The Modelling of Electric Field, Capacitance and

Dissipation Factor of a High Voltage Bushing over

Varying Frequency
D. J. Smith, S. G. McMeekin, B. G. Stewart and P. A. Wallace
School of Engineering & Built Environment,
Glasgow Caledonian University,
Glasgow, G4 0BA, Scotland, UK.
Email: david.smith2@gcu.ac.uk

Abstract- Within a high voltage substation, power voltage (HV) conductor to the flange. Alternatively, whilst
transformer bushings are key components and an assessment of the bushing is connected to the transformer winding, the UST
their condition is important to ensure operational reliability. measures values from the HV conductor to the bushing test
Bushings represent a large proportion of transformer failures,
where most issues are as a result of moisture ingress. Moisture point. There are two main capacitances of interest in
ingress affects the distribution of the electric field and changes bushings – the main insulation capacitance (commonly
the capacitance and dissipation factor (tanδ) of the insulation. denoted as C1) and the tap capacitance (commonly denoted as
In this paper, a numerical model is built for an oil impregnated C2). The model presented in this paper evaluates the main
paper (OIP) condenser bushing. The simulated dielectric insulation capacitance and dissipation factor, as would be
frequency response (DFR) dependence of transformer oil and measured using the UST.
OIP with varying moisture content is given. Simulations are It has been reported that measuring the dissipation factor at
made of the AC and very low frequency (approximated to DC)
potential and electric field distributions. Furthermore, the various temperatures is an established technique for assessing
capacitance and dissipation factor over a frequency range of the moisture content within a bushing at power frequency.
between 1mHz to 1kHz is presented. The results are found to be However, it is not standard practice in industry.
consistent with typical bushing manufacturers’ data. Measurement at multiple temperatures in bushings is time
Index Terms— bushing, capacitance, dielectric frequency consuming, and corrections for component temperature are
response, dissipation factor, electric field, finite element method, not well understood, particularly for deteriorated and aged
high voltage. bushings [5]. More recently, there is a focus on DFR
measurements, whereby the capacitance and dissipation
factor is measured over a frequency range typically between
I. INTRODUCTION 1mHz to 1kHz [6]. For bushings, this method can provide a
Transformer bushings are fundamental components of high more sensitive assessment of the insulation moisture content
voltage power transformers; their reliability is imperative for [7] using a single temperature measurement. Furthermore, an
transformers and electrical networks. The OIP condenser accurate temperature correction can be made using Arrhenius
design is the most common in service and it accounts for 80% equation [8]. However, low frequency tests can be time
of the world’s operational bushings [1]. It has been reported consuming and there are no limits on accepted values.
that bushing faults represent between 25% to 30% of all Reference [9] studied the changes in electric field of
power transformer failures [2], and it is suggested that often different regions of a bushing using boundary element
bushing life is far less than the design life of the transformer method. This study provided a good insight into the stresses
[3]. The majority of failures within bushings are attributed to associated with a bushing; however, the model is basic, and
moisture ingress, where moisture can enter through the not representative of an actual bushing in service. DFR
deterioration of seals and fittings. Moisture within a bushing measurements on bushings were made by Ref. [10] for
reduces the dielectric strength and life of the insulation, thus varying weather conditions, Ref. [11] for resin impregnated
increasing the risk of unpredicted failure. paper (RIP) condenser bushings; and Ref. [12] for an OIP test
Currently in industry, the most common test method is the bushing at various stages of manufacturing. Reference [7]
measurement of capacitance and dissipation factor at power summarised the measurement technique for bushings and
frequency. This measurement is important, as it provides an reported on typical dissipation factor characteristics for
indication of any dielectric deterioration from moisture various condenser types. Furthermore, Ref. [8] detailed a
ingress, age and short-circuit condenser layers. The grounded technique to more accurately correct for temperature from
specimen test (GST) and the ungrounded specimen test (UST) variable frequency measurements on bushings. However,
are two common connection methods for testing bushings there are no studies which simulate the capacitance and
offline [4]. When the bushing is disconnected from the dissipation factor for varying moistures contents over varying
transformer winding, the GST measures values from the high frequency.
 A. Field Modelling
Under AC conditions, the electric field has a capacitive
distribution, which is determined by the geometry and the
permittivity of the insulating materials. However, under very
low frequency and DC conditions, the electric field is more
complex, due to the transition from a capacitive field to a
resistive field, and also the presence of accumulated surface
charge.
In this paper, a two-dimensional axisymmetric model is
used for the geometry shown in Fig. 1, and the bushing is
