252IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008
Investigations of Temperature Effects on the
Dielectric Response Measurements of Transformer
Oil-Paper Insulation System
Tapan K. Saha, Senior Member, IEEE, and Prithwiraj Purkait, Member, IEEE
Abstract—Dielectric testing techniques, in both time and fre-
quency domains, are currently widely used by power utilities
for assessment of the condition of transformer oil-paper insula-
tion systems. However, it has been reported that results of these
tests are highly influenced by the operating temperature during
measurements. The distribution, migration and equilibrium
of moisture between oil and paper in a complicated insulation
system is highly temperature dependent. It requires adequate
experience and proper understanding to interpret the dielectric
response results in the presence of temperature variations and
thermal instability. Proper analysis of the dielectric test result
is only possible with an understanding of the physical behavior
of the insulation system in response to temperature. A circuit
model, which describes the dielectric behavior of the transformers
main insulation system, has been investigated in this paper. The
values of the parameters of the model have been identified from
the dielectric tests. A correlation has been observed between the
operating temperature and the equivalent model parameters that
can be used as additional information for better interpretation of
the dielectric test results. This paper thus reports a detailed study
on the effects of temperature on dielectric measurements of a
transformer under controlled laboratory conditions. Some results
of practical on-site testing are also presented to demonstrate the
analysis unless temperature effects are taken into consideration.
Index Terms—Conductivity, depolarization current, dielectric
response, dissipation factor, equivalent model, polarization cur-
rent, recovery voltage, temperature, transformer insulation.
by thermal stress on the insulating oil and paper. Temperature
along with oxygen and moisture are key factors in accelerating
the ageing process.
Recovery voltage (RV) – and polarization and depolar-
ization current (PDC) – measurement techniques are now
RANSFORMER life is significantly influenced by degra-
dation of the insulation materials, which is caused largely
Manuscript received November 15, 2005; revised June 28, 2007. Paper no.
T. K. Saha is with the School of Information Technology and Electrical En-
gineering, University of Queensland, Brisbane, Qld 4072, Australia (e-mail:
P. Purkait is with the Electrical Engineering Department, HIT, Haldia, WB
721657, India (e-mail: firstname.lastname@example.org).
Color versions of one or more of the figures in this paper are available online
Digital Object Identifier 10.1109/TPWRD.2007.911123
However, measurement results of these tests are strongly influ-
enced by several environmental factors, predominantly by the
temperature –. This temperature effect is more promi-
nent in an open substation environment, where the external en-
vironmental conditions are hardly predictable and controllable.
Hence it is very important to study the effect of temperature on
dielectric behavior of an oil/paper insulation system in a field
The dielectric behavior of the insulation system is also influ-
enced by moisture content of oil and paper. In a transformer, the
total mass of dissolved water is distributed between paper and
oil. This distribution or equilibrium of moisture is temperature
dependent. When temperature increases, water migrates from
paper to oil and vice versa. Hence a small change in tempera-
ture modifies the relative water content of the oil and paper. It is
therefore essential to study the effect of temperature, and hence
impact of moisture distribution on the dielectric behavior of oil
and paper separately.
the RVM and PDC measurement results with temperature. This
paper reports laboratory test results of RVM and PDC measure-
ments performed on a transformer with controlled variations of
Based on PDC measurement results, an equivalent model of
the insulation system has been identified –. An attempt
has been made to describe the effect of temperature on oil and
paper from a detailed study of the derivedmodel. Test results on
transformers under outdoor conditions are also reported. These
on-site test results demonstrate the effect of temperature on di-
electric measurements and their impact on condition assess-
II. TIME-DOMAIN DIELECTRIC MEASUREMENTS
A. PDC and RVM
For dielectric response (RV and PDC) measurements , ,
a dc step voltage
with the following characteristics is ap-
plied to an initially relaxed insulation system
During the initial charging period, the step voltage is applied
. In this time, the charging current (po-
0885-8977/$25.00 © 2007 IEEE
SAHA AND PURKAIT: TEMPERATURE EFFECTS ON THE DIELECTRIC RESPONSE MEASUREMENTS 253
Fig. 1. Polarization, depolarization current, and recovery voltage measure-
larization current) given by (2) will flow through the insulation
sured capacitance at or near power frequency and
fective permittivity of the composite insulation system at power
is the vacuum permittivity,
ductivity of the composite insulation system and
electric response function of the composite insulation. The re-
describes the fundamental memory prop-
erties of the dielectric system and can provide significant infor-
mation about the insulation material .
