Determine the equivalent winding resistance:

A 50 kVA, 2200/110 V, 50 HZ' transformer contain an HV winding resistance of 0.15 Ω and a leakage reactance of 0.45 Ω. The LV winding contain a resistance of 0.006 Ω and a leakage reactance of 0.012 Ω. Determine the equivalent winding resistance, reactance and impedance referred to the HV and LV sides.

Solution

Z'1 = r₁ + j x₁ = 0.15 + j 0.45

Z'₂  = r₂  + j x₂  = 0.006 + j 0.012

Z' (HV ) = Z'₁ + Z'₂′

Z'₂′ = ( 2200 )²   /110  (0.006 + j 0.012) = (2.4 + j 4.8) Ω

Z'(HV ) = (0.15 + j 0.45) + (2.4 + j 4.8) = (2.55 + j 5.25) Ω

Likewise

Z' (LV ) = Z'₁′ + Z'₂

= (110 /2200)²  (0.15 + j 0.45) + (0.006 + j 0.012) Ω

= (0.006375 + j 0.01312) Ω