Investigation of acoustic noise sources in medium frequency, medium voltage transformers

Peng Shuai and Jürgen Biela, Member, IEEE,

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Investigation of Acoustic Noise Sources in MediumFrequency, Medium Voltage Transformers

Peng Shuai, Jurgen BielaLaboratory for High Power Electronic Systems, ETH Zurich

Email: shuai@hpe.ee.ethz.ch

Keywords<<Transformer>>, <<Acoustic noise>>

AbstractMedium voltage, medium frequency transformers (MFTs) are much smaller in size and weight com-pared to conventional low frequency transformers. The MFTs are very attractive for applications wherefull control of the power flow and high power density are required, such as power electronic interfaces insmart grids and traction converter systems. Due to the limitation of high voltage semiconductor switches,the MFTs are usually operated in the kHz range, which results in acoustic noise radiated from the trans-former. In this paper, the origins of acoustic noise associated with MFTs are investigated based on vibra-tion and acoustic measurements. The investigation focuses on the core materials widely used for MFTs,i.e. the amorphous and the nanocrystalline alloy. Experimental results show that the nanocrystallinecore features lower level of vibration and acoustic noise emission than the amorphous core. Comparingcore shapes, the toroidal core has better vibration and acoustic performance than the U-shape core. Theexistence of air gap in case of a cut core leads to excessive vibrations and therefore higher acoustic noiselevel due to increased magnetic forces compared with uncut core. Based on analysis of measurementresults, recommendations for low noise MFT design are proposed.

IntroductionIn modern electric power systems, renewable energy sources are increasingly integrated. Since thesepower sources are inherently fluctuating, power electronic interfaces are essential for dynamic control ofpower flow and power quality improvement. The typical configuration of the interfaces are usually basedon DC-DC converters isolated with medium frequency transformers as shown in Fig. 1. As the mediumfrequency power conversion systems are operating in the kHz range, significant reduction of weight andsize can be achieved compared to conventional line frequency transformers. For medium voltage high

Figure 1: Medium frequency power conversion system.Main specifications of designed DAB converters are: MVDC-link voltage 2400 V, LV DC-link voltage 400 V, nominalpower 25 kW and switching frequency 4 kHz.

Figure 2: Volume reduction for optimal MFT de-sign with VITROPERM500F by increasing fre-quency from 1 kHz to 16 kHz.

power applications, the DC-DC converters are usually cascaded and connected to the medium voltage(MV) grid. The design challenges are mainly high efficiency, thermal management and high insulationvoltage in case of reduced size and higher operating frequency.The optimal design of the MFT for a DC-DC converter has been discussed in [1], where the isolationvoltage level aims for 24 kV∗. The volume dependency on switching frequency as shown in Fig. 2 in-dicates that the volume reduction with increasing frequency is not significant above 4 kHz. The benefitof reducing the size by increasing operating frequency is limited by isolation requirement and thermalstress above 4 kHz. Furthermore, the switching losses of the converter increases significantly with thefrequency, especially for the MV side switches. Therefore, in the considered design the operating fre-quency is selected as 4 kHz, which is in the audible frequency range.In the past few decades, the acoustic noise emission from electromagnetic components has been con-stantly investigated. There exist extensive studies for electrical machines, e.g. [2, 3, 4] and a largenumber of research focusing on power transformers operating at line frequency can be found [5, 6, 7].However, in the medium frequency range, literature regarding this topic is rare, especially for MFTs.The investigation on acoustic performance of electromagnetic components operating in the medium fre-quency range are presented in [8, 9, 10, 11, 12, 13] for inductors. In [8], a noise reduction method isproposed for inductors with distributed air gaps in iron cores by handling the frequency of free modesvibration. In [9], the noise reduction of electrical steel based inductors is achieved by reducing the fluxdensity and modification of the air gap filler. The measurements of sound pressure level (SPL) are per-formed for inductors built with grain-oriented steel and ferrite cores under diverse excitation conditionsin [10]. The magnetostriction and acoustic noise of Si-Fe powder compressed cores are measured in [11]for inductors employed in photovoltaic generators. In the extensive studies carried out for single-phaseand three-phase inductors in [12, 13], the authors propose to reduce the noise by improvement of the airgap distribution in grain-oriented steel core and by optimizing the hardness of the air gap filler.Regarding transformers, in [14], the SPL of several spacecraft power transformers built with Si-Fe andNi-Fe-Mo cores are measured and compared. The study is focusing on the influences of the core typesand air gap and recommendations for low noise transformer design are proposed. The dependency ofacoustic noise on frequency and magneto-mechanical resonance is investigated in [15] for 3-phase 3-limb transformer. Finally, the acoustic characteristics of 3-phase transformers built with amorphous coresoperating at 60 Hz are introduced in [16, 17]. The work focuses on the influence of bending structure ofcores on vibration and acoustic noise.As aforementioned, acoustic noise emission from electromagnetic components operated in medium fre-quency range is still a problem to be dealt with. A model for predicting the acoustic noise level needsto be established and better methods to reduce the noise need to be found. Regarding MFT design, thesignificance of each acoustic noise source is still unclear and the vibration related properties of core ma-terials used for MFTs are seldom investigated. Therefore, in this paper the acoustic noise sources areinvestigated based on vibration and acoustic measurements with focus on amorphous and nanocrystallinetape wound cores, which are widely used for MFT design in high power applications.

