Page 102 - Power Electronic Control in Electrical Systems

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90 Transmission system compensation

Fig. 3.7 Receiving-end voltage magnitude jV r j as a function of load P/P 0 for a 300-km lossless radial line, at
different power factors.

3.3.2 Uncompensated symmetrical line: variation of voltage
and reactive power with load

The symmetrical line in Figure 3.8 has equal voltages at the sending and receiving
ends, and the mid-point voltage and current are V m and I m respectively. The phasor
diagram is shown in Figure 3.9. The equations for the sending-end half of the line are
y y
E s ˆ V m cos ‡ jZ I m sin
0
2 2 (3:14)
V m y y
I s ˆ j sin ‡ I m cos
Z 0 2 2
At the mid-point,

P m ‡ jQ m ˆ V m I ˆ P (3:15)
m

Fig. 3.8 Symmetrical line.