considered to be new, with a moisture content of 0.2%.
Simulations of electric field are made using both frequency
domain and stationary studies, for AC and low frequency
conditions respectively. To simplify the calculation of low
frequency electric fields, a DC simulation was used to
evaluate the electric field distribution for frequencies less
then 1Hz. A free triangular meshing scheme was used,
comprising of 22,182 elements. The domain and boundary
conditions used in the model are shown in Table 1.
TABLE I
DOMAIN AND BOUNDARY CONDITIONS
Region Material Boundary Condition
A, F & H Aluminium Electrical potential
B&I Oil Continuity (around bushing)
Fig. 1. OIP bushing and the layered condenser geometry in axisymmetrical Electric insulation (outer boundaries)
view (both not to scale). A. high voltage cap, B & I. transformer oil, C. outer C&G Porcelain Continuity
porcelain sheds, D. OIP condenser, E. ground flange, F. high voltage D OIP Electrical potential (first foil)
conductor, G. lower porcelain body, H. end shield, and J. air. (Image [18])
Electric shielding
In this paper, a numerical model is built for an OIP bushing Ground (final foil)
to analyse the potential and electric field distributions, E Aluminium Ground
capacitance and dissipation factor for frequencies between J Air Continuity (around bushing)
1mHz to 1kHz. Simulations are made for a bushing with four Electric insulation (outer boundaries)
moisture contents - 0.2%, 0.5%, 1.0%, and 4.0% (where it is
assumed the complete bulk insulation has the same moisture
content percentage). The dielectric properties and results B. DFR Modelling
from the numerical model are all calculated for a reference It was found that using the complete bushing model shown
temperature of 20oC. The capacitance and dissipation factor in Fig. 1, for frequencies less than 10Hz, numerical
results are compared to manufacturer’s data and field convergence with a relative error suitable for accurate
measurements. From this work, the sensitivity to moisture capacitance and dissipation factor evaluation, could not be
ingress is highlighted and the capacitance and dissipation achieved. Therefore, a simplified equivalent circuit model of
factor values for different moisture contents are quantified. the condenser was developed, using only the OIP and oil. A
similar equivalent circuit has been used for analytical DFR
evaluation of power transformers, commonly known as the
II. NUMERICAL MODEL X-Y model [14]. Using this bushing equivalent circuit,
For numerical analysis, the geometry of a 52kV OIP numerical convergence (relative error <0.001) was achieved
condenser bushing was used; the dimensions are based on over the complete frequency range analysed in this paper.
external measurements taken from a similar bushing [13]. An accurate and efficient simulation of dielectric properties
The internal design of the condenser comprises of eight requires special attention to the meshing. For this study, a
equally spaced OIP layers, each having a thickness of 2mm. mapped quadrilateral meshing scheme was used, which
The main sections of the bushing used in the simulations are comprises of four elements for every 1mm2. Numerically, an
shown in Fig. 1. admittance output variable was used to calculate the
The electric currents application mode in COMSOL capacitance and dissipation factor.
Multiphysics (v.4.2a) was used to evaluate the potential and
electric field distributions and admittance. This application III. DIELECTRIC MATERIAL PROPERTIES
mode solves Poisson’s equation for electric potential, using
the material properties specified for each geometry section. For this study, aluminium (ɛr=n/a σ=3.7*10-7S/m),
porcelain (ɛr=6 σ=3*10-11S/m) and air (ɛr=1 σ=8*10-15S/m)
are considered to be frequency independent. However, oil σ DC
and OIP have been shown to be frequency dependent [15]. ε (ω )*OIL = ε r − j (2)
Furthermore, both of these are also dependent on moisture ε oω
content and temperature. In the frequency domain, it is For the bushing model in this paper, the DC conductivity
common to characterise a material by its complex permittivity of oil was considered to linearly increase from 1*10-13S/m for
ɛ* (dimensionless) [6], as given by (1), where ɛ’ is the real a 0.1% moisture content, to 1*10-9S/m for a 10% moisture
permittivity, ɛ” is the imaginary permittivity, and ω is the content, based on values reported for power transformers [6].
angular frequency (radians/second). The complex permittivity characteristics for these two
moisture contents is shown in Fig. 2.
ε (ω )* = ε (ω )'− jε (ω )' ' (1) OIP has a much more complicated characteristic, and its
complex permittivity values are typically taken from
The complex permittivity of transformer oil ɛ*OIL, over the experimental data. For this work, the complex permittivity
frequency range of this paper, is given as (2) [6], where ɛr is characteristics where taken from the literature [15] [16] and
the relative permittivity of oil usually 2.2, σDC is the DC interpolated for 0.2%, 0.5%, 1.0% and 4.0% moisture
conductivity of oil (S/m), and ɛ0 is the vacuum permittivity contents, as shown in Fig. 3. As can be seen, there is a large
(8.85*10-12F/m). distinction in complex permittivity between moisture contents
at lower frequencies.
Polynomial equations were fitted to the OIP real and
imaginary permittivity characteristics, and then combined,
2
50Hz
forming (1) for each moisture content. For numerical
1*10-13 S/m ε,,
10
analysis, (1) and (2) were directly entered into the numerical
1*10-9 S/m ε,,
ε,
model and assigned to the OIP and oil domains.
Complex Permittivity, ε *

