Dynamic Absorption of Transformer Tank Vibrations and Active Canceling of the Resulting Noise C. A. Belardo, F. T. Fujimoto, J. A. Jardini, S. R. Bistafa, P. Kayano, B. S. Masiero, V. H. Nascimento, F. Ribeiro, E. Mercato, R. G. Lima, L. Chavez, E. Tamai. Abstract Various stages of the development of noise control measures for power transformers are discussed. In part A, the use of dynamic vibration absorbers (DA) and noise reduction are addressed. Although both techniques are not new, their implementation is still matter of technological development. The vibration of a transformer panel is transferred to the DA, which has minimal acoustic coupling with air. Preliminary experimental results show that it is possible to diminish the transformer panel vibrations. In part B, the use of acoustic active canceling is addressed. Firstly a simple control system is developed, as to validate de active noise control theory. Following, simulations were done to determine the number of transducers and their positioning. Finally, the achieved results are then commented. Key Words Active Noise Control, Acoustic Applications, Acoustic Fields, Acoustic Noise, Adaptive Control, Dynamic Absorbers, Genetic Algorithm, Power Transformers, Vibration and Sound, Vibration Absorption. N I. INTRODUCTION oise generated by power transformers is a kind of environmental sound pollution that affects the life of people living nearby electric substations. The usual noise control methods applied in these situations are classified as active or passive. Usual passive method consists on the placement of an acoustic barrier between the sound source (transformer) and the receivers (community). In general, an attenuation of up to db is obtained, as long as the receivers are located under the acoustic shadow generated by this barrier. This solution is not viable to protect receivers in high-rise buildings. The first part of this paper addresses vibration absorption by means of Dynamic Vibration Absorbers (DA) springmass system attached to the panels of the transformer, acting to reduce the vibration on the transformers tank (vibration control). It is a passive system, and becomes an active system if it has automatic damping cancellation and automatic tuning. This method is useful when vibration problems occur over a very narrow frequency range []. Part of the mechanical energy is transferred to the DA, which has small acoustic coupling with air []. The second part of this paper is concerned with the active noise control in open space; by attenuating the acoustic field generated by the transformer tank vibration though destructive acoustic wave interference. This method requires acoustic energy injection via loudspeakers, and noise monitoring at the receivers positions via microphones, and therefore requires an efficient control system. PART A TRANSFORMER NOISE CANCELING WITH DYNAMIC ABSORBERS II. NOMENCLATURE OF PART A Symbol Denomination Unit k p Equivalent panel stiffness N/m k DA stiffness N/m M Panel equivalent mass kg M Mass of DA kg c p Panel damping coefficient Ns/m c DA damping coefficient Ns/m F(t) Panel excitation force N & x& Panel acceleration m/s x& Panel velocity m/s X Panel displacement m & x& DA acceleration m/s x& DA velocity m/s X DA displacement m f n Panel frequency Hz c velocity of sound m/s ρ Air density Kg/m v ref Reference velocity = -9 m/s V m Mean velocity m/s I ref Reference sound intensity = - W/m L I Intensity Level db L v Velocity Level db III. METHODS A lumped model for a dynamic absorber attached to the transformer tank panel is a damped two-spring-two-mass system, with an excitation force as shown in Figure. The equivalent stiffness k p and mass M were computed using the finite element method, taking into account the dimensions and material of the transformer tank. The damping coefficient c p is usually experimentally obtained. The equation of movement of the panel with AD attached is M.&& x + cp + c. x& c. x& + kp + k. x k. x = F( t) () ( ) ( ) mx.&& + cx.& cx& + kx. kx. =. () This work is being financed by AES Eletropaulo.
