Impact of Core Shape and Material on the Acoustic NoiseEmission of Medium Frequency, Medium Voltage

Transformers

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

Email: shuai@hpe.ee.ethz.ch

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

AbstractAcoustic noise emission of transformers is mainly due to core vibration induced by reluctance force and magne-tostriction which is highly dependent on the core material and geometry. This paper investigates the vibration andacoustic noise of nanocrystalline cores with different geometric shapes based on FEM simulation and experimentalmeasurements. Furthermore, the optimal design of medium frequency transformers (MFT) by using different corematerials and geometric shapes is analyzed to find the most suitable core for MFT design with high efficiency, highpower density and low acoustic noise emission.

1 IntroductionIn recent years, the application of solid state transformers (SST) (e.g. Fig. 1) in smart grids and traction systemshave been widely investigated, e.g. [1, 2]. As key component of SST, the isolated DC-DC converter with integratedmedium frequency transformer (MFT) is the focus of many publications. Much effort has been put on the optimaldesign of the MFT aimed on high power density and high efficiency [3, 4]. Due to the cooling and isolationrequirement, the size reduction of the MFT by increasing the operating frequency is limited in the higher frequencyrange. This can be seen in Fig. 2 for the optimal design of MFT based on nanocrystalline cores. More detail aboutthe design and optimization of the MFT can be found in [4]. In the considered application, the optimal switchingfrequency, which results in a minimal volume, is only a few kHz and leads to acoustic noise emission.The vibration and acoustic noise emission of electromagnetic devices is not a new research area. However, thefocus in the past has been on electrical machines and line frequency transformers, which have been thoroughlyinvestigated, e.g. in [5–7]. The applicability of these results on the MFT is limited because of the following reasons:Firstly, vibration is highly related to the magnetic and mechanical properties of the material (especially in case ofmagnetostriction). Magnetic cores of electrical machines and line frequency power transformers usually employSiFe based electrical steels, which is not suitable for MFT due to the high power losses. Secondly, the mechanismsof noise generation in electrical machines differs from that in transformers, since electrical machines have rotatingparts and a large air gap in the magnetic path. Moreover, due to the operation in kHz range, MFTs are smallerin size and weight compared to line frequency transformers for the same power level. Therefore, the mechanicalproperties of MFTs such as eigenfrequencies are significantly different from line frequency transformer.

Figure 1: Example configuration of medium frequency solid statetransformer. Figure 2: Minimized volume for a MFT design with VIT-

ROPERM 500F for switching frequencies from 1 kHz to16 kHz, detail in [4].

In a recent publication [8], vibration and acoustic noise measurements have been performed on several magneticcores composed of various materials and with different geometric shapes. The comparison of measurement resultsbasically indicate that the ring core based on nanocrystalline material exhibits lower vibration and noise emission.However, this kind of core may increase the total boxed volume of the transformer. As a trade-off between thepower density and acoustic performance, the oval core is suggested for MFT design but its acoustic performancehas not been verified.Although the acoustic noise emission is directly related to the vibration of the structure, the quantities of sound,e.g. the sound pressure level (SPL), indicate only the overall information about the vibration of the structure. Incontrast, the vibrational quantities, e.g. surface velocities, directly indicate the local vibrational intensity, whichis more practical for the analysis of the origin of the noise. In section 2, the basics of vibration modeling formagnetic cores are introduced, where a numerical model based on 2D FEM to simulate the core deformation ispresented. This model is used to estimate the deformation of cores with different geometric shape in static case.In section 3, vibration and acoustic measurements are performed on several nanocrystalline cores (VITROPERM500F) including rectangular, ring and oval shapes. In section 4, the optimal designs of MFT in terms of powerdensity for different core materials and geometric shapes are compared. As conclusion, the results in previoussections are combined and the best core material/shape for MFT design which is not only quiet but also compactand efficient is identified.

2 FEM Model for Core VibrationAcoustic noise emission of MFTs basically involves:

• generation of electromagnetic force by the electrical excitation of power electronic converters;

• structural vibration of magnetic cores and windings induced by magnetic force and magnetostriction;

• sound radiation from the surfaces of the transformer bodies and sound wave propagation in air.

