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## 08/11/2017

### Per unit Resistance and Reactance

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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