analysis of thermal behavior of high frequency transformers using finite element method

8/3/2019 Analysis of Thermal Behavior of High Frequency Transformers Using Finite Element Method

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J. Electromagnetic Analysis & Applications, 2010, 2, 627-632doi:10.4236/jemaa.2010.211082 Published Online November 2010 (http://www.scirp.org/journal/jemaa)

Copyright 2010 SciRes. JEMAA

Analysis of Thermal Behavior of High Frequency

Transformers Using Finite Element MethodHossein Babaie, Hassan Feshki Farahani

Ashtian Branch, Islamic Azad University, Tehran, Iran.Email: {hbabaei2002, hfeshki}@yahoo.com

Received August 15th, 2010; revised September 17th, 2010; accepted September 20th, 2010.

ABSTRACT

High frequency transformer is used in many applications among the Switch Mode Power Supply (SMPS), high voltagepulse power and etc can be mentioned. Regarding that the core of these transformers is often the ferrite core; their

functions partly depend on this core characteristic. One of the characteristics of the ferrite core is thermal behaviorthat should be paid attention to because it affects the transformer function and causes heat generation. In this paper, atypical high frequency transformer with ferrite core is designed and simulated in ANSYS software. Temperature risedue to winding current(Joule-heat) is considered as heat generation source for thermal behavior analysis of the trans-former. In this simulation, the temperature rise and heat distribution are studied and the effects of parameters such asflux density, winding loss value, using a fan to cool the winding and core and thermal conductivity are investigated.

Keywords: High Frequency Transformers, Thermal Behavior, Ferrite Core and Finite Element Analysis

1. Introduction

Magnetic components design plays a key role in achiev-ing high efficiency, low volume and reasonable price of

power electronic equipment. With the advent of higherswitching frequencies and power densities in power elec-tronic circuits, it is important to ensure that magneticcomponents, such as transformers and inductors, operatewithin the limits defined by the thermal specifications ofthe circuit. Temperature rise depends on the power lossesthrough the laws of the heat transfer theory. In order toobtain an accurate value of the maximum temperature ofthe device during the design process, it is necessary toapply an accurate thermal model. It is necessary of atrade-off between thermal distribution accuracy (direc-tions through heat transfer is considered, constant ther-mal properties, feedback with the magnetic model,steady state models, etc) and the complexity of the ther-mal model that is obtained.

Losses in the magnetic components are important designparameters. In many high-frequency designs, magnets arelimited by their losses. Thus, it is extremely important forthe designer to have a good practical model for estimatingthe losses under various excitations that are frequently en-countered in power electronics design. There are two majorcomponents of the losses [1-9] in a magnetic component:the core loss (i.e., the losses in the magnetic material whichis used as core) and the winding losses. High-frequency

conductor losses for power electronics applications havebeen considered by a number of authors [8,9]. There aremodels provided by different manufacturers [10-12], that

are synthesized in a simple expression for the calculation ofthe temperature rise. They provide the average temperaturein the outer surface of the device.

Most of thermal models for magnetic components areanalytical and assume 1D heat transfer [13-15]. Thesemodels are based on thermal networks and commonlyconsider only steady state, constant thermal properties,concentrated and uniform power losses and no thermalfeedback with the electric properties. However, the ther-mal distribution is 2D/3D for most of cases, even if themagnetic field exhibits a 1D distribution.

The thermal design is usually somewhat neglected asit is often not clear which theory and coefficients should

be used and experiments are time consuming. In thisarticle, by designing a typical high-frequency trans-former with ferrite core, its thermal behavior is investi-gated. Many parameters such as flux density, windingloss value, using a fan to cool the winding and core andthermal conductivity have effects on the ferrite tempera-ture which is simulated with ANSYS software.

2. Calculating the Heat Generation Causedby Winding and Investigating ItsEffective Parameters

Heat generating sources are transformer windings which
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Analysis of Thermal Behavior of High Frequency Transformers Using Finite Element Method628

generate heat by passing the current and this heat is

transmitted to other parts. For a winding with resistance

Rj, the power loss can be written as:

2

,cu j j jP I R (1)

Which the jth winding resistance is as follow:

,

j

j

w j

lR

A (2)

Where:

j jl n MLT (3)

,

A u j

w j

j

W KA

n

(4)

In Equation (3), MLT is mean length per turn (cm). By

considering Equation (2) to Equation (4), the power loss

of jth winding is as follow:

2 2

,

j j

cu j

A u j

n i MLT P

W K

(5)

And the total power dissipation is the sum of the power

losses for each winding:

2 2,

1

kj

cu tot jA u j

n IMLTP

W K

(6)

The loss in winding is optimal providing that [16]:

, 1

k

cu tot j jjA u

MLT

P W K

n I (7)

According to Equation (7), it can be found out that the

power loss or generated heat depends on parameters such

as (wire effective resistivity), Ku (winding fill factor),

turns, winding current and MLT (mean length per turn).

