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A \( 3 \phi \) cylindrical-rotor synchronous machine (SM) and a separately excited dc machine (DCM) are mechanically coupled to transfer power from a dc source to an ac source and vice versa. The ratings of the machines are \( \checkmark S M: 12 \mathrm{kVA}, 208 \mathrm{~V}, X_{s}=3.0 \Omega \) \( \checkmark \) DCM: \( 12 \mathrm{~kW}, 220 \mathrm{~V}, R_{A}=0.3 \Omega \) Considering only the losses in DCM's armature resistance \( \mathrm{R}_{\mathrm{A}} \). All other losses are neglected. The DCM is connected to a \( 220 \mathrm{~V} \) dc bus, and the SM is connected to a \( 3 \phi, 208 \mathrm{~V}, 60 \mathrm{~Hz} \) bus. a) The power is transferred from dc source to the ac source, when the SM is delivering full load at unity power factor, 1) Find the excitation voltage, \( \mathrm{E} \), and the power angle, \( \delta \) of the SM 2) Find the back-emf, \( E_{c} \), of the DCM

Part (a): Synchronous Machine (SM): As the power is transferred from dc source to the ac source, the SM acts as a

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