Transformer tank panel k p M F(t) x Vibration Absorber x k m A (m) -5....6.4.5 c e c -6 Fig.: A lumped model for the dynamic absorber attached to the transformer tank panel. The spring stiffness k of the DA is calculated with the following equation: ( π ) k =. f n. m () The frequency f n is the excitation frequency of the panel. Figure shows the Amplitude of the panel displacement (x ) and of the DA displacement (x ), for several damping coefficients. It can be seen in Figure that the damping coefficient is not relevant when the DA mass is above of kg. Figure shows the percentage of reduction of the panel displacement. When the DA mass is kg the displacement reduction is around 7%. IV. RESULTS Several DAs were built with different masses. The DA was attached to the center of one of the panels of the transformer tank, as can be seen in the photograph shown on Figure 4. The points used to attach two accelerometers are also indicated. The test was performed during normal operation of the transformer. The acceleration signal was collected near the AD, then below the AD and, finally, above the AD, using different values of the AD mass. Three different AD masses were tested, namely: 8.5 kg, kg and kg. The plots of vibration energy versus the AD mass are shown on Figure 5. The best performance was obtained using kg. The computation of sound intensity near the panel surface [] can be made by the following formula I = v ρc. (4) m - DA mass (kg) Fig. : Vibration amplitude A vs. DA mass for damping ratios with the following values:.,.,.,.6,.,.4,., and.5. (%) 9 8 7 6 5 4 DA mass (kg)) Fig. : Reduction of displacement vs. DA mass..... 6. 4. 5 Fig. 4: Photograph of the DA attached to one of the panels of a /4 KVA power transformer.
Energy (rms).8.6.4..8 Energy point Energy point Energy point. kg 8.5 kg. kg. kg m (kg) Energy (rms).8.6.4..8. kg 8.5 kg. kg. kg m (kg) Energy (rms).8.6.4..8. kg 8.5 kg. kg. kg m (kg) Fig. 5: Vibration energy (RMS) as a function of the three DA mass for three panel positions. The comparison of the panel acceleration with and the DA is shown on Figure 6. a (m /s ) a (m /s ).. Point - Comparation of aceleration without. kg kg 5 5 5 5 4 45 5.. Point - Comparation of aceleration. kg kg sound intensity level. Figure 8 shows a comparison, with and without DA, of PSD of the vibration velocity in one-third octave bands from 5 Hz to 4 Hz. Note the reduction of the vibration velocity in the Hz and 5Hz frequency bands. This will result, in average, in a reduction of the sound intensity level of about db. V. PARTIAL CONCLUSIONS OF PART A A dynamic vibration absorber can reduce the vibration and the soun d radiation of the transformer tank panels. The results obtained so far may be improved by: a) optimizing the size and the fixing point of the DA on the panel, by taking into account the coincidence of the wavelength of the panel flexural vibrations and the wavelength of sound in air; b) canceling the damping of the dynamic absorber; and c) fine tuning the natural frequency of the dynamic absorber. These measures will be further investigated during the course of this research. PSD of velocity (m/s).5.5.5 x -6.5 PSD of Velocity 5. kg kg 5 5 5 5 4 45 5 Distance m Frequency (Hz) a (m /s )..5 Point - Comparation of aceleration. kg kg Fig. 7: Power Spectral Density of the velocity of vibration as a function of the frequency for three panel positions. 5 5 5 5 4 45 5 Frequency(Hz) Fig. 6: Comparison of the panel acceleration with and without the DA. The relationship between the sound intensity level and the velocity level of the panel vibration is given by v ρc vref LI = log + log (5) v I ref ref PSD of velocity (m/s) x -7 PSD.8.6.4..8.6.4 Simulations were done considering air at o C ( ρc = 46 Rayls, I = ref watts / m ). A com parison of the velocity Power Density Spectral (PSD), with and without the DA is shown in the Figure 7. According to (5), a clear reduction of the velocity level can be seen, what may result in a corresponding reduction in the. 5 5 5 5 4 Frequency(Hz) Fig. 8: Comparison of PSD of the vibration velocity in one-third octave bands for three panel positions.
