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 )

• 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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