0
10
IV. RESULTS AND DISCUSSION
A. Potential and Electric Field
10
-2
The objective of a bushing, is to have an evenly distributed
potential distribution. This minimises high electric field
stress areas where discharges may occur. Under AC
10
-4
conditions, the condenser layers control the electric field
distribution. Whilst under DC conditions, the fields are
-2 0 2 typically controlled using dielectric barriers [17].
10 10 10
Frequency (Hz) When an AC bushing operates at low frequency (simulated
as DC), the potential distribution becomes non-uniform, as
Fig. 2. Complex permittivity of transformer oil during DC conductivities of
1*10-13S/m and 1*10-9S/m.

2
10
50Hz
0.2% ε,
0.5% ε,
1
10 1.0% ε,
Complex Permittivity, ε *

4.0% ε,
0.2% ε,,

0 0.5% ε,,
10 1.0% ε,,
4.0% ε,,

-1
10

-2
10 -2 0 2
10 10 10
Frequency (Hz)

Fig. 3. Complex permittivity of OIP at 0.2%, 0.5%, 1.0% and 4.0% moisture
contents (real permittivities 0.2%, 0.5% and 1.0% are superimposed). Fig. 4. Simulated AC (50Hz) and DC surface potential plots of the bushing
at 52kV.
 nameplate a major problem [20]. In the literature, a change
25 5 greater than 10% to 15% of the nameplate, is often
DC
AC considered to be a potential short-circuit between layers [20].
The main insulation capacitance was modelled over the
20 4
four moisture contents at 1mHz, 50Hz, and 1kHz. As shown
DC Electric Field (kV/mm)

