TRANSFORMER CORE NOISE MEASUREMENT AND PREDICTION

Transcription

1 TRANSFORMER CORE NOISE MEASUREMENT AND PREDICTION R. HAETTEL *,1, A. DANERYD 1, C. PLOETNER 2 and J. ANGER 3 1 ABB Corporate Research Sweden, 2 ABB Transformers Germany, 3 ABB Transformers Sweden *Corresponding author: Västerås Sweden, romain.haettel@se.abb.com ABSTRACT Today, lowering noise pollution is a matter of increasing importance worldwide. Power transformers, as any other industrial products, shall comply with various requirements on noise levels. It is thus essential to predict transformer sound levels with a sufficient accuracy at an early stage of the product design to select the most appropriate strategy for noise control. The paper will focus on core noise which is a typical multiphysics phenomenon involving electromagnetism, mechanics and acoustics. A finite element model coupling the different physical fields will be used to study the vibro-acoustic behaviour of a specific transformer operating in no-load conditions. The prediction model provides a fairly accurate tool to carry out various parametric studies. Furthermore, some data obtained from sound and vibration measurements will be presented to explain the mechanism implying core noise generation and to show the correlation between experimental and predicted results. KEYWORDS: Transformer, Measurement, Prediction, No-Load, Core Noise and Vibration. 1. INTRODUCTION Low noise levels are nowadays requested for power transformers in order to comply with customer specifications and environmental legislations [1,2]. Consequently, manufacturers have to improve the acoustic performances of their products, while, at the same time, limiting the costs. It is thus of great importance to predict sound levels with a sufficient accuracy at an early stage of the product design. Three main sources of sound can be identified in transformers: 1) No-load noise or core noise generated by magnetostriction in the core steel laminations [3], 2) Load noise produced by electromagnetic forces acting on windings and tank walls [4,5] and 3) Noise due to auxiliary equipment such as fans and pumps used in the cooling system. The paper describes a method to predict core noise which constitutes a typical multiphysics phenomenon involving electromagnetism, mechanics and acoustics. When an alternating voltage is applied to one or more windings of a transformer, a magnetic flux is generated in the transformer core laminations made of grain oriented electrical steel. This material has a non-linear anisotropic property called magnetostriction implying alternating changes of the core dimensions due to the varying magnetic flux in the laminations. Those magnetostrictive forces cause core vibrations which are transmitted to the tank via the insulation oil and the core clamping points. Part of the mechanical energy is eventually radiated by the tank walls as noise in the surrounding environment. Due to the complexity of the structure and the strong coupling with oil, an analytical model cannot be used to predict the sound radiation. In general, empirical methods based on statistics and dimensional basic parameters are used by most transformer manufacturers. This approach presents limitations when applied to new designs and does not enable accurate parametric studies. Therefore, prediction models based on finite element formulations shall be utilized to describe accurately the complex interactions of the various design parameters and the coupling of the physical fields. In this paper, experimental tests performed in air on the scale model of a large power transformer core are presented in section 2. In section 3, the equations governing the electromagnetic, mechanical and acoustic fields in a transformer core are implemented in a multiphysics software using a finite element approach. This FEmodel is then applied to the scale model of the core and the results obtained by computation can be compared to the experimental data in order to validate partially the FE-formulation. Finally, some data obtained by performing vibration measurements on the core of a full-scale power transformer are reported in section ACOUSTIC TESTING ON SCALE MODEL OF TRANSFORMER CORE Acoustical measurements were performed in laboratory conditions on a specific test core in order to identify and describe clearly the mechanisms implying no-load noise in transformers. As a matter of fact, a scale model was designed to be approximately one fourth of a core as used for a typical medium power transformer. The core was manufactured by stacking grain oriented steel sheets clamped by two pressplates made of glass-reinforced plastic. Both pressplates were joined together by means of bolts and nuts to clamp the core at a suitable pressure. The main characteristics of the test core are given in Table I.

