MODULE: ELECTRICAL ENGINEERING TECHNOLOGY IV/ELECTRICAL MACHINES & CONTROL II
UNIT 3: TRANSFORMER
INTRODUCTION
The transformer is probably one of the most useful electrical devices ever invented. It can change the magnitude of
alternating voltage or current from one value to another. This useful property of transformer is mainly responsible for
the widespread use of alternating currents rather than direct currents i.e., electric power is generated, transmitted and
distributed in the form of alternating current. Transformers have no moving parts, rugged and durable in
construction, thus requiring very little attention. They also have a very high efficiency—as high as 99%.
A transformer may be defined as a static electric device that transfers electrical energy from one circuit to another
circuit at the same frequency but with changed voltage (or current or both) through a magnetic circuit.
CLASSIFIACTION OF TRANSFORMER
Transformer is generally divided into two types:
1. Single phase Transformer
2. Three phase Transformer
PRINCIPLES OPERATION
The principle of operation of a transformer is explained with the aid of Fig.1. A transformer works on the principle of
electromagnetic induction between two or more coupled circuits.
When an alternating voltage V1 is applied to the primary winding of a transformer, a current (termed exciting current,
If) flows through it. The exciting current produces an alternating flux (f) in the core, which links with both the
winding (primary and secondary). According to Faraday’s laws of electromagnetic induction, the flux will cause self-
induced emf E1 in the primary and mutually induced emf E2 in the secondary winding. But according to Lenz’s law,
primary induced emf will oppose the applied voltage. Therefore, emf induced in the primary winding is equal and
opposite to the applied voltage.
When a load is connected to the secondary side, current will start flowing in the secondary winding. Voltage induced
in the secondary winding is responsible to deliver power to the load connected to it. In this way, power is transferred
from one circuit (primary) to another (secondary) winding through a magnetic circuit by electromagnetic induction.
This is the working principle of the transformer. The induced emf in the secondary E2 is also in phase opposition to
the applied voltage V1 at primary. If the secondary is open circuited, terminal voltage V2 at the secondary is equal in
magnitude and in phase with the induced emf at secondary.
Figure 1: Schematic diagram of Single-phase transformer.
EMF EQUATION OF A SINGLE-PHASE TRANSFORMER
E.M.F EQUATION OF TRANSFORMER
In a transformer, source of alternating current is applied to the primary winding. Due to this, the current in the
primary winding (called as magnetizing current) produces alternating flux in the core of transformer. This alternating
flux gets linked with the secondary winding, and because of the phenomenon of mutual induction an emf gets
induced in the secondary winding. Magnitude of this induced emf can be found by using the following EMF
equation of the transformer.
Prepared by Omondi Ferdinand – 0735 766 013/0712 747 442 1
Engineering Trainer – KMTC - Kisumu Campus
, MODULE: ELECTRICAL ENGINEERING TECHNOLOGY IV/ELECTRICAL MACHINES & CONTROL II
UNIT 3: TRANSFORMER
Figure 6
Let,
N1 = Number of turns in primary winding
N2 = Number of turns in secondary winding
Φm = Maximum flux in the core (in Wb) = (Bm x A)
f = frequency of the AC supply (in Hz)
As, shown in the fig.6(ii), the flux rises sinusoidally to its maximum value Φ m from 0. It reaches to the maximum
value in one quarter of the cycle i.e in T/4 sec (where, T is time period of the sin wave of the supply = 1/f).
Therefore,
average rate of change of flux = Φm /(T/4) = Φm /(1/4f)
Therefore,
average rate of change of flux = 4f Φm ....... (Wb/s).
Now,
Induced emf per turn = rate of change of flux per turn
Therefore, average emf per turn = 4f Φ m ..........(Volts).
Now, we know, Form factor = RMS value / average value
Therefore, RMS value of emf per turn = Form factor X average emf per turn.
As, the flux Φ varies sinusoidally, form factor of a sine wave is 1.11
Therefore, RMS value of emf per turn = 1.11 x 4f Φm = 4.44f Φm.
