Question 9.9: A balanced three-phase wye-connected generator delivers powe......
A balanced three-phase wye-connected generator delivers power to a balanced three-phase delta–wye connected load as shown in Fig. 9.35. Determine the power per phase and the total power delivered by the source.
Delta load is converted to wye load as,
Z_{1}={\frac{4|\underline{-15^{\circ}}}{3}}=1.33|\underline{-15^{\circ}}\,\Omega (9.165)
The value of the parallel loads is,
Z_{2}={\frac{1.33|\underline{-15^{\circ}}\times6|\underline{10^{\circ}}}{1.33|\underline{-15^{\circ}}+6|\underline{10^{\circ}}}}=1.10|\underline{-10.54^{\circ}}\Omega (9.166)
The line current is calculated as,
I_{\mathrm{Aa}}={\frac{200|\underline{-20^{\circ}}}{0.02+j5+1.10|\underline{-10.54^{\circ}}}}=40.62{|\underline{{-97.07^{\circ}}}}\mathbf{A} (9.167)
Power delivers by the first line is calculated as,
P_{A}=V_{\mathrm{AN}}I_{\mathrm{Aa}}\cos(\theta_{\nu}-\theta_{i})=200\times40.62\cos(-20^{\circ}+97.07^{\circ})=1817.83\,\mathrm{W} (9.168)
Total power delivered by the source is,
P_{t}=3P_{A}=3\times1817.83=5453.49\,\mathrm{W} (9.169)