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TECHNIQUES FOR ESTIMATION OF HOT SPOT
TEMPERATURES IN TRANSFORMERS
Vivian Ohis
vivian.ohis@eng.monash.edu.au
Tadeusz Czaszejko
t.czaszejko@eng.monash.edu.au
Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Victoria 3800, Australia
Centre for Electrical Power Engineering, Monash University, Clayton, Victoria 3800, Australia
Abstract
This paper contains a review of methods published by two standards organizations on the estimation of
the hot spot temperature within a transformer, addressing some issues concerning the accuracy of their
results. Included are summaries of articles on modelling techniques and the reasons offered by their
authors regarding their effectiveness, focussing on their advantages and disadvantages. The paper also
engages in some discussion on the current use of Artificial Intelligence (AI) systems on the dissolved
gas analysis (DGA) results of transformer oils, and how similar AI systems are being adopted to
estimate hotspot temperatures. Finally, some mention is made of the application of fibre temperature
probes that have been recently developed. Such technology has been valuable to corroborate results and
secure the validity of works done in this area. But there are limitations on their application, and these
are discussed, highlighting the economic and safety implications.
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INTRODUCTION
Put into perspective, power transformers are probably
the single most expensive asset within an electrical
transmission and distribution network [1], and that
alone justifies the requirement of developing
appropriate reliable systems ensuring their availability
and reliability.
They are designed with a nominal life expectancy in
years, evaluated for a rated load under ideal conditions
as indicated by their nameplate. Excluding unusual
circumstances unrelated to the normal functioning of a
power transformer, failure is expected to occur as the
windings’ paper insulation erodes past its limit to
sustain appropriate structural and electrical stresses.
The degradation is cumulative and adversely affected
by the presence of both heat and oil contaminants,
including gases and water [2].
Limited excessive loading beyond the transformer’s
nameplate rating is permissible and often experienced
during emergency conditions, but the trade-off is an
accelerated demise of the transformer towards an endof-life condition.
In Australia, the privatisation of the electricity utilities
has met with increasing pressure by investors and
shareholders to maximise Return-On-Investment
(ROI). Utilities in the electricity industry must now reexamine operating strategies on long term, back up
and failure procedures balancing the demands for both
reliable and economic performance. Obviously, under
utilised equipment, especially at the size of expense of
power transformers, is undesirable. Ultimately the
target will be to set transformers to run at “Full Warp
Drive” as the normal mode of operation.
However, the techniques used to predict a
transformer’s loading limits are still too primitive to
provide any guarantees. Any inadvertent abuse, where
the transformer’s temperature thresholds are exceeded
will compromise the performance of the transformer, a
result caused by the application of stresses beyond the
anticipated design limits, and possibly generating
undetected incipient faults. Albeit the transformer may
survive, avoiding premature failure, there will remain
a high level of doubt concerning its state of reliability.
An obvious resolution to this matter lies in the ability
to accurately predict the safe limitations of power
transformers and the associated loss-of-life trade-off.
Such calculations will enable operational strategies
that address economic and reliability issues without
exceeding those thresholds that result in transformer
damage or failure.
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DYNAMIC LOADING
“…A candle that burns twice as bright lasts half as
long …”. So too transformers can run at over rated
loadings within limits, consequently shortening their
expected service life. A transformer’s loading capacity
is related to the exposure of its insulation to heat, the
highest temperature of which is referred to as the Hot
Spot Temperature (HST). The HST’s effect on the
windings’ paper insulation 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.
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THE BENEFITS OF ACCURATE HOT
SPOT ESTIMATION
Development of an accurate method of estimating the
dynamic loading limitations, and consumption of
service life of a transformer, has economical and
operational benefits.
Economically, deferral of expenditure on expensive
plant by “driving them harder”, has always been
recognised as a wise business strategy. Conversely,
but equally wise, being able to correlate the cost of
depreciation on a transformer with usage in kilowatt
hours (kWhs) allows for a more financially equitable
method for assessing asset performance, thereby
enabling the calculation of the most appropriate time
for retiring older equipment. It also assists in planning
for network growth and reducing expensive risks.