Sources of acoustic noise in MFTsThe electromagnetic forces induce vibrations in the transformer structure which cause vibrations of par-ticles in the surrounding air. These vibrations produce the acoustic waves which propagates throughmedium (usually air) to the ears and generate acoustic noise. In some cases, noise may also be causedby the auxiliary equipments such as fans and oil pumps, which is out of the scope of this paper. InMFTs, the structural vibrations are excited by three types of electromagnetic forces: Maxwell force,magnetostrictive force and Lorentz force.The Maxwell force is acting on the boundaries (surfaces) between two magnetic media with differentmagnetic properties (reluctivity), which is typically associated with the air gap regions and the joints ofcores in transformers. The Maxwell force can be calculated by the surface integration of the local forcedensity based on Maxwell stress tensor as ~F =

∫∫(~H · (~B ·~n)− 1

2(~H ·~B) ·~n) dS, where ~F is the force, ~H

is the magnetic field strength,~B is the magnetic flux density and~n is the vector in normal direction to thesurface S. To reduce the eddy current losses, the magnetic cores of MFTs are usually constructed withlaminated sheets. The effects of the Maxwell force at the joints of core lamination sheets and betweenthe sheets are introduced in [5]. In case of MFT, tape wound cut cores are widely used which normallydo not have any joints.Accordingly, three mechanisms due to Maxwell force can be assumed for U-shape tape wound core (cf.Fig. 3): repulsive forces between lamination sheets; in-plane attractive forces between the sheet ends (airgap region); off-plane attractive forces between the lamination sheets near the air gaps.The Magnetostrictive force is caused by magnetostriction (MS), which represents the deformation ofmagnetic materials under the effect of magnetic field. In case of core materials for transformer design,the major deformations are due to the Joule magnetostriction [2]. This effect is anisotropic and causesan elongation or contraction of the lamination sheets in the direction of the applied magnetic field. Atthe same time, shrink or expansion can be observed in the orthogonal directions to the magnetic field, asthe total volume of the sheet remains constant. Magnetostriction is quantified as the mechanical strain λ

∗Considering 5 modules cascaded and connect to 6.6 kV AC grid on MV side. For safety reason, the isolation voltage isdefined as two times of the MV DC-link voltage level.

Figure 3: Mechanisms of Maxwellforce in tape wound cut core.

Figure 4: Mechanisms of magne-tostriction in tape wound cut core.

