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Transformers
Transformer
 It is a static device.
 It transfers electrical energy from one electrical circuit to other
with desired change in voltage and current, without changing
the frequency(f=50Hz) and power.
 Constant flux device
 Magnetically coupled and electrically isolated
 Electro magnetic conversion device.
Principle of operation
It is based on
principle of MUTUAL
INDUCTION.
According to which
an e.m.f. is induced
in a coil when
current
in
the
neighbouring
coil
changes.
Constructional detail : Shell type
 Parallel magnetic circuit
 Windings are wrapped around the central limb of a laminated
core.
 Sandwitch winding to reduce the leakage flux
 Less amount of copper & more amount of insulation is
required
Constructional detail : Core type
 Series magnetic circuit
 Windings are wrapped around two sides of a laminated square
core.
 More amount of copper & less amount of insulation is
required.
 Economical for high voltage applications
Sectional view of transformers
Note:
High voltage conductors are smaller cross section conductors
than the low voltage coils
Core type
Fig1: Coil and laminations of
core type transformer
Fig2: Various types of cores
Shell type
Fig: Sandwich windings
• The HV and LV
windings are split
into no. of sections
• Where HV winding
lies between two LV
windings
• In sandwich coils
leakage can be
controlled
Cut view of transformer
Transformer with conservator and
breather
Working of a transformer
1. When current in the primary coil
changes being alternating in
nature, a changing magnetic field
is produced
2. This changing magnetic field gets
associated with the secondary
through the soft iron core
3. Hence magnetic flux linked with
the secondary coil changes.
4. Which induces e.m.f. in the
secondary.
Ideal Transformers
• Zero leakage flux:
-Fluxes produced by the primary and secondary currents
are confined within the core
• The windings have no resistance:
- Induced voltages equal applied voltages
• The core has infinite permeability
- Reluctance of the core is zero
- Negligible current is required to establish magnetic
flux
• Loss-less magnetic core
- No hysteresis or eddy currents
Ideal transformer
V1 – supply voltage ;
V2- output voltgae;
Im- magnetising current;
E1-self induced emf ;
I1- noload input current ;
I2- output current
E2- mutually induced emf
Phasor diagram: Transformer on Noload
Transformer on load assuming no
voltage drop in the winding
Fig shows the Phasor diagram of a transformer
on load by assuming
1. No voltage drop in the winding
2. Equal no. of primary and secondary turns
Transformer on load
Fig. a: Ideal transformer on load
Fig. b: Main flux and leakage
flux in a transformer
Equivalent circuit of a transformer
No load equivalent circuit:
Equivalent circuit parameters referred to
primary and secondary sides respectively
Transferring secondary parameters to primary side
Cu loss after transfer = cu loss before transfer
I 12 R2'  I 22 R2
 I2
R  
 I1
R2
 2
k
'
2
2

 R2

Where R21 - Equivalent secondary resistance w.r.t primary
R01 = R1 + R21
Where R01 – Total primary resistance referred to secondary
Equivalent circuit referred to primary side :
Transferring primary parameters to secondary side :
Cu loss after transfer = cu loss before transfer
I 22 R1'  I12 R1
 I1
'
R1  
I
 2
2


 R1

= k2 R1
Where R11 - Equivalent primary resistance w.r.t secondary
R02 = R2 + R11
Where R01 – Total secondary resistance referred to primary
Equivalent circuit referred to secondary side :
Equivalent circuit w.r.t primary :
where
Approximate equivalent circuit
Since the no load current is 1% of the full load current, the no
load circuit can be neglected
Transformer Tests
•The performance of a transformer can be calculated on the basis of
equivalent circuit
•The four main parameters of equivalent circuit are:
- R01 as referred to primary (or secondary R02)
- the equivalent leakage reactance X01 as referred to primary
(or secondary X02)
- Magnetising susceptance B0 ( or reactance X0)
- core loss conductance G0 (or resistance R0)
•The above constants can be easily determined by two tests
- Oper circuit test (O.C test / No load test)
- Short circuit test (S.C test/Impedance test)
•These tests are economical and convenient
- these tests furnish the result without actually loading the
transformer
Electrical Machines
Open-circuit Test
In Open Circuit Test the transformer’s secondary winding is open-circuited, and
its primary winding is connected to a full-rated line voltage.
Core loss  Woc  V0 I 0 cos 0
cos 0 
Woc
V0 I 0
I c or I w  I 0 cos 0
R0 
V0
Iw
V0
I
I
G0  w
V0
X0 
• Usually conducted on H.V side
I m or I   I 0 sin 0  I 02 -I w2
I
• To find
I
B0 
I 0  V0 Y0 ;  Yo  0
V0
V0
(i) No load loss or core loss
W
(ii) No load current Io which is
Woc  V02 G 0 ;  Exciting conductanc e G 0  oc2
V0
helpful in finding Go(or Ro )
and Bo (or Xo )
& Exciting susceptanc e B0  Y02  G02
Short-circuit Test
In Short Circuit Test the secondary terminals are short circuited, and the
primary terminals are connected to a fairly low-voltage source
The input voltage is adjusted until the current in the short circuited windings
is equal to its rated value. The input voltage, current and power is
measured.
Full load cu loss  Wsc  I sc2 R01
• Usually conducted on L.V side
• To find
(i) Full load copper loss – to pre determine the efficiency
(ii) Z01 or Z02; X01 or X02; R01 or R02 - to predetermine the
voltage regulation
R 01 
Wsc
I sc2
Z 01 
Vsc
I sc
 X 01  Z 012  R012
Voltage regulation 
recall
no - load voltage  full - load voltage
no - load voltage
Vs N s

Vp N p
Secondary voltage on no-load
 N2 

V2  V1 
 N1 
V2 is a secondary terminal voltage on full load
 N2 
  V2
V1 
N1 

Voltage regulation 
 N2 

V1 
 N1 
Substitute we have
Formula: voltage regulation
In terms of secondary values
I 2 R02 cos 2  I 2 X 02 sin 2
0 V2  V2
% regulation 

0 V2
0 V2
where ' ' for lagging and '-' for leading
In terms of primary va lues
V1  V2' I1 R01 cos 1  I1 X 01 sin 1
% regulation 

V1
V1
where ' ' for lagging and '-' for leading
Transformer Efficiency
Transformer efficiency is defined as (applies to motors, generators and
transformers):
Pout

 100%
Pin
Pout

 100%
Pout  Ploss
Types of losses incurred in a transformer:
Copper I2R losses
Hysteresis losses
Eddy current losses
Therefore, for a transformer, efficiency may be calculated using the following:
VS I S cos 

x100%
PCu  Pcore  VS I S cos 
Electrical Machines
Losses in a transformer
Core or Iron loss:
Total cu losses =
=
=
Condition for maximum efficiency :
The load at which the two losses are equal =
All day efficiency :
ordinary commercial efficiency 
 all day 
out put in watts
input in watts
output in kWh
( for 24 hours)
Input in kWh
•All day efficiency is always less than the commercial efficiency