Hello I am just stuck on a three phase transformer question.

A 5KVA, 3 phase transformer, Y-Y (Star) has a primary line voltage of 500V and secondary line voltage of 200V, supplying to a load of 75 ohm with the line impedance of 40. Calculate the line current in primary.

I have attempted it by adding doing the following 500/(75+40)=I ... but the answer does not seem to be correct

 

Y connection transformers is used in systems with earthed neutral, but theoretically it can be analyzed and isolated neutral version and the load connected only between the three phases of the system. So, we have two cases.

As the neutral or middle star is connected to the ground, in this case, the phase current equal to the line current.

Then, before calculating the current will have to calculate the characteristic impedance of the transformer (resistance Rt and reactance xt of the transformer):

Rt = (dP_Cu [kW] x Us^2 [kV]) / St^2 [kVA];

where: dP_Cu - copper losses of the transformer; Us - output voltage transformer; St - apparent power of the transformer.

xt = (usc [%] / 100) x (Us^2 [kV]/ St [kVA]);

where: usc is the percentage of short circuit voltage of the transformer.

Zt = SQRT(Rt^2 + xt^2)

Thereafter, the supply side will have:

R_line =? ohm
x_line =? ohm.
---> Z_line = 40 ohm.

And finally add resistive consumer: R_load = 75 Ohm.

And the final formula will be:

I_load = ~ Up / (Zt + Z_line + R_load) - where Up is phase intput voltage of the transformer.

or, much easier, LATER EDIT: I_load = Us / (Z_line + R_load)

To calculate Zt you need some additional data.