Correlation of magnetostriction variation on magnetic loss and noise for powertransformerShan-Jen Cheng, Jui-Jung Liu, Yeong-Hwa Chang, Chao-Ming Fu, Chang-Hung Hsu, Chun-Yao Lee, and Chia-Wen Chang Citation: Journal of Applied Physics 117, 17E716 (2015); doi: 10.1063/1.4919122 View online: http://dx.doi.org/10.1063/1.4919122 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 Magnetic flux distribution in power transformer core with mitred joints J. Appl. Phys. 117, 17D522 (2015); 10.1063/1.4919119 Suppressing magneto-mechanical vibrations and noise in magnetostriction variation for three-phase powertransformers J. Appl. Phys. 117, 17D524 (2015); 10.1063/1.4919040 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 Core loss behavior in high frequency high power transformers—I: Effect of core topology J. Renewable Sustainable Energy 4, 033112 (2012); 10.1063/1.4727910 Loss analysis of permanent-magnet synchronous motor using three-dimensional finite-element method withhomogenization method J. Appl. Phys. 103, 07F126 (2008); 10.1063/1.2833313

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Correlation of magnetostriction variation on magnetic loss and noise forpower transformer

Shan-Jen Cheng,1 Jui-Jung Liu,2 Yeong-Hwa Chang,3 Chao-Ming Fu,4

Chang-Hung Hsu,5,6,a) Chun-Yao Lee,7 and Chia-Wen Chang8

1Department of Aircraft Engineering, Army Academy R.O.C., Tao-Yuan 320, Taiwan2Department of Multimedia and M-Commerce, Kainan University, Tao-Yuan 33857, Taiwan3Department of Electrical Engineering, Chang Gung University, Tao-Yuan 33302, Taiwan4Department of Physics, National Taiwan University, Tai-Pei 10617, Taiwan5Division of Electrical Engineering, Fortune Electric Company Ltd., Tao-Yuan 320, Taiwan6Department of Electronics and Information Engineering, Army Academy R.O.C., Tao-Yuan 320, Taiwan7Department of Electrical Engineering, Chung Yuan Christian University, Tao-Yuan 320, Taiwan8Department of Information and Telecommunication Engineering, Ming Chuan University, Tai-Pei 33348, Taiwan

(Presented 7 November 2014; received 22 September 2014; accepted 9 January 2015; published

online 5 May 2015)

Magnetostriction (MS)-caused strain in single-phase three-legged cores with different core cutting

forms, which suffer from induced magnetic loss and noise, was studied. It is found that adopting each

different core form types induces magnetostriction e variation in a transformer core operating with a

high-frequency AC signal. The results are compared with finite element analysis simulations. It is also

indicated that magnetostriction e variations are significant in the rolling direction and along limbs and

yokes. In this paper, it is proposed that core corner sides and T-joint parts without cutting structure,

the core exhibits lower core loss and lower heat dissipation due to the fact that the magnetic flux that

passes through corner sides shows lower magnetostriction variation. The magnetic properties resulting

from magnetostriction variation in core loss and heat dissipation phenomena are significantly different

from other core forms because of stronger contributions from magnetostatic forces. The main contribu-

tion for reducing core loss and noise, making them much less in corner numbers and cutting-fabricated

forms, can be expected to come from lower magnetic flux and magnetostriction variation. VC 2015AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4919122]

Magnetostriction (MS) and core loss in grain-oriented

(GO) silicon-steel have been considerably improved in recent

years.1 The power loss of transformer core steel depends on

several physical parameters that regulate the structure of the

core in many complex ways. It has presented a way to investi-

gate the corresponding dependencies for a series characteristic

in MS, which is the most significant source of no-load loss and

noise.2,3 Besides, there is interesting problems for core research

by industrial producers and academic researchers who attempt

to improve the material properties. Noise levels are strongly

increasing in importance, due to the fact that rising energy

demands tend to bring transformers closer to residential areas.