AC Electric Field (kV/mm)

in Table II, there was little distinction between capacitances
15 3 for moisture contents less than 1% at frequencies greater than
50Hz, and values were not above the undesirable value given
in the final row. This is consistent with reported capacitance
10 2 from field measurements [10]. However, for a 4% moisture
content, an increased capacitance of 6.3% and 3.9% was
5 1
calculated at 50Hz and 1kHz respectively. It was found that
the distinction between moisture contents was more
distinguishable at lower frequencies, as shown in Table II at
0 0 1mHz. Consequently, at 1% and 4% moisture contents, the
0.01 0.015 0.02 0.025 0.03 0.035
Condenser Distance (m) capacitance increased by 4.6% and 103.0% respectively.
TABLE II
Fig. 5. Simulated DC and AC radial electric field plots of the bushing CONDENSER (C1) CAPACITANCE
condenser system at 52kV.
Moisture Content Frequency (Hz) / Capacitance (pF)
shown in Fig. 4. This is particularly evident on the air-side of (%) 1m 50 1k
the bushing, where, in the AC case, there is a uniform grading 0.2 216.0 204.1 203.9
of surface potential along the sheds. However, in the DC 0.5 219.0 205.0 204.5
case, there is a concentration of surface potential at the top of 1.0 225.4 207.7 206.0
the bushing. 4.0 438.5 217.0 214.2
Under DC conditions, equipotential non-uniformity is as a Undesirable 222.48 210.2 210.0
result of the resistivity of the condenser insulation being capacitance (+3%)
much higher than the oil [17]. Consequentially, the
equipotentials tend to concentrate within the condenser, C. Dissipation Factor
particularly within the lower third of the bushing, near the Capacitance measurements are normally taken in
high voltage conductor [17]. This can be observed by conjunction with dissipation factor. The dissipation factor is
analysis of the radial electric field distribution across the a key indicator of a potential problem, as this parameter is
very sensitive to moisture ingress. When testing the
condenser system, as shown in Fig. 5. Under AC conditions,
dissipation factor of a bushing, the measured value is
there is an even distribution of electric field between each of
referenced back to 20oC for comparison. Typically at
the eight layers of approximately 3.3kV/mm. Under DC
reference temperature, the dissipation factor between 0.2% to
conditions, the electric field is confined within the first few 1% moisture content is similar [4], and in some cases the
layers, next to the high voltage conductor (at 0.014m). moisture content may not be distinguishable.
Furthermore, a maximum electric field of 22.7kV/mm was
Manufacturers of OIP bushings provide limits of change
simulated in the first layer. This suggests that measurements
in dissipation factor at reference temperature. One
of capacitance and dissipation factor may be more sensitive to
manufacturer’s bushing product line, having a nameplate
variation in material properties within the first few layers
dissipation factor between 0.3% to 0.35%, considers an
under low frequency conditions. increase in dissipation factor of double to be undesirable [20].
B. Capacitance A manufacturer with a similar product line, with a nameplate
Manufacturers build their bushings to have a constant rating of approximately 0.4%, considers a dissipation factor
capacitance over the asset life. Therefore, variation in of greater than 0.7% undesirable [20]. However another
capacitance can be used as an indicator of a potential manufacturer, having a bushing product line with nameplate
problem. In general, a new bushing will have a moisture rating between 0.35% to 0.5%, considers 0.6% to 0.7% to be
content of less than 0.2%. For the modelled geometry, 0.2% undesirable [4] [20]. Based on the results from the
moisture content at 50Hz resulted in a capacitance of 204.1pF manufacturers, Table III provides a general guide for
as shown in Table II, which is a consistent value with a evaluating change in dissipation from nameplate at 200C at
power frequency.
bushing of similar construction [18].
An increase in capacitance greater than 3% to 5% is TABLE III
CHANGE IN DISSIPATION FACTOR AT 20OC AT 50HZ
typically accepted as an indication of a problem within a
Change in tanδ (%) from nameplate Recommendation
bushing. Most manufacturers consider a change in
<25% Acceptance
capacitance of greater than 3% to be undesirable [4] [19]. 25% - 40% Re-check
However, some consider a change greater than 5% from the 40% - 75% Undesirable
first test to be undesirable, and greater than 10% to 20% from >75% Remove from service
 Fig. 6 shows the simulated dissipation factor of the bushing
10
3
over variable frequency. In the figure, the 50Hz line
50Hz
0.2%
represents the values shown in Table IV. For this bushing
0.5% geometry, distinction between moisture contents was more
distinguishable at lower frequencies, particularly less than
Dissipation Factor, tanδ (%)

