A three$-$phase $50$ Hz$,200$ MVA, $220/66$ kV transformer has a clock number of Yd$1.$ The

transformer winding resistances are $2\mathrm{.}0$ and $0\mathrm{.}15,$ and the leakage reactances are $10$

and $0\mathrm{.}65$ for the high voltage side and low voltage side respectively.

$($a$)$ What is the meaning of the letters and number combination Yd$1?$

$($b$)$ Sketch the phasor diagrams and the connection diagram for the high voltage side

and the low voltage side of the transformer.

$($c$)$ Calculate the per$-$unit impedance of the transformer referred to the high$-$voltage

side.

$($d$)$ Derive the equation for the approximate voltage regulation of the transformer, and

use the derived equation to calculate the full$-$load voltage regulation of the

transformer if the load power factor is $0\mathrm{.}80$ lagging.

$($e$)$ If the load power factor is improved to $0\mathrm{.}98$ lagging, what will be the full$-$load

voltage regulation?