Open Journal of Applied Sciences, 2013, 3, 24-29
doi:10.4236/ojapps.2013.32B005 Published Online June 2013 (http://www.scirp.org/journal/ojapps)
Effect of Climate Change on Transformers Loading
Conditions in the Future Smart Grid Environment
Murtaza Hashmi1, Matti Lehtonen2, Seppo Hänninen1
1Energy Systems Knowledge Centre, VTT Technical Research Centre of Finland, Finland
2Department of Electrical Engineering, Aalto University, Finland
Received 2013
ABSTRACT
The steady-state calculations are performed using IEC guidelines to determine the hot spot temperatures of distribution
and power transformers in the worst projected Finnish environment due to long summer periods. Moreover, the effect of
increase in winding resistance due to increase in ambient temperatures has been taken into account. The primary objec-
tive of the research is to investigate the possible extreme circumstances due to climate change. It is concluded that the
power and distribution transformers should be progressively de-rated under such circumstances for their safe operations,
which will not only prove cost-effective for utilities but also improve the reliability of the power supply to their valued
customers in the challenging future smart grid environment.
Keywords: Distribution Transformer; Power Transformer; Winding Resistance; Climate Change; Electricity
Distribution Company; Reliability; Smart Grid
1. Introduction
Power transformers are used in power generation units,
transmission, and distribution networks to step up or
down the voltage of the power system. The capacity is
usually between a few MVA and about 100 MVA. To be
able to use the real capacity of power transformers, it is
important to know the duration and level to which power
transformers can be thermally stressed. Because of in-
creasing age coupled with higher loading and the need to
more efficiently utilize expensive components such as
transformers, increasing demands are being imposed on
the liquid and solid insulating materials with regard to
operating reliability and overloading capability.
The impact of large power transformer failure on power
systems is due to their high cost, the impact on system
operation due to their location and role in the network,
and the fact that they are encased in tanks of flammable
and toxic fluid, which is a potential risk to people, prop-
erty and the environment [1]. These factors surely pre-
sent a strong motivation for utilities to monitor the health
of their power transformers. In short, power transformers
are likely to be the most expensive asset within electrical
networks [2], and so their availability and reliability is of
paramount importance. Their nominal life expectancy is
expressed in years, corresponding to their nameplate
rated load and ideal conditions [3]. Failure will eventu-
ally occur as the paper insulation on the windings erodes
and passes the limit where the structural and electrical
stresses can be sustained. This unavoidable degradation
is cumulative and is further increased by the presence of
both heat and oil contaminants, including gases and wa-
ter [4].
The designer aims to ensure that temperatures are kept
to reasonable levels in a transformer when loaded up to
continuous maximum rating. Practically, a power trans-
former has a significant thermal capacity largely arising
from the insulating oil. This allows the possibility of
loading for short periods beyond the continuous rated
nameplate value [5]. Limitations on acceptable conductor
and oil temperatures are typically stated in the transformer
specification, and these in turn are likely to be based on
recommendations in such documents as the international
standard loading guide for oil immersed power trans-
formers, IEC-354 [6].
A transformer’s loading capacity is related to the ex-
posure of its insulation to heat, the highest temperature of
which is referred to as the hot spot temperature. The hot
spot temperature effect on the paper insulation of wind-
ing is used to quantify the limit of its temperature range
over a calculated period of time. The problem, however,
is that these limits are dynamic due to the changing
transformer characteristics and varying ambient climate
conditions.
2. Temperature Effects in Transformer
When a current is passed through a conductor, heating

