We all know that the per-phase analysis of a star-delta transformer requires converting the delta-side into an equivalent-star connection. Upon doing this, we find that the new equivalent secondary delta-side phase lags by 30 degrees with respect to the primary star-side phase. We usually represent this by multiplying the term e^(j30deg) to the equivalent per-phase transformation-ratio a:1 from primary to secondary; ie, the new transformation ratio is a.e^(j30deg) : 1 .

Now, if we were to transfer an impedance from the secondary-side to the primary-side, applying the transformation rule of Z(referred_to_primary) = (primary-to-secondary transformation-ratio)^2 x Z(secondary), we would get :

Z(referred_to_primary) = (a.e^(j30deg))^2 x Z(secondary)

= a^2 x e^(j60deg) x Z(secondary).

This implies that even a purely resistive balanced-load on the delta side would reflect as an inductive load on the primary side, which is not possible. Calculations based on this would then go on to give erroneous results (as I have myself tried out and confirmed).

So where lies the contradiction ?! Please help !! I can furnish further details as well as a specific problem.

Thanks !!