Transformer, Electromagnetic WavesTheory

By Mohammed AboAjmaa SDU
T.C
SÜLEMAN DEMİREL UNIVERSITY
FEN BİLİMLERİ ENSTİTÜSÜ
Mühendislik fakültesi
ELEKTRONİK VE HABERLEŞME
MÜHENDİSLİĞİ
Electromagnetic Waves Theory
A COURSE OFFERED BY
Prof. Dr. Mustafa MERDAN
RANSFORMERTREPORT ABOUT
Submitted by
MSc. Student
Mohammed Mahdi AboAjamm
Student No. 1330145006

TRANSFORMER
What is Transformer?
A transformer is a static device that transfers electrical energy from
one circuit to another by electromagnetic induction without the
change in frequency. The transformer, which can link circuits with
different voltages, has been instrumental in enabling universal use
of the alternating current system for transmission and distribution
of electrical energy. Various components of power system, viz.
generators, transmission lines, distribution networks and finally the
loads, can be operated at their most suited voltage levels. As the
transmission voltages are increased to higher levels in some part
of the power system, transformers again play a key role in
interconnection of systems at different voltage levels.
Transformers occupy prominent positions in the power system,
being the vital links between generating stations and points of
utilization.

The transformer is an electromagnetic conversion device in which
electrical energy received by primary winding is first converted into
magnetic energy which is reconverted back into a useful electrical
energy in other circuits (secondary winding, tertiary winding, etc.).
Thus, the primary and secondary windings are not connected
electrically, but coupled magnetically. A transformer is termed as
either a step-up or step-down transformer depending upon
whether the secondary voltage is higher or lower than the primary
voltage, respectively. Transformers can be used to either step-up
or step-down voltage depending upon the need and application;
hence their windings are referred as high-voltage/low-voltage or
high-tension/low-tension windings in place of primary/secondary
windings. links between generating stations and points of
utilization.

Magnetic circuit:
Electrical energy transfer between two circuits takes place through
a transformer without the use of moving parts; the transformer
therefore has higher efficiency and low maintenance cost as
compared to rotating electrical machines. There are continuous
developments and introductions of better grades of core material.
The important stages of core material development can be
summarized as: non-oriented silicon steel, hot rolled grain oriented
silicon steel, cold rolled grain oriented (CRGO) silicon steel, Hi-B,
laser scribed and mechanically scribed. The last three materials
are improved versions of CRGO. Saturation flux density has
remained more or less constant around 2.0 Tesla for CRGO; but
there is a continuous improvement in watts/kg and volt-amperes/kg
characteristics in the rolling direction. The core material
developments are spearheaded by big steel manufacturers, and
the transformer designers can optimize the performance of core by
using efficient design and manufacturing technologies.
The core building technology has improved from the non-mitred to
mitred and then to the step-lap construction. A trend of reduction of
transformer core losses in the last few years is the result of a
considerable increase in energy costs. The better grades of core
steel not only reduce the core loss but they also help in reducing
the noise level by few decibels. Use of amorphous steel for
transformer cores results in substantial core loss reduction (loss is
about one-third that of CRGO silicon steel). Since the
manufacturing technology of handling this brittle material is
difficult, its use in transformers is not widespread.

Windings:
The rectangular paper-covered copper conductor is the most
commonly used conductor for the windings of medium and large
power transformers. These conductors can be individual strip
conductors, bunched conductors or continuously transposed cable
(CTC) conductors.
In low voltage side of a distribution transformer, where much
fewer turns are involved, the use of copper or aluminum foils may
find preference. To enhance the short circuit withstand capability,
the work hardened copper is commonly used instead of soft
annealed copper, particularly for higher rating transformers. In the
case of a generator transformer having high current rating, the
CTC conductor is mostly used which gives better space factor and
reduced eddy losses in windings. When the CTC conductor is
used in transformers, it is usually of epoxy bonded type to enhance
its short circuit strength. Another variety of copper conductor or
aluminum conductor is with the thermally upgraded insulating
paper, which is suitable for hot-spot temperature of about 110°C. It
is possible to meet the special overloading conditions with the help
of this insulating paper. Moreover, the aging of winding insulation
material will be slowed down comparatively.
For better mechanical properties, the epoxy diamond dot paper
can be used as an interlayer insulation for a multi-layer winding.
High temperature superconductors may find their application in
power transformers which are expected to be available
commercially within next few years. Their success shall depend on
economic viability, ease of manufacture and reliability
considerations.

