Transformer

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Transformer is a static device or a machine that transfers electrical energy from one electrical circuit to another through medium of magnetic field without change in frequency. It is an electromagnetic energy conversion device and can raise or lower the voltage with a corresponding decrease or increase in current. A transformer consists of two conducting coils (or windings) having a mutual inductance. These coils are wound on a laminated core made of high permeability magnetic material. The coil which receives electrical energy from supply terminals is called
primary winding and the winding which delivers power to the external load circuit is called secondary winding. The windings of a transformer are coupled magnetically but are not connected electrically and thus a transformer provides isolation.

Construction of a Transformer:

There are two types transformers core type and shell type. In core type the windings surround the steel core as shown in the below figure. In shell type core the core surrounds the winnings. A core type requires less iron and more conducting material in comparison with an equivalent shell type transformer. Core type is used for high power application and the shell type is used for low power applications.

shell type transformer

core type transformer

Principle of working of a transformer:

The transformer works on the principle of faraday’s law of electromagnetic induction. The physical basis of a transformer is mutual induction between two circuits linked by a common magnetic flux through a path of low reluctance as shown in the figure.

transformer

The two coils possess high mutual inductance. If one coil is connected to a source of alternating current, an alternating flux is set up in the laminated core. Most of it is linked up with the other coil, in which it produces mutually induced emf according to Faraday’s laws electromagnetic induction.

i.e.,

e = M di/dt

Where, e = induced emf

             M = mutual inductance

When the secondary circuit is closed, a current flows in it. Thus electric energy is transferred from the primary coil to secondary coil.  

Ideal Transformer:

Though no such a transformer exist, to understand the working of transformer a transformer is assumed to an ideal one considering certain assumptions such as the resistanceof the windings are negligible, all the flux at the primary links the secondary, neglecting core losses and the core has constant permeability. The below figure shows the equivalent circuit of an ideal transformer.

Emf equation:

N₁=number of primary turns.

N₂=number of secondary turns.

Ф_m=maximum flux in the core in Weber=B_m×A

 B_m=flux density in the transformer core.

A=area of cross section of the transformer core

f=frequency of AC input voltage

Flux increases from its zero value to maximum value Ф_m  in one quarter of the cycle.

The rate of Change of flux per turn i.e. induced emf in volts/ turn = 4f Ф_m volts

If flux Ф_m varies sinusoidal, then rms value of induced emf is obtained by multiplying the average value with form factor.
Form factor = RMS value/average value=1.11

variation of flux in transformer

RMS value of emf/turn =1.11x4f Ф_m volts

RMS value of the induced emf in the whole primary winding = (induced emf/turn) x number of primary turns

E₁ = 4.44fN₁Ф_m

E₁ = 4.44fN₁B_mA volts

Exact equivalent circuit of practical transformer:

The following circuit shows the exact equivalent circuit of a practical transformer considering all the losses and parameters.

exact equivalent circuit of transformer
(image curtsey https://commons.wikimedia.org)

Transformer losses:

The losses in a transformer are classified as below:

1. Iron losses
2. Copper losses

Iron losses or core losses:

It includes two types of losses namely hysteresis and eddy current losses

1. hysteresis loss: occurs due to the continuous magnetic reversal in the care material.

Hysteresis loss = K_hfB^1.6 _max

where, f = frequency in Hz

B_max = the maximum flux density in core                                  

K_h = constant

2. Eddy current loss: Due to the flow of eddy currents in the core material. Thin laminations insulated from each other are used to reduce this loss.

Eddy current loss = K_ef²B²_max

Copper losses:

These losses are due to the ohmic resistance of the transformer windings.
Total copper losses = I₁²R₁ + I₂²R₂

Transformer tests:

The parameters of a transformer can be calculated on the basis of its equivalent circuits. The following are the various test conducted to determine in performance and efficiency.

1. Open-circuit or no load test to determine the core loss, the shunt parameters of equivalent circuit
2. Short-circuit or impedance test to determine the equivalent impedance and resistance, copper loss at full load of the transformer

Three phase transformer:

For bulk power requirements, people have tried from single phase to 12 phases and finally, as a techno economical consideration three phase power supply is being adopted all over the world .The voltage transformation in a three phase network can be had by means of either a bank of three single phase transformers or a single three phase transformer. A single unit three phase transformer consist essentially of three single phase transformers with their three cores united in to a single core assembly. Like single phase transformers, three phase transformers are of also of core type and shell type.