Table I: In-plane saturation magne-tostriction of core materials withoutmechanical stress

Material λs [µm/m]2605SA1

(Amorphous)27

VITROPERM500F(Nanocrystalline)

0.5

3.0% Silicon steel 106.5% Silicon steel 0

TDK PE90 (ferrite) -0.6a

aNegative value means contraction.The quantification of magnetostrictionfor ferrite is related to the crystal direc-tions.

induced in the material in the absence of a restraint as λ = ∆l/l(µm/m or ppm), where l is the length ofthe sample and ∆l is the change of the length. In general, λ is proportional to the square of magnetic fluxdensity B and reaches the maximum value at the saturation point of the material. This maximum valueis defined as the saturation magnetostriction λs, which is a material parameter. Typical values of λs forseveral core materials are listed in Table I. However, it should be noticed that magnetostriction is alsodependent on the mechanical stress.The Lorentz forces are acting on the current-conducting windings and the volume force density~f v iscalculated as ~f v =~J ×~B, where ~J is the current density in the conductor and ~B is the magnetic fluxdensity. In literature, the contribution of Lorentz force is usually considered to be less significant thanthe other two sources. Both magnetostriction and Maxwell force are assumed to be more pronouncedsources of acoustic noise emission [5] associated with transformers. However, it is concluded in [8] thatthe winding is always a source of mechanical stress, so it can not be ignored in the mechanical analysis.The impact of the Lorentz force on vibrations will be discussed later in this paper based on simulationand measurement results.At the air gap region, the in-plane attractive forces pulls the sheet ends in two core halves towards eachother. This mechanism is more significant than the repulsive forces between lamination sheets. The in-plane magnetostriction causes the elongation (or contraction) of the lamination sheets along the magneticflux line. Due to the magnetic fringing field near the air gap, the off-plane attractive forces arise and acttogether with the off-plane magnetostriction on the sheet ends. As illustrated in Fig. 3 and Fig. 4, thesetwo mechanisms enhance with each other and cause expansions of the sheet ends. Therefore, the air gapmay lead to excessive vibrations in MFTs due to increased Maxwell and magnetostriction forces.Moreover, a coincidence of the vibration frequencies with the eigenfrequencies of the transformer struc-ture will amplify the vibration and therefore generate more acoustic noise. In order to identify thecontribution of each source as well as the relevance of electromagnetic and mechanical properties of thetransformer to the acoustic noise emission, both vibration and acoustic measurements are performed onseveral magnetic cores. The details of the measurements are introduced in the following sections.

Measurement setupIn this work, the measurement is mainly performed on a pair of cut and uncut standard nanocrystallinecores (VITROPERM500F T60102-L2157-W159), which is selected for the MFT prototype design in [1].For comparison, an amorphous core and a ferrite core with similar size are also chosen for measurement.The size of these cores are shown in Fig. 5 and listed in Table II.The measurement setup as shown in Fig. 6 has been built for both the vibration and the acoustic noisemeasurements. The excitation voltage/current for the test unit (TU) is generated by a signal generator,amplified with a power amplifier and then fed to the primary winding of the TU. A capacitor bank with atotal capacitance of 5 mF is connected in series with the TU to decouple the DC component which mightbe induced by the power amplifier. To control the magnetic flux density, the voltage on the secondarywinding of the TU is measured by the digital multimeter (NI PXI-4071) and sent to PC as feedbacksignal to regulate the output voltage of the signal generator by using LabVIEW software.The vibration of TU is measured with a laser scanning vibrometer (Polytec PSV-400) controlled withcontroller (Polytec OFV-5000), which allows a non-contact measurement without altering the structureof TU as in case of using a contact type accelerometer. The TU is placed on a vibration isolated table to

Table II: Dimensions of cores for measurement

CoreDimensions[mm]

A B C D W H

VAC VTROPERM500FT60102-L2157-W159

29.6 30 95 26.6 90 157.5

Metglas 2605SA1PS0509CA

28.6 30 95 30 87.2 152.2

Kaschke K2008U93/30/76

28 34.6 96 30 93 152 Figure 5: Symbol of core dimen-sions.