M. HASHMI ET AL. 25
losses are produced in the form of i2r losses, where i is
the magnitude of current passing through the conductor
having resistance r. An equilibrium conductor tempera-
ture is reached if the heat can be removed at the same
rate as that at which it is produced. Physical and chemi-
cal effects governing the interaction between materials
are generally temperature-dependent and chemical reac-
tion rates typically increase with increasing temperature
[5].
Monitoring the transformers through temperature sen-
sors is one of the simplest and most effective condition
monitoring techniques for the asset management in smart
distribution grid. Abnormal temperature readings almost
always indicate some type of insulation failure in a trans-
former. For this reason, it has become common practice
to monitor the hot spot, main tank, and bottom tank tem-
peratures on the shell of a transformer. As the transfor-
mer begins to heat up, the winding insulation may start
deteriorating and the value of the dielectric constant of
the mineral oil reduces from the standard value.
According to the IEC guide, the ageing of the paper
insulation system is such that the stated transformer life
can be achieved for a continuous maximum hotspot tem-
perature of 98℃. Beyond this temperature, it is assumed
that the rate of ageing doubles for every increase of 6℃.
At temperatures of the order of 150℃, accelerated age-
ing tests in the laboratory demonstrate that the useful life
of the paper may only be a few days. This clearly limits
the life of the transformer and is one of the governing
factors on the maximum load that should be used [5].
3. Transformers Ratings Calculations
Emergency and/or planned overloading of power trans-
formers beyond their nameplate rating depends on sev-
eral factors, including design and operating characteris-
tics, daily load curve, historical loading data, testing and
maintenance programs, and the particular applications.
The overloading capabilities depend primarily on the wind-
ing hottest spot temperature. Determining accurately the
hottest spot temperature is very critical to the transformer
overall life expectancy assessment.
3.1. IEC-354 Based Transformer Loading Guide
Short duration and cyclic loadings are normally calcu-
lated following the principles in IEC-354. The loading
guide tables are based solely on the equations for wind-
ing hotspot and oil temperatures, without regard for other
factors. This is because the effects such as heating by
stray losses are very dependent on design and in any case
not easy to calculate. However, in constructing loading
guide tables, the transformer user needs to be aware of
restrictions on loading other than winding temperature
and the circumstances in which those restrictions might
apply [5].
The IEC standard provides a series of simplified equa-
tions that describe a mathematical model for the calcula-
tion of operating temperatures in a transformer. The as-
sumptions listed in these standards include: a linear tem-
perature rise in the oil from the bottom of the tank to the
top, a parallel temperature rise in the windings, and an
allowance for stray losses that is used to assess the hot
spot temperature. As this standard points out for large
power transformers, the results for hot spot temperatures
(based on temperature rise tests) may not be valid due to
the significance and complexity of the contribution of
flux leakage to the heating of the windings. Therefore,
this method has a limited use, restricted at or below the
transformer’s rated capacity. A further note in this stan-
dard adds that corrections to account for load losses and
oil viscosity can be dismissed as either insignificant, or
that the effects cancel each other.
A number of semi-empirical equations have been de-
rived to predict the hottest spot temperature rise in trans-
formers at their rated full load. Of these, the most com-
mon model used for this and top oil temperature calcula-
tions is described in IEC-354 [6]. A simplified trans-
former temperature distribution based on this model is
shown in Figure 1 [7]. The steady state temperature rela-
tions in IEEE are similar to Figure 1, which have been
extracted from the IEC loading guide [4].
3.2. Different Temperatures in Transformer
The ultimate hot spot temperature for a transformer un-
der any load K is equal to the sum of the ambient tem-
perature, the top oil temperature rise over ambient, and
the hot spot temperature rise over top oil. This can be
expressed by the following well-known equation already
used by many researchers.
HTOAH








(1)
where 
A is the ambient temperature in C,

T0 is the top
oil temperature rise over ambient inC,

H is the hot
Figure 1. Transformer thermal diagram as per IEC-354 [7].

M. HASHMI ET AL.
26
spot temperature rise over top oil temperature in℃, and

H is the ultimate hot spot temperature in℃. The top oil
temperature over ambient temperature is given by the
following equation:
n
RTOTO R
KR










