PARAMETRIC MODEL OF AN PARAMETRIC MODEL OF AN AIR-CORE MEASURING TRANSFORMERTRANSFORMER

DEJANA HERCEGFACULTY OF TECHNICAL SCIENCES

N S O NO SA S AUNIVERSITY OF NOVI SAD, SERBIA

COMSOL Conference 2010 Paris

Presented at the COMSOL Conference 2010 Paris

Introduction

determining power qualityin power distributionsystems

harmonic distortion in thevoltage and currentwaveforms

measurements of suchvoltage with harmonics

new developed instrument the input unit: the input unit:

small air-core transformer base probe

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Air-core transformer base probe p

Non-sinusoidal measured voltage on primary coil: Non sinusoidal measured voltage on primary coil:

n - number of harmonics; f - frequency (50-2.5kHz) Induced voltage on secondary coil:

Transformer ratio should be constant for all freq.

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External EM fields and shieldingg

The goal of this work is to design a feromagnetic The goal of this work is to design a feromagneticshield around the probe in order to protect it from the impact of external magnetic field. p g Optimize the shield shape to cancel the impact of

external magnetic field as much as possible (shielding effectiveness was investigated)

Minimize the influence of the shield shape on the f b dtransformer probe reading

(transformer linearity coefficient was investigated)

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Shield shapes

The probe was centered inside different types of

p

The probe was centered inside different types of ferromagnetic shields

Shape, size, thickness, material properties (, )5/22

Modeling - COMSOL Multiphysics 3.5a g p y

Application Mode:pp Axial symmetry 2D AC/DC Module Quasi-Statics, Magnetic Azimuthal Induction Currents, Mag. Vector Potential Time-harmonic analysis

20

1r Aj A J

Subdomain Integration Variable (secondary coil)

0 r

N2 22

2

4 NEMF U j f r AA

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Parametric model approachpp

Several ways to create a parametric model can be Several ways to create a parametric model can be employed geometric parametric sweeps option in COMSOL

Multiphysics v3.5a, in connections with a specialized CAD software, such as SolidWorks and AutoDesk Inventor,

moving mesh (ALE model) moving mesh (ALE model) programming in MATLAB.

The last approach was chosen as it allows varying The last approach was chosen as it allows varying geometric dimensions without changing the model topology in numerical simulations.

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Connection with MATLAB

Creating Creating parametric model

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Geometry modelingy g

Using COMSOL GUI or MATLABg Basic geometry objects: rect2, circ2, curve2… geometry

functions: geomcomp, geomcsg, …

Analyze and update the geometry data by using geomanalyze (e g moving objects)geomanalyze (e.g. moving objects)

If the indexing of subdomains stays constant while the If the indexing of subdomains stays constant while the values of geometry parameters are changing, then geomanalyze is not needed.

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Creating the meshg

The number of mesh elements will be changed inside The number of mesh elements will be changed inside the loop, depending on the skin depth and the thickness of shield.

Element size of the shield subdomain is related to the skin depth of the ferromagnetic material of shield p g

The skin depth is about 7 times smaller for the 50th

harmonic than for the fundamental frequency at 50Hz.

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External magnetic field in simulationsg

Standard CEI EN 61000-4-8: circular or square coil testing area can be up to 60% the of the coil diameter up to 3dB inhomogenity of magnetic field

In simulations: magnetic field strength magnetic field strength

100A/m (5. level) Diameter 1m Inside the testing area (less than 10% of the diameter), the

amplitude of time harmonic magnetic field is changed not more than 5%.

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When the external magnetic field (50Hz) is present, the magnetic field inside the shielded probe is approx. 20A/m (5 times less than without the shield)(5 times less than without the shield)

without shield with shield

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without shield with shield (R=28.5mm, H=2R, d=0.5mm)

Reduced potentialp

Magnetic vector potential Magnetic vector potential

Reduced potential Circular coil

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Reduced potential Circular coil

The shielding effectiveness and th t f li it ffi i t the transformer linearity coefficient

The shielding effectiveness is defined as a ratio of The shielding effectiveness is defined as a ratio of the two magnetic flux densities, without and with the shield present.p

The transformer linearity coefficient was defined as

(unshielded case 0.1553 mV/Hz) The normalized transformer linearity coefficient is

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Shielding efficiency as a function of H/R ratio for different shield shapes (thickness of shield 0 5mm)

 5.5

6.0 R [mm]

28.5

shapes (thickness of shield 0.5mm)

4.5

5.0

28.5

38

57

3.5

4.0S e

57

85.5

sphere 38mm

2 5

3.0

3.5 sphere 38mm

sphere 57mm

ellipsoid v

2.0

2.5

0 1 2 3 4

ellipsoid v

ellipsoid h

H/R

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Normalized coefficient kN in function of H/R ratio for different shield shapes (same thickness 0 5mm and r 550 for all shields)

1.25 R [mm]

28.5

shapes (same thickness 0.5mm and r 550 for all shields)

1 15

1.2028.5

38

57

1.10

1.15

k N

57

85.5

sphere 38mm

1.05

sphere 38mm

sphere 57mm

ellipsoid v

1.000 1 2 3 4

ellipsoid v

ellipsoid h

H/R

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Distribution of magnetic flux density along the shield due to external time harmonic magnetic field at 50Hz (thickness of the shields 0 5mm and 5mm)(thickness of the shields 0.5mm and 5mm)

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Impact of external magnetic field is expressed by the transformer linearity coefficient as a function of magnetic field frequency

-2

00 500 1000 1500 2000 2500

6

-4

2

V/H

z]

unshielded

-8

-6

freq

) [m

V

shielded d=0.5mmshielded d=5mm

-12

-10

log(

emf/

-16

-14

6freq[Hz]

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Shield shape influence on transformer linearity coefficient as function of frequency of input signal on primary winding

0.1620

0.1630unshieldedshielded d=0.5mm

0 1590

0.1600

0.1610

mV

/Hz] shielded d=5mm

0 1570

0.1580

0.1590

f/fre

q [m

0 1550

0.1560

0.1570

emf

0.1540

0.1550

0 500 1000 1500 2000 25000 500 1000 1500 2000 2500freq [Hz]

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Conclusion

COMSOL Multiphysics is a very useful FEM COMSOL Multiphysics is a very useful FEM based tool for a wide range of applications.

The parameterized probe model was created p pand used for a large number of simulations in order to find appropriate solution of this particular task.

Parametrizing the models can be complicated. From the discussed range of the shields, the

spherical shields performed best, as expected f th from theory.

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Conclusion

However without COMSOL it would be However, without COMSOL it would be impossible to conclude what shield shapes and sizes are most appropriate. sizes are most appropriate.

A cylinder of particular dimensions can be a sufficiently good solution sufficiently good solution.

Future work will employ an optimization technique together with an appropriate fitness technique together with an appropriate fitness function introduced into COMSOL and used for the optimum searchthe optimum search.

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Acknowledgementg

This paper is a part of the two projects no. 11024 This paper is a part of the two projects no. 11024 and 18043, supported by the Ministry of Science and Technological Development, Republic of Serbia. g p , pThe author is also grateful to DAAD and TU Ilmenayfor the continuing support.

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