The insulation is then grounded (short circuited) for a subse-
quent time period
; the magnitude of the depolariza-
tion current is given by (3)
is the geometric capacitance (is the mea-
is the ef-
is theaverage con-
is the di-
, ground (short circuit) is removed from the in-
sulation and a voltmeter is connected across it. Depending on
how long the test object is grounded,
polarised molecules get totally relaxed, but some are not. Po-
larization processes which were not totally relaxed during the
grounding period will relax and give rise to a recovery voltage
across the electrodes of the insulation. Fig. 1 shows the na-
ture of the polarization, depolarization current, and the recovery
voltage. The test object is charged from
the polarization current is measured and then grounded from
when the depolarization current is measured. After
, the grounding is removed, the insulation ter-
minals are open circuited and the voltage appearing across the
two electrodes is measured. This voltage is called the recovery
voltage or the return voltage.
, some of the previously
B. Estimation of Conductivity
From measurements of polarization and depolarization cur-
rents, it is possible to estimate average conductivity
test object (oil-paper) , , and . If the test object is
charged and discharged for sufficient time so that
(2) and (3) can be combined to express the average conductivity
of the oil-paper system as
, of the
Fig. 2. ? ? ? arrangement structure of oil and paper.
Fig. 3. Series arrangement structure of oil and paper.
The conductivity for a given insulation system thus is found
to be dependent upon the difference between polarization and
model, as shown in Fig. 2. In this model, a parameter
defined as the ratio of the sum of thickness of all the barriers in
the duct, lumped together, and divided by the duct width. The
when sufficient information about insulation is not available for
along with the composite dielectric response function
The range of
is typically 20% to 50% and
10% to 30%  for a transformer. Values of
calculated more precisely only when the exact structure of the
insulation system and all its design parameters are available.
For series arrangement of oil and paper according to , ,
the average conductivity may be written in terms of paper and
oil conductivities (
, respectively) as
The effective permittivity
can also be similarly estimated as
ative permittivity of the oil duct.
Once the values of effective permittivity
thedifferencebetween polarizationand depolarizationcurrents.
The initial polarization current (after the first transient that is
normally not recorded) can be written as 
is the relative permittivity of paper andis the rel-
can be determined using (4) from
254 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008
On the other hand, long-time polarization current (steady dc
) can be related to paper conductivity as
If, then from (5), we get
Combining (9) and (10), we get
ductivity may be written in terms of paper and oil conductivities
and, respectively) as
model (as shown in Fig. 2), the composite con-
If we take
After rearrangement of the above equation
It can be observed that (10) is a special case of (15) with
III. INSULATION MODEL FOR DIELECTRIC RESPONSE
Over the last few years, several researchers , –
have proposed a number of equivalent circuitsfor modelling the
of the dielectric response. In essence, all of the models pro-
posed so far have been derived from an extended Debye ap-
proach based on a simple RC model.
In the presence of an electric field, polarization current is de-
veloped due to the tendency of dipoles to align in the direction
of the field. When the field is removed, the dipoles relax and
return to their original state , , . In a polymer di-
electric, every polar group can have a different configuration of
application of an electric field may differ from one to another
of branches each containing a series connection of resistor and
Fig. 4. Equivalent circuit to model a linear dielectric.
