A three$-$phase Y$-$connected induction motor is rated $60$Hz$,280$Vll$.$ It has $4$ poles

RR $=0\mathrm{.}5,$ Rs $=0\mathrm{.}2,$ Lm $=250$mH Lls $=$ Llr $=5\mathrm{.}7$mH$.$ It is supplied from a $600$V line$-$

to$-$line three$-$phase source through a full$-$wave three$-$phase diode and PWM inverter. For motor operation at $3000$rpm$,20$N m calculate:

a$.$ The motor current and its power factor.

Is $=7\mathrm{.}6623\mathrm{.}59$ A

pf $=0\mathrm{.}92$ lagging

b$.$ The modulation index of the PWM inverter.

ma $=0\mathrm{.}96$

c$.$ The current and voltage input $($DC$)$ of the PWM inverter.

Vd$,$inv $=810$VDC

Id$,$inv $=7\mathrm{.}17$ A

d$.$ The AC current of the rectifier

Is$,$rect $=5\mathrm{.}59$ A

Please show all work, answers are provided