Question 16.22: In Figure 16–26, the source at bus 1 and the load at bus 2 a......
In Figure 16–26, the source at bus 1 and the load at bus 2 are interconnected by a transmission line with ZW = 1.5 + j8.5 Ω/phase. The load at bus 2 draws a complex power of S2 = 70 + j35 kVA. Assuming that VL2 = 2400 V(rms), find the complex power produced by the source and the line voltage at bus 1.
For the given values of VL2 and S2, 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
S1 = S2 + SW = 71.6 + j44 kVA
Now that we have IL1 and S1, 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 VL1 = 2.58 kV(rms), IL1 = 18.8 A(rms), and VL2 = 2.4 kV(rms) will produce the required load power flow. This set of conditions is not unique and many other solutions exist.