PWM Inverters. Rijil Ramchand Associate Professor NIT Calicut

Transcription

1 PWM Inerters Rijil Rmchnd Associte Professor NI Clicut

2 Inerters Clssifictions Single phse & three phse oltge Source & Current source wo-leel & Multi-leel 5/15/15 PEGCRES 15

3 oltge Source Inerter opics Sinusoidl PWM Spce ector modultion Why Use PWM echniques? o control inerter output frequency (fundmentl) o control inerter output oltge (fundmentl) o minimize hrmonic distortion 5/15/15 PEGCRES 15

4 oltge Source Inerter Open loop oltge control ref PWM SI AC motor Closed loop current-control i ref PWM SI AC motor i f/bck 5/15/15 PEGCRES 15 4

5 oltge Source Inerter Inerter Configurtion 5/15/15 PEGCRES 15 5

6 oltge Source Inerter (SI) Six-Step SI Gting signls, switching sequence nd line to negtie oltges Weforms of gting signls, switching sequence, line to negtie oltges for six-step oltge source inerter. 4

7 oltge Source Inerter (SI) Six-Step SI Switching Sequence: 561 ( 1 ) 61 ( ) 1 ( ) 4 ( 4 ) 45 ( 5 ) 456 ( 6 ) 561 ( 1 ) where, 561 mens tht S 5, S 6 nd S 1 re switched on Six inerter oltge ectors for six-step oltge source inerter. 5/15/15 PEGCRES

8 oltge Source Inerter (SI) Six-Step SI Line to line oltges ( b, bc, c ) nd line to neutrl oltges ( n, bn, cn ) Line to line oltges b = N - bn bc = bn - cn c = cn - N Phse oltges n = / N - 1/ bn - 1/ cn bn = -1/ N + / bn - 1/ cn cn = -1/ N - 1/ bn + / cn Weforms of line to neutrl (phse) oltges nd line to line oltges for six-step PEGCRES oltge 15 source inerter. 5/15/15 8 6

9 oltge Source Inerter (SI) Six-Step SI Hrmonic spectrum of squre we 5/15/15 PEGCRES 15 9

10 oltge Source Inerter (SI) Six-Step SI Amplitude of line to line oltges ( b, bc, c ) Fundmentl Frequency Component ( b ) 1 ( b ) 1 (rms) 4 dc 6 dc.78 dc Hrmonic Frequency Components ( b ) h : mplitudes of hrmonics decrese inersely proportionl to their hrmonic order (b ) h (rms).78 h dc where, h 6n 1 (n 1,,,...) 5/15/15 PEGCRES

11 oltge Source Inerter (SI) Six-Step SI Chrcteristics of Six-step SI It is clled six-step inerter becuse of the presence of six steps in the line to neutrl (phse) oltge weform Hrmonics of order three nd multiples of three re bsent from both the line to line nd the line to neutrl oltges nd consequently bsent from the currents Output mplitude in three-phse inerter cn be controlled by only chnge of DC-link oltge ( dc ) 5/15/15 PEGCRES

12 Sinusoidl PWM Modulting nd Crrier Wes cr ma mb mc ˆm ˆcr t cr Crrier we (tringle) Amplitude modultion index m Modulting we (sine) Frequency modultion index 5/15/15 PEGCRES 15 ˆm m ˆcr mf f cr fm 1

13 Sinusoidl PWM m f should be n odd integer if m f is not n integer, there my exist sub-hmonics t output oltge if m f is not odd, DC component my exist nd een hrmonics re present t output oltge m f should be multiple of for three-phse PWM inerter An odd multiple of nd een hrmonics re suppressed 5/15/15 PEGCRES 15 1

14 Sinusoidl PWM Gte Signl Genertion ma cr g1 g 4 AN d Phse A ( 4 ) ma cr ma cr g1 g 1 ( 1 ) g 4 g 4 S on off ) ( S 4 AN d S on S off ) ( 1 AN 5/15/15 g1 nd g4 re PEGCRES complementry 15 14

15 Sinusoidl PWM Line-to-Line oltge AB cr ma mb m C P ˆcr ˆm t S 1 S S5 AN d A B d t C BN S 4 S 6 S d t AB AB1 N d t 5/15/15 PEGCRES 15 15

16 Sinusoidl PWM Weforms nd FF AB d HD = 9.7% m =.8, m f = 15, f m = 6Hz, f cr = 9Hz AO i A d / HD = 9.7% HD = 7.7% Switching frequency f sw = f cr = 9Hz n / AB d..1 AB d m f m f 1 HD = 9.7% m f 4 1 m f n 5/15/15 PEGCRES 15 16

