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EE 8407 Topic 9 1  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 1 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 Power Converter Systems Graduate Course EE 8407 Ryerson Campus. Bin Wu Ph. D, PEng Professor ELCE Department Ryerson University Contact Info Office: ENG 328 Tel: (416) 979 -5000 ext: 6484 Email: [email protected] ryerson. ca http: //www. ee. ryerson. ca/~bwu/

EE 8407 Topic 9 2  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 2 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 PWM CSI fed MV drive Topic 9 PWM Current Source Inverters (CSI) Courtesy of Rockwell Automation

EE 8407 Topic 9 3  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 3 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 Lecture Topics • Single Bridge Inverter • Trapezoidal Modulation (TPWM) • Selective Harmonic Elimination (SHE) • Space Vector Modulation (SVM) • Dual Bridge Inverter. PWM Current Source Inverters

EE 8407 Topic 9 4  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 4 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Inverter Topology Features: — Simple topology – no antiparallel diodes — Reliable short circuit protection – constant dc current — Very low dv/dt on motor terminals Symmetrical GCTs 1 S 2 S 3 S 5 S 4 S 6 S d. I wi ci si f. C 4 g 6 g 2 g 1 g 3 g 5 g A B C f. C LOAD O ABv Function of C f : — Assist GCT commutation — Reduce harmonic distortion. Single Bridge Inverter

EE 8407 Topic 9 5  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 5 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • DC Current Source I d Implementation of dc current source: — use a large size dc choke – making I d smooth; — use dc current feed back control – keeping I d constant. SCR or PW M Rectifier PW M Inverter Controller d. Id. L * d. I Utility Supply M asv bsv csv f. C A B C d. ISingle Bridge Inverter

EE 8407 Topic 9 6  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 6 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Trapezoidal PWM (TPWM) • Selective Harmonic Elimination (SHE) • Space Vector Modulation (SVM) • Constraints on Switching Pattern Design — dc current I d cannot be interrupted — inverter output current waveform must be defined. • At any time instant, only two switches are turned on, one connected to the positive dc bus, and the other to the negative dc bus. 1 S 2 S 3 S 5 S 4 S 6 S d. I wi 4 g 6 g 2 g 1 g 3 g 5 g A B C P N • Modulation Techniques Single Bridge Inverter

EE 8407 Topic 9 7  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 7 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Trapezoidal PWM (TPWM) Number of pulses per half cycle: N p = 71 gv 2 gv 3 gv 4 gv 5 gv 6 gv 0 wi 3 3 22 t t t t d. I 2 3 3 2 t crvmv m. Vˆcr. Vˆ 02 Trapezoidal Modulation

EE 8407 Topic 9 8  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 8 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Harmonic Content (TPWM) • N p = 15 • Fundamental does not change much with m a • m a = 0. 85 Trapezoidal Modulation

EE 8407 Topic 9 9  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 9 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Waveforms (TPWM)Hz 180 , 13, Hz 8. 131 sw p f Nf Hz 155 , 31, Hz 55 sw p f Nf Trapezoidal Modulation

EE 8407 Topic 9 10  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 10 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Principle • Not all the switching angles are independent. • Only two harmonics can be eliminated with N p = 5. • No modulation index control – the magnitude of inverter output current is controlled by I d • Number of harmonics to be eliminated: 2/)1(p. Nk 3 3 2212 6 23 d. I t wi 13 0 Selective Harmonic Elimination (SHE)

EE 8407 Topic 9 11  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 11 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Fourier Analysis 1 )sin()( n nwtnati even. k )()sin(. . . )()sin( ; oddk )()sin(. . . )()sin( 4 2 3 3 6 2 3 3 3 6 1 1 2 1 tdtntdtn I a k k k dc n 2 0 )()sin()( 4 tdtntiawn Selective Harmonic Elimination

EE 8407 Topic 9 12  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 12 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 even. k ) 6 cos()] 3 (cos[)cos(. . . )] 3 (cos[)cos( ; oddk ) 6 cos()] 3 (cos[)cos(. . . )] 3 (cos[)cos( 4 2211 nnn nnnn n I a kk kk dc n. Expression for a n • Fourier Analysis Selective Harmonic Elimination

EE 8407 Topic 9 13  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 13 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Switching Angle Calculation To Eliminate n th harmonic, set a n = 0 ki. Fki. . . , , 2 , 1 0). . . , , (321 For 5 th , 7 th and 11 th harmonic elimination: 0) 6 11 cos()] 3 (11 cos[)11 cos( 0) 6 7 cos()] 3 (7 cos[)7 cos( 0) 6 5 cos()] 3 (5 cos[)5 cos( 33 22113 33 22112 33 22111 F F FSelective Harmonic Elimination