Fig. 5. Internal winding arrangement of test transformer.
capacitor as shown in the circuit of Fig. 4, –. These
dipoles, represented as
have associated time constants given by
the polarization current, conduction current also flows in the in-
sulation due to the presence of an electric field. The conduction
current in the insulation is due to the insulation resistance
as shown in Fig. 4.
represents geometric capacitance of the
tional capacitance measurement techniques at power frequency
(50 or 60 Hz) divided by relative permittivity of the oil-paper
insulation system , .
For this model, most of the circuit parameters can be derived
from measured polarization and depolarization currents (
and ). The insulation resistance
difference between polarization and depolarization currents at
larger values of time . Details of the model identification
technique have been reported earlier in .
, are randomly distributed, and
. Apart from
is calculated from the
IV. EXPERIMENTAL PROCEDURE
The insulation system of the pancake transformer model 
under study consists of oil and cellulose. The structure of the
insulation system, ratio of oil-paper, etc. are similar to a real
transformer. The winding arrangement and constructional de-
tails of the test transformer is shown in Figs. 5 and 6.
The insulation system of the transformer model consists of
three windings insulated with oil and cellulose, as it is in a real
power transformer. Geometric details of the winding are given
in Table I. Based on the geometric information provided by the
elling purposes are calculated to be 60% and 40%, respectively.
SAHA AND PURKAIT: TEMPERATURE EFFECTS ON THE DIELECTRIC RESPONSE MEASUREMENTS 255
Fig. 6. Internal construction details of test transformer.
GEOMETRIC DETAILS OF TEST TRANSFORMER MODEL
A temperature sensor of type 100-Ohm Pt 385 was inserted
into the tank to measure the actual temperature inside.
The amount of solid insulation in the model is approximately
1445 g and oil is 8400 g; the ratio of oil/solid insulation is 5.8:1.
The ratio of oil/cellulose material is about 10:1 to 6:1 in a real
transformer. The whole model was kept inside a temperature
accuracy was used to vary temperature of thetransformer at dis-
crete steps over a pre-defined range. Temperature of the control
cabinet (and hence the model transformer) was set at discrete
values of 25 C (ambient), 30 C, 40 C, 45 C, and 65 C.
A temperature sensor was placed inside the transformer tank
to make sure that the temperature inside the tank was equal
to that of the set temperature. After the temperature inside the
transformer tank was found to reach the temperature set in the
control cabinet, it was allowed to remain like that for ten days.
This ensured that the oil and paper could achieve a new state of
moisture equilibrium at the elevated temperature. This was fur-
ther verified by measuring PDC at seven, eight, and nine days
as well. The variation of currents was almost unchanged after
Fig. 7. RV spectra plotted against charging time at different temperatures.
seven days. The transformer tank was completely sealed from
outside ambient conditions, thereby ensuring that test results
are solely affected by the variations of temperature. RVM and
humidity of the cabinet was also controlled at a value of 65%.
This was done to ensure that the experimental results were only
influenced by temperature and not by humidity. The PDC and
RV measuring equipment ,  developed at the University of
Queensland was used for all the measurements.
V. ANALYSIS OF RESULTS
A. RVM Results
For obtaining RV spectra at a particular temperature, re-
covery voltage measurements were performed with the ratio
of charging to discharging time being set at 2. Recovery
voltages after each of these charging-discharging cycles were
measured. Peak of this recovery voltage in each cycle and its
corresponding time were recorded. These cycles were repeated
for charging times varying from 0.5 s to 1024 s in increasing
powers of 2 s. The peak of each RV cycle when plotted against
the corresponding charging time produces the RV spectra, as
shown in Fig. 7.
It can be seen that the effect of temperature causes significant
displacement of the RV spectra peaks. The exact time of occur-
rence of peak RV value from each RV measurement is defined
as the dominant time constant for that particular charging/dis-
charging time. Values of these dominant time constants for each
RV measurement were extracted from the recorded data of each
atureare showninTable IIandgraphicallyplottedinFig.8.The
the dominant time constant) has been reported to be indicative
of the condition of insulation –.
in the paper; at higher temperature,s however, the moisture mi-
grates from the paper towards the oil. At high temperatures, the
peak-shifting has been attributed to increased water availability
in oil at high temperatures . Variations of the dominant time
constants with corresponding temperature are summarised in
256 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008
Fig. 8. Dominant time constant versus temperature.
