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Vibration Analysis of Power Capcitors and Vibration
Reduction with Damping Structures
Jinyu Li, Lingyu Zhu, Shengchang Ji, Hantao Cui, Yuhang Shi
School of Electrical Engineering
Xi’an Jiaotong Universtiy
Xi’an, China
[email protected]
Abstract—Vibration of AC filter capacitor generates loud
noises in HVDC converter stations, which would reach 105dB.
Currently, vibration features are not investigated thoroughly.
The objective of this work was to measure vibration velocity
distribution on AC filter capacitor surfaces and to investigate the
vibration features. In the experiments, the capacitor was applied
currents consist of three components of 50 Hz, 550 Hz and 650
Hz. The root mean squared values were 30 A, 25 A and 4.6 A,
respectively. A portable digital vibrometer was conducted to
measure the vibration velocity on capacitor surfaces. In order to
obtain velocity data simultaneously, voltage squared was used as
a datum signal to calibrate the time offset. It was found that
velocities on different measure points on a capacitor surface were
not synchronous, and had different phases. On the bottom
surface, vibrations performed entirely transverse oscillating. On
the broad side surfaces, there were two bending wave generated
from the edges connected to bottom and top surfaces. It was
concluded that the internal vibration of elements excited firstly
on the bottom surface, and then through the edges of bottom and
broad side surface, it transmitted on broad side surfaces. A
damping structure was designed and applied on the bottom
surface to increase the damping coefficient between contact
surfaces and to reduce vibration transmitted to broad side
surfaces. The sound measurement result shown that the dampstructure capacitor had sound power which was 73.3% of that
generated from the conventional capacitor.
Keywords—power capacitor;
vibration type; vibration reduction
vibration;
acoustic
noise;
I. INTRODUCTION
Power capacitors are usually considered as quiet equipment
in power substations. However in HVDC converter stations,
audible noise generated by operating AC filter capacitors
would reach to 105 dB [1], which is as loud as power
transformers and reactors. Over a hundred of can-type
capacitor units are mounted on several high towers in a
converter station. This results in a large area suffered from loud
acoustic noise. The noise is in connection with vibrations on
capacitor surfaces. Noise mitigation of the capacitors must be
studied first from a vibration perspective. Therefore, the
vibration on AC filter capacitor surfaces should be
Project Supported by National Natural Science Foundation of China,
Grant NO. 51377130 & NO. 51507128.
investigated, and vibration reduction measure need to be
designed.
Vibration on capacitor surfaces was proved to be related
with harmonic current flowing through capacitor elements [2].
It is excited by the inner electric forces acting on capacitor
elements, which is proportional with squared of voltage applied
on the capacitor [2, 3]. AC filter capacitor current contains
fundamental and numerous harmonics, so the noise of AC filter
capacitors is louder than that of ordinary ones. Cox and Guan
studied the relationship between harmonic current distortion
and the acoustic frequencies generated by capacitors, and
found that acoustic frequencies were composed of twice of
harmonic current frequencies and addition and subtraction
between each of two harmonic frequencies [3]. For example,
given that capacitor current has 50 Hz component as a
fundamental component and 250 Hz as a harmonic, vibration
frequency spectrum contains 100 Hz, 200 Hz, 300 Hz and 500
Hz. In our previous study[4, 5], a capacitor was proved to be
linear system with squared voltage as input and vibration
velocity as output, so vibrations with different frequency could
be studied separately. Besides, it was currently assumed that
vibration on capacitor wide surfaces was transferred from
internal vibration through dielectric liquids [1, 2], but it was
not tested. Although these previous study presented a
preliminary acknowledgement on capacitor vibration and
noise, no quantitative data of vibration velocity was measured
and the relation between each point on surfaces was not clear.
The objective of this work was to measure vibration
velocity on AC filter capacitor surfaces and to investigate
relationship of vibration between different points. The
vibration velocity was measured in the experiments of distorted
current. Based on the vibration analysis, a capacitor with
damping structure was designed and tested.
II. VIBRATION AND NOISE MEASUREMENT OF
CAPACITORS
A. Capacitor Sructures
AC filter capacitors used in HVDC converter station are
typically can-type capacitors, which would be referred to as
power capacitor in this paper. The structure is shown in Fig. 1.
