IEC 60076-10-1:2016

IEC 60076-10-1 ®
Edition 2.0 2016-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Power transformers –
Part 10-1: Determination of sound levels – Application guide

Transformateurs de puissance –
Partie 10-1: Détermination des niveaux de bruit – Guide d'application

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IEC 60076-10-1 ®
Edition 2.0 2016-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Power transformers –
Part 10-1: Determination of sound levels – Application guide

Transformateurs de puissance –

Partie 10-1: Détermination des niveaux de bruit – Guide d'application

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 29.180 ISBN 978-2-8322-3253-8

– 2 – IEC 60076-10-1:2016  IEC 2016
CONTENTS
FOREWORD . 5
1 Scope . 7
2 Normative references. 7
3 Basic physics of sound . 7
3.1 Phenomenon . 7
3.2 Sound pressure, p . 7
3.3 Particle velocity, u . 8
3.4 Sound intensity, I . 8
3.5 Sound power, W . 8
3.6 Sound fields . 9
3.6.1 General . 9
3.6.2 The free field . 9
3.6.3 The diffuse field . 9
3.6.4 The near-field . 9
3.6.5 The far-field . 10
3.6.6 Standing waves . 10
4 Sources and characteristics of transformer and reactor sound . 11
4.1 General . 11
4.2 Sound sources . 11
4.2.1 Core . 11
4.2.2 Windings . 14
4.2.3 Stray flux control elements . 14
4.2.4 Sound sources in reactors . 15
4.2.5 Effect of current harmonics in transformer and reactor windings . 15
4.2.6 Fan noise . 18
4.2.7 Pump noise . 18
4.2.8 Relative importance of sound sources . 18
4.3 Vibration transmission . 18
4.4 Sound radiation . 19
4.5 Sound field characteristics . 19
5 Measurement principles . 20
5.1 General . 20
5.2 A-weighting . 20
5.3 Sound measurement methods . 22
5.3.1 General . 22
5.3.2 Sound pressure method . 23
5.3.3 Sound intensity method . 24
5.3.4 Selection of appropriate sound measurement method . 27
5.4 Information on frequency bands . 27
5.5 Information on measurement surface . 29
5.6 Information on measurement distance . 29
5.7 Information on measuring procedures (walk-around and point-by-point) . 30
6 Practical aspects of making sound measurements . 31
6.1 General . 31
6.2 Orientation of the test object to avoid the effect of standing waves . 31
6.3 Device handling for good acoustical practice . 32

6.4 Choice of microphone spacer for the sound intensity method . 33
6.5 Measurements with tank mounted sound panels providing incomplete
coverage . 33
6.6 Testing of reactors . 34
7 Difference between factory tests and field sound level measurements . 34
7.1 General . 34
7.2 Operating voltage . 34
7.3 Load current . 34
7.4 Load power factor and power flow direction . 35
7.5 Operating temperature . 35
7.6 Harmonics in the load current and in voltage . 35
7.7 DC magnetization . 36
7.8 Effect of remanent flux . 36
7.9 Sound level build-up due to reflections . 36
7.10 Converter transformers with saturable reactors (transductors) . 37
Annex A (informative) Sound level built up due to harmonic currents in windings . 38
A.1 Theoretical derivation of winding forces due to harmonic currents . 38
A.2 Force components for a typical current spectrum caused by a B6 bridge . 39
A.3 Estimation of sound level increase due to harmonic currents by calculation . 42
Bibliography . 44

