16–67 In Figure P16–67, the source at bus 1 supplies two load buses through transmission lines with wire impedances of ZW1 = 6 + j33 Ω=phase and ZW2 = 3 + j15 Ω=phase. The load at bus 2 draws an apparent power 4MVA at a lagging power factor of 0:95. The load at bus 3 draws an apparent power of 3MVA at a lagging power factor of 0:9. The line voltage at bus 3 is VL3 = 138 kV ðrmsÞ. 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 ILL S -VLI Zwi 41,2 Zw2 Bus 2 Bus 3 VL.2 $2 $3 FIGURE P16-67 -VL3