Accordingly, to calculate the acoustic noise emission of MFT, three physical models need to be taken into account.Due to the complexity of the physical process, analytical methods are usually only applicable for simple geometriesand their accuracy is limited. For more accurate results, the couplings between these physical models need to beconsidered. Obviously, this requires more complicated models and more computational effort. For these reasons,the vibration/acoustic modeling of transformer is usually based on numerical methods, e.g. FEM.

Figure 3: Modeling process of core vibration.

Table I: Properties of some magnetic materials [9].

MaterialSaturation

fluxdensity [T]

Saturationmagnetostriction

[µm/m]

Loss @0.2T/20kHz

[W/kg]6.5% SiFe

(50 µm) 1.8 0 60

MnZn ferrite 0.45∼0.55 -2∼0 10∼15Fe-based

amorphousMetglas

2605SA1

1.56 27 8∼10

Co-basedamorphousVITROVAC

6025

0.58 <0.2 3

NanocrystallineVITROPERM

500F1.2 <0.5 1.8

Figure 4: Model of the laminated structure of tape woundcore.

2.1 Introduction of FEM model for core vibrationAs shown in Fig. 3, the calculation of core vibration includes three steps:

• A. the electromagnetic model for solving the magnetic field distribution according to the electrical excitation;

• B. the model for calculating magnetic forces and magnetostrictive strain based on the field distribution;

• C. the mechanical model to solve the displacement (static case) or velocity/acceleration (dynamic case) dueto the magnetic force and the magnetostriction.

For calculation of the SPL, the acoustic model (D) as shown in the block with dashed line can be added after themechanical model. In this work, the modeling only focuses on the core vibration.

2.1.1 Electromagnetic model (A in Fig. 3) In electromagnetic model, the electrical excitation and the mag-netic properties of the material together with the magnetic boundary conditions are employed to determine themagnetic field distribution, i.e. the local values of flux density and magnetic field strength.

2.1.2 Magnetic force and magnetostriction calculation (B in Fig. 3) In this step, the magnetic field dis-tribution is used as input to calculate the magnetic force (including Maxwell force and Lorentz force) and themagnetostriction.The Maxwell force is acting on the boundaries (surfaces) between two magnetic media with different magneticpermeabilities, which is typically associated with air-gap regions and joints of cores in transformers. The Maxwellstress tensor can be calculated according to the local distribution of the magnetic field as

σm = ~H · (~B ·~n)− 12(~H ·~B) ·~n (1)

where σm is the Maxwell stress tensor, ~H is the magnetic field strength, ~B is the magnetic flux density and~n is thevector in normal direction to the surface. For laminated cores, the effects of Maxwell force at the joints of corelamination sheets and between the sheets are introduced in [7].The Lorenz force is acting on the current-conducting windings and its volume force density~f v is calculated as

~f v =~J×~B (2)

where~J is the current density in the conductor and~B is the magnetic flux density at the location of the conductors.Magnetostriction model is an important part of the core vibration model. Generally, magnetostriction is describedas the relative dimension change of the material in the direction of the applied magnetic field. However, magne-tostriction is also dependent on the mechanical stress σ. Therefore, the magnetostrictive strain λ in the direction ofmagnetic field can be expressed as a function of magnetic field strength and the mechanical stress, i.e. λ = f (H,σ).In case of SiFe, the magnetostriction is anisotropic and the saturation magnetostriction λs is dependent on the Sicontent. The 6.5% SiFe has approximately zero-magnetostriction [9], which is excellent in terms of acoustic per-formance. In case of amorphous and nanocrystalline alloys, the magnetostriction is isotropic. The saturation fluxdensity Bs of Fe-rich amorphous alloy (e.g. Metglas 2605SA1) is relative high but the value of λs is also large.On the other hand, Co-rich amorphous alloy (e.g. VITROVAC 6025) could reach near-zero magnetostriction butthe value of Bs is relative low. For Fe-based nanocrystalline alloy such as VITROPERM 500F, the Si contentcan be controlled at around 15-16at% (atomic percent) so that a near-zero magnetostriction can be achieved afternanocrystallization [9]. In Table I, the properties of some core materials are listed. Among these materials, thenanocrystalline alloy is the most suitable for MFT application due to the low specific loss and near-zero magne-tostriction. Also, its relative hight saturation flux density enables high power density designs.For the considered materials, only the Joule magnetostriction is taken into account, which means the volume ofthe material is constant. By modeling, the magnetostrictive strain in the direction of the magnetic field λp can beevaluated from the flux density B as

