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1 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 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: bwu@ee. ryerson. ca http: //www. ee. ryerson. ca/~bwu/

2 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 VDM 5000 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 EE 8407 Topic 5 • 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 EE 8407 Topic 5 • Inverter Configuration Assumption: dc capacitor very large dc voltage ripple free Sinusoidal PWM

5 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Modulating and Carrier Waves • v cr – Carrier wave (triangle) • Amplitude modulation indexcr m a V V m ˆ ˆ • Frequency modulation index m cr f f f m • v m – Modulating wave (sine) Sinusoidal PWM

6 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Gate Signal Generation crm. Avv 01 gv )0(4 gv 1 S on )off(4 S d. ANVv Phase A crm. Avv 04 gv )0(1 gv 4 S on )off(1 S 0 ANv V g 1 and V g 4 are complementary Sinusoidal PWM

7 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Line-to-Line Voltage v ABABv BNv ANv 0 0 0 vm Av. Bmv. Cmv cr Vˆm. Vˆ d. V 2 t t 1 ABv. Sinusoidal PWM

8 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Waveforms and FFT • m a = 0. 8, m f = 15, f m = 60 Hz, f cr = 900 Hz • Switching frequency f sw = f cr = 900 Hz Sinusoidal PWM

9 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Harmonic Content • Low order harmonics n < ( m f -2) are eliminated • V AB 1 versus m a is linear • V AB 1, max = 0. 612 V d Sinusoidal PWM

10 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Over-Modulation • Fundamental voltage ↑ • Low-order harmonics ↑Sinusoidal PWM

11 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Third Harmonic Injection PWMcrm. VVˆˆ1 • — Fundamental voltage increased crm. AVVˆˆ • — No low order harmonics produced • 3 rd harmonic – zero sequence (to appear in v AN and v BN ) • No triplen harmonics in v AB ( v AB = v AN — v BN ) 3/3/22 3 mv 1 mv 31 mmm. Avvv 0 v t 1ˆm. Vm. AVˆcr. VˆSinusoidal PWM

12 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Switching States. Leg A Leg B Leg C Switching State 1 S 4 S ANV 3 S 6 S BNV 5 S 2 S CNV P On Off d. V O Off On 0 Space Vector Modulation

13 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Switching States (Three-Phase) • Eight switching states. Space Vector Modulation

14 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Space Vector Diagram 1 V 0 V 3 V 2 V 4 V 5 V 6 V j POO PPOOPO OPP OOPPOP ref. V OOOPPPSECTOR III SECTOR IV SECTOR VI SECTOR V SECTOR II • Active vectors: to (stationary, not rotating) • Zero vector: 1 V 6 V 0 V • Six sectors: I to VISpace Vector Modulation

15 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Space Vectors • Three-phase voltages 0)()()(tvtvtv. COBOAO • Two-phase voltages )( )( )( 34 sin 32 sin 0 sin 34 cos 32 cos 0 cos 32 )( )( tv tv tv CO BO AO • Space vector representation )()()(tvjtvt. V (2) (3) 3/43/20)()()( 3 2 )(j CO j BO j AOetvetvetvt. V where xjxejxsincos (3)(1) (2) (4)Space Vector Modulation

16 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Space Vectors (Example) Switching state [POO] S 1 , S 6 and S 2 ONd. BOd. AOVtv. Vtv 3 1 )(, 3 2 )(d. COVtv 3 1 )( and (5) (4) (7) (5) (6) 0 1 3 2 j de. VV Similarly, 3)1( 3 2 kj dke. VV . 6. . . , , 2, 1 k 1 V 0 V 3 V 2 V 4 V 5 V 6 V j POOPO OPP OOP POP ref. V OOOPPP 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 EE 8407 Topic 5 • Active and Zero Vectors. Space Vector Switching State (Three Phases) On-state Switch Vector Definition [PPP] 531, , SSS Zero Vector 0 V [OOO] 264, , SSS 00 V 1 V [POO] 261, , SSS 0 13 2 j de. VV 2 V [PPO] 231, , SSS 323 2 j de. VV 3 V [OPO] 234, , SSS 3 2 33 2 j de. VV 4 V [OPP] 534, , SSS 3 3 43 2 j de. VV 5 V [OOP] 564, , SSS 3 4 53 2 j de. VV Active Vector 6 V [POP] 561, , SSS 3 5 63 2 j de. VV • Active Vector: 6 • Zero Vector: 1 • Redundant switching states: [PPP] and [OOO] Space Vector Modulation

18 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 (8) • Reference Vector V ref • Definition 1 V 0 V 3 V 2 V 4 V 5 V 6 V j POOPO OPP OOP POP ref. V OOOPPP SECTOR III SECTOR IV SECTOR VI SECTOR V SECTOR II • Angular displacement t dtt 0 )( (9) j refrefe. VV • Rotating in space at ωSpace Vector Modulation f

19 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Relationship Between V ref and V AB • V ref is approximated by two active and a zero vectors • V ref rotates one revolution, V AB completes one cycle • Length of V ref corresponds to magnitude of V ABSpace Vector Modulation

20 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Dwell Time Calculation • Volt-Second Balancing 0 0021 TTTT TVTV basref (10) • T a , T b and T 0 – dwell times for and , 21 VV 0 V • T s – sampling period • Space vectors d j refref. VVe. VV 3 2 , 1 3 2 j de. VV 00 V , and (11) (10) bdsref bdadsref TVTVTV 3 1 )(sin 3 1 3 2 )(cos : Im : Re (11) (12)Space Vector Modulation

