Question

A 1-phase voltage source inverter is controlled in a single pulse width modulation mode with a pulse width $2d={150}^{\circ }$ in each half cycle. The total harmonic distortion of output ac voltage waveform is_____%.

Answer 1

$\%THD=\frac{\sqrt{V_{0,rms}^2-V_1^2}}{V_1}\times 100$

Rms value of output voltage

$=V_s\sqrt{\frac{2d}{2\pi }}$

$\text{Pulse width, 2d}={150}^{\circ }\left(given\right)$

$d={75}^{\circ }$

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

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

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

$\%THD=31.75\%$