Similarly, strategic maintenance and operational
procedures are best formulated where the performance
of existing plant has been accurately assessed.
Unexpected failures are rarely welcome, especially
with increasing pressure to minimise backup resources
such as redundant transformer capacity.
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CONDITION MONITORING
Over recent years, condition monitoring of power
transformers has become a far more affordable
exercise; in actual fact, the true cost of not having
adequate online monitoring is arguably much greater,
especially if an avoidable incident should occur
resulting in damage and injury. Several companies
have already developed monitoring systems with
simple algorithms that activate alarms and protection
devices when monitored inputs have exceeded static
thresholds. These thresholds are unquestionably
conservative, perhaps through lack of confidence,
which intuitively reduces any risk of damage or
failure, but also under utilises the transformers’ true
performance.
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THE STANDARDS
Several Standards have been developed to estimate the
temperature of hotspots within a transformer as a
function of current load and ambient climate
conditions. Many electricity companies have used
these as the basis of their operating procedures,
developing tables and charts that highlight their
exposure to risks within their network. As previously
mentioned, there is often a policy among decision
makers in this field to bias all errors on the side of
caution. In this paper are presented two such
Standards: IEC 354:1991 and IEEE Std. C57.91-1995.
5.1
International Electrotechnical Commission
IEC 354:1991
“IEC: Loading guide for oil-immersed power
transformers”
The IEC Standard [3] provides a series of simplified
equations that describe a mathematical model for the
calculation of operating temperatures in a transformer.
The assumptions listed in these standards include: a
linear temperature 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 HST.
As this Standard points out, for large power
transformers, the results for hotspot 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 transformers rated capacity.
A further note in this Standard adds that corrections to
account for load losses and oil viscosity, can be
dismissed as either insignificant, or that the effects
cancel each other.
5.2
The Institute of Electrical and Electronic
Engineers
IEEE Std C57.91-1995
“IEEE Guide for Loading Mineral-Oil-Immersed
Transformers”
In the IEEE [2] Standard there are two methods of
calculating the HST. The first method, as with the IEC
Standard, is a mathematical model. In the calculation
there is the assumption that the oil temperature across
the windings is equal to that of the top oil temperature.
However, at the commencement of the Standard there
is an admission on the validity of this assumption.
After measurements were taken with recently
available direct thermocouple and fibre optic devices,
it was revealed to be incorrect. A paper written by
Lesieutre et al. [4] also points out that the method
does not adequately account for variations in the
ambient temperature for which they [4] have
suggested a modification and claimed to have verified.
The second method in the IEEE Standard (Annex G)
takes into account these observations and attempts to
correct them, including thermal effects and liquid
viscosity during overload conditions.
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MODELLING
While Mathematical Models, as those represented in
IEEE [2] and IEC [3] Standards are based on the
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simplified observation of the exponential cooling of
lumped heated bodies, others such as Swift et al. [5]
have suggested that a thermodynamic and heat transfer
approach would be more appropriate.
They explain that by incorporating the significance of
the heat transfers between mediums such as the
transformer oil and transformer tank-wall, a more
practical and accurate estimation is probable. But even
this model suggests the need for accurate parameter
estimation and the assumption that the transformer is
operating in an environment that supports nominal
operation.
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ARTIFICIAL INTELLIGENCE (AI)
Owing to the complexity and variations in transformer
design and operation, the expectation that a reliable
and accurate “one size fits all” mathematical model is
possible, is questionable. In any case, isolated
experiments conducted using this method have met
with the requirement for precision that is impractical,
as discovered by Tylavski et al. [6]. Ultimately, such
models are not capable of identifying and adjusting for
the effects of aging, inaccurate inputs, and incipient
faults. The identification of these difficulties has
ignited particular interest in two categories of AI:
Fuzzy Logic and Neural Networks.