The can-type capacitor is composed of a stainless steel case
and two bushings. A pair of fixing lugs is welded on two
surfaces with a certain distance to the edge. It will reduce the
vibrations on side surfaces and the results will be discussed in
next section.
B. Experimental Systems
An experimental system was set up to investigate the
vibrations on capacitor surfaces and acoustic noise around a
Fig. 3.
Experimental circuit to load fundamental and harmonic
currents into capacitors.
Fig. 1. Structure of power capacitors.
surfaces for capacitors mounting on a stack tower. The case is
filled with dielectric liquid and contains a capacitor element
package. The capacitor element is made by two aluminum foils
and a number of polypropylene films wound on a cylindrical
mandrel. The mandrel is removed and the wound cylinder is
flattened as a capacitor element in rectangular shape. The
elements are insulated by Kraft papers and packed in a package
cell by horizontal position when the bushings are upward. The
capacitor package and the bottom are in direct contact, while
there is a compressible spacer between the package and the top,
in order to give more insulated distance from bushings.
It is appointed that the surface where bushings are installed
is called the top surface in this paper, and the opposite is the
bottom surface. The other four side surfaces are called the
narrow side surfaces and the broad side surfaces according to
their breadth individually.
Besides, welding structure of the bottom surface plays an
important role in capacitor vibrations. Conventionally, bottom
surfaces are welded just right on the edge of side surfaces, as
shown in Fig. 2. In this paper, a new welding structure was
used to increase contact damping. The bottom was bended to
create a larger contact surface, which was welded to side
capacitor. The main experimental circuit, as shown in Fig. 3,
was made up of a capacitor bridge, a compensation reactor, a
harmonic source and a fundamental frequency voltage source.
The bridge circuit allowed fundamental and harmonic currents
to flow through capacitors at the same time. One of capacitors
in the bridge was mounted in a hemi-anechoic chamber, which
created an acoustic isolated environment for sound measuring.
The tested capacitor has the ratings with voltage of 6.35 kV,
frequency of 50 Hz and reactive power of 500 kvar. A portable
digital vibrometer (PDV) was used to measure the vibrations of
the capacitor surfaces by emitting a beam of helium neon laser
at a certain circular point with a diameter of 1mm. It would
measure vibration velocity at a very small pin-point area, and
the vibration status of the object would not be disturbed.
Moreover, an array of microphones was fixed on certain
positions to measure the sound pressure around the tested
capacitors in the hemi-anechoic chamber.
C. Experimental Procedure
Firstly, capacitor surfaces were divided with small grid, as
shown in Fig. 4. Excluding margins, the grids were evenly
marked. Each intersection of two dashed lines was a vibration
measure point, and the laser beam of PDV was aimed at these
points in experiments.
Fig. 2. Welding structure of capacitor bottom surfaces
Fig. 4. Vibration measure points on capacitor surfaces.
voltage squared (force). In the experiments, the tested capacitor
was subjected to currents with components of 50 Hz, 550 Hz
and 650 Hz. The resultant vibration velocity had a frequency
spectrum of 100 Hz, 500 Hz, 600 Hz, 700 Hz, 1100 Hz and
1300 Hz, e.g. velocity at central point of bottom surface, as
illustrated in Fig. 7. The frequency spectrum of capacitor
vibration was concentrated at certain frequencies, which was
consistent with frequency spectrum of excitations. So each
component of the vibration velocity could be picked up with
different frequencies and investigated individually. The 500 Hz
vibration velocities at central line of broad surface were
separated and shown in Fig. 8. It was found that the sinusoidal
Fig. 5. Sound measure points around the capacitor.
The sound measure points were set on a hypothetical
parallelepiped box, as defined in Fig.5. The capacitor was
mounted above the total reflecting plane of hemi-anechoic
chamber with a distance of 0.5 m, and measure distance d was
1 m. The surface of parallelepiped box was divided into eight
rectangle elements, and microphones were arranged on
vertexes and central points of each elements, except for those
on reflecting plane.
