3D Finite Element Analysis of the Stray Loss in Power Transformer Structure Parts

doi:10.4236/epe.2013.54B207

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Energy and Power Engineering, 2013, 5, 1089-1092

doi:10.4236/epe.2013.54B207 Published Online July 2013 (http://www.scirp.org/journal/epe)

3D Finite Element Analysis of the Stray Loss in Power

Transformer Structure Parts*

Yan Li, Longnv Li, Yongteng Jing, Bo Zhang

Research Institute of Special Electrical Machines, Shenyang University of Technology, Shenyang, China

Email: [email protected]

Received March, 2013

ABSTRACT

In order to analyze the leakage magnetic field and stray loss in power transformer, leakage magnetic field and stray loss

in structure parts of a power transformer are calculated by three-dimensional (3-D) non-linear time harmonic finite ele-

ment method (FEM). The results show th at stray loss and loss density in structure parts are large an d which may lead to

local overheating and affect performance of the transformer. The magnetic shields are used to reduce the stray loss and

loss density of power transformer. Effects of these shields on stray loss and loss density of structure parts are discussed.

The results show that stray loss and local overheating can be reduced and eliminated effectively by adding magnetic

shields. It provides some references for the analysis of stray loss and optimization design in transformer.

Keywords: Finite Element Method; Stray Loss; Leakage Magnetic Field; Local Overheating; Magnetic Sh ields

1. Introduction

Power transformer is the core of energy conversion and

transmission in power network, which is also the most

important and expensive equipment. So it will have an

essential impact of power network whether the trans-

former is safe, reliable and economic operation or not [1].

With the increase of capacity of the transformer, the

magnetic leakage field is increasing which may enlarge

the stray loss in the structure parts of power transformer.

In the large power transformer, leakage magnetic field

generated by the winding current will produce losses in

the metal structure parts, and these losses is part of the

transformer load losses, it often tend to local overheating

because of its unevenly distribution. So it is quite neces-

sary to study the magnetic leakage and stray loss deeply

and accurately [2,3].

In this paper, a practical power transformer model of

type SZ10-5000 0kVA/110k V was app lied to research the

stray loss problem in large power transformer by using

3-D nonlinear time harmonic analysis. Detailed calcula-

tion and analysis was proceeded in order to determine the

concentration of stray loss in transformer structure parts,

and magnetic shields were used to reduce stray loss and

prevent local overheating.

2. 3D Calculation Model and Calculation

Method

The 3-D finite element model in this paper is established

as shown in Figure 1. The analysis has been made with

the following simplification and assumptions: 1) The 1/2

model of whole transformer model is established in order

to reduce the computational time; 2) All field quantity

sinusoidal variation with time, do not consider the high-

order harmonic; 3) eddy current, circulation in winding

and eddy current in iron core are being neglected.

Non-linear magnetic properties of tank, core and

magnetic shields material were considered to calculate

leakage magnetic field and stray loss. Magnetic shields

material was disposed as anisotropic material based on

“homogenization method [4,5]”, anisotropic of the shield

conductivity analog laminated effect. According to the

continuity condition of B/H between silicon steel sheet

and air, the permeability of magnetic shields along lami-

nation direction (y-direction) can be described as the

following equation:

Core

Tank

Clamp

Magnetic

shields

*This work was supported by NSFC, under Project 51177103 and

Program for LNIRT in University (LT2011002). Figure 1. Structure diagram of winding.

Y. LI ET AL.

1090

0/(1 )

uu c

(1)

where

u is permeability of magnetic shields along

lamination direction, 0 is permeability of vacuum, c is

lamination coefficient, taken as 0.97. The permeability of

the other two directions

u and

u are given by B/H

curve.

The eddy current generated in the silicon steel sheet

near the winding side can not be ignored, the model of

conductivity:

00 00

000

00 00

σσ

σσ cσ

σσ























(2)

In the other silicon steel sheet, the model of conductiv-

ity can be governed by following equation:

00 00

0000

00 00

σσ











(3)

According to Maxwell equations, transformer steady

state magnetic field problem can be described as:



AJ t







 







 (4)

where e



is permeability,



 is magnetic vector po-

tential,

 is current density,



is conductivity.