avoid the disturbance from the environment. The measured signal is decoded to velocity and acquired bythe data recorder and sent to PC for further analysis.The acoustic measurement is done by measuring the sound pressure level through a single 1/4 inchmicrophone with integrated pre-amplifier (G.R.A.S. 40PH), where the measured signal is acquired bythe dynamic signal analyzer (NI PXI-4462) and then sent to PC. The TU is located in the center of ananechoic room, the size of which is much larger than the TU. The microphone is located 1 m away fromthe surface of the TU.The vibration measurements are performed on three surface areas on the magnetic cores as indicated inFig. 7, i.e. front, side and top. Accordingly, the acoustic measurement are also performed from thesedirections separately. During both vibration and acoustic measurements, the sensor (vibrometer or mi-crophone) is fixed at the same location while the TU is moved in order to measure each surface/direction.

Analysis of measurement resultsThe vibration and acoustic measurement are performed separately on different cores excited with sinu-soidal voltage/current. The results are analyzed and discussed below.

Eigenfrequencies and mode shapes of uncut core To investigate the eigenmode of the magneticcores, the vibration of the VITROPERM uncut core is measured by means of a frequency sweep. Thecore is hanging as shown in Fig. 9 to enable a ’free’ vibration condition. The core is turned over for 90degrees to measure the top surface. The excitation voltage on the core feeding to a 4-turn winding is achirp signal amplified 20 times with the power amplifier. To avoid the LC-resonance between the ca-pacitor bank and the magnetizing inductance, the frequency sweep is started from 300 Hz and performedup to 20 kHz. Since the flux density is lower at higher frequency with the same amplitude of excitingvoltage, the induced magnetic force is also reduced with the increase of the frequency. In order to have aclearer mechanical response of the core in the whole measuring frequency range, the frequency sweep isdivided into 3 sub ranges with different amplitude of excitation voltage: from 300 Hz to 5 kHz with 2 V,from 5 kHz to 10 kHz with 20 V and from 10 kHz to 20 kHz with 40 V.The scanning vibrometer measures a set of points located on the measured surfaces. The vibration in thedirection perpendicular to the surface at these points are measured. In Fig. 8, the frequency spectrum ofmeasured average velocity of each selected surface area are shown together. To have a better visibility,the magnitude of velocity from 300 Hz to 5 kHz and from 5 kHz to 10 kHz are multiplied by a factor of 20and 2 respectively. As can be seen from the frequency response in the figure, several eigenmodes of thiscore are within the audible frequency range and may coincide with the frequency of the excitation voltage

Figure 6: Schematic of measurement setup.

Figure 7: Surface ar-eas of vibration mea-surement.

Figure 8: Frequency spectrum of measured average surface velocity of VIT-ROPERM uncut core by means of frequency sweep.

Figure 9: Vibration measure-ment setup for eigenmode anal-ysis.

Figure 10: First 3 dominant eigenmodes of VITROPERM uncut core identified from vibration measurement.

and its harmonics and result in mechanical resonance. The comparison of the measured amplitude ondifferent surfaces evidently shows that above 5 kHz the top surface has the most significant vibration,followed by the side surface while the vibration on the front surface is relative weak. This indicates thatthe tape wound core is more prone to vibrate in the directions perpendicular to the lamination layers.Since the tape wound core is composed of magnetic material together with epoxy resin as isolationbetween the lamination layers as well as varnish outside of the core, the mechanical properties of the coreis anisotropic. As introduced e.g. in [4], the laminated core can be modeled as orthotropic structure wherethe in-plane (lamination layer) material property is assumed to be the same while the material exhibitsdifferent properties in the directions perpendicular to the plane. However, an accurate model requiresaccurate material parameters which usually need to be determined by experimental measurements. Incase of the measured core, the vibration measured on side and top surfaces demonstrates the out-of-plane behavior while the vibration on front surface is related to the in-plane properties. As illustrated inFig. 10 for the first 3 dominant eigenmodes identified by measurement, similar mode shapes are observedon the side and top surfaces which are different as the mode shapes on the front surface. The first andthird mode shapes illustrate the flexure deformation of the core limbs and yokes while the second modeshape shows the torsional deformation. At higher frequency, the mode shapes are mixed with low ordervibration modes and can not be clearly distinguished.

