Question 16.22: In Figure 16–26 the source at bus 1 and the load at bus 2 ar......
In Figure 16–26 the source at bus 1 and the load at bus 2 are interconnected by a transmission line with Z_{W} = 1.5 + j8.5 Ω/phase. The load at bus 2 draws a complex power of S_{2} = 70 + j35 kVA. Assuming that V_{L2} = 2400 V(rms), find the complex power produced by the source and the line voltage at bus 1.
For the given values of V_{L2}, and S_{2} we find the line current as
I_{L1} =\frac{|S_{2}|}{\sqrt{3}V_{L2}}=\frac{|(70 + j35) × 10^3|}{\sqrt{3} × 2400} =18.83 A(rms)
The power lost in the line is
S_{W} = 3I^2_{L}Z_{W} = 3 × (18.83)^2 (1.5 + j8.5)
= 1.6 + j9.0 kVA
The source at bus 1 must supply the load power at bus 1 plus the losses in the line. Hence, the complex power produced by the source is
S_{1} = S_{2} + S_{W} = 71.6 + j44 kVA
Now that we have I_{L1}, and S_{1}, we find the line voltage at bus 1 as
V_{L1} =\frac{|S_{2}|}{\sqrt{3}I_{L1}}=\frac{|(71.6 + j44) × 10^3|}{\sqrt{3} × 18.83}=2.577 kV (rms)
In round numbers, the conditions V_{L1} = 2.58 kV, I_{L1} = 18.8A, and V_{1.2} = 2.4 kV will produce the required load power flow. This set of conditions is not unique and many other solutions exist.