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EE8407 Power Converter Systems Topic 5 Graduate Course EE8407 Bin Wu PhD, PEng Professor ELCE Department Ryerson University Contact Info Office: ENG328 Tel: (416) 979-5000 ext: 6484 Email: [email protected] http://www.ee.ryerson.ca/~bwu/ Ryerson Campus Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 1 EE8407 Topic 5 Topic 5 Two-Level Voltage Source Inverter (VSI) Source: Alstom VDM5000 Two-level VSI Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 2 EE8407 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 EE8407 Topic 5 Sinusoidal PWM • Inverter Configuration P S1 S3 S5 iA A Vd iB B Cd C O iC LOAD S4 S6 S2 N Assumption: dc capacitor very large dc voltage ripple free Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 4 EE8407 Topic 5 Sinusoidal PWM • Modulating and Carrier Waves v v cr v mB vmA vmC Vˆm Vˆcr 0 t • vcr – Carrier wave (triangle) • Amplitude modulation index • vm – Modulating wave (sine) • Frequency modulation index Vˆm ma Vˆcr mf f cr fm Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 5 EE8407 Topic 5 Sinusoidal PWM • Gate Signal Generation vmA v cr 2 0 v g1 vg 4 v AN Vd 0 Phase A v mA v cr v g1 0 (v g 4 0) S1 on ( S 4 off ) v AN Vd v mA v cr v g 4 0 (v g1 0) S 4 on ( S1 off ) v AN 0 Vg1 and Vg4 are complementary Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 6 EE8407 Topic 5 Sinusoidal PWM • Line-to-Line Voltage vAB v vcr vmA vmB vmC Vˆm Vˆcr t 0 P S1 S3 S5 v AN Vd A t B Vd C vBN Vd S4 S6 S2 t 0 v AB v AB1 N Vd 0 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 2 t 7 EE8407 Topic 5 Sinusoidal PWM • Waveforms and FFT v AB THD = 92.07% Vd 0 2 3 v AO THD = 92.07% 2V d / 3 0 iA • ma = 0.8, mf = 15, fm = 60Hz, fcr = 900Hz THD = 7.73% 0 2 3 V AB n / V d • Switching frequency fsw = fcr = 900Hz V AB1 0.49 Vd 0.2 mf THD = 92.07% 2m f 1 2 3m f 2 0.1 4m f 1 0 1 5 10 15 20 25 30 35 40 45 50 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 55 60 n 8 EE8407 Topic 5 Sinusoidal PWM • Harmonic Content V AB n THD (%) Vd n 1 THD • Low order harmonics n < (mf -2) are eliminated 300 0.3 2m f 1 mf 0.2 200 • VAB1 versus ma is linear • VAB1,max = 0.612Vd 2 3m f 2 4m f 1 0.1 100 3m f 4 0 0 0.2 0.4 0.6 0.8 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 ma 0 9 EE8407 Topic 5 Sinusoidal PWM • Over-Modulation v mA 2 v mB v mC v cr 1 0 -1 -2 v AB Vd 0 • Fundamental voltage ↑ i 2 3 A • Low-order harmonics ↑ 0 2 3 V AB n / V d V AB 1 0.744 Vd 0.2 0.1 0 1 5 10 15 20 25 30 35 40 45 50 55 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 60 n 10 EE8407 Topic 5 Sinusoidal PWM • Third Harmonic Injection PWM v m1 v v mA v m1 v m 3 vm 3 0 /3 Vˆm1 Vˆcr VˆmA 2 / 3 2 t • Vˆm1 Vˆcr - Fundamental voltage increased • VˆmA Vˆcr - No low order harmonics produced • 3rd harmonic – zero sequence (to appear in vAN and vBN ) • No triplen harmonics in vAB (vAB = vAN - vBN) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 11 EE8407 Topic 5 Space Vector Modulation • Switching States P S1 S3 S5 iA A iB B Vd O iC C LOAD