Question

A 230V, 50 Hz, one pulse SCR converter is connected to RE load as shown in figure. Assuming SCR as ideal, the average charging current is

Answer 1

${\theta }_1={\sin }^{-1}\left(\frac{150}{230\sqrt{2}}\right)$
$={27.46}^{\circ }$
${\theta }_2={180}^{\circ }-{\theta }_1={152.54}^{\circ }$
Average charging current=
$I_0=\frac{1}{2\pi }{\int }_{{\theta }_1}^{{\theta }_2}\left(\frac{V_m\sin \omega t-E}{R}\right)d\omega t$
$=\frac{1}{2\pi R}{[-V_m\cos \omega t-E\omega t]}_{27.46}^{152.54}(\theta =\omega t)$
$=\frac{1}{2\pi R}[-230\sqrt{2}(\cos {152.54}^{\circ }-cos{27.46}^{\circ })-150\left\{\right({152.54}^{\circ }-{27.46}^{\circ }\left)\frac{\pi }{{180}^{\circ }}\right\}]$
$=\frac{1}{2\pi \times 8}\left[325.27\right(1.755)-150(2.183\left)\right]$
$=4.97A$