2 Table I. Test core dimensions and characteristics. Core Height 650 mm Core Length 750 mm Limb Pitch 300 mm Core Sheet Thickness 158 mm Core Material Grain-oriented steel of HiB type Sheet Thickness 0,27 mm Core Construction 6 sheet step lap with single sheet stacking Pressplate Material Glass-reinforced plastic Pressplate Thickness 25 mm The acoustical measurements were carried out on the test core suspended elastically in a reverberant room to create free boundary conditions, as shown in Fig. 1 and 4. Prior to the tests, a well-defined static pressure was applied by the pressplates on the core by using bolts and nuts in combination with Belleville washers. Figure 1. Scale Model of the transformer core suspended by elastic ropes in the reverberant room. The vibration levels were measured by 22 accelerometers placed at different locations on the core laminations and on the core clamping plates, as shown in Fig. 3. The sound pressure level was recorded by one microphone mounted on a rotating boom, as shown in Fig. 4. The sound power level radiated by the test core was estimated by using a calibrated reference sound source to determine the room characteristics, as shown in Fig. 4. In addition, the voltage was controlled under testing by using four search coils wound around the three limbs and the upper yoke Figure 2. Dimensions of core and clamping plates given in mm. The time signals provided by the 22 accelerometers, the microphone and the three search coils were acquired simultaneously by 26 input channels of the measurement system. The vibration measurements were performed for different positions of the accelerometers on the core, as shown in Fig. 3. The accelerometers were mounted on core laminations to measure vibrations in all directions. The expression "in-plane" and "out-of-plane" are used to describe vibrations of the core in the YZ-plane and in the X-direction, respectively. The Y and Z-directions are represented in Fig. 3.

3 F E U D G C H P Q O R N S T M Z B I V Y J K L A Figure 3. Accelerometer positions selected on the core laminations and the clamping plates. A tailor-made excitation system was used to generate a magnetic field with three phases in the core at varying frequencies, providing a realistic electromagnetic excitation due the magnetostriction. Therefore, the acoustical behaviour of the test core in operation could be investigated thoroughly by means of a frequency sweep at constant magnetic flux density. To produce a magnetic field with three phases, a winding with several turns was wound around each limb of the core, as shown in Fig. 1 and 3. The three windings were Y connected and the voltage supplied to each winding was delayed with a determined time constant to simulate the no-load testing conditions used for a three-phase transformer. Reference sound source Rotating boom with microphone Figure 4. The Experimental set-up with the reference sound source and the microphone mounted on a rotating boom used for the acoustic calibration of the reverberant room. The excitation system mainly consisting of a frequency generator, a controller, a digital crossover, three amplifiers and power resistors was connected to the winding cables wound around the core limbs to form an electrical circuit with an adjustable frequency. The voltage applied to the circuit was kept sinusoidal and sufficiently large to produce a magnetic flux density in the core generating measurable levels of sound and vibration. The voltage was increased linearly with increasing frequency to keep a constant magnetic flux density in the core during the entire sweep, as expressed in Equation (1). It is here assumed that the magnetostrictive excitation varies exclusively as a function of the voltage on the entire frequency range for the tests. Therefore, by using a constant magnetic flux density, the magnetostrictive forces can also be considered as constant for the entire frequency sweep, implying that sound and vibration levels can be compared directly without a normalization procedure.

4 Measurement: Freq_Sweep M_01_200Hz V peak Ch. 24 Volt_Limb [Hz] 11.0 [V] [Hz] [V] [Hz] [V] 100m 10m 1m 100µ 10µ Frequency - Hz Figure 5. Voltage spectrum measured by the search coil on limb 1 for electrical excitation at 200 Hz. During the tests, the voltage levels supplied to each of the three windings were checked at each frequency step. In addition, the phase currents were observed and limited to a maximum value to control losses in the core and the power electronic feeding system. The voltage level applied to the windings and the magnetic flux density in the core are related according to the expression U = 2πf NBA (1) where U is the supplied voltage, B the flux density, N the number of winding turns, A the cross area of the core limb and f the frequency of the electrical circuit. Measurement: Freq_Sweep M_01_200Hz db(lin) [1e-6m/s²] peak Ch. 5 Acc5_MidUpYoke [Hz] 82.4 [db(lin)] [Hz] 60.9 [db(lin)] [Hz] 56.4 [db(lin)] [Hz] 59.2 [db(lin)] [Hz] 37.2 [db(lin)] [Hz] 38.4 [db(lin)] Frequency - Hz Figure 6. Acceleration spectrum measured on upper yoke at point E for electrical excitation at 200 Hz. The magnetic field induced in the core varies at the same frequency as the voltage provided by the electrical circuit. The magnetostrictive forces are generated by the magnetic field at even multiples of the current s fundamental frequency for a purely AC excitation [6,7,8]. Those forces imply core lamination vibrations which eventually are transmitted to the air surrounding the core as sound. The electrical frequency of the circuit was varied stepwise from 200 Hz to 1220 Hz, in general, with a resolution of 10 Hz. The procedure thus provided an acoustical frequency sweep extending from 400 Hz to 2440 Hz with a resolution of 20 Hz. Acceleration, sound pressure and voltage levels were recorded for a period of 60 seconds at each of the 102 frequency steps of the frequency sweep.