The stray loss of transformer is generally consist hys-

teresis loss and eddy current loss. The eddy current loss

can be calculated by the following equation:





d

(5)

The average eddy current loss of time-harmonic field

can be governed by following equatio n:

00ssrmsrms

evv

JJJ J

pdv









 

(6)

The hysteresis loss can be introduced in leakage mag-

netic field calculated on the basis of curve.

WB

 







Nii

hhm

ppBV





i

(7)

where h is hysteresis loss, N is number of finite ele-

ment units, is hysteresis loss of the unit,

is peak flux density of the unit,



p i





is conductivity,

is volume element.



VThe total stray loss p can be governed:

pp p

(8)

3. Verification of Calculation Method

Leakage magnetic field and stray loss were calculated for

type SFP-17000 kVA/37.6 kV practical transformer and

transformer loss reference model TEAM Problem 21-B，

TEAM Problem 21c-M1，TEAM Problem 21a-0 in order

to confirm the calculation method effectiveness of leak-

age magnetic field and stray loss. The practical trans-

former leakage magnetic field test position diagram is

shown in Figure 2. Calculation value (contain shields)

and measured value of stray loss in steel plate of three

models comparison results were shown in Table 1.

In Figure 2, the position II is near outer surface of C

phase winding, from the winding center to the end. Cal-

culation value and measured value of magnetic flux den-

sity amplitude direction component (By) comparison

results was respectively shown in Figure 3(a) and (b).

The loss calculation error was less than 2% in Table 1;

Calculation result and measured value was consistent in

Figure 3, therefore, the loss calculation method used in

the paper is effective.

4. Analysis of Calculation Results

4.1. Calculation and Analysis of Loss

In this paper, The MagNet software was using to calcu-

late eddy current field and structure parts loss in trans-

former. And further, stray loss distributions in the tank

wall and yoke clamp were discussed.

The loss density distribution of yoke clamp surface

and tank side wall inner surface were respectively given

in Figure 4 and Figure 5. Maximum loss appears in the

Posit i on I

Top view side view

tank

Position I

winding

A phaseB phaseC pha s e

Po si ti o n II

Figure 2. Test position of leakage magnetic field.

Table 1. Comparison of calculation value and measured

value of loss.

Model Measured

value/W Calculation

value/W Error/%

TEAM Problem 21-B 11.97 12.20 1.92

TEAM Problem 21c-M13.72 3.66 1.6

TEAM Problem 21a-09.17 9.24 0.76

Y. LI ET AL. 1091

200

150

100

350

700

1050

The axial height/mm

/10-4T

Measured

value

Calculation

value

(a) Position I

500

400

300

200

100

0 0 100 200 300 400

Measured

value

Calculati o

value

The axial height/mm

By/10

-4

(b) Position II

Figure 3. Comparison of calculation value and measured

value of magnetic flux density at assigned position.

H(mm)

Loss density(W/m

)

L(mm)

Figure 4. Diagram of loss density distribution on surface of

yoke clamp.

H(mm)

Loss den sity(W/m

)

L(mm)

Figure 5. Diagram of loss density distribution on inner sur-

face of tank side wall.

corresponding position of A and C phase end winding,

and the maximum loss density appears in the lower

clamp; the loss in transformer tank was mainly concen-

trated in the tank side wall near C phase and tank wall

corresponding to the middle of the three-phase windings.

The H and L in diagram were respectively expressed the

length and height of the tank (or clamp). The length of

the tank side wall and clamp were 790mm and 3760mm,

and the heights were 2730mm and 535mm. The stray

loss and loss density of transformer tank and clamp were

shown in Table 2.

4.2. Calculation and Analysis of Loss by Adding

Magnetic Shields

The stray loss uneven distribution of transformer structure

parts can cause local overheating and affect the normal

performance of transformer, through adding magnetic

shields can reduce the stray loss.

