Q$4.(25$ pts$)$ A $1500-$kVA,$34500\frac{V}{400}V,$ three$-$phase, $50$ Hz $,$ distribution transformer is connected as Y $-$Y$.$ It has a ries resistance of $1\%$ and a reactance of $9\%.$ Answer the following questions by using the rated parameters of the transformer as base values and neglecting magnetizing branch:

a$)$ Find secondary line current at rated load conditions at unity power factor when secondary voltage is $400$ V $(L-L).$

b$)$ Find the rms value of the line$-$to$-$line voltage of the primary side at rated conditions at unity power factor when secondary voltage is $400$ V $($L$-$L$).$

c$)$ Find the voltage regulation of the transformer.

d$)$ Find the input power factor of the transformer. State also it is leading, lagging, or unity.