Figure 11: Maxwell force and Lorentz forces distribution at the same magnetic fluxdensity in inductors and transformers with or without air gaps. The inductor windinghas 4 turns and the transformer winding has 40 turns (turns ratio 1:1). If no air gapexists, the Maxwell force and Lorentz forces are comparable. In case that an air gap ispresent, large attractive forces are acting on the two core halves and pull them together.The flux density in the middle of core limbs is approximately 0.5 T in all cases with apeak value at around 1.5 T at the corners.

Figure 12: Comparisonof measured velocity ofthe winding and the VIT-ROPERM uncut core ex-cited to 0.5 T at 4 kHz onthe front surface.

Contribution of Lorentz force As mentioned before, the Lorentz force is considered to be less sig-nificant than the other two sources of acoustic noise. However, the simulation results shown in Fig. 11indicate that in case of uncut core, the Maxwell force and Lorentz force are actually comparable. Tocompare the vibration of winding and core simultaneously during operation, the VITROPERM uncutcore is excited to 0.5 T with a 4-turn winding fed with 4 kHz sinusoidal voltage. This induces the magne-tizing current with the peak value of approximately 0.6 A in the winding. The vibration measurement isperformed on part of the front surface of the core limb and on the surface of one turn of the winding. Asthe measurement result shows, in this case the measured surface velocity of the winding and the core arein the same range, which is similar as the simulation result shown in Fig. 11 (a). As will be revealed infollowing sections, the vibration on the front surface of the core is relative small compare to the other twosurfaces. In case of a cut core excited to the same flux density, the magnetizing current will be larger,and the Lorentz force acting on winding will also increase. Measurement of a pure winding fed with20 A peak sinusoidal current shows that the maximum surface velocity can reach 300 µm/s. However,compared with the core surface, on which some areas could reach a velocity of over 10 mm/s, this valueis still much lower. Therefore, the vibration of winding due to Lorentz force can be considered to havevery limited contribution to acoustic noise.

Comparison of various core materials and shapes To compare the vibration and acoustic perfor-mance of magnetic cores with various materials and shapes, several cores are measured under sameexcitation conditions. During the measurement, all the cores are placed directly on the table without anyadditional mechanical fixation. In Table III, the measurement results of VITROPERM cut and uncutcores together with the Metglas cut core are compared. All the cores are excited with 4 kHz sinusoidalvoltage to the flux density levels given in the table. Since only the harmonics in audible range are ofinterest, all the results are RMS values calculated with the 1st to 5th harmonics.The comparison of both measured surface velocity and sound pressure among different surfaces / direc-tions for each core indicate similar results: the most significant vibration exists on the top surface of thecore while the measured acoustic noise emission in the normal direction to this surface is also the largest.The side surface is subject to less vibration as well as noise emission compared to the top surface butmore than the front surface. The relationship of degree of vibration / noise emission among the mea-sured surfaces, i.e. top surface > side surface > front surface, is consistent with the results obtained byfrequency sweep measurement for the VITROPERM uncut core.The comparison between the VITROPERM cut and uncut cores indicates that with air gaps, vibrationsand noise emission increase by a factor of more than 10. The increase of vibration is more significanton the side and top surfaces, i.e. in the direction perpendicular to the lamination layers. In case ofcut cores, the difference of vibration intensity between the perpendicular and parallel directions of thelamination layers is more apparent due to the increased Maxwell force induced by the air gaps. It shouldbe pointed out that the measured surface velocity exclusively indicate the vibration on the measuredsurfaces. On the other hand, the measured sound pressure in one direction is mainly radiated from thesurface perpendicular to this direction, but the noise emission from other surfaces also has impact andcan not be completely excluded from the measurement results.In Fig. 13, the areas with relative high surface velocity on the measured surfaces of each core at variousflux density levels are indicated. Here the vibration of the highlighted areas are not in phase, i.e. the