5 The time signals provided by the 22 accelerometers, the microphone and the four search coils were processed by means of the analyzer to obtain vibration, sound and voltage levels with respect to frequency. The general parameters used to perform the Fast-Fourier Transform (FFT) are given in Table II. Table II. The FFT parameters used for the measured data analysis. Sampling Frequency 8192 Hz Frequency Resolution 1 Hz Number of Frequency Lines 3201 Average Type Linear Number of Averages Variable Window Types Hanning Overlap 66,7% Function Class Autospectrum and Cross-spectrum When a magnetic field is induced in the core for a given frequency, a number of peaks can be observed in the frequency spectra for voltage, vibration and sound pressure obtained from the FFT-analysis, as shown in Fig. 5, 6 and 7, respectively. Measurement: Freq_Sweep M_01_200Hz 60 db(lin) [2e-5Pa] peak Ch. 23 Mic [Hz] 33.2 [db(lin)] [Hz] 17.0 [db(lin)] Frequency - Hz Figure 7. Sound pressure spectrum recorded by the microphone mounted on the rotating boom for electrical excitation at 200 Hz. During the measurements, the voltage supplied to the circuit is kept sinusoidal. Therefore, the voltage spectrum measured for example at side limb 1 presents mainly a single dominating peak at the fundamental frequency of the electrical circuit, as shown in Fig. 5. The sound pressure and vibration spectra exhibit usually a main peak at twice the fundamental electrical frequency and other peaks at multiples of this fundamental acoustical frequency, as presented in Fig. 6 and 7. In fact, for an AC-excitation, the magnetostrictive forces are generated at even multiples of the fundamental electrical frequency as long as there are no additional disturbances such as, for example, a DC-component in the exciting voltage. Hence, the peaks identified in the sound pressure and vibration spectra at even multiples of the fundamental electrical frequency correspond to the mechanical responses of the core. The fundamental acoustic frequency is defined as twice the double fundamental electrical frequency. The peaks observed at odd frequencies in the acoustic spectra can be considered mostly as electromagnetic disturbances affecting various parts of the measurement chain. The voltage signal can be somewhat distorted due to the non-infinite stiff power source and the ohmic resistance of the leads and windings. The levels recorded by the accelerometers and the microphone were selected in the vibration and sound pressure spectra at the fundamental acoustical frequency for each step of the frequency sweep while the voltage levels were recorded at the fundamental electrical frequency. That means that the higher harmonic components were not considered further on. This procedure allows an accurate evaluation of the acoustical behaviour of the core. As a matter of fact, for a low magnetic flux density the sound and vibration spectra present mainly a dominating peak at the fundamental acoustical frequency whereas the peak amplitudes of the harmonics are significantly lower.

6 Levels db Peak Vibration Levels db Ref. 5e-8 m/s The vibration data collected at the fundamental acoustic frequency are averaged for in-plane, out-of-plane and both directions. Moreover, the sound pressure data selected at the fundamental acoustic frequency are used to estimate the sound power level radiated by the test core. 110 Averaged Velocity Levels on Core Averaged Velocity In-Plane Averaged Velocity Out-of-Plane Averaged Velocity Both Directions Frequency Hz Figure 8. Averaged vibration levels measured on the test core for in-plane, out-of-plane and both directions. The averaged vibration levels for in-plane, out-of-plane and both directions are plotted in Fig. 8. The curve for the averaged in-plane vibration levels displays a shape with distinct parts over the frequency range. The curve starts with a rather linear increase of level from 400 Hz to 1300 Hz followed by a steep rise and decrease of level between 1300 Hz and 1600 Hz implied by the peaks at 1380 Hz and 1520 Hz. The curve then continues with some level variations about a line more or less horizontal up to a new rise due to a peak at 2340 Hz. The averaged out-of-plane vibrations present higher levels at low frequencies and generally lower levels at higher frequencies than the in-plane vibrations. As a result, the total average of the vibration levels is dominated mostly by the contribution of the in-plane vibrations from approximately 600 Hz, as it can be observed in Fig. 8. The out-of-plane vibrations provide a contribution to the total vibration average at low frequencies and are the result of global modes which occur because the core stiffness in X-direction is significantly lower than in Y and Z-directions. In general, the larger contribution of in-plane vibrations to the core motion can be attributed to the magnetostrictive excitation acting mainly in the YZ-plane. In addition, the clamping plates may have a restraining effect on the vibration transmission in X-direction. Sound Power and Averaged Velocity Levels Averaged Velocity In-Plane and Out-of-Plane Ref. 8e-5 m/s Sound Power db Ref. 1 pw Frequency Hz Figure 9. Averaged vibration levels for in-plane and out-of-plane directions and sound power levels radiated by the test core. The sound power level determined from the sound pressure measurements made with the microphone mounted on the rotating boom are plotted in Fig. 9. It can be observed that the sound power radiated by the core follows closely the same trend as the averaged vibration level, as clearly displayed in Fig. 9. The discrepancies observed between sound power and vibration levels can be attributed especially at low frequencies to the unknown radiation efficiency which is lower than one at frequencies lower than 800 Hz. In addition, the limited number

