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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.

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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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W. Zaengl, “Dielectric Response Methods for Diagnostics of Power

Transformers”, CIGRE Technical Brochure no. 254 - Report of the Task

Force D1.01.09, Paris, 2002.

[2] N. Hashemnia, A. Abu-Siada, S. Islam, “Detection of power transformer

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[3] A. Mikulecky, Z. Stih, “Influence of temperature, moisture content and

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[4] E. Kuffel, W.S. Zaengl, J. Kuffel, High Voltage Engineering:

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[5] V. Bego, “Instrument Transformers”, Školska knjiga, Zagreb, 1977.

[6] J. A. Güemes, M. Postigo, A. Ibero, “Influence of Leader Shields in the

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[7] J. A. Güemes, M. Postigo, F.E. Hernando, “Influence of Leader Shields

in the Electric Field Distribution in Bushings”, Conference Record of

the IEEE Industry Applications Conference, Vol. I, Rome, Italy, 2000,

pp. 698-703.

[8] E. Lesniewska, “The Use of 3-D Electric Field Analysis and the

Analytical Approach for Improvement of a Combined Instrument

Transformer Insulation System”, IEEE Transaction on Magnetics,

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Main Insulation of HV Instrument Transformers”, International

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th

Croatian CIGRÉ Session, Cavtat, Croatia, 2005.

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on Solid Dielectrics (ICSD), Bologna, 2013, pp. 960-962.

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[16] S. Yakov, “Volt-time Relationships for PD Inception in Oil Paper

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bushings for alternating voltages above 1000 V, July 2008.

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.