Second International Conference on Electrical and Computer Engineering
ICECE 2002, 26-28 December 2002, Dhaka, Bangladesh
In-Situ Determination of Transformer Winding Temperature Rise
Using Genetic Algorithm Based Parameter Estimation
S. Hosimin Thilagar and G. Sridhara Rao
Department of Electrical Engineering, Indian Institute of Technology Madras
Chennai – 600 036, India
Abstract - This paper presents a novel method for the
determination of average winding temperature rise of
transformers under its field operating conditions. Rise
in the winding temperature is determined from the
estimated values of winding resistance during the heat
run test. The method uses genetic algorithm as a
parameter estimation tool to estimate the winding
resistance in an in-situ basis using the easily
measurable signals viz., supply voltage, current, input
power and load resistance of the transformer. This
method finds its application in overload management
and monitoring of health of transformers. Results of
the method are validated experimentally from the
measured value of hot resistance.
condition of transformers in an in-situ basis. The
estimated results are experimentally validated through
the direct measurement of resistance. The method has
used the search optimization tool the Genetic
Algorithm (GA) as a parameter estimation tool to
estimate the resistances from the measured signals
during the heat run test. Principles of GA can be
obtained from [6].
This method would be useful to suggest the
overload capability of the transformer, which
essentially depends on the average winding
temperature rise but not the load current. Temperature
rise in the primary and secondary windings can be
separately determined apart from the computation of
the losses in the windings using the estimated
parameters. The method also finds its application to
monitor the health of the transformers.
Section 2 of this paper presents the nature of the
problem and the proposed method to solve it. Section3 deals with the experiments, implementation of the
method, results and discussions. Section 4 presents the
conclusions of this paper.
Keywords: Transformers, Average temperature rise,
Parameter estimation, Genetic algorithm.
1. INTRODUCTION
Transformers can be overloaded to the extent of
allowable limits of average winding temperature rise.
Moreover the rise in average winding temperature
beyond a limit is an index of the deteriorating health
of the transformers. Therefore the knowledge of
average temperature rise of transformers under its
operating condition is imperative.
The average temperature rise of transformers is
measured by determining the change in winding
resistance in accordance with the IEEE/ANSI
standards [1] for dry type power transformers. Various
techniques are suggested for the measurement of
average and hot spot temperature rise in regard to
ventilated dry type transformers and oil immersed
transformers [2,3]. On the other hand direct
temperature measurement at hot spots and average
temperature rise in windings are done [4] using optic
fiber sensors. The overload capability of transformers
and its management are dealt in [5].
The present paper suggests a method for the in-situ
determination of average winding temperature rise in
transformers. The estimation of hot-resistance in the
course of a heat-run test is presented in the paper
followed by the computation of winding temperature
rise. The estimation could be done using the readily
measurable signals of supply voltage, primary current
and input power of the transformer. A practical case of
normal load test is also considered to demonstrate that
the method could be applied in the field operating
ISBN 984-32-0328-3
GLOSSARY
V1,est, V1,mea, I1,mea, I1,est P1,mea, P1,est – Measured and
estimated values of supply voltage phasor, Volts, primary
current phasor, Amps and input power, Watts
I' 2,mea, Icore – Measured secondary current phasor and c ore
loss current phasor, Amps
Rè1, Rè2 – Resistance of windings at ambient temperature è1
and at changed temperature è 2 respectively, Ohms
r1, r'2, x1, x'2 – Resistances and leakage reactances of primary
and secondary winding, referred to primary side, Ohms
RM, XM – Core loss equivalent resistance and magnetising
winding reactance, Ohms
R'L – Load resistance referred to primary side, Ohms
Z 1, Z'2, Z M , Z'1,est – Impedances of primary, secondary and
tertiary windings and equivalent impedance of transformer
referred to primary side, Ohms
k – a scalar constant
2. THE PARAMETER ESTIMATION METHOD
2.1. Problem Formulation
Monitoring of rise in average winding temperature
is important to ascertain the overload capability and
the protection of power transformers. The temperature
measurement methods would have to take into account
of the factors viz., variations in ambient temperature,
thermal time constant of the windings, etc. Moreover
91
in-situ measurement of temperature rise of the
windings is necessary to achieve on-line variation of
the operating load margin of power transformer so that
the transformer can be overloaded beyond its
nameplate for a short or long time. Indeed the on-line
method of temperature measurement using fiber-optic
technique is quite costlier. Temperature measurement
based on thermal models requires solution of nonlinear expressions and the knowledge of transformer
geometrical and thermal parameters. Methods
involving measurement of average rise in oil
temperature are influenced by the secondary effects
like deterioration of oil property, in case of oil
immersed
transformers.
