UNIT 2:- Transformer

Definition :-
• The transformer is the static device which works on the principle of
electromagnetic induction. It is used for transferring the electrical
power from one circuit to another without any variation in their
frequency. In electromagnetic induction, the transfer of energy from
one circuit to another takes places by the help of the mutual induction.
i.e the flux induced in the primary winding is linked with the secondary
winding.
Construction :-
• The primary winding, secondary winding and the magnetic core are the three
important of the transformer. These coils are insulated from each other. The
main flux is induced in the primary winding of the transformer. This flux passes
through the low reluctance path of the magnetic core and linked with the
secondary winding of the transformer.

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 Working principle :-
• The basic principle on which the transformer works is Faraday’s Law of
Electromagnetic Induction or mutual induction between the two coils. The
working of the transformer is explained below. The transformer consists of
two separate windings placed over the laminated silicon steel core.

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• The winding to which AC supply is connected is called primary winding and
to which load is connected is called secondary winding as shown in the
figure. It works on the alternating current only because an alternating flux
is required for mutual induction between the two windings.
• The induced emf in the primary and secondary windings depends upon
the rate of change of flux linkage that is (N dϕ/dt).
• dϕ/dt is the change of flux and is same for both the primary and
secondary windings. The induced emf E1 in the primary winding is
proportional to the number of turns N1 of the primary windings (E1 ∞ N1).
Similarly induced emf in the secondary winding is proportional to the
number of turns on the secondary side. (E2 ∞ N2).
 Transformer on DC supply:-
• As discussed above, the transformer works on AC supply, and it cannot
work not DC supply. If the rated DC voltage is applied across the primary
winding, a constant magnitude flux will set up in the core of the
transformer and hence there will not be any self-induced emf generation,
as for the linkage of flux with the secondary winding there must be an
alternating flux required and not a constant flux.
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According to Ohm’s Law,

• The resistance of the primary winding is very low, and the primary current
is high. So this current is much higher than the rated full load primary
winding current. Hence, as a result, the amount of heat produced will be
greater and therefore, eddy current loss (I2R) loss will be more.
• Because of this, the insulations of the primary windings will get burnt, and
the transformer will get damaged.
 Turn Ratio:-
• It is defined as the ratio of primary to secondary turns.

• If N2 > N1 the transformer is called Step-up transformer

• If N2 < N1 the transformer is called Step down transformer

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 Transformation Ratio:-
• The transformation ratio is defined as the ratio of the secondary voltage to
the primary voltage. It is denoted by K.

• As (E2 ∞ N2 and E1 ∞ N1)

• This is all about the working of the transformer.

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 .
 Transformer on load:-
• When the transformer is on the loaded condition, the secondary of
the transformer is connected to load. The load can be resistive,
inductive or capacitive. The current I2 flows through the secondary
winding of the transformer. The magnitude of the secondary
current depends on the terminal voltage V2 and the load
impedance. The phase angle between the secondary current and
voltage depends on the nature of the load.
• When the load is connected to the secondary of the transformer,
I2 current flows through their secondary winding. The secondary
current induces the magneto motive force N2I2 on the secondary
winding of the transformer. This force set up the flux φ 2 in the
transformer core. The flux φ2 opposes the flux φ, according
to Lenz’s law.

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•
As the flux φ2 opposes the flux φ, the resultant flux of the transformer
decreases and this flux reduces the induced EMF E1. Thus, the strength of
the V1 is more than E1 and an additional primary current I’1 drawn from
the main supply.
• The circuit diagram of the transformer on load condition is as shown in fig
below.

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• The additional current is used for restoring the original value of the flux in
the core of the transformer so that V1 = E1. The primary current I’1 is in
phase opposition with the secondary current I2. Thus, it is called
the primary counter-balancing current.
• The additional current I’1 induces the magnetomotive force N1I’1. And this
force set up the flux φ’1. The direction of the flux is the same as that of the
φ and it cancels the flux φ2 which induces because of the MMF N2I2.
• Now, N1I1’ = N2I2
Therefore,

 Real/practical Transformer:-
• The transformer which consist all type of losses is known as real
transformer. It is an practical transformer that has iron, copper losses and
leakage flux.

