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On Electric Stresses at Wedge-shaped Oil Gaps in

Power Transformers with Application to Surface

Discharge and Breakdown

H.-Z. Ding (1), Z. D. Wang (1) and P. Jarman (2)(1) University of Manchester, School of Electrical and Electronic Engineering

P. O. Box 88, Sackville Street, Manchester M60 1QD, UK

(2) National Grid, NG House, Warwick Technology Park, Warwick CV34 6DA, UK

Abstract- The problem of a high-voltage applied to a wedge-

shaped oil gap in power transformers is considered as far as

induced distortions and tangential electric stresses are concerned.

Near-tip distortions and electric stress concentration occur due to

the essentially difference in the relative permittivity between the

insulating oil and the pressboard. When the magnitude of

tangential electric stress intensity reaches a critical threshold

value, surface discharge and breakdown occurs at the

oil/pressboard interface. In this work, a simplified computation

model is developed for the quantitative analysis of thedistribution of electric stress and the breakdown electric field

strength in the wedge-shaped oil gap in power transformers. The

detailed computation results on the effects of pressboard

permittivity and thickness on the surface discharge inception

voltage are presented. It shows that the surface discharge

inception voltage is a function of pressboard permittivity and

thickness; and the value of surface discharge inception voltage

decreases with increasing dielectric permittivity.

I. INTRODUCTION

Surface discharge and breakdown is a phenomenon thatcommonly occurs in the composite oil-pressboard insulation

system in oil-filled power transformers [1-6], and likely one of

the most dangerous failure modes that typically results in a

catastrophic failure of power transformer at normal operating

conditions [7,8]. The problem comes from the design of the

high voltage insulation structure of oil-filled power

transformers, where the withstand and the breakdown

strengths of the coil section of oil-filled transformers are

dominated by the partial discharge inception voltage of the

wedge-shaped oil gaps that, as shown in Fig. 1, are usually

made of the paper insulated conductors, mineral insulating oil

and the pressboard barriers. Due to the essentially difference

in the relative permittivity between the oil and the pressboard

which causes the electric field stress concentration on the

insulating oil gap, the wedge-shaped oil gaps are in fact the

insulating weak parts in transformers [1,3,5]. When the partial

discharges are caused by various factors within the wedge-

shaped oil gap, these discharges will develop onto the

oil/pressboard interface to initiate surface discharge under AC

voltage condition. Such a phenomenon in some cases occurs

continuously and causes deterioration of pressboard surface,

which ultimately results in failure of transformer insulation

system. In practical insulation system, however, this is a

progressive phenomenon which may not be noticed during the

early stages of its occurrence due to its low magnitude.

In order to explore the quantitative description for surface

discharge occurrence and development on the pressboard

surface in oil, one needs to know something of the distribution

of electric stress and the breakdown electric field strength in

the wedge-shaped oil gap. Very little has been published with

regard to the surface discharge characteristics of pressboard intransformer mineral oil. This may be because this topic almost

exclusively involves very inhomogeneous stresses, and a

rigorous analysis of the electric stress distribution in the

wedge-shaped oil gap and particularly the tangential electric

stress induced at the oil/pressboard interfaces should be based

on nonlinear field theories. However, it is insightful to proceed

with simpler calculations based on a quasi-uniform field in a

narrow oil gap. This paper will attempt to show that a

simplified computation analysis of the electric stress

distribution at wedge-shaped oil gap can lead to a quantitative

prediction of the relationship between the surface discharge

inception voltage and the dielectric permittivity of the

surrounding medium. The evidence for the validity of thisrelationship is discussed briefly.

II. THE MODELS

A. Determining the wedge-shaped oil gap length

Without loss of generality, a partially sphere to partially

sphere brass electrode system is selected for illustrating the

electric stress analysis and wedge-shaped oil gap length

calculation. A cross-section of the tested electrode geometry

and pressboard arrangement that is used in this study is shown

in Fig. 2. The oil gap length in the wedge-shaped oil gap can

be considered as the length ROW in the radical direction from

the surface of the high-voltage electrode, and a simple

mathematical computation gives

= 1

cos

1

RROW (1)

Where 25=R mm is the radius of spherically-capped

electrodes, and is the polar angle on the spherically-capped

electrode counted from the symmetry axis.

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Fig.1. Schematic description of the cross section of disc type high voltage

windings and its insulating structure

B. Electric stress distribution within the wedge-shaped oil gap

Consider first the electric stress distribution in an oil gaponly between two conductive spheres of the same radius. For a

quasi-uniform field in a narrow oil gap between two spherical

electrodes, the electric stress distribution on the electrode

surface near the symmetry axis can be calculatedapproximately by [9]

)cos1(2 +

Rd

VEoil (2)

Where V is the applied AC voltage, d is the oil gap length

along an axis between electrodes, R and are the same aspreviously noted.

Then, with pressboard inserted between two spherical

electrodes, the electric stress in the wedge-shaped oil gap will be redistributed. Numerical computations on electric field

behavior at a triple junction in composite dielectric

arrangements have shown that near and at the point of contact

between the electrode and the pressboard, the electric field

stress can be expressed approximately as [10]

( ) ( )( ))cos1(22

1

2

1,

+

+=

+

Rd

VEE ssoil

sspboil (3)

where oilpbs = is the relative permittivity.