So, these are effective parameters on generation heat

source. In a transformer, if the primary voltage is like

Figure 1, then the following equations will be written:

2

11 1

t

tv t dt (8)

1

max 11 m2 2c cB n

n A B A

1

ax

(9)

By substituting Equation (9) in Equation (7), the result

can be written as:

2 2 22 11 2 2

1tot totcu

A u u A c max

A B C

MLT I MLT IP n

W K k W A B

(10)

where:

1 1

kj

tot jj

nI I

n

Area 1

t1 t2

Vg

-Vg

0 0

v1(t)

Figure 1. Transformer primary voltage.

Equation A i

lectrical ore and

(10) consists of three parts in which part

characteristics and B and C include c

s

e

magnetic characteristics respectively.

The core loss is obtained from the following equation:

e fe max c mP k B A l (12)

Kfefrequencies. Ac is core cross-section

agnet

and its effec-

tiv rmer for full bridge con-

is core loss coefficient which is different for variousal area and lm is

m ic path length. The typical value of for ferritecore is 2.6 < < 2.8. Kfe is drastically increased by in-creasing the frequency. In addition, Kfe depends on coretemperature and Bmax. The dependency of Kfe on fre-quency, Bmax and temperature can be obtained from corecharacteristics. In choosing the core when combined withdifferent alloys, there has been always trade-off betweensaturated magnetic flux density and the core loss. Usingmaterials with high Bsat leads to volume, size and pricereduction. But these materials cause more core loss.

3. Transformer Characteristic forFull-Bridge Converter

To study the temperature rise in ferrite core

e parameters, a sample transfo

verter with two secondary windings and one primary

winding is chosen which can be seen in Figure 2 [16].

Figure 2. Transformer for full bridge converter with two

outputs and one input.(11)



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Analysis of Thermal Behavior of High Frequency Transformers Using Finite Element Method 629

Table 1. Parameters of designed transformer for full bridge

converter

75kHzTransformer frequency

110 :5 :15ratioTurn

0.75Duty cycleEE40

Selected core

/T cm3

410 -cm

-sec

x

0 mW

7.6 Wkfe

2.6

0.25-6

Ku

1.72

800 V1

5.7 AI1

66.1 AI2

9.9AI3

14.4 AItot

80 mTBma

22n1

1n2

3n3

23Pfe

3.89 WPcu

4.12 WPtot

The ined parameters for th mer are listed

in ble 1. The core and winding losses calculated for

tra

indings isFigure 3.

in Table 2.

that the heat transfer be-

the transformer has been

obta is transfor

Ta

nsformer are equal to 230 mW and 3.89 W respectively.

These losses can be used as heat generating source in

modeling and simulating the transformer in ANSYS.

4. Transformer Modeling in ANSYS

In this part, transformer with two secondary wmodeled in ANSYS software which is shown in

The distance between each winding is 0.5 mm. the pri-

mary winding is 20 mm long and 2 mm wide which this

cross-sectional area includes 22 turns primary winding.

This area for secondary winding is 20 mm2 (1 mm 20

mm) which is for one turn. Also, another secondary

winding is 20mm long and 0.5mm wide which consists of

three turns.

The electrical and thermal characteristics for different

parts of transformer are listed

5. Simulation Results

In this simulation, it is assumed

tween winding and core of

naturally done (natural convection). So, the film coeffi-

cient varies from 10 W/m2C to 25 W/m2C when there

is natural convection. The film coefficient is considered

equal to 10 W/m2C. The total cross-section of area is 70

mm2 and the power dissipation in this area is 3.89W.

Therefore, the value of watt per square meter of area is

equal to 55570 W/m2 which is used for heat generation

source in ANSYS. In Figure 4, temperature distribution

CoreWinding

Air

Air

Figure 3. Modeled transformer in ANSYS.

Table.2 ifferent

arts of transformer

Electrical and thermal characteristics for d

p

MaterialParameter

AirFerrite CoreCopper

1.098900Density, 3] 8900 [kg/m

1006750387Specif kgC]

T ,

ic heat, c [J/

0.0270.004385hermal conductivity

[W/(mK)]

Figure 4. Thermal distribution in transformer.

throug ottest

oint is primary winding and middle leg of ferrite core

h the transformer is shown. In this figure, the h

p

which is about 61.962C. By paying attention to this fig-

ure, it is clear that the core corners have lower tempera-

ture in comparison with other parts. It should be noticed

that in this case, the secondary windings temperature are

lower than that in primary one. The heat distribution in

ferrite core is shown in Figure 5.



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Analysis of Thermal Behavior of High Frequency Transformers Using Finite Element Method630

Figure 5. Thermal distribution in core.

Therma and it is

m ized in primary winding corners which are about

42

ity variation on tem-

has been investigated.

. In

l flux in this case is shown in Figure 6

axim

8.69 W/m2. Regarding this matter and according to

Figure 4, it can be pointed out that the corners tempera-

tures are lower than that in other parts.

