# Power Converter Systems .ppt

27 May 2023
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### Power Converter Systems .ppt

• 1. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 1 Power Converter Systems Graduate Course EE8407 Ryerson Campus 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/
• 2. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 2 VDM5000 Two-level VSI Topic 5 Two-Level Voltage Source Inverter (VSI) Source: Alstom
• 3. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 3 • Sinusoidal PWM • Space vector modulation Lecture Topics • To control inverter output frequency (fundamental) • To control inverter output voltage (fundamental) • To minimize harmonic distortion Why Use PWM Techniques? Two Level Voltage Source Inverter
• 4. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 4 • Inverter Configuration Assumption: dc capacitor very large  dc voltage ripple free d C 1 S 2 S 3 S 5 S 4 S 6 S A B C P N LOAD A i O B i C i d V Sinusoidal PWM
• 5. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 5 • Modulating and Carrier Waves • vcr – Carrier wave (triangle) • Amplitude modulation index cr m a V V m ˆ ˆ  • Frequency modulation index m cr f f f m  0 v mA v B m v C m v cr v cr V ˆ m V ˆ t  • vm – Modulating wave (sine) Sinusoidal PWM
• 6. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 6 • Gate Signal Generation 1 g v 4 g v d V 0 AN v   2 mA v cr v 0 cr mA v v  0 1  g v ) 0 ( 4  g v 1 S on ) off ( 4 S d AN V v  Phase A cr mA v v  0 4  g v ) 0 ( 1  g v 4 S on ) off ( 1 S 0  AN v Vg1 and Vg4 are complementary Sinusoidal PWM
• 7. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 7 • Line-to-Line Voltage vAB AB v BN v AN v 0 0 0 v mA v B m v C m v cr v cr V ˆ m V ˆ d V d V d V   2 t  t  t  t  1 AB v 1 S 2 S 3 S 5 S 4 S 6 S B C P N d V A Sinusoidal PWM
• 8. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 8 • Waveforms and FFT • ma = 0.8, mf = 15, fm = 60Hz, fcr = 900Hz • Switching frequency fsw = fcr = 900Hz 0.1 0.2 0 0 0 THD = 92.07% THD = 92.07% THD = 7.73% THD = 92.07% d V 3 / 2 d V AB v AO v A i 2  f m 1 2  f m 2 3  f m 1 4  f m n  3  3  2  2   0 1 5 10 15 20 25 30 35 40 45 50 55 60 d V VAB 49 . 0 1  d n V VAB / Sinusoidal PWM
• 9. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 9 • Harmonic Content • Low order harmonics n < (mf -2) are eliminated • VAB1 versus ma is linear • VAB1,max = 0.612Vd a m 1 2  f m 2  f m 1 4  f m 2 3  f m 4 3  f m d n AB V V 1  n 0.2 0.4 0.6 0.8 0.1 0.2 0.3 0 0 100 200 300 0 THD (%) THD Sinusoidal PWM
• 10. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 10 • Over-Modulation • Fundamental voltage ↑ • Low-order harmonics ↑ 0 0.1 0.2 0 d V  2  3  0 1 2 -1 -2 mA v mC v mB v cr v AB v n 0 A i  2  3  d V VAB 744 . 0 1  d n V VAB / n 1 5 10 15 20 25 30 35 40 45 50 55 60 Sinusoidal PWM
• 11. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 11 • Third Harmonic Injection PWM cr m V V ˆ ˆ 1  • - Fundamental voltage increased cr mA V V ˆ ˆ  • - No low order harmonics produced • 3rd harmonic – zero sequence (to appear in vAN and vBN ) • No triplen harmonics in vAB (vAB = vAN - vBN) 3 /  3 / 2   2 3 m v 1 m v 3 1 m m mA v v v   0 v t  1 ˆ m V mA V ˆ cr V ˆ Sinusoidal PWM
