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)

http://en.wikipedia.org/wiki/Linearity

http://en.wikipedia.org/wiki/Magnetic_coupling

http://en.wikipedia.org/wiki/Transformer#Energy_Losses

http://en.wikipedia.org/wiki/Flux

http://en.wikipedia.org/wiki/Magnetic_core

http://en.wikipedia.org/wiki/Permeability_(electromagnetism)

http://en.wikipedia.org/wiki/Magnetomotive_force


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 are direction 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 a the only c

diamagnet. Unlike a ferromagnet, a diamagnet is not a permanent

(the permeability 0magnet. 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 from but a

a thin layer at the surface.Diamagnetic materials, like water, or

water based materials, have a relative magnetic permeability that

bility is less than or equal to 1, and therefore a magnetic suscepti

less than or equal to 0, since susceptibility is defined as

− 1. r= μ mχ


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 (I2R 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 (I2R 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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