SAB 2032
ELECTRICAL TECHNOLOGY
Weeks 13-14
Transformer
06/07/2009
INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformers
INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformers
A transformer is a static machine which step voltage/current
up or down
Unlike in rotating machines, there is no electromechanical
energy conversion
The transfer of energy takes place through the magnetic field
and all currents and voltages are AC
Transformer can be categorized as:
 The ideal transformers
 Practical transformers
 Special transformers
 Three phase transformers
INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformers
INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformers
INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformers
INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformers
Applications of the transformer
A typical power system consists of generation, transmission
and distribution
Power from plant/station is generated around 11-13-20-30kV
(depending upon manufacturer and demand)
This voltage is carried out at a distance to reach for utilization
through transmission line system by step up transformer at
different voltage levels depending upon distance and losses
Its distribution is made through step down transformer
according to the consumer demand
INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformers
Transformer is one of the most useful electrical devices
ever invented
Functions of transformer:
Raise or lower voltage or current in AC circuit
Isolate circuit from each other
Increase or decrease the apparent value of a capacitor,
inductor or resistor
Enable to transmit electrical energy over great distances
Distribute safely in homes and factories
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Principles of Transformer
A transformer consists of two electric circuits called primary and
secondary
A magnetic circuit provides the link between primary
and secondary
When an AC voltage is applied to the
primary winding Vp of the transformer,
an AC current Ip will result
Ip sets up a time-varying magnetic flux Ф
in the core
A voltage is induced to the secondary
circuit Vs according to
the Faraday’s law
INSPIRING CREATIVE AND INNOVATIVE MINDS
Core Types of Transformer
The magnetic (iron) core is made of thin laminated steel
sheet. The reason of using laminated steel is to minimize the
eddy current loss by reducing thickness
There are two common cross section of
core which include square
or (rectangular) for small transformers
and circular (stepped) for the large
and 3 phase transformers.
INSPIRING CREATIVE AND INNOVATIVE MINDS
Configuration of Single phase
transformer
Primary
Winding
Multi-layer
Laminated
Iron Core
Secondary
Winding
H1 H2
X1
X2
Winding
Terminals
INSPIRING CREATIVE AND INNOVATIVE MINDS
3 Phase Transformer
The three phase transformer iron core has three legs
A phase winding is placed in each leg
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Construction of Transformer
This can be divided into 2 types:
 Core (U/I) Type: Is constructed from a stack of U and I shaped
laminations. In a core-type transformer, the primary and secondary
windings are wound on two different legs of the core
 Shell Type: Is constructed from a stack E and I shaped laminations. In a
shell-type transformer, the primary and secondary windings are wound on
the same leg of the core, as concentric windings, one on top of the other.
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Construction of a Small Transformer
Iron core
Insulation
Secondary
winding
Terminals
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformer with Cooling System
High voltage
bushing
Oil tank
Bushing
Low voltage
bushing
Steel
tank
Iron core
behind the steel
bar
Cooling
radiators
Winding
Insulation
Radiator
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INSPIRING CREATIVE AND INNOVATIVE MINDS
The Ideal Transformer
For an ideal transformer, we assume
► No losses
► Core is infinitely permeable
► Flux produced by the primary is completely linked by the
secondary and vice versa
► No leakage flux of any kind
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INSPIRING CREATIVE AND INNOVATIVE MINDS
The Ideal Transformer
►
►
►
Primary and secondary posses N1 and N2 turns
respectively
Primary is connected to a sinusoidal source Eg
Magnetizing current Im creates a flux of Φm
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INSPIRING CREATIVE AND INNOVATIVE MINDS
The Ideal Transformer
►
►
The flux is completed linked by the primary and secondary
windings – mutual flux
Flux varies sinusoidally and reaches a peak value of Φm
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INSPIRING CREATIVE AND INNOVATIVE MINDS
The Ideal Transformer
A transformer with more turns in its primary
than its secondary coil will reduce voltage and
is called a step-down transformer
One with more turns in the secondary than the
primary is called a step-up transformer
06/07/2009
INSPIRING CREATIVE AND INNOVATIVE MINDS
The Ideal Transformer
The sinusoidal current Im produces a sinusoidal mmf NIm
which in turn creates a sinusoidal flux. The flux induces an
effective voltage E across the terminals of the coil
Induces Voltages:
► The effective induced emf in primary winding is
E1  4.44 fN1m
►
Where N1 is the number of winding turns in primary
winding, Фm the maximum (peak) flux and f the
frequency of the supply voltage
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INSPIRING CREATIVE AND INNOVATIVE MINDS
The Ideal Transformer
This equation shows that for a given frequency and a given
number of turns, Фm varies in proportion to the applied
voltage Eg
This means that if Eg is kept constant, the peak flux must
remain constant
Similarly, the effective induced emf in secondary winding:
E2  4.44 fN2m
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INSPIRING CREATIVE AND INNOVATIVE MINDS
The Ideal Transformer - at No Load
E1 N1

a
E2 N 2
a = Turn ratio
E1 = Voltage induced in the primary [V]
E2 = Voltage induced in the secondary [V]
N1 = Number of turns on the primary
N = Number of turns on the primary
2
INSPIRING CREATIVE AND INNOVATIVE MINDS
Ideal Transformer under load:
Current ratio
Let us connect a load Z across the secondary of the ideal
transformer. A secondary current I2 will immediately flow.
