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A $3$-phase grid-connected voltage source converter with $\text{DC}$ link voltage of $1000$ $\text{V}$ is switched using sinusoidal Pulse Width Modulation $\text{(PWM)}$ technique. If the grid phase current is $10$$\text{ A}$ and the $3$-phase complex power supplied by the converter is given by $\left(-4000\: – \: j3000 \right)$ $\text{VA}$, then the modulation index used in sinusoidal $\text{PWM}$ is _____________. (round off to two decimal places)

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