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EE8407 Power Converter Systems Topic 4 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 4 Topic 4 Multi-pulse SCR Rectifiers Z Llk ia I d Ld 20 Ls iA Llk ia~ Llk ia 0 Z L O A D vd 20 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 2 EE8407 Multi-pulse SCR Rectifiers Topic 4 Lecture Topics • Six-pulse SCR Rectifier (Building Block) • 12-, 18- and 24-pulse SCR Rectifiers • THD and PF Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 3 EE8407 Multi-pulse SCR Rectifiers Topic 4 Why Use Multi-pulse SCR Rectifiers? • To reduce line THD • To improve input power factor • To avoid semiconductor devices in series. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 4 EE8407 Topic 4 Six-pulse SCR Rectifier • Converter Configuration I d Ld P g1 va GND vb vc a ia b ib c ic g5 g3 S3 S1 S5 L O A D vd g4 g6 Id g2 S4 S6 N S2 (a) (b) • Assumption: 1) Ideal SCRs - no power loss 2) Ld dc current ripple free • Use constant current source Id as a load Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 5 EE8407 Topic 4 Six-pulse SCR Rectifier • Waveforms va v vb 0 ig 3 ig 4 3 2 t ig 2 area A1 Vd /3 1 / 2 vab d (t ) / 6 /3 3 2 ig1 • Average dc voltage vc ig 5 I ig 6 v 6 6 va II 2 vP 5 6 7 6 vb 9 6 t 11 6 vc va vb t 0 vd v ab vN v ac vbc vba v ca vcb v ab v ac A1 Vd t VLL cos 1.35VLL cos ia 1 1 Id 0 ib 0 2 S 6 , S1 ON ia1 t S1 , S 2 ON Id t ic 0 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 t 6 EE8407 Topic 4 Six-pulse SCR Rectifier • Fourier Analysis ia 1 1 1 I d sint 1 sin 5t 1 sin 7t 1 sin11t 1 5 7 11 1 1 1 sin13t 1 sin17t 1 sin19t 1 .... 13 17 19 2 3 • RMS current 1 Ia 2 2 0 1/ 2 ia 2 d ( t ) 1/ 2 11 1 56 2 2 I d d ( t ) 76 I d d ( t ) 6 2 6 2 I d 0.816 I d 3 • THD THD I a2 I a21 I a1 (0.816I d ) 2 (0.78I d ) 2 0.311 0.78I d Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 7 EE8407 Six-pulse SCR Rectifier Topic 4 • Power Factor (PF) • Displacement Power Factor 1 2 1 DPF cos 1 cos • Overall Power Factor PF cos1 0.955 cos 2 1 THD Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 8 EE8407 Topic 4 Six-pulse SCR Rectifier • Waveforms at Various Firing Angles 45 v 90 va vb vc vP 0 vN vd vab vac vbc 2 vba vca vd v P v N vab vac 0 vP vd vab vac vba vca vcb 2 2 vca vba vc vN va vP vcb vab vb vac vbc vba vca 2 t Vd 2 t vcb vd vP v N 0 t 180 vc vb vbc 2 (b) 90 135 vN vbc 2 va vc vd (a) 45 v vb vN vcb Vd 0 vP va 2 t Vd (c) 135 vd (d) 180 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 9 EE8407 Topic 4 Six-pulse SCR Rectifier • Effect of Line Inductance Ls Id P va vb GND vc a ia Ls S3 S1 Ld S5 v Ls b ib Ls c ic Ls L O A D S4 S6 vd S2 N Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 10 EE8407 Topic 4 Six-pulse SCR Rectifier • Waveform During SCR Commutation g vP Ag va 0 2 6 1 i ( v a vc ) / 2 9 / 6 5 / 6 g 2 1 vP vc t va ia1 6 ic ia Id ib t 0 g Id Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 11 EE8407 Six-pulse