(Solved): A synchronous generator is supplying power to three motors through a transformer as shown below. T ...

A synchronous generator is supplying power to three motors through a transformer as shown below. The sub transient reactance values are known to be: $${\mathrm{X}}_{\mathrm{g}}{}^{??}=0.20{\mathrm{X}}_{\mathrm{m}1}{}^{??}=0.60{\mathrm{X}}_{\mathrm{m}2}{}^{??}=0.30{\mathrm{X}}_{\mathrm{m}3}{}^{??}=0.20{\mathrm{X}}_{\mathrm{T}}=0.10$$ Each motor is consuming $$0.5$$ pu power at a power factor of $$0.8$$ lagging and the voltage at bus 2 is $$1.0?0^{?}\mathrm{pu}$$ Determine the currents $${\mathrm{I}}_{\mathrm{g}},{\mathrm{I}}_{\mathrm{T}},{\mathrm{I}}_{\mathrm{m}},{\mathrm{I}}_{\mathrm{m}2}$$, and $${\mathrm{I}}_{\mathrm{m}3}$$ under the "healthy" conditions described above.