In addition, careful choice of a step-lap lamination core

design leads to reduced no-load losses and noise level.4,5

The lateral step-lap enables a favorable assembly for the

upper yoke.6,7

Experiments were performed on a single-phase three-limb

transformer core magnetized around 1.68 T and operated

between 60 and 1000 Hz. In accordance with the results of the

finite element analysis (FEA) simulations, the core was con-

structed with a width and length of 90 mm� 90 mm. Each sin-

gle core transformer had 30 turns of wire, as shown in Fig. 1.

The core thickness was stacked with ten layers of conventional

grain-oriented (CGO) SiFe-sheets (23ZDMH90). Five different

independent prototype core forms were investigated. These

included triangle, rectangular, and oval cores without core cut-

ting form, and butt-lap and half mitre-lap cores with core cut-

ting structures, as shown in Figure 1.

The magnetostriction and B-H curve properties of the

magnetic core were measured, as shown in Figure 2. The

magnetostriction was measured to be around 28.7 ppm, and a

vibrating sample magnetometer (VSM) measured the coer-

civity (Hc) and saturation flux density to be around 38 Oe

and 18 893 (G).

For transformer core loss calculation, there are three types

of magnetic loss components to be considered in the core;

these losses occur in ferromagnetic materials excited by a vari-

able magnetic field.9 These losses include hysteresis loss and

eddy current loss. For a periodically varying flux density, all of

the loss densities are calculated in watts per unit weight (W/

FIG. 1. Different core specification and prototype of five-typed core.

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

chshiu@fortune.com.tw.

0021-8979/2015/117(17)/17E716/4/$30.00 VC 2015 AIP Publishing LLC117, 17E716-1

JOURNAL OF APPLIED PHYSICS 117, 17E716 (2015)

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kg). So, it is well known that hysteresis loss Ph (W) and eddy

current losses Pe(W) are two most important parameters in

computation of transformer core loss Pc (W) in joint regions

where the magnetic flux density is uniform (most of the lami-

nation length, but excluding the joint zone). In this study, we

have used the classic formulation given by

Pc ¼ Ph þ Pe ¼ khfB1:6m þ

1

24r 2pfð Þ2d3pLB2

k ; (1)

where kh is a material parameter, eddy current losses in the

kth lamination, f ðHzÞ is the operation frequency, SðS=mÞ is

the lamination conductivity, dðmÞ is the lamination thick-

ness, pðmÞ is the lamination width, LðmÞ is lamination

length, and Bk(Tesla) is average magnetic flux density in the

lamination.

For a core joint with step-lapped structure, transformer

cores have shown rotations of magnetization with strong

restrictions of location and time.4,6 The basic origin of rota-

tional magnetostriction (RM) is normally given by two fac-

tors, as core designs use mired joints, which exhibit sharp

ends of outer two limb laminations, and having a V-lapped

joint in the middle of the core. Meanwhile, a higher

anisotropy of HGO SiFe, with detours of flux and global flux

in core corner sides, is significant affect by magnetostriction

variation, as shown in Fig. 3. For magnetostriction theory,11

the rotation of moments to align with the applied field can be

modeled by the quadratic relation

k ¼ 3

2ks

M

Ms

� �2

; (2)

where ks and Ms, respectively, denote the saturation magne-

tostriction and magnetization. So, transformer core was

tested with different forming structures, including no-cutting

structures and cutting in limb with 00, 900, and V-lapped

forms. Compared to core limbs, the yoke shows slightly

higher values of Bm, which can be attributed to weak RM.

It is well known that silicon steel of soft material exhib-

its superior magnetic properties such as easy magnetization

direction of silicon steel distribution along the rolling direc-

tion (RD), RD with high induction, low magnetostriction,

and low iron loss. Equation (1) used for the core loss calcula-

tion kh shows that the magnetic parameter affects the loss

variation which is due to the refinement process and the

bending stress of material impacting the core magnetostric-

tion. In Figure 3, the FEA simulation results show the mag-

netic flux density variation of transformer cores. It is

indicated that at any instant in time the outer-limbs carries

zero total flux. The symbol denoted as F1 and F2 detour flux

FIG. 2. Magnetic properties of soft material 23ZDMH90: (a) magnetostric-

tion and (b) hysteresis loop.