5.1. Variation of Flux Density

In this part, the effect of flux dens

perature distribution in transformer

For this purpose, the flux density is decreased from 80 mT

to 120 mT. According to Equation (10), the power loss is

in inverse proportion with the square of flux density and

by this change, the power loss is decreased 2.25 times.

The heat distribution for this condition is shown in

Figure 7 in which the hottest point is about 55.309C

Figure 7. Thermal distribution in transformer (Decreasin

is case, one of the secondary windings temperatures

sed in

gure 4 with Figure 8, we can maketh

2C to 120

the fan, almost all windings have the same

te

g a Fan to Cool the Core

cooled by a fan

to this figure, the core ambient temperature is almost

g

flux density).

th

(neighbor of primary winding) is approximately equal to

primary winding temperature (the highest temperature).

5.2. Variation of the Ambient Temperature

In this case, it is supposed that the transformer is u

40C temperature. So, it is observed that the maximum

temperature inside the transformer has been slightly in-

creased and has reached to 61.971C. In this case, the

maximum temperature is in primary winding and core

middle leg as well.

By comparing Fie conclusion that regarding the proximity of core sides

to heat source and warmer environment, the sides tem-

perature are higher than that in up and down of core.

5.3. Using a Fan to Cool the Winding

The film coefficient varies from 50 W/m

W/m2C when there is forced convection. For this case

the film coefficient has been changed from 10 W/m2C

to 50 W/m2C. The temperature distribution is shown in

Figure 9.

By using

mperature of 52.508C. By comparing this figure with

Figure 4, it can be understood that using the fan leads to

winding temperature reduction from 61.962C to

52.508C. By this analysis, the appropriate fan can be

chosen.

5.4. Usin

In this case, it is supposed that core is

(the film coefficient is 50 W/m2.C). The heat distribu-

tion in this condition is plotted in Figure 10. According

Figure 6. Thermal flux in transformer.



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Analysis of Thermal Behavior of High Frequency Transformers Using Finite Element Method 631

Figure 8. Thermal distribution in transformer (Increas ng

the ambient temperature).

i

Figure 9. Thermal distribution in transformer (Using fan to

cool the winding).

shows that changing the film coeffi-

ient causes suitable increase in core temperature

nductivity

W/(m.K).

ffect (61.95C) on the temperature but the ther-

m

ermal behavior of different cores has

his purpose, first for a typical trans-

equal. This figure

c

(61.95C).

5.5. Variation of Thermal Conductivity

On of the other studied parameters is thermal co

that it is changed from 0.004 W/(mK) to 0.008Thermal distribution for this mode is shown in Figure

11.

This figure shows that the thermal conductivity has a

little e

aldistribution around the transformer is uniform as a

circle from centre of transformer.

6. Conclusions

In this paper, the th

been studied. For t

Figure 10. Thermal distribution in transformer (Using fan to

cool the core).

Figure 11. Thermal distribution in transformer (Increasing

thermal conductivity).

heat is computed then it is totally

imulated in ANSYS software. In this simulation, the

s-

fo

former, the generation

s

thermal analysis and heat distribution were studied. Then,

the effects of parameters such as flux density, winding

loss value, the film coefficient have been investigated.

According to obtained results, in case of using a fan tocool the winding, the maximum temperature of tran

rmer has been decreased. Furthermore, it was shown

that by decreasing the flux density, the temperature of

the hottest point in transformer has been decreased which

is due to the power loss reduction in windings. Moreover,

it is explained in the paper that the core temperature can

be controlled by increasing the film coefficient (by using

a fan). As a result, with the findings of this analysis, an

appropriate fan can be chosen in order to cool the whole

transformer. In the paper, it is also elaborated that the



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Analysis of Thermal Behavior of High Frequency Transformers Using Finite Element Method


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rromagnetic Materi-

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EE

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/n1, n3/n1, etc

ion (W)

t (W/cm3T)

area (cm2

)

core corners have the lower temperature in comparison

with other parts. This part has the maximum thermal flux

as well.

r and J. R. Bailey, Hys,IEEE Transactions o

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Nomenclature

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tot

n2 Desired turns ratios (V-sec)

1

P

Applied primary volt-sec

tot

K

Allowed total power dissipat

u

Winding fill factor

Core loss exponent

K fe

A

Core loss coefficien

c

W

Core cross-sectional )

Core window area (cm2)A

MLT

l

Mean length per turn (cm)

e

A 1, Magnetic path length (cm

w

B

Wire areas (cm2)

Peak ac flux density (T)
http://www.amazon.com/Robert-W.-Erickson/e/B001HOFSRI/ref=sr_ntt_srch_lnk_1?_encoding=UTF8&qid=1278960647&sr=1-1http://www.amazon.com/Robert-W.-Erickson/e/B001HOFSRI/ref=sr_ntt_srch_lnk_1?_encoding=UTF8&qid=1278960647&sr=1-1

analysis of thermal behavior of high frequency transformers using finite element method

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