λp = λs · (B/Bs)2 (3)

Accordingly, in transverse directions to the magnetic field, the magnetostrictive strain is

λt =−0.5 ·λp (4)

The negative sign indicates that the strain in the transverse directions is opposite to the strain in field direction. If thestress dependence of the magnetostriction is also considered, a series of λ(B) curves which define the λ = f (B,σ)function should be implemented in the model.

2.1.3 Mechanical model (C in Fig. 3) In a mechanical system with multi-Degree-of-Freedom (DoF), thenumber of DoFs is dependent on number of finite elements in FEM. In dynamic case, the mechanical problem isdescribed by the equation of motion as

M · u+C · u+K ·u = f (5)

where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, f is the force vector and u isthe displacement vector. The first and second order derivatives of u with respect to time, i.e. u and u, are theacceleration vector and the velocity vector, respectively.In mechanical model, the Maxwell stress tensor is applied as boundary load to the surface of the magnetic core andLorentz force is applied as body load to the winding. The calculated magnetostriction is added to element strain ε,which is also a vector derived from the element displacement. With these input quantities and the elastic model ofthe materials, (5) is solved numerically under the given boundary conditions to obtain the surface velocities of thestructure, which is used as the input quantity of the acoustic model to solve the sound pressure.

2.1.4 Material model of core (A2, C1 in Fig. 3) The accuracy of the model is highly dependent on the ma-terial parameters, especially for the mechanical model. In case of transformers, the materials include the magneticcore, winding and other parts used for mechanical damping and mounting, electrical isolation and cooling. In thiswork, only the vibration of the core is of interest. Therefore, the discussion of the material modeling is focusingon the magnetic material. For line frequency transformers, grain oriented (GO) SiFe alloy is widely used corematerial, which exhibits different properties in rolling direction (RD) and transverse direction (TD) as shown inFig. 4 for laminated core. In MFT applications, Fe-based amorphous alloy and nanocrystalline alloy are widelyused. Due to the extremely low residual anisotropy [9], the thin ribbons (thickness of 10 µm to 30 µm) of bothmaterials can be approximately modeled as isotropic material (no difference between RD and TD). Nevertheless,the practical core is wound with ribbons and consists of thousands of laminated layers which are isolated withepoxy resin. As a result, the overall material properties of the core are different as the ribbon and the propertiesin LD differ from that in RD and TD. In practice, it is not feasible to model the laminated core in detail includ-ing every single layer. Instead, the core is considered as a uniform material by employing equivalent parameters.The simplest way is to ignore the laminated structure and consider the laminate as isotropic material by using theparameters of magnetic material. However, this approach usually leads to low accuracy since the epoxy resin alsohas influence and leads to anisotropic properties. Therefore, more accurate model requires the anisotropy of thematerials to be considered.For magnetic model, the permeability in three directions (RD/TD/LD) need to be included. However, normallyonly the permeability for the magnetic material is available, and the permeability in each direction have to bedetermined by measurement. For higher accuracy, the Villari effect, i.e. the influence of mechanical stress onmagnetizing should also be taken into account, which is the strong coupling of electromagnetic and mechanicalmodel. If the B(H) curve is used for magnetic model, then it can be replaced by the B(H,σ) function. Otherwise,for a magnetic model without consideration of saturation, a simple µ = f (σ) function can be used.In case of elastic model, the material is considered to be linear elastic. According to Hook’s law, the relationbetween the stress σ and the strain ε conforms to

σ = E · ε (6)

where E is the fourth-order stiffness tensor in matrix form, including 36 components which are defined by theelastic parameters of the material. For an anisotropic material, there are 21 independent components in the stiffnesstensor. For engineering applications, the tape wound core can be considered as transversely isotropic material,where the elastic properties in TD and RD are considered to be identical while in LD different parameters areapplied. In this case, only 5 elastic parameters are required to determine the stiffness tensor. These parameterscan be determined by experimental measurements [6] or alternatively, can be derived analytically according toelementary mixture rules as presented in [10] for fiber-reinforced laminae.

