Improving Power-Angle Characteristics

Noting that the sending end apparent power is V_S I_S* , we can write

(10.22)

Similarly the receiving end apparent power is given by

(10.23)

Hence the real power transmitted over the line is given by

(10.24)

The power-angle characteristics of a series compensated power system are given in Fig. 10.12. In this figure the base power is chosen as V² / X . Three curves are shown, of which the curve P₀ is the power-angle curve when the line is not compensated. Curves which have maximum powers greater than the base power pertain to capacitive mode of operation. On the other hand, all curves the inductive mode of operation will have maximum values less than 1. For example, in Fig. 10.12, the curve P₁ is for capacitive mode and the curve P₂ is for inductive mode of operation.

Fig. 10.12 Power-angle characteristics in constant reactance mode.

Let us now have a look at the reactive power. For simplicity let us restrict our attention to capacitive mode of operation only as this represents the normal mode of operation in which the power transfer over the line is enhanced. From (10.20) and (10.21) we get the reactive power supplied by the compensator as

Solving the above equation we get

(10.25)

In Fig. 10.13, the reactive power injected by the series compensator is plotted against the maximum power transfer as the compensation level changes from 10% to 60%. As the compensation level increases, the maximum power transfer also increases. However, at the same time, the reactive injection requirement from the series compensator also increases. It is interesting to note that at 50% compensation level, the reactive power injection requirement from a series compensator is same that from shunt compensator that is regulating the midpoint voltage to 1.0 per unit.

Fig. 10.13 Reactive power injection by a series compensator versus maximum power transfer as the level of compensation changes in constant reactance mode.