Figure 1 – Simulation of the spatially averaged sound intensity level (solid lines) and
sound pressure level (dashed lines) versus measurement distance d in the near-field . 10
Figure 2 – Example curves showing relative change in lamination length for one type
of electrical core steel during complete cycles of applied 50 Hz a.c. induction up to
peak flux densities B in the range of 1,2 T to 1,9 T . 11
max
Figure 3 – Induction (smooth line) and relative change in lamination length (dotted line)
as a function of time due to applied 50 Hz a.c. induction at 1,8 T – no d.c. bias . 12
Figure 4 – Example curve showing relative change in lamination length during one
complete cycle of applied 50 Hz a.c. induction at 1,8 T with a small d.c. bias of 0,1 T . 12
Figure 5 – Induction (smooth line) and relative change in lamination length (dotted line)
as a function of time due to applied 50 Hz a.c. induction at 1,8 T with a small d.c. bias
of 0,1 T . 13
Figure 6 – Sound level increase due to d.c. current in windings . 13
Figure 7 – Typical sound spectrum due to load current . 14
Figure 8 – Simulation of a sound pressure field (coloured) of a 31,5 MVA transformer
at 100 Hz with corresponding sound intensity vectors along the measurement path . 20
Figure 9 – A-weighting graph derived from function A(f) . 21
Figure 10 – Distribution of disturbances to sound pressure in the test environment . 24
Figure 11 – Microphone arrangement . 25
Figure 12 – Illustration of background sound passing through test area and sound
radiated from the test object . 26
Figure 13 – 1/1- and 1/3-octave bands with transformer tones for 50 Hz and 60 Hz
systems . 28
Figure 14 – Logging measurement demonstrating spatial variation along the
measurement path . 31
Figure 15 – Test environment . 32
Figure A.1 – Current wave shape for a star and a delta connected winding for the
current spectrum given in Table A.2 . 40

– 4 – IEC 60076-10-1:2016  IEC 2016

Table 1 – A-weighting values for the first fifteen transformer tones . 22
Table A.1 – Force components of windings due to harmonic currents . 39
Table A.2 – Current spectrum of a B6 converter bridge . 39
Table A.3 – Calculation of force components and test currents . 41
Table A.4 – Summary of harmonic forces and test currents . 42

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
POWER TRANSFORMERS –
Part 10-1: Determination of sound levels – Application guide

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
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6) All users should ensure that they have the latest edition of this publication.
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60076-10-1 has been prepared by technical committee 14: Power
transformers.
This second edition cancels and replaces the first edition published in 2005. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) extended information on sound fields provided;
b) effect of current harmonics in windings enfolded;
c) updated information on measuring methods sound pressure and sound intensity given;
d) supporting information on measuring procedures walk-around and point-by-point given;
e) clarification of A-weighting provided;
f) new information on frequency bands given;

– 6 – IEC 60076-10-1:2016  IEC 2016
g) background information on measurement distance provided;
h) new annex on sound-built up due to harmonic currents in windings introduced.
This standard is to be read in conjunction with IEC 60076-10.
The text of this standard is based on the following documents:
FDIS Report on voting
14/847/FDIS 14/850/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts in the IEC 60076 series, published under the general title Power
transformers, can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC website under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
POWER TRANSFORMERS –
Part 10-1: Determination of sound levels – Application guide

1 Scope
This part of IEC 60076 provides supporting information to help both manufacturers and
purchasers to apply the measurement techniques described in IEC 60076-10. Besides the
introduction of some basic acoustics, the sources and characteristics of transformer and
reactor sound are described. Practical guidance on making measurements is given, and
factors influencing the accuracy of the methods are discussed. This application guide also
indicates why values measured in the factory may differ from those measured in service.
This application guide is applicable to transformers and reactors together with their
associated cooling auxiliaries.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60076-10:2016, Power transformers – Part 10: Determination of sound levels
3 Basic physics of sound
3.1 Phenomenon
Sound is a wave of pressure variation (in air, water or other elastic media) that the human ear
can detect. Pressure variations travel through the medium (for the purposes of this document,
air) from the sound source to the listener’s ears.
The number of cyclic pressure variations per second is called the ‘frequency’ of the sound
measured in hertz, Hz. A specific frequency of sound is perceived as a distinctive tone or
pitch. Transformer ‘hum’ is low in frequency, typically with fundamental frequencies of 100 Hz
or 120 Hz, while a whistle is of higher frequency, typically above 3 kHz. The normal frequency
range of hearing for a healthy young person extends from approximately 20 Hz to 20 kHz.
3.2 Sound pressure, p
The root-mean-square (r.m.s.) of instantaneous sound pressures over a given time interval at
a specific location is called the sound pressure. It is measured in pascal, Pa.
Sound pressure is a scalar quantity, meaning that it is characterised by magnitude only.
The lowest sound pressure that a healthy human ear can detect is strongly dependent on
frequency; at 1 kHz it has a magnitude of 20 µPa. The threshold of pain corresponds to a
sound pressure of more than a million times higher, 20 Pa. Because of this large range, to
avoid the use of large numbers, the decibel scale (dB) is used in acoustics. The reference
level for sound pressure for the logarithmic scale is 20 µPa corresponding to 0 dB and the
20 Pa threshold of pain corresponds to 120 dB.