Insulation and cooling:
Pre-compressed pressboard is used in windings as opposed to the
softer materials used in earlier days. The major insulation
(between windings, between winding and yoke, etc.) consists of a
number of oil ducts formed by suitably spaced insulating
cylinders/barriers. Well profiled angle rings, angle caps and other
special insulation components are also used. Mineral oil has
traditionally been the most commonly used electrical insulating
medium and coolant in transformers. Studies have proved that oil-
barrier insulation system can be used at the rated voltages greater
than 1000 kV. A high dielectric strength of oil-impregnated paper
and pressboard is the main reason for using oil as the most
important constituent of the transformer insulation system.
Manufacturers have used silicon-based liquid for insulation and
cooling. Due to non-toxic dielectric and self-extinguishing
properties, it is selected as a replacement of Askarel. High cost of
silicon is an inhibiting factor for its widespread use. Super-
biodegradable vegetable seed based oils are also available for use
in environmentally sensitive locations.
There is considerable advancement in the technology of gas
immersed transformers in recent years. SF6 gas has excellent
dielectric strength and is nonflammable. Hence, SF6 transformers
find their application in the areas where firehazard prevention is of
paramount importance. Due to lower specific gravity of SF6 gas,
the gas insulated transformer is usually lighter than the oil
insulated transformer. The dielectric strength of SF6 gas is a
function of the operating pressure; the higher the pressure, the
higher the dielectric strength. However, the heat capacity and
thermal time constant of SF6 gas are smaller than that of oil,
resulting in reduced overload capacity of SF6 transformers as
compared to oilimmersed transformers. Environmental concerns,
sealing problems, lower cooling capability and present high cost of
manufacture are the challenges which have to be overcome for the
widespread use of SF6 cooled transformers.

PRINCIPLES For Transformer:
It is very common, for simplification or approximation purposes, to
analyze the transformer as an ideal transformer model as
represented in the two images. An ideal transformer is a
theoretical, linear transformer that is lossless and
perfectly coupled; that is, there are no energy losses and flux is
completely confined within the magnetic core. Perfect coupling
implies infinitely high core magnetic permeability and winding
inductances and zero net magneto motive force. varying current in
the transformer's primary winding creates a varying magnetic flux
in the core and a varying magnetic field impinging on the
secondary winding. This varying magnetic field at the secondary
induces a varying electromotive force(EMF) or voltage in the
secondary winding. The primary and secondary windings are
wrapped around a core of infinitely high magnetic permeability[d]
so that all of the magnetic flux passes through both the primary
and secondary windings with a voltage connected to theprimary
winding and load impedance connected to the secondary winding
the transformer currents flow in the indicated directions. (See also
Polarity.)
According to Faraday's law of induction, since the same magnetic
flux passes through both the primary and secondary windings in an
ideal transformer, a voltage is induced in each winding]
, according
to eq. (1)

In the secondary winding case, according to eq. (2) in the primary
winding case.

The primary EMF is sometimes termed counter EMFThis is in
accordance with Lenz's law, which states that induction of EMF
always opposes development of any such change in magnetic
field. The transformer winding voltage ratio is thus shown to be
directly proportional to the winding turns ratio according to eq. (3).
According to the law of Conservation of Energy(In physics, the law
of conservation of energy states that the total energy of an isolated
system cannot change—it is said to be conserved over time.
Energy can be neither created nor destroyed, but can change
form, for instance chemical energy can be converted to kinetic
energy in the explosion of a stick of dynamite. A consequence of
the law of conservation of energy is that a perpetual motion
machine of the first kind cannot exist. That is to say, no system
without an external energy supply can deliver an unlimited amount
of energy to its surroundings.) any load impedance connected to
the ideal transformer's secondary winding results in conservation
of apparent, real and reactive power consistent with eq. (4).