In
this
background
achievement
of
simplicity
of
temperature
measurement method seems to be difficult.
magnetizing circuit parameters are ignored in the
equivalent circuit. According to the GA based method
suggested by the paper the equivalent circuit
parameters are estimated by maximizing the fitness
function (FF) given by (1). By applying the measured
value of supply voltage, load current and input power
in (1) the equivalent resistance and reactance
components could be determined. From the estimated
value of resistance the temperature at various instants
of time is computed using (7).
k
max ( FF ) =
(1)
2
f1 + f 2 2
where, f1 =
f2 =
2.2 Proposed Solution
The average temperature rise of transformers –
both air-cooled and oil immersed types – due to
constant and variable losses, variation in ambient
temperature and change in the thermal time constant
of transformer are reflected through the change in the
winding resistance. Therefore it is proposed to
estimate the resistance of the windings based on the
equivalent circuit structure of the transformer, using
which the rise in average winding temperature is to be
determined. The estimation of resistance along with
other equivalent circuit parameters is formulated as a
search problem and the search-optimization tool GA is
applied for the parameter estimation.
V1,mea
×100
( 2)
× 100
(3)
V1,mea
P1,mea − P1,est
P1,mea
V1,est = Z '1,est × I 1,mea
( 4)
2
P1,est = I 1,mea × ( r1 + r ' 2 )
(
Z '1,est = sqrt (r1 + r ' 2 )2 + ( x1 + x' 2 ) 2
(5 )
)
( 6)
 234 .5 + θ1 

Rθ1 = Rθ2 × 
(7 )

 234 .5 + θ2 
To apply the method in a generalized case, where
the transformer is in its loaded condition, the GA
based method is modified accordingly using the exact
equivalent circuit model, shown in fig. 2, as follows.
2.3 Proposed Method
The average winding temperature rise of
transformer is obtained using the equivalent loading
method, as suggested by the IEEE standards [1].
According to this method a constant circulating
current is passed through the short -circuited windings
for one hour. This current is equivalent to the full load
current plus the equivalent current supplying the
constant and variable losses of the transformer.
Parameter estimation is to be done based on the
equivalent circuit of the transformer under shortcircuited condition, as shown in fig. 1, using the
readily measurable signals of voltage, current and
input power.
r1+r'2
V1,mea − V1,est
r1
+
x1
x'2
I1, mea
RM
V1, mea
–
r'2
Icore
XM
R'L
I'2,mea
Fig.32: Exact equivalent circuit of a single -phase transformer
under loaded condition
Expression (1) would be applied for the parameter
estimation in which (5) and (6) are modified into (8)
and (9) based on fig. 2. Using the estimated resistance
parameters of the exact equivalent circuit in fig. 2 the
rise in average winding temperature could be
determined in an in-situ basis. This also provides the
advantage of computing the variable and constant
losses separately and their specific contribution to the
rise in heat in the respective windings and core.
x1+x'2
I1,mea
Fig. 1: Equivalent circuit of a single -phase transformer
under short -circuited condition
P1,est = I 1, mea 2 × r1 + I ' 2 , mea 2 × (r ' 2 + R ' L ) + ...
