7) with (8) gives:
0
1
1n
2i 1
i
0
1
0
1n
lnlnln r
r
l
l
r
r
r
r







=−
∑
−
=
−
. (9)
Expression (9) can be written as:
∑
−
=
−
=
1n
1i 1
i
0
1
0
1n
lnln l
l
r
r
r
r
. (10)
In the case of uniform distribution of axial fields, radial
distribution, as mentioned above, may not be linear, but has a
saddle shape. In this case, the most favourable situation is if
the values of the radial field for the first and the last capacitor
are equal:
1n
n
1n
n
0
1
0
1
lnln
−
−
=
r
r
r
U
r
r
r
U
. (11)
As the potential distribution is linear or voltages across
capacitors are equal, from the expression (11) it follows:
0
1
1n
n
1n
0
ln
ln
r
r
r
r
r
r
−
−
=
. (12)
If the right side of (12) is substituted with (8) for i=n then the
following expression is obtained:
α==
−1
n
1n
0
l
l
r
r
, (13)
where the parameter α represents the ratio of the length of the
last and the first shield. From the expressions (9) and (13) it
follows:
α
=
∑
−
=
1
lnln
1n
1i 1
i
0
1
l
l
r
r
. (14)
A parameter λ is introduced that depends on the applied
voltage U, the diameter of the central tube r
0
and a given radial
field E
r
:
r0
2Er
U
=λ
. (15)
Since the radial field is highest in the first and the last
capacitor, from (15) and (3) it follows:
nr
r
λ
=2
ln
0
1
. (16)
Inserting expression (16) into (14) gives:
α=
λ
−
∑
−
=
ln
2
1n
1i
i
1
l
nl
. (17)
The length of the last shield l
n
can be expressed by the length
of the first shield l
1
, the number of shields n and the sum of
axial distances from the air side a, and the oil side c:
(
)
(
)
canll +−−= 1
1n
. (18)
From (18), for a+c=∆, it follows:
1
n1
−
−
=∆
n
ll
. (19)
The sum of the lengths of all shields except the last one may
be expressed by the length of the first shield, the sum of axial
distances and the number of shields:
( ) ( ) ( )( )
∆−−++∆−+∆−+=
∑
−
=
2...2
11
1n
1i
11i
nlllll
(20)
( ) ( )( )
∑
−
=
−+++∆−−=
1n
1i
1i
2...211 nlnl
(21)
( )
(
)
(
)
∑
−
=
−−
∆−−=
1n
1i
1i
2
12
1nn
lnl
(22)
( )
(
)
∑
−
=
∆−−
−=
1n
1i
1
i
2
22
1nl
nl
. (23)
Inserting expression (19) into (23) gives:
(
)
∑
−
=
−+
=
1n
1i
n1
i
2
2lnnl
l
. (24)
Inserting expression (24) into (17) gives:
( )
nn
n
+−
−=
α
α
λ
2
ln
. (25)
In the expression (25) the only unknown parameter α
represents the ratio of the lengths of the last and the first
shield. This equation has no analytical solution and it can be
solved only numerically. Once parameter α is determined, the
length of the first shield can be obtained from (19), for l
n
= αl
1
:
α
−
−
∆=
1
1
1
n
l
. (26)
Afterwards, the lengths of all other shields can be determined
from:
(
)
∆−−= 1
1i
ill
. (27)
Finally, when the lengths of all shields are determined, their
radiuses, starting from the first, are calculated from the

following recursive expression that is obtained after inserting
expression (16) into (8):
1
i
2
1ii
nl
l
err
λ
−
=
. (28)
So, for the given input parameters from the expressions (1), (2)
and (15) axial distances from the air and oil sides are
determined. Afterwards, the numerical solution α of the
equation (25) is obtained, which gives the ratio of the lengths
of the last and the first shield. With the known parameters of
the equations (26)-(28), the lengths and radiuses of all shields
are determined that provide an ideal voltage distribution.
