7 November 2017

Voltage Regulation of the Transformer at different Power Factor

  • 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 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 = 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.

From the vector diagram, 
      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%   ( As Sin F= 0 )
             = [ I1R01 / 0V2 ] × 100%  ( As Cos F2 = 1 )
General equation for voltage regulation

% 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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