FIG. 3. FEA results: (a) global flux and detour flux paths in the different

core, V-lapped and triangular form and (b) different core region flux density

variation.

17E716-2 Cheng et al. J. Appl. Phys. 117, 17E716 (2015)

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comes from the outer-limbs in order to flow into the middle-

limb, as shown in Figure 3(a). However, this flux takeover is

complicated due to the step-lapped structure. Generally, the

transformer core energized saturation magnetostriction and

magnetization, as Eq. (2). The V-lapped flux variation, being

oriented in the vertical direction, faces an obstacle since the

transverse direction (TD) impacts the flux flow-path as G1

and G2 global flux paths, as shown in Figure 3(a), one of

sample simulated core Bm is shown as triangular core. The

upper half of the yoke flux flows into the left half of the mid-

dle limb. It is significant to note that a detour flux has

increased with rising anisotropy. The flux makes a detour

into the yoke region, with a rotating condition causing it to

flow back and enter the middle-limb. A larger strain from

magnetostriction, in the RD, seems to arise also in the core

corner sides, which will reduce permeability due to TD

effect.

Figure 3(b) shows FEA results with different core form

structures including the middle limb, yoke, core corner, and

outer limb. Compared to different core limbs, the core cor-

ners generally show higher MS due to magneto-static

forces.8 Rather low values of MS are observed in the straight

parts of the yoke despite the weak RM. Note that the triangu-

lar core form showed more stable magnetic flux density as

well as lower core loss in comparison with the other cores

due to the fact that the lesser corner number structures have

smaller bending stress, lower magnetic flux and magneto-

striction variation, compared with others type of the core, as

shown in Figure 4. It is well-known that when the magnetic

flux lines have smaller variation which can be induced lower

magnetostriction depend on lower magnetic loss due to

lesser core corner number of the core.

In addition to the concept of material grain direction, the

T-joint part of the core in V-lapped structure also takes

advantage of the above stated improvements in regions that

show alternating magnetization (AM) in RD of the limbs and

yokes.9,10 The T-joint regions and partly also yokes tend to

show RM with considerably high components of induction

in the TD of material. This results in strong regional

increases of losses. The strain values are higher for the cut-

ting core structure compared to the no cutting core structure.

This is due to the worse magnetostrictive behavior of the

given cutting process including butt lap and V-lap especially

under AM. In all regions, the strain in RD is higher than in

TD.4 According to the author research work,11 the core with

smaller bending stress and less core corner numbers will

reduce core loss and exciting power, as shown in Figure 5.

In order to validate the core performance, the hysteresis

variation, the exciting current of core inside dependent on

the heat dissipation and magnetostriction variation, have

been measured in Figure 6. Comparison of different fre-

quency experimental and FEA results are shown in Table I.

Clearly, the lower core heat dissipation and hysteresis loss

have indeed resulted in lower core loss. Besides, the no-

cutting core with triangular or oval form has better perform-

ance of inter-laminar off-plane flux close to air gaps due to

lower bending stress. For heat dissipation results, it is shown

that core magnetized has induced heat variation, which

seems to be dependent on flux-line disturbance, induces

atomic friction occurring heat disturbance in the core corner

sides is significant by FEA.

Measurement of the magnetic loss of core per cycle7

indicates that the core heat dissipation is proportional to the

local heat source density of core material and that the excita-

tion frequency corresponding to the average loss over the

FIG. 4. Magnetic flux density variation at different core insides: (a) middle

leg near yoke, (b) middle leg, (c) core corner, and (d) outer leg.

FIG. 5. The measured result in magnetic properties at 60 Hz: (a) core loss

and (b) exciting power.

17E716-3 Cheng et al. J. Appl. Phys. 117, 17E716 (2015)

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163.25.115.238 On: Mon, 01 Jun 2015 02:59:17

sample volume is also proportional to the heat temperature.

According to the previous discussion, the core shows higher

magnetic reluctance and magnetic flux-line flows to parts

with smaller magnetic reluctance. Meanwhile, the core con-

sists of laminate and is constructed with outline-cored forms.