S4 S2 S6 N Switching State Leg A Leg B S1 S4 V AN S3 S6 P On Off Vd On Off O Off On 0 Off On Leg C VBN S5 Vd 0 S2 On Off Off On VCN Vd 0 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 12 EE8407 Space Vector Modulation Topic 5 • Switching States (Three-Phase) P S1 S3 S5 A B Vd C S4 S6 S2 N • Eight switching states Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 13 EE8407 Topic 5 Space Vector Modulation • Space Vector Diagram jb r V3 r V2 OPO r r • Active vectors: V1 to V6 (stationary, not rotating) r • Zero vector: V0 • Six sectors: I to VI PPO SECTOR II SECTOR III r V4 r Vref SECTOR I r V1 q PPP OPP OOO a POO r V0 SECTOR IV SECTOR VI SECTOR V OOP r V5 r POP V6 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 14 EE8407 Topic 5 Space Vector Modulation • Space Vectors • Three-phase voltages v AO (t ) vBO (t ) vCO (t ) 0 (1) • Two-phase voltages 2 cos 0 cos va (t ) 2 3 v (t ) 3 sin 0 sin 2 b 3 4 v AO (t ) 3 v (t ) 4 BO sin vCO (t ) 3 cos (2) • Space vector representation r V (t ) va (t ) j v b (t ) (2) (3) r 2 V (t ) v AO (t ) e j 0 v BO (t ) e j 2 / 3 vCO (t ) e j 4 / 3 3 (3) (4) jx where e cos x j sin x Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 15 EE8407 Topic 5 Space Vector Modulation • Space Vectors (Example) Switching state [POO] S1, S6 and S2 ON 2 1 v AO (t ) Vd , v BO (t ) Vd 3 3 1 v ( t ) Vd and CO 3 r 2 V1 Vd e j 0 3 k 1, 2, ..., 6. r V2 OPO (6) PPO SECTOR II SECTOR III r V4 Similarly, r 2 j ( k 1) 3 Vk Vd e 3 jb r V3 (5) (4) (5) r Vref SECTOR I r V1 q PPP OPP OOO POO r V0 (7) SECTOR IV a SECTOR VI SECTOR V OOP r V5 r POP V6 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 16 EE8407 Topic 5 Space Vector Modulation • Active and Zero Vectors P Space Vector S1 S3 S5 Zero Vector A r V1 B Vd r V0 Switching State (Three Phases) [PPP] S1 , S 3 , S 5 [OOO] S4 , S6 , S2 [POO] S1 , S 6 , S 2 C S4 S6 S2 N Active Vector • Active Vector: 6 • Zero Vector: 1 • Redundant switching states: [PPP] and [OOO] Vector Definition On-state Switch r V2 [PPO] S1 , S 3 , S 2 r V3 [OPO] S 4 , S3 , S 2 r V4 [OPP] S 4 , S3 , S5 r V5 [OOP] S4 , S6 , S5 r V6 [POP] S1 , S 6 , S 5 r V0 0 r 2 V1 Vd e j 0 3 r 2 j V2 Vd e 3 3 2 r 2 j V3 V d e 3 3 3 r 2 j V4 Vd e 3 3 4 r 2 j V5 V d e 3 3 5 r 2 j V6 V d e 3 3 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 17 EE8407 Topic 5 Space Vector Modulation • Reference Vector Vref • Definition r Vref Vref e jq SECTOR III (8) 0 dt PPO SECTOR II r V4 r Vref PPP r V1 OPP OOO a POO r V0 SECTOR IV t SECTOR I q • Angular displacement q (t ) r V2 OPO • Rotating in space at ω 2 f jb r V3 SECTOR VI SECTOR V (9) OOP r V5 r POP V6 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 18 EE8407 Topic 5 Space Vector Modulation • 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 r V2 r Vref Tb r V2 Ts SECTOR I Q q Ta r V1 Ts Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 r V1 19 EE8407 Topic 5 Space Vector Modulation • Dwell Time Calculation r V2 • Volt-Second Balancing r r r r Vref Ts V1 Ta V2 Tb V0 T0 Ts Ta Tb T0 (10) r r r Vref Tb r