4 PART B ACTIVE CANCELING OF TRANS- FORMER NOISE Active noise canceling (ANC) is achieved by introducing a canceling, anti-noise wave (wave with same amplitude and opposite phase), through an appropriate array of secondary sources. These secondary sources are interconnected through an electronic system using a specific signal processing algorithm for the particular cancellation scheme. Reductions in sound pressure levels up to about db may be achieved as long as the phase errors remain considerably small. Such precision in phase can be achieved with adaptive control. This type of control can compensate: a) noise fluctuations caused by variations in the supply of voltage, current and power demand ) variations in the acoustic path, caused for instance, in variations of meteorological conditions. In a typical ANC, error microphones are used to pick up the noise generated by primary and secondary sources. When the cancelling region is a wide open space, the ANC is said to be global. In these cases, the error microphones should be positioned near the primary source, otherwise, instability and convergence problems would appear in the control algorithm [4]. For cancellation on areas far from the primary source, the positioning of secondary sources and error microphones is of extreme importance. Simulations are current underway to find optimum placement of these transducers. VI. IMPLEMENTATION As a first approach to the ANC problem, a simple one microphone, one loudspeaker system was implemented. Two primary sources were used: a small three-phase bench transformer and a loudspeaker reproducing noise recorded near the transformer under consideration in the substation. A feed forward control was used. For the first primary source, the reference signal was extracted from the electric network through a simple voltage divider and then processed in order to obtain the desired harmonics out of the main network frequency. The new signal is then filtered by a filtered X LMS type adaptive filter, implemented in a digital signal processing (DSP) board, and the output of this filter (the antinoise ) is sent to a power amplifier and then to the loudspeaker. The error microphone picks up the transformer noise plus the anti-noise and sends this signal to the DSP board, which in turn uses this signal to feed the filter, in order to minimize the noise level at the error microphone. The acoustic path between the loudspeaker and the error microphone the secondary acoustic path must be characterized and taken into account in the adaptation algorithm. The secondary acoustic path can be characterized by its impulse response, which can be measured using the MLS method [5]. This method for obtaining the secondary path impulse response was also implemented in the DSP board. A. Results It s obvious that only one secondary source and one error sensor is not a viable solution for the attenuation of the noise at a large power transformer. However, in order to gain some experience in the operation of an ANC system, and also because of its simplicity, it was the chosen model for the first implementation. The results obtained using the ANC with the three-phase bench transformer as a primary source can be seen on the following figures. Figure 9 shows the spectrum of the emitted noise with the ANC turned off, and Figure with the ANC turned on. With the ANC turned on, attenuations of around db can be observed on the first two harmonics. For the actual transformer in the substation, attenuations up to the sixth harmonic will be sought. This will considerably increase the complexity of the control system, which will be further studied during the course of this research. This model was made using only one error microphone and one loudspeaker, due to our DSP board limitations. A new DSP board capable of dealing with up to six I/O channels has been recently acquired, for the implementation of a prototype of the system under consideration. The position of this larger number of transducers will be critic, and a digital model to simulate and optimize their positioning has been developed. Fig. 9: Noise spectrum emitted by the transformer, without ANC. Fig. : Noise spectrum emitted by the transformer, with ANC turned on.