3 EXPERIMENTAL TESTING OF
INSULATION MODEL
3.1 TEST SETUP
The model that represents the condenser-type insulation consists
of three capacitive shields placed inside oil-paper insulation that is
wound around an aluminium tube with diameter 49.5 mm (Fig. 3).
The thickness of the insulation between shields and axial spacing
correspond to those used in real bushings, and the thickness of the
shield is 20 µm.
Three samples were dried along with real bushings in the
production. They were subjected to standard vacuum drying
with hot air for 7 days followed by impregnation with dried
and degassed oil. A settling time of 7 days was provided
before the commencement of HV tests.
The test voltage levels were chosen to cause levels with low,
medium and high probabilities of partial discharges. Voltage
was applied on the central tube and the outermost shield was
earthed. The voltage on each sample was maintained until
partial discharge inception occurred or up to one hour in the
event of no discharges. If the partial discharges occurred at a
certain voltage, the next test value was one level lower or, in
case of no occurrence, one level higher. This test procedure is
classified as non-destructive and, when the sample is given a
suitable rest time after the test, it can be considered that
insulation properties return to the initial condition [16]. In this
way, many tests can be repeated on the same sample.
3.2 TEST RESULTS
For each voltage level, test results (given in Table 1) consist
of a series of values of the time elapsed until partial discharge
inception. These values are grouped into five time intervals.
The number of partial discharge inceptions N
i
for each interval
expressed as a percentage of the total number of tests N at that
voltage level gives the probability P of partial discharge
inception in percentage terms.
constt
)(
=
=
UfP . (29)
The results in Table 1 can be presented in the form of a
family of curves. Partial discharge inception probability can be
accurately represented using the Weibull distribution with a
lower limit equal to zero:
)(
1
βα
−
−=
tAU
eP , (30)
where A, α and β are constants. The experimental results of
Table 1 are plotted on a special chart having the P scale
proportional to ln(ln(1/(1-P))), and the U scale proportional to
ln(U). Using the method of least squares a family of almost
parallel straight lines is defined as shown in Fig. 4. The insulation
system with very low probability of partial discharge inception
during a 1 minute power-frequency voltage withstand test can
be considered as highly reliable. If the straight line for time
interval t<1 min is extrapolated, then the probability of partial
discharge inception value of 1 % corresponds to a voltage
value of 49.9 kV.
Aluminium tube
Paper Shields
295 mm
265 mm
235 mm
110 mm
125 mm
140 mm
500 mm
20 mm
Φ 60 mm
Φ 49.5 mm
Aluminium tube
Paper Shields
295 mm
265 mm
235 mm
110 mm
125 mm
140 mm
500 mm
20 mm
Φ 60 mm
Φ 49.5 mm
Figure 3. Sample of insulation
Table 1. Results obtained on samples
U (kV) N t <1 min t <5 min t <10 min t <30 min t <60 min
N
i
P (%) N
i
P (%) N
i
P (%) N
i
P (%) N
i
P (%)
56 36 2 5.56 3 8.33 4 11.11 5 13.89 6 16.67
60 56 10 17.86 16 28.57 22 39.29 26 46.43 30 53.57
64 34 12 35.29 17 50 20 58.82 24 70.59 26 76.47

P /%
U /kV
60 min
30 min
10 min
3 min
1 min
99
90
50
10
5
1
56
58
60
62
64
Figure 4. Weibull curves showing probability of partial discharge inception
Finally, each sample was subjected to various kinds of
increasing dielectric stress until breakdown occurred. The first
sample was subjected to a lightning impulse voltage (LI), the
second to a switching impulse voltage (SI), and the third to AC
voltage. The breakdown voltage values are given in Table 2.
Table 2. Breakdown voltage values
Sample no.
1
2
3
Type of breakdown voltage LI SI AC
U (kV) 201.2 171.6 77.0
Fig. 5 shows insulation breakdown pathway in sample no. 2.