As a research tool, the Fuzzy Inference System (FIS)
has been applied to a variety of similar projects where
there has been a need to address the issue of
inaccurate information and also apply heuristic
reasoning [7].
Similarly, Artificial Neural Networks (ANN) has
found implication where dynamic parameters are
difficult to define mathematically [7] where training of
the model can recognise trends and the dynamic
nature of some of the parameters that might once had
been believed to be constant.
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FIBRE OPTIC TEMPERATURE PROBES
Fibre Optic Temperature Probes are the obvious new
technology, hailed as the easy, cost effective remedy
for determining transformer HSTs. But seen
objectively, the ultimate task of transformers is to
provide reliable, efficient operation at the lowest
possible cost. At the bare minimum, a transformer is
little more than an iron core, wrapped with windings,
bathed in a tank of oil. Anything else adds complexity
and cost through design, maintenance and supervision.
It is from this premise that the addition of measuring
equipment may not always be the most advisable
approach.
Also, whilst for new transformers the task of
embedding fibre optic cable into its windings is a
seemingly easy and inexpensive task, it provides no
reprieve for the vast majority of older transformers,
many of which have operated undisturbed for the past
few decades, and for economic reasons, may be wisely
left that way.
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DGA USING AI SYSTEMS
A common method for identifying developing faults
in power transformers is the Dissolved Gas Analysis
(DGA) [8]. Analysis of ratios of specific dissolved gas
concentrations, their generation rates, and the measure
of total combustible gases are used as the attributes for
classification. Thresholds are designed to partition the
attributes into intervals. Specific combinations of
these intervals are then used to identify the fault.
However, in much the same way as determining
hotspots, the results can differ, dependent on the
thresholds used, coupled with the almost infinite
variations and combinations of factors that influence
the results. These are the classic characteristics that
advocate the use of Fuzzy Sets (FS) and Artificial
Neural Network (ANN) systems.
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CONCLUSIONS
A variety of models and techniques have been
assessed over the years, with claims of improvement
and higher dependability. Works done in this area by
D.J. Tylavsky et al. [8] convincingly show that there is
a balance between complexity and accuracy of results,
and that in fact the major sources of error occurred
from imprecision at the input.
AI systems are customarily designed for these types of
problems. Coupled with physical and mathematical
models would assist in the development of a system
that was both accurate and simple to implement.
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REFERENCES
[1]
O. Roizman, V. Davydov, “Neuro-Fuzzy
Computing for Large Power Transformers Monitoring
and Diagnostics”, Fuzzy Information Processing
Society, 1999. NAFIPS. 18th International Conference
of
the
North
American,
1999
Page(s): 248 -252
[2]
IEEE Std. C57.91-1995 “IEEE Guide for
Loading Mineral-Oil-Immersed Transformers”
[3]
IEC 354 1991-09 “Loading Guide for OilImmersed Power Transformers”
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[4]
B.C. Lesieutre, W.H. Hagman, J.L. Kirtley
Jr., “An 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, January 1997
[5]
G.Swift, T.S. Molinski, W. Lehn, “A
Fundamental Approach to Transformer Thermal
Modeling – Part I: Theory and Equivalent Circuit”,
IEEE Transaction on Power Delivery, Vol. 16, No. 2,
April 2001
[6]
J.R.
D.J. Tylavsky, Q. He, J. Si, G.A. McCulla,
Hunt, “Transformer Top-Oil Temperature
Modeling and Simulation”, IEEE Transactions on
Industry Applications, Vol. 36, No. 5, Sept/Oct 2000
[7]
M. Kezunovic, “Intelligent Systems in
Protection Engineering”, Power System Technology,
2000. Proceedings. PowerCon 2000. International
Conference
on,
Volume:
2,
2000
Page(s): 801 -806 vol.2
[8]
Y.C. Huang, H.T. Yang, C.L. Huang,
“Developing a New Transformer Fault Diagnosis
System through Evolutionary Fuzzy Logic” IEEE
Trans on Power Delivery, Vol. 12, No. 2, April 1997.