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International Electrical Engineering Journal (IEEJ) Vol. 5 (2014) No.8, pp. 1519-1525

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International Electrical Engineering Journal (IEEJ) Vol. 5 (2014) No.8, pp. 1519-1525
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.8, pp. 1519-1525
ISSN 2078-2365
http://www.ieejournal.com/
Frequency Response Analysis for New
Magnetic Power Transformer Composite
Crystalline Core
O. E. Gouda1, A. Thabet2
Faculty of Engineering, Cairo University
2
Faculty of Energy Engineering, Aswan University
1
[email protected]
2
[email protected]
1
Abstract---Characterization of composite materials is an
important topic in modern electromagnetics, thus, suggested
new microstructure electromagnetics materials that will be
enable to realize enhancing the electromagnetic properties of
transformer core and its characterization has been studied in
this paper. This paper also presents a theoretical analysis to
study the effective permeability prediction of the suggested
magnetic composite materials with adding various types and
percentages of particles (Fe, Silicon steels, Metglas, Co-Fe, NiFe, MnZn, MgZn, NiZn) for formulating new magnetic
composite transformer core materials. Theoretical analysis is
introduced to study the influence of inclusion types and their
concentration on the permeability. Numerical results show that
significant aberration of inclusion types and their
concentration on the effective permeability with respect to
conventional magnetic materials. Frequency Response Analysis
(FRA) is used to investigate transformer core magnetic
composites and specifying enhancing magnetic effective
complex relative permeability of transformer core magnetic
composites with respect to variant frequencies (10-2Hz –
103Hz).
Index
Terms—
Magnetic
Composites,
Transformer Core, Permeability, Magnetism.
I.
Particles,
INTRODUCTION
Nowadays, computer modeling and simulations of
electromagnetic processes in power transformers have
become a popular method for analyzing their performance
and defining ways for design improvements. The
characterization and the study of artificial materials is an
important topic in modern electromagnetics. The properly
designed micro-structured materials may enable the
realization of compact resonators, and the formation of
transformer equivalent circuits [1-4]. The main goal of
material science is developing new magnetic composite
industrial materials. Thus, it is concluded that Mn-Zn
ferrites present high permeability and permittivity
simultaneously within the frequency range of kHz through
MHz [5-11]. Also, it is established that Silicon steel is the
most popular soft magnetic material in the electric power
industry as the core material of electrical machines. Grainoriented silicon steel is mainly used in manufacturing of
transformer cores, which provides the required magnetic
anisotropy and lowest losses when magnetized in the rolling
direction [12, 13]. In order to estimate the effective material
parameters of the composite materials and mixtures so far
Maxwell–Garnett and Bruggeman formulas are introduced
[14-18].
Recently, frequency response analysis (FRA) has been
recognized as the most reliable monitoring technique for
transformer winding displacement and deformation
assessment. It is established upon the fact that the shape of a
winding frequency response at high frequencies is
associated with winding geometry. The appearance of clear
shifts in resonance frequencies or new resonant points on a
response may characterize faulty conditions of windings
[19, 20]. Fig 1 shows the Frequency Response Analysis
(FRA) spectral regions and the associated dominant parts of
the transformer. Research activities have been undertaken to
utilize FRA in the development of suitable lumped
parameter mathematical models of transformer windings
[21-25].This method is especially useful when the quantities
of interest cannot be measured directly. Such situations
appear, for example, when evaluating inductances of
transformer windings at their first resonance frequencies,
which are necessary for interpretation of FRA data [26, 27].
1519
Gouda and Thabet
Frequency Response Analysis for New Magnetic Power Transformer Composite Crystalline Core
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.8, pp. 1519-1525
ISSN 2078-2365
http://www.ieejournal.com/
The new developed materials become particularly
important because its physical properties change
dramatically with the size and with the local structure of the
grains. One important application is considered for
transformer core materials, these materials should be of low
cost and easy to prepare, allowing them to be highly
competitive with the conventional existing ones. With
respect to soft magnetic materials that play an important role
in broad applications, such as transformers. These materials
are used in electromagnetic applications, can be described as
ferromagnetic powder particles surrounded by an electrical
insulating film [28-31]. The objective of this work is to
characterize magnetic behavior of power transformer
composite crystalline core using frequency response
analysis which has become increasingly popular for the
assessment of mechanical integrity in power transformers.
