## 07/11/2017

### Voltage Regulation of the Transformer

• When the secondary of the transformer is not loaded, the secondary terminal voltage 0V2 is equal to secondary induced emf E2.

E2 = V2 + I2 ( R2 + jX2 )

E2 = 0V2  ( At no load I2 = 0 )

Voltage Regulation
• The voltage regulation is defined as the change in terminal voltage from no load to full load.
• The percentage voltage regulation is defined as

% Voltage regulation ( Down ) = [ ( 0V2 – V2 ) / 0V2 ] × 100%
% Voltage regulation ( Up ) = [ ( 0V2 – V2 ) / V2 ] × 100%
• The regulation is always taken as negative if anything not specify.

Equation of voltage regulation

OA = Secondary terminal voltage V2 is taken as reference
AE = Voltage drop I2R02
EF = Voltage drop I2X02
AF = Impedance drop I2Z02
OF = No load voltage 0V2
Taking O as Center and OF as radius and draw an arc which cut the horizontal axis at point D. Obviously
OF = OD
= OA + AB + BC + CD
= OA + AB + BC ( As CD is very small )
Now in triangular ABC
• AB = I2R02 Cos F2

Similarly in triangular EFG
• EG = I2X02 Sin F2
• BC = EG = I2X02 Sin F2

From equation AF = OA + AB + BC
0V2 = V2 + I2R02 Cos F2 + I2X02 Sin F2
0V2 – V2 = I2R02 Cos F2 + I2X02 Sin F2

• This equation indicates approximate voltage drop in the transformer winding at a given load condition. Simple the equation

[ 0V2 – V2 / 0V2 ] = [( I2R02 Cos F2 + I2X02 Sin F2 ) / 0V2 ] × 100%
% Voltage regulation =

[( I2R02 Cos F2 + I2X02 Sin F2 ) / 0V2 ] × 100%

Vector Diagram for leading power factor

The vector diagram for leading power factor is shown in the Figure B.

OC = OD
≈ OE
= OF – EF
= ( OA + AF ) – EF
In triangular ABF
• AF = I2R02 Cos F2

In triangular GBC
• BG = EF = I2X02 Sin F2
• OC = ( OA + AF ) – EF
• 0V2 = V2 + I2R02 Cos F2 – I2X02 Sin F2
• 0V2 – V2 = [( I2R02 Cos F2 – I2X02 Sin F2 )
• ( 0V2 – V2 / 0V2 ) = [( I2R02 Cos F2 – I2X02 Sin F2 ) / 0V2 ] × 100%

% Voltage regulation =

[( I2R02 Cos F2 – I2X02 Sin F2 ) / 0V2 ] × 100%

Vector Diagram for unity power factor
% Voltage regulation
= [ I1R01 Cos F2  / 0V2 ] × 100%

= [ I1R01 / 0V2 ] × 100%  ( As Cos F2 = 1 )

General equation for voltage regulation
= [( I2R02 Cos F2 ± I2X02 Sin F2 ) / 0V2 ] × 100%
+ Sign for lagging power factor and
– Sign for leading power factor
If the value of R01, X01 and I1 is known
% Voltage regulation =
[( I1R01 Cos F2 – I1X01 Sin F2 ) / 0V2 ] × 100%
Describe the significance of voltage regulation?

• The voltage regulation indicates percentage voltage drop in the transformer winding at given load condition.
• Lesser the voltage regulation better transformer and vice versa.
• Let the transformer A and transformer B has voltage regulation 5% and 8% respectively. Which transformer is better? The transformer A is better than transformer B.
Which parameters greatly affect the voltage regulation of the transformer?
• The voltage regulation of the transformer depends upon resistance and reactance of the winding ( R1, R2, X1 and X2 ), load current and power factor of the load.

Describe the condition for maximum voltage regulation at lagging power factor?
Voltage regulation =
[( I2R02 Cos F2 + I2X02 Sin F2 ) / 0V2 ]
Maximum voltage regulation occurs when
d ( V.R. ) / dF2 = 0
( I2R02 / 0V2 )( – Sin F2 ) + ( I2X02 )( Cos F2 ) = 0
– R02 Sin F2 + X02 Cos F2 = 0
tan F2 = X02 / R02
F2 = tan –1 [ X02 / R02 ]
= tan –1 [( I2X02 / 0V2 ) / ( I2X02 / 0V2 )]
= tan –1 [( % Reactance drop ) / ( % Resistance drop )]
= ………………….

• Power factor at which voltage regulation becomes maximum = Cos F2

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