 1
12
 (2)
where

TO  R is the top oil temperature rise over ambient
at rated load, R is the ratio of load losses at rated current
to no load current losses, and K is the load factor (sup-
plied load/rated load). The hot spot temperature rise over
top oil temperature is given by:
m
HKgH 2
  (3)
where 
H is the hot spot to top oil rise, H is the hot
spot factor due to increased eddy losses at the winding
end, and g is the average winding to average oil tem-
perature rise at rated load; n and m are empirically de-
rived exponents that depends on the cooling method. The
four modes of cooling used are: natural convection of oil
in the transformer and natural convection of cooling air
over the radiators (OA/ONAN), natural convection of oil
with forced convection of air over the radiators (FA/
ONAF), non-directed forced oil flow and forced air flow
(NDFOA/OFAF), and directed forced oil flow and forced
air flow (DFOA/ODAF). The above mentioned expo-
nents used are given in Table 1.
3.3. Simplified Transformer Overloading Guide
It is quite common practice to exceed the nameplate rat-
ing when loading power and distribution transformers for
short times. Simplified transformer overloading guide-
lines take into consideration ambient temperature, name-
plate rating, design fundamentals, long-time emergency
loading, short-time overloading, moisture contents (every
0.5% increment of content reduces insulation life by half),
etc.
Some of the key features are given for clarity and better
understanding in [8-11], e.g. transformer hot spot tem-
peratures above 98‒ cause the winding insulation to age
faster. The rate at which transformer insulation deterio-
rates increases exponentially with temperature up to
140°C; it doubles for every temperature rise of 6°C. The
Table 1. Exponents used in temperature calculations.
IEC IEEE
Types of cooling
n m n m
OA/ONAN 0.9 0.8 0.8 0.8
FA/ONAF 0.9 0.8 0.9 0.8
NDFOA/OFAF 1 0.8 0.9 0.8
DFOA/ODAF 1 1 1 1
insulation will rapidly deteriorate at temperatures above
this level.
Notwithstanding, transformers can occasionally be run
over their nameplate rating for a limited period, i.e. a few
days, without dramatically reducing the life of the trans-
former. The relative rate of using life is given in [12]. If,
e.g., a transformer is run at a continuous loading level
that gives a winding temperature of 104℃, the ageing
rate would be doubled, i.e. the transformer will age two
days in one day. If such periods are restricted to a few
days and do not occur very often, the loss of life over its
normal life span will be negligible. The converse is also
true, periods of lower than 98℃ operation will tend to
“pay back” periods of moderate overloading. The num-
ber of hours per day of operation at any given value of
winding hot spot temperature that will use one day's life
are also given in [12]. A winding hot spot of 116℃ that
prevails for three hours would produce ageing equivalent
to one day according to this modeling. In general, the
application of load in excess of nameplate rating involves
a degree of risk and accelerated aging. These effects
(short term transformer failure, under overloading condi-
tions, and long duration overload) are summarized in
[13].
3.4. Transformer Loading in “Worst” Finnish
Environment
The ambient temperature plays an important role for the
determination of the hot spot temperature of a trans-
former determined by its loading profile. The hot spot
temperature increases linearly by increasing the ambient
temperature. Roughly, for every 1℃ increment in ambi-
ent temperature, the loading capacity can be decreased by
1% without any loss-of-life and vice versa.
On average, the ambient temperature is increasing to
some extent every year due to the effect of overall global
warming. This has been realized by monitoring ambient
temperatures over the last several years. The IEC loading
guide is recommended for transformers operating with an
ambient temperature of 20℃. However, it does not give
the actual hot spot temperature at varying ambient tem-
peratures. Table 2 gives the future ambient temperatures
of different locations in Finland which is based on
weather forecasts [14]. It is revealed that ambient tem-
perature may increase up to 33.8℃ in Helsinki during
the years 2016 - 2045.
4. Hot Spot Temperatures Calculations
In this paper, steady-state calculations are performed to
calculate the hot spot temperature of distribution and
power transformers for possible future ambient tempera-
tures in Finland varying from 20-40C. The value of g in
the calculations is assumed to be 23C. The value of H is