FRA technique is made of the fact that the shape of the
response at higher frequencies is uniquely determined by the
geometrical construction of the transformer.
Therefore, new magnetic composite transformer core
materials have been suggested for enhancing power
transformer magnetic characterization response related to
types and concentrations of selected particles. Numerical
results predict that power transformer core characterization
results in difference between conventional types than those
using variant types of particles in cores. This is will be good
agreement with experimental results. Therefore, many
microparticle composites with different particles are
investigated to reach the best fillers significantly increase of
magnetic permeability.
II.
ANALYTICAL MODEL
This paper focuses on calculation techniques for the
effective permeability of magnetic composite transformer
core materials consisting of micron/submicron-sized
particles embedded in different matrices. So that, based on
the previous analytical models [14, 18] have been used to
formulate theoretical models for predicting the effective
permeability of magnetic composite materials. With respect
to Maxwell-Garnett formula that plays an important role in
two dimensions composite materials [14], the effective
permeability for random distribution of particle size as two
dimensions spherical shapes significantly is given as
follows:
 =  + 2
 −
 + −( −)
(1)
Where,
µi is permeability of inclusions in the composites,
µm is permeability of main matrix of the composites,
φ is the volume fraction of inclusions inside the main
matrix.
For more accurate approach it is assumed that
estimation of the magnetic composite material structure to
be periodic, and the unit cell, which is the minimum volume,
is regarded as homogeneous magnetic substances [18]. The
effective permeability of magnetic composite materials is
defined on the basis of magnetic energy balance in the unit
cell, and it is assumed, in this approach, that the original cell
and the homogenized cell include equivalent magnetic
energy when both unit cells are immersed in equivalent
magnetic field as shown in Fig. 2.
Thus, this method has possibility to apply to any
structure as follows:
 =
.
|ℎ .|
∫
ℎ
.
 . 
∫
ℎ
(2)
Where,
Shomo is the square of the original cell, Bhomo is the magnetic
flux density, and Horig is the magnetic field.
Fig. 1 FRA Spectral Regions and Associated Dominant Parts of
Transformer
1520
Gouda and Thabet
Frequency Response Analysis for New Magnetic Power Transformer Composite Crystalline Core
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.8, pp. 1519-1525
ISSN 2078-2365
http://www.ieejournal.com/
Phase A
Phase B
Phase C
(a) Schematic Diagram of Three-Limb Transformer
Φ
RA
Fig. 2 Homogenization of composite material
FA
Schematic diagram and the equivalent magnetic circuit of
the transformer core model [20] are established as shown in
Fig. 3. The magnetic core of the transformer is divided into
three sections with respect to uniform fluxes φA, φB, and
φCof each transformer limb. Each section of the magnetic
core is represented by its reluctance Re, the reluctance of a
section is determined by the magnetic parameters of
lamination and the core geometry as follows [3, 4]:
 =

∅
=

(3)
  
Where, F is the magneto-motive force that required for
establishing the flux along the length of the section. ϕ is
produced magnetic flux. l is the length of the magnetic flux
path a long each section. A is the cross section area of the
core, μcoreeff is complex effective relative permeability of
transformer core, and µo is the free space permeability.
Therefore, the effective local magnetic permeability of
suggested magnetic composite transformer core materials
can be predicted by using the above approaches based on
inclusions permeability, weight percentages of inclusions
inside the matrix and main matrix permeability of magnetic
transformer core composite materials. Thus, the complex
effective relative permeability of transformer core is defined
as follows:
′
′′
 = 
− 


=  
ℎ((1+)⁄ )
((1+)⁄ )
C
RB
1
Φ
RC
B
2
(b) Equivalent Magnetic Circuit
Fig.3 Schematic Diagram and Equivalent Magnetic Circuit For Three-Limb
Transformer Core
Where, δ is the skin depth, kfe=2b/h represents the
stacking factor, h and 2b are the thicknesses of a single
lamination sheet of the core with and without insulation
layer included respectively, and µr is the local magnetic
permeability. The skin depth δ depends on the angular
frequency ω of the magnetic field as follows:
 = √2⁄ 
(5)
Where, σ is the conductivity of lamination materials,
whatever, using composite crystalline materials for
transformer core laminations required deterministic the
effective conductivity [32, 33].However, in this paper, the
influence of types and concentration of inclusions particles
on the performance of effective permeability of magnetic
composite power transformer core is investigated.