Magnetic shields material with high permeability at-

tract the leakage magnetic field into the magnetic shields,

prevent leakage magnetic into tank and other structure

parts, thereby reduce the stray loss in the structure parts

of transformer. Transformer adding magnetic shields is

shown in Figure 1. Loss density of tank and clamp add-

ing shields was decline in Figure 6 and Figure 7, maxi-

mum loss still appear near clamp and tank side wall,

maximum loss density of clamp decreased by 43.1%

compared to non-magnetic shields, maximum loss den-

sity of tank decreased by 11.1%. The maximum stray

loss and loss density of transformer structure parts with

magnetic shields as shown in Table 3.

Table 2. Loss and Loss Density of Transformer Structure

Parts.

Component Tank Clamp

Loss density(W/m3) 1.8106 1.6



107

Eddy current loss(W) 9846.76 4720.4

Hysteresis loss (W) 3603.79 942.68

Total loss(W) 13 450.55 5663.08

Loss density(W/m

)

L(mm) H(mm)

Figure 6. Diagram of loss density distribution on surface of

yoke clamp with magnetic shields.

Y. LI ET AL.

1092

H(mm)

Loss den si ty(W/m

)

L(mm)

(

)

L(mm)

(

)

Figure 7. Diagram of loss density distribution on inner sur-

face of tank side wall with magnetic shields. Figure 9. Diagram of magnetic flux density distribution on

surface of yoke clamp without magnetic shields.

Table 3. Loss and Loss Density of Transformer

Structure Parts with Magnetic Shield.

ComponentTankCla mp

Loss density(W/m3)1.6



106 9.1



106

Eddy current loss (W)5708.37 2313.94

Hysteresis loss (W)2626.9 579.46

Total loss (W)8335.27 2893.4

1) The results get by 3D finite element analysis are

consistent with theoretical analysis, illustrate the validity

of the method.

2) Loss and the loss density in the local place of trans-

former structure parts can be reduced effectively by add-

ing magnetic shield. After adding magnetic shield to tank

and yoke clamp, the maximum stray loss and loss density

of tank are reduced by 38% and 11.1%, the maximum

stray loss and loss density of clamp are reduced by

48.9% and 43.1%.

4.3. Magnetic Shields Effect on Structure Parts

of Leakage Magnetic Field 3) The density of magnetic flux leakage into the clamp

is decreased obviously after adding magnetic shields.

The magnetic flux densities of clamp surface with and

without magnetic shields were shown in Figure 8 and

Figure 9. Magnetic shields provide a conduction path for

leakage magnetic of transformer interface winding. It can

be seen from the Figure, leakage magnetic flux density

significantly lower by adding magnetic shields.

REFERENCES

[1] M. Rizzo, A. Savini and J. Turowski, “Influence of Flux

Collectors on Stray Losses in Transformers,” IEEE

Transactions on Magnetics, Vol. 36, No. 4, 2000, pp.

1915-1918. doi:10.1109/20.877821

5. Conclusions [2] A. S. Reddy and M. Vijaykumar, “Hot Spot and Life

Evaluation of Power Transformer Design Using Finite

Element Method,” Journal of Theoretical and Applied

Information Technology, Vol. 4, No. 3, 2008, pp.

238-243.

In this paper, 3D finite element method is used to calcu-

late the stray loss of transformer structure parts, and the

conclusions are as follows: [3] N. Takahashi, T. Sakura and Z. Cheng, “Nonlinear

Analysis of Eddy Current and Hysteresis Losses of 3-D

Stray Field Loss Model Problem 21,” IEEE Transactions

on Magnetics, Vol. 37, No. 5, 2011, pp. 3672-3675.

doi:10.1109/20.952687

(

)

L(mm)

(

)

[4] K. Laurent, D. Patrick and Z. Tarek, “Homogenization of

Lamination Stacks in Linear Magneto Dynamics,” IEEE

Transactions on Magnetics, Vol. 40, No. 2, 2004, pp.

912-915. doi:10.1109/TMAG.2004.825435

[5] K. Hiroyuki, K. Akihisa and F. Koji, “FEM Computation

of Magnetic Field and Iron Loss in Laminated Iron Core

Using Homogenization Nethod,” IEEE Transactions on

Magnetics, Vol. 43, No. 4, 2007, pp. 1405-1408.

doi:10.1109/TMAG.2007.892429

Figure 8. Diagram of magnetic flux density distribution on

urface of yoke clamp with magnetic shields.