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# (Solved): A $$3 \phi$$ cylindrical-rotor synchronous machine (SM) and a separately excited dc machine (DCM) ...

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

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