TRANSFORMER

Dhruv Parekh,PU,EE
 Ferromagnetic Materials
• The ferromagnetic materials are those substances which exhibit strong
magnetism in the same direction of the field, when a magnetic field is
applied to it.
• First, we have to know what a domain is. It is actually a tiny area in
ferromagnetic materials with a specific overall spin orientation due to
quantum mechanical effect.
• This effect is really exchange interaction. That is; when we consider some
unpaired electrons, they will interact with each other between two atoms
and they line up themselves in a tiny region with the direction of magnetic
field (Figure 1).
• This mechanism of the ferromagnetic material is ferromagnetism. It can
be defined as some materials (cobalt, gadolinium, iron etc) will become
permanent magnet with the use of magnetic field.

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Properties of Ferromagnetic Materials
• When a rod of this material is placed in a magnetic field, it
rapidly aligns itself in the track of the field.
• It is strongly attracted by the magnet.
• The ferromagnetism mechanism is not present in liquids and
gases.
• The intensity of magnetization (M), magnetic susceptibility
(χm), relative permeability (µr), and magnetic flux density (B)
of this material will be always prominent and positive.

• µ0 → Magnetic permittivity of free space. H → Applied

peripheral magnetic field strength.
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 Hysteresis Loop
• Hysteresis loop is a four quadrant B-H graph from
where the hysteresis loss, coercive force and
retentively of s magnetic material are obtained.
• Current I is directly proportional to the value of
magnetizing force (H) as
• Where, N = no. of turn of coil and l is the effective
length of the coil.
• The magnetic flux density of this core is B which
is directly proportional to magnetizing force H.
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 Hysteresis Loop
• Definition of Hysteresis
Hysteresis of a magnetic material is a property by virtue of which
the flux density (B) of this material lags behind the magnetizing
force (H).
• Definition of Coercive Force
Coercive force is defined as the negative value of magnetizing force
(-H) that reduces residual flux density of a material to zero.
• Residual Flux Density
Residual flux density is the certain value of magnetic flux per unit
area that remains in the magnetic material without presence of
magnetizing force (i.e. H = 0).
• Definition of Retentivity
It is defined as the degree to which a magnetic material gains its
magnetism after magnetizing force (H) is reduced to zero.

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Hysteresis Loop

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 Hysteresis Loop
• Step 1: When supply current I = 0, so no existence of flux density (B)
and magnetizing force (H). The corresponding point is ‘O’ in the
graph above.
• Step 2: When current is increased from zero value to a certain
value, magnetizing force (H) and flux density (B) both are set up and
increased following the path o – a.
• Step 3: For a certain value of current, flux density (B) becomes
maximum (Bmax). The point indicates the magnetic saturation or
maximum flux density of this core material. All element of core
material get aligned perfectly. Hence Hmax is marked on H axis. So
no change of value of B with further increment of H occurs beyond
point ‘a’.
• Step 4: When the value of current is decreased from its value of
magnetic flux saturation, H is decreased along with decrement of B
not following the previous path rather following the curve a – b.

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 Hysteresis Loop
• Step 5: The point ‘b’ indicates H = 0 for I = 0 with a certain value of B. This
lagging of B behind H is called hysteresis. The point ‘b’ explains that after
removing of magnetizing force (H), magnetism property with little value
remains in this magnetic material and it is known as residual magnetism
(Br). Here o – b is the value of residual flux density due to retentivity of the
material.
• Step 6: If the direction of the current I is reversed, the direction of H also
gets reversed. The increment of H in reverse direction following path b – c
decreases the value of residual magnetism (Br) that gets zero at point ‘c’
with certain negative value of H. This negative value of H is called coercive
force (Hc)
• Step 7: H is increased more in negative direction further; B gets reverses
following path c – d. At point‘d’, again magnetic saturation takes place but
in opposite direction with respect to previous case. At point‘d’, B and H get
maximum values in reverse direction, i.e. (-Bm and -Hm).
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 Hysteresis Loop
• Step 8: If we decrease the value of H in this direction, again B
decreases following the path de. At point ‘e’, H gets zero valued but
B is with finite value. The point ‘e’ stands for residual magnetism (-
Br) of the magnetic core material in opposite direction with respect
to previous case.
• Step 9: If the direction of H again reversed by reversing the current
I, then residual magnetism or residual flux density (-Br) again
decreases and gets zero at point ‘f’ following the path e – f. Again
further increment of H, the value of B increases from zero to its
maximum value or saturation level at point a following path f – a.
• The path a – b – c – d – e – f – a forms hysteresis loop.
• [NB: The shape and the size of the hysteresis loop depend on the
nature of the material chosen]
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 Importance of Hysteresis Loop
The main advantages of hysteresis loop are given
below,
– Smaller hysteresis loop area symbolizes less hysteresis
loss.
– Hysteresis loop provides the value of retentivity and
coercivity of a material. Thus the way to choose
perfect material to make permanent magnet, core of
machines becomes easier.
– From B-H graph, residual magnetism can be
determined and thus choosing of material for
electromagnets is easy.