2.2 Modeling and simulation resultsFor an accurate numerical model, the accuracy of the material parameters is essential. However, as mentioned in[5], the complete properties of the magnetic materials are usually not available. On the other hand, the purposeof the numerical modeling in this work is focusing on the comparison of different cores. Therefore, instead ofmeasurement, the material parameters are derived from data sheet or other literatures. For the magnetic model, thecore material is considered to be isotropic and the B(H) curve from the data sheet is used to include the magneticsaturation without consideration of the Villari effect. For the mechanical model, the material is considered astransversely isotropic and the equivalent parameters are obtained analytically according to elementary mixturerules. For simplicity, the 2D model of the core is used under the approximation of plane stress, where the stress inTD is neglected. Moreover, the FEM simulation is performed in static case to simulate the deformation of the coreat the peak value of excitation current. In this case, the first and second terms on the left side of (5) are ignored.In Fig. 5, the simulated deformation of different cores under the same excitation are shown. The consideredmaterial is VITROPERM 500F and the flux density in the middle of core legs is around 1 T. In the model, allcores are with the same magnetic length of approximately 0.34 m and the core leg width is 30 mm. With the sameexcitation current, only the ring core is not saturated at any location. Comparing the flux density and displacementdistribution, one can see that the locations with high flux density are subjected to higher magnetostriction and havelarger displacement. Due to the magnetic force and the magnetostriction, the cores are all enlarged from a fewnm up to approximately 20 nm. The deformation of the ring and square cores is symmetric due to their geometric

Table II: Displacements of points indicated in Fig. 5 obtained by static simulation.

Disp.[nm]

Ring Square Oval Rectangularx y total x y total x y total x y total

A -0.008 15.88 15.88 0.64 9.29 9.31 0.01 21.78 21.78 0.59 14.3 14.31B -15.92 -0.01 15.92 -9.41 0.65 9.43 -2.03 0.001 2.03 -1.91 0.32 1.94C -11.25 11.25 15.91 -11.69 12.76 17.31 -5.33 18.45 19.2 -5.08 14.85 15.69D N/A N/A N/A -11.55 8.22 14.18 -4.53 11.23 12.11 -4.4 11.06 11.9E N/A N/A N/A -6.93 12.08 13.93 N/A N/A N/A -1.7 15.06 15.16

Figure 5: Simulated core deformations in static case. (a)-(d): magnetic flux density distribution, (e)-(f): deformation (scalingfactor 106).

symmetry while the oval and rectangular cores show larger deformation in y-axis since the elongation of theircore legs due to magnetostriction is larger since the leg in y-direction is longer. (The change of dimension ∆l isproportional to the length l due to magnetostriction.)For comparison, the displacement of some points on the outer surface of the cores as indicated in Fig. 5 areevaluated and listed in Table II. In case of the ring core, the total displacement of points on the outer surface areapproximately equal which is around 16 nm. The maximum deformation of square core is on the corners with atotal displacement of more than 17 nm and the middle of the core legs (point A and B) has the lowest displacement(below 10 nm). The oval core has the largest deformation in the middle point of the curved part which is morethan 20 nm in y-direction but the deformation of its straight legs is rather small (point B). The deformation of therectangular core is also mainly in y-direction with the maximum deformation on the corners (point C).

3 Vibration and Acoustic Noise MeasurementTo evaluate the influence of the shape on vibration and acoustic noise emission of magnetic cores, measurementsare performed on three nanocrystalline (VITROPERM 500F) uncut cores. The three sample cores have the same

Figure 6: Sample cores and their dimensions (in [mm]). Figure 7: Mechanical setup used for vibration measurement.