– 8 – IEC 60076-10-1:2016  IEC 2016
An additional and very useful aspect of the decibel scale is that it gives a better approximation
to the human perception of loudness than the linear pascal scale as the ear responds to
sound logarithmically.
In the field of acoustics it is generally accepted that
• 1 dB change in level is imperceptible;
• 3 dB change in level is perceptible;
• 10 dB change in level is perceived to be twice as loud.
Human hearing is frequency dependent. The sensitivity peaks at about 1 kHz and reduces at
lower and higher frequencies. An internationally standardized filter termed ‘A-weighting’
ensures that sound measurements reflect the human perception of sound over the whole
frequency range of hearing (see 5.2).
3.3 Particle velocity, u
The root-mean-square (r.m.s.) of instantaneous particle velocity over a given time interval at a
specific location is called particle velocity. It is measured in metres per second, m/s.
This quantity describes the oscillation velocity of the particles of the medium in which the
sound waves are propagating. It is characterised by magnitude and direction and is therefore
a vector quantity.
3.4 Sound intensity,
I
The time-averaged product of the instantaneous sound pressure and instantaneous particle
velocity at a specific location is called sound intensity:
(1)
I = (p(t)×u (t))dt
∫
T
T
It is measured in watts per square metre, W/m .
Sound intensity describes the sound power flow per unit area and is a vector quantity with
magnitude and direction. The normal sound intensity is the sound power flow per unit area
measured in a direction normal, i.e. at 90º to the specified unit area.
The direction of the sound power flow is determined by the phase angle of the particle velocity
at the specific location.
3.5 Sound power, W
Sound power is the rate of acoustic energy radiated from a sound source. It is stated in watts.
A sound source radiates power into the surrounding air resulting in a sound field. Sound
power characterises the emission of the sound source. Sound pressure and particle velocity
characterise the sound at a specific location. The sound pressure which is heard or measured
with a microphone is dependent on the distance from the source and the properties of the
acoustic environment. Therefore, the sound power of a source cannot be quantified by simply
measuring sound pressure or intensity alone. The determination of sound power requires an
integration of sound pressure or sound intensity over the entire enveloping surface. Sound
power is more or less independent of the environment and is therefore a unique descriptor of
the sound source.
3.6 Sound fields
3.6.1 General
A sound field is a region through which sound waves propagate. It is classified according to
the manner in which the sound waves propagate.
When sound pressure and particle velocity are in phase, the corresponding sound field is said
to be active. When sound pressure and particle velocity are 90° out of phase, the
corresponding sound field is said to be reactive. With an active field the sound energy
propagates entirely outwards from the source, as it does (approximately) in far-fields (see
3.6.5). In case of a reactive field the sound energy is travelling outwards but it will be returned
at a later instant; the energy is stored as if in a spring. Examples for reactive fields are the
diffuse field of a reverberant room (see 3.6.3) and standing waves (see 3.6.6). Averaged over
a cycle, the net energy transfer in a reactive field is zero and hence the measured sound
intensity is zero, although sound pressure and particle velocity are present.
A practical sound field is composed of both active and reactive components.
3.6.2 The free field
A sound field in a homogeneous isotropic medium whose boundaries exert a negligible effect
on sound waves is called a free field. It is an idealised free space where there are no
disturbances and through which active sound power propagates.
These conditions hold in the open air when sufficiently far away from the ground and any
walls, or in a fully anechoic chamber where all the sound striking the walls, ceiling and floor is
absorbed.
Sound propagation from a theoretical point source within a free field environment is
characterised by a 6 dB drop in sound pressure level and intensity level each time the
distance from the source is doubled. This is also approximately correct when the distance
from an area source is large enough for it to appear as a theoretical point source.
When measuring power transformer sound levels free field conditions will be approached with
the exception of reflections from the floor.
IEC 60076-10 requires all sound measurements to be made over a reflecting surface.
Therefore, measurements in fully anechoic chambers are not allowed.
3.6.3 The diffuse field
In a diffuse field, multiple reflections result in a sound field with equal probability of direction
and magnitude, hence the same sound pressure level exists at all locations and the sound
intensity tends to zero. This field is approximated in a reverberant room. According to the law
of conservation of energy, an equilibrium condition will occur when the sound power absorbed
by or transmitted through the room boundaries equals the sound power emitted by the source.
This phenomenon may result in very high sound pressure levels in environments having low
sound absorption or transmission characteristics.
A practical example of a diffuse field may be the interior of a transformer sound enclosure.
3.6.4 The near-field
The acoustic near-field is considered to be the region adjacent to the vibrating surface of the
sound source, usually defined as being within a distance of ¼ of the wavelength of the
particular frequency of interest. This region is characterized by the existence of both active
and reactive sound components. The reactive sound component decays exponentially with
distance from the vibrating surface of the sound source.