• 12. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 12 • Switching States Leg A Leg B Leg C Switching State 1 S 4 S AN V 3 S 6 S BN V 5 S 2 S CN V P On Off d V On Off d V On Off d V O Off On 0 Off On 0 Off On 0 1 S 2 S 3 S 5 S 4 S 6 S B C P N d V A LOAD A i O B i C i Space Vector Modulation
• 13. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 13 • Switching States (Three-Phase) • Eight switching states 1 S 2 S 3 S 5 S 4 S 6 S B C P N d V A Space Vector Modulation
• 14. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 14 • Space Vector Diagram a 1 V r 0 V r 3 V r 2 V r 4 V r 5 V r 6 V r b j POO PPO OPO OPP OOP POP ref V r q OOO PPP SECTOR I SECTOR III SECTOR IV SECTOR VI SECTOR V SECTOR II  • Active vectors: to (stationary, not rotating) • Zero vector: 1 V r 6 V r 0 V r • Six sectors: I to VI Space Vector Modulation
• 15. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 15 • Space Vectors • Three-phase voltages 0 ) ( ) ( ) (    t v t v t v CO BO AO • Two-phase voltages                            ) ( ) ( ) ( 3 4 sin 3 2 sin 0 sin 3 4 cos 3 2 cos 0 cos 3 2 ) ( ) ( t v t v t v t v t v CO BO AO     b a • Space vector representation ) ( ) ( ) ( t v j t v t V b a   r (2)  (3)   3 / 4 3 / 2 0 ) ( ) ( ) ( 3 2 ) (   j CO j BO j AO e t v e t v e t v t V    r where x j x ejx sin cos   (3) (1) (2) (4) Space Vector Modulation
• 16. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 16 • Space Vectors (Example) Switching state [POO]  S1, S6 and S2 ON d BO d AO V t v V t v 3 1 ) ( , 3 2 ) (    d CO V t v 3 1 ) (   and (5)  (4) (7) (5) (6) 0 1 3 2 j d e V V  r Similarly, 3 ) 1 ( 3 2    k j d k e V V r . 6 ..., , 2 , 1  k a 1 V r 0 V r 3 V r 2 V r 4 V r 5 V r 6 V r b j POO PPO OPO OPP OOP POP ref V r q OOO PPP SECTOR I SECTOR III SECTOR IV SECTOR VI SECTOR V SECTOR II  Space Vector Modulation
• 17. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 17 • Active and Zero Vectors Space Vector Switching State (Three Phases) On-state Switch Vector Definition [PPP] 5 3 1 , , S S S Zero Vector 0 V r [OOO] 2 6 4 , , S S S 0 0  V r 1 V r [POO] 2 6 1 , , S S S 0 1 3 2 j d e V V  r 2 V r [PPO] 2 3 1 , , S S S 3 2 3 2   j d e V V r 3 V r [OPO] 2 3 4 , , S S S 3 2 3 3 2   j d e V V r 4 V r [OPP] 5 3 4 , , S S S 3 3 4 3 2   j d e V V r 5 V r [OOP] 5 6 4 , , S S S 3 4 5 3 2   j d e V V r Active Vector 6 V r [POP] 5 6 1 , , S S S 3 5 6 3 2   j d e V V r • Active Vector: 6 • Zero Vector: 1 • Redundant switching states: [PPP] and [OOO] 1 S 2 S 3 S 5 S 4 S 6 S B C P N d V A Space Vector Modulation
• 18. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 18 (8) • Reference Vector Vref • Definition a 1 V r 0 V r 3 V r 2 V r 4 V r 5 V r 6 V r b j POO PPO OPO OPP OOP POP ref V r q OOO PPP SECTOR I SECTOR III SECTOR IV SECTOR VI SECTOR V SECTOR II  • Angular displacement   t dt t 0 ) (  q (9) q j ref ref e V V  r • Rotating in space at ω Space Vector Modulation f   2 
• 19. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 19 • Relationship Between Vref and VAB • Vref is approximated by two active and a zero vectors • Vref rotates one revolution, VAB completes one cycle • Length of Vref corresponds to magnitude of VAB 1 V r 2 V r ref V r q 1 V T T s a r 2 V T T s b r SECTOR I Q Space Vector Modulation
