Load sound power levels for specification purposes of three-phase 50 Hz and 60 Hz liquid-filled power transformers. In the industry there is an increasing awareness observed that load sound, depending on transformer parameters and loading, contributes to, and may even dominate the total sound level of a transformer in service. This results in a growing tendency to specify the permissible sound level not only for no-load operation, but also for the loaded transformer when purchasing new transformers. Specifying a realistic load sound level for power transformers is often challenging due to limited availability of reliable and validated information. This easily leads to physically unrealistic load sound level specifications, either unnecessary high, e.g. NEMA TR 1 standard [1], or, as has been a trend in recent years, unachievable low without using external sound mitigation measures.

1. datasets, collected by 14 independent transformer
manufacturers World-wide.
The presented work about load sound is part of the scope
of CIGRE WG A2.54 task to study “Power Transformer
audible sound requirements”. The intention of Study
Committee A2 in establishing this Working Group was to
provide support information and guidance for the industry
for sound level specification of new power transformer
purchases [3, 4]. This article, written on behalf of CIGRE
WG A2.54 is meant to be complementary to the CIGRE
paper “No-load sound power levels for specification
purposes derived from more than 1000 measurements
– a representative figure for three-phase transformers”
[3] as well as to the first interim report of WG A2.54
published in ELECTRA 302, February 2019 [5].
Causes of load sound
Load sound of a transformer is the sound caused by the
physical effects of load currents flowing in transformer
windings, as illustrated in Figure 1. The contributing
elements to load sound are:
 Windings (usually dominant),
 Stray flux control elements,
 Structural parts.
At the right side in Figure 1, the current, leakage field
and resulting forces are indicated. At the left and bottom
side, elements’ vibrations and paths for the vibrations
towards the tank are illustrated. At the transformer air
side, vibrations of the tank are passed to the surrounding
air, emitting an audible sound. •••
Introduction and background
information
In the industry there is an increasing awareness observed
that load sound, depending on transformer parameters
and loading, contributes to, and may even dominate the
total sound level of a transformer in service. This results
in a growing tendency to specify the permissible sound
level not only for no-load operation, but also for the
loaded transformer when purchasing new transformers.
Specifying a realistic load sound level for power
transformers is often challenging due to limited availability
of reliable and validated information. This easily leads
to physically unrealistic load sound level specifications,
either unnecessary high, e.g. NEMA TR 1 standard [1],
or, as has been a trend in recent years, unachievable
low without using external sound mitigation measures.
To provide guidance towards more realistic load sound
level specifications, an improved model, based on the
physics behind load noise and on the Reiplinger load
sound equation [2] is developed for three-phase 50 Hz
and 60 Hz transformers.
The results are presented in the form of easy to use
curves, giving the typical load sound levels. The load
sound model is defined in such a way that with the
information available during the transformer procurement
process, it is possible to estimate the load sound level.
The parameters of the developed load sound model are
based on statistical analysis on an in the industry unique
large database, containing 1359 carefully selected
Members
C. PLOETNER, Convenor (DE), E. ALMEIDA, Secretary (PT), A. AL-ABADI (DE),
H. BRUNE (DE), F. CORNELIUS (DE), J. DICKINSON (GB), J. DONCUK (CZ), G. FEI (CN),
M. GILLET (FR), W. GOETTE (DE), S. KANO (JP), J. KIM (KR), K.H. LEE (KR),
G. NADOR (HU), Y. ODARENKO (AU), M. PIRNAT (SI), B. SIMONS (NL),
P. TARMAN (SI), F. TRAUTMANN (DE), M. WARREN (CA), K. YAMAGUCHI (JP),
J.C. YANG (KR), J. YOO (KR), H. YU (CN), S. YUREKTEN (TR)
Load sound power levels for
specification purposes of three-phase
50 Hz and 60 Hz liquid-filled power
transformers
Progress report prepared by Bart Simons (NL)
No. 310 - June 2020 ELECTRA 57
WG A2.54
REPORT

2. the vibration of the windings are therefore minimal and the
fundamental mechanical frequency (twice the excitation
frequency) is dominant for the vibration and therewith the
load sound. Higher harmonics in the load sound spectrum
as shown in Figure 2 - Example of a typical Load sound
spectrum (Source IEC 60076-10-1:2016 [6]) are mainly
caused by vibrations from stray flux control elements and
structural parts.
Relation between load sound and
transformer rated quantities
As described before, the dominant contribution to the
load sound of a transformer is the vibrations of the
windings. The vibrations of the windings are caused by
Lorentz forces acting on the windings.