Does E2 change when we connect the load?
1) In an ideal transformer the primary and secondary windings
are linked by the mutual flux, Фm, consequently voltage ratio
will be the same as at no load
2) If the supply voltage Eg is kept fixed, then the primary induced
voltage E1 remain fixed. Consequently, Фm also remains
fixed. It follows that E2 also remain fixed
We conclude that E2 remains fixed whether a load is connected or not
INSPIRING CREATIVE AND INNOVATIVE MINDS
Ideal Transformer under load:
Current ratio
Let us now examine the mmf created by the primary and
secondary windings. First, current I2 produces a secondary mmf
N2I2. If it acted alone, this mmf would produce a profound
change in the Фm. But we just saw that Фm does not change
under load.
We conclude that flux Фm can only remain fixed if the primary
develops a mmf which exactly counterbalances N2I2 at every
instant. Thus, a primary current I1 must flow so that
N1 I1  N 2 I 2
06/07/2009
INSPIRING CREATIVE AND INNOVATIVE MINDS
Ideal Transformer under load:
Current ratio
To obtain the required instant-to-instant bucking effect, current I1
and I2 must increase and decrease at the same time
In other words, the current must be in phase
(a)Ideal transformer under load
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(b)Phasor relationships under
load
INSPIRING CREATIVE AND INNOVATIVE MINDS
Ideal Transformer under load:
Current ratio
I 2 N1 1


I1 N 2 a
I 1 = Primary current [A]
I 2 = Secondary current [A]
= Number of turns on the primary
N 2 = Number of turns on the secondary
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N1
INSPIRING CREATIVE AND INNOVATIVE MINDS
Transformer Impedance
Z L' 
VP
IP
Primary Impedance:
Primary impedance in terms of
Z L'  a 2 Z L
secondary impedance :
VP  aVS
Primary Voltage :
I
I

Primary Current :
a
S
P
INSPIRING CREATIVE AND INNOVATIVE MINDS
Example problem
A transformer coil possesses 4000 turns and
links an ac flux having a peak value of 2 mWb.
If the frequency is 60 Hz, calculate the
effective value of the induced voltage E.
Ans: 2131V
INSPIRING CREATIVE AND INNOVATIVE MINDS
Example problem
A coil having 90 turns is connected to a 120V,
60 Hz source. If the effective value of the
magnetizing current is 4 A, calculate the
following:
a. The peak value of flux
b. The peak value of the mmf
c. The inductive reactance of the coil
d. The inductance of the coil.
INSPIRING CREATIVE AND INNOVATIVE MINDS
Real Transformer
Leakage Flux: Not all of the flux produced by the primary
current links the winding, but there is leakage of some flux
into air surrounding the primary. Similarly, not all of the flux
produced by the secondary current (load current) links the
secondary, rather there is loss of flux due to leakage. These
effects are modelled as leakage reactance in the equivalent
circuit representation.
INSPIRING CREATIVE AND INNOVATIVE MINDS
Magnetization Current in a Real
Transformer
Although the output of the transformer is open circuit, there will
still be current flow in the primary windings
•
•
Magnetization current, iM
Core-loss current, ic
The relation between current and flux is proportional since
F  NI  S
S
i
N
INSPIRING CREATIVE AND INNOVATIVE MINDS
Magnetization Current in a Real
Transformer
Therefore, in theory, if the flux produce in core is sinusoidal,
than the current should also be a perfect sinusoidal.
Unfortunately, this is not true.