DOMINANT TIME CONSTANT VERSUS TEMPERATURE
It was reported by Kozlovskis et al.  that the dominant
time constants from the RV spectrum follows an exponential
response, whichis dependentontemperature andthemovement
in shape can be described by the following equation:
surement temperature of
stant at some different measurement temperature of
the temperature difference
a parameter related to the polarization process inside the insula-
visible in the plot of Fig. 8.
is the dominant time constant at a reference mea-
, is the dominant time con-
is . The constant
B. PDC Results
Figs. 9 and 10, respectively, show the polarization and de-
polarization currents obtained at different temperatures. In each
case, the transformer was charged (polarized) with 500 volts for
10000 s and then discharged (depolarized) for 10,000 s. It can
be seen from Figs. 9 and 10 that magnitude of the polarization
and depolarization currents tends to shift to higher values with
were considered. Variation of paper conductivity due to these
two models is not significant (Table III). It is worth noting that
oil conductivity is not dependent on the
Figs. 11 and 12 show the nature of variation of oil and paper
conductivity with temperature (considering the
Initial currents are considered for oil conductivity calcula-
tion and hence initial current will be taken from the measure-
ment conducted at the temperature during the start of measure-
Fig. 9. Variation of polarization current with temperature.
Fig. 10. Variation of depolarization current with temperature.
EFFECT OF ? ? ? VALUES ON THE CALCULATION OF PAPER CONDUCTIVITY
ment and corrected accordingly for the ambient (using Fig. 11).
Similarly, since final currents are considered for paper conduc-
tivity calculation, the final current will be taken from the cor-
responding measurement at the last temperature and corrected
accordingly using Fig. 12.
Both the oil and paper conductivities are found to increase
exponentially with temperature. It was also reported by ,
 that conductivity follows an exponential law:
is the absolute temperature in Kelvin,is a constant
SAHA AND PURKAIT: TEMPERATURE EFFECTS ON THE DIELECTRIC RESPONSE MEASUREMENTS 257
Fig. 11. Variation of oil conductivity with temperature.
Fig. 12. Variation of paper conductivity with temperature.
MEASURED RESISTANCE AT DIFFERENT TEMPERATURES
arithm on both sides of (17), it can be shown that the conduc-
. It is interesting to note that both oil and paper con-
ductivities separately demonstrate linear variation with inverse
of absolute temperature.
is the activation energy. Taking natural log-
C. Insulation Model Parameters
The equivalent circuit model parameters were obtained using
a non-linear optimisation procedure with the help of software
obtained from the polarization and depolarization currents at
different temperatures. The reduction in insulation resistance
with increasing temperature is due to increased mobility of the
charge carriers inside the insulation at higher temperatures.
branch values of the equivalent insulation model
have been calculated at different temperatures and are plotted
in Figs. 13 and 14.
Resistance values are in
and capacitances are in nF.
Fig. 13. Variation of model branch resistances with temperature.
Fig. 14. Variation of model branch capacitances with temperature.
It was found that the number of branches in most practical
models varies from six to ten depending upon the nature of the
were considered and found by best possible curve fittings with
are more likely to be dependent on the condition of paper.
Whereas, higher indexed branches of
to lower time constants) in the model represent the condition of
oil. For example,branches
likely to be dependent on oil condition.
It is observed from Figs. 13 and 14 that
ferent branches change with a change in temperature. It is ob-
have changed due to an increase in temperature. At higher tem-
peratures, the branch resistance values have decreased—indica-
tion of a higher mobility of the charge carriers.
