Question 16.21: In Figure 16–23 the three-phase source produces an apparent ......
In Figure 16–23 the three-phase source produces an apparent power of 3.5 kVA at a power factor of 0.8 lagging and a line current of I_{L} = 4.6 A(rms). The three lines connecting the source to the load have impedances of Z_{W} = 1 + j6 Ω/phase. Find the complex power delivered to the load and the line voltage at the load.
The complex power produced by the source is
S_{S} = |S_{S}|\left(pf + j\sqrt{1 – pf^2}\right)= 3.5 × 10^3 \left(0.8 + j\sqrt{1 – 0.8^2}\right)
= (2.8 + j2.1) kVA
The complex power lost in any one wire is I^2_{L}Z_{W}, so the total line loss is
S_{W} = 3I^2_{L}Z_{W} = 3 × (4.6)^2 (1 + j6)
= 63.5 + j381 VA
The complex power delivered to the load equals the power produced by the source minus the line losses. Hence
S_{L} = S_{S} – S_{W} = 2.74 + j1.72 kVA
Accordingly, we get the line voltage at the load as
V_{L} =\frac{|S_{L}|}{\sqrt{3}I_{L}}=\frac{|2.74 × 10^3 + j1.72 × 10^3|}{\sqrt{3} × 4.6}= 406 V (rms)