TransformerTransformer

DEFINATIONDEFINATION

A A transformertransformer is a static is a static

device that transfers electrical device that transfers electrical

energy from one circuit toenergy from one circuit to

another without any changeanother without any change

in frequency but change in in frequency but change in

Voltage and current. Voltage and current.

PRINCIPLE OF OPERATION PRINCIPLE OF OPERATION

MUTUAL MUTUAL INDUCTIONINDUCTION

A changing magnetic field within a A changing magnetic field within a coil of wire induces a voltage across coil of wire induces a voltage across the ends of the coil (the ends of the coil (electromagnetic inductionelectromagnetic induction). Changing ). Changing the current in the primary coil the current in the primary coil changes the magnetic flux that is changes the magnetic flux that is developed. The changing magnetic developed. The changing magnetic flux induces a voltage in the flux induces a voltage in the secondary coil. secondary coil.

Types and constructionTypes and constructionCore form Shell form

Power transformers

Windings are wrapped around two sides of a laminated square core.

Windings are wrapped around the center leg of a laminated core.

Usually, windings are wrapped on top of each other to decrease flux leakage and, therefore, increase efficiency.

Constructional view of transformerConstructional view of transformer

Ideal transformerIdeal transformerWe consider a lossless transformer with an input (primary) winding having Np turns and a secondary winding of Ns turns.

The relationship between the voltage applied to the primary winding vp(t) and the voltage produced on the secondary winding vs(t) is

( )

( )p p

s s

v t Na

v t N (4.8.1)

Equivalent ckt. Of TransformerEquivalent ckt. Of Transformer

The exact equivalent circuit The exact equivalent circuit of a real transformerof a real transformer

The transformer’s equivalent circuit

However, the exact circuit is not very practical.

Therefore, the equivalent circuit is usually referred to the primary side or the secondary side of the transformer.

Equivalent circuit of the transformer referred to its primary side.

Equivalent circuit of the transformer referred to its secondary side.

Approximate equivalent Approximate equivalent circuit of a transformercircuit of a transformer

For many practical applications, approximate models of transformers are used.

Referred to the primary side.

Without an excitation branch referred to the primary side.

Referred to the secondary side.

Without an excitation branch referred to the secondary side.

The values of components of the transformer model can be determined experimentally by an open-circuit test or by a short-circuit test.

The transformer phasor diagramThe transformer phasor diagram

A transformer operating at a lagging power factor:

It is seen that Vp/a > Vs, VR > 0

A transformer operating at a unity power factor:

It is seen that VR > 0

A transformer operating at a leading power factor:

If the secondary current is leading, the secondary voltage can be higher than the referred primary voltage; VR < 0.

The open-circuit test.The open-circuit test.Full line voltage is applied to the primary side of the transformer. The input voltage, current, and power are measured. From this information, the power factor of the input current and the magnitude and the angle of the excitation impedance can be determined.

To evaluate Ro and XM, we determine the conductance of the core-loss resistor is:

Ro = Vo / Iw Xm = Vo / Im

cos oc

oc oc

PPF

V I

Since the input voltage is low, the current flowing through the excitation branch is negligible; therefore, all the voltage drop in the transformer is due to the series elements in the circuit. The magnitude of the series impedance referred to the primary side of the transformer is:

The short-circuit test

SCSE

SC

VZ

I

.

Fairly low input voltage is applied to the primary side of the transformer. This voltage is adjusted until the current in the secondary winding equals to its rated value.

The input voltage, current, and power are again measured.

(4.36.1)

The power factor of the current is given by:

cos SC

SC SC

PPF

V I (4.36.2)

The autotransformerThe autotransformer

Sometimes, it is desirable to change the voltage by a small amount (for instance, when the consumer is far away from the generator and it is needed to raise the voltage to compensate for voltage drops).

In such situations, it would be expensive to wind a transformer with two windings of approximately equal number of turns. An autotransformer (a transformer with only one winding) is used instead.

Diagrams of step-up and step-down autotransformers:

Common winding

Series winding

Series winding

Common winding

Variable-voltage Variable-voltage autotransformersautotransformers

It is a common practice to make variable voltage autotransformers.

The effective per-unit impedance of an autotransformer is smaller than of a conventional transformer by a reciprocal to its power advantage. This is an additional disadvantage of autotransformers.

Three phase transformerThree phase transformer