Discussion
The thyristor-controlled reactor FACTS (Flexible AC Transmission) devices connected as shunt compensator in transmission line. The parameters are \(V = 220\) V, frequency \(f = 50\) Hz, reactance \(X = 1.0\ \Omega\), power \(P = 48.4\) kW. What is the value of phase angle \(\alpha\)?
Answer: A
The key gives \(60^\circ\). For a thyristor controlled reactor the fundamental susceptance depends on the firing angle \(\alpha\) through
\[ \begin{aligned} B(\alpha) \\ &= \frac{1}{X}\left(\frac{2(\pi - \alpha) + \sin 2\alpha}{\pi}\right) \end{aligned} \]
The full reactor at 220 V and 1 ohm would absorb \(220^2/1 = 48.4\) kVA, and the stated power of 48.4 kW is that full value, which corresponds to full conduction. The conduction angle in the item is given in a different convention from the one used here, so I could not reproduce the \(60^\circ\) independently. The explanation follows the key, option A.
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