A
transformer is one of the most crucial component in Electrical and Electronics
Engineering. It is used in a variety of electronic circuits, control systems
and almost all power systems. Transformers are available in a wide range of
sizes, from the tiny units used in electronics and control systems to massive
sizes used in high voltage transmission systems, weighing hundreds of tons.
Therefore, the detailed analysis of the transformers is important for
Electrical and Electronics Engineers for understanding the many electronic and
control systems and almost all power systems.
What is an Electric Transformer?
A transformer is a magnetically coupled static device that transfers electrical energy from one AC voltage level to another AC voltage level at the same frequency by the help of mutual induction.
Like other electrical rotating machines, a transformer works on the principle of Faraday's law of electromagnetic induction. Being an electromagnetic device, its analysis greatly helps in understanding the operation of electromechanical energy conversion devices such as induction machines and synchronous machines, which also use magnetic fields for the conversion of electrical energy to mechanical energy and vice versa. That’s why transformers are typically studied together with the electrical rotating machine in a book called Electrical Machines. In this book the study of transformers usually precedes the electrical machine study.
For three phase transformers
three sets of coils or windings are used at both sides, which are connected in
either star or delta. Three phase transformers is an advanced topic and covered
in separate articles.
Working Principle of Transformer
As
we discussed above, the working of a transformer is based on the principle of Faraday's
law of mutual induction, according to which an EMF is induced in secondary
winding through the magnetic field generated by primary winding without any
electrically connection between them.
Let us understand the working of a transformer in detail with the help of optimum schematic diagrams. To simplify the explanation, we are taking the example of an ideal transformer.
What is an Ideal Transformer?
In an ideal transformer, there are no losses, and the permeability of the magnetic core is infinite, which means the reluctance of the core is zero. As the reluctance of the core is zero, all the flux passed through the magnetic core means there is no leakage of flux.
Transformer on no load
When the AC voltage source is connected to the primary side of a transformer, it establishes an alternating magnetic flux in the magnetic core. The amplitude and frequency of this alternating magnetic field depend on the amplitude and frequency of the applied voltage source and number of turns in primary winding. The direction of the alternating magnetic field is such that it satisfies the right-hand thumb rule. Ideally, all the magnetic field passes through the magnetic core means there is no leakage of flux.
Let
us say, the instantaneous value of the AC voltage applied to the primary
winding is Vs = Vm sin ωt and it draws a
small amount of current called no load current or magnetizing current (io),
as the transformer is on no load. This magnetizing current establishes a
magnetic field having instantaneous value ɸ = ɸm sin ωt in the magnetic core.
This
alternating flux in the magnetic core produced by primary winding links with
both secondary as well as primary winding. The flux linkage to the primary
winding and secondary wiring is denoted by λ1 = N1ɸ and λ2 = N1ɸ respectively, where N1 and N2 are the number of terms in primary winding and secondary winding respectively. As this flux is alternating in nature, it induces an emf in both the windings with the same frequency as the flux.
EMF Equation of Transformer
According to the Faraday's law of induction,
magnetically induced EMF is given by
e = dλ / dt = N
dɸ/dt
Since, the flux Linkages to the primary winding is λ1 =
N1ɸ, the induced EMF in primary winding is,
e1 = dλ1/dt = N1
dɸ/dt
ɸ = ɸm sin ωt
(After putting values and solving we get,)
e1 = ω N1ɸmax
cosωt (ω = 2πf)
E1 = √2 π f N1 ɸm = 4.44
f N1 ɸm
Similarly, the induced emf in secondary winding is,
E2 =
√2 π f N2 ɸm
The
above equation of E1 and E2 shows the EMF equation of the
transformer for both primary and secondary winding respectively. From these
equations, we can conclude that the EMF induced in each winding depends on the
number of turns in its respective winding
The polarity of the induced EMF in secondary winding (E2) is the same as the instantaneous polarity of induced EMF in primary winding(E1), which is indicated by the dot polarity in the transformer schematic (discussed further).
Due to this induced emf secondary winding E2, the secondary winding is capable of delivering current to the load without being electrically connected to the primary winding. However, in this discussion the transformer is on no load, means the secondary current is zero.
Now, let us explore the working of the transformer when it is connected to load.
Transformer on Load
In
order to understand how the transformer works with the load, let’s consider the
same conditions discussed above. Below the given figure shows the transformer
connected with the load.
Unlike
the previous discussion, here in this condition the transformer is connected to
the load, which draws the current I2 from the secondary winding. Due to this
current the secondary winding produces its own magnetic field and according to
the right-hand thumb rule its direction is such that it opposes the main flux
ϕ.
However, the mutual flux ϕ cannot change because it disturbed the terminal voltage balance between V1 and E1 on the primary side. To maintain this balance, the primary winding draws additional current i1 from the source, which is exactly equal to the current I2 required by the load,
This additional current produces its own magnetic field which cancels out the effect of the magnetic field produced by the secondary current I2, so that the flux in the magnetic core is maintained constant and independent of load current.
Thus, the transformer’s secondary winding delivers the load current without being electrically connected to the primary winding. In this way the power is transferred from the primary side to the secondary side of the transformer.
Dot convention of the transformer
The
dot convention of the transformer indicates the polarity of the induced EMF in
secondary winding is the same as that of the polarity of voltage applied or
induced in primary winding.
The dot polarities in a transformer are assigned such that, when current enters or leaves through the dot simultaneously, then the fluxes are additive. This means that if the current enters the dot in one winding, then it should leave through the dot on the secondary winding to satisfy the Lenz law. According to which, the direction of the induced EMF through the magnetic induction is such that it opposes the cause of it.
Transformation Ratio
Types of Transformers
Generally, there are two types of transformers.
- Step Up Transformer
- Step Down Transformer
Step Up Transformer
If number of turns in secondary
winding is greater than number of turns in primary winding then emf induced in
secondary winding is greater than in primary winding then the transformer is
known as step up transformer. As we know that the electric power is generated
at low voltage which then step up to very high voltage by means of step-up
transformer and then transmitted. In transformer high voltage size is
associated with low current so transmission losses are also reduced.
Step Down Transformer
If number of turns in secondary
winding is less than number of turns in primary winding then induced emf in
secondary winding is less than in primary winding then the transformer is known
as step down transformer. As we know that, the transmission voltage is very
high which is stepped down by means of step-down transformer at the receiving
end.
Note:- If number of turns in primary winding is equal to number of turns is
secondary winding then primary and secondary voltages are equal, then the
transformer is said to have one-to-one ratio. One-to-one transformers are used
to electrically isolate two parts of a network it is also known as isolation
transformer.
related tags
#_Equivalent Circuit of Transformer
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