- 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 )
- The secondary voltage of the transformer V2 reduces due to voltage drop in the winding resistance R2 and reactance X2.
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
- Figure A shows vector diagram of transformer as refer to secondary side under lagging power factor load.
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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