In mechanical terms, the combination of load current and
leakage field results in the Lorentz forces. In electrical
terms however, the combination load current and leakage
field is the reactive power Q of a transformer. Reactive
power Q and Lorentz force are proportional and can be
related to each other via the magnetic energy Wm
, stored
in the leakage field of the transformer.
The magnetic energy is defined as:
The product XI2
is the reactive power Q required to
establish the leakage field of the transformer. The
reactive power can also be expressed in terms of (rated)
apparent power Sr
and pu impedance voltage uk
:
Figure 1 - Cross-section of a transformer illustrating
the generation process of load sound
The vibrations emitted from the windings are usually the
dominant contributor to the load sound. Since the magnetic
field is proportional to the load current, the resulting force
is proportional to the load current squared, at twice the
excitation frequency. The magnitude of the vibrations
depends also on the elastic properties of the conductor,
the electrical insulation and the proximity of mechanical
resonance frequencies of the complete winding assembly
(e.g. windings, insulation, insulating liquid, clamping
construction, clamping pressure). The elastic moduli
of the conductors but also of the insulation material are
approximately constant in a well designed and produced
winding at normal operating currents. Higher harmonics in
Figure 2 - Example of a typical Load sound spectrum (Source IEC 60076-10-1:2016 [6])
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58 No. 310 - June 2020 ELECTRA

3. Combining these relations, a direct relation between
reactive power and total force acting on the transformer
windings is found:
As the proportional relation of force and vibration is also
applicable to the load sound level Ll
, a direct relation
between load sound level and reactive power of the
transformer is established:
Collected datasets
The developed load sound model is based on statistical
analysis on a large database, containing 1359 datasets,
collected by 14 independent transformer manufacturers
World-wide. Each individual dataset was carefully quality
checked to ensure a reliable database.
Following boundary conditions are set to the collected
datasets:
 Transformer power range from 4 MVA to 1500 MVA,
 Power frequency 50 Hz and 60 Hz,
 Three-phase and single-phase transformers,
 Liquid-filled transformers, no distinction is made
between different liquids,
 Transformer cooling: ONAN/ODAN/OFAN/ODWF/
OFWF (i.e. no running fans during sound test),
 Core-form and shell-form transformers,
 “Standard” transformers, including typical sub-station
and generator transformers. Transformers for special
applications including HVDC transformers, phase-
shifting transformers, testing transformers, mobile
transformers, and furnace/rectifier transformers are
excluded,
 No external sound mitigation measures applied
(panels or enclosures),
 Sound power levels in database are based on the
sound intensity measurement method,
 In case the sound pressure measurement was
used, the sound level was corrected to a sound
intensity level by following simplified correction:
LIntensy
= LPressure
–3dB.
 A-weighting is applied to all measurements,
 Sound measurements are performed according the
rules given in IEC 60076-10:2001 [7] or 2016 [8] or
according IEEE C57.12.90-2010 [9] or 2015 [10],
 Measurements using the walk-around procedure and
the point-to-point procedure both apply.
The validated datasets are split into three-phase and
single-phase, and in 50 Hz and 60 Hz transformers. The
number of datasets per group are shown in Table 1.
The model presented in this article is valid for three-
phase 50 Hz and 60 Hz transformers. Single-phase
transformers are not analyzed because a reliable
statistical analysis is not possible due to the small
number of datasets and the many different types of
single-phase transformers.
Figure 3 presents all three-phase datasets. It is obvious
that 50 Hz and 60 Hz transformers behave differently,
therefore for the further analysis a distinction is made
between them. More information on the differences can
be found in [11].
Figure 3 - Collected dataset for three-phase 50 Hz
and 60 Hz transformers
Model description
Reiplinger load sound equation
The Reiplinger load sound equation [2] estimates
the load sound power level of three-phase 50 Hz
transformers and is based on the rated apparent power
Sr
in MVA (So
=1MVA):
The equation was first presented in 1988 [2] and is still
used today, simply because there is, up to now, no better,
i.e. more accurate and easy to use alternative available
Table 1
Number of phases Frequency Number of datasets
Three-phase
50 Hz 1085
60 Hz 190
Single-phase
50 Hz 44
60 Hz 40
•••
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WG A2.54
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4. parameter used in [6] and drops to a standard deviation
of 5,3 dB(A) with a mean value of 0,2 dB(A) for the newly
derived model parameters.
Improved load sound model
As shown in the previous paragraph, the Reiplinger load
sound equation results in a rather good prediction of the
load sound power level. Considering the physics behind
load sound, it is clear that the apparent power is a major
parameter though it does not fully represent it. The
Reiplinger load sound equation can therefore be improved
by using the reactive instead of the apparent power.
