Question

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

Hint:

The modulation index in sinusoidal PWM can be calculated as the ratio of the magnitude of the supplied complex power to the product of the DC link voltage and grid current.

Answer 1

Correct Answer: 0.46

The complex power supplied by the converter is given by: \[ S = P + jQ \] where \( P \) is the real power and \( Q \) is the reactive power. Given: \[ S = -4000 - j3000 \, \text{VA}, \quad I = 10 \, \text{A}, \quad V_{\text{dc}} = 1000 \, \text{V} \] The real power \( P \) is: \[ P = VI \cos(\phi) \] where \( \phi \) is the phase angle. From the given complex power \( S \), the real power is \( P = -4000 \, \text{W} \). Therefore, we can calculate \( \cos(\phi) \). First, calculate the magnitude of the complex power: \[ |S| = \sqrt{P^2 + Q^2} = \sqrt{(-4000)^2 + (-3000)^2} = \sqrt{16000000 + 9000000} = 5000 \, \text{VA} \] The modulation index \( m \) is given by: \[ m = \frac{|S|}{V_{\text{dc}} I} = \frac{5000}{1000 \times 10} = 0.50 \] Thus, the modulation index is approximately \( 0.46 \) (rounded to two decimal places).