In the experiments, the capacitor was excited by the current
with components of 50 Hz, 550 Hz and 650 Hz. The root mean
squared values are 30 A, 25 A and 4.6 A, respectively. Then
vibration velocities of every measure point were recorded one
by one. Theoretically, all the vibration velocities of the points
on one surface should be measured simultaneously Limited by
the measurement device, only one point was measured at one
time. In order to obtain simultaneous relation of velocities, the
signals of all the points were calibrated by correcting the phase
with exciting voltage as a datum signal. The correction
procedure was shown in Fig. 6.
Fig. 7. Waveform and frequency spectrum of vibration velocity at centre
measure point of bottom surface.
The voltage signals recorded on each point were considered
identical on time domain. The vibration velocity signal of a
measurement point and the voltage signal were recorded by a
digital storage oscilloscope at the same time, and the velocity
signals were then corrected according to the phase of the
excitation voltage. In this study, velocity phases were
presented as difference with phases of voltage squared, which
stood for forces on capacitor electrodes as a precise physical
excitation. As to multi-frequency circumstance, the differences
are between each frequency component of vibration velocity
and that of voltage squared.
III. RESULT OF VIBRATION AND NOISE OF CAPACITORS
A. Vibration Features of Capacitors
Vibration velocities on capacitor surfaces were excited by
Fig. 6. Phase correction of vibration velocities at different points.
Fig. 8. waveforms of 500 Hz vibration velocities on five different
measure points at central line of the broad wide surface.
waveforms of velocity had different amplitude and phases. The
phase offset between points near bottom and top surfaces were
more than that near the central region.
In order to represent the vibration shape of capacitor
surfaces, velocities on all measure points were assembled
according to both the amplitudes and phases of a certain
frequency vibration. The 500 Hz vibration velocity shapes on
bottom and broad side surfaces were shown in Fig. 9 and Fig.
10, respectively. At each individual point on a surface, the
vibration presented as a sinusoidal waveform in time domain.
Considering the amplitude and phase of different measure
points, the surfaces preformed different characteristics. These
figures were like photographs that were taken at three different
moments. They represented the dynamics of capacitor surfaces.
The velocity on bottom surface had a feature of entirely
(a)
t = T/4
(b)
t = T/2
(c)
t = 3T/4
Fig. 9. Velocity distribution on the bottom surface at three different
moments
oscillating. All of measure points reach to peak and go down to
troughs simultaneously. Phase offsets of different points were
small and the bottom surface performed an approximate
synchronous vibration. The center of bottom had larger
vibration amplitude than points near the edges.
Vibration on broad surface had a different feature from
bottom surface apparently. At a specific moment, some points
vibrated upwards and others vibrated downwards. The
vibration on broad side surface was not synchronous, and it had
a waving feature. The wave peaks and troughs were parallel to
the edges of top surface and bottom surfaces. These peaks and
troughs travelled from two edges, which were connect to
bottom and top surfaces, to the central area of broad wide
surface. Amplitudes of waves were decaying with distance
from the edges during travelling. It was like that in a rectangle
water surface, two parallel edges were disturbed and two water
waves were generated and propagated on the surface. It was
inferred that the vibration on broad side surface was directly
(d)
t = T/4
(e)
t = T/2
(f)
t = 3T/4
Fig. 10. Velocity distribution on the broad wide surface at three different
moments
excited by bottom and top surface, rather than through liquid in
the capacitor.
In order to reduce the vibration on broad side surfaces, a
damping structure on bottom surface was applied on the
The sound generated from the capacitor was concentrated
to the direction of top and bottom surfaces. As the damping
structure was applied on bottom surface, the sound around it
was relatively smaller than conventional capacitors, while the
sound near top surfaces were approximately the same.
On the basis of ISO standard, the sound power of
capacitors was calculated. The conventional capacitor had a
sound power of 56.82 dB, and the damp-structure capacitor’s
sound power was 55.47 dB. The power emitted from the dampstructure capacitor decreased to 73.3% of conventional
capacitors.
