Question

A single phase voltage source inverter is controlled in a single pulse width modulation mode with a pulse width 2d = 150° in each half cycle. The total harmonic distortion of output ac voltage waveform is _____ %.

• A. 31.75

Answer 1

The correct option is A 31.75

$\%THD=\frac{\sqrt{V{{}_0^2}_{,rms}-V_1^2{,}_{rms}}}{V_{1,rms}}\times 100$

Rms value of output voltage $=V_s\sqrt{\frac{2d}{\pi }}$
Pulse width, 2d = 150° (given)
d = 75°

$V_{0,rms}=V_s\sqrt{\frac{2\times 75}{180}}=0.9128V_s$

$V_{01,rms}=\frac{4V_s}{\sqrt{2}\pi }\sin \frac{\pi }{2}\sin 75{}^{\circ }=0.87V_s$

$\%THD=\frac{\sqrt{{\left(0.9128V_s\right)}^2-{\left(0.87V_s\right)}^2}}{0.87V_s}\times 100$

%$THD=31.75\%$