Figure 5. Sample no. 2 – insulation breakdown pathway
It was found that in all three samples a critical place where a
breakdown occurs is from the shield’s edge towards the central
tube. This proves the fact that designing process of the
insulation system should take into account the maximum
electric field value on the shield’s edge, which is discussed in
the following chapter.
4
METHOD
FOR
CALCULATION
OF
ELECTRIC
FIELD
AT
SHIELD’S
EDGE
The numerical calculation has been performed using the FEM-
based software ElecNet. Owing to the axial symmetry present in
this part of the insulation system, ElecNet's 2D Axially Symmetric
Static solver was used. The calculation model, with relative
permittivity of oil 2.2 and relative permittivity of oil-impregnated
paper 3.6, is shown in Fig. 6 and it corresponds to experimental
samples (Fig. 3).
Figure 6. Model of insulation for numerical calculation
A voltage was applied on the central tube while two inner
shields are represented as floating electrodes at free potential. The
peak value of electric field occurs at the place with the highest
potential gradient. That place is the edge of the last (outer) shield
which is grounded. Since the shields are very thin, their thickness
compared to the largest model dimension yields an order of four.
Therefore, a different approach for calculation of electric field on
shield’s edge was applied that consists of two steps.
In the first step, a large-scale model with sufficiently fine mesh
is used to determine the potential distribution near the shield's edge
(Fig. 7).
Selected
equipotential
line
Figure 7. Method for calculation of electric field strength at the edge of shield – selection of equipotential line

An equipotential line near the shield’s edge is selected to represent
one of the boundaries of a fine scaled model for calculation of
electric field at the shield’s edge (Fig. 8). Post-processing software
analyses large scale model field and extracts points that lie on the
equipotential line with tolerance ±1%. Other boundaries are
electric field lines. Software extracts points that lie on electric field
lines by moving in the direction of highest field.
Figure 8. Selected borders of a new scaled model for calculation of electric
field strength around shield’s edge
In the second step, a fine scaled model is formed which contains
the shield’s edge and the surrounding insulation. In this model, it is
possible to obtain a fine mesh of finite elements and thus to
calculate electric field at shield’s edge with sufficient accuracy.
The result of numerical calculation for the model shown in Fig.
6 is shown in Fig. 9. The maximum value of electric field
0.25 kV/mm was obtained at the last shield’s edge which is
grounded when 0.1 kV was applied on the central tube. The
value of the electric field for any other value of the applied
voltage U (kV) can be determined as:
)kV/mm(
1
.
0
25.0
s
U
E=
. (31)
When related to experimental test results, the value of the
electric field on the shield’s edge with a low probability of partial
discharge occurrence for certain time intervals can be calculated.
For example, when the applied voltage is 49.9 kV (t<1 min,
P=1%) the observed electric field value reaches almost 125
kV/mm and is established as a criterion for dielectric field stress at
the shield’s edge. It should be noted that field values at the edge
of the shields should be lower than the proposed 125 kV/mm.
The reason for this is that the physical mechanism of partial
discharges is not sufficiently known and may change with time
and shield arrangement. Also, the mathematical model used
may not be valid for extended time ranges and the effect of
temperature and moisture on partial discharge occurrence was
not investigated. Furthermore, stressed insulation volume in
considered models is smaller than the one in actual insulation
systems. Therefore, a safety margin must be taken into
consideration and the permissible electric field should be
lower than 100 kV/mm.
Edge of the outer
grounded shield
Figure 9. Distribution of electric field strength and equipotential lines
5 NEW
ANALYTICAL
EXPRESSION
FOR
CALCULATION
OF
ELECTRIC
FIELD
AT
SHIELD’S
EDGE
In the previous section the procedure for calculating electric
field on the edge of the shield was described. However, inside
the condenser-type bushing there are many shields and it
would be very time consuming to perform that procedure on
each of them. Therefore, an analytical expression for electric
field at the shield’s edge was derived. Numerical field
calculations were performed in order to obtain the relationship
between electric field value at the edge of the shield and the
thickness of insulation between two adjacent shields, axial
distance between edges of two adjacent shields and the
thickness of the shield itself.
