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Transformer on load, Resistance and Leakage Reactance and more knowledge of Equivalent Circuit. [ CHAPTER :- 1 part :- B ]

TRANSFORMER ON LOAD

The Transformer is said to be loaded, when it's secondary Circuit is complete through an impedance or load. The magnitude and phase of secondary Current [ i.e., Current following through secondary ] I2 with respect to secondary terminals depends upon the characteristic of the load i.e., Current I2 will be in phase lag behind and lead the terminal Voltage V2 respectively when  the load is non- inductive, inductive and capacitive. The net flux passing through the core reamins almost constant from no load to full load irrespective of load conditions and so core losses remain almost constant From no load to full load. Phaser diagram for an ideal Transformer supplying inductive load in shown in fig.

An Ideal Transformer ON load
An Ideal Transformer ON load


The Primary Current, 

I1 = I1 + I0 = KI2 + I0


Phaser diagram of Inductive load
Phaser diagram For Inductive load


RESISTANCE AND LEAKAGE REACTANCE

In actual practice, both of the primary and secondary windings have got some ohmic resistance causing voltage drops and copper losses in the windings.
In actual practice, the total flux created does not Link both of the primary and secondary windings is but devided in to Three components namely the main of mutual fluxΦ Linking both of the primary and secondary winding, primary leakage flux ΦL1 linking with primary winding only and secondary leakage flux Φ L2 linking with secondary winding only. The primary leakage flux Φ L1 is Produced by Primary amps turns and is Proportional to primary Current, number of primary turns being fixed. The primary leakage flux Φ L1 is in phase with I1 produces and self induced EMF EL1 given as 2πfL1 I1 in the primary winding. The self induced EMF devided by primary current gives the reactance of primary and is denoted by X1.

                    EL1         2πfL1 I1 
i.e.,   X1 = ------ = -------------- = 2πfL1
                     I1                 I1 

Similarly leakage reactance of secondary

              EL2         2πfL2 I2 
  X2 = ------- = --------------- = 2πfL2
               E2                I2

A Transformer with magnetic leakage and winding resistance is equivalent to an ideal Transformer ( having resistance and leakage reactance ) having inductive and resistive coils connected in series with each winding as shown in fig.

When a practical Transformer is loaded 

Induced EMF is Secondary winding
E2 = V2 + I2 ( R2 + jX2 ) = V2 + I2 Z2

Induced EMF in primary 
E1 = E2 / k

And applied voltage to primary winding
V1 = -E1 + I1 ( R1 + jX1 ) = -E1 + I1 Z1

EQUIVALENT RESISTANCE AND REACTANCE

The Equivalent resistance and Reactances of Transformer referred to primary and secondary sides are given as follows;



            An Equivalent Diagram of actual                                   Transformer

Referred to primary Side
                                                               R2
Equivalent Resistance R01 = R1 + -------
                                                              K^2

                                                                X2
Equivalent Reactances X01 = X1 + -------
                                                               K^2

Referred to Secondary side

Equivalent Resistance R02 = K^2 R1 + R2
Equivalent Reactance X02 = K^2 X1 + X2
Where K is Transformation ratio.

Approximate Voltage drop in the transformer referred to Secondary 

= I2 ( R02 CosΦ +- X02 sinΦ ) 

+ Ve sign for lagging power factor and -Ve sign leading power factor.

EQUIVALENT CIRCUIT

The Equivalent Circuit of any device can be quite helpful is predetermination of the behavior of the device under various condition of operation and it can be drawn if the equations describing it's behavior are known.


EQUIVALENT CIRCUIT OF A TRANSFORMERS
EQUIVALENT CIRCUIT OF A TRANSFORMERS

         Equivalent Circuit of a Transformer

Equivalent Circuit of a transformer having Transformation ratio 
              E2
    K = ------- is shown in fig.
              E1
Transformer Related more knowledge
So click the link

[ Transformer Basic Knowledge A ]

[ Transformer Types B ]

               




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