III.
(4)
Φ
A
SELECTED PARTICLES AND MAGNETIC INDUSTRIAL
MATERIALS
Nowadays, nanotechnology science can be made huge
enhancement in the magnetic properties of transformer core
materials, then; the choice of magnetic composite material is
complex and depends on many factors, the primary ones
being frequency, the size of the component, the physical
1521
Gouda and Thabet
Frequency Response Analysis for New Magnetic Power Transformer Composite Crystalline Core
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.8, pp. 1519-1525
ISSN 2078-2365
http://www.ieejournal.com/
Table. I Permeability and Resistivity of Suggested Transformer Core
Materials
Materials
µr
Metglas
106
ρ (Ω.m)
142x10-8
Fe (High Purity)
105
10x10-8
Silicon Steels
104
45x10-8
MnZn_Ferrite
5000
1
MgZn_Ferrite
800
0.5
IV.
RESULTS AND DISCUSSIONS
Magnetic transformer core can enormously concentrates
the strength and increases the effect of magnetic fields
produced by electric currents and permanent magnets. The
effect of core laminations is to confine eddy currents to
highly elliptical paths that enclose little flux, and so reduce
their magnitude, the; thin core laminations are generally
used on high-frequency transformers, with some of very thin
steel laminations able to operate up to 10 kHz. In practice,
the parameters of core transformer, such as dimension of
winding, core lamination…etc. is usually determined using a
lamination sample [26, 27]. The following are results of
study carried out on the complex effective relative
permeability and reluctance of the new transformer core
composite magnetic materials that have been suggested for
enhancing the magnetic characterization response with
respect to types and concentrations of selected particles.
A. Magnetic Characterization of Cost-fewer
Composites Materials
Using analytical model described above by MATLAB
program for the simulation of the transformer core model
composites materials has been investigated to study the
characterization of effective permeability of the composites
with various types and concentrations to obtain cost-fewer
composite materials. The results will be verified the ability
of the suggested composites to modify the core lamination
parameters with respect to the reference values. With respect
to the growing interest in investigating high-frequency
phenomena in transformers, this paper presents suggested
composites for parameter identification of a laminated core
of power transformers based on reference frequency
response analysis. Fig4 shows complex effective relative
permeability of various magnetic composites by various
percentages of iron, Metglas, Silicon steels, and Ferrite
MgZn particles randomly distributed, then; Fig. 4 shows
enhancing effective complex relative permeability of
magnetic composite materials that requires adding magnetic
particles have higher permeability than the base matrix and
via.
1.2
Effective Composite Relative
Material Permeability* 106
strength and the magnetic properties. Thus, the suggested
particles size like Iron high purity particles (single crystals
in preferred directions), Silicon steels, Metglas, Co-Fe, NiFe, MgZn_Ferrite, and NiZn_Ferrite have been depicted the
enhancement in performance of transformer core magnetic
properties. Table I depicts the main electrical description
properties of usage of particles which have been used for
enhancing magnetic properties of transformer core
materials.
Iron + Silicon steels
Iron + Metglas
Silicon steels + Metglass
Iron + Ferrite MgZn
1
0.8
0.6
0.4
0.2
0
0
0.5
Volume fraction
1
Fig. 4 Effective Complex Relative Permeability With various Volume
Fractions of Soft Magnetic Particles
Noting that, type of particles has the main factor for
specifying performance of the effective permeability of the
composites as shown in Fig. 4.Metglas particles are
effective particles for enhancing effective permeability of
the composites, whatever; MgZn, and Silicon steels particles
have bad effect effective permeability of the composites.
B. FRA for Cost-fewer Transformer Core Magnetic
Composites
Fig. 5 shows effective complex relative permeability of
various transformer core magnetic composites that has been
varied by adding certain distribution percentage (30%wt) of
Metglas, Silicon steels, Ferrite MnZn, and Ferrite MgZn
particles to iron base matrix. Frequency response analysis
(FRA) of cost-fewer transformer core magnetic composites
has been investigated (10-2Hz – 103Hz) for specifying
enhancing magnetic effective complex relative permeability
of transformer core magnetic composites depends on higher
permeability of magnetic particles the base matrix and via.