deformation of these areas do not appear at the same time. The numbers only represent the highestamplitudes of measured surface velocity in the areas. On the top surface, the area with largest vibrationis located in the middle of the measured surface, which is the same for all three cores. This is related tothe bending mode of the yoke as shown in Fig. 10. On the front surface, the intensive vibration appears onthe corner as shown for VITROPERM cores and is related to the torsion mode. View on side surface, thebending areas (near the corners) are subject to high degrees of vibration which is related to the bendingmode of the core limb. In case of VITROPERM cut core, the air gaps amplify the vibrations in theseareas. The air gaps of Metglas cut core directly cause strong vibrations in the nearby regions similar asshown for front surface of VITROPERM cut core. It is noticed that the vibration measured on the upperside and lower side half cores are not symmetric. The reason is that the vibration of the lower side halfcore is influenced by the gravity of the upper side half core and also the friction with the surface of thetable. Also, this phenomenon can be observed by the measurement results of other cut cores which willbe shown later.For comparison, the measurement results of the ferrite core at 0.2 T is also listed in Table III. In spite ofthe non-laminated structure and the right angle at the joints of core limbs and yokes (rectangular shape),the ferrite core shows similar relationship of vibration intensity and noise emission on different surfacesas the U-shape lamination core. At the same flux density level, ferrite core presents less vibration/noiseemission than VITROPERM and Metglas cut cores.For further comparison, a pair of cut and uncut toroidal cores made of VITROVAC 6025F amorphousalloy together with the ferrite core are measured at 0.4 T. The dimensions and the measured areas ofthe toroidal cores are shown in Fig. 14 and the results are given in Table IV and Fig. 15. As can beseen, the areas with high degrees of vibration on the surface of measured ferrite core is quite similaras the other U-shape cores. In case of toroidal cores, there exists no part with large curvature as thebending region of the U-shape cores. As a result, the magnetic flux in toroidal cores is relative welldistributed, which lead to relative equal distributions of local magnetic forces. Similarly, with laminatedstructure, the VITROVAC toroidal cores also present larger vibration / noise emission in the directionperpendicular to the lamination layers (the radial direction). Furthermore, the VITROVAC uncut toroidal

Table III: Comparison of vibration and sound pressure measurement results for nanocrystalline and amorphouscores under excitation of 4 kHz sinusoidal voltage to different flux density levels.

Core Flux density [T]Average surface velocity [µm/s] Sound pressure [µPa]

Front Side Top Front Side TopVITROPERM uncut

0.2

6.0 9.1 27.2 133 289 762VITROPERM cut 63.7 351.6 455.9 2344 4870 7718

Metglas 64 347 540 7443 15555 13304Ferrite 86.7 90.7 207.9 1759 2002 2609

VITROPERM uncut0.5

15.2 35.2 86.7 615 804 1873VITROPERM cut 415.4 1965.6 2439.5 13149 30662 54707

Metglas 450 2819 3341 41831 68181 72996VITROPERM uncut

1.047.9 136.2 402.3 3959 3814 6547

VITROPERM cut 1522.9 4269.7 5367.2 19800 95055 164111Metglas 1663 6786 7690 173865 227276 271848

Figure 13: Areas with relative high velocity on measured surfaces of nanocrystalline and amorphous cores excitedto different flux density levels with 4 kHz sinusoidal voltage. The numbers indicate the points with maximumsurface velocity (RMS value) in [µm/s] calculated with 1st to 5th harmonics.

core shows extremely low degree of vibration as well as low noise level while the air gaps of cut corescause excessive vibration and noise emission.