C. Determining the breakdown electric field strengthdistribution within the wedge-shaped oil gap

The relationship between the oil gap distance d (mm) and

the breakdown electric stress BE (kV/mm) in the oil gap can

be experimentally determined as follows [11]

237.0784.34 = dEB (4)

Assuming that (4) is still valid for the relationship between the breakdown field strength and the gap length in the wedge-

shaped oil gap. Substituting (1) into (4) derives

237.0

, 1cos

1221.16

=

OWBE (5)

This is the breakdown electric field strength equation in the

wedge-shaped oil gap.

III. THE RESULTS

A. Electric stress and strength distributions within the wedge-

shaped oil gap

Figs. 3-5 show the electric stress distribution curves and the

strength curve of the wedge-shaped oil gap as a function of the

polar angle on the spherically-capped electrode counted from

the symmetry axis (equivalently the oil gap width), for three

different pressboard thicknesses of 3.0, 1.8 and 1.5 mm,

respectively.

Partial breakdown of the wedge-shaped oil gap can be

considered as occurring when the electric stress is higher than

the strength of the oil. As a result, for example in Fig. 3, for

applied AC voltages less than 54 kV, the strength of the oil is

higher than the stress, and so dielectric breakdown of the

wedge-shaped oil gap does not occur. When the applied AC

voltage is increased to 54 kV, both the stress and the strength

curves intersect for the first time at 2.11= and E = 41.16

kV/mm, i.e. at this contact point the electric field stress is

equal to the strength of the oil, so that the first partialbreakdown of the oil gap occurs here. The applied AC voltage

value of 54 kV can therefore be viewed as the estimated

inception voltage for the occurrence of surface discharges at

the oil and the pressboard interface for pressboard thickness of

3.0 mm. Further, if the magnitude of tangential component of

electric field stress that results in surface discharge occurrence

(due to the wedge-shaped oil gap breakdown) could be

assumed as a criterion of dielectric surface strength of

pressboard, then the magnitude of tangential component of

R=25mm

A

Pressboard

Mineral oil

HV

Earth electrode

= 1

cos

1

RRow

pb

Fig. 2. Electric stress analysis and oil gap length

computation model

Pressboard

Wedge-shaped

oil gap

Coil

Insulating paper

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electric stress could be estimated in terms of the polar angle2.11= and E= 41.16 kV/mm as 11.8=tE kV/mm.

In the same way, the estimated inception voltage for the

occurrence of surface discharges for both 1.8 and 1.5 mm

thicknesses of pressboard can be found 36.5 kV and 31.8 kV;

and the corresponding tangential electric stress is 7.16 and

6.82 kV/mm, respectively. The calculated results of electric

stresses for occurrence of surface discharges are summarizedin Table 1. It is interesting to note that these calculated

tangential electric stresses are in good agreement with the

reported data by Sokolov who claimed that surface discharge

could occur subjected to an electric stress of 6.5-12.5 kV/mm

on condition if for virgin dry and clean insulation, and ratio of

average and maximum field intensity in oil gap is 0.4-0.5 or

less [7, 8].

0 5 10 15 200

20

40

60

80Electric breakdown strength in the oil gap

20 kV

30 kV

70 kV

60 kV

54 kV

50 kV

40 kV

(11.2o

, 41.16 kV/mm)

Electricstress(kV/mm

)

Angle (degree)

Fig.3. Electric stress and strength in the wedge-shaped oil gap for mineral oilwith 3 mm thick virgin pressboard (oil = 2.2, pb = 4.4)

0 5 10 15 200

20

40

60

80

25 kV

Electric breakdown strength in the oil gap

20 kV

40 kV

36.5 kV

30 kV

(8.8o, 46.25 kV/mm)

Elec

tricstress(kV/mm)

Angle (degree)

Fig.4. Electric stress and strength in the wedge-shaped oil gap for mineral oil

with 1.8 mm thick virgin pressboard (oil = 2.2, pb = 4.4)

TABLE 1

CALCULATED ELECTRIC STRESSES FORTHE OCCURRENCE OF SURFACEDISCHARGE AT THE PRESSBOARD SURFACE

Pressboard thickness (mm) 3.0 1.8 1.5

Oil gap breakdown voltage (kV) 54 36.5 31.8

Polar angle (, degree) 11.2 8.8 8.1

E (kV/mm) 41.16 46.25 47.92

Et = E * tan() (kV/mm) 8.11 7.16 6.82

0 5 10 15 200

20

40

60

8040 kV

35 kV

20 kV

30 kV

Electric breakdown strength in the oil gap

31.8 kV

25 kV

(8.1o, 47.92 kV/mm)

Electricstress(kV/mm)

Angle (degree)

Fig.5. Electric stress and strength in the wedge-shaped oil gap for mineral oil

with 1.5 mm thick virgin pressboard (oil = 2.2, pb = 4.4)

3.0 3.5 4.0 4.5 5.0 5.5 6.00

20

40

60

80

100

Surfacedischargeinceptionvoltage(kV)

