Describe how a variable speed drive $($VSD$)$ is used to control the speed of an induction motor. $[4$ marks$]$ A star$-$connected $3-$phase supply, in which the e$.$m$.$f$.$ generated in each phase is $450$ V$,$ supplies a delta connected $100$ hp induction motor which has a full load efficiency of $96\%$ and a power factor of $0\mathrm{.}85$ lagging. Calculate $($a$)$ the line current for the supply $[5$ marks$]($b$)$ the terminal voltages on the motor $[3$ marks$]($c$)$ the phase current for the induction motor $[3$ marks$]($d$)$ the impedance per phase and the equivalent star$-$connected impedance per phase of the induction motor. $[5$ marks$]$