Frequency domain analysis The analysis of sound and vibration is often performed in frequency do-main. Since the magnitude of both Maxwell force and magnetostriction are proportional to the squareof flux density, the fundamental harmonic of vibration is twice of the excitation frequency. Theoreti-cally, if the core is excited with a sinusoidal voltage of frequency fs, the magnetic flux has only oneharmonic at fs in frequency spectrum. Therefore, the induced magnetic forces and then the vibrationvelocity as well as the radiated sound power have one harmonic at 2 · fs in frequency spectrum. However,the excitation voltage usually contains harmonics. Furthermore, the mechanical response of the core isnonlinear. Therefore, additional harmonics of magnetic forces will be induced. The MFT is usually op-erated under excitation of rectangular voltage. The flux density is then with a quasi triangular waveformwhich contains a number of harmonics. If the frequency of one of these harmonics coincides with oneof the mechanical resonant frequencies of the transformer structure, additional vibration as well as noiseemission can be induced.Although the excitation voltage is expected to be purely sinusoidal, a small portion of harmonics stillexist during the measurement in this work, which maybe generated from the power amplifier. As anexample, the measured waveform of excitation voltage and the square of the voltage waveforms as wellas their frequency spectra are shown in Fig. 16. As can be seen, both the voltage and its square containseveral harmonics, where the fundamental harmonic (4 kHz) and the 2nd harmonic are dominant in eachwaveform respectively. Consequently, the measured surface velocity and sound pressure also containthese harmonics. In Table V, the first 4 harmonics of the surface velocity and the sound pressure of theVITROPERM cut core under excitation with this voltage are listed. As example, the frequency spectra ofaverage velocity and SPL of side surface are also shown in Fig. 16 (e) and (f) respectively. As expected,the 2nd harmonic has the most contribution to vibration and noise. Therefore, the operating frequencyof MFT at half of the eigenfrequency of the structure should be absolutely avoided. If possible, byoperating the transformer at over 10 kHz, the dominant harmonic of magnetic forces will be out of theaudible frequency range and the acoustic noise can be effectively reduced.

Dependency of SPL on flux density and frequency In this section, the results of sound pressure mea-surements performed on the aforementioned cores under excitation with voltage of various frequenciesand amplitudes are compared. In Fig. 17 and Fig. 18, the unweighted and A-weighted SPL averaged

Table IV: Comparison of vibration and sound pressure measurement results forferrite and VITROVAC cores under excitation of 4 kHz sinusoidal voltage to fluxdensity of 0.4 T.

CoreAverage surface velocity [µm/s] SPL [µPa]Front Side Top Front Side Top

Ferrite 192.6 255.6 851.5 6802 7740 9481VITROVAC cut 351.2 735.7 N/A 7541 24242 N/A

VITROVAC uncut 3.3 3.9 N/A 32 57 N/A

Figure 14: Surface areas of vi-bration measurement for VIT-ROVAC toroidal core.

Figure 15: Areas with relative high velocity on measured surfaces of ferrite and VITROVAC cores excited to fluxdensity of 0.4 T with 4 kHz sinusoidal voltage. The numbers indicate the points with maximum surface velocity(RMS value) in [µm/s] calculated with 1st to 5th harmonics.

Figure 16: Waveforms of measured excitation voltage (a), the square of the voltage (c) and their frequency spectra(b) & (d). The voltage is measured on the secondary winding (turns ratio is 1:1). Accordingly, frequency spectrumof measured average velocity (e) and SPL (f) on the side surface of VITROPERM cut core when excited to fluxdensity of 0.5 T at 4 kHz with this voltage.

from measured results in three directions are shown in dB values (referred to 20 µPa). The measuredbackground noise of the anechoic room is 38.2 dB unweighted or 30.4 dB A-weighted.As expected, the increases of SPL with the flux density level can be observed on all the measured coresexcept for the VITROVAC uncut core. The reason is that the noise emission of this core is extremelylow and can not be separated from the background noise. On the other hand, different cores exhibitdifferent dependencies of SPLs on operating frequencies, which is related to the eigenfrequencies ofeach core. When excited at 1 kHz and 2 kHz, the two dominant harmonics of the noise are all in the mostsensitive frequency range of human ears (1 kHz to 6 kHz), in which the A-weighting curve has a gainlarger than 0 dB. As can be seen in some of the results, the A-weighted SPL value may even be higherthan the unweighted SPL value. If the transformer is operated over 3 kHz, the second harmonic of thenoise which is normally the dominant harmonic will be shifted in the less sensitive frequency range andlead to better performance in terms of acoustic noise. Naturally, further increase of operating frequencywill lead to even lower noise, especially when over 10 kHz as already explained in previous section.Unfortunately, the operating frequency of MFT is normally limited due to the switching losses of highvoltage switches and / or requirements of efficiencies and power densities of the converter systems.