– 10 – IEC 60076-10-1:2016  IEC 2016
Reactive sound components are created if the bending wavelength of the vibrating structure is
shorter than the wavelength of the radiated sound. Sound radiation at this condition is
characterised by acoustic short-circuits between adjacent regions with over-pressure and
under-pressure. In such acoustic short-circuits the air acts as a mass-spring system storing
and releasing energy in every cycle. As a result, a part of the sound power is always being
circulated and not all of it is radiated into the far-field (see 3.6.5).
The extent of the near-field reduces with increasing frequency.
Sound pressure measurements applied in the near-field will result in a systematic
overestimation (Figure 1) because of the inherent phase difference between the sound
pressure and particle velocity in the near-field (see 3.6.1). As a result, spatially averaged
sound pressure levels are typically 2 dB to 5 dB higher whilst spot measurements may be up
to 15 dB higher than the corresponding measured sound intensity level.
100 Hz
75 200 Hz
300 Hz
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
d (m)
IEC
Figure 1 – Simulation of the spatially averaged sound intensity level (solid lines) and
sound pressure level (dashed lines) versus measurement distance d in the near-field
3.6.5 The far-field
The sound field beyond a certain distance from the source where inherent disturbances due to
the size and shape of the source as well as other interfering disturbances become
insignificant is called the far-field. In this field the source can be treated as a theoretical point
source and approximate free field conditions exist.
3.6.6 Standing waves
Standing waves are the result of interference between two sound waves of the same
frequency travelling in opposite directions. Standing waves are formed as a result of
reflections between a sound source and structural discontinuities such as the boundaries of
the sound field, emphasised if the reflecting surfaces are parallel and when the relationship
between sound frequency and distance meets certain conditions. The existence of standing
depends upon the distance d between the reflecting walls as follows:
waves of frequency f
ν
c
(2)
f = ν
ν
2 d
where c is the speed of sound in air in m/s (at 20 °C, c = 343 m/s), ν = 1,2,3….
A standing wave does not transmit energy to the far-field; it is an example of a reactive field.
L (dB)(A)
Within the region of a standing wave
• large variations in measured sound pressure will occur over small distances with the
tendency to overestimate sound pressure;
• sound intensity measurements tend to be inaccurate and underestimate the actual sound
intensity.
4 Sources and characteristics of transformer and reactor sound
4.1 General
Transformer and reactor sound has several inherent physical origins. The significance of
those origins of sound generation depends on the design of the equipment and its operating
conditions. The design will impact the sound producing vibrations and their propagation from
the origin to the transformer tank or enclosure surface and finally the sound radiation into the
air.
4.2 Sound sources
4.2.1 Core
Magnetostriction is the change in dimension observed in ferromagnetic materials when they
are subjected to a change in magnetic flux density (induction). In electrical core steel this
dimensional change is in the range of 0,1 µm to 10 µm per metre length (µm/m) at typical
induction levels. Figure 2 shows magnetostriction versus flux density for one type of core
lamination measured at five different flux densities. Each loop describes one 50 Hz cycle with
flux density B .
max
B = 1,9 T
max
B = 1,8 T
max
0 B = 1,6 T
max
B = 1,4 T
max
B = 1,2 T
–1 max
–2
–3
–2 –1 0 1 2
Flux density  T
IEC
Figure 2 – Example curves showing relative change in lamination length for one type