7 of measurement points used to measure vibrations on the core may have an impact on the averaged value of the vibration levels at certain frequencies. Figure 10. Out-of-plane motion at 500 Hz with middle limb bending in X-direction. Figure 11. In-plane motion at 2380 Hz with side limb bending in YZ-plane. An Operational Deflection Shape (ODS) was performed by using the vibration signals acquired by the accelerometers at the main acoustic frequencies corresponding in general to the main peaks in Fig. 9 in order to identify the motion patterns of the core. For example, two clear motion shapes, one out-of-plane at 500 Hz and another one in-plane at 2380 Hz, are shown as fixed pictures in Fig. 10 and 11, respectively. To confirm the presence of global mode shapes, an Experimental Modal Analysis (EMA) was carried out on the test core suspended by elastic ropes. The mechanical excitation was provided by an electrodynamic shaker attached to the laminations at an oblique angle of 45º, as shown in Fig. 12. The input excitation from the shaker in the YZ-plane was measured by a force transducer and the vibration levels generated by the shaker excitation were recorded in X, Y and Z-directions by a roving tri-axial accelerometer positioned at 60 different points on the test core, as shown in Fig. 13. Electrodynamic Shaker Force Transducer Tri-Axial Accelerometer Figure 12. Electrodynamic shaker attached to the core laminations by a rod at an angle of 45º to provide the mechanical excitation. Figure 13. Shaker excitation measured by force transducer and vibrations recorded by triaxial accelerometer. The measurement method is designated as the Single Input Multiple Output (SIMO) procedure since the excitation is applied at one fixed point and the vibration levels are recorded at 60 different measurement points in three directions. As a result, 180 Frequency Response Functions (FRF) were measured as accelerances defined as acceleration through force. The overlaid traces of all measured FRF are presented in Fig. 14. At some frequencies, distinct peaks clearly indicate the presence of structural modes. The formal EMA enabled the eigenfrequencies and the mode shapes of the test core to be identified systematically. In fact, a great number of flexible modes could be found: 65 global and local modes were

8 detected in the frequency range from 200 Hz to 3200 Hz. For example, the deformation shapes in Fig. 10 and 11 could be related to two mode shapes presenting similar vibration patterns at the same frequencies. Out-of-plane modes from 400 Hz to 600 Hz In-plane modes near 1400 Hz In-plane modes near 2300 Hz Figure 14. Overlaid traces of the 180 FRF measured on the test core for the EMA. The deformation shapes identified by ODS on the test core clearly corresponded to particular global mode shapes found by performing the proper EMA. As a matter of fact, the peaks displayed by the plots for sound power and the averaged vibration level, as shown in Fig. 9, could be associated with certain specific modes obtained by the EMA. The sound power radiated by the test core is strongly coupled to the averaged vibration velocity of the core. Moreover, the vibration levels of the core excited by a realistic magnetic field are influenced by the structural mode shapes of the test core. Therefore, the magnetostrictive excitation at the fundamental acoustic frequency, but even at the corresponding harmonics for higher magnetic flux densities, can efficiently interact with the mechanical resonances of the core to cause increased sound levels. If the scale model is assumed to be roughly a one-fourth model of the core for a typical medium power transformer, the first main resonance for the corresponding full-scale model would thus be found in the vicinity of 350 Hz. This resonance frequency would be rather close to the frequency of 360 Hz corresponding to the third harmonic of the magnetostrictive force generated by the typical network frequency of 60 Hz. In fact, the resonance peak is fairly wide and may cause an amplification of the sound level at 360 Hz. This observation highlights the need of a procedure at the design stage to identify and avoid core resonances. The experimental studies carried out in laboratory conditions on the core scale model provide some insight into the general mechanisms leading to transformer no-load noise. Moreover, the experimental data can be used to validate and calibrate the models used to predict the core noise of power transformers. 3. PREDICTION MODEL AND SIMULATION RESULTS 3.1 Electromagnetic Model At no-load condition, an alternating voltage is applied to the phase windings on one side of the transformer while the windings on the other side (usually called primary side) are left open. The excited windings will carry the magnetizing current and a magnetic flux will be induced in the core. To obtain the magnetic flux density in the core at no-load, Maxwell s equations are used with the additional expressions. B = μh (2) where μ is the magnetic permeability in the core material and H the magnetic field strength. J = σe (3) where J is the current density and E the electric field density.