SCR Rectifier Topic 4 • DC Voltage Reduction (caused by commutation) • S1 and S5 on (during commutation) vP va Ls from which vP dia di vc Ls c dt dt va vc Ls dia dic 2 2 dt dt • Since ia + ic = Id, and id is constant dia di c 0 dt dt from which vP va vc 2 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 12 EE8407 Six-pulse SCR Rectifier Topic 4 • DC Voltage Reduction • Shaded Area Aγ Ag 6 6 g va vP d (t ) • Since va v p Ls dia / dt Ag Id 0 Ls dia Ls I d • Average dc voltage loss Ag 3Ls V Id /3 • Average dc output voltage Vd 1.35VLL cos 3Ls Id Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 13 EE8407 Six-pulse SCR Rectifier Topic 4 • Commutation Interval • Aγ can be rearranged as g v VLL 6 ac cos cos ( g ) Ag d (t ) 2 2 6 v 2 V sin( t ) d (t ) where ac LL 6 • Substitute Ls I d into the above equation VLL cos cos ( g ) Ls I d 2 from which g cos1 cos 2 Ls I d VLL Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 14 EE8407 Six-pulse SCR Rectifier Topic 4 • Line Current Waveforms 2.00 ia ib 1.00 ia1 1.41pu 0.00 -1.00 -2.00 (a) = 0°, Ia1 = 1 pu 2.00 ib ia Ls = 0.05pu 1.00 0.00 -1.00 -2.00 2 0 Harmonics n I an / I a1 (%) 0 I an / I a1 (%) 30 (b) = 30°, Ia1 = 1 pu 3 2 2 11 13 17 19 23 25 THD % 18.6 12.4 6.32 4.58 2.40 1.73 1.02 0.87 23.9 19.7 14.1 8.58 7.27 5.16 4.62 3.43 3.16 28.3 5 7 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 15 EE8407 Topic 4 Six-pulse SCR Rectifier • Line Current THD 32 THD (%) 32 THD (%) A A: L s= 0 B: Ls= 0.05pu C: Ls= 0.10pu 29 B 26 = 0 C 29 B A ° 26 C 23 A: = 20 ° B: = 40 ° C: = 60 ° 23 Ls = 0.05pu 20 0 0.2 0.4 0.6 (a) 0.8 20 IA1 (pu) 0 0.2 0.4 0.6 0.8 (b) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 IA1 (pu) 16 EE8407 Six-pulse SCR Rectifier Topic 4 • Power Factor 1.0 PF A B 0.8 C 0.6 A: = 0° B: = 20 ° C: = 40 ° 0.4 L s= 0.05pu 0.2 0 0.2 0.4 0.6 0.8 IA1 (pu) Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 17 EE8407 Topic 4 12-pulse SCR Rectifier • Topology I d Ld Llk i A ia ia~ Ls iA ia 0 L O A D Llk vd ia~ 30 • Main Benefits - Low line current THD - No SCRs in series Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 18 EE8407 Topic 4 12-pulse SCR Rectifier • Application Example Ld 0 M Cf 30 • Used for current source inverter (CSI) fed drive Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 19 EE8407 12-pulse SCR Rectifier Topic 4 • Waveforms of Idealized Rectifier (Ls = Llk = 0) ia Id 0 /6 2 5 / 6 t ia~ Id t 0 ia Id 2 0 t ia~ 0 iA 1 3 Id 1 2 3 t Id 1 1 Id 2 0 2 3 1 2 3 Id t Id Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 20 EE8407 12-pulse SCR Rectifier Topic 4 • Fourier Analysis • Secondary currents 1 1 1 1 I d sin t sin 5t sin 7t sin 11t sin 13t 5 7 11 13 1 1 sin 17t sin 19t .... 17 19 ia 2 3 ia~ 2 3 1 1 1 I d sin(t 30) sin 5(t 30) sin 7(t 30) sin 11(t 30) 5 7 11 1 1 1 sin 13(t 30) sin 17(t 30) sin 19(t 30) .... 