V2 Ts r • Ta, Tb and T0 – dwell times for V1 , V2 and V 0 • Ts – sampling period SECTOR I Q q Ta r V1 Ts r V1 • Space vectors r r 2 r 2 r j jq Vref Vref e , V1 Vd , V2 Vd e 3 and V0 0 3 3 (11) (11) (10) 2 1 Re : V (cos q ) T V T Vd Tb ref s d a 3 3 Im : Vref (sin q ) Ts 1 Vd Tb 3 (12) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 20 EE8407 Topic 5 Space Vector Modulation • Dwell Times Solve (12) Ta Tb T0 Ts 3 Ts Vref Vd 3 Ts Vref Vd sin ( sin q 3 q ) 0 q /3 (13) Ta Tb Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 21 EE8407 Topic 5 Space Vector Modulation • Vref Location versus Dwell Times r V2 r Vref Tb r V2 Ts SECTOR I Q q r V1 Ta r V1 Ts r V ref Location Dwell Times q 0 Ta 0 Tb 0 0 q Ta Tb 6 q 6 6 Ta Tb q Ta Tb 3 q 3 Ta 0 Tb 0 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 22 EE8407 Topic 5 Space Vector Modulation • Modulation Index Ta Ts ma sin ( 3 q ) Tb Ts ma sin q T0 Ts Tb Tc ma 3 Vref (15) (16) Vd Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 23 EE8407 Topic 5 Space Vector Modulation • Modulation Range jb r V3 OPO • Vref,max 2 3 Vd Vref , max Vd 3 2 3 (17) PPO SECTOR II SECTOR III r V4 r Vref PPP r V1 OOO a POO r V0 SECTOR IV (17) (16) SECTOR I q OPP • ma,max = 1 r V2 SECTOR VI SECTOR V • Modulation range: 0 ma 1 r POP V6 OOP r V5 (18) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 24 EE8407 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 EE8407 Topic 5 Space Vector Modulation • Seven-segment Switching Sequence r V0 r V1 OOO POO • Selected vectors: V0, V1 and V2 v AN • Dwell times: Ts = T0 + Ta + Tb vBN r V2 r V0 r V2 r V1 r V0 PPO PPP PPO POO OOO Vd 0 Vd 0 vCN Vd 0 T0 4 Ta 2 Tb 2 T0 2 Tb 2 Ta 2 T0 4 Ts • Total number of switchings: 6 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 26 EE8407 Space Vector Modulation Topic 5 • Undesirable Switching Sequence • Vectors V1 and V2 swapped r V0 r V2 OOO PPO r V1 r V0 r V1 POO PPP POO v AN r V2 r V0 PPO OOO Vd 0 vBN Vd 0 vCN Vd 0 T0 4 Tb 2 Ta 2 T0 2 Ta 2 Tb 2 T0 4 Ts • Total number of switchings: 10 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 27 EE8407 Space Vector Modulation Topic 5 • Switching Sequence Summary (7–segments) Sector I II Switching Sequence r V0 r V1 r V2 PPO r V0 PPP r V2 r V0 OOO r V0 POO r V3 r V2 OOO r V0 OPO r V3 rPPO rPPP rPPO rOPO rOOO V4 V0 V4 V3 V0 OOO r OPO r V5 rOPP rPPP rOPP rOPO rOOO V4 V0 V4 V5 V0 r OOO V0 r OOP V5 rOPP rPPP rOPP rOOP rOOO V6 V0 V6 V5 V0 r OOO rOOP V1 rPOP rPPP rPOP r OOP rOOO V6 V0 V6 V1 V0 OOO POO r V0 PPO r V1 r V2 POO r V3 OOO r V0 III V0 IV V V0 VI POP PPP POP POO OOO 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 EE8407 Topic 5 Space Vector Modulation • Simulated Waveforms Sector V VI V IV VI IV III II I II I III v AB Vd 0 2 3 v AO 2Vd / 3 0 iA 0 2 3 f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 29 EE8407 Topic 5 Space Vector Modulation • Waveforms and FFT v AB THD =80.2% Vd 0 2 v AO THD =80.2% 2V d / 3 0 iA THD =8.37% 0 3 2 V AB n / V d THD =80.2% V AB 1 0.566V d 0.2 0.1 0 1 5 10 15 20 25 30 35 40 45 50 55 