The new load sound model is defined to enable the
load sound power level estimation based only on the
functional properties of the transformer, which are
known at an early stage in the procurement process and
which are the same for possible suppliers. Furthermore,
the model is kept as simple as possible to make it easy
to use. The load sound power level Lw
of the transformer
is defined as:
Ll
is standing for the load sound power level estimated
with the model using the apparent power and
impedance voltage as input parameters. The model
is described as
with a and b being constants determined from the
statistical analysis of the collected datasets. The apparent
power Sr
expressed in MVA, the impedance voltage uk
expressed in pu at a power of Sr
and Qo
=1MV Ar. The
relation between Ll
and Sr
uk
is logarithmic because the
sound level Ll
is expressed in decibels. The influence of
frequency (50 Hz or 60 Hz) is included in the constants
a and b and results in two different curves for three-
phase transformers at 50 Hz and 60 Hz, presented in
next chapter.
Lo
comprises all other factors impacting the load sound
level of a transformer. Such are related to design
and manufacturing, to measurement uncertainty and
tolerances. Lo
is the difference between the actual
transformer sound power level Lw
and the estimated
sound power level Ll
.
Model parameter estimation
To determine the parameters for the load sound model,
the following constraints are set:
 Three-phase transformers considered only,
 50 Hz and 60 Hz transformers handled separately,
 No distinction made between different types of
“standard” transformer,
 Impact of tap position to sound level is ignored,
 Impact of core design is ignored.
to the industry. Considering the physics of load sound as
outlined in the paragraph “Relation between load sound
and electrical transformer parameter”, it is clear that
the apparent power is a major determining parameter.
Therefore, the Reiplinger load sound model is predicting
the load sound level of a transformer rather accurate,
specifically for transformers with “normal, average”
impedance voltage. Because the Reiplinger load sound
equation is still frequently used today, and to prove that
the newly developed model is an improvement versus
the Reiplinger load sound equation, at first a statistical
evaluation of the Reiplinger load sound equation is
made using the relevant datasets of the collected
database: The statistical evaluation results in a standard
deviation of 5,3 dB(A) and a mean value of -0,6 dB(A).
It is found the Reiplinger equation overestimates the
load sound power level for the power range < 100 MVA
and underestimates it for transformers > 100 MVA, see
Figure 4.
Figure 4 - Three-phase 50 Hz transformers comparison with the
Reiplinger load sound model
By applying a linear regression to the relevant datasets
of the collected database, a new set of model parameters
for the Reiplinger model is found:
With this set of parameters, the standard deviation is
found to be 5,1 dB(A) and the mean value - 0,4 dB(A),
see Figure 4.
For three-phase 60 Hz transformers, the same analysis
has been performed with following results:
The standard deviation was found to be of 5,5 dB(A)
with a mean value of -0,3 dB(A) for the original model
WG A2.54
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5. Three-phase 50 Hz transformers
For 50 Hz transformers in total 1085 datasets were
received and analysed. The parameters and for the
load sound model are determined by linear regression
using the least square error method. After determining
the model parameters, a statistically analysis has been
performed to determine the accuracy of the model.
For 50 Hz three-phase transformers the following model
is found:
The statistical analysis shows that the model results in a
standard deviation of 4,7 dB(A) and a mean value of 0,5
dB(A), see Figure 5.
Figure 5 - Three-phase 50 Hz transformers
A standard deviation of 4,7 dB(A) means that the
measured load sound power level of approximately 95 %
of the transformers is within ±10 dB(A) of the estimated
load sound power level using the new model. The
spread of 20 dB(A) between the noisiest and most quiet
transformer at the same reactive power rating can be
fully accounted to Lo
, i.e. the sound level contribution by
all factors other than contained in the model, see above.
This large spread indicates the challenge of predicting
the load sound power level of a transformer during
the design stage, because for the load sound level
no distinct control parameter exists (such as the core
induction for no-load sound level control) and the spread
consequently being induced by many different factors.
To improve the accuracy of the model, the factors and
their impact have to be understood and the relevant
parameters be added to the model. As such parameters
are mainly design parameters and are only known by
the manufacturers, they are exceeding the scope of WG
A2.54 and will not be discussed here.
Three curves are presented in Figure 6 - Load sound
power level curves for specification: Three-phase 50 Hz
transformers giving the typical range of load sound power
level for 50 Hz three-phase transformers. The curve in the
middleisthetypicalaveragecurvedescribedwithequation
Ls
=53 + 19log10
(Sr
uk
/Qo
). This curve indicates that 50 %
of the transformer population produces a higher and
50 % a lower sound level than given by the curve. In
other words, specifying a transformer at the average
curve results in a reasonable chance that specific sound
control and mitigation measures are required, resulting
in a more expensive design.
