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A 3 ϕ 180°-mode bridge inverter has star-connected load of R = 8 Ω and L-30 mH. The inverter is fed from 220 V dc and its output frequency is 50 Hz. Find the RMS value of 3rd harmonic of line current (in A)
Correct answer is '0'. Can you explain this answer?
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A 3 ϕ 180°-mode bridge inverter has star-connected load of R ...
All triplen harmonics are absent from the line voltage
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A 3 ϕ 180°-mode bridge inverter has star-connected load of R ...
Given Data
- Bridge inverter: 3-phase, 180° mode
- Load: Star-connected, R = 8 Ω, L = 30 mH
- Input voltage: 220 V DC
- Output frequency: 50 Hz
Calculating Line Current
- The line current can be calculated using the formula:
\(I_{line} = \sqrt{2} \times I_{rms}\)
- In a 3-phase system, the RMS value of the line current is given by:
\(I_{rms} = \sqrt{\frac{P}{3V_{ph}cos(\phi)}}\)
- Where P is the power, Vph is the phase voltage, and φ is the power factor angle.
Calculating Harmonic Current
- The RMS value of the nth harmonic current can be calculated using the formula:
\(I_{n} = \frac{V_{n}}{\sqrt{R^{2}+(\omega L)^{2}}}\)
- Where Vn is the amplitude of the nth harmonic voltage, R is the resistance, L is the inductance, and ω is the angular frequency.
Solution
- For the 3rd harmonic (n = 3), the amplitude of the voltage is 3 times the fundamental frequency voltage.
- Since the 3rd harmonic current is directly proportional to the 3rd harmonic voltage, the 3rd harmonic current is 0 A.
- This is because the 3rd harmonic voltage is 0 for a 3-phase 180° mode bridge inverter.
Therefore, the RMS value of the 3rd harmonic of the line current is 0 A.
- Bridge inverter: 3-phase, 180° mode
- Load: Star-connected, R = 8 Ω, L = 30 mH
- Input voltage: 220 V DC
- Output frequency: 50 Hz
Calculating Line Current
- The line current can be calculated using the formula:
\(I_{line} = \sqrt{2} \times I_{rms}\)
- In a 3-phase system, the RMS value of the line current is given by:
\(I_{rms} = \sqrt{\frac{P}{3V_{ph}cos(\phi)}}\)
- Where P is the power, Vph is the phase voltage, and φ is the power factor angle.
Calculating Harmonic Current
- The RMS value of the nth harmonic current can be calculated using the formula:
\(I_{n} = \frac{V_{n}}{\sqrt{R^{2}+(\omega L)^{2}}}\)
- Where Vn is the amplitude of the nth harmonic voltage, R is the resistance, L is the inductance, and ω is the angular frequency.
Solution
- For the 3rd harmonic (n = 3), the amplitude of the voltage is 3 times the fundamental frequency voltage.
- Since the 3rd harmonic current is directly proportional to the 3rd harmonic voltage, the 3rd harmonic current is 0 A.
- This is because the 3rd harmonic voltage is 0 for a 3-phase 180° mode bridge inverter.
Therefore, the RMS value of the 3rd harmonic of the line current is 0 A.
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A 3 ϕ 180°-mode bridge inverter has star-connected load of R = 8 Ω and L-30 mH. The inverter is fed from 220 V dc and its output frequency is 50 Hz. Find the RMS value of 3rdharmonic of line current (in A)Correct answer is '0'. Can you explain this answer?
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