M. HASHMI ET AL. 27
Table 2. Extreme temperatures for the periods 1961 - 1990
and 2016 - 2045 (ilmatieteen laitos 1991).
Extreme temperatures (˚C)
1961 1990 20162045
Helsinki -35.9 31.9 -28.4 33.8
Tampere -37 31.6 -30 33.5
Vaasa -38.6 31.8 -31.6 33.7
Kuopio -39.3 32.6 -32.6 34.6
Kuusamo -45.2 31.2 -39.2 33.1
Sodankylä -44.7 31.3 -38.8 32.9
assumed to be 1.1 for distribution transformers and 1.3
for medium size and large power transformers. The value
of 
TO  R is selected in such a fashion (57.8℃ for distri-
bution transformers and 54.1℃ for power transformers)
that the ultimate hot spot temperature works out to be 98
℃ for an ambient temperature of 20℃. A 500 kVA
transformer having load losses of 5 kW at ambient tem-
perature 20℃ and a 20 MVA transformer having load
losses of 106 kW at ambient temperature 20℃ are con-
sidered for calculations.
4.1. Calculations for Distribution Transformers
The data for secondary line transformers is given in Ap-
pendix 1 [15]. The values of n and m are taken as 0.9 and
0.8, respectively, for the ONAN mode of cooling. R is
defined as the ratio between load losses at rated current
to no load losses. The load losses at rated current given
by the manufacturer are estimated at an ambient tem-
perature of 20℃. However, their value increases due to
increase in the resistance of the windings at higher am-
bient temperatures. A 0.4% increase in load losses due to
a 1℃ rise in ambient temperature is a good approxima-
tion for this calculation. The load losses at rated current
(given in Appendix 1) also include this incremental fac-
tor. For example, the load losses at rated current for a 50
kVA transformer are given as 1330 W at an ambient
temperature of 20℃ [15]. The hot spot temperature is to
be calculated at 33.8℃ (the projected maximum tem-
perature in Helsinki in 2045). The increase in ambient
temperature is 13.8℃, which increases the load losses by
73 W. Therefore, the total load losses are estimated to be
1403 W. The value of R is recalculated due to the in-
crease in load losses. The rated load of the transformer
slightly increases due to increases in load losses (tem-
perature dependent) at higher ambient temperatures;
therefore, the supplied load is also increased to the same
extent for unity load factor conditions (K = 1). For de-
termining the actual de-rating factor of the transformers,
the calculated value (including the effect of temperature
dependent load losses) is divided by the same incre-
mental factor.
The hot spot temperature for an ambient temperature
of 33.8℃ (Helsinki maximum future temperature in
2045) is calculated to be 115℃ for a variety of distribu-
tion transformers. Conversely, the transformers should be
de-rated to approximately 86% - 87% of their maximum
load for a hot spot temperature of 98℃ (as per IEC guide).
The value of the hot spot temperature is approximately
the same for different ratings of transformers. The ratings
of the transformers do not have significant effect on the
load factor, i.e. the de-rated values of load factors for
distribution transformers are in the same range.
4.2. Calculations for Power Transformers
The data for primary line transformers is given in Ap-
pendix 2 [15]. The assumptions stated in sub-section 4.1
have also been implemented in the calculations for power
transformers. The load losses at rated current (given in
Appendix 2) also include the incremental factor ex-
plained in sub-section 4.1. For example, the load losses
at rated current for a 16 MVA transformer are given as
88 kW at an ambient temperature of 20℃ [13]. The hot
spot temperature is to be calculated at 33.8℃ (Helsinki
maximum future temperature in 2045). The increase in
ambient temperature is 13.8℃ which increases the load
losses by 4.9 kW, and so the total load losses are esti-
mated to 92.9 kW.
The hot spot temperature for an ambient temperature
of 33.8℃ (Helsinki's maximum future temperature in
2045) is calculated to be 115℃. Conversely, the trans-
formers should be de-rated to approximately 86% - 87%
of their maximum load to maintain a hot spot tempera-
ture of 98℃ (as per IEC guide). The value of the hot
spot temperature is approximately the same for different
ratings of transformers. The ratings of the transformers
do not have a significant effect on the load factor, i.e. the
derated values of load factors for power transformers are
in the same range. The different values of hot spot tem-
peratures and load factors due to variation in ambient
temperature are calculated for distribution and power
transformers and are given in Table 3.
5. Results and Discussion
The results are extracted from the hot spot temperatures
calculations performed in the previous section. It is re-
vealed from Figure 2 that by increasing the ambient
temperature, the hot spot temperature also increases. This
relationship is not quite linear because the temperature
dependent winding resistance effects have been taken
into account. The rated load losses depend on ambient
temperature and this has been considered during the cal-
culations. The effect of ambient temperature on the rating

M. HASHMI ET AL.
28
of transformers (load factor) is depicted in Figure 3,
which highlights the fact that transformers must be de-
rated to avoid excessive ageing and loss-of-life.
Table 3. Hot spot and load factor values at various ambient
temperatures for distribution and power transformers.
Distirbution transformer Power transformer




for
 
K (for


=98°C)


for
 
K (for


=98°C)
20 98 1 98 1
22 100.5 0.981 100.5 0.98
24 103.1 0.961 103.1 0.962
26 105.6 0.94 105.6 0.942
28 108.1 0.921 108.1 0.923
30 110.6 0.901 110.7 0.904
32 113.1 0.881 113.2 0.884
34 115.6 0.861 115.7 0.865
36 118.2 0.841 118.2 0.845
38 120.7 0.821 120.8 0.824
40 123.2 0.8 123.3 0.805
20 22 24 2628 3032 34 36 38 40
95
100
105
110
115
120
125
Ambient temperature (

