derive power angle equation

Dear student,

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

Similarly the receiving end apparent power is given by

Hence the real power transmitted over the line is given by

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.

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