Question

A single phase full converter has output voltage waveform as shown in figure. Source inductance is 1.4 mH with rated voltage of 230 V at 60 Hz. If the firing
angle $\alpha ={30}^{\circ }$ and power delivered is 3 kW, then the value of the shaded area (volt radians) is________

Answer 1

$V_0=(\frac{2V_m}{\pi }\cos \alpha -\Delta V_d)$

$P=V_0{I}_0$
$300=(\frac{2\times 230\sqrt{3}}{\pi }\cos {30}^{\circ }-4\times 60\times 1.4\times {10}^{-3}\times I_0)I_0$
$0.336I_0^2-179.33I_0+3000=0$
$I_0=516.43,17.29$
$I_0=17.29A$
Area $A_u=4\pi f{L}_x{I}_0$
$=4\pi \times 60\times 1.4\times {10}^{-3}\times 17.29$
$=18.25Voltrads$