C)
Hot spot temperature (

C)
Distribution transformer
Power transformer
Figure 2. Effect of ambient temperature on hot spot tem-
perature for distribution and power transformers.
20 2224 26 2830 3234 36 3840
0. 8
0. 85
0. 9
0. 95
1
Ambient temperature (

C)
Rated load (pu)
Distribution transformer
Power transformer
Figure 3. Effect of ambient temperature on load factor for
distribution and power transformers.
It is proposed that power transformers should be
de-rated to a greater extent than distribution transformers
(please see Figure 2, where the hot spot temperatures of
power transformers seem slightly higher than distribution
transformers). However, this fact is not revealed in Fig-
ure 3 due to different values of R for distribution and
power transformers used in the calculations; the available
data does not cover a variety of ratings. Moreover, the
same values of m and n have been used for distribution
and power transformers, but these values should be dif-
ferent in a more comprehensive analysis. For example,
considering the DFOA/ODAF mode of cooling for power
transformers (n = 1 and m = 1) at the same ambient tem-
perature, the hot spot temperature would rise higher than
in a distribution transformer, while it would be de-rated
to a lower extent than a distribution transformer. The
difference in hot spot temperatures and rated loads of
distribution and power transformers at extreme tempera-
ture (40℃) in Figure 2 and Figure 3 are only 0.08% and
0.6%, respectively, which may increase by changing the
mode of cooling for power transformers.
6. Conclusions
Hot spot temperature calculations for the projected future
ambient temperature are performed using IEC guide. The
hot spot temperature increases almost linearly by in-
creasing the ambient temperature. Conversely, the trans-
formers should be de-rated from their given loading val-
ues (provided by the manufacturers).
The hot spot temperature of distribution and power
transformers may increase up to 115℃ in Helsinki (due
to increase in ambient temperature up to 33.8℃), there-
fore, the transformers must be progressively de-rated to
86% - 87% of their actual ratings without loss-of-life. If
hot spot temperatures increase up to 115℃, the relative
rate of using life of transformers may decrease up to 8
times if operated continuously.
To prevent transformers from early ageing, they
should only be operated less than 3 hours per day in this
worst environmental condition as stated above. This
study will be useful for electric power utilities to revise
the allowable loadings of their transformers to avoid
damage, as well as for the safe and reliable distribution
of power to their valued customers. The investigation
carried out will be helpful to analyze for how long the
new distribution and power transformers installations can
be partially delayed and how better and reliable asset
management can be carried out in the challenging future
smart grid environment.
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M. HASHMI ET AL.
29
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Appendix 1. Hot spot temperature calculations at extreme temperature (33.8℃) for distribution transformers.
Rating
(kVA)
Voltage level
(kV/kV)
Mode of
cooling
No load
losses (W)
Load losses at rated
current (W) R








for  

K (for 
H=98℃)
50 20/0.4 ONAN 150 1403 9.3 60.4 21.3 115.5 0.868
100 20/0.4 ONAN 245 1973 8 60.3 21.3 115.5 0.867
200 20/0.4 ONAN 465 2743 5.9 60.2 21.3 115.4 0.864
500 20/0.4 ONAN 930 5276 5.7 60.2 21.3 115.4 0.863
1000 20/0.4 ONAN 1500 8864 5.9 60.2 21.3 115.4 0.864
Appendix 2. Hot spot temperature calculations at extreme temperature (33.8℃) for power transformers.
Core Rating
(MVA)
Mode of
cooling
No load
losses (kW)
Load losses at
rated current (kW)R






for   K (for

H = 98℃)
Al 16 ONAN 16.1 92.9 5.8 56.4 25.2 115.4 0.865
Cu 20 ONAN 16.8 111.8 6.6 56.4 25.2 115.5 0.867
Cu 31.5 ONAN/ONAF 24.5 143.5 5.8 56.4 25.2 115.4 0.865
Al 40 ONAN/ONAF 33.5 187.8 5.6 56.4 25.2 115.4 0.865