8 November 2017

Per unit Resistance and Reactance of the Transformer Winding

Per unit resistance
  • It is defined as the resistance drop at rated current and frequency expressed at rated voltage.
Per unit resistance = I1R01 / V1

                              = I2R02 / V2
Where
  • R01 = Transformer winding resistance as referred to primary
  • R02 = Transformer winding resistance as referred to secondary
  • I1 = Rated primary current
  • I2 = Rated secondary current
  • V1 = Primary voltage
  • V2 = Secondary voltage
% Resistance = [ I1R01 / V1 ] × 100%
                      = [ I2R02 / V2 ] × 100%
                      = [ I22 R02 / I2V2 ] × 100%
                      = [ Full load copper losses / transformer rating ] × 100%
  • Similarly the per unit reactance drop at rated current and frequency expressed as a rated voltage.
Per unit reactance
Per unit reactance = I1X01 / V1
                             = I2X02 / V2
% Reactance = [ I1X01 / V1 ] × 100%
                      = [ I2X02 / V2 ] × 100%
  • It is not very easy to calculate total resistance of the transformer winding. 
  • The primary winding resistance and secondary winding resistance is added directly if the voltage ratio of the transformer is unity but it is not possible. 
  • The important advantage of expressing resistance and reactance of a transformer in per unit / percentage is that both resistance and reactance have same values whether determined as referred to primary side or secondary side. 
  • When they expressed in ohms, they have different values as referred to primary side and secondary side.

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