21 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Dwell Times Solve (12) bas d refs b d refs a TTTT V VT T 0 sin 3 ) 3 (sin 3 3/0 (13)Space Vector Modulation

22 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • V ref Location versus Dwell Times ref. V Location 0 6 0 6 36 3 Dwell Times 0 0 b a T T ba TT ba. TT 0 0 b a T T 1 V 2 V ref. V 1 V TT s a 2 V TT s b SECTOR I QSpace Vector Modulation

23 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Modulation Index cbs asb asa TTTT m. TT 0 sin ) 3 (sin (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 EE 8407 Topic 5 • Modulation Range • V ref, max 32 3 3 2 max, d dref V VV (17) 1 V 0 V 3 V 2 V 4 V 5 V 6 V j POOPO OPP OOP POP ref. V OOOPPP SECTOR III SECTOR IVSECTOR VI SECTOR V SECTOR II (17) (16) • m a, max = 1 • Modulation range: 0 m a 1 (18)Space Vector Modulation

25 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Switching Sequence Design • Basic Requirement: Minimize the number of switchings per sampling period T s • 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 EE 8407 Topic 5 • Seven-segment Switching Sequenced. V 2 0 T 2 a. T 2 b. T 2 a. T BNv ANv CNv 0 1 V 1 V 2 V 0 V 2 V POOOOOPPOPPPPPOPOOOOO d. V 4 0 T 2 b. T s. T 0 0 0 V 0 V • Total number of switchings: 6 • Selected vectors: V 0 , V 1 and V 2 • Dwell times: T s = T 0 + T a + T b. Space Vector Modulation

27 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Undesirable Switching Sequence • Vectors V 1 and V 2 swappedd. V 2 0 T 2 a. T 2 b. T 2 a. T BNv ANv CNv 0 1 V 1 V 2 V 2 V POOOOOPPOPPPPPOPOOOOO d. V 4 0 T 2 b. T s. T 0 0 0 V 0 V 0 V • Total number of switchings: 10 Space Vector Modulation

28 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Switching Sequence Summary (7–segments)Sector Switching Sequence 0 V 1 V 2 V 0 V 2 V 1 V 0 V I OOO PPO PPP PPO POO OOO 0 V 3 V 2 V 0 V 2 V 3 V 0 V II OOO OPO PPP PPO OOO 0 V 3 V 4 V 0 V 4 V 3 V 0 V III OOO OPP PPP OPO OOO 0 V 5 V 4 V 0 V 4 V 5 V 0 V IV OOO OOP OPP PPP OOP OOO 0 V 5 V 6 V 0 V 6 V 5 V 0 V V OOO OOP PPP POP OOO 0 V 1 V 6 V 0 V 6 V 1 V 0 V VI OOO POP PPP 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 EE 8407 Topic 5 • Simulated Waveforms. ABv AO v 0 0 0 Ai d. V 3/2 d. V 23 23 VIVI Sector I II III IV V f 1 = 60 Hz, f sw = 900 Hz, m a = 0. 696, T s = 1. 1 ms. Space Vector Modulation

30 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Waveforms and FFT Space Vector Modulation

31 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Waveforms and FFT (Measured)Space Vector Modulation

32 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Waveforms and FFT (Measured)Hz 601 fsec 720/1 s. T ( and )Space Vector Modulation

33 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Even-Order Harmonic Elimination Type-A sequence (starts and ends with [OOO]) 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 EE 8407 Topic 5 • Even-Order Harmonic Elimination Space vector Diagram Space Vector Modulation

35 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Even-Order Harmonic Elimination • Measured waveforms and FFT Space Vector Modulation

36 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Even-Order Harmonic Elimination Hz 601 fsec 720/1 s. T ( and )Space Vector Modulation

37 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Five-segment SVMd. V 2 a. T b. T 2 a. T BNv ANv CNv 0 1 V 1 V 2 V 0 V POOOOOPPOPOOOOO d. V s. T 0 0 0 V 2 0 T d. V a. T 1 V 2 V 0 V PPPPPOPOOPPP d. V s. T 0 V 2 0 T (a) Sequence A 2 V PPO d. V 2 b. T (b) Sequence B Space Vector Modulation

38 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Switching Sequence ( 5 -segment) Sector Switching Sequence ( A ) 0 V 1 V 2 V 1 V 0 V I OOO PPO POO OOO 0 CNv 0 V 3 V 2 V 3 V 0 V II OOO OPO PPO OOO 0 CNv 0 V 3 V 4 V 3 V 0 V III OOO OPP OPO OOO 0 ANv 0 V 5 V 4 V 5 V 0 V IV OOO OOP OPP OOO 0 ANv 0 V 5 V 6 V 5 V 0 V V OOO OOP POP OOO 0 BNv 0 V 1 V 6 V 1 V 0 V VI OOO POP POO OOO 0 BNv Space Vector Modulation

39 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic 5 • Simulated Waveforms ( 5 -segment)d. V 24 1 gv 3 gv 5 gv ABv 0 0 Ai 3/2 24 24 • No switching for a 120 ° period per cycle. • Low switching frequency but high harmonic distortion • f 1 = 60 Hz, f sw = 600 Hz, m a = 0. 696, T s = 1. 1 ms. Space Vector Modulation

40 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley — IEEE Press, 2006 EE 8407 Topic