Figure 17: Measured unweighted and A-weighted SPL of VITROPERM and Metglas cores under excitation ofsinusoidal voltage of different frequencies (1 kHz, 2 kHz, 4 kHz, 8 kHz and 16 kHz) to various flux density level.

Figure 18: Measured unweighted and A-weighted SPL of ferrite and VITROVAC cores under excitation of sinu-soidal voltage of different frequencies (1 kHz, 2 kHz, 4 kHz, 8 kHz and 16 kHz) to various flux density level.

Table V: First 4 harmonics of measured surface velocity and sound pressure of VITROP-ERM cut core when excited to flux density of 0.5 T at 4 kHz.

Measurementsuface/direction

Harmonics ofsurface velocity [µm/s]

Harmonics ofsound pressure [µPa]

1st 2nd 3rd 4th 1st 2nd 3rd 4thFront 20.3 587.1 1.1 9.7 296.6 13141 6.4 367.2Side 146.3 2774.2 19.9 96.5 234 30654 31.6 695.6Top 128.1 3446.6 6.6 80 497.3 54699 47.1 784

Figure 19: Oval corewith small curvature atthe bending part.

ConclusionsIn this paper, the acoustic noise sources in MFT for high power applications are investigated based onvibration and acoustic measurements. The measurements are performed on magnetic cores made of dif-ferent materials and with various shapes with focus on the most widely used materials for MFT design.Measurement results confirmed that the winding has relative weak vibration compared to the core espe-cially in case of cut cores and therefore can be considered to have minor contribution to acoustic noise.Regarding the core materials, ferrite features low noise but the application in MFT with requirementof high power density maybe limited due to the low saturation flux density. The nanocrystalline mate-rial VITROPERM500F has much better acoustic performance compared to amorphous material Metglas2605SA1 and it also features other advantages, e.g. low loss density. Therefore, this material could bemost suitable for low noise MFT design.Vibration measurements indicate that the direction perpendicular to the lamination layers of tape woundcore is subject to higher vibration and more noise radiation compared to the direction parallel to thelamination layers. In case of the most popular U-shape cores for MFT application, the large curvatureat the corners leads to intensive vibrations at the surfaces nearby which is related to the bending modeshapes of the core. On the other hand, a toroidal core has relative lower level of vibration and noiseemission. The vibration measurement results confirm that the air gap can induce excessive vibrationdirectly near the air gap region and enhance the vibrations near the bending parts. As a result, the cut corehas much higher noise emission compared with its counterpart. The frequency spectra of the measuredvibration and sound pressure show that the harmonic with double excitation frequency is dominant andtherefore particular attention needs to be paid to avoid the frequency coincidence of this harmonic withthe eigenmodes.Based on the analysis and experimental results, for a low noise MFT design, the nanocrystalline corewith toroidal shape and without cutting would be preferred. The drawback is that the power densitymaybe reduced compared to a MFT constructed with the traditional U-shape core. As a compromisebetween acoustic performance and power density, an uncut oval core as shown in Fig. 19 maybe moresuitable for MFT design. This core shape takes the advantage of toroidal core with small curvature at thebending part without increasing much of size compared to the U-shape core. However, this kind of coreshape is not standard product and the availability is very limited. In future work, further investigation onthe acoustic performance of this core shape is necessary.

AcknowledgmentThe authors would like to thank ECPE, the European Power Electronics Research Network, for financialsupport of the research project and VACUUMSCHMELZE GmbH for providing the core samples andvaluable information about the core materials.

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