In Figure P16-51, the three buses are interconnected by transmission lines with wire impedances of \(Z_{\mathrm{W}_{1}}=100+j\) \(600 \Omega /\) phase and \(Z_{\mathrm{W}_{2}}=120+j 800 \Omega /\) phase. The source at bus 2 produces an apparent power of \(\left|S_{2}ight|=300 \mathrm{kVA}\) at a lagging power factor of 0.85 . The load at bus 3 draws an apparent power of \(\left|S_{3}ight|=600 \mathrm{kVA}\) at a lagging power factor of o.8. The line voltage at bus 3 is \(V_{\mathrm{L} 3}=161 \mathrm{kV}\) (rms). Find the apparent power produced by the source at bus 1 , the source power factor, and the line voltages at bus 1 and bus 2 .

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Bus 1 ILI VLI Zwi Bus 2 VL2 Zw2 L2 Bus 3 S3 VL3