Flexible AC Transmission System - Theory

Theory

In the case of a no-loss line, voltage magnitude at the receiving end is the same as voltage magnitude at the sending end: Vs = Vr=V. Transmission results in a phase lag that depends on line reactance X.

\begin{align} \underline{V_s}&=V \cos\left(\frac{\delta}{2}\right) +jV \sin\left(\frac{\delta}{2}\right)\\ \underline{V_r}&=V \cos\left(\frac{\delta}{2}\right)-jV \sin\left(\frac{\delta}{2}\right)\\ \underline{I}&=\frac{\underline{V_s}-\underline{V_r}}{jX}=\frac{2V\sin{\left(\frac{\delta}{2}\right)}}{X} \end{align}

As it is a no-loss line, active power P is the same at any point of the line:

Reactive power at sending end is the opposite of reactive power at receiving end:

As is very small, active power mainly depends on whereas reactive power mainly depends on voltage magnitude.

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