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Dhruv Parekh,PU,EE
 Definition of Transformer
• Electrical power transformer is a static device
which transforms electrical energy from one
circuit to another without any direct electrical
connection and with the help of mutual
induction between two windings.
• It transforms power from one circuit to
another without changing its frequency but
may be in different voltage level.

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 Working Principle of Transformer
• The working principle of transformer is very simple. Mutual
induction between two or more windings is responsible for
transformation action in an electrical transformer.
• The alternating current through the winding produces a continually
changing flux or alternating flux that surrounds the winding.
• If any other winding is brought nearer to the previous one,
obviously some portion of this flux will link with the second. As this
flux is continually changing in its amplitude and direction, there
must be a change in flux linkage in the second winding or coil.
• According to Faraday's law of electromagnetic induction, there
must be an EMF induced in the second. If the circuit of the later
winding is closed, there must be a current flowing through it. This is
the simplest form of an electrical power transformer, and this is the
most basic of working principle of transformer.

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 Working Principle of Transformer
The winding which takes electrical power from the source, is known as the primary
winding of a transformer. Here in our above example, it is first winding.

The winding which gives the

desired output voltage due to
mutual induction in the
transformer is commonly known
as the secondary winding of the
transformer. Here in our example,
it is second winding.

Dhruv Parekh,PU,EE
 Working Principle of Transformer
• The form mentioned above of a transformer is theoretically
possible but not practically, because in open air very tiny
portion of the flux of the first winding will link with second; so
the current that flows through the closed circuit of later, will
be so small in amount that it will be difficult to measure.
• The rate of change of flux linkage depends upon the amount
of linked flux with the second winding. So, almost all flux of
primary winding should link to the secondary winding. This is
effectively and efficiently done by placing one low reluctance
path common to both of the winding. This low reluctance
path is core of transformer, through which the maximum
number of flux produced by the primary is passed through
and linked with the secondary winding.
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Single Phase Voltage Transformer

Where:
VP - is the Primary Voltage
VS - is the Secondary Voltage
NP - is the Number of Primary
Windings
NS - is the Number of
Secondary Windings
Φ (phi) - is the Flux Linkage

Dhruv Parekh,PU,EE
 Main Constructional Parts of
Transformer
The three main parts of a transformer are,
• Primary Winding of Transformer
Which produces magnetic flux when it is connected to
electrical source.
• Magnetic Core of Transformer
The magnetic flux produced by the primary winding, that will
pass through this low reluctance path linked with secondary
winding and create a closed magnetic circuit.
• Secondary Winding of Transformer
The flux, produced by primary winding, passes through the
core, will link with the secondary winding. This winding also
wounds on the same core and gives the desired output of the
transformer. Dhruv Parekh,PU,EE
Main Constructional Parts of
Transformer

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 Transformer Construction of the Core
• The two most common and basic designs of transformer construction are
the Closed-core Transformer and the Shell-core Transformer.
• In the “closed-core” type (core form) transformer, the primary and
secondary windings are wound outside and surround the core ring. In the
“shell type” (shell form) transformer, the primary and secondary windings
pass inside the steel magnetic circuit (core) which forms a shell around the
windings as shown below.