1522
Gouda and Thabet
Frequency Response Analysis for New Magnetic Power Transformer Composite Crystalline Core
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.8, pp. 1519-1525
ISSN 2078-2365
http://www.ieejournal.com/
Iron + 30%wt Silicon steels
Iron + 30%wt Metglas
Iron + 30%wt Ferrite_MnZn
Iron + 30%wtFerrite_MgZn
60000
40000
6
0.1
10
Frequency (Hz)
1000
Fig. 5 FRA for effective complex transformer core relative permeability
with various magnetic particles
50000
40000
30000
Iron + 10%wt Ferrite_MgZn
Iron + 30%wt Ferrite_MgZn
Iron + 50%wt Ferrite_MgZn
Iron + 70%wt Ferrite_MgZn
Iron + 90%wt Ferrite_MgZn
Reluctance*106 (A/Wb)
20000
0
0.001
Effective Complex Transformer Core
Relative Permeability
Transformer core reluctance of cost-fewer magnetic
composites has been investigated (10-2Hz – 103Hz)with
respect to varying types at certain concentration of magnetic
particles as shown in Fig. 7. It illustrates the reluctance of
various transformer core magnetic composites that has been
varied by adding certain percentage (30%wt) of Metglas,
Silicon steels, Ferrite MnZn, and Ferrite MgZn particles
randomly distributions to iron base matrix.
Iron + 30%wt Silicon steels
Iron + 30%wt Metglas
Iron + 30%wt Ferrite_MnZn
Iron + 30%wtFerrite_MgZn
2
0.1
10
Frequency (Hz)
1000
Fig. 7 Reluctance of transformer core with various magnetic particles
6
20000
10000
0
0.001
4
0
0.001
0.1
10
Frequency (Hz)
1000
Fig. 6 FRA for effective complex transformer core relative permeability
with various percentages of Ferrite_MgZn particles
Fig 6 shows performance of effective complex
transformer core relative permeability with various volume
fractions of Ferrite_MgZn particles randomly scattered in
iron matrix material. Whatever, the obtained results are in
close with that obtained by [32, 33]. Also, Fig. 6 shows that
by adding between 10%wt to 30%wt of Ferrite_MgZn by
weight to iron increases the effective complex transformer
relative permeability in low frequencies.
C. Reluctance of Cost-fewer Magnetic Composites
Reluctance*106 (A/Wb)
Effective Complex Transformer
Core Relative Permeability
80000
4
Iron + 10%wt Ferrite_MgZn
Iron + 30%wt Ferrite_MgZn
Iron + 50%wt Ferrite_MgZn
Iron + 70%wt Ferrite_MgZn
Iron + 90%wt Ferrite_MgZn
2
0
0.001
1
Frequency (Hz)
1000
Fig. 8 Reluctance of transformer core with various Ferrite_MgZn particles
On the other hand, Fig. 8 shows performance of transformer
core reluctance with various volume fractions of
Ferrite_MgZn particles randomly scattered in iron matrix
material. Magnetic particles in the composite occur
1523
Gouda and Thabet
Frequency Response Analysis for New Magnetic Power Transformer Composite Crystalline Core
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.8, pp. 1519-1525
ISSN 2078-2365
http://www.ieejournal.com/
changing inmagnetic reluctance of the composite with
respect to changing effective complex transformer core
relative permeability .The obtained results are in agreement
with that reported by [32, 33].
V.



CONCLUSION
Enhancing the effective complex relative permeability
of magnetic composite materials requires adding
magnetic particles having higher permeability than the
base matrix and via, then; cost-fewer transformer core
magnetic composites depend on the used magnetic
particles type.
Magnetic reluctance of the magnetic composite
materials varies with respect to changing effective
complex transformer core relative permeability; thus, it
will be changing magnetic equivalent circuit
reluctances.
Mixing magnetic composite for transformer core
magnetic composites resultant changing in the effective
permeability of magnetic composite with respect tothe
change of their other electrical properties at lower and
higher frequencies with respect to points out.
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Frequency Response Analysis for New Magnetic Power Transformer Composite Crystalline Core
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Vol. 5 (2014) No.8, pp. 1519-1525
ISSN 2078-2365
http://www.ieejournal.com/
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