Transformer Total Voltage Drop


Total Approximate Voltage Drop of a Transformer

During the no-load condition, induced voltages at the primary and secondary windings are equal to the applied voltage and secondary terminal voltage respectively. If 0V2 be the secondary terminal voltage at no load, we can write E2 = 0V2.

When the transformer is on no-load, then V1 is approximately equal to E1. Hence E2 = KE1 = KV1

Also,
E2 = 0V2 
where 0V2 is the secondary terminal voltage on no-load, 
hence no-load secondary terminal voltage is KV1.


The secondary voltage on load is V2. The difference between the two is I2 Z02 as shown in Figure below. The approximate voltage drop of the transformer as referred to secondary is found thus.

Total Approximate Voltage Drop of a  Transformer at Lagging Power Factor


With O as the centre and radius OC draw an arc cutting OA produced at M. The total voltage drop I2

Z02 = AC = AM which is approximately equal to AN. From B draw BD perpendicular on OA produced.

Draw CN perpendicular to OM and draw BL parallel to OM.

Approximate voltage drop
= AN =AD+DN
= I2R02 cosφ + I2X02sinφ
where φ1 = φ2 = φ (approx).

This is the value of the approximate voltage drop for a lagging power factor.

The different figures for unity and leading power factors are shown below.


Total Approximate Voltage Drop of a  Transformer at Unity Power Factor


Total Approximate Voltage Drop of a  Transformer at Leading Power Factor


The approximate voltage drop for the leading power factor becomes (I2R02cosφ ± I2X02 sinφ).

In general, the approximate voltage drop is 
(I2 R02 cosφ ± I2X02 sin /φ).

It may be noted that approximate voltage drop as referred to primary is=

(I1R01 cosφ ± I1 X01sinφ)

% voltage drop in the secondary is
=[(I2 R02 cosφ ± I2X02 sin /φ)/0V2]*100
=[(100*I2Ro2)/0V2]cosφ ±[(100*I2Xo2)/0V2]sinφ
=vrcosφ ± vxsinφ

where,
vr= (100*I2Ro2)/0V2  =percentage resitive drop=(100*I1R01)/V1
vx=(100*I2Xo2)/0V2=percentage reactive drop=(100*I1X01)/V1


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