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 Transformer Construction of the Core
• In both types of transformer core design, the magnetic flux linking
the primary and secondary windings travels entirely within the core
with no loss of magnetic flux through air.
• In the core type transformer construction, one half of each winding
is wrapped around each leg (or limb) of the transformers magnetic
circuit as shown above.
• The coils are not arranged with the primary winding on one leg and
the secondary on the other but instead half of the primary winding
and half of the secondary winding are placed one over the other
concentrically on each leg in order to increase magnetic coupling
allowing practically all of the magnetic lines of force go through
both the primary and secondary windings at the same time.
However, with this type of transformer construction, a small
percentage of the magnetic lines of force flow outside of the core,
and this is called “leakage flux”.

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 Transformer Construction of the Core
• Shell type transformer cores overcome this leakage flux as both the
primary and secondary windings are wound on the same centre leg
or limb which has twice the cross-sectional area of the two outer
limbs.
• The advantage here is that the magnetic flux has two closed
magnetic paths to flow around external to the coils on both left and
right hand sides before returning back to the central coils.
• This means that the magnetic flux circulating around the outer
limbs of this type of transformer construction is equal to Φ/2.
• As the magnetic flux has a closed path around the coils, this has the
advantage of decreasing core losses and increasing overall
efficiency.

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 Transformer Laminations
• But you may be wondering as to how the primary and secondary windings
are wound around these laminated iron or steel cores for this types of
transformer constructions.
• The coils are firstly wound on a former which has a cylindrical, rectangular
or oval type cross section to suit the construction of the laminated core.
• In both the shell and core type transformer constructions, in order to
mount the coil windings, the individual laminations are stamped or
punched out from larger steel sheets and formed into strips of thin steel
resembling the letters “E”s, “L”s, “U”s and “I”s as shown below.

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 Transformer Winding Arrangements
• Transformer windings form another important part of a transformer
construction, because they are the main current-carrying
conductors wound around the laminated sections of the core.
• In a single-phase two winding transformer, two windings would be
present as shown.
• The one which is connected to the voltage source and creates the
magnetic flux called the primary winding, and the second winding
called the secondary in which a voltage is induced as a result of
mutual induction.
• If the secondary output voltage is less than that of the primary
input voltage the transformer is known as a “Step-down
Transformer”.
• If the secondary output voltage is greater then the primary input
voltage it is called a “Step-up Transformer”.
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 EMF Equation of Transformer
• When a sinusoidal voltage is applied to the primary
winding of a transformer, alternating flux ϕm sets up in
the iron core of the transformer.
• This sinusoidal flux links with both primary and
secondary winding. The function of flux is a sine
function. The rate of change of flux with respect to
time is derived mathematically.
• Let
ϕm be the maximum value of flux in Weber
f be the supply frequency in Hz
N1 is the number of turns in the primary winding
N2 is the number of turns in the secondary winding
Φ is the flux per turn in Weber

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 EMF Equation of Transformer
• By Faraday’s Law,
• Let E1 is the emf induced in the primary winding,
• Φ = Φmax sinωt,

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 Ideal Transformer
• An ideal transformer is an imaginary transformer which has
- no copper losses (no winding resistance)
- no iron loss in core
- no leakage flux
• In other words, an ideal transformer gives output power
exactly equal to the input power. The efficiency of an idea
transformer is 100%.
• Actually, it is impossible to have such a transformer in
practice, but ideal transformer model makes problems easier.

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Ideal Transformer

Dhruv Parekh,PU,EE
 Ideal Transformer
• Consider an ideal transformer on no load i.e., secondary is open-
circuited as shown in figure. Under such conditions, the primary is
simply a coil of pure inductance.
• When an alternating voltage V₁ is applied to the primary, it draws a
small magnetizing current Im which lags behind the applied voltage
by 90°.
• This alternating current Im produces an alternating flux ϕ which is
proportional to and in phase with it.
• The alternating flux ϕ links both the windings and induces e.m.f. E₁
in the primary and e.m.f. E₂ in the secondary.
• The primary e.m.f. E₁ is, at every instant, equal to and in opposition
to V₁ (Lenz’s law). Both e.m.f.s E₁ and E₂ lag behind flux ϕ by 90°.
However, their magnitudes depend upon the number of primary
and secondary turns.

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 Practical Transformer
• A practical transformer differs from the ideal
transformer in many respects. The practical
transformer has
1. iron losses
2. winding resistances and
3. magnetic leakage, giving rise to leakage
reactance.