Relative permittivity of pressboard, pb

Pressboard thickness

3.0 mm

1.8 mm

1.5 mm

Fig.6. Calculated values for the surface discharge inception voltage as a

function of pressboard permittivity and thickness (oil = 2.2)

B. Effect of pressboard permittivity and thickness on thesurface discharge inception voltage

Fig. 6 summarizes the calculated values for the surface

discharge inception voltage as a function of pressboard

permittivity and thickness, for dry and clean mineral oil with

relative permittivity ofoil = 2.2. It is evident that the surface

discharge inception voltage decreases with increasing

dielectric permittivity of the pressboard. This finally leads to

the possibility of comparing a theoretically determined surface

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discharge inception voltage with the individual experimentally

measurable values and their mean values.

IV. VERIFICATION OF MAXIMUM ELECTRIC STRESS SITE

BY SIMULATION

The distribution of the electric field stress between the tested

partially sphere electrodes has been simulated using the FEM

simulation package-OPERA-3D. Figs. 7 and 8 show simulatedequi-potential lines and electric stress distribution between

electrodes, respectively. It has been found that the maximum

electric stress occurs at the site of the polar angle 63.7=

for 1.8 mm thick pressboard, and 15.11= for 3.0 mm

thick pressboard. The good agreement between the 3-D FEM

simulated results and the theoretically calculated values (see

Table 1) on the maximum electric stress site provides evidence

for the validity of the proposed simpler modeling approach.

Fig.7. Simulated equi-potential lines between partially sphere electrodes

having a pressboard. High potential = 40kV (pink conductor), low potential

= 0 (blue conductor), and pressboard thickness = 1.8mm

Fig.8. Simulated electric stress distribution showing the electrically stressedwedge-shaped oil gaps between the electrode and the pressboard surface

V. CONCLUSIONS

This study has focused on electric stresses at wedge-shaped

oil gaps in power transformers with application to surface

discharge and breakdown. The findings are summarized as

follows:

(1) The breakdown electric field strength equation in the

wedge-shaped oil gap can be expressed as237.0

, 1cos

1221.16

=

OWBE .

(2) The surface discharge inception voltage in the wedge-shaped oil gap in power transformers depends on both the

dielectric permittivity and thickness. For dry and clean oil

and pressboard (oil = 2.2, pb = 4.4), it has been found that

surface discharge will occur once the tangential electric

stress being larger than 6.82 kV/mm for 1.5 mm

pressboard; 7.16 kV/mm for 1.8 mm pressboard; and 8.11

kV/mm for 3.0 mm pressboard.

ACKNOWLEDGMENT

We would like to thank the National Grid for the financial

support of this research work. Also thanks to Imadullah Khan

for his help with the FEM simulation.

REFERENCES

[1] H. P. Moser and V. Dahinden, Transformerboard II. H. Weidmann AG,CH-8640 Rapperswil, 1987.

[2] R. M. Del Vecchio, B. Poulin, P. T. Feghali, D. M. Shah and R. Ahuja,Transformer Design Principles, New York: Gordon and Breach, 2001.

[3] R. J. Taylor, Effect of permittivity matching on the flashover ofsolid/liquid interfaces,Proc. IEE, vol. 124, pp. 899-904, 1977.

[4] P. N. Nikolopoulos, G. C. Sakkas and D.N.Diamantopoulos, The

practical aspects of the behaviour of the pressboard oil insulation oflarge electric equipment under impulse and alternating voltages, Cigr,

paper 15-03, 1982.

[5] J. K. Nelson, An assessment of the physical basis for the application ofdesign criteria for dielectric structures, IEEE Trans. Electr. Insul,, vol.24, pp. 835-847, 1989.

[6] G. Han and D. Y. Zhu, Surface discharge characteristics ofimpregnated pressboard under AC voltages, inProc. 3rd Inter. Conf. on

Properties and Applications of Dielectric Materials (ICPADM 1991),vol. 1, pp. 313-316, 1991.

[7] A. K. Lokhanin, G. Y. Shneider, V. Sokolov and V. M. Chornogotsky,Internal insulation failure mechanisms of HV equipment under service

conditions, Cigr, paper 15-201, 2002.[8] V. Sokolov, Understanding failure modes of transformers, in

Proceedings of the Euro TechCon, pp. 43-65, 2005.[9] A. L. Kupershtokh1, E. I. Palchikov1, D. I. Karpov1, I. Vitellas, D. P.

Agoris and V. P. Charalambakos, Stochastic model of breakdown

initiation in dielectric liquids, J. Phys. D: Appl. Phys., vol. 35, pp.31063121, 2002.

[10] T. Takuma, Field behavior at a triple junction in composite dielectricarrangements,IEEE Trans. Electr. Insul,, vol. 26, pp. 500-509, 1991.

[11] H.-Z. Ding, Z. D. Wang and P. Jarman, Dielectric strength of agedtransformer oils: experimental studies and statistical analysis of

breakdown voltage, in Proc. the XIVth Inter. Symposium on HighVoltage Engineering, paper C-10, August 2005.

Stressed wedge-shaped oil gap

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