Suppressing magneto-mechanical vibrations and noise in magnetostriction variationfor three-phase power transformersChang-Hung Hsu, Jui-Jung Liu, Chao-Ming Fu, Yi-Mei Huang, Chia-Wen Chang, and Shan-Jen Cheng Citation: Journal of Applied Physics 117, 17D524 (2015); doi: 10.1063/1.4919040 View online: http://dx.doi.org/10.1063/1.4919040 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/117/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Correlation of magnetostriction variation on magnetic loss and noise for power transformer J. Appl. Phys. 117, 17E716 (2015); 10.1063/1.4919122 Magnetostrictive vibrations model of a three-phase transformer core and the contribution of the fifth harmonic inthe grid voltage J. Appl. Phys. 115, 17A316 (2014); 10.1063/1.4863931 Publisher's Note: “Effects of magnetomechanical vibrations and bending stresses on three-phase three-legtransformers with amorphous cores” [J. Appl. Phys. 111, 07E730 (2012)] J. Appl. Phys. 114, 059901 (2013); 10.1063/1.4816341 Numerical computation for a new way to reduce vibration and noise due to magnetostriction and magnetic forcesof transformer cores J. Appl. Phys. 113, 17A333 (2013); 10.1063/1.4800077 Effects of magnetomechanical vibrations and bending stresses on three-phase three-leg transformers withamorphous cores J. Appl. Phys. 111, 07E730 (2012); 10.1063/1.3678459

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Suppressing magneto-mechanical vibrations and noise in magnetostrictionvariation for three-phase power transformers

Chang-Hung Hsu,1,2,a) Jui-Jung Liu,3 Chao-Ming Fu,4 Yi-Mei Huang,5 Chia-Wen Chang,6

and Shan-Jen Cheng7

1Division of Electrical Engineering, Fortune Electric Company Ltd., Tao-Yuan 320, Taiwan2Department of Electronics and Information Engineering, Army Academy R.O.C., Tao-Yuan 320, Taiwan3Department of Multimedia and M-Commerce, Kainan University, Tao-Yuan 33857, Taiwan4Department of Physics, National Taiwan University, Tai-Pei 10617, Taiwan5Department of Mechanical Engineering, National Central University, Tao-Yuan 32001, Taiwan6Department of Aircraft Engineering, Army Academy R.O.C., Tao-Yuan 320, Taiwan7Department of Information and Telecommunication Engineering, Ming Chuan University, Tai-Pei 33348,Taiwan

(Presented 6 November 2014; received 22 September 2014; accepted 4 January 2015; published

online 5 May 2015)

This study investigated the effect of magnetostriction-induced core magnetomechanical vibrations

and noise on the magnetic properties of power transformers. The magnetostriction of grain-oriented

Si steels was found to be extremely sensitive to compressive stress applied along the rolling

direction and to tensile stress applied along the transverse direction. The compressive stress

increased the variation in the magnitude of magnetostriction, which is correlated with core vibration

and noise. A 2D model of the power transformer was used to simulate the noise and vibration varia-

bles through a finite element analysis. VC 2015 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4919040]

Energy saving and noise reduction in power transformers

are crucial issues that require urgent solutions.1 An attractive

magnetic property of Si steel sheets with grains of approxi-

mately 0.5-mm diameter is that they show a large induction

Bm of approximately 1.9 T while exhibiting a 35% lower core

loss than conventional grain-oriented materials.2 To improve

the transformer core structure, a finite difference method

(FDM) was used to analyze the variation in flux density for dif-

ferent lap-joint structures of Si steel cores.3–5 It was indicated

that the flux density is much lower for a step-lap joint than for

a conventional lap joint. The step-lap joint is advantageous in

that it affords lower core loss and magnetostriction than a con-

ventional lap joint. The hysteresis curves of ac magnetostric-

tion were previously reported for a step-lap joint.6 In addition,

the variation in ac magnetostriction is correlated with harmon-

ics, and the spectra of noise induced in a power transformer

were analyzed by using finite element analysis (FEA).7–9

The variation in the magnetostriction as a function of

the core properties and manufacturing techniques has been

widely investigated, as shown in Figure 1. The magnetostric-

tion of grain-oriented Si steel was found to be extremely

sensitive to compressive stress applied along the rolling

direction (RD) and to tensile stress along the transverse

direction (TD).10 The compressive stress increases the mag-

nitude of magnetostriction, which can also be affected by the

noise in the core. This creates the need to develop a reliable

technique with the MSL joint to reduce the magnetostriction

in grain-oriented Si steels under various stress conditions.

The magnetostriction and hysteresis loop result from

bringing the shorter tetragonal axis to coincide with, or be

close to, the direction of the applied magnetic field, as shown

in Figure 2. Therefore, the magnetostriction depends on the

angle, as per the following equation:

k ¼ ð3=2Þks½ cos2h� 1=3�; (1)

where h is the angle between Ms and H and ks is the satura-

tion magnetostriction.