At increased temperatures, due to increased mobility of the
of all the branches are found to decrease. This indicates that at
deteriorates in performance. This change in resistance values,
however, does not indicate permanent degradation of the insu-
lation, since the effect is reversed when temperature is lowered.
of charge carriers within the insulation and can not be attributed
thus, to a permanent insulation degradation.
,, and, are more
values of dif-
258 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008
STUDY OF OUTDOOR FIELD TRANSFORMER AFFECTED BY TEMPERATURE
Fig. 15. Polarization current plots for transformer. (A) Under downward tem-
perature transition. (C) At ambient temperature of 28 ?.
VI. IMPACTS OF TEMPERATURE TRANSITION
DURING PDC MEASUREMENTS
It is often experienced in actual field testing that the trans-
former to be tested was previously connected to the electricity
grid and was in an operating condition. During normal oper-
ating conditions, the temperature inside a transformer is much
higher than ambient, depending upon the loading condition. For
PDCmeasurementpurposes,if atransformer is takenout ofser-
vice, it must be givenadequate time for the temperature to settle
down to ambient condition before commencing the actual PDC
information is provided in Table V.
PDC measurement has been done while the transformer was in
the process of cooling down. Before the start of the test, the
transformer was running at a temperature of 60
former was then switched off from the supply and allowed to
cool down to ambient temperature. The PDC measurement was
done during this cooling down process. The temperature was
found to cool down from a starting value of 60
during the initial polarization period of 3 h. Finally, at the end
of 3 h of depolarization current measurement, the temperature
had dropped to 28
It waspointedoutinthatif athermalstepis appliedtoan
insulation sample, due to displacement of charges a current ap-
pears in the external circuit. This current interferes with polar-
ization and depolarization currents under measurement giving
rise to unwanted errors. As seenin Figs. 15and 16, thepolariza-
tion and depolarization currents corresponding to the case when
. The trans-
Fig. 16. Depolarization current plots for transformer. (B) Under downward
temperature transition. (D) At ambient temperature of 28 ?.
OIL AND PAPER CONDUCTIVITIES FOR DOWNWARD TRANSITION
transformer temperature was under transition are higher than
their ambient temperature counterparts. This may result in er-
roneous calculation of the response function and conductivities.
Conductivity values for oil and paper calculated from polariza-
tionanddepolarizationcurrentsundersuch conditionsare given
in Table VI. Errors in conductivity calculations due to transition
of temperature are clearly visible in Table VI. Under transition
of temperature from a higher to a lower value, the polarization
current is higher than the corresponding values at ambient tem-
perature. In particular, this is higher in the initial part of the po-
larization current, when temperature was much higher than the
ambient, while after a couple of hours of transition, the final po-
larization current becomes closer to the current at ambient tem-
perature. The difference in current between high temperature
and ambient can produce erroneous results in conductivity es-
timation. Midway through the depolarization current measure-
down to ambient temperature. Thus, the depolarization currents
at transition condition and ambient condition are overlapping
after a certain period of time. This higher magnitude of initial
ductivities as shown in Table VI.
temperature to settle down to ambient before commencing the
actual PDC test. Otherwise, the prediction based on these test
results will be erroneous.
A reverse temperature transition effect on PDC measurement
can be observed while field testing is performed in open substa-
tions, where the ambient temperature varies widely during the
day. The ambient temperature during summer may start with
in the morning and may increase to 35-40
midday. In effect, the temperature inside the transformer tank
will also go up. This may have a noticeable impact on the PDC
measurement. Both the polarization and depolarization currents
SAHA AND PURKAIT: TEMPERATURE EFFECTS ON THE DIELECTRIC RESPONSE MEASUREMENTS 259
of temperature. (C) At ambient.
Fig. 18. Depolarization current plots for transformer. (B) Under upward tran-
sition of temperature. (D) At ambient.
variation during the measurement period may introduce some
unwanted variations in the currents.
An experiment was performed in the laboratory with the test
transformer being put inside a temperature controlled chamber.