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 Practical Transformer
Winding resistances
• Since the windings consist of copper conductors, it
immediately follows that both primary and secondary
will have winding resistance.
• The primary resistance R₁ and secondary resistance R₂
act in series with the respective windings as shown in
figure.
• When current flows through the windings, there will be
power loss as well as a loss in voltage due to IR drop.
• This will affect the power factor and E₁ will be less than
V₁ while V₂ will be less than E₂.
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Practical Transformer

Dhruv Parekh,PU,EE
 Practical Transformer
Leakage reactances
• Both primary and secondary currents produce flux. The flux ϕ
which links both the windings is the useful flux and is called
mutual flux.
• However, primary current would produce some flux ϕ which
would not link the secondary winding. Similarly, secondary
current would produce some flux ϕ that would not link the
primary winding.
• The flux such as ϕ₁ or ϕ₂ which links only one winding is called
leakage flux. The leakage flux paths are mainly through the air.
• The effect of these leakage fluxes would be the same as though
inductive reactance were connected in series with each winding
of transformer that had no leakage flux as shown in figure.
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 Practical Transformer
• In other words, the effect of primary leakage flux ϕ₁ is to
introduce an inductive reactance X₁ in series with the primary
winding as shown. Similarly, the secondary leakage flux ϕ₂
introduces an inductive reactance X₂ in series with the
secondary winding.
• There will be no power loss due to leakage reactance. However,
the presence of leakage reactance in the windings changes the
power factor as well as there is voltage loss due to IX drop.
Note: Although leakage flux in a transformer is quite small (about 5%
of ϕ) compared to the mutual flux ϕ, yet it cannot be ignored. It is
because leakage flux paths are through air of high reluctance and hence
require considerable e.m.f.
It may be noted that energy is conveyed from the primary winding to the
secondary winding by mutualDhruv
fluxParekh,PU,EE
f which links both the windings.
Equivalent Circuit Of Transformer

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Equivalent circuit of transformer with
secondary parameters referred to the
primary.

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 Transformer Losses
• In any electrical machine, 'loss' can be defined
as the difference between input power and
output power.
• An electrical transformer is an static device,
hence mechanical losses (like windage or
friction losses) are absent in it.
• A transformer only consists of electrical losses
(iron losses and copper losses).

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 (I) Core Losses Or Iron Losses
• Eddy current loss and hysteresis loss depend upon the magnetic
properties of the material used for the construction of core. Hence these
losses are also known as core losses or iron losses.
• Hysteresis loss in transformer: Hysteresis loss is due to reversal of
magnetization in the transformer core. This loss depends upon the volume
and grade of the iron, frequency of magnetic reversals and value of flux
density. It can be given by, Steinmetz formula:
• Wh= ηBmax1.6fV (watts)
where, η = Steinmetz hysteresis constant
V = volume of the core in m3
• Eddy current loss in transformer: In transformer, AC current is supplied to
the primary winding which sets up alternating magnetizing flux. When this
flux links with secondary winding, it produces induced emf in it. But some
part of this flux also gets linked with other conducting parts like steel core
or iron body or the transformer, which will result in induced emf in those
parts, causing small circulating current in them. This current is called as
eddy current. Due to these eddy currents, some energy will be dissipated
in the form of heat. Dhruv Parekh,PU,EE
 (II) COPPER LOSS IN TRANSFORMER
• Copper loss is due to ohmic resistance of the
transformer windings. Copper loss for the primary
winding is I12R1 and for secondary winding is I22R2.
• Where, I1 and I2 are current in primary and secondary
winding respectively, R1 and R2 are the resistances of
primary and secondary winding respectively.
• It is clear that Cu loss is proportional to square of the
current, and current depends on the load. Hence
copper loss in transformer varies with the load.

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 Efficiency Of Transformer
• Efficiency of a transformer can be defined as the output
power divided by the input power. That is efficiency =
output / input .
• Transformers are the most highly efficient electrical
devices. Most of the transformers have full load efficiency
between 95% to 98.5% .
• As a transformer being highly efficient, output and input
are having nearly same value, and hence it is impractical to
measure the efficiency of transformer by using output /
input.
• A better method to find efficiency of a transformer is
using, efficiency = (input - losses) / input = 1 - (losses /
input).

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Condition For Maximum Efficiency

Hence, efficiency of a transformer will

be maximum when copper loss and
iron losses are equal. That is Copper
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loss = Iron loss.