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 Ideal transformer:-
• An ideal transformer is an imaginary transformer which does not have any
loss in it, means no core losses, copper losses and any other losses in
transformer. Efficiency of this transformer is considered as 100%.
 Comparison between Practical and ideal transformer:-
S.N Ideal Transformer Practical Transformer

1. The resistance of their primary and The resistance of their primary and
secondary winding becomes zero. secondary winding.
2. The core of the ideal transformer has The core of the practical transformer
infinite permeability. The infinite has definite permeability. The
permeable means less magnetizing definite permeable means more
current requires for magnetizing their magnetizing current requires for
core. magnetizing their core.
3. The leakage flux of the transformer The leakage flux of the transformer is
becomes zero, considered.
4. The ideal transformer has 100 The ideal transformer has less than
percent efficiency, i.e., 100 percent efficiency,

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 Equivalent circuit of single phase transformer
• The simplified equivalent circuit of a transformer is drawn by representing
all the parameters of the transformer either on the secondary side or on
the primary side. The equivalent circuit diagram of the transformer is
shown below:

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Where,
R₁= primary winding resistance
R₂= secondary winding resistance
X₁= primary winding reactance
X₂= secondary winding reactance
V₁= input voltage
V₂= output voltage
E₁= E.M.F induced in primary side of transformer
E₂= E.M.F induced in secondary side of the transformer
Iw= working current
Im= magnetizing current
R₀= no load resistance
X₀= no load reactance

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 Losses in the transformer
• As the electrical transformer is a static device, mechanical loss in
transformer normally does not come into picture. We generally consider
only electrical losses in transformer. Loss in any machine is broadly
defined as difference between input power and output power. When input
power is supplied to the primary of transformer, some portion of that
power is used to compensate core losses in transformer i.e. Hysteresis
loss in transformer and Eddy current loss in transformer core and some
portion of the input power is lost as I2R (copper loss) and dissipated as
heat in the primary and secondary windings.
• Core losses:-
• Hysteresis loss and eddy current loss, both depend upon magnetic
properties of the materials used to construct the core of transformer and
its design. So these losses in transformer are fixed and do not depend
upon the load current. So core losses in transformer which is alternatively
known as iron loss in transformer can be considered as constant for all
range of load.

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• Hysteresis loss in transformer is denoted as,

• Eddy current loss in transformer is denoted as,

Where, Ke – co-efficient of eddy current

Bm – maximum value of flux density in wb/m2
t – thickness of lamination in meters
f – frequency of reversal of the magnetic field in Hz
V – volume of magnetic material in m3

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 Efficiency and Voltage Regulation:-
• The Efficiency of the transformer is defined as the ratio of useful output
power to the input power. The input and output power are measured in
the same unit. Its unit is either in Watts (W) or KW. Transformer
efficiency is denoted by Ƞ.

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Where,
• V2 – Secondary terminal voltage
• I2 – Full load secondary current
• Cosϕ2 – power factor of the load
• Pi – Iron losses = hysteresis losses + eddy current losses
• Pc – Full load copper losses = I22Res
 Voltage Regulation:-
• The voltage regulation is defined as the change in the magnitude of
receiving and sending voltage of the transformer. The voltage regulation
determines the ability of the transformer to provide the constant voltage
for variable loads.
• When the transformer is loaded with continuous supply voltage, the
terminal voltage of the transformer varies. The variation of voltage
depends on the load and its power factor.

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• Mathematically, the voltage regulation is represented as:

Where,
E2 – secondary terminal voltage at no load
V2 – secondary terminal voltage at full load

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 Auto-transformer:-
• An Auto Transformer is a transformer with only one winding wound on a
laminated core. An auto transformer is similar to a two winding
transformer but differ in the way the primary and secondary winding are
interrelated. A part of the winding is common to both primary and
secondary sides.
• On load condition, a part of the load current is obtained directly from the
supply and the remaining part is obtained by transformer action. An Auto
transformer works as a voltage regulator.
• In an ordinary transformer, the primary and the secondary windings are
electrically insulated from each other but connected magnetically as
shown in the figure below. While in auto transformer the primary and the
secondary windings are connected magnetically as well as electrically. In
fact, a part of the single continuous winding is common to both primary
and secondary.

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.

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Let,
• V1 – primary applied voltage
• V2 – secondary voltage across the load
• I1 – primary current
• I2 – load current
• N1 – number of turns between A and B
• N2 – number of turns between C and B
 Instruments Transformer:-
• Instrument Transformers are used in AC system for measurement of
electrical quantities i.e. voltage, current, power, energy, power factor,
frequency. Instrument transformers are also used with protective relays
for protection of power system.
• Basic function of Instrument transformers is to step down the AC System
voltage and current. The voltage and current level of power system is very
high. It is very difficult and costly to design the measuring instruments for
measurement of such high level voltage and current
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• There are two types of instruments transformer, which are explained as
below
 Potential transformer(P.T)
• The potential transformer may be defined as an instrument transformer
used for the transformation of voltage from a higher value to the lower
value. This transformer step down the voltage to a safe limit value which
can be easily measured by the ordinary low voltage instrument like a
voltmeter, wattmeter and watt-hour meters, etc.
• The potential transformer is connected in parallel with the circuit. The
primary windings of the potential transformer are directly connected to
the power circuit whose voltage is to be measured. The secondary
terminals of the potential transformer are connected to the measuring
instrument like the voltmeter, wattmeter, etc.
• The secondary windings of the potential transformer are magnetically
coupled through the magnetic circuit of the primary windings

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• The constructional diagram of potential transformer is as shown in fig
below

• The primary terminal of the transformer is rated for 400V to several

thousand volts, and the secondary terminal is always rated for 400V. The
ratio of the primary voltage to the secondary voltage is termed as
transformation ratio or turn ratio.