Figure 8: Setup for vibration and acoustic noise measurement.

thickness of about 25 mm and are wound as rectangular, oval and ring shape respectively as shown in Fig. 6 wheretheir dimensions are also indicated. To fix the cores mechanically, an additional setup as shown in Fig. 7 is used forthe vibration measurement, where a part of the core is fixed on a metal plates with relative large weight comparedto the sample cores. To reduce the mechanical influence from the setup, soft foam materials are inserted betweenthe sample cores and metal plate for damping. In Fig. 8, the schematic of the measurement setup is illustrated.The core is excited with a sinusoidal voltage to exclude the influence of harmonics from the electrical source. Themeasurements are performed on different surfaces with excitation of the core at 3 flux density levels. (For ringcore, only two surfaces are measured due to its symmetry.)In Fig. 9 the measured average surface velocities ∗ on the surfaces of the sample cores are shown. Looking atthe results, it is concluded that the vibration in LD direction is obviously stronger than in the parallel directionsto the laminations regardless of the geometric shape. This is in accordance with the results presented in [8]. Thecomparison of velocities on each surface among the sample cores show that the ring core features the smallestvibration, followed by the oval core while the vibration of rectangular core is the most intensive one. According tothe measurement results, the hypothesis proposed in [8] is confirmed: the vibrations are reduced by modifying thecore from rectangular to oval shape.For more detailed analysis, the dominant harmonics of the average vibration velocities in the audible frequencyrange are shown in Fig. 10, where the cores are excited to 1 T at 4 kHz. It can be seen that the major contribution ofvibration is by the 8 kHz and 16 kHz harmonics, which are the first and second harmonics of magnetostriction. Thefirst harmonic is usually the most significant and is the most important to acoustic noise generation. Accordingly,the deformation of the cores due to the 8 kHz harmonic at the instance when the maximum positive displacement(towards the laser) appears are shown in Fig. 11. Due to the low saturation magnetostriction of the nanocrystallinematerial, the maximum deformation is within a very low range (< 20 nm) even at this high flux density level (1 T).Despite of the inaccuracy of the material parameters and neglecting the higher order terms in (5), the results ofthe static simulation show good agreement with the measurements. In case of the rectangular core, the short leg

∗The laser vibrometer measures the velocity in the direction of the laser. For curved surface, the measured velocity is not equal to thenormal velocity of the surface.

Figure 9: Measured average surface velocities ofnanocrystalline uncut cores with different shapes underexcitation of 4 kHz sinusoidal voltage to different fluxdensity levels (only harmonics up to 20 kHz are taken intoaccount).

Figure 10: Harmonics (up to 20 kHz) of average surface ve-locity of nanocrystalline uncut cores with different shapes un-der excitation of 4 kHz sinusoidal voltage at 1 T.

Figure 11: Snapshot from vibration animation of 8 kHz harmonic at the instance when cores show maximum outward defor-mation (towards the laser) under excitation of 4 kHz sinusoidal voltage to 1 T.

Figure 12: Measured SPL of nanocrystalline uncut coreswith different shapes under excitation of 4 kHz sinusoidalvoltage to different flux density levels (only harmonics upto 20 kHz are taken into account).

Figure 13: A-weighted sound pressure level of nanocrys-talline uncut cores with different shapes under excitationof sinusoidal voltage to 1 T at various frequencies.