EE 8407 Topic 9 14  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 14 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Switching Angles (SHE) Switching Angles Harmonics Eliminated 1 2 3 4 5 18. 00 — — 7, 11, 17 11. 70 14. 12 24. 17 — 7 21. 43 — — 7, 13, 17 12. 69 14. 97 24. 16 — 11 24. 55 — — 7, 13, 19 13. 49 15. 94 24. 53 — 13 25. 38 — — 11, 13, 17 14. 55 15. 97 25. 06 — 5, 7 7. 93 13. 75 — 11, 13, 19 15. 24 16. 71 25. 32 — 5, 11 12. 96 19. 14 — 13, 17, 19 17. 08 18. 23 25. 84 — 5, 13 14. 48 21. 12 — 13, 17, 23 18. 03 19. 22 26. 16 — 7, 11 15. 23 19. 37 — 5, 7, 11, 13 0. 00 1. 60 15. 14 20. 26 7, 13 16. 58 20. 79 — 5, 7, 11, 17 0. 07 2. 63 16. 57 21. 80 7, 17 18. 49 23. 08 — 5, 7, 11, 19 1. 11 4. 01 18. 26 23. 60 11, 13 19. 00 21. 74 — 5, 7, 13, 17 1. 50 4. 14 16. 40 21. 12 11, 17 20. 51 23. 14 — 5, 7, 13, 19 2. 56 5. 57 17. 82 22. 33 11, 19 21. 10 23. 75 — 5, 7, 19 4. 59 7. 96 17. 17 20. 55 13, 17 21. 19 23. 45 — 5, 11, 13, 17 4. 16 6. 07 16. 79 22. 04 13, 19 21. 71 23. 94 — 5, 11, 13, 19 5. 13 7. 26 17. 57 22. 72 5, 7, 11 2. 24 5. 60 21. 26 5, 11, 17, 19 6. 93 9. 15 17. 85 22. 77 5, 7, 13 4. 21 8. 04 22. 45 5, 13, 17, 19 7. 80 9. 82 18. 01 23. 25 5, 7, 17 6. 91 11. 96 25. 57 7, 11, 13, 17 5. 42 6. 65 18. 03 22. 17 5, 11, 13 7. 81 11. 03 22. 13 7, 11, 13, 19 6. 35 7. 69 18. 67 22. 74 5, 11, 17 10. 16 14. 02 23. 34 7, 11, 17, 19 8. 07 9. 44 19. 09 22. 93 5, 13, 17 11. 24 14. 92 22. 98 7, 13, 17, 19 8. 88 10. 12 19. 35 23. 22 7, 11, 13 9. 51 11. 64 23. 27 11, 13, 17, 19 10. 39 11. 14 20. 56 23. 60 Selective Harmonic Elimination

EE 8407 Topic 9 15  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 15 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Inverter Waveforms (SHE) Harmonic eliminated: 5 th , 7 th and 11 th ; f sw = 420 Hz. Selective Harmonic Elimination

EE 8407 Topic 9 16  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 16 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Waveforms (SHE)0 7, 20 )( 1175 1 www p III NHzf a 0 3, 60 )( 5 1 w p I NHzf c 0 5, 35 )( 75 1 ww p II NHzf b. Selective Harmonic Elimination

EE 8407 Topic 9 17  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 17 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Space Vector Modulation • Six active current vectors and one zero vector • Six sectors. SECTOR III SECTOR IV SECTOR VISECT OR V j SECTOR II 1 I 2 I 3 I 6 I 5 I 4 I ref. I 0 I Space Vector Modulation

EE 8407 Topic 9 18  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 18 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Switching State 1 S 2 S 3 S 5 S 4 S 6 S d. I LOAD wi ci oi f. C 4 g 6 g 2 g 1 g 3 g 5 g A B C f. C Z Space Vector Modulation

EE 8407 Topic 9 19  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 19 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Switching States & Space Vectors [1]: Upper switch on [-1]: Lower switch on [0]: None of the switches in a leg turned on [2]: Both switches in a leg turned on (bypass mode) Space Vector Modulation

EE 8407 Topic 9 20  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 20 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Dwell Time Calculation 021 002211 TTTT TITI s sref )( 3 1 )(sin )()(cos 21 21 TTITI dsref : Im : Re Following the same principle of SVM for the NPC inverter Space Vector Modulation

EE 8407 Topic 9 21  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 21 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Dwell Time Calculation 210 2 1 ) 6 (sin TTTT T I I T s s d ref 210 2 1 ) 6 (sin TTTT Tm. T s sa sa d w d ref a I I m 1 ˆ Space Vector Modulation

EE 8407 Topic 9 22  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 22 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Switching Sequence Requirements: 1) Transition from one switching state to the next involves only two switches 2) At any time only two switches are on. Space Vector Modulation

EE 8407 Topic 9 23  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 23 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Switching Sequence (Over one cycle)1 gv Sector 10610 6 VIIIIVV 201201302302 wi 02 d. I. . . 3, 2, 1 I s. T )(6 I 2 gv 3 gv 4 gv 5 gv 6 gv. Space Vector Modulation

EE 8407 Topic 9 24  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 24 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Inverter Output Waveforms (SVM) f 1 = 60 Hz, f sw = 540 Hz, N p = 9 and m a = 1 Space Vector Modulation

EE 8407 Topic 9 25  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 25 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Harmonic Spectrum (SVM) f 1 = 60 Hz, f sw = 540 Hz, N p = 9 and m a = 1 Space Vector Modulation

EE 8407 Topic 9 26  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 26 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Harmonic Content (SVM)Space Vector Modulation

EE 8407 Topic 9 27  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 27 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Converter Configuration Dual-Bridge Inverter

EE 8407 Topic 9 28  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 28 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Space Vector Diagram 19 vectors and 51 switching states Dual-Bridge Inverter

EE 8407 Topic 9 29  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 29 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 Current paths with switching state [16; 56] • DC Current Balance Control Dual-Bridge Inverter

EE 8407 Topic 9 30  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 30 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • DC Current Balance Control Current paths with switching state [16; 56] Dual-Bridge Inverter

EE 8407 Topic 9 31  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 31 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • Space Vector Diagram Dual-Bridge Inverter

EE 8407 Topic 9 32  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 32 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 • PWM Scheme Comparison Summary

EE 8407 Topic 9 33  Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley -EE 8407 Topic 9 33 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press,