Current in a transformer has the following characteristics:
• It is not sinusoidal but a combination of high frequency
oscillation
• The current lags the voltage at 900
• At saturation, the high frequency components will be
extreme
INSPIRING CREATIVE AND INNOVATIVE MINDS
Magnetization Current in a Real
Transformer
Core-loss current:
• Eddy current loss- is dependent upon the rate of change of flux
• Hysteresis loss - a non linear loss
At no-load, the primary windings is known as the excitation
current
i  im  ic
INSPIRING CREATIVE AND INNOVATIVE MINDS
The equivalent circuit of a transformer
Taking into account real transformer, there are several losses
that has to be taken into account in order to accurately model
the transformer, namely:
1- Copper (I2R) Losses
2- Eddy current Losses
3- Hysteresis Losses
4- Leakage flux
INSPIRING CREATIVE AND INNOVATIVE MINDS
Equivalent circuit of a Real Transformer
Equivalent Circuit of a Two-winding, 1-phase:
Rc : Core loss component, this resistance models the active
loss of the core
Xm : magnetization component, this resistance models the
reactive loss of the core
Rp and Xp : are resistance and reactance of the primary winding
Rs and Xs : are resistance and reactance of the secondary winding
INSPIRING CREATIVE AND INNOVATIVE MINDS
Equivalent circuit of a Real Transformer
Impedance Transfer:
To model a transformer, it is important to understand how
impedance are transferred from one side to another, that is
primary to secondary or secondary to primary
Impedance transfer is used to calculate the current/voltage
easier and also to get the voltage and current ratio for the rest
of the calculation
In general any impedance transferred from secondary side to
primary side must be multiplied by the square of the turn ratio,
a2
INSPIRING CREATIVE AND INNOVATIVE MINDS
Equivalent circuit-seen from primary side
The terminal voltage (Vp,Vs) is not constant and changes
depends on the load current.
Secondary parameters transferred to primary
INSPIRING CREATIVE AND INNOVATIVE MINDS
Equivalent circuit of a Real Transformer
Equivalent Circuit
a) referred to primary side
b) referred to secondary side
INSPIRING CREATIVE AND INNOVATIVE MINDS
Approximate equivalent circuit
Approximate equivalent circuit
c) Referred to primary side (no exicitation) d) Referred to
secondary side (no excitation)
INSPIRING CREATIVE AND INNOVATIVE MINDS
Approximate equivalent circuit
In this model, the parameters from secondary are transferred
to primary side.
where, Rep and Xep are equivalent resistance and reactance
from primary winding side
INSPIRING CREATIVE AND INNOVATIVE MINDS
Voltage Regulation
Is defined as the change in the magnitude of the secondary
voltage as the load current changes from the no-load to full
load
The primary side voltage is always adjusted to meet the
load changes; hence V’s and Vs are kept constant.
VNL  VFL
%VR 
100
VNL
 V p  aVs  aVs  100


 V p  Vs' Vs'  100
INSPIRING CREATIVE AND INNOVATIVE MINDS
Efficiency of Transformer
As always, efficiency is defined as power output to power
input ratio
  Pout Pin 100%
Pin  Pout  Pcore  Pcopper
Pcopper represents the copper losses in primary and
secondary windings. There are no rotational losses.
INSPIRING CREATIVE AND INNOVATIVE MINDS
Example Problem
A not-quite-ideal transformer having 90 turns on the
primary and 2250 turns on the secondary is connected
to a 120 V, 60 hz source. The coupling between the
primary and the secondary is perfect but the
magnetizing current is 4 A. calculate:
a. The effective voltage across the secondary
terminals
b. The peak voltage across the secondary terminals.
c. The instantaneous voltage across the secondary
when the instantaneous voltage across the primary
is 37 V.
Ans: 3000V, 4242 V, 925 V.
43
Example Problem
An ideal transformer having 90 turns on the primary and
2250 turns on the secondary is connected to a 200 V,
50 Hz source. The load across the secondary draws a
current of 2 A at a power factor of 80 per cent lagging.
Calculate :
a. The effective value of the primary current
b. The instantaneous current in the primary when the
instantaneous current in the secondary is 100 mA.
c. The peak flux linked by the secondary winding.
Ans: 50 A, 2.5 A, 10 mWb
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QUESTION
06/07/2009
INSPIRING CREATIVE AND INNOVATIVE MINDS
Example Problem
• A 125 kVA transformer has 500 turns on the primary
and 80 turns on the secondary. The primary and
secondary resistances are 0.5 Ω and 0.025 Ω
respectively, and the corresponding leakage
reactances are 2.5 Ω and 0.025 Ω respectively. The
supply voltage is 2.2 kV. Calculate:
The voltage regulation and the secondary terminal
voltage for full load having a power factor of 0.85
lagging
46
Example Problem
• The primary and secondary windings of a 400 kVA
transformer have resistances of 0.3 Ω and 0.0015 Ω
respectively. The primary and secondary voltages are
15 kV and 0.4 kV respectively. If the core loss is 2.5
kW and the power factor of the load is 0.80, calculate
the efficiency of the transformer on full load.
47