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 = I1X01 / V1
                                   = I2X02 / V2
              % Reactance = [ I1X01 / V1 ] × 100%
                                   = [ I2X02 / V2 ] × 100%

Importance of Per Unit System
  • 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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