Parameters in fig. 1 represent the equivalent
resistance and reactance value of the primary and
secondary windings referred to primary side of the
transformer under short-circuited condition. The
I core 2 × R M
92
(8)
 Z' ×ZM
Z '1,est = Z 1 +  2
 Z '2 + Z M
(




Z ' 2 = sqrt (r ' 2 + R ' L )2 + (x ' 2 )2
1
ZM =
YM
(9 )
)
(10 )
(11)
Table II: Estimated and measure d resistance
1
j
YM =
−
RM
XM
(12 )
E1 = V1,mea − Z 1 × I 1,mea
(13 )
I ' 2 ,mea =
I core =
resistance of primary and secondary windings is
measured directly using the Wheatstone bridge
method [19] at the same intervals of time to validate
the estimated results. The estimated and the measured
values of the equivalent resistance referred to primary
side are provided in Table II.
E1
Z '2
E1
RM
Time
(Min)
Estimated
Measured
Resistance
Resistance
(Ohms)
(Ohms)
0
4.0004
4.0112
5
4.3203
4.3260
10
4.4781
4.5020
15
4.6350
4.6430
20
4.6722
4.6857
25
4.7250
4.7434
30
4.7580
4.7736
35
4.7580
4.7956
40
4.7979
4.8192
45
4.7979
4.8324
50
4.8373
4.8498
55
4.8373
4.8587
60
4.8373
4.8615
The rise in winding temperature is estimated from
the estimated values of winding resistance, using (7).
The estimated and measured temperature is plotted in
fig. 3. From the results it could be found that the
estimated value based on short circuit test results
(Estimated 1) possess less than three-percentage error
with respect to measured value of winding
temperature determined from the measured resistance.
To demonstrate the applicability of the method in a
practical situation, the parameter estimation is also
done based on the load test data of supply voltage,
primary current, input power and the load resistance
obtained from output power and secondary current.
The load test data is recorded at the same time
intervals as in the previous case and given in Table III.
(14 )
(15 )
3. RESULTS AND DISCUSSIONS
A 230 / 50V, 1 kVA, 50 Hz single-phase
transformer is considered for the experimental studies.
The transformer is a naturally cooled and dry type. A
heat run test is performed in the transformer as per the
specifications of IEEE test standards [1]. That is a
constant current of 5A – equivalent to the full load
current and the current supplying for the losses in the
transformer – is circulated in the short-circuited
windings of transformer for one hour. The voltage,
current and equivalent losses in the primary side of the
transformer is recorded during the heat run test at
equal intervals of time using analog measuring
instruments of 0.5 class accuracy. The observed values
are provided in Table I.
Table I: Equiv alent loading test data
Time
(Min)
Primary
Primary
Power
Voltage
Current
Dissipated
(Volts)
(Amps)
(Watts)
0
21.0
5.0
100.0
5
22.5
5.0
108.0
10
23.0
5.0
112.0
15
23.4
5.0
116.0
20
23.6
5.0
117.0
25
23.8
5.0
118.0
30
23.9
5.0
119.0
35
23.9
5.0
119.0
40
24.0
5.0
120.0
45
24.0
5.0
120.0
50
24.1
5.0
121.0
55
24.1
5.0
121.0
60
24.1
5.0
121.0
These values are used to estimate the equivalent
resistance and the reactance value of the transformer at
the corresponding operating points by applying them
in (1). Though a closed form solution is
straightforward for the determination of equivalent
resistance, the in-situ parameter estimation method
using GA is also demonstrated. The winding
Table III: Load test data of single -phase transformer at
230 Volts, 5 Amps supply
Time
(Min)
0
5
10
15
20
25
30
35
40
45
50
55
60
Power
Input
(Watts)
1104
1108
1110
1111
1112
1113
1114
1114
1115
1115
1116
1116
1116
Secondary
Voltage
(Volts)
47.5
47.0
46.6
46.3
46.1
45.9
45.8
45.8
45.7
45.7
45.6
45.6
45.6
Secondary
Current
(Amps)
22.0
22.0
22.0
22.0
22.0
22.0
22.0
22.0
22.0
22.0
22.0
22.0
22.0
Power
Output
(W atts)
1029.5
1011.0
1004.0
1001.0
997.5
995.0
994.0
994.0
993.5
993.5
993.0
993.0
993.0
Parameter estimation is done using (1) – based on the
exact equivalent circuit model – and the rise in
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on the change in winding temperature as it is reflected
through the winding resistance. Therefore special
attention on these factors need not be exercised to
determine the maximum overload capability.