9 Figure 15. Permeabilities in rolling and cross-rolling directions for the core steel sheets. The resulting magnetic flux density B induced by the total currents (Ampere turns) of the windings can be expressed as B = A (4) where A is the magnetic vector potential. Figure 16. Magnetic flux density distribution in Tesla for a three phase transformer core at one specific point on wave. By combining Maxwell s equations and the vector potential formulation, the governing equation for the magnetic field is given by the relationship σ A + t ( A ) = J (5) μ The model is investigated in two dimensions by considering one single core package at a time. The core is surrounded by air. A magnetically insulating boundary condition is used on the outer boundary imposing the constraint n H = 0 (6) where the normal component of the magnetic field is set to zero. Experimental data for a specific steel type are used in the model to describe the magnetic properties of the core material. The core steel sheets are magnetically oriented and the permeabilities in the rolling and cross-rolling directions present different non-linear virgin curves, as shown in Fig. 15.

10 The excitation of the simulation model is provided by voltages shifted by a phase of 120º applied to the windings to simulate a three phase transformer. The analysis is then carried out in the time domain to obtain a magnetic field density in the core, as displayed in Fig. 16. Figure 17. Magnetostriction strains with respect to induction in rolling direction for the fundamental frequency and nine harmonics. By applying a Fast Fourier Transform to the time signals, the main frequency components of the magnetic flux density in rolling and cross rolling directions can be calculated at each node point of the mesh. The fundamental magnetic flux density components at each node can then be systematically associated with magnetostrictive strains provided in tables gathering experimental data specific for each steel grade, as shown in Fig. 17. Those values relating the magnetic flux density and the magnetostrictive strains are used as input data to the mechanical simulations performed in the frequency domain. 3.2 Mechanical Model In the mechanical model, the linear elasticity equations are used to describe the in-plane motion of the core implied by the magnetostrictive strains. The Navier s equation is given by the expression σ = F v (7) where σ is the stress tensor and Fv the volume forces. The stress tensor σ is a function of the strain tensor ε mech as given in Hooke's law σ = E ε mech (8) where E is the elasticity tensor. Since the electric steel has different elasticity properties in rolling and cross rolling directions, the elasticity tensor is specified for an orthotropic material. Then, the magnetostriction strain is introduced into Hooke s law σ = E (ε mech ε mag ) (9) where ε mag is the magnetostriction strain. The back-coupling effects corresponding to magnetostriction strain influencing magnetic field, are considered as negligible. In a finite element formulation, displacements are approximated in elements as u = N N u N (10) where N N is the array of interpolating functions and u N the nodal displacement. The strain can thus be expressed as ε = D N u N (11) where D N is the spatial derivative of N N.

11 The governing equation for the motion of the core subjected to magnetostrictive strain is given by the relationship Mu N + Cu N + Ku N = f N (12) where M, C and K represent the inertia, damping and stiffness terms, respectively and the term f N gives the load array containing the forces applied at the nodes. In the present model, the core is excited by the magnetostrictive strains. This yields f N = B T Eε mag dv (13) The displacement field for each selected core induction can be finally obtained from the magnetostrictive strains and for instance be analyzed in detail in the vicinity of the fundamental acoustic frequency as well as around the first acoustic harmonics. To obtain a better understanding of the core motion, a modal analysis is carried out with a suitable software to calculate the core resonances and, as an example, an eigenmode is identified at 2390 Hz, as displayed in Fig. 18. The resonance at 2390 Hz corresponds to the clear peak displayed in Fig. 9. This resonance could be easily excited by the magnetostrictive strains and causes the high vibration amplification at this frequency, as shown in Fig. 9. Figure 18. Mechanical resonance of the test core at 2390 Hz obtained by modal analysis. 3.3 Acoustic Model The core motion generates sound waves propagating in a surrounding fluid, such as air or oil, as described by the equation 2 p 1 c 2 2 p t 2 = 0 (14) where p is the acoustic pressure and c the speed of sound. The fluid is considered here as non-viscous. The fluid loading of the core gives a first boundary condition and is defined as f p = pn (15) where p is the fluid pressure and n a vector normal to the structure surface. The second boundary condition is given by the particle velocity continuity between structure and fluid, thus yielding v f = u t n (16) where v f is the particle velocity of the fluid and u the displacement vector. The relationship between pressure and velocity is obtained by using the linear equation of motion yielding ρ u = p (17) t where ρ gives the fluid density and u the displacement vector.

