Question

A single-phase semiconverter is operated from 120 V, 50 Hz ac supply. The load current with an average value $I_{dc}$ is continuous and ripple free, firing angle $\alpha =\pi /6$. Input power factor is

• A. 0.827 leading
• B. 0.827 lagging
• C. 0.956 lagging
• D. 0.923 lagging

Answer 1

The correct option is D 0.923 lagging

Input power factor $=\frac{I_{rms1}}{I_{runs}}cos\frac{\alpha }{2}$

Supply rms current $I_{rns}=I_{dc}{(1-\frac{\alpha }{\pi })}^{1/2}={(1-\frac{1}{6})}^{1/2}{I}_{dc}$
$=0.91I_{dc}$

Fundamental component of input current,
$I_{rms,1}=\frac{2\sqrt{2}}{\pi }{I}_{dc}\cos \frac{\alpha }{2}$

$=\frac{2\sqrt{2}}{\pi }\times \cos {15}^o{I}_{dc}=0.869I_{dc}$

Input power factor $=\frac{I_{rms,1}}{I_{rms}}cos\frac{\alpha }{2}=\frac{0.869I_{dc}}{0.91I_{dc}}cos{15}^o=0.923\left(lagging\right)$