Problem #$3$ A brushless DC motor is fed from a $3-$phase source of $230$Vll through a full$-$wave

controlled rectifier.Vd$0$

Vll

Is$1$

Id$0$

Controller

Brushless DC

a$.$ First, two tests are run for machine characterization:

$1)$ The rectifier delay angle is set at $45,$ no load is connected to the shaft and the speed is

measured to be $3100$rpm$.$

$2)$ The rectifier delay angle is set to $85,$ the rotor is held locked and the current is measured

to be $20$A$.$

What are the parameters, k and R$,$ of the brushless DC motor?

k $=0\mathrm{.}68$ V s

R $=1\mathrm{.}35$

b$.$ The motor is operating with a load of $10\mathrm{.}5$N m$,$ at $2000$rpm$.$

i$.$ Calculate the DC current into the brushless DC motor.

Id$0=15\mathrm{.}44$ A

ii$.$ Calculate the fundamental of the AC current into the rectifier.

Is$1=12\mathrm{.}04$ A

iii. Calculate the DC voltage Vdo.

Vd$0=163\mathrm{.}26$ V

iv$.$ Calculate the delay angle, $,$ of the rectifier.

$=58\mathrm{.}28$