(top) deforms more than the long leg (side), where on both legs more deformation is observed on the two endsthan in the middle. Similarly, this deformation is also observed on the straight leg of the oval core. The simulationresult of the oval core shows that the middle of the curved leg (point A in Fig. 5 (g)) has the largest displacement.This is due to the magnetostrictive elongation of the curved leg and the straight leg which act together and inducea large deformation in y-direction. However, the measurement shows that the displacement in the middle of thecurved leg is smaller and not in phase with its two ends. At the instance shown in Fig. 11 (b), when the positivedisplacement appears at the two ends, the middle part is mainly deformed inwards. This deformation is generatedby the combination of eigenmodes which can not be seen from static simulation. Overall, the deformation ofthe oval core is smaller than the rectangular core. The deformation of ring core is mainly in radial direction, themeasured displacements on its side surface are comparable to the side surface of the oval core but smaller than thetop surface.For all three cores, the deformation of the front surfaces is generally very small (<3 nm). The vibration in thenormal direction to this surface is mainly induced by the transverse magnetostriction. According to (4), the mag-netostrictive strain is only half of the value in RD. Furthermore, the thickness of the core is much smaller comparedto the length of the magnetic tape. Therefore, the induced deformation by magnetostriction is much smaller. It isnoticed that the measured deformations are not symmetric as the simulated deformation. This might be inducedby local asymmetry/inhomogeneity of mechanical properties (e.g. stiffness) and magnetic properties (which leadto uneven distribution of the flux density) of the sample cores.

The acoustic noise measurements are performed in an anechoic room, where the sample cores are located 1 maway from the microphone. The mechanical setup is removed during the measurements to avoid its influence onmeasurement results due to reflection of the sound waves. In Fig. 12, the measured sound pressure of the samplecores are shown. The results clearly show that the ring core has the lowest noise level while the oval core alsoexhibits obviously lower noise emission than the rectangular core. The acoustic noise measurement results arein accordance with the vibration measurements and confirm that the vibration intensity and noise emission of thesample cores have the following relation: ring core < oval core < rectangular core. In case of the rectangularcore the sound emission from different surfaces shows the same relation as the vibration velocity, i.e. top > side> front surface . However, for oval and ring cores, the lowest sound pressure is measured towards the curvedsurfaces on which the highest vibration velocity are detected. This could be induced by the scattering of soundwaves emitted from curved surface which propagate towards different directions. On the other hand, from a flatsurface, the emitted sound waves mainly propagate towards the normal direction to the surface, i.e. towards themicrophone.The measured SPL of the sample cores under excitation at different frequencies are shown in Fig. 13. The flux den-sity level in the core is 1 T and the SPL values are A-weighted. The measured background noise is approximately30 dBA in the anechoic room. The SPL values shown are averaged from the measured sound pressure from threedirections. As indicated in the graph, the ring core features the lowest acoustic noise emission at all frequenciesfor measurement. The SPL of the oval core is a few dB higher than ring core but lower than the rectangular core.All three cores show obviously higher noise emission under excitation at 8 kHz which might be near one of theeigenfrequency of the cores.

4 Optimal Design of MFT with Different Core Materials and ShapesThe optimization algorithm for MFT design including improved thermal model and the consideration of isolationhas been discussed in [4]. In medium frequency range, a core material with high saturation flux density and lowloss is essential for transformers featuring high power density. In Fig. 15, the specific losses at 4 kHz of several corematerials suitable for medium frequency applications are compared. As indicated in the figure, the nanocrystalinematerial features slightly lower loss compared to the Co-based amorphous alloy which is lower than Fe-basedamorphous material. The specific loss of ferrite lies between the two amorphous materials.By employing the optimization model in Fig. 14, the optimal designs of the MFT with the specifications givenin Table III by using the above mentioned core materials are derived. The construction of the transformer isconsidered to be shell type with concentric winding as in [4]. In Fig. 16, the pareto fronts of MFTs are shown,which are derived by changing the boxed volume of the transformer. As indicated for the nanocrystalline material,the power density of MFT based on this core material can exceed 10 kW/dm3 due to its low loss and high saturationflux density. Depending on the core loss, the efficiency of MFTs with the same boxed volume is lower whenusing materials with higher loss. Compared with VITROPERM 500F, the maximal achievable power density ofMFTs based on VITROVAC 6030F is lower due to the low saturation flux density (0.82 T) and further decreaseof the maximal power density is seen for MFTs based on Ferrite core. Among these four core materials, the Fe-based amorphous alloy Metglas 2605SA1 has the highest saturation flux density (1.56 T). However, the maximumachievable power density of transformers using this core material is the lowest due to the thermal limitation sincethis material has relative high loss.For MFTs, rectangular cores are commonly used (e.g. [3]). To compare the power density of MFTs with differentcore shapes, the mentioned optimization algorithm is also applied to the other three shapes based on VITROPERM500F, i.e., the square, the oval and the ring core. The same construction of the transformer as in case of the

Figure 14: Flow chart for MFT optimization.