Transformer cores having a joint with a step-lapped

structure have shown rotations of magnetization with strong

restrictions in location and time.10,11 The pressure corre-

sponding to Maxwell’s forces between two successive lami-

nations can be expressed as

p ¼ B2e

2lo

: (2)

Equation (2) shows that p components contain a pre-

vailing fundamental frequency term that is twice the value

of the excitation one. In this study, a transformer core with

an MSL joint structure and V-lapped form is considered.

Compared to core limbs, the yoke shows slightly higher

values of Bm, which can be attributed to weak rotational

magnetization.

A significant amount of noise is related to the parame-

ters of the core materials,10 which implies that the core

vibration acceleration is proportional to the magnetostriction,

i.e., acore / es. In general, the fundamental frequency of the

winding vibration acceleration is 120 Hz, which is twice the

rated power frequency. Magnetostriction forces are known to

cause core vibrations, and the core vibration acceleration

induced by magnetostriction can be expressed as11

a)Author to whom correspondence should be addressed. Electronic mail:

chshiu@fortune.com.tw

0021-8979/2015/117(17)/17D524/4/$30.00 VC 2015 AIP Publishing LLC117, 17D524-1

JOURNAL OF APPLIED PHYSICS 117, 17D524 (2015)

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acore ¼ �2esLU2

0

N1ABsð Þ2cos 2xt; (3)

where es is the coefficient of saturation magnetostriction of

the soft magnetic material sheet, L is the length of the mate-

rial sheet, U0 is the magnitude of the voltage-driving source,

x ¼ 2pf (f is the frequency of the voltage-driving source in

hertz; 60 Hz in Taiwan), N1 is the number of primary turns,

A is the cross-sectional area of the core limb, and Bs is the

saturation magnetic flux density.

Transformer vibrations are mainly induced by the core,

winding, and clamp system. In order to reduce transformer

vibrations, this study aims to develop a structure-supported

tank incorporated with the MSL core as a distribution trans-

former. The amount of audible noise is related to the core ma-

terial and the tank structure. For an assembled transformer,

the noise (in decibels) of the transformer is calculated as

dBi ¼ Cþ 19 log Wt � 20 log Uþ k1ðBm � k2Þ þ k3; (4)

where C denotes the material type. C¼ 40 for Si steel and

C¼ 45 for an amorphous material. The parameters k1 and k2

are constants, and k3 is a compensation factor when operat-

ing at a frequency of 60 Hz. Wt denotes the core weight (in

tons), U denotes the cross-section length of the core, and Bm

is the magnetic flux density (in Tesla). Recall Eq. (4) which

explains the influence of physical parameters ½Wt;U;Bm� on

the audible noise of a transformer. The core design needs to

achieve a low audible noise dBi.

FIG. 1. Soft magnetic material in variation of magnetic properties: (a)

Magnetostriction and (b) B-H curves.

TABLE I. PSO method used to the auto-tuning transformer geometry and

magnetic parameter.

PSO results (A) (B) (C) (D) (E)

PSO laminating number 7 9 11 13 20

Cost (�106, TWD) 5.51 5.13 4.89 4.80 4.77

Cross length of the core, U (mm) 497 473 453 439 427

Wt (ton) 15.6 13.0 11.3 10.5 9.8

TLT (ton) 118 128 138 146 154

THT (ton) 698 756 815 860 912

Bm (T) 1.33 1.36 1.38 1.39 1.40

FIG. 2. MSL core showing lower total

cost with the PSO method for magnetic

parameter variation: (a) total cost, (b)

core weight Wt, (c) cross-sectional

length of the core U, (d) secondary coil

turns TLT , (e) primary coil turns THT ,

and (f) and magnetic flux density Bm.

17D524-2 Hsu et al. J. Appl. Phys. 117, 17D524 (2015)

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In this paper, an optimization theorem is used to regulate

each step of a particle towards the optimal position, which

both of core and winding in geometry forming correlated

with totally cost consideration have been developed. Particle

swarm optimization (PSO) can be used for automatically reg-

ulating the magnetic noise dependent on the magnetic flux

density and lowering transformer cost. To enhance the ability

of PSO to reduce transformer cost, the simulation results and

design values were compared. The PSO algorithm is based

on swarm intelligence, which is an artificial intelligence

technique that studies collective behavior in decentralized,

self-organized groups. It utilizes a population of potential sol-

utions, or particles, which move around the design space with

every iteration. The movement of these particles is devel-

oped. Table I indicates that the transformer design parameters

correlated with the response results, which are displayed in

Figs. 2(a)–2(e). In addition, to compare simulated results and

design values of PSO, the PSO calculation results and trans-

formers costs down improvement ratio are listed in Table II.

The PSO method afforded a significantly lower cost.

