A three$-$phase $12-$pulse two$-$level bi$-$directional boost AC$-$DC converter $($GTO based VSC coupled with transformers having primaries connected in series to ac mains with the star$/$delta and star$/$star secondaries connections in parallel to a common de bus$)$ feeding $30$ kW from a de battery of $720$ V to a $254$V per phase, $50$Hz$,3-$phase ac mains, and sinusoidal wave voltage. TheAplacement Eactor $\text{'}$s Cofreced dose to unt : The $1$Sc Is opetated to cancel S$"$ anaTheharmonics in VSC output voltage. Determine $($a$)$ both transformer turns ratios, $($b$)$ value phase shift in fundamental component of VSC ac voltage and supply voltage, $($c$)$ fundamental phase current, $($d$)11"$ harmonic current in ac mains, $($e$)$ THD in VSC ac voltage, $(1)$ the value of ac inductor and $($g$)$ THD in ac mains current.