The ideal transformer identity shown in eq. (5) is a reasonable
approximation for the typical commercial transformer, with voltage
ratio and winding turns ratio both being inversely proportional to
the corresponding current ratio.
By Ohm's Law and the ideal transformer identity: the secondary
circuit load impedance can be expressed as eq. (6)
The apparent load impedance referred to the primary circuit is
derived in eq. (7) to be equal to the turns ratio squared times the
secondary circuit load impedance.

MAGNETIC CORE:
A magnetic core is a piece of magnetic material with a high
permeability(permeability is the measure of the ability of a material
to support the formation of a magnetic field within itself. In other
words, it is the degree of magnetization that a material obtains in
response to an applied magnetic field. Magnetic permeability is
typically represented by the Greek letter μ. The term was coined in
September 1885 by Oliver Heaviside. The reciprocal of magnetic
permeability is magnetic reluctivity.In SI units, permeability is
measured in henries per meter (H·m−1
), or newtons per ampere
squared (N·A−2
). The permeability constant (μ0), also known as the
magnetic constant or the permeability of free space, is a measure
of the amount of resistance encountered when forming a magnetic
field in a classical vacuum. The magnetic constant has the exact
(defined) value µ0 = 4π×10−7
H·m−1
≈ 1.2566370614…×10−6
H·m−1
or N·A−2
).) used to confine and guide magnetic fields in electrical,
electromechanical and magnetic devices such as electromagnets,
transformers, electric motors, generators, inductors, magnetic
recording heads, and magnetic assemblies. It is made of
ferromagnetic metal such as iron, or ferromagnetic compounds
such as ferrites. The high permeability, relative to the surrounding
air, causes the magnetic field lines to be concentrated in the core
material. The magnetic field is often created by a coil of wire
around the core that carries a current. The presence of the core
can increase the magnetic field of a coil by a factor of several
thousand over what it would be without the core.
The use of a magnetic core can enormously concentrate the
strength and increase the effect of magnetic fields produced by
electric currents and permanent magnets.

The properties of a device will depend crucially on the following
factors:
 the geometry of the magnetic core.
 the amount of air gap in the magnetic circuit.
 the properties of the core material (especially permeability
and hysteresis).
 the operating temperature of the core.
 whether the core is laminated to reduce eddy currents.
In many applications it is undesirable for the core to retain
magnetization when the applied field is removed. This property,
called hysteresis can cause energy losses in applications such as
transformers. Therefore 'soft' magnetic materials with low
hysteresis, such as silicon steel, rather than the 'hard' magnetic
materials used for permanent magnets, are usually used in cores.
:SOFT IRON
is used in magnetic assemblies, electromagnets and in some
electric motors; and it can create a concentrated field that is as
much as 50,000 times more intense than an air core. Iron is
desirable to make magnetic cores, as it can withstand high levels
of magnetic field without saturating (up to 2.16 teslas) It is also
used because, unlike "hard" iron, it does not remain magnetised
when the field is removed, which is often important in applications
where the magnetic field is required to be repeatedly
switched.Unfortunately, due to the electrical conductivity of the
metal, at AC frequencies a bulk block or rod of soft iron can often
suffer from large eddy currents circulating within it that waste
energy and cause undesirable heating of the iron.

VITREOUS METAL:
Amorphous metal (also known metallic glass or glassy metal) is a
solid metallic material, usually an alloy, with a disordered atomic-
scale structure. Most metals are crystalline in their solid state,
which means they have a highly ordered arrangement of atoms.
Amorphous metals are non-crystalline, and have a glass-like
structure. But unlike common glasses, such as window-glass,
which are typically insulators, amorphous metals have good
electrical conductivity. There are several ways in which amorphous
metals can be produced, including extremely rapid cooling,
physical vapor deposition, solid-state reaction, ion irradiation, and
mechanical alloying.
More recently, batches of amorphous steel have been produced
that demonstrate strengths much greater than conventional steel
alloys is a variety of alloys that are non-crystalline or glassy. These
are being used to create high-efficiency transformers. The
materials can be highly responsive to magnetic fields for low
hysteresis losses, and they can also have lower conductivity to
reduce eddy current losses. China is currently making widespread