13 17 19 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 21 EE8407 12-pulse SCR Rectifier Topic 4 • Fourier Analysis (continued) • Secondary currents referred to the primary side ia ia~ 3 1 1 1 1 I d {sin t sin 5t sin 7t sin 11t sin 13t 5 7 11 13 1 1 sin 17t sin 19t ....} 17 19 3 1 1 1 1 I d {sin t sin 5t sin 7t sin 11t sin 13t 5 7 11 13 1 1 sin 17t sin 19t ....} 17 19 • Primary line current i A ia ia~ 2 3 I d {sin t 1 1 1 sin 11t sin 13t sin 23t 11 13 23 1 sin 25t ....} 25 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 22 EE8407 12-pulse SCR Rectifier Topic 4 • Line Current THD • Secondary side I a2 I a21 I a25 I a27 I a211 I a213 ... THDia I a1 I a1 1/ 2 31.1% • Primary side I A2 I A21 I A211 I A213 I A2 23 I A2 25 ... THDi A I A1 I A1 1/ 2 15.3% Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 23 EE8407 12-pulse SCR Rectifier Topic 4 • Line Current Waveform (Ls 0 ) 1.50 0.75 ia 2 ia1 0.00 -0.75 -1.50 (a) 1.50 0.75 2 iA 0.00 i A1 -0.75 -1.50 0 Harmonics n I an / I a1 (%) I An / I A1 (%) 2 (b) 5 7 11 13 3 17 19 4 23 25 THD (%) 18.8 12.7 6.78 5.05 2.77 2.01 1.01 0.75 24.6 0 0 6.78 5.05 0 0 1.01 0.75 8.61 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 24 EE8407 Topic 4 12-pulse SCR Rectifier • THD and PF 16 THD (%) A: L s=0 B: L s= 0.05pu C: L s= 0.10pu 13 1.0 PF A B 0.8 L lk= 0.05pu = 0 ° 10 C A 0.6 A: = 0 ° B: = 20 ° C: = 40 ° B 7 4 C 0 0.2 0.4 0.6 (a) 0.8 IA1 (pu) 0.4 0.2 0 L s= 0 Llk= 0.05pu 0.2 0.4 0.6 0.8 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 IA1 (pu) 25 EE8407 Topic 4 18-pulse SCR Rectifier • Rectifier Configuration i A ia ia~ ia Z Llk ia I d Ld 20 Ls i A Llk ia~ Llk ia 0 Z L O A D vd 20 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 26 EE8407 18-pulse SCR Rectifier • Waveforms 0.60 Topic 4 ia~ 0.30 ia~ 1 2 3 0.00 -0.30 -0.60 (a) 0.60 i a ia 0.30 0.00 -0.30 -0.60 (b) 1.50 iA 0.75 0.00 -0.75 -1.50 Harmonics n / I a 1 (%) I an I An / I A1 (%) 2 (c) 0 5 7 11 13 3 17 19 4 23 25 18.8 12.7 6.78 5.05 2.77 2.01 1.01 0.75 0 0 0 0 2.77 2.01 0 0 THD (%) 24.6 3.54 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 27 EE8407 Topic 4 18-pulse SCR Rectifier • Line Current THD 10 THD (%) 10 A: L s = 0 B: L s = 0.05pu C: L s = 0.10pu 8 A 6 2 0.2 0.4 B 8 A 6 C 0 C L lk = 0.05pu = 0 ° B 4 THD (%) A: = 20 ° B: = 40 ° C: = 60 ° 4 0.6 0.8 2 IA1(pu) Ls = 0.05pu Llk= 0.05pu 0 0.2 0.4 0.6 0.8 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 IA1 (pu) 28 EE8407 Topic 4 24-pulse SCR Rectifier • Rectifier Configuration Id Z Llk Ld ia 15 i A ia ia~ ia ia Ls iA Llk ia~ 0 Z Vd Llk ia 15 Llk ia 30 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 29 EE8407 Topic 4 24-pulse SCR Rectifier • Line Current THD 8 THD (%) 8 A: L s = 0 B: Ls = 0.05pu C: Ls = 0.10pu 6 THD (%) C 6 B L lk = 0.05pu = 0 ° A 4 4 A: = 20 ° B: = 40 ° C: = 60 ° A B 2 0 2 C 0 0.2 0.4 0.6 0.8 0 IA1 (pu) L s = 0.05pu L lk = 0.05pu 0 0.2 0.4 0.6 0.8 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 IA1 (pu) 30 EE8407 Topic 4 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 31