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 Current transformer(C.T):-
• A current transformer is a device that is used for the transformation of
current from a higher value into a proportionate current to a lower value.
It transforms the high voltage current into the low voltage current due to
which the heavy current flows through the transmission lines is safely
monitored by the ammeter.
• The primary and secondary current of the current transformers are
proportional to each other. The current transformer is used for measuring
the high voltage current because of the difficulty of inadequate insulation
in the meter itself. The current transformer is used in meters for
measuring the current up to 100 amperes.
• The current transformer is used with the AC instrument, meters or control
apparatus where the current to be measured is of such magnitude that
the meter or instrument coil cannot conveniently be made of sufficient
current carrying capacity.

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The current transformer is shown in the figure below.

• The primary and the secondary windings are insulated from the cores and
each other. The primary winding is a single turn winding (also called a bar
primary) and carries the full load current. The secondary winding of the
transformers has a large number of turns.

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• The ratio of the primary current and the secondary current is known as
a current transformer ratio of the circuit
• The current ratio of the transformer is usually high. The secondary current
ratings are of the order of 5A, 1A and 0.1A. The current primary ratings
vary from 10A to 3000A or more.
 Three phase transformer:-
• A three phase transformer is used to transfer a large amount of power.
The three phase transformer is required to step-up and step-down the
voltages at various stages of a power system network. The three phase
transformer is constructed in two ways.
1. Three separate single phase transformer is suitably connected for three
phase operation.
2. A single three-phase transformer in which the cores and windings for all
the three phases are merged into a single structure.
• The three single-phase transformer can be used as a three-phase
transformer when their primary and secondary winding are connected to
each other.

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 Advantages and disadvantages of single unit three phase
transformer:-
• It is found that generation, transmission, and distribution of electrical
power are more economical in three phase system than a single phase
system. For a three-phase system, three single-phase transformers are
required. Three phase transformation can be done in two ways, by using a
single three-phase transformer or by using a bank of three single phase
transformers. There are advantages and disadvantages to each option.
• A single 3 phase transformer costs around 15 % less than a bank of three
single phase transformers. Again former occupies less space than later. For
a very big transformer, it is impossible to transport a large three-phase
transformer to the site and is instead easier to transport three single-
phase transformers, which are erected separately to form a three-phase
unit.
• Another advantage of using a bank of three single phase transformers is
that, if one unit of the bank becomes out of order, then the bank can be
run as an open delta transformer.

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 Types of transformer connections:-
• The three phase transformer consists three transformers either separate
or combined with one core. The primary and secondary of the transformer
can be independently connected either in star or delta. There are four
possible connections for a 3-phase transformer bank.
1. Star-star transformer connections:-
• Star-star transformer is formed in a 3 phase transformer by connecting
one terminal of each phase of individual side, together. The common
terminal is indicated by suffix 1 in the figure below. If terminal with suffix 1
in both primary and secondary are used as common terminal, voltages of
primary and secondary are in same phase. That is why this connection is
called zero degree connection or 0o – connection.
• star-star transformer connection is called 180o-connection, of three phase
transformer.

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• The connection diagram of star- star transformer is as shown in fig below

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2. Delta-Delta Transformer:-

• In delta-delta transformer, 1 suffixed terminals of each phase primary

winding will be connected with 2 suffixed terminal of next phase primary
winding.

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• If primary is HV side, then A1 will be connected to B2, B1 will be connected
to C2 and C1 will be connected to A2. Similarly in LV side 1 suffixed
terminals of each phase winding will be connected with 2 suffixed
terminals of next phase winding. That means, a1 will be connected to b2,
b1 will be connected to c2 and c1 will be connected to a2.

• If transformer leads are taken out from primary and secondary 2 suffixed
terminals of the winding, then there will be no phase difference between
similar line voltages in primary and secondary. This delta delta
transformer connection is zero degree connection or 0o-connection. But in
LV side of transformer, if, a2 is connected to b1, b2 is connected to c1 and c2
is connected to a1. The secondary leads of transformer are taken out from
2 suffixed terminals of LV windings, and then similar line voltages in
primary and secondary will be in phase opposition. This connection is
called 180o-connection, of three phase transformer.