of electrical core steel during complete cycles of applied 50 Hz a.c. induction
up to peak flux densities B in the range of 1,2 T to 1,9 T
max
NOTE 1 Mechanical stresses in core laminations will have a strong influence on magnetostriction.
The strain does not depend on the sign of the flux density, only on its magnitude and
orientation relative to certain crystallographic axes of the material. Therefore, when excited by
a sinusoidal flux, the fundamental frequency of the dimensional change will be twice the
exciting frequency. The effect is highly non-linear, especially at induction levels near
saturation. This non-linearity will result in a significant harmonic content of the strain and this
causes the vibration spectrum of the core. Figure 3 shows the magnetostriction for a
sinusoidal induction with B = 1,8 T and a frequency of 50 Hz. It has a periodicity of double
max
the exciting frequency with peaks at 5 ms and 15 ms which are indistinguishable.
Strain (µm/m)
– 12 – IEC 60076-10-1:2016  IEC 2016
The sound emitted by transformer cores depends on the velocity of the vibrations, i.e. the rate
of change of the magnetostriction (dotted line in Figure 3). This results in an amplification of
the harmonics (distortion) in relation to the fundamental which is at double the exciting
frequency. Several even multiples of the exciting frequency will be seen in the spectrum; in
such cases the fundamental component at double the exciting frequency is seldom the
dominant frequency component of the A-weighted sound.
3 3
2 2
1 1
0 0
–1 –1
–2 –2
–3 –3
0 10 20 30 40
Time (ms)
IEC
Figure 3 – Induction (smooth line) and relative change in lamination length (dotted line)
as a function of time due to applied 50 Hz a.c. induction at 1,8 T – no d.c. bias
If the flux has a d.c. bias, for example due to remanence in the core from preceding testing of
the windings’ resistance, or due to a d.c. component in the current, the strong non-linearity of
magnetostriction causes a significant increase in vibration amplitudes. With a d.c. bias on the
induction, the peaks in magnetostriction at the positive and negative peak flux density differ
significantly; obvious in the magnetostriction loop in Figure 4.
–1
–2
–3
–2 –1 0 1 2
Flux density (T)
IEC
Figure 4 – Example curve showing relative change in lamination length
during one complete cycle of applied 50 Hz a.c. induction at 1,8 T
with a small d.c. bias of 0,1 T
The vibration pattern is now repeated every cycle, that is every 20 ms in a 50 Hz system,
indicating a magnetostriction at exciting frequency (see Figure 5). The presence of odd
harmonics in the sound spectrum is a clear indication of d.c. bias in the induction.
Flux density (T)
Strain (µm/m)
Strain (µm/m)
3 3
0 0
–1 –1
–2 –2
–3 –3
0 10 20 30 40
Time (ms)
IEC
Figure 5 – Induction (smooth line) and relative change in lamination length (dotted line)
as a function of time due to applied 50 Hz a.c. induction at 1,8 T
with a small d.c. bias of 0,1 T
A d.c. bias in magnetization can significantly affect the sound level of a transformer.
Therefore, a transformer undergoing sound tests shall be energised until the temporary
effects of inrush currents and remanence have decayed and the sound levels have stabilised.
The ratio between the d.c. bias current and the r.m.s. no-load current is a useful parameter
for predicting the increase in sound power due to the d.c. bias current. The relationship
between d.c. bias current over no-load current and sound level increase has been measured
on a number of large power transformers; Figure 6 shows one set of this data.
Y
B = 1,6 T
max
B = 1,7 T
max
0 1 2 3 4 5 6 7 8 9 10 11 12
X
IEC
Key
X axis d.c. bias current as per unit of a.c. no-load current (r.m.s.)
Y axis increase in total sound level in dB(A)