5 A. Genetic Algorithm VII. TRANSDUCERS POSITIONING Several articles in the field of ANC deals with the positioning of error sensors and secondary sources, because of the importance of transducer location in the success of an ANC. In practice, the difficulty of finding an optimal transducer placement lies on the huge number of possible combinations of positions, from which to choose a few possible candidates. In general, such a problem can not be uniquely solved using optimization algorithms based on gradient descend methods. Reference [6] proposes the use of genetic algorithms to the optimization of ANC transducer positioning problems. Genetic algorithms (GA) are stochastic global optimization procedures for finding the global maximum (or minimum) of a multi-modal function. GA requires the variables of the prob- lem s to be coded as a finite length string containing alphanumeric characters called genes (bits in this case). A GA starts with a population of randomly selected strings and the fitness value for each member of this initial population is then calcu- first generation are then selected lated. The strings of this at random, but with a probability proportional to their fitness, in order to perform a reproduction operation to generate the next generation of strings. After selection, various genetic operators such as mutation, cross-over and reproduction are used to extract common properties shared by two good strings, witch are then mated to provide offsprings for the next generation. Those processes are repeated until convergence is achieved to a population dominated by the global maximum of the fitness function or satisfying user defined conditions. B. Simulation ) Number of transducers Yet not using GA, some simulations were undertaken in order to verify the influence of the number of transducers on the quality of the ANC. The primary source was modeled by a group of eight point sources, distributed along the vertices of a cube with sides of m. Point sound sources positioned near this cube were used as secondary sources. Error sensors were modeled as omnidirectional point receivers. With one secondary source, the system was simulated for different numbers of error sensors. With one error sensor, a null sound pressure point is verified, precisely where this error sensor is located. As the number of error sensors was increased, a broader attenuation area was detected instead of null pressure points. In one of the simulations four fixed error sensors were considered, and the number of secondary sources was varied. Global attenuation is achieved by increasing the number of secondary sources. When then number of secondary sources and error sensors are the same, null pressure points are forced at the location of the four fixed error sensors, which does not necessarily provide a better global attenuation. Reference [7] proposes the use of fewer secondary sources than error sensors. The behavior of a subdetermined system was also verified, with one error sensor and three secondary sources. This system has the same behavior of a system with only one secondary source. ) Transducers Position Simulations using the genetic algorithm with the same digital model described in the last section were also made, varying the positioning of secondary sources and error sensors. Firstly, only the secondary source positioning was simulated, using as control surface two square areas, at a certain distance from the primary source, simulating the windows of the two neighboring high-rise apartments, from which complaints were received by the power utility company, regarding the noise from the substation. This is not viable model, as it does not use error microphones, and so can not be an adaptive control system. As the recent acquired EZ-ANC DSP board has six outputs, this simulation was done for six secondary sources. Here, 84 candidate points were defined around the primary source. After around iterations, the algorithm found a global minimum position for the frequencies of Hz, 4 Hz, 6 Hz and 48 Hz, giving attenuations of about db in these frequencies. By keeping the same secondary source positioning found, as above described, candidate positions for the error sensors were defined in a hemisphere that contains the primary and secondary sources. Seven microphone positions were chosen in order to maximize the attenuation of the sound field on the square control surfaces. The resulted attenuation was now considerably smaller than that obtained in the simulation without error microphones. VIII. PARTIAL CONCLUSIONS OF PART B Active noise control is a viable solution for noise related problems generated by large power transformers, especially for the control of the first harmonics contained in noise. However, for meaningful attenuations, great care should be exercised with the adaptive control algorithms and with the positioning of the error microphones and the secondary sources, which have to be properly simulated in order to find their optimal placement. In the near future, an in situ acoustic holography mapping of the transformer noise will be undertaken. From these results, a more detailed acoustical behavior of the primary source will be available, allowing more realistic simulations. In this regard, the simulations done so far do confirm the importance of optimum transducer placement for the success of ANC. IX. REFERENCES [] Bies D. and Hansen C., 996, Engineering Noise Control, E & FN Spon p 47. [] Den Hartog J. P., 97, Vibration in systems mechanics, McGraw-Hill Book Company, inc. pg77 [] Takatsubo J., Ohno S., and Suzuki T., 98, Calculation of the sound pressure produced by structural Vibration using the result of vibration
6 analysis. Bulletin of the Japanese Society of mechanical Engineers, 6, 97-976. [4] P.A. Nelson & S.J. Elliot, Active Control of Sound, Academic Press, London, 99. [5] Masiero, B. Estudo e Implementação de Métodos de Medição de Resposta Impulsiva em Salas de Pequeno Porte, 4; [online] available: http://gsd.ime.usp.br/acmus/publi/relat_medicao.pdf [6] K. H. Baek and S. J. Elliot Natural algorithms for choosing source locations in active control systems, Journal of Sound and Vibration, vol. 86. pp. 45-67, 995 [7] Martin, T., Roure, A. Active Noise Control of Acoustic Sources Using Spherical Harmonics Expansion and a Genetic Algorithm: Simulation and Experiment. In Journal of Sound and Vibration (998) (), 5-5.