The top curve is the typical natural upper limit curve, which
is the average curve plus 10 dB(A). All transformers •••
Figure 6 - Load sound power level curves for specification: Three-phase 50 Hz transformers
WG A2.54
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No. 310 - June 2020 ELECTRA 61

6. standard deviation of 4,8 dB(A) and a mean value of 0,1
dB(A), shown in Figure 7.
Figure 7 - Three-phase 60 Hz transformers
In Figure 8, the typical range of load sound power levels
for 60 Hz three-phase transformers is given. Remarks
given to the curves shown in Figure 6 - Load sound
power level curves for specification: Three-phase 50 Hz
transformers for 50 Hz transformers apply likewise for
60 Hz transformers.
Load sound power level at transformer
loading other than
As outlined above, the input quantity for the load
sound power level estimation at rated transformer
loading with the new load sound model is the reactive
transformer power at rated loading, i.e. the product of Sr
and uk
. To calculate the load sound power level at any
other transformer loading condition, there are several
possibilities:
produced should be able to comply with this upper
limit without making use of sound mitigation measures,
resulting in a for sound purposes, low cost design.
The bottom curve is the typical natural lower limit curve,
which is the average curve minus 10 dB(A). Almost all
transformers are noisier than this lower limit. Specifying
at this limit will likely lead to an increase in costs and in
most cases require external sound mitigation measures
to be applied.
In cases where the load sound power level has to be
specified below the average curve, possible solutions
should be discussed at first with the transformer
manufacturers but potentially also with the suppliers of
sound mitigation solutions to come up with a realistic
technical and economical solution. To guarantee sound
power levels below the average curve in Figure 6 - Load
sound power level curves for specification: Three-phase
50 Hz transformers without foreseen external sound
mitigation measures is for manufacturers only limited
possible.
Therefore, WG A2.54 recommends specifying normally
only above the average curve in Figure 6.
Three-phase 60 Hz transformers
For three-phase 60 Hz transformers the same analysis
has been performed as for the 50 Hz transformer class.
The following model is found:
The used model and model parameters result in a
Figure 8 - Load sound power level curves for specification: Three-phase 60 Hz transformers
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7. References
[1] NEMA TR 1-2013, Transformers, Step Voltage Regulators and
Reactors, 2013.
[2] E. Reiplinger, „Study of noise emitted by power transformers
based on today's viewpoint,” in CIGRE Internation Conference
on Large High Voltage Electric Systems, Paris, 1988.
[3] C. Ploetner, „No-load sound power levels for specification
purposes derived from more than 1000 measurements – a
representative figure for three-phase transformers,” in CIGRE
Study Committee A2 colloquium, Krakow, 2017.
[4] CIGRE, 9 10 2015. [Online]. Available: https://www.cigre.
org/userfiles/files/News/2018/TOR_WG_A2_54_Power_
transformer_audible_sound_requirements.pdf. [Accessed 16
March 2020].
[5] ELECTRA 302, Interim report of WG A2.54, February 2019.
[6] IEC 60076-10-1, Power transformers - Part 10-1: Determination
of sound levels - Application guide, 2016.
[7] IEC 60076-10, Power Transformers - part 10: Determination of
sound levels, 2001.
[8] IEC 60076-10, Power Transformers part 10: Determination of
sound levels, 2016.
[9] IEEE C57.12.90, IEEE standard for Standard General
Requirements for Liquid-Immersed Ditribution, Power, and
Regulating Transformers, 2010.
[10] IEEE C57.12.90, IEEE Standard Test Code for Liquid-
Immersed Distribution, Power, and Regulating Transformers,
2015.
[11] M. Pirnat en M. Gillet, „Difference between 50 Hz and 60 Hz
transformer load noise levels,” in CIGRE Colloquium SC A2 /
SC B2 / SC D1, New Delhi, India, 2019. 
1. Calculation based on known sound power level at
rated power by applying the so-called “40 Log” rule:
Ll
– sound power level at actual loading
Llr
– sound power level at rated loading
S – actual apparent power
Sr
– rated apparent power
2. Calculation by applying the new load sound
model using the actual apparent power and actual
impedance voltage as model input parameter. It
is worth mentioning that this methodology applies
generally. Using the actual parameters S and uk
for
whatever transformer loading conditions (including
different tap positions) will return the associated
load sound power level.
3. Calculation by applying the new load sound model
with the input quantity Sr
uk
being multiplied with the
square of the actual loading factor.
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