2 1.0%
10 4.0%
0.1Hz. This is consistent with the findings reported for power
transformers [6]. There are currently no International
10
1 Standards which specify the dissipation factor limits for
bushings at variable frequency. However, Ref. [7] suggests
the limits for an aged bushing at 10Hz, 50Hz, and 400Hz to
10
0 be 0.7%, 0.5%, 0.7% respectively. Using these limits for the
simulated bushing, a moisture content of greater than 1% is
considered aged.
-1 As discussed, different manufacturers will have different
10
10
-2
10
0
10
2
dissipation factors at rated voltage. Thus, measurements over
Frequency (Hz) variable frequency will differ, however, the general
characteristic should be similar. Fig. 7 shows the typical
Fig. 6. Simulated dissipation factor (%) of the bushing condenser having
moisture contents of 0.2%, 0.5%, 1.0% and 4.0%. dissipation factor characteristics for various condenser types.
In this figure, the dissipation factor of the simulated bushing
with 0.2% moisture content is superimposed. As can be seen,
For the bushing analysed in this paper, Table IV shows a
its characteristic is consistent with actual measurements,
comparison of dissipation factor between a similar bushing
validating the accuracy of the numerical model.
and the simulated bushing, at 200C at power frequency. As
can be seen there is a good correlation between the results.
The differences between the reported and simulated results V. CONCLUSIONS
are due to the approximated values of dielectric material
In this paper, numerical models are built to evaluate the
properties used.
potential and electric field distribution, capacitance and
TABLE IV dissipation factor of a high voltage OIP power transformer
DISSIPATION FACTOR AT 20OC AT 50HZ
bushing. The DFR characteristics of oil and OIP are given
Moisture Content Dissipation Factor (%) and used to accurately evaluate the bushing response over a
(%) Reported [4] Simulated
frequency range between 1mHz to 1kHz.
0.2 0.37 0.36
It was found that at lower frequencies, the radial electric
0.5 0.46 0.45
fields are higher in amplitude and confined within the first
1.0 0.52 0.49 few condenser layers. Furthermore, changes in capacitances
4.0 2.60 2.37 exceeding the undesirable (greater than 3% from nameplate)
value, were equivalent to a moisture content of 1% at 50Hz.
The distinction between varying moisture contents using
the dissipation factor is more distinguishable at lower
100% frequencies. The dissipation factor is more sensitive to
50%
changes in moisture content, thus it is a more accurate
SIMULATED
parameter to evaluate the insulation in relation to moisture
20% OIP (MC=0.2%) ingress. Finally, the results are compared to manufacturers’
data and field measurements, where they were found to be
10%
consistent.
5%

