Space Vector PWM $($SVPWM$)(30$ Points$)$

Suppose the voltage reference for the three$-$phase dc$-$ac inverter, operating at a

frequency $=60$ z$,$ is:

va$0$ref $=1202$ cos$($ t $+$ $/6)$

vb$0$ref $=1202$ cos$($ t $+$ $/62$

$3)$

vc$0$ref $=1202$ cos$($ t $+$ $/6+2$

$3)$

A$.$ If $0$ is the neutral of the wye$-$connected load connected at the three$-$phase inverter output,

i$.$ Derive the voltage reference signals v$$ref and v$$ref using Clarke$$s transformation of

va$0$ref$,$ vb$0$ref$,$ and vc$0$ref$.($Refer: Lecture #$22$ or #$23$ notes for the transformation

matrix$)(5$ points$)$

ii$.$ Represent the $3-$phase reference space vector in the complex $-$ plane?

Note: Reference space vector, $=+.(5$ points$)$