Magnetic Components in Electric Circuits

Understanding thermal behaviour and stress

Peter R. Wilson, University of Southampton

2School of Electronics and Computer Science, University of Southampton, UK

What are we trying to understand?

How are Magnetic Materials Affected by Temperature?

What is the impact on Magnetic Components?

How does this affect electric circuit behaviour?

-0.4-0.3-0.2-0.1

00.10.20.30.40.5

-150 -100 -50 0 50 100 150H (A/m)

B (T

)

T=27 T=95 T=154

3School of Electronics and Computer Science, University of Southampton, UK

Magnetic Material Characteristics

Ferrous Magnetic Materials exhibit hysteresis The magnetization of the material is partly reversible (no

loss) and partly irreversible (loss)

M

H

TotalMagnetization

(Stored Energy)

ReversibleMagnetization

Happlied

IrreversibleMagnetization(Lost Energy)

4School of Electronics and Computer Science, University of Southampton, UK

Energy Lost in Magnetic Materials

The Material will therefore dissipate energy as heat under heavy loading:

B (T)

H (At/m)

dB

BH CurveAnhysteretic Fn.

RecoveredEnergy

DissipatedEnergy

5School of Electronics and Computer Science, University of Southampton, UK

The effect of environmental Temperature?

How does the overall temperature of the material affect its behaviour? Eventually the Curie point is reached and the material

ceases to have any effective permeability

-0.4-0.3-0.2-0.1

00.10.20.30.40.5

-150 -100 -50 0 50 100 150H (A/m)

B (

T)

T=27 T=95 T=154

Data for a 3F3 Material, 10mm Toroid obtained by the author, measured using a Griffin-Grundy oven to control the temperature

6School of Electronics and Computer Science, University of Southampton, UK

Modeling Magnetic Materials

Modeling Magnetic Materials is particularly complex, with several choices Jiles Atherton, Preisach, Hodgdon, et al

The Jiles Atherton model is often used in circuit simulators:

+

+M

H e

M r e v

M i r r

M a n

H

a

aH

)/tanh(

1

c

c

1

H

c1

1

sM

)( MMk

MM

an

an

AHMM S /*0 B

7School of Electronics and Computer Science, University of Southampton, UK

Jiles Atherton Model

The results are particularly good at predicting the BH loop behaviour in ferrites, however the Preisach model is often better for “square” loop materials

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-150 -100 -50 0 50 100 150

H (At/m)

B (

T)

Measured Simulated

8School of Electronics and Computer Science, University of Southampton, UK

Building a Magnetic Component

To build a component (e.g. inductor) for electric circuits, we need both a core model and a winding:

MagneticDomain

ElectricalDomain

dt

dnv p

pp

F=

pppinmmf *=

pF

pi

CorecF

cmmf

9School of Electronics and Computer Science, University of Southampton, UK

Adding the Thermal Dependence

To add dynamic thermal behaviour, use a network to effectively model the thermal aspects of the material and the environment

Jiles-AthertonNon-LinearCore Model

H B

DefaultModelParameters

Modified ModelParameters

ThermalNetwork

T(°C)

Power

ParameterFunctions

WindingLossCurrent

Power

EddyCurrent

Loss

Power

10School of Electronics and Computer Science, University of Southampton, UK

Thermal Network Modeling

We have choices to make regarding the thermal network, in particular a distributed or lumped model In most cases a lumped model is perfectly adequate

Hysteresis+ Eddy Current

+ WindingPower Loss

Convection

Cth - Core

Tsurface

Tair

AmbientTemperature

Emission

11School of Electronics and Computer Science, University of Southampton, UK

Characterize the Magnetic Material

It is a relatively simple matter to characterize the magnetic material model by measuring its behaviour and calculating the resulting model parameters

Np

Ri

Ns

CH1

CH2

PowerAmplifier

DS345Signal

Generator

TektronixTDS220DigitalOscilloscope

Griffin-Grundy OvenRS 206-3750Temperature

Meter TN10 - 3F3

30.00

32.00

34.00

36.00

38.00

40.00

42.00

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0

Temperature (Degrees Celsius)A

(-)

A(Measured) A(Second Order Fit)