industrial and power grid usage of these transformers for new
installations.Currently the most important application is due to the
special magnetic properties of some ferromagnetic metallic
glasses. The low magnetization loss is used in high efficiency
transformers (amorphous metal transformer) at line frequency and
some higher frequency transformers. Amorphous steel is a very
brittle material which makes it difficult to punch into motor
laminations. Also electronic article surveillance (such as theft
control passive ID tags,) often uses metallic glasses because of
these magnetic properties.
BEHAVIOR OF MAGNETIC MATERIALS:
In Eq. ( M=XmH), we describe the macroscopic magneticproperty
of a linear. isotropicmedium) defining the magnetic
susceptibilityXm.which is unit less. The magnetic susceptibilityand
the relative permeability are related as follows:
Magnetic material can be roughly classifiedinto three maim group
inaccordance with theμrvalues.
Diamagnetic, if μ r≤ 1 (Xm is a very small negative number).
Paramagnetic. if μ r≥ 1 (Xm is a very small positive number).
Ferromagnetic, if μr>> 1(Xm is a large positive number).

DIAMAGNETISM:
Diamagnetic materials create an induced magnetic field in a
an externally applied magnetic field, and aredirection opposite to
repelled by the applied magnetic field. In contrast, the opposite
behavior is exhibited by paramagnetic materials. Diamagnetism is
a quantum mechanical effect that occurs in all materials; when it is
ontribution to the magnetism the material is called athe only c
diamagnet. Unlike a ferromagnet, a diamagnet is not a permanent
(the permeability0magnet. Its magnetic permeability is less than μ
of free space). In most materials diamagnetism is a weak effect,
superconductor repels the magnetic field entirely, apart frombut a
a thin layer at the surface.Diamagnetic materials, like water, or
water based materials, have a relative magnetic permeability that
bilityis less than or equal to 1, and therefore a magnetic suscepti
less than or equal to 0, since susceptibility is defined as
− 1.r= μmχ

This means that diamagnetic materials are repelled by magnetic
fields. However, since diamagnetism is such a weak property its
effects are not observable in everyday life. For example, the
magnetic susceptibility of diamagnets such as water is χm =
−9.05×10−6
. The most strongly diamagnetic material is bismuth, χm
= −1.66×10−4
, although pyrolytic carbon may have a susceptibility
of χm = −4.00×10−4
in one plane. Nevertheless, these values are
orders of magnitude smaller than the magnetism exhibited by
paramagnets and ferromagnets. Note that because χm is derived
from the ratio of the internal magnetic field to the applied field, it is
a dimensionless value.
All conductors exhibit an effective diamagnetism when they
experience a changing magnetic field. The Lorentz force on
electrons causes them to circulate around forming eddy currents.
The eddy currents then produce an induced magnetic field
opposite the applied field, resisting the conductor's motion.
:PARAMAGNETISM
is a form of magnetism whereby certain materials are attracted by
an externally applied magnetic field, and form internal, induced
magnetic fields in the direction of the applied magnetic field. In
contrast with this behavior, diamagnetic materials are repelled by
magnetic fields and form induced magnetic fields in the direction
opposite to that of the applied magnetic field. Paramagnetic
materials include most chemical elements and some compounds;
they have a relative magnetic permeability greater than or equal to
1 ( μ r≥ 1 ) (i.e., a positive magnetic susceptibility) and hence are
attracted to magnetic fields. The magnetic moment induced by the
applied field is linear in the field strength and rather weak. It
typically requires a sensitive analytical balance to detect the effect
and modern measurements on paramagnetic materials are often
conducted with a SQUID magnetometer.

Paramagnetic materials have a small, positive susceptibility to
magnetic fields. These materials are slightly attracted by a
magnetic field and the material does not retain the magnetic
properties when the external field is removed. Paramagnetic
properties are due to the presence of some unpaired electrons,
and from the realignment of the electron paths caused by the
external magnetic field. Paramagnetic materials include
magnesium, molybdenum, lithium, and tantalum.
Unlike ferromagnets, paramagnets do not retain any magnetization
in the absence of an externally applied magnetic field because
thermal motion randomizes the spin orientations. Some
paramagnetic materials retain spin disorder at absolute zero,
meaning they are paramagnetic in the ground state. Thus the total
magnetization drops to zero when the applied field is removed.
Even in the presence of the field there is only a small induced
magnetization because only a small fraction of the spins will be
oriented by the field. This fraction is proportional to the field
strength and this explains the linear dependency. The attraction
experienced by ferromagnetic materials is non-linear and much
stronger, so that it is easily observed, for instance, by the attraction
between a refrigerator magnet and the iron of the refrigerator itself.