Figure 15: Core losses of different materials as functionof flux density @4 kHz.

Table III: Considered specifications for MFT design.

Voltage at MV DC-link VMV 2400 VVoltage at LV DC-link VLV 400 V

Nominal power Pn 25 kWOperating frequency fs 4 kHzLeakage inductance Lσ 115 µH

Turns ratio Nw 3 < Nw < 3.2Max. fill factor of core windowa 40%Maximal allowable temperature 120 ◦C

Cooling system performance index b 5 W/K/dm3

Maximum flux density Bmax 80% of BsatMaximum electric field strength Emax

c 8 kV/mm

aRatio of copper area to core window area (without area requiredfor isolation and leakage inductance)

bConsider forced air coolingcHalf of the value of dielectric strength of isolation material

rectangular core is considered for the square and the oval core, while for the ring core, only one core is consideredwith the low voltage winding mounted directly on the core and the high voltage winding wound outside. Thecalculation models used in the optimization algorithm such as the thermal model are adapted to match the newconstruction for the ring core.In Fig. 17, the pareto fronts of MFTs with the same specifications based on different core shapes are shown. It canbe seen that transformers based on the rectangular core reach the highest power density followed by the square,the oval and the ring core. The achievable power densities are in the range of 10 - 14 kW/dm3 for all consideredcore shapes. In Table IV, the major parameters of the optimal designs for each core shape as indicated in Fig. 17are listed and the 2D views of the winding arrangement are shown.For a given boxed volume, the highest reachable efficiency is limited by the maximum electric field strength, i.e.the isolation requirement, and the required leakage inductance, which results in additional space and leads to anincreased core size and winding length and causes additional losses. On the other hand, the maximum achievablepower density is limited by the allowable temperature (thermal limitation). Basically, the square and the rectangularcores have a similar shape and can achieve a very similar maximum power density. For the oval core, the curvedyokes are disadvantageous in terms of boxed volume compared to the rectangular core and therefore the achievablemaximal power density is also smaller. In case of the ring core, the heat generated in the core due to core losseshas to be transfered through the windings and then dissipated to the ambient via the outer winding surface. Themounting of a heat sink directly on the core surface, as in case of transformers constructed with the other cores, isnot possible. In order to dissipate the heat, a large surface area is necessary, which requires the winding size to beincreased. Consequently, in the optimal design of the ring core transformer, the core losses are relative small while

Figure 16: Pareto fronts of MFT designs with the same spec-ifications given in Table III by using different core materi-als. The boxed volume of the transformers is considered forpower density calculation.

Figure 17: Pareto fronts of MFT designs with the same spec-ifications given in Table III by using VITROPERM 500Fcores with different geometric shapes. The boxed volume ofthe transformers is considered for power density calculation.

Table IV: Comparison of optimal design at maximum power density by using different cores.

ParameterCore Rectangular Square Oval Ring

Core cross section area [mm2] 3403.2 5029.2 2177.6 997.2Window area [mm2] 1703.2 1184.5 2663.9 3728.1

Magnetic length [mm] 208.2 175.4 238 291.8Core volume [dm3] 0.708 0.882 0.518 0.291

Boxed volume [dm3] 1.83 1.9 2.25 2.35Number of turns 28:9 19:6 44:14 97:32Copper fill factor 26.13% 25.42% 28.28% 30.91%

Core loss [W] 32.32 39.98 23.35 12.83Winding loss [W] 67.95 76.57 69.01 107.64

Efficiency 99.6% 99.54% 99.63% 99.52%Bmax [T] 0.96 0.957 0.955 0.945

Emax [kV/mm] 7.83 7.94 7.99 7.93Maximum temperature [◦C] 119 119 118 118.6

Power density [kW/L] 13.66 13.16 11.11 10.87

2D View (for rectangular, squareand oval core, only one core

is shown)

much more losses are generated in the winding. Therefore, both the power density and the efficiency of the ringcore based transformers are limited due to the heat dissipation capability.