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3. Star-Delta Transformer:-
• Here in star-delta transformer, star connection in HV side is formed by
connecting all the 1 suffixed terminals together as common point and
transformer primary leads are taken out from 2 suffixed terminals of
primary windings.

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• The delta connection in LV side is formed by connecting 1 suffixed terminals of
each phase LV winding with 2 suffixed terminal of next phase LV winding. More
clearly, a1 is connected to b2, b1 is connected to c2 and c1 is connected to a 2. The
secondary (here it considered as LV) leads are taken out from 2 suffixed ends of
the secondary windings of transformer.
• The transformer connection diagram is shown in the figure beside. It is
seen from the figure that the sum of the voltages in delta side is zero. This
is a must as otherwise closed delta would mean a short circuit. It is also
observed from the phasor diagram that, phase to neutral voltage
(equivalent star basis) on the delta side lags by − 30 o to the phase to
neutral voltage on the star side; this is also the phase relationship
between the respective line to line voltages. This star delta transformer
connection is therefore known as − 30o-connection. Star-delta + 30o-
connection is also possible by connecting secondary terminals in following
sequence. a2 is connected to b1, b2 is connected to c1 and c2 is connected
to a1. The secondary leads of transformer are taken out from 2 suffixed
terminals of LV windings,

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4. Delta-Star Transformer
• Delta-star transformer connection of three phase transformer is similar to
star – delta connection. If any one interchanges HV side and LV side of
star-delta transformer in diagram, it simply becomes delta – star
connected 3 phase transformer. That means all small letters of star-delta
connection should be replaced by capital letters and all small letters by
capital in delta-star transformer connection.

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5. V/V or open delta connections of transformer:-

• If one transformer of delta-delta connection is damaged or accidentally

opened, then the defective transformer is removed, and the remaining
transformer continues to work as a three phase bank. The rating of the
transformer bank is reduced to 58% of that of the actual bank. This is
known as the open delta or V-V delta. Thus, in open winding transformer,
two transformers are used instead of three for the 3-phase operation.

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 Choice between star and delta connections of three phase
transformer:-
• In star connection with earthed neutral, phase voltage i.e. phase to
neutral voltage, is 1/√3 times of line voltage i.e. line to line voltage. But in
the case of delta connection phase voltage is equal to line voltage. Star
connected high voltage side electrical power transformer is about 10%
cheaper than that of delta connected high voltage side transformer.
 Parallel operation of single phase and three phase
transformer:-
 Parallel operation of single phase:-
• Parallel Operation of a Single Phase Transformer means that the two or
more transformers having the same polarities, same turn ratios, same
phase sequence and the same voltage ratio are connected in parallel with
each other.
• The circuit diagram of two single-phase transformer A and B connected in
parallel are shown below:

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 .

• The parallel operation of a transformer has some advantages likes it

increases the efficiency of the system, makes the system more flexible and
reliable. But it increases the short-circuit current of the transformers.
Reasons For Parallel Operation:-
Parallel operation of a transformer is necessary because of the following
reasons are given below:
• It is impractical and uneconomical to have a single large transformer for
heavy and large loads. Hence, it will be a wise decision to connect a
number of transformers in parallel.
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• In substations, the total load required may be supplied by an appropriate
number of the transformer of standard size. As a result, this reduces the
spare capacity of the substation.
• If the transformers are connected in parallel, so there will be scope in
future, for expansion of a substation to supply a load beyond the capacity
of the transformer already installed.
• If there will be any breakdown of a transformer in a system of
transformers connected in parallel, there will be no interruption of power
supply, for essential services.
• If any of the transformer from the system is taken out of service for its
maintenance and inspection, the continuity of the supply will not get
disturbed.
Necessary Conditions For Parallel Operation:-
• For the satisfactory parallel operation of the transformer, the two main
conditions are necessary. One is that the Polarities of the transformers
must be the same. Another condition is that the Turn Ratio of the
transformer should be equal.

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The other three desirable conditions are as follows:-
• The voltage at full load across the transformer internal impedance should
be equal.
• The ratio of their winding resistances to reactances should be equal for
both the transformers. This condition ensures that both transformers
operate at the same power factor, thus sharing their active power and
reactive volt-amperes according to their ratings.
• The phase sequence or the order in which the phases reach their
maximum positive voltage, must be identical for two parallel transformers.
Otherwise, during the cycle, each pair of phases will be short circuited.

• Fig :-parallel operation of three phase transformer is different other things

are same.
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