The method does not address the issue of
determination of hot spot temperature, which finds its
application in the detection of incipient faults and also
the overload limit of transformer. Nonetheless from
the knowledge of winding resistance and the
equivalent reactance values this method could also
suggest the general health of the transformer by
comparing against the database of the estimated
parameters under healthier condition. Therefore using
this method the general health of the transformer could
also be monitored under its field operating conditions.
Fig. 3: Average temperature rise in the
windings of transformer
temperature are computed using (7). Results are
plotted in fig. 3. The average winding temperature rise
after one hour in all the three cases is approximately
60 C, which is above the ambient temperature of 40
C, as found in fig. 3. The rise in temperature
determined from the load test results (Estimated 2) at
initial time periods shows a slight deviation from the
measured value, which is due to the fact that the
transformer is slightly overloaded above the rated
value. The final steady state rise in temperature after
one hour is found to be closer to the measured value.
The results demonstrate that the suggested method
could be used for the estimation of rise in average
winding temperature of the transformer in an in-situ
basis by applying the easily measurable signals of the
primary side and load side of the transformer
periodically. From the estimated parameters the rise in
winding temperature in the primary and secondary
windings can be also separately determined as shown
in fig. 4.
4. CONCLUSIONS
The paper has demonstrated an in-situ estimation
of the rise in average winding temperature of the
transformer using the easily measurable signals. The
applicability of the method has been experimentally
demonstrated with the heat run test, by both the short
circuit and actual load tests. Apart from the
determination of average temperature rise of
transformers the method could also estimate the
constant and variable losses and their specific
contribution towards the temperature rise.
This method could be directly applied for the
overload management of power transformer operating
under varying load conditions, changing ambient
temperature and thermal time constant of transformer.
The health of the transformer also can be monitored
using the database of the estimated parameters under
healthier operating conditions.
References:
[1] “IEEE Standard Test Code for Dry -Type Distribution
and Power Transfo rmers” , ANSI / IEEE C57.12.91,
1992.
[2] P. W. Linden , “Thermal Considerations in Specifying
Dry Type Transformers”, IEEE Transactions on
Industry Applications, vol. 30, no. 4 July -Aug 1994,
pp. 1090 - 1098.
[3] B.C Lesieutre, W. H. Hagman, and J. L. Jr. Kirtley,
“Improved Transformer Top Oil Temperature Model
for use in an On -Line Monitoring And Diagnostic
System”. IEEE Transactions on Power Delivery,
vol. 12, no. 1, Jan 1997, pp. 249-256.
[4] M. P. Saravolac, “Use of Optic Fibers for Temperature
Monitoring in Power Transformers”. IEE Colloquium
(Digest), no. 75, Mar 22 1994.
[5] P. K Sen, “Transformer Overloading”. International
Journal of Power and Energy Systems, vol. 19, no. 1,
1999, pp. 52-56.
[6] K. F. Man, K. S. Tang and S Kwong, “Genetic
algorithms: Concepts and Applications”, IEEE
Transactions on Industrial Electronics, vol. 43, no. 5,
1996, pp. 519-534.
[7] Sawhney A K., “Electrical and Electronics
Measurements and Instrumentation”, 1997 Edition.
Fig. 4: Estimated temperature rise in
primary and secondary windings
Here, the secondary winding has a higher rise in
temperature, as it lies inside the primary winding. It
was found that the current density of both the
windings is the same, that is 0.7074 A/mm2 . Therefore
the heating of the secondary winding is faster and
higher.
By monitoring the rise in average winding
temperature the overload capability could be
determined directly. This means that the need for
costlier fiber-optic temperature sensors could be
avoided. Moreover the suggested method inherently
accounts the effect of various factors like variation in
ambient temperature, winding thermal time constant
94