# Practical Transformer

Practical Transformer is different from the ideal transformer due to the non-ideal nature of the practical transformer. In a working transformer, the performance aspects like magnetizing current, losses, voltage regulation, efficiency, etc are important. The effects of the non-idealization like finite permeability, saturation, hysteresis and winding resistances have to be added to an ideal transformer to make it a practical transformer.

The finite permeability of the magnetic circuit necessitates a finite value of the current to be drawn from the mains to produce the MMF required to establish the necessary flux. The current and MMF required is proportional to the flux density B that is required to be established in the core.

A = the area of cross section of the iron core

H = the magnetizing force

The magnetizing force and the current vary linearly with the applied voltage as long as the magnetic circuit is not saturated. The current has to vary in a nonlinear manner to establish the flux of sinusoidal shape. This non-linear current can be resolved into fundamental and harmonic currents. This is discussed to some extent under harmonics.

The current drawn from the mains is assumed to be purely sinusoidal and directly proportional to the flux density of operation. This current can be represented by a current drawn by an inductive reactance in the circuit as the net energy associated with the same over a cycle is zero. The energy absorbed when the current increases is returned to the electric circuit when the current collapses to zero. This current is called the magnetizing current of the transformer.

The magnetizing current Im is given by

Im = E1/Xm where Xm is called the magnetizing reactance

Losses arise out of hysteresis, eddy current inside the magnetic core. These are given by

Where Ph = Hysteresis loss (watt)

F = Frequency of operation (Hz )

B = Flux density of operation (Tesla)

t = Thickness of the laminations of the core (m)

Active power consumption by the no-load current can be represented in the input circuit as a resistance Rc connected in parallel to the magnetizing reactance Xm.

No-load current I0  may be made up of  Ic (loss component) and Im (magnetizing component)

I0   =  Ic  –  j Im

Ic2Rc = total core losses ( hysteresis + eddy current loss)

Im2Xm = Reactive volt amperes consumed for establishing the mutual flux

Flux lines which did not link the secondary winding is called as leakage flux. As the path of the leakage flux is mainly through the air the flux produced varies linearly with the primary current I1. Even a large value of the current produces a small value of flux. This flux produces a voltage drop opposing its cause, which is the current I1.

The primary leakage reactance

The secondary leakage reactance

## Equivalent circuit of Practical Transformer

The primary and secondary windings are wound with copper (sometimes aluminum in small transformers) conductors thus the windings have a finite resistance. The resistance is represented by r1 and r2 respectively on the primary and secondary sides.

I2 in the circuit represents the primary current component that is required to flow from the mains in the primary T1 turns to neutralize the demagnetizing secondary current I2 due to the load in the secondary turns. The total primary current

I1  = I2 + Io

The transformer of turns ratio T1 : T2 if the turns ratio could be made unity by some transformation the circuit becomes very simple to use. This is done here by replacing the secondary by a hypothetical secondary having T1 turns which is equivalent to the physical secondary. The equivalence implies that the ampere-turns, active and reactive power associated with both the circuits must be the same. Then there is no change as far as their effect on the primary is considered.

Where a = turn ratio =T1 \ T2

The equivalent circuit can be derived by analytically using the Kirchoff’s equations applied to the primary and secondary.

Multiply both sides of by ‘a’