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Transformer
A transformer is a static
piece of apparatus for
transferring power from one
circuit into another without
change in the frequency.
It can raise or lower the
voltage with a
corresponding increase or
decrease in current.
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Why transformer is necessary ?
• One of the main advantages of a.c.
transmission and distribution is the ease with
which an alternating voltage can be increased
or reduced.
• Although transformer are generally associated
with power system application, they also
occur in many low-power applications
including electronic circuits.
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General Arrangement of a Transformer
Limbs
Yokes
A steel core of laminated sheet
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Core factors
• The flux linking coils can be greatly improved
by the introduction of a ferromagnetic core.
• Core Loss=Hysteresis loss+ Eddy current Loss
• The varying flux in the core induces emfs and
hence the current in the core material. This
gives rise to the I2R losses or eddy current
losses.
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Ferromagnetic Core
• A magnetic core is a piece of
magnetic material with a
high permeability used to
confine and guide magnetic
fields in electrical and
electromechanical devices
• Soft iron are used in the
magnetic core
Hysteresis Loop
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Principle of Operation
Ampere’s law
Magnetomotive force=Ni
Where N=no. of turns and i= current flowing through the coil
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Principle of action of a Transformer
When a changing voltage is applied to the primary
winding, an emf is induced in the primary winding. A
current in the primary winding produces magnetic field in
the core. The magnetic field is almost confined in the
iron core and couples around through the secondary coil.
The induced voltage in the secondary is also given by
faradays law.
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Transformer Action
Induced Voltage in the Primary
VP = − N p
dΦ
dt
..(1) where NP= the primary no. of turns
Induced Voltage in the Secondary
VS = − N S
dΦ ..(2) where N = the secondary no. of turns
s
dt
The rate of change of flux is the same
VS N S
=
VP N P
Dividing eq.(1) by eq. (2)
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Step up and Step down Transformer
• If N P N S > 1 then the transformer is called
step up transformer
Step up transformer is used to increase the
voltage
• If N P N S < 1 then the transformer is called
step down transformer
While it is necessary to lower the voltage, step
down transformer is used
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Ideal Transformer Power Equation
• In ideally transformer all the incoming energy is transformed
from the primary circuit to the magnetic field and into the
secondary circuit. If this condition is met, the incoming
electrical power must equal the outgoing power:
Pincoming=Poutgoing
I PVP = I SVS
VS N S I P
=
=
VP N P I S
giving the ideal transformer equation
Transformers normally have high efficiency, so this formula is
a reasonable approximation.
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Example
A 250 kVA, 11000 V/415 V, 50 Hz single-phase transformer has
80 turns in the secondary. Calculate:
(a) The approximate values of the primary and secondary
currents
(b) The approximate number of primary turns
(c) The maximum value of the flux
Lets solve the problem
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Leakage flux
In practice, some flux traverses paths that take it
outside the windings, which is termed as leakage flux
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Methods of Reducing Leakage flux
The principle methods used in practice are:
1. Making the transformer window long and
narrow.
2. Arranging the primary and secondary winding
concentrically
3. Sandwiching the primary and secondary
windings concentrically.
4. Using Shell type construction
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EMF equation of a Transformer
V
Let Np=No. of turns in primary
NS=No. of turns in secondary
ϕm=maximum flux in core
=Bm×A
f= frequency of ac input
t
T/4f
T=1/f
Flux increases from its zero value to maximum value ϕm
in one quarter of the cycle i.e. 1/4f second
ϕm
Average rate of change of flux= 1 =4fϕm
4f
Average emf/turn= 4fϕm volts
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EMF equation (continued)
If flux varies sinusoidally, the rms value of induced
emf is obtained by multiplying the average value
with form factor.
r.m.s. value emf/turn= 1.11×4fϕm volts
r.m.s. value of the emf in the primary, EP =4.44 fNpϕm
EP=4.44 fNpBmA
r.m.s. value of the emf in the secondary, ES = 4.44 fNSϕm
ES =4.44 fNSBmA
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Energy Losses
• Losses in the transformer arise from :
(a) Winding resistance: Current flowing through the winding
causes resistive heating.
(b) Hysteresis loss: Each time magnetic field is reversed, a small
amount of energy is lost due to hysteresis within the core.
(c) Eddy current: As ferromagnetic materials are good conductor,
the eddy current causes resistive heating. Therefore, laminated
core is used to reduce eddy current.
(d) Magnetostriction: Magnetic flux in the ferromagnetic material
causes it physically expand and contract in each cycle and
produces sound.
(e) Mechanical Loss: Fluctuating force causes mechanical
vibrations and causes buzzing sound.
(f) Stray Loss: Leakage
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Types of Transformer
According to construction
(a) Core type
(b) Shell type
A shell type transformer is one where the windings are
completely surrounded by transformer steel in the
plane of the coil while in the core type
According to type of cooling
(a)Oil filled self –cooled
(b)Oil filled water-cooled
(c)Air-blast
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