RMS value of induced emf in whole primary winding (E1) = RMS value of emf per turn X Number of turns in
primary winding
E1 = 4.44f N1 Φm ............................. eq 1
Similarly, RMS induced emf in secondary winding (E 2) can be given as
E2 = 4.44f N2 Φm. ............................ eq 2
from the above equations 1 and 2,
Prepared by Omondi Ferdinand – 0735 766 013/0712 747 442 2
Engineering Trainer – KMTC - Kisumu Campus
UNIT 3: TRANSFORMER
INTRODUCTION
The transformer is probably one of the most useful electrical devices ever invented. It can change the magnitude of
alternating voltage or current from one value to another. This useful property of transformer is mainly responsible for
the widespread use of alternating currents rather than direct currents i.e., electric power is generated, transmitted and
distributed in the form of alternating current. Transformers have no moving parts, rugged and durable in
construction, thus requiring very little attention. They also have a very high efficiency—as high as 99%.
A transformer may be defined as a static electric device that transfers electrical energy from one circuit to another
circuit at the same frequency but with changed voltage (or current or both) through a magnetic circuit.
CLASSIFIACTION OF TRANSFORMER
Transformer is generally divided into two types:
1. Single phase Transformer
2. Three phase Transformer
PRINCIPLES OPERATION
The principle of operation of a transformer is explained with the aid of Fig.1. A transformer works on the principle of
electromagnetic induction between two or more coupled circuits.
When an alternating voltage V1 is applied to the primary winding of a transformer, a current (termed exciting current,
If) flows through it. The exciting current produces an alternating flux (f) in the core, which links with both the
winding (primary and secondary). According to Faraday’s laws of electromagnetic induction, the flux will cause self-
induced emf E1 in the primary and mutually induced emf E2 in the secondary winding. But according to Lenz’s law,
primary induced emf will oppose the applied voltage. Therefore, emf induced in the primary winding is equal and
opposite to the applied voltage.
When a load is connected to the secondary side, current will start flowing in the secondary winding. Voltage induced
in the secondary winding is responsible to deliver power to the load connected to it. In this way, power is transferred
from one circuit (primary) to another (secondary) winding through a magnetic circuit by electromagnetic induction.
This is the working principle of the transformer. The induced emf in the secondary E2 is also in phase opposition to
the applied voltage V1 at primary. If the secondary is open circuited, terminal voltage V2 at the secondary is equal in
magnitude and in phase with the induced emf at secondary.
Figure 1: Schematic diagram of Single-phase transformer.
EMF EQUATION OF A SINGLE-PHASE TRANSFORMER
E.M.F EQUATION OF TRANSFORMER
In a transformer, source of alternating current is applied to the primary winding. Due to this, the current in the
primary winding (called as magnetizing current) produces alternating flux in the core of transformer. This alternating
flux gets linked with the secondary winding, and because of the phenomenon of mutual induction an emf gets
induced in the secondary winding. Magnitude of this induced emf can be found by using the following EMF
equation of the transformer.
Prepared by Omondi Ferdinand – 0735 766 013/0712 747 442 1
Engineering Trainer – KMTC - Kisumu Campus
, MODULE: ELECTRICAL ENGINEERING TECHNOLOGY IV/ELECTRICAL MACHINES & CONTROL II
UNIT 3: TRANSFORMER
Figure 6
Let,
N1 = Number of turns in primary winding
N2 = Number of turns in secondary winding
Φm = Maximum flux in the core (in Wb) = (Bm x A)
f = frequency of the AC supply (in Hz)
As, shown in the fig.6(ii), the flux rises sinusoidally to its maximum value Φ m from 0. It reaches to the maximum
value in one quarter of the cycle i.e in T/4 sec (where, T is time period of the sin wave of the supply = 1/f).
Therefore,
average rate of change of flux = Φm /(T/4) = Φm /(1/4f)
Therefore,
average rate of change of flux = 4f Φm ....... (Wb/s).
Now,
Induced emf per turn = rate of change of flux per turn
Therefore, average emf per turn = 4f Φ m ..........(Volts).
Now, we know, Form factor = RMS value / average value
Therefore, RMS value of emf per turn = Form factor X average emf per turn.
As, the flux Φ varies sinusoidally, form factor of a sine wave is 1.11
Therefore, RMS value of emf per turn = 1.11 x 4f Φm = 4.44f Φm.
RMS value of induced emf in whole primary winding (E1) = RMS value of emf per turn X Number of turns in
primary winding
E1 = 4.44f N1 Φm ............................. eq 1
Similarly, RMS induced emf in secondary winding (E 2) can be given as
E2 = 4.44f N2 Φm. ............................ eq 2
from the above equations 1 and 2,
Prepared by Omondi Ferdinand – 0735 766 013/0712 747 442 2
Engineering Trainer – KMTC - Kisumu Campus
