Improving Power-Angle Characteristics
The apparent power supplied by the source is given by
Similarly the apparent power delivered at the receiving end is
Hence the real power transmitted over the line is given by
Combining (10.6)-(10.8), we find the reactive power consumed by the line as
The power-angle characteristics of the shunt compensated line are shown in Fig. 1. In this figure Pmax = V2/X is chosen as the power base.
Fig. 1 Power-angle characteristics of ideal shunt compensated line.
Fig. 1 depicts Pe - δ and QQ - δ characteristics. It can be seen from fig 2 that for a real power transfer of 1 per unit, a reactive power injection of roughly 0.5359 per unit will be required from the shunt compensator if the midpoint voltage is regulated as per (10.1). Similarly for increasing the real power transmitted to 2 per unit, the shunt compensator has to inject 4 per unit of reactive power. This will obviously increase the device rating and may not be practical.