Controlled Rectifiers

For a fully controlled single-phase bridge with continuous current (highly inductive load):

$V_{dc} = \frac{2V_m}{\pi}\cos\alpha$

Three-phase fully controlled bridge:

$V_{dc} = \frac{3\sqrt{2}\,V_L}{\pi}\cos\alpha \approx 1.35\,V_L\cos\alpha$

For $\alpha > 90°$ the average voltage becomes negative and the converter inverts — returning power to the AC side (regenerative braking, HVDC inverters). Controlled rectifiers draw a lagging current, lowering the input power factor as $\alpha$ increases.