IV. DISCUSSION
Fig. 11. Velocity amplitude comparison between conventional capacitor
and damped-structure capacitor.
capacitor, as shown in Fig. 2. Vibration on broad side surface
of the damp-structure capacitor was tested and compared with
the conventional one. The velocity amplitudes of the central
line were illustrated in Fig. 11. Near the bottom, dampstructure capacitor had smaller vibration amplitude, while
amplitudes were nearly the same on the top side, because the
top surface was welded normally. The damped welding
structure would reduce the vibration near the bottom, and it
indicated that vibration on broad surfaces was actually excited
by bottom and top surface of capacitors.
B. Sound Pressure and Sound Power of Capacitors
Sound field surrounding the tested capacitor was measured
in the hemi-anechoic chamber. Fourteen measure points of
sound pressure, as introduced in Fig. 5, were arranged
according to ISO sound test standards. Capacitors were applied
with three current components of 50 Hz, 30 A, 550 Hz, 25 A
and 650 Hz, 4.6 A at the same time. The A-weighted sound
pressure level generated by capacitors was illustrated in Fig.
12. The values in parentheses were related to the damp-
As introduced above, power capacitors are composed of
internal capacitor elements, package cells and electric liquids.
The vibration original excitation is electric force, which is
actually applied on the internal elements. Then, vibration was
transferring from the internal capacitor elements to the surface
outside. Normally, surface vibration was considered to be
transmitted from the vibration of internal elements through
liquids, therefore the forces on surfaces were uniformly
distributed. However, the result in this paper indicated that the
bottom and broad side surfaces had different vibration type.
The bottom surface was in the form of entirely transverse
vibration, while the broad side surfaces had banding waves
propagating on it.
Vibrations in most of industrial situation performs
synchronously, i.e. vibrations at different points on an
equipment reach to maximum and minimum at the same time
and the phase offset of these points are either 0° or 180°. This
is because that metal materials have a rather small damping on
vibration. Incident wave and reflected wave are in
superposition and perform a stationary vibration. As to the
power capacitors, the vibration of steel surfaces are influenced
by the internal liquid material. The liquids put a strong
damping effect on the surfaces. The broad side surface did not
perform a synchronous vibration, because the reflected waves
were damped by liquids to a relative small level, just leaving
the incident waves being generated continually.
Considering the capacitor’s internal structure shown in Fig.
1, the bottom surface was in direct contact with internal
capacitor elements, and there was a relative wide liquid layer
between broad side surfaces and internal elements. So the
liquids had more damping effect on broad side surfaces than
bottom surface. Moreover, direction of forces on elements
were perpendicular to the bottom surface. Therefore, vibration
on bottom surface was directly excited by internal elements,
and transmitted on the broad side surfaces.
V. CONCLUSION
Figure 12: A-weighted sound pressure level around conventional capacitor
and damp-structure capacitor.
structure capacitor for comparison.
The power capacitors performed different vibration type on
different surfaces. Entirely transverse vibrations were on the
bottom surface, while banding waves were on the broad side
surfaces. It was found that the internal vibration transmitted
firstly on the bottom surface, and then through the edges of
bottom and broad side surface, it transmitted on broad side
surfaces. Due to the liquids’ damping effect on broad side
surfaces, it performed a bending-wave-type vibration. This
refreshed the understanding about the vibration mechanism of
power capacitors.
[2]
Vibration on broad side surfaces could be reduced by
increasing the contact surface damping of edges between broad
side surfaces and bottom surfaces. Capacitors with the damping
structure generated less sound power than conventional
capacitors.
[3]
[4]
[5]
REFERENCES
[6]
[1]
HVDC Stations Audible Noise, No. 202 W.G 14.26 France, CIGRE
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G. McDuff, "Electrical Power Losses Due To Acoustic Wave
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of the 1988 Eighteenth Power Modulation Symposium, IEEE, New
York, pp. 367-372.
M. D. Cox, and H. H. Guan, “Vibration and Audible Noise of
Capacitors Subjected to Nonsinusoidal Waveforms,” IEEE Transactions
on Power Delivery, Vol. 9, No. 2, pp. 856-862, 1994.
L. Zhu, S. Ji and Q. Shen, “A Noise Level Prediction Method Based on
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J. Li, S. Ji, Lu. Zhu and P. Wu, “Vibration Characteristics of Filter
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