Figure 6 – Sound level increase due to d.c. current in windings
NOTE 2 Figure 6 shows the results for a certain design of large power transformers with a core having a path for
flux return and the core made from high permeable electrical steel. For other constructions, for example with
different core form or different electrical steel type, the curve can deviate in detail but will contain the same upward
trend.
Flux density (T)
Strain (µm/m)
– 14 – IEC 60076-10-1:2016  IEC 2016
4.2.2 Windings
Load currents in transformer and reactor windings generate a magnetic field that oscillates at
the excitation frequency. The resultant electromagnetic forces on the windings act both axially
and radially. The magnitude of these forces depends on the magnitude of the load current and
on the magnetic field, which itself is a function of the load current. Thus, the magnetic forces
on the windings are proportional to the square of the load current while their frequency is
twice the excitation frequency. The resulting vibration amplitudes depend on the elastic
properties of the conductor, those of the electrical insulation and the proximity of the
mechanical eigenfrequencies (natural frequencies of the windings) to the vibration frequency.
In a well clamped and tightly wound winding, the elastic properties of the insulating material
are almost linear in the range of displacements occurring under normal operating currents.
Metals have very linear elastic moduli. Therefore harmonic vibration is normally minimal and
the fundamental frequency (double the exciting frequency) dominates the vibration spectrum
of windings (see Figure 7).
Winding deflections and their vibrational velocities are proportional to the excitation force
which is proportional to the square of the load current. The sound power radiated from a
vibrating body is proportional to the square of the vibration velocity (see 4.4). Consequently,
the sound power generated by windings varies with the fourth power of the load current.
Harmonics in the load current appear in the sound spectrum at twice their electrical frequency
and at the sum and difference of all their frequencies. They can contribute significantly to the
transformer or reactor sound level. For more details see 4.2.5.
0 200 400 600 800 1 000 1 200 1 400 1 600 1 800 2 000
Frequency (Hz)
IEC
Figure 7 – Typical sound spectrum due to load current
4.2.3 Stray flux control elements
Magnetic stray flux in loaded transformers is linked to windings and connection leads. This
stray flux shall be controlled to avoid the overheating of inactive metal parts such as the tank
by reducing eddy current losses. There are in principle three possibilities to control magnetic
stray flux:
• by application of laminated electrical steel the stray flux is guided in a controlled way.
Elements providing this guidance are commonly called ‘shunts’ or ‘tank shunts’;
A-weigthed sound pressure level (dB)(A)

• by application of copper or aluminium shields the stray flux is repelled by eddy current
loops in the shield;
• by sizing the tank such that stray flux control is not necessary.
Elements used for stray flux control as well as the tank itself are also sources of vibration due
to electromagnetic forces and magnetostriction and they impact the overall sound power level.
The method of attachment of stray flux control elements may influence the sound power level.
4.2.4 Sound sources in reactors
There are several types of single-phase and three-phase reactors, generally utilising two
different technologies in their design.
• In air-core reactors, the sound power produced by the winding due to the load current is
dominant. The interaction of the current flowing through the winding and its magnetic field
lead to vibrational winding forces. While the oscillating forces can be clearly determined
...