FERROMAGNETISM:
Is the basic mechanism by which certain materials (such as iron)
form permanent magnets, or are attracted to magnets. In physics,
several different types of magnetism are distinguished.
Ferromagnetism (including ferrimagnetism) is the strongest type: it
is the only one that typically creates forces strong enough to be
felt, and is responsible for the common phenomena of magnetism
encountered in everyday life. Substances respond weakly to
magnetic fields with three other types of magnetism,
paramagnetism, diamagnetism, and antiferromagnetism, but the
forces are usually so weak that they can only be detected by
sensitive instruments in a laboratory. An everyday example of
ferromagnetism is a refrigerator magnet used to hold notes on a
refrigerator door. The attraction between a magnet and
ferromagnetic material is "the quality of magnetism first apparent to
the ancient world, and to us today".
Permanent magnets (materials that can be magnetized by an
external magnetic field and remain magnetized after the external
field is removed) are either ferromagnetic or ferrimagnetic, as are
other materials that are noticeably attracted to them. Only a few
substances are ferromagnetic. The common ones are iron, nickel,
cobalt and most of their alloys, some compounds of rare earth
metals, and a few naturally-occurring minerals such as lodestone.
Ferromagnetism is very important in industry and modern
technology, and is the basis for many electrical and
electromechanical devices such as electromagnets, electric
motors, generators, transformers, and magnetic storage such as
tape recorders, and hard disks.

:CARBONYL IRON
Powdered cores made of carbonyl iron, a highly pure iron, have
high stability of parameters across a wide range of temperatures
and magnetic flux levels, with excellent Q factors between 50 kHz
and 200 MHz. Carbonyl iron powders are basically constituted of
micrometer-size spheres of iron coated in a thin layer of electrical
insulation. This is equivalent to a microscopic laminated magnetic
circuit (see silicon steel, above), hence reducing the eddy currents,
particularly at very high frequencies. A popular application of
carbonyl iron-based magnetic cores is in high-frequency and
broadband inductors and transformers.
:IRON POWDER
Powdered cores made of hydrogen reduced iron have higher
permeability but lower Q. They are used mostly for
electromagnetic interference filters and low-frequency chokes,
mainly in switched-mode power supplies.

EDDY CURRENTS AND WINDING STRAY LOSSES:
The load loss of a transformer consists of losses due to ohmic
resistance of windings (I2
R losses) and some additional losses.
These additional losses are generally known as stray losses,
which occur due to leakage field of windings and field of high
current carrying leads/bus-bars. The stray losses in the windings
are further classified as eddy loss and circulating current loss. The
other stray losses occur in structural steel parts. There is always
some amount of leakage field in all types of transformers, and in
large power transformers (limited in size due to transport and
space restrictions) the stray field strength increases with growing
rating much faster than in smaller transformers. The stray flux
impinging on conducting parts (winding conductors and structural
components) gives rise toeddy currents in them. The stray losses
in windings can be substantially high in large transformers if
conductor dimensions and transposition methods are not chosen
properly.
Today’s designer faces challenges like higher loss capitalization
and optimum performance requirements. In addition, there could
be constraints on dimensions and weight of the transformer which
is to be designed. If the designer lowers current density to reduce
the DC resistance copper loss (I2
R loss), the eddy loss in windings
increases due to increase in conductor dimensions. Hence, the
winding conductor is usually subdivided with a proper transposition
method to minimize the stray losses in windings.
In order to accurately estimate and control the stray losses in
windings and structural parts, in-depth understanding of the
fundamentals of eddy currents starting from basics of
electromagnetic fields is desirable. The fundamentals are
described in first few sections of this chapter.

