EE 8407 Power Converter Systems Topic 5 Graduate

EE 8407 Power Converter Systems Topic 5 Graduate Course EE 8407 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/ Ryerson Campus Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 1

EE 8407 Topic 5 Two-Level Voltage Source Inverter (VSI) Source: Alstom VDM 5000 Two-level VSI Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 2

EE 8407 Two Level Voltage Source Inverter Topic 5 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 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 3

EE 8407 Sinusoidal PWM Topic 5 • Inverter Configuration Assumption: dc capacitor very large dc voltage ripple free Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 4

EE 8407 Sinusoidal PWM Topic 5 • Modulating and Carrier Waves • vcr – Carrier wave (triangle) • Amplitude modulation index • vm – Modulating wave (sine) • Frequency modulation index Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 5

EE 8407 Sinusoidal PWM Topic 5 • Gate Signal Generation Vg 1 and Vg 4 are complementary Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 6

EE 8407 Sinusoidal PWM Topic 5 • Line-to-Line Voltage v. AB Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 7

EE 8407 Sinusoidal PWM Topic 5 • Waveforms and FFT • ma = 0. 8, mf = 15, fm = 60 Hz, fcr = 900 Hz • Switching frequency fsw = fcr = 900 Hz Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 8

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

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

EE 8407 Sinusoidal PWM Topic 5 • Third Harmonic Injection PWM • - Fundamental voltage increased • - 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) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 11

EE 8407 Space Vector Modulation Topic 5 • Switching States Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 12

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

EE 8407 Space Vector Modulation Topic 5 • Space Vector Diagram • Active vectors: to (stationary, not rotating) • Zero vector: • Six sectors: I to VI Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 14

EE 8407 Topic 5 Space Vector Modulation • Space Vectors • Three-phase voltages (1) • Two-phase voltages (2) • Space vector representation (3) (2) (3) (4) where Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 15

EE 8407 Topic 5 Space Vector Modulation • Space Vectors (Example) Switching state [POO] S 1, S 6 and S 2 ON and (5) (4) (6) Similarly, (7) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 16

EE 8407 Space Vector Modulation Topic 5 • Active and Zero Vectors • Active Vector: 6 • Zero Vector: 1 • Redundant switching states: [PPP] and [OOO] Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 17

EE 8407 Space Vector Modulation Topic 5 • Reference Vector Vref • Definition • Rotating in space at ω (8) • Angular displacement (9) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 18

EE 8407 Space Vector Modulation Topic 5 • 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 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 19

EE 8407 Topic 5 Space Vector Modulation • Dwell Time Calculation • Volt-Second Balancing (10) • Ta, Tb and T 0 – dwell times for and • Ts – sampling period • Space vectors , and (11) (10) (12) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 20

EE 8407 Topic 5 Space Vector Modulation • Dwell Times Solve (12) (13) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 21

EE 8407 Space Vector Modulation Topic 5 • Vref Location versus Dwell Times Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 22

EE 8407 Topic 5 Space Vector Modulation • Modulation Index (15) (16) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 23

EE 8407 Space Vector Modulation Topic 5 • Modulation Range • Vref, max (17) (16) • ma, max = 1 • Modulation range: 0 ma 1 (18) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 24

EE 8407 Space Vector Modulation Topic 5 • 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. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 25

EE 8407 Space Vector Modulation Topic 5 • Seven-segment Switching Sequence • Selected vectors: V 0, V 1 and V 2 • Dwell times: Ts = T 0 + Ta + Tb • Total number of switchings: 6 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 26

EE 8407 Space Vector Modulation Topic 5 • Undesirable Switching Sequence • Vectors V 1 and V 2 swapped • Total number of switchings: 10 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 27

EE 8407 Space Vector Modulation Topic 5 • Switching Sequence Summary (7–segments) Note: The switching sequences for the odd and ever sectors are different. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 28

EE 8407 Space Vector Modulation Topic 5 • Simulated Waveforms f 1 = 60 Hz, fsw = 900 Hz, ma = 0. 696, Ts = 1. 1 ms Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 29

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

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

EE 8407 Space Vector Modulation Topic 5 • Waveforms and FFT (Measured) ( and ) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 32

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

EE 8407 Space Vector Modulation Topic 5 • Even-Order Harmonic Elimination Space vector Diagram Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 34

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

EE 8407 Space Vector Modulation Topic 5 • Even-Order Harmonic Elimination ( and ) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 36

EE 8407 Space Vector Modulation Topic 5 • Five-segment SVM Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 37

EE 8407 Space Vector Modulation Topic 5 • Switching Sequence ( 5 -segment) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 38

EE 8407 Space Vector Modulation Topic 5 • Simulated Waveforms ( 5 -segment) • f 1 = 60 Hz, fsw = 600 Hz, ma = 0. 696, Ts = 1. 1 ms • No switching for a 120° period per cycle. • Low switching frequency but high harmonic distortion Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 39

EE 8407 Topic 5 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 40