- When the
secondary of the transformer is not loaded, the secondary terminal voltage
_{0}V_{2}is equal to secondary induced emf E_{2}.

E

_{2}= V_{2}+ I_{2}( R_{2}+ jX_{2})
E

_{2}=_{0}V_{2}( At no load I_{2}= 0 )- The secondary
voltage of the transformer V
_{2}reduces due to voltage drop in the winding resistance R_{2}and reactance X_{2}.

**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 )

= [ (

_{0}V_{2}– V_{2}) /_{0}V_{2}] × 100%
% Voltage
regulation ( Up )

= [ (

_{0}V_{2}– V_{2}) / V_{2}] × 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 V

_{2}is taken as reference
AE = Voltage
drop I

_{2}R_{02}
EF = Voltage
drop I

_{2}X_{02}
AF = Impedance
drop I

_{2}Z_{02}
OF = No load
voltage

_{0}V_{2}- Taking O as centre 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 = I

_{2}R_{02}Cos F_{2}- Similarly in triangular EFG

EG = I

_{2}X_{02}Sin F_{2}
BC = EG = I

_{2}X_{02}Sin F_{2}- From equation AF = OA + AB + BC

_{ 0}V

_{2}= V

_{2 }+ I

_{2}R

_{02}Cos F

_{2}+ I

_{2}X

_{02}Sin F

_{2}

_{ 0}V

_{2 }– V

_{2}= I

_{2}R

_{02}Cos F

_{2}+ I

_{2}X

_{02}Sin F

_{2}

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

[

_{0}V_{2 }– V_{2}/_{0}V_{2}] = [( I_{2}R_{02}Cos F_{2}+ I_{2}X_{02}Sin F_{2}) /_{0}V_{2 }] × 100%- % Voltage regulation =

[( I

_{2}R_{02}Cos F_{2}+ I_{2}X_{02}Sin F_{2}) /_{0}V_{2 }] × 100%**Vector Diagram for leading power factor**

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

From the vector diagram,

OC = OD

≈ OE

= OF – EF

= ( OA + AF ) – EF

- In triangular ABF

AF = I

_{2}R_{02}Cos F_{2}- In triangular GBC

BG = EF = I

_{2}X_{02}Sin F_{2}
OC = ( OA + AF )
– EF

_{ 0}V

_{2 }= V

_{2 }+ I

_{2}R

_{02}Cos F

_{2}– I

_{2}X

_{02}Sin F

_{2}

_{ 0}V

_{2 }– V

_{2 }= [( I

_{2}R

_{02}Cos F

_{2}– I

_{2}X

_{02}Sin F

_{2})

(

_{0}V_{2 }– V_{2}/_{0}V_{2}) = [( I_{2}R_{02}Cos F_{2}– I_{2}X_{02}Sin F_{2}) /_{0}V_{2 }] × 100%- % Voltage regulation =

[( I

_{2}R_{02}Cos F_{2}– I_{2}X_{02}Sin F_{2}) /_{0}V_{2 }] × 100%**Vector Diagram for unity power factor**

% Voltage
regulation

= [ I As Sin F

_{1}R_{01}Cos F_{2}/_{0}V_{2 }] × 100% (_{2 }= 0 )
= [ I

_{1}R_{01}/_{0}V_{2 }] × 100% ( As Cos F_{2 }= 1 )**General equation for voltage regulation**

% Voltage Regulation

= [( I

_{2}R_{02}Cos F_{2}± I_{2}X_{02}Sin F_{2}) /_{0}V_{2 }] × 100%
+ Sign for
lagging power factor and

– Sign for
leading power factor

If the value of
R

_{01}, X_{01}and I_{1}is known- % Voltage regulation =

[( I

_{1}R_{01}Cos F_{2}– I_{1}X_{01}Sin F_{2}) /_{0}V_{2 }] × 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 ( R
_{1}, R_{2}, X_{1}and X_{2}), load current and power factor of the load.

**Describe the condition for maximum voltage regulation at lagging power factor?**

Voltage regulation =

[( I

_{2}R_{02}Cos F_{2}+ I_{2}X_{02}Sin F_{2}) /_{0}V_{2 }]
Maximum voltage
regulation occurs when

d ( V.R. ) / dF

_{2 }= 0
( I

_{2}R_{02}/_{0}V_{2 })( – Sin F_{2}) + ( I_{2}X_{02})( Cos F_{2}) = 0
– R

_{02}Sin F_{2 }+ X_{02}Cos F_{2}= 0
tan F

_{2 }= X_{02}/ R_{02}
F

_{2}= tan^{–1}[ X_{02}/ R_{02}]
= tan

^{–1}[( I_{2}X_{02 }/_{0}V_{2}) / ( I_{2}X_{02 }/_{0}V_{2})]
= tan

^{–1}[( % Reactance drop ) / ( % Resistance drop )]
= _____________

Power factor at
which voltage regulation becomes maximum = Cos F

_{2}_{}

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