Equation (2) indicates that the joint of the core is the

key region affecting the dynamic behavior of the magnetic

properties. In order to minimize the core loss and the vibra-

tion and noise of the cores, a step-lap joint consisting of five

or six step structures has been used to improve the magnetic

properties. In addition, the waveform of magnetostriction is

a reflection of the waveform of local induction, and noise

reduction afforded by the cores with multi step-lap joints is

caused by the reduction of harmonics in the magnetostriction

of cores,5 as Eq. (3).

Moreover, by using FEA in the transformer vibration

simulation, the simulated results of the transformer vibration

and noise were analyzed. Both the time domain and FFT fre-

quency of the vibration were used for assembling trans-

former detection. It presents the experimental results in the

time domain. FFT was performed to carry out the vibration

analysis of an assembling transformer. Figure 3 shows that

the time domain and frequency domain of core vibration

waves of the assembling transformer were nearly the same

as those obtained in the FEA results because the

FIG. 3. Measured results of transformer vibration: (a) time-domain data and

(b) FFT frequency analysis.

TABLE II. Comparison of the PSO optimization design and real design

values.

Category

PSO optimization

values Design values

Improvement

ratio (%)

Cost (�106, TWD) 4.77 4.98 4.22

Cross length of

the core, U (mm)

427 420 �1.67

[Wt;TLT ;THT] [9.86, 154, 912] [9.62, 154, 884] N/A

Bm (T) 1.40 1.45 3.45

FIG. 4. Frequency spectra of noise produced by extreme-low-noise-power

transformer core: (a) schematic of vertical view transformer noise testing (b)

with no load test and (c) with 70% loading test.

17D524-3 Hsu et al. J. Appl. Phys. 117, 17D524 (2015)

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magnetostriction variation has reduced suitably. The fre-

quency spectra of the vibration were measured.

From Eq. (4), the background environment noise was

measured to be 32 dB. This study is aimed at the transformer

industry, and it satisfies the noise testing procedures speci-

fied in the IEEE and IEC transformer testing standards. The

frequency spectrum of transformer noise basically depends

on the type of core material, magnetic flux density, winding

structure, and tank radiator cooling fan component. Actually,

the magnitude of the frequency component of transformer

noise probably induces transformer resonance exceeding

5 dB.

Figure 4 shows the transformer core noise frequency

component up to 500 Hz for a number of 50 Hz transformers

with a wide range of designs of three-phase three-limb cores

operating at typical flux densities of 1.3 T. Figures 4(a) and

4(b) show measurements under the eight-point frequency

spectrum of transformer noise with no-load test and 70%

loading testing, respectively. A comparison of the measured

results shows a difference of at least 4–8 dB because loading

testing including the winding vibration and cooling fan oper-

ation of the tank shows higher noise. In Figure 5, the noise

level of the designed power transformer with no-load, oper-

ated with magnetic flux density of 1.3 (T), is less than 48

(dB), and Bm lies in a wide range between 1.15 (T) and 1.55

(T); this is acceptable for realizing a comfortable residential

environment. According to the measurement results, the

transformer is suitable for installation and operation at the

designated location in Kiama City, Australia.

A compressive stress increases the magnitude of magne-

tostriction, which is affected by the noise and vibration of

the core. This study reports the results of a simulation per-

formed to validate the cost reduction in the core geometry

and winding structure for a 25-MVA power transformer by

using the PSO method. The characteristics of noise and

vibration variables were analyzed using FEA. We achieved a

definite relationship between the magnetostrictive character-

istics of the core with multi step-lapped joints consisting of

five or six steps and the reduced core vibration and noise

response. The transformers were successfully installed in a

resident city, Australia.

1A. Makino et al., J. Appl. Phys. 105, 07A308 (2009).2T. Tomida et al., J. Appl. Phys. 93, 6680–6682 (2003).3B. Verbrugge et al., J. Appl. Phys. 85, 4895–4897 (1999).4G. F. Mechler et al., IEEE Trans. Power Delivery 15, 198–203 (2000).5A. Ilo, IEEE Power Eng. Rev. 22, 43–47 (2002).6A. Ilo et al., J. Magn. Magn. Mater. 215–216, 637–640 (2000).7H. Magi et al., IEEE Trans. Magn. 35, 3364–3366 (1999).8M. Rausch et al., J. Sound Vib. 250, 323–338 (2002).9R. A. Jabr, IEEE Trans. Magn. 41, 4261–4269 (2005).

10I. Hern�a�andez et al., IET Electr. Power Appl. 4(9), 761–771 (2010).11Chang-Hung Hsu et al., J. Appl. Phys. 115, 17E718 (2014).

FIG. 5. Transformer testing results: (a) prototype of extreme-low-noise

power transformer with a capacity of 25 MVA and (b) noise dependence on

magnetic induction in different testing condition.

17D524-4 Hsu et al. J. Appl. Phys. 117, 17D524 (2015)

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