The cores are clamped together which can induce stresses in

the material and lead to magnetostrictive losses. Another rea-

son of increased losses can be due to burrs on the core lami-

nation edges, which can create locally high eddy current

losses. Furthermore, constructed form of the material can

also decrease the permeability and increase magnetic core

losses.

Material strain and magnetostriction affects the noise

and vibration of a core and can be denoted by q / B2=2l0.

The core vibration force Fc is also proportional to the satura-

tion magnetostriction force Fc / es, where the es is saturation

magnetostriction force.

In Figure 7(a), the Total harmonic distortion (THD) is

measured at no-load condition for each core. Actually, the

total harmonic distortion is proportional to fundamental rated

current ITHD / 1=If undamental ffi Irated. Then, it shows a typical

measurement of the harmonic content of strain in the RD of

middle limb. The measured harmonic result indicates that in-

tensity values for the triangular core are significantly higher

than others cores due to lower exciting power (VA). For

noise level results, it is significant to observe that the noise

level induced by magnetostriction variation, core bending

stress, weight, core circumference, and cross section of

area,12 respectively, as shown in Figure 7(b). Generally,

reducing noise level for transformer core in control lower

magnetostriction variation, forming core structure, and core

joint way is significant.

This paper investigates magnetostriction variation and

core strain that the results show the effect of core limbs, cor-

ner sides, being V-lapped, and different core structures are

significantly correlated due to mere magnetostriction being a

weak effect of AM. It is interesting that the triangle type of

core form has better properties than do other core forms due

to lower bending stress and lesser core corner number. A

detour flux and a global flux passing through core-limb cor-

ners and V-lapped sides are significantly different. The main

contribution in this paper for reducing core loss and noise

comes from lower magnetic flux disturbance and magneto-

striction variation. For no-cutting core form, the reduction is

much greater for corner sides and for cutting-fabricated core

forms.

1G. Shilyashki, IEEE Trans. Magn. 50(1), 8400115 (2014).2I. Hirotaka et al., J. Appl. Phys. 115(17), 17A332 (2014).3F. Fiorillo et al., IEEE Trans. Magn. 45(10), 4242–4245 (2009).4I. Hern�a�andez et al., IET Electr. Power Appl. 4(9), 761–771 (2010).5Y. Wang et al., Appl. Phys. Lett. 93(11), 113503 (2008).6A. Ilo et al., J. Magn. Magn. Mater. 215–216, 637–640 (2000).7M. LoBue et al., J. Appl. Phys. 109(7), 07D308 (2011).8M. Enokizono et al., J. Appl. Phys. 83(11), 6486 (1998).9E. G. Nyenhuis, IEEE Trans. Power Delivery 15(1), 204–209 (2000).

10J. L. Liu, J. Appl. Phys. 109(7), 07A326 (2011).11C.-H. Hsu, IEEE Trans. Magn. 49(7), 3862–3865 (2013).12Y.-H. Chang et al., J. Appl. Phys. 109(7), 07A318 (2011).

FIG. 6. Heat dissipation in transformer cores at a 60 Hz operation frequency:

(a) triangular type, (b) oval type, (c) butt-lapped type, and (d) mitre-lapped

type.

TABLE I. Comparison of FEA and measured results for different core

structures.

Category

core loss Pc,

(W/kg)

No cutting Cutting structure

(1) (2) (3) (4) (5)

Tria.

core

Oval

core

Rect.

core

Butt-lapped

core

Half mitre-lapped

core

60 Hz, FEA 1.23 1.98 1.62 2.45 2.39

60 Hz, Exp. 1.28 1.78 1.69 2.66 2.59

1000 Hz, FEA 46.38 48.5 57.9 66.9 64.37

1000 Hz, Exp. 47.33 49.48 59.09 68.27 65.68

FIG. 7. Magnetic properties under different frequencies: (a) THD and (b)

noise.

17E716-4 Cheng et al. J. Appl. Phys. 117, 17E716 (2015)

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