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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) VA, then the modulation index used in sinusoidal PWM is ____ . (round off to two decimal places).
Correct answer is '0.47'. Can you explain this answer?
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A 3-phase grid-connected voltage source converter with DC link voltage...
Calculating Modulation Index for Sinusoidal PWM
Given parameters:
- DC link voltage (Vdc) = 1000 V
- Grid phase current (Ig) = 10 A
- Complex power supplied by the converter (S) = -4000 -j3000 VA
To calculate the modulation index (m) for sinusoidal PWM, we need to use the following formula:
m = (2/π) * sin^-1(sqrt(3/2) * (|S|/Vdc) / Ig)
Here, |S| represents the magnitude of the complex power, and sqrt(3/2) is a constant factor for 3-phase systems.
Substituting the given values in the formula, we get:
m = (2/π) * sin^-1(sqrt(3/2) * (5000/1000) / 10)
m = 0.47 (rounded off to two decimal places)
Therefore, the modulation index used in sinusoidal PWM is 0.47.
Explanation:
Sinusoidal PWM is a technique used to control the output voltage of a voltage source converter (VSC) by modulating the width of the pulses in a sinusoidal waveform. The modulation index in sinusoidal PWM determines the amplitude of the output voltage waveform.
In this question, we are given the DC link voltage, grid phase current, and complex power supplied by the converter. Using the formula for modulation index in sinusoidal PWM, we can calculate the value of the modulation index.
The formula involves taking the inverse sine of a certain expression, which is a function of the complex power, DC link voltage, and grid phase current. By substituting the given values and simplifying the expression, we obtain the value of the modulation index as 0.47.
This indicates that the amplitude of the output voltage waveform will be 47% of the DC link voltage.
Given parameters:
- DC link voltage (Vdc) = 1000 V
- Grid phase current (Ig) = 10 A
- Complex power supplied by the converter (S) = -4000 -j3000 VA
To calculate the modulation index (m) for sinusoidal PWM, we need to use the following formula:
m = (2/π) * sin^-1(sqrt(3/2) * (|S|/Vdc) / Ig)
Here, |S| represents the magnitude of the complex power, and sqrt(3/2) is a constant factor for 3-phase systems.
Substituting the given values in the formula, we get:
m = (2/π) * sin^-1(sqrt(3/2) * (5000/1000) / 10)
m = 0.47 (rounded off to two decimal places)
Therefore, the modulation index used in sinusoidal PWM is 0.47.
Explanation:
Sinusoidal PWM is a technique used to control the output voltage of a voltage source converter (VSC) by modulating the width of the pulses in a sinusoidal waveform. The modulation index in sinusoidal PWM determines the amplitude of the output voltage waveform.
In this question, we are given the DC link voltage, grid phase current, and complex power supplied by the converter. Using the formula for modulation index in sinusoidal PWM, we can calculate the value of the modulation index.
The formula involves taking the inverse sine of a certain expression, which is a function of the complex power, DC link voltage, and grid phase current. By substituting the given values and simplifying the expression, we obtain the value of the modulation index as 0.47.
This indicates that the amplitude of the output voltage waveform will be 47% of the DC link voltage.
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Community Answer
A 3-phase grid-connected voltage source converter with DC link voltage...
S = (-4000 - J3000) VA
VL1(rms) = 288.675 V
3-φ VSI - SPWM, MA ≤ 1
MA = 0.47
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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) VA, then the modulation index used in sinusoidal PWM is ____ . (round off to two decimal places).Correct answer is '0.47'. Can you explain this answer?
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