Per unit Resistance and Reactance

Per unit resistance & Per unit 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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