12 For the acoustic analysis, the 2D-model used for the mechanical simulations has to be extruded to a 3D-model. In addition, perfectly matched layers (PML) are implemented to create a free space for sound propagation, as shown in Fig. 19. Figure 19. Sound pressure field radiated by the vibrating core given at a specific frequency. 4. TESTING ON FULL SCALE TRANSFORMER CORE Measurements were performed on the core of a full scale transformer in order to detect potential effects of resonances on the vibration levels. Sensors were mounted on the core of a power transformer to record the vibration levels during Factory Acceptance Test. The 117 MVA transformer selected for the tests was manufactured in a fairly standard way with a three limb core. Seven accelerometers were attached at different positions on the upper yoke, as shown in Fig. 20. Accelerometers on Core Figure 20. Seven accelerometers mounted with magnets on the upper yoke of a 117 MVA transformer. The vibration signals from the accelerometers were acquired simultaneously when the transformer was operated at nominal voltage (100% U nom) in no-load conditions at 50 Hz. Potential resonance near 480 Hz Figure 21. Zoom on acceleration spectrum measured by one sensor placed on the upper yoke.

13 The measurements performed on the transformer operating at no-load provided vibration data from the core immersed in oil. For example, a potential resonance near 480 Hz implying an increase of the vibration level can be observed clearly in the acceleration spectrum acquired on the operating core, as shown in Fig. 21. Those valuable vibration data will be used to validate and calibrate the prediction tools under development. 5. CONCLUSION Sound and vibration measurements were performed on the scale model of a transformer core in order to investigate in laboratory conditions the multiphysics phenomena implying no-load noise. The main resonance frequencies of the core could be identified experimentally by performing a frequency sweep of the input voltage. Furthermore, prediction models based on a finite element formulation were developed to describe the complex interactions in the core structure and the coupling of the physical fields. Measurements carried out on a full scale transformer indicate the influence of resonances on the vibration levels of the core. 6. REFERENCES 1. G. Ramsis, J. Anger, D. Chu, The Sound of Silence Designing and Producing Silent Transformers, ABB Review, 2/2008, Pages (2008) 2. IEC , Power Transformers Part 10 1: Determination of Sound Levels Application Guide (2005) 3. B. Weiser, H. Pfützner, J. Anger, Relevance of Magnetostriction and Forces for the Generation of Audible Noise of Transformer Cores, IEEE Transactions on Magnetics, Volume 36, Pages (2000) 4. M. Rausch, M. Kaltenbacher, H. Landes, R. Lerch, J. Anger, J. Gerth and P. Boss, Combination of Finite and Boundary Element Methods in Investigation and Prediction of Load-Controlled Noise of Power Transformers, Journal of Sound and Vibration, Volume 250, Pages (2002) 5. R. Haettel, M. Kavasoglu and C. Ploetner, Prediction of Transformer Load Noise, Proceedings of the Comsol Conference, Paris (2010) 6. E. Reiplinger, Assessment of Grain Oriented Transformer Sheets with Respect to Transformer Noise, Journal of Magnetism and Magnetics Materials 21 (1980) 7. J. Anger and A. Daneryd, Noise in Power Transformers Model for Generation, Transmission and Propagation, Proceedings of the Conference Noise in Machines, UK Magnetics Society, Wolfson Centre for magnetics, Cardiff University (2009) 8. M. Mizokami, M. Yabumoto and Y. Okazaki, Vibration Analysis of a Three-Phase Model Transformer Core, Electrical Engineering in Japan, Vol. 119, No. 1 (1997) 7. ACKNOWLEDGEMENTS C.-G. Johansson, M. Kavasoglu and C. Lagerström are greatly acknowledged for their contribution to this work.