• 20. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 20 • Dwell Time Calculation • Volt-Second Balancing          0 0 0 2 1 T T T T T V T V T V T V b a s b a s ref r r r r (10) • Ta, Tb and T0 – dwell times for and , 2 1 V V r r 0 V r • Ts – sampling period • Space vectors d j ref ref V V e V V 3 2 , 1   r r q 3 2 3 2  j d e V V  r 0 0  V r , and (11)  (10)           b d s ref b d a d s ref T V T V T V T V T V 3 1 ) (sin 3 1 3 2 ) (cos q q : Im : Re (11) (12) 1 V r 2 V r ref V r q 1 V T T s a r 2 V T T s b r SECTOR I Q Space Vector Modulation
• 21. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 21 • Dwell Times Solve (12)                  b a s d ref s b d ref s a T T T T V V T T V V T T 0 sin 3 ) 3 ( sin 3 q q  3 / 0  q   (13) Space Vector Modulation
• 22. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 22 • Vref Location versus Dwell Times ref V r Location 0  q 6 0  q   6  q  3 6  q    3  q  Dwell Times 0 0   b a T T b a T T  b a T T  b a T T  0 0   b a T T 1 V r 2 V r ref V r q 1 V T T s a r 2 V T T s b r SECTOR I Q Space Vector Modulation
• 23. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 23 • Modulation Index              c b s a s b a s a T T T T m T T m T T 0 sin ) 3 ( sin q q  (15) d ref a V V m 3  (16) Space Vector Modulation
• 24. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 24 • Modulation Range • Vref,max 3 2 3 3 2 max , d d ref V V V    (17) a 1 V r 0 V r 3 V r 2 V r 4 V r 5 V r 6 V r b j POO PPO OPO OPP OOP POP ref V r q OOO PPP SECTOR I SECTOR III SECTOR IV SECTOR VI SECTOR V SECTOR II  (17)  (16) • ma,max = 1  • Modulation range: 0  ma  1 (18) Space Vector Modulation
• 25. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 25 • 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. Space Vector Modulation
• 26. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 26 • Seven-segment Switching Sequence d V 2 0 T 2 a T 2 b T 2 a T BN v AN v CN v 0 1 V r 1 V r 2 V r 0 V r 2 V r POO OOO PPO PPP PPO POO OOO d V d V 4 0 T 4 0 T 2 b T s T 0 0 0 V r 0 V r • Total number of switchings: 6 • Selected vectors: V0, V1 and V2 • Dwell times: Ts = T0 + Ta + Tb Space Vector Modulation
• 27. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 27 • Undesirable Switching Sequence • Vectors V1 and V2 swapped d V 2 0 T 2 a T 2 b T 2 a T BN v AN v CN v 0 1 V r 1 V r 2 V r 2 V r POO OOO PPO PPP PPO POO OOO d V d V 4 0 T 4 0 T 2 b T s T 0 0 0 V r 0 V r 0 V r • Total number of switchings: 10 Space Vector Modulation
• 28. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 28 • Switching Sequence Summary (7–segments) Sector Switching Sequence 0 V r 1 V r 2 V r 0 V r 2 V r 1 V r 0 V r I OOO POO PPO PPP PPO POO OOO 0 V r 3 V r 2 V r 0 V r 2 V r 3 V r 0 V r II OOO OPO PPO PPP PPO OPO OOO 0 V r 3 V r 4 V r 0 V r 4 V r 3 V r 0 V r III OOO OPO OPP PPP OPP OPO OOO 0 V r 5 V r 4 V r 0 V r 4 V r 5 V r 0 V r IV OOO OOP OPP PPP OPP OOP OOO 0 V r 5 V r 6 V r 0 V r 6 V r 5 V r 0 V r V OOO OOP POP PPP POP OOP OOO 0 V r 1 V r 6 V r 0 V r 6 V r 1 V r 0 V r VI OOO POO POP PPP POP POO OOO Note: The switching sequences for the odd and ever sectors are different. Space Vector Modulation
• 29. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 29 • Simulated Waveforms AB v AO v 0 0 0 A i d V 3 / 2 d V   2  3   2  3 VI VI Sector I II III IV V I II III IV V f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms Space Vector Modulation