The PDC test was started at 20
temperature was increased at a steady rate of 2
while the test was continuing. Figs. 17 and 18 show
polarization and depolarization currents with the temperature
around the transformer tank rising steadily from 20
during the test. Figs. 17 and 18 also includes polarization and
depolarization currents when the same transformer was tested
at a constant temperature of 20
The final value of the polarization current (current at
at the upward transition temperature (plot A, Fig. 17) slightly
varies from the corresponding final polarization current mea-
sured at 20
(plot C, Fig. 17). It is observed that initial values
of the depolarization current under temperature transition (plot
B, Fig. 18) vary significantly from the measurement conducted
(plot D, Fig. 18). The temperature in the beginning of
the polarization measurement is close to 20
rises to a test chamber value of about 25
measurement, which is reflected on the last part of the polariza-
tion current. While the depolarization measurement now starts
, thusthedeviationfrom the20
and then the test-chamber
per hour up
and then slowly
at the end of this
OIL AND PAPER CONDUCTIVITIES FOR UPWARD TRANSITION
is more pronounced at the beginning. This has also been re-
flected in the oil/paper conductivity calculations.
Oil conductivity calculated from the current measurements
under transition is lower than the oil conductivity calculated
from the current measurements at 20
the change in paper conductivity is in the opposite direction. It
is thus clear from Figs. 17, 18, and Table VII that any dielec-
tric response function and conductivity computed from polar-
ization and depolarization currents obtained under such temper-
aturetransition during the PDC measurement will be erroneous.
. On the other hand,
The dielectric response measurements are currently being
used for the diagnosis of transformer insulation condition.
Interpretation of RVM and PDC test results still remains a
difficult task as it is influenced by insulation ageing condition,
geometry of insulation, moisture content, and also the operating
temperature. The condition of oil paper insulation is strongly
affected by the presence of moisture and the moisture distribu-
tion between oil and paper is highly dependent on the operating
For correct interpretation of dielectric test results, it is essen-
tial that an understanding of temperature effects is available. In
this paper, dielectric test results on a model transformer under
in field measurement have been reported.
the paper insulation inside a transformer appears to exhibit de-
graded performance compared to lower operating temperatures.
The dominant time constant of the RVM tends to shift towards
lower values of time as the temperature increases. Polarization
and depolarization current magnitudes and oil and paper con-
ductivities estimated from these currents tend to be higher at
higher temperatures. An equivalent insulation model has been
results.Theoiland paperconductivity,and insulationresistance
paper conductivities calculated from the measured currents are
found to have a certain mathematical relationship with temper-
On-site test results presented in the paper indicates the neces-
sity of careful understanding of the effect of temperature on the
dielectric response measurement for correct analysis and inter-
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Tapan K. Saha (SM’97) was born in Bangladesh,
India, and immigrated to Australia in 1989. Cur-
gineering, University of Queensland, Brisbane, Qld,
Australia. Previously, he taught at the Bangladesh
University of Engineering and Technology, Dhaka,
India, for three-and half years and then at James
Cook University, Townsville, Australia, for two
and half years. His research interests include power
systems, power quality, and condition monitoring of
Dr. Saha is a Fellow of the Institution of Engineers, Australia.
Prithwiraj Purkait (M’99) was born in Kolkata,
India, in 1973. He received the B.E.E., M.E.E., and
Ph.D. degrees from Jadavpur University, Kolkata,
India, in 1996, 1999, and 2002, respectively.
He was involved in post-doctoral research at the
University of Queensland, Brisbane, Qld, Australia
during 2002–2003, and for higher research during
2005. He was also a Design Engineer with M/s
Crompton Greaves Ltd., Mumbai, India, for one
year during 1996–1997. Presently, he is an Associate
Professor and Head of the Department of Electrical
Engineering, Haldia Institute of Technology, Haldia, India. His current research
includes transformer insulation condition assessment techniques and advanced
signal processing applications in high-voltage engineering.