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# Inverter

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### Inverter

1. 1. INVERTER
2. 2. Inverter Topologies The harmonic free sinusoidal output is a major area that has been investigated for many years as it is highly desirable in most inverter applications. • Some switching techniques are utilized for the purpose of enhancing the magnitude of the fundamental component and reducing the harmonics to obtain minimized total harmonic distortion.
3. 3. In the harmonic elimination techniques the lower order harmonics are effectively reduced from output voltage by fundamental switching, so smaller output filters can easily be used to eliminate the remaining higher order harmonics. The topologies are explained in the following sequence: • • • • • • Circuit Diagram. Output Voltage waveform. Fourier Analysis. Switching Angles Calculation. Spectrum of Output Sinusoidal waveform. Calculation of Total Harmonic Distortion
4. 4. Fundamental idea of harmonic Elimination 6 Fundamental Component 3rd Harmonic 4 2 120 Degree Conduction 210 330 0 30 150 120 Degree Conduction -2 -4 -6 0 50 100 150 200 250 300 Degree Elimination of 3rd Harmonic via Switching 350
5. 5. Half Bridge (PWM) S1 D1 S2 Vdc/2 D2 Vdc LOAD 0 Vdc/2 Half-Bridge PWM inverter V0 Vdc/2 ωt 0 -Vdc/2 π 2π π/2 α1 α2 α3 α4 Phase voltage waveform of PWM inverter
6. 6. Fourier Analysis The Fourier series of the quarter-wave symmetric m-pulse PW waveform is:
7. 7. Fourier Analysis
8. 8. Fourier Analysis
9. 9. Fourier Analysis for Half Bridge Waveform V0 Vdc/2 ωt 0 -Vdc/2 π π/2 α1 α2 α3 α4 2π
10. 10. Fourier Analysis
11. 11. Fourier Analysis
12. 12. Angle Computation
13. 13. Angle Computation
14. 14. THD Table
15. 15. Half bridge single phase 100 90 Normalized Harmonic Magnitude 80 70 60 50 40 30 20 10 0 0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 Frequency Hz Half Bridge PWM Inverter Output Voltage Specturm for M=0.85 Half Bridge 150 100 50 0 -50 -100 -150 0 0.005 0.01 0.015 0.02 0.025 0.03 t Half Bridge PWM Inverter Output Voltage Waveform for M=0.85 0.035
16. 16. Full Bridge (PWM) S1 D1 S3 D3 S4 D4 Vdc LOAD D2 S2 Single-phase Full- Bridge PWM inverter V0 E1 0 α1α2 α3 α4 α5 π/2 π E-1 Phase voltage waveform of PWM inverter ωt 2π
17. 17. Fourier Analysis The Fourier series of the quarter-wave symmetric m-pulse PW waveform is:
18. 18. Fourier Analysis
19. 19. Switching Angles Computation The equations used to calculate switching angles are:
20. 20. Switching Angles Computation ( MATLAB CODE)
21. 21. PWM Inverter Output Voltage Waveform for M=0.82 Voltage Spectrums Normalized to Fundamental Component
22. 22. for M=0.9 for M=0.9 6 100 4 THD=36.48% 80 Harmonics Magnitude Voltage Vo 2 0 -2 -4 60 40 20 -6 0 0.002 0.004 0.006 0.008 Time t 0.01 0.012 0.014 0.016 0 0 for M=0.87 for M=0.87 100 6 THD=34.29% 4 Harmonics Magnitude 80 2 Voltage Vo 60 120 180 240 300 360 420 480 540 600 660 Frequency Hz 0 -2 60 40 20 -4 -6 0 0 0.002 0.004 0.006 0.008 Time t 0.01 0.012 0.014 0.016 0 60 120 180 240 300 360 420 480 540 600 660 Frequency Hz
23. 23. Diode Clamped Multilevel Inverter (DCMLI) E4 Sa S'e Vdc Da Sb Db Sc De S'f E3 Df S'g Vdc Dc Sd Dg S'h A LOAD E2 B S'a S'b S'c Se D'a Sf D'b D'c Sg D'e Vdc D'f E1 D'g Vdc S'd Sh 0 Diode Five-Level Bridge Multilevel Inverter E0
24. 24. Five-level DCMLI voltage levels and their corresponding switch states. V0 E4 E3 E2 E1 E0 E-1 E-2 E-3 E-4 ωt α1 α2 α3 α4 π/2 π Phase voltage waveform of 5-level inverter 2π
25. 25. Fourier Analysis The Fourier series of the quarter-wave symmetric 5-level DCMLI multilevel waveform Switching Angles Computation The equations used to calculate switching angles are:
26. 26. 5-Level DCMLI Output Voltage Waveform for M=0.82 Voltage Spectrums Normalized to Fundamental Component
27. 27. Pulse Width Modulated (PWM) multilevel Inverters E1 Sa S'c Vdc Da Sb Dc S'd A LOAD E1 B S'a D'a Sc D'c Vdc S'b Sd 0 E0 Single-phase Full- Bridge PWM inverter 3-level PWM DCMLI voltage levels and corresponding switch states.
28. 28. V0 E2 E1 E0 α1α2 α3 α4 α5 π/2 π ωt 2π E-1 E-2 3-level PWM output voltage waveform Fourier Analysis The Fourier series of the quarter-wave symmetric 3-level PWM voltage waveform is: output
29. 29. Switching Angles Computation The equations used to calculate switching angles are:
30. 30. 3-level PWM Inverter Output Voltage Waveform for M=0.82 Voltage Spectrums Normalized to Fundamental Component
31. 31. Conclusion • The PWM inverter though took four switches for implementation (less than other two) but Simulation resulting THD is greater of all. results of • The DCMLI resulting THD is lowest of all but it three took too many devices for implementation. different 1- • The PWM in DCMLI (Combination of PWM φ inverters and DCMLI) have less number of switches were than the DCMLI and low THD than PWM inverter, implying that this technique is presented economically and technically best to implement