5 ConclusionsMedium frequency transformers are small in size and weight compared with conventional line frequency trans-formers. The major challenges associated with MFTs are cooling and isolation as well as the acoustic noiseemission. In this paper, the influence of core shapes on the vibration and acoustic noise emission of magnetic coresare investigated based on FEM simulation and measurements. The modeling methods of the core vibration areinvestigated and a 2D model to calculate the deformation of the core under electrical excitation is implementedand used to simulate the deformation of several cores with different geometric shapes in static case. The vibrationand acoustic measurements are performed on nanocrystalline material VITROPERM 500F based uncut cores withrectangular, oval and ring shapes. The measured maximum deformation at the base frequency of magnetostrictionshows good agreement with the results of static simulation. Both vibration and acoustic measurements confirmthat the nanocrystalline material is superior for low noise transformer design. Moreover, this material is also ad-vantageous in terms of power density and efficiency compare to other core materials, which makes nanocrystallinealloy the most suitable one for highly efficient, compact and quiet MFT design. Compared to the conventionalrectangular core, oval core has lower vibration and noise emission and further reduction can be achieved by usinga ring core in which case the measured SPL is below 40 dBA by avoiding the excitation near resonant frequency.For the same specifications, MFTs based on rectangular core can achieve higher power density compared to squareand oval core based transformers. Due to the limitation of heat dissipation, the achievable power density of trans-formers based on ring core is even lower compared to the aforementioned core shapes. Nevertheless, the paretofronts of optimal designs of MFTs based on different core shapes show that the difference is not significant. There-fore, in case that low acoustic noise emission needs to be considered, nanocrystalline material based uncut corewith oval shape is a good choice for MFT design without sacrificing much power density compared to rectangularcore.

AcknowledgmentThe authors would like to thank ECPE, the European Power Electronics Research Network, for financial support ofthe research project and VACUUMSCHMELZE GmbH for providing the core samples and valuable informationabout the core materials.

References[1] T. Kjellqvist, S. Norrga, and S. Ostlund, “Design considerations for a medium frequency transformer in a line side power

conversion system,” in IEEE 35th Annual Power Electronics Specialists Conference (PESC), vol. 1, June 20-25 2004, pp.704–710.

[2] Y. Du, S. Baek, S. Bhattacharya, and A. Huang, “High-voltage high-frequency transformer design for a 7.2kV to120V/240V 20kVA solid state transformer,” in 36th Annual Conference on IEEE Industrial Electronics Society (IECON),Nov. 7-10 2010, pp. 493–498.

[3] I. Villar, “Multiphysical characterization of medium-frequency power electronic transformers,” Ph.D. dissertation, EPFL,Switzerland, 2010.

[4] P. Shuai and J. Biela, “Design and optimization of medium frequency, medium voltage transformers,” in 15th EuropeanConference on Power Electronics and Applications (EPE), 2013, pp. 1–10.

[5] A. Belahcen, “Magnetoelasticity, magnetic forces and magnetostriction in electrical machines,” Ph.D. dissertation,Helsinki University of Technology, 2004.

[6] M. van der Giet, “Analysis of electromagnetic acoustic noise excitations: a contribution to low-noise design and to theauralization of electrical machines,” Ph.D. dissertation, RWTH Aachen University, 2011.

[7] B. Weiser, H. Pfutzner, and J. Anger, “Relevance of magnetostriction and forces for the generation of audible noise oftransformer cores,” IEEE Transactions on Magnetics, vol. 36, no. 5, pp. 3759–3777, 2000.

[8] P. Shuai and J. Biela, “Investigation of acoustic noise sources in medium frequency, medium voltage transformers,” in16th European Conference on Power Electronics and Applications (EPE), 2014, pp. 1–11.

[9] R. Hilzinger and W. Rodewald, Magnetic Materials - Fundamentals, Products, Properties, Applications. Publics Pub-lishing, 2013.

[10] H. Altenbach, J. Altenbach, and W. Kissing, Mechanics of Composite Structural Elements. Springer Verlag, 2004.