12School of Electronics and Computer Science, University of Southampton, UK

Building a Circuit Model…

Using the characterized thermally dependent model of the core, winding models and a thermal network, we can make the electric circuit model (in this case a transformer) dynamically affected by temperature

MMF

winding_th5

2

1 3

4

expja_th63

1 2

V127+

-

vp

I2

R310

MMF

emission

5

2

13

4

U2

R41k

winding_th

U1 U3

rconv

R11G ctherm

tair

tcore

1

2

2

1

1

2

PARAMETERS___Area 293uCth 0.07D 3.8e-3

PARAMETERS___C 700Dens 4750Vol 188n

U6

U4

U5

13School of Electronics and Computer Science, University of Southampton, UK

Results of Dynamic Thermal behaviour

At ambient Temperatures, the model behaves very closely to the measured data

-0.1-0.08-0.06-0.04-0.02

00.020.040.060.080.1

0 0.005 0.01 0.015 0.02 0.025

Time (s)

Vo

ltag

e (V

)

Measured Simulated

14School of Electronics and Computer Science, University of Southampton, UK

Results of Dynamic Thermal behaviour

At increased temperatures, the transformer output voltage drops due to reduced permeability

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.005 0.01 0.015 0.02 0.025

Time (s)

Vo

ltag

e (V

)

Measured Simulated

15School of Electronics and Computer Science, University of Southampton, UK

Dynamic Magnetic and thermal behaviour

The Flux Density decreases as the magnetic core temperature increases

-0.4-0.3-0.2-0.1

00.10.20.30.4

0 0.05 0.1 0.15 0.2

Time (s)

B (

T)

B

0

10

20

30

40

50

60

70

0 0.02 0.04 0.06 0.08 0.1

Time (s)

Co

re S

urf

ace

Tem

per

atu

re

(Deg

rees

C)

tcore

16School of Electronics and Computer Science, University of Southampton, UK

Conclusions

The magnetic material can be modelled to reflect not only the complex BH curve, but also its dependence on temperature

The temperature can be introduced dynamically to the magnetic material model

The component can be modelled using a thermal network to accurately predict the dynamic thermal behaviour

A complete electric circuit can be simulated that includes dynamic thermally dependent magnetic component and accurately predicts its behaviour

17School of Electronics and Computer Science, University of Southampton, UK

References

1. Wilson, P. R., Ross, J. N. and Brown, A. D. “Magnetic Material Model Optimization and Characterization Software”. In: Compumag, 2001

2. Wilson, P. R., Ross, J. N. and Brown, A. D. “Dynamic Electrical-Magnetic-Thermal Simulation of Magnetic Components”. In: IEEE Workshop on Computers in Power Electronics, COMPEL 2000

3. P.R. Wilson, J.N Ross & A.D. Brown, “Predicting total harmonic distortion in asymmetric digital subscriber line transformers by simulation”, IEEE Transactions on Magnetics, Vol. 40 , Issue: 3 , 2004, pp. 1542–1549

4. P.R. Wilson, J.N Ross & A.D. Brown, “Modeling frequency-dependent losses in ferrite cores”, IEEE Transactions on Magnetics ,Vol. 40 , No. 3 , 2004, pp. 1537–1541

5. P.R. Wilson, J.N Ross & A.D. Brown, “Magnetic Material Model Characterization and Optimization Software”, IEEE Transactions on Magnetics, Vol. 38, No. 2, Part 1, 2002, pp. 1049-1052

6. P.R. Wilson, J.N Ross & A.D. Brown, "Simulation of Magnetic Component Models in Electric Circuits including Dynamic Thermal Effects", IEEE Transactions on Power Electronics, Vol. 17, No. 1, 2002, pp. 55-65

7. P.R. Wilson & J.N Ross, "Definition and Application of Magnetic Material Metrics in Modeling and Optimization", IEEE Transactions on Magnetics, Vol. 37, No. 5, 2001, pp. 3774-3780

8. P.R. Wilson, J.N Ross & A.D. Brown, "Optimizing the Jiles-Atherton model of hysteresis using a Genetic Algorithm", IEEE Transactions on Magnetics, Vol. 37, No. 2, 2001, pp. 989-993