At first, the influence of insulation thickness d (radial
distance) between two adjacent shields and thickness d
s
of the
shield itself were analysed on a model shown in Fig. 10. The
model consists of a metal tube with a radius r
0
to which a
voltage is applied and a grounded shield with a radius r
1
.
Figure 10. Model for determining the influence of insulation and shield’s
thickness on the electric field value at the edge of the shield

Four different thicknesses of the shield (20, 50, 100 and 140
µm) were considered as well as ten different thicknesses of
insulation. The influence of insulation thickness and shield’s
thickness on the electric field value at the edge of the shield is
shown in Fig. 11.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.5 1 1.5 2 2.5
E
s
(kV/mm)
d(mm)
20 µm
50 µm
100 µm
140 µm
Figure 11. Influence of insulation thickness and shield’s thickness on the
electric field value at the edge of the shield for a voltage of 100 V (the lines
are fitted according to expression (32))
After the fitting of results, it is shown that these two parameters
affect the field value according to the following expression:
2
1s
K
dKE
−
=
. (32)
K
1
is a parameter proportional to the voltage between two adjacent
shields and it decreases as the thickness of the shield is increased:
47.0
s1
12.0
−
=dK
. (33)
K
2
is a parameter which increases linearly with the thickness of the
shield:
51.049.0
s2
+
=
dK
. (34)
Expression (32) can now be used to obtain the electric field
value at the shield’s edge.
The influence of axial distance a between the edges of two
adjacent shields on the electric field value at the edge of the shield,
while all other dimensions remained constant, was analysed using
the model shown in Fig. 12 which consists of two shields.
Figure 12. Model for determining the influence of axial distance between
edges of two adjacent shields on the electric field value at the edge of the
shield
A voltage was applied
on the inner shield with a radius r
1
,
while the outer shield with a radius r
2
was grounded. Electric
field was calculated at the edge of the grounded shield. The
results showed that in actual design the influence of axial distance
between the edges of two adjacent shields on the electric field
value at the edge of the shield can be neglected. This statement is
valid only when axial distances are significantly larger than radial
distances, which is normally the case in practice.
6 APPLICATION
OF
A
NEW
CRITERION
FOR
DIMENSIONING
OF
CONDENSER-TYPE
INSULATION
SYSTEM
A new criterion for dimensioning condenser-type insulation
systems, which is based on maximum electric field at sharp
edge of capacitive shield, was applied in the case of
transformer bushing with highest voltage for equipment
U
m
=245 kV. Typically, the number of shields is obtained by
dividing the AC withstand voltage in kV with number between
10 and 15, meaning that one shield is added for each 10 to 15
kV of AC withstand voltage. AC withstand voltage for
transformer bushing with U
m
=245 kV is 506 kV, so the
selected number of shields is 40.
First, traditional approach was used where capacitive shields
within oil-paper insulation were arranged in such a way that
the electric stress in radial direction did not exceed 13 kV/mm
and axial stress did not exceed a value 0.5 kV/mm for the air
side, and 1.3 kV/mm for the oil side of the bushing. After that,
electric field at the shields edges was calculated with (32).
Calculated electric field in the radial direction E
r
and electric
field at the shield’s edge E
s
as a function of shield’s number
are shown in Figs. 13 and 14.
In traditional approach, maximum value of E
r
does not
exceed 13 kV/mm, while maximum value of E
s
is 96.5 kV/mm.
This value is lower than the proposed critical value of 100
kV/mm. By applying a new criterion, maximum value of E
s
is
limited to 100 kV/mm, what caused E
r
to rise above 13 kV/mm
and reach 13.9 kV/mm.