2% REFERENCES
1% [1] L. Jonsson and R. Johnansson, "High voltage bushings, 100 years of
technical advancement," ABB, Review 3 2009.
0.5%
[2] D. J. Smith, S. G. McMeekin, B. G. Stewart, and P. A. Wallace,
"Transformer bushings - modelling of electric field and potential
0.2% distributions within oil impregnated paper with single and multiple
spherical cavities," in 45th International Universities' Power
1e-3 1e-2 1e-1 1e0 1e1 1e2 1e3
Engineering Conference, Wales, Cardiff, 2010.
Fig. 7. Typical dissipation factor measurements of bushings [7] with the [3] A. K. Lokhanin, T. I. Morozova, G. Y. Shneider, V. V. Sokolov, and V.
simulated 0.2% moisture content result superimposed. M. Chornogotsky, "Internal insulation failure mechanisms of HV
equipment under service conditions," CIRGE 15-201, pp. 1-6, 2002.
[4] ABB, "Bushing diagnostics and conditioning," Power Technology
Products, Product Information 2750 515-142 en, 2000.
[5] M. Karlstrom, P. Werelius, and M. Ohlen, "Moisture assessment using
dielectric frequency response and temperature dependence of power
factor," Megger, 2009.
[6] P. Patel and M. Perkins, "DFR - An Excellent Diagnostic Tool for
Power Transformers," in Weidmann Annual Diagnostic Solutions
Technical Conference, New Orleans, LA, 2008, pp. 1-16.
[7] M. Krüger et al., "New Diagnostic Tools for High Voltage Bushing,"
CIGRE, France, International Workshop on Power Transformers VI
Workspot, 2010.
[8] D. M. Robalino, "Accurate Temperature Correction of Dissipation
Factor Data for Oil-Immersed Bushings: Field Experience," in CEIDP,
Cancun, Mexico, 2011, pp. 251-254.
[9] S. Chakravorti and H. Steinbigler, "Capacitive-resistive field
calculations on HV bushings using the boundary-element method,"
IEEE Transactions on Dielectric and Electrical Insulation, vol. 5, no. 2,
pp. 237-244, April 1998.
[10] J. Blennow, C. Ekanayake, K. Walczak, B. García, and S. M. Gubanski,
"Field Experiences With Measurements of Dielectric Response in
Frequency Domain for Power Transformer Diagnostics," IEEE
Transactions on Power Delivery, vol. 21, no. 2, pp. 681-688, April
2006.
[11] C. Sumereder and M. Muhr, "Dielectric response measurements at high
voltage bushings," in IEEE - International Conference on Condition
Monitoring and Diagnosis, Beijing, China, 2008, pp. 1150-1153.
[12] I. Fofana, M. Farzaneh, A. Setayeshmehr, H. Borsi, E. Gockenbach, A.
Beroual, and N. T. Aka A. Bouaicha, "Dielectric spectroscopy
techniques as quality control tool: A feasibility study," IEEE Electrical
Insulation Magazine, vol. 25, no. 1, pp. 6-14, 2009.
[13] ABB, "Transformer bushings (type GOB)," Technical guide 1ZSE
2750-102 en, 2007.
[14] U. Gafvert, L. Adeen, M. Tapper, P. Ghasemi, and B. Jonsson,
"Dielectric Spectroscopy in Time and Frequency Domain Applied to
Diagnostics of Power Transformers," in International Conference on
Properties and Applications of Dielectric Materials, Xi'an, China, 2000,
pp. 825-830.
[15] D. Linhjell, L. Lundgaard, and U. Gafvert, "Dielectric Response of
Mineral Oil Impregnated Cellulose and the Impact of Aging," IEEE
Transactions on Dielectrics and Electrical Insulation, vol. 14, no. 1, pp.
156-169, February 2007.
[16] O.L. Hestad, U. Gafvert, and L.E. Lundgaard, "Dielectric Response of
Oil-impregnated Cellulose from 0.1 mHz to 3 MHz," in ICDL, Osaka,
Japan, 2005, pp. 277-280.
[17] A. G. Sellars and S.J. MacGregor, "The design of dielectric barriers for
HVDC bushings," in IEE Colloquium on Field Modelling: Applications
to High Voltage Power Apparatus, London, UK, 1996, pp. 3/1-3/6.
[18] ABB, "Transformer bushings (type GOB)," Installation and
Maintenance Guide 2750 515-12 en, 2010.
[19] HSP, "Transformer Bushing (Type SETF-t)," Mounting, Operating and
Maintenance Instructions Service Instructions BAL SETFt /04e, 2010.
[20] Western Area Power, "Testing and maintenance of high-voltage
bushings," Golden, Colorado, Power Systems Maintenance Manual
1999.