• 30. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 30 • Waveforms and FFT 0 0.1 0.2 n 0 0 AB v AO v A i THD =80.2% THD =80.2% THD =8.37% THD =80.2% d V 3 / 2 d V  2 d V VAB 566 . 0 1  1 5 10 15 20 25 30 35 40 45 50 55 60 d n V VAB / 0  2   3 Space Vector Modulation
• 31. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 31 • Waveforms and FFT (Measured) 23 AO v AB v d n V VAB 0.2 0.1 0 (a) Waveforms 2ms/div (b) Spectrum (500Hz/div) 14 34 10 47 58 THD = 80.3% 8 16 29 43 Space Vector Modulation
• 32. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 32 0 0.2 0.4 0.6 0.8 0 0.05 0.10 0.15 10 16 20 d n AB V V / a m 1  n 2  n 4 8 14 (a) Even order harmonics 5 7 11 13 17 n = 19 0.05 0.10 0.15 d n AB V V / 0 0.2 0.4 0.6 0.8 a m 1  n (b) Odd order harmonics 0 100 200 300 0 THD (%) THD • Waveforms and FFT (Measured) Hz 60 1  f sec 720 / 1  s T ( and ) Space Vector Modulation
• 33. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 33 • Even-Order Harmonic Elimination BN v AN v CN v 0 5 V r 4 V r 0 V r OOP OOO OPP PPP OPP OOP OOO 0 0 0 V r 0 V r AB v 0 d V  4 V r 5 V r d V d V d V Type-A sequence (starts and ends with [OOO]) BN v AN v CN v 0 0 0 AB v 0 d V  5 V r OOP 4 V r OPP d V d V d V 4 V r OPP 5 V r OOP PPP 0 V r 0 V r OOO PPP 0 V r Type-B sequence (starts and ends with [PPP]) Space Vector Modulation
• 34. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 34 • Even-Order Harmonic Elimination 1 V r 3 V r 2 V r 4 V r 5 V r 6 V r SECTOR I SECTOR III SECTOR IV SECTOR VI SECTOR V SECTOR II a b a a a a a b b b b b Type-A sequence Type-B sequence  30  30 Space vector Diagram Space Vector Modulation
• 35. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 35 • Even-Order Harmonic Elimination (a) Waveforms 2ms/div AO v AB v 0.2 0.1 0 d n V VAB (b) Spectrum (500Hz/div) 23 13 47 35 7 17 65 THD = 80.5% 41 5 • Measured waveforms and FFT Space Vector Modulation
• 36. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 36 • Even-Order Harmonic Elimination 17 19 13 7 5 11 100 200 300 0 THD (%) 0 0.2 0.4 0.6 0.8 a m 0 0.1 0.2 0.3 d n AB V V / 1  n THD Hz 60 1  f sec 720 / 1  s T ( and ) Space Vector Modulation
• 37. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 37 • Five-segment SVM d V 2 a T b T 2 a T BN v AN v CN v 0 1 V r 1 V r 2 V r 0 V r POO OOO PPO POO OOO d V s T 0 0 0 V r 2 0 T 2 0 T d V a T 1 V r 2 V r 0 V r PPP PPO POO PPP d V s T 0 V r 2 0 T 2 0 T (a) Sequence A 2 V r PPO d V 2 b T 2 b T (b) Sequence B Space Vector Modulation
• 38. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 38 • Switching Sequence ( 5-segment) Sector Switching Sequence (A) 0 V r 1 V r 2 V r 1 V r 0 V r I OOO POO PPO POO OOO 0  CN v 0 V r 3 V r 2 V r 3 V r 0 V r II OOO OPO PPO OPO OOO 0  CN v 0 V r 3 V r 4 V r 3 V r 0 V r III OOO OPO OPP OPO OOO 0  AN v 0 V r 5 V r 4 V r 5 V r 0 V r IV OOO OOP OPP OOP OOO 0  AN v 0 V r 5 V r 6 V r 5 V r 0 V r V OOO OOP POP OOP OOO 0  BN v 0 V r 1 V r 6 V r 1 V r 0 V r VI OOO POO POP POO OOO 0  BN v Space Vector Modulation
• 39. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 39 • Simulated Waveforms ( 5-segment) d V  2  4 1 g v 3 g v 5 g v AB v 0 0 A i 3 / 2  2  4  2  4 • No switching for a 120° period per cycle. • Low switching frequency but high harmonic distortion • f1 = 60Hz, fsw = 600Hz, ma = 0.696, Ts = 1.1ms Space Vector Modulation
• 40. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 EE8407 Topic 5 40