EDDY CURRENTS:
Eddy currents (also called Foucault currentsare circular
electric currents induced within conductors by a changing
magnetic field in the conductor, due to Faraday's law of
induction. Eddy currents flow in closed loops within
conductors, in planes perpendicular to the magnetic field.
They can be induced within nearby stationary conductors by
a time-varying magnetic field created by an AC electromagnet
or transformer, for example, or by relative motion between a
magnet and a nearby conductor. The magnitude of the current
in a given loop is proportional to the strength of the magnetic
field, the area of the loop, and the rate of change of flux, and
inversely proportional to the resistivity of the material.
By Lenz's law, an eddy current creates a magnetic field that
opposes the magnetic field that created it, and thus eddy
currents react back on the source of the magnetic field. For
example, a nearby conductive surface will exert a drag force
on a moving magnet that opposes its motion, due to eddy
currents induced in the surface by the moving magnetic field.
This effect is employed in eddy current brakes which are used
to stop rotating power tools quickly when they are turned off.
The current flowing through the resistance of the conductor
also dissipates energy as heat in the material. Thus eddy
currents are a source of energy loss in alternating current
(AC) inductors, transformers, electric motors and generators,
and other AC machinery, requiring special construction such
as laminated magnetic cores to minimize them. Eddy currents
are also used to heat objects in induction heating furnaces
and equipment, and to detect cracks and flaws in metal parts
using eddy-current testing instruments. Under certain
assumptions (uniform material, uniform magnetic field, no
skin effect, etc.) the power lost due to eddy currents per unit
mass for a thin sheet or wire can be calculated from the
following equation:

where
P is the power lost per unit mass (W/kg),
Bp is the peak magnetic field (T),
d is the thickness of the sheet or diameter of the wire (m),
f is the frequency (Hz),
k is a constant equal to 1 for a thin sheet and 2 for a thin wire,
ρ is the resistivity of the material (Ω m), and
D is the density of the material (kg/m3).
This equation is valid only under the so-called quasi-static
conditions, where the frequency of magnetisation does not result in
the skin effect; that is, the electromagnetic wave fully penetrates
the material.
:SKIN EFFECT
In very fast-changing fields, the magnetic field does not penetrate
completely into the interior of the material. This skin effect renders
the above equation invalid. However, in any case increased
frequency of the same value of field will always increase eddy
currents, even with non-uniform field penetration
The penetration depth for a good conductor can be calculated from
the following equation:

HEAT TRANSFER EFFECTS:
A load serving transformer not only experiences an electrical
process but also goes through a thermal process that is driven by
heat. The heat generated by the no-load and load losses is the
main source of temperature rise in the transformer. However, the
losses of the windings and stray losses seen from the structural
parts are the main factors of heat generation within the
transformer. The thermal energy produced by the windings is
transferred to the winding insulation and consequently to the oil
and transformer walls. This process will continue until an
equilibrium state is reached when the heat generated by the
windings equals the heat taken away by some form of coolant or
cooling system . This heat transfer mechanism must not allow the
core, windings, or any structural parts to reach critical
temperatures that could possibly deteriorate the credibility of the
winding insulation. The dielectric insulating properties of the
insulation can be weakened if temperatures above the limiting
values are permitted . As a result, the insulation ages more rapidly,
reducing its normal life. Due to the temperature requirements of
the insulation, transformers utilize cooling systems to control the
temperature rise. The best method of absorbing heat from the
windings, core, and structural parts in larger power transformers is
to use oil .For smaller oil-field transformers, the tank surface is
used to dissipate heat to the atmosphere. For larger transformers,
heat exchangers, such as radiators, usually mounted beside the
tank, are employed to cool the oil. The standard identifies the type
of cooling system according to Table 1.

THE MAGNETIC CIRCUIT:
The magnetic core has been introduced, an understanding of the
magnetic circuit is necessary to quantify the relationships between
voltage, current, flux, and field density.

References….
1. Measurement and characterization of magnetic
materials, F. Fiorillo, Elsevier Academic Press,
2004
2. http://en.wikipedia.org/wiki/Transformer.
3. Elements of Electromagnetics by Matthew N.O.
Sadiku.
4. Fundamentals ofEngineering Electromagnetics,
Cheng. David K. Copyright 1993 by Addison-
Weceley Publishing Company, In c.
5. Transformer Engineering Design and Practice,
S.V.Kulkarni., S.A.Khaparde., Indian Institute of
Technology, Bombay,Mumbai, India., MARCEL
DEKKER, INC.

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