0 5 10 15 20 25 30 35 40
10.5
11
11.5
12
12.5
13
13.5
14
Shield's number
E
r
(kV/mm)
Traditional approach
New criterion
Figure 13. Electric field in the radial direction as a function of shield’s
number

0 5 10 15 20 25 30 35 40
86
88
90
92
94
96
98
100
Shield's number
E
s
(kV/mm)
Traditional approach
New criterion
Figure 14. Electric field at the shield’s edge as a function of shield’s number
Fig. 15 shows geometrical arrangement of shields within the
insulation system obtained by traditional approach and the new
criterion. As can be seen from Fig. 15, the dimensions of the
insulation system were reduced when a new criterion was
applied. In the particular case, the volume of paper insulation
was reduced by 7.3 %.
60 70 80 90 100 110 120 130 140 150
0
500
1000
1500
2000
2500
r
(mm)
l
(mm)
Traditional approach
New criterion
Figure 15. Geometrical arrangement of shields within the insulation system
obtained by traditional approach and the new criterion
7 CONCLUSION
A new criterion for dimensioning of condenser-type
insulation systems is presented which is based on maximum
electric field strength at sharp edge of capacitive shield. The
maximum electric field strength at the shield's edge should not
exceed the partial discharge inception stress, which was
determined through numerous laboratory tests on samples that
represent bushing insulation. A method for more accurate
calculation of electric field at shield’s edge is proposed based
on finite element method.
Since an insulation system of the condenser-type bushing
contains many shields, it would be very time consuming to
perform calculations of electric field at shield’s edge based on
finite element method. Therefore, an analytical expression for
calculation of electric field at the shield’s edge was derived
which has been applied in the development of insulation system
for HV transformer bushings with highest voltage
U
m
=245 kV. The volume of the transformer bushing insulation
system obtained with the new criterion, which is based on
maximum electric field at sharp edge of capacitive shield, was
reduced by 7.3 % compared to traditional approach, which is
based on electric fields in the radial and axial direction. The
bushing successfully passed all routine and type tests in
accordance with [17].
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th
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Dalibor Filipović-Grčić was born in Sinj, Croatia, in 1980. He received the
Ph.D. degree in electrical engineering and computing from the University of
Zagreb, Croatia, in 2010. Currently, he is the Head of the High-Voltage
Laboratory, Transformer Department, Končar Electrical Engineering Institute,
Zagreb. His areas of interest include high-voltage test and measuring
techniques, instrument and power transformers, and insulation systems
optimization. Dr. Filipović-Grčić is a member of the technical committees TC
E 38 Instrument Transformers and TC E 42 High Voltage Test Techniques.
Božidar Filipović-Grčić (S’10–M’13) was born in Sinj, Croatia, in 1983. He
received the B.Sc. and Ph.D. degrees in electrical engineering and computing
from the University of Zagreb, Zagreb, Croatia, in 2007 and 2013,
respectively. Currently, he is with the Faculty of Electrical Engineering and
Computing (Department of Energy and Power Systems), University of
Zagreb. He is the Head of Quality in the High Voltage Laboratory. His areas
of interest include power system transients, insulation coordination, and high-
voltage engineering. Dr. Filipović-Grčić is a member of the CIGRÉ Study
Committees A3 – High Voltage Equipment and C4 – System Technical
Performance.
Miroslav Poljak was born in Sinj, Croatia, in 1955. He received his M.Sc.
and Ph.D. degrees in electrical engineering from the University of Zagreb,
Faculty of Electrical Engineering and Computing in 1988 and 2006,
respectively. Since 1978 he has been working in Končar – Group on research
and development of instrument transformers. Currently, he is Member of the
Managing Board of Končar-Electrical Industry Inc. His research activity is
focused on computation and analysis of transient performance of instrument
transformers, high-voltage tests, diagnostics of power and instrument
transformers. He is Chairman of National technical committees TC E 38
Instrument Transformers and a member of the CIGRÉ Study Committees A3
– High Voltage Equipment.