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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 Tech. Rep., 2002. G. McDuff, "Electrical Power Losses Due To Acoustic Wave Generation In Repetitive Pulsed Capacitors", IEEE Conference Record 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 Electro-Mechanical Frequency Response Function for Capacitors,” PloS One, 2013, Vol. 8, No. 12, e81651. J. Li, S. Ji, Lu. Zhu and P. Wu, “Vibration Characteristics of Filter Capacitors Used in HVDC Converter Stations”, IEEE Transactions on Power Delivery, Early Access Articles, 2015. M. P. Norton and D. G. Karczub, Fundamentals of Noise and Vibration Analysis for Engineers (2nd), Cambridge University Press, 2003.