Key Parameters Identification

Identify the given parameters for the 3-phase Voltage Source Inverter (VSI) using Sinusoidal Pulse Width Modulation (SPWM).

• Modulating Waveforms Peak Amplitude ($A_m$): $0.8 \text{ V}$
• Carrier Wave Amplitude ($A_c$): $1$
• Fundamental Frequency ($f_m$): $40 \text{ Hz}$
• Carrier Frequency ($f_c$): $10 \text{ kHz}$
• DC Link Voltage ($V_{dc}$): $600 \text{ V}$

Modulation Index Calculation

The modulation index ($m_a$) is the ratio of the modulating signal amplitude to the carrier signal amplitude.

$m_a = \frac{A_m}{A_c} = \frac{0.8}{1} = 0.8$

Fundamental Output Voltage Calculation

For a VSI operating in the linear region with SPWM, the peak fundamental phase voltage ($V_{ph, \text{peak}}$) is calculated as:

$V_{ph, \text{peak}} = m_a \times \frac{V_{dc}}{2}$

Substituting the known values:

$V_{ph, \text{peak}} = 0.8 \times \frac{600 \text{ V}}{2} = 0.8 \times 300 \text{ V} = 240 \text{ V}$

The fundamental RMS phase voltage ($V_{ph, \text{RMS}}$) is obtained by dividing the peak voltage by $\sqrt{2}$.

$V_{ph, \text{RMS}} = \frac{V_{ph, \text{peak}}}{\sqrt{2}} = \frac{240 \text{ V}}{\sqrt{2}}$

$V_{ph, \text{RMS}} \approx \frac{240}{1.41421356} \text{ V} \approx 169.71 \text{ V}$

Final Answer

The per phase fundamental RMS motor voltage is closest to 169.71 V.