60 n Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 30 EE8407 Topic 5 Space Vector Modulation • Waveforms and FFT (Measured) V AB n Vd v AB THD = 80.3% 23 0.2 14 0.1 v AO 47 10 16 29 34 43 58 8 0 (a) Waveforms 2ms/div (b) Spectrum (500Hz/div) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 31 EE8407 Topic 5 Space Vector Modulation • Waveforms and FFT (Measured) V AB n / Vd V AB n / Vd THD (%) n 1 n 1 300 0.15 0.15 10 14 16 20 THD 0.10 0.10 n2 4 200 n = 19 8 17 13 11 7 100 0.05 0.05 0 0 0.2 0.4 0.6 0.8 0 ma 0 0.2 0.4 0.6 0.8 ma 0 (b) Odd order harmonics (a) Even order harmonics ( f1 60Hz 5 and Ts 1 / 720 sec ) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 32 EE8407 Topic 5 Space Vector Modulation • Even-Order Harmonic Elimination r V0 r V5 r V4 r V0 r V4 OOO OOP OPP PPP OPP v AN r V5 r V0 OOP OOO Vd 0 vBN Vd 0 0 vBN r V4 r V5 r V0 r V5 r V4 r V0 PPP OPP OOP OOO OOP OPP PPP Vd Vd 0 vCN Vd 0 vCN 0 0 v AB v AN r V0 Vd 0 v AB Vd Type-A sequence (starts and ends with [OOO]) Vd Type-B sequence (starts and ends with [PPP]) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 33 EE8407 Space Vector Modulation Topic 5 • Even-Order Harmonic Elimination r V3 b SECTOR III r V4 a a 30 30 a a b a b a r V5 SECTOR I b b SECTOR IV r V2 SECTOR II SECTOR VI b SECTOR V r V1 Type-A sequence Type-B sequence r V6 Space vector Diagram Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 34 EE8407 Topic 5 Space Vector Modulation • Even-Order Harmonic Elimination V AB n Vd v AB THD = 80.5% 23 0.2 17 v AO 47 13 0.1 41 7 5 65 35 0 (a) Waveforms 2ms/div (b) Spectrum (500Hz/div) • Measured waveforms and FFT Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 35 EE8407 Topic 5 Space Vector Modulation • Even-Order Harmonic Elimination V AB n / Vd THD (%) 0.3 THD 300 n 1 200 0.2 17 19 13 0.1 7 0 0 0.2 ( f1 60Hz 0.4 0.6 and 100 5 11 0.8 ma 0 Ts 1 / 720 sec ) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 36 EE8407 Topic 5 Space Vector Modulation • Five-segment SVM r V0 r V1 r V2 r V1 r V0 r V0 r V2 r V1 r V2 r V0 OOO POO PPO POO OOO PPP PPO POO PPO PPP Tb 2 T0 2 v AN Vd Vd 0 vBN Vd Vd 0 vCN Vd 0 T0 2 Ta 2 Tb Ts (a) Sequence A Ta 2 T0 2 T0 2 Tb 2 Ta Ts (b) Sequence B Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 37 EE8407 Space Vector Modulation Topic 5 • Switching Sequence ( 5-segment) Sector I Switching Sequence (A) r V0 OOO II r V1 POO r V2 PPO r V1 POO r V0 OOO r V0 r V3 r V2 r V3 OOO r OPO r rPPO V4 rOPO rOOO V3 V0 rOPP V4 rOPO rOOO V5 V0 rOOP rOOO V5 V0 V0 V3 OOO r OPO r r V0 III V0 V5 r OOO r OOP IV V V0 V5 rOPP V6 r OOO rOOP V1 rPOP r OOP rOOO V6 V1 V0 OOO POO V0 v CN 0 v CN 0 v AN 0 v AN 0 v BN 0 v BN 0 VI POP POO OOO Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 38 EE8407 Space Vector Modulation Topic 5 • Simulated Waveforms ( 5-segment) v g1 2 / 3 vg 3 2 vg 5 vAB 0 4 Vd 2 4 iA 0 2 4 • 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 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 39 EE8407 Topic 5 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 40