17 Sinusoidl PWM Oer-Modultion ma mb mc 1 cr -1 - AB d Fundmentl oltge i A Low-order hrmonics n / AB d. AB d.1 5/15/ PEGCRES n 17

18 Sinusoidl PWM () c c m(t) S 1 ON period = AO is DC c c m(t) S ON period = c c AO is DC c 1 (t) (t) AO erge for period c + + c c c DC m(t) c c m c c m DC 5/15/15 PEGCRES 15 c 18

19 Spce ector Modultion Switching Sttes (hree-phse) P S 1 S S5 A d B C S 4 S 6 S N Eight switching sttes 5/15/15 PEGCRES 15 19

20 Spce ector Modultion Spce ector Digrm SECOR III OPO jb r SECOR II r r qref PPO SECOR I Actie ectors: to r 6 (sttionry, not rotting) r 1 r 4 OPP PPP OOO r 1 POO Zero ector: r SECOR I r SECOR SECOR I Six sectors: I to I OOP r r 6 5 POP 5/15/15 PEGCRES 15

21 Spce ector Modultion Spce ectors hree-phse oltges ) ( ) ( ) ( t t t CO BO AO wo-phse oltges ) ( ) ( ) ( 4 sin sin sin 4 cos cos cos ) ( ) ( t t t t t CO BO AO b Spce ector representtion ) ( ) ( ) ( t j t t b r () () / 4 / ) ( ) ( ) ( ) ( j CO j BO j AO e t e t e t t r where x j x e jx sin cos () (1) () (4) 5/15/15 1 PEGCRES 15

22 Spce ector Modultion Spce ectors (Exmple) Switching stte [POO] S 1, S 6 nd S ON AO 1 1 ( t) d, BO ( t) d, CO ( t) (5) (4) r 1 d e j SECOR III OPO d jb r SECOR II r PPO r qref SECOR I r k d e j ( k 1) k 1,,..., 6. r 4 5 r 1 PPP OOO r POO OOP r r POP 5/15/15 PEGCRES 15 6 OPP SECOR I SECOR I SECOR

23 Spce ector Modultion Actie nd Zero ectors P N d S 1 A S 4 S 6 S S5 Actie ector: 6 Zero ector: 1 Redundnt switching sttes: [PPP] nd [OOO] B S C Spce ector Zero ector Actie ector Switching Stte (hree Phses) On-stte Switch [PPP] S 1, S, S5 r [OOO] S 4, S 6, S r 1 [POO] S 1, S6, S ector Definition r r 1 d e j r [PPO] S 1, S, S j d e r [OPO] S 4, S, S j d e 4 [OPP] 4, S, S5 r 5 [OOP] S 4, S 6, S5 r 6 [POP] S 1, S6, S5 r r S r j 4 d e r r 5 6 d e d e 5/15/15 PEGCRES 15 4 j 5 j

24 Spce ector Modultion Reference ector ref Definition r e ref ref jq Rotting in spce t ω SECOR III OPO jb r SECOR II r r qref PPO SECOR I f (8) r 4 OPP PPP OOO r 1 POO Angulr displcement q ( t) t dt (9) SECOR I 5 r SECOR OOP r r 6 POP SECOR I 5/15/15 PEGCRES 15 4

25 Spce ector Modultion Reltionship Between ref nd AB ref is pproximted by two ctie nd zero ectors r ref rottes one reolution, AB completes one cycle r b s Q r ref SECOR I Length of ref corresponds to 1 mgnitude of r AB 1 s 5/15/15 PEGCRES 15 5 q r

26 Spce ector Modultion Dwell ime Clcultion olt-second Blncing r s ref s r 1 b r b r, b nd dwell times for s smpling period (1) r r, 1 nd r r b s q r Q r 1 s r ref SECOR I r 1 Spce ectors r j e, 1 (11) (1) r q ref ref d Re: Im : ref (cosq ) (sin q ) s r j, nd d e d 1 1 r 5/15/15 PEGCRES 15 6 ref s d b d b (11) (1)

27 Spce ector Modultion Dwell imes Sole (1) b s s s d d ref ref sin ( q ) sin q b q / (1) 5/15/15 PEGCRES 15 7

28 Spce ector Modultion ref Loction ersus Dwell imes r r b s Q r ref SECOR I r Loction q ref Dwell imes b q q 6 r 1 s q 6 b b r 1 q 6 b q b 5/15/15 PEGCRES 15 8

29 Spce ector Modultion Modultion Index b m s m s s sin ( q ) sin q b c (15) m ref (16) d 5/15/15 PEGCRES 15 9

30 Spce ector Modultion ref,mx ref, mx Modultion Rnge d d (17) SECOR III r 4 OPP OPO jb r SECOR II PPP OOO r r qref PPO SECