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Power Converter Systems Graduate Course EE8407

This course covers sinusoidal PWM and space vector modulation techniques for controlling voltage source inverters, focusing on minimizing harmonic distortion and optimizing output frequency and voltage. Discussions include gate signal generation, harmonic content, over-modulation, third harmonic injection, switching states, reference vectors, modulation range, and switching sequence design. Practical examples and waveform analyses are used to illustrate the concepts.

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Power Converter Systems Graduate Course EE8407

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  1. Power Converter Systems Graduate Course EE8407 Bin Wu PhD, PEng Professor ELCE Department Ryerson University Contact Info Office: ENG328 Tel: (416) 979-5000 ext: 6484 Email: bwu@ee.ryerson.ca http://www.ee.ryerson.ca/~bwu/ Ryerson Campus

  2. Topic 5 Two-Level Voltage Source Inverter (VSI) Source: Alstom VDM5000 Two-level VSI

  3. Two Level Voltage Source Inverter Lecture Topics • Sinusoidal PWM • Space vector modulation Why Use PWM Techniques? • To control inverter output frequency (fundamental) • To control inverter output voltage (fundamental) • To minimize harmonic distortion

  4. Sinusoidal PWM • Inverter Configuration Assumption: dc capacitor very large  dc voltage ripple free

  5. Sinusoidal PWM • Modulating and Carrier Waves • vcr – Carrier wave (triangle) • Amplitude modulation index • vm – Modulating wave (sine) • Frequency modulation index

  6. Sinusoidal PWM • Gate Signal Generation Vg1 and Vg4 are complementary

  7. Sinusoidal PWM • Line-to-Line Voltage vAB

  8. Sinusoidal PWM • Waveforms and FFT • ma= 0.8, mf= 15, • fm= 60Hz, fcr= 900Hz • Switching frequency • fsw= fcr = 900Hz

  9. Sinusoidal PWM • Harmonic Content • Low order harmonics • n < (mf-2) are eliminated • VAB1 versus ma is linear • VAB1,max = 0.612Vd

  10. Sinusoidal PWM • Over-Modulation • Fundamental voltage ↑ • Low-order harmonics ↑

  11. Sinusoidal PWM • Third Harmonic Injection PWM • - Fundamental voltage increased • - No low order harmonics produced • 3rd harmonic – zero sequence (to appear in vANandvBN ) • No triplen harmonics in vAB (vAB = vAN - vBN)

  12. Space Vector Modulation • Switching States

  13. Space Vector Modulation • Switching States (Three-Phase) • Eight switching states

  14. Space Vector Modulation • Space Vector Diagram • Active vectors: to • (stationary, not rotating) • Zero vector: • Six sectors: I to VI

  15. Space Vector Modulation • Space Vectors • Three-phase voltages (1) • Two-phase voltages (2) • Space vector representation (3) (2)  (3) (4) where

  16. Space Vector Modulation • Space Vectors (Example) Switching state [POO] S1, S6 and S2 ON and (5) (5)  (4) (6) Similarly, (7)

  17. Space Vector Modulation • Active and Zero Vectors • Active Vector: 6 • Zero Vector: 1 • Redundant switching • states: [PPP] and [OOO]

  18. Space Vector Modulation • Reference Vector Vref • Definition • Rotating in space at ω (8) • Angular displacement (9)

  19. Space Vector Modulation • Relationship Between Vref and VAB • Vrefis approximated by two active • and a zero vectors • Vrefrotates one revolution, • VAB completes one cycle • Length of Vref corresponds to • magnitude of VAB

  20. Space Vector Modulation • Dwell Time Calculation • Volt-Second Balancing (10) • Ta, Tb and T0– dwell times for and • Ts– sampling period • Space vectors , and (11) (11)  (10) (12)

  21. Space Vector Modulation • Dwell Times Solve (12) (13)

  22. Space Vector Modulation • VrefLocation versus Dwell Times

  23. Space Vector Modulation • Modulation Index (15) (16)

  24. Space Vector Modulation • Modulation Range • Vref,max (17) (17)  (16) • ma,max= 1  • Modulation range: 0 ma 1 (18)

  25. Space Vector Modulation • Switching Sequence Design • Basic Requirement: Minimize the number of switchings per sampling period Ts • Implementation: Transition from one switching state to the next involves only two switches in the same inverter leg.

  26. Space Vector Modulation • Seven-segment Switching Sequence • Selected vectors: • V0, V1 and V2 • Dwell times: • Ts = T0 + Ta + Tb • Total number of switchings: 6

  27. Space Vector Modulation • Undesirable Switching Sequence • Vectors V1 and V2 swapped • Total number of switchings: 10

  28. Space Vector Modulation • Switching Sequence Summary (7–segments) Note: The switching sequences for the odd and ever sectors are different.

  29. Space Vector Modulation • Simulated Waveforms f1 = 60Hz, fsw= 900Hz,ma = 0.696, Ts = 1.1ms

  30. Space Vector Modulation • Waveforms and FFT

  31. Space Vector Modulation • Waveforms and FFT (Measured)

  32. Space Vector Modulation • Waveforms and FFT (Measured) ( and )

  33. Space Vector Modulation • Even-Order Harmonic Elimination Type-A sequence (starts and ends with [OOO]) Type-B sequence (starts and ends with [PPP])

  34. Space Vector Modulation • Even-Order Harmonic Elimination Space vector Diagram

  35. Space Vector Modulation • Even-Order Harmonic Elimination • Measured waveforms and FFT

  36. Space Vector Modulation • Even-Order Harmonic Elimination ( and )

  37. Space Vector Modulation • Five-segment SVM

  38. Space Vector Modulation • Switching Sequence ( 5-segment)

  39. Space Vector Modulation • Simulated Waveforms ( 5-segment) • f1 = 60Hz, fsw= 600Hz, ma = 0.696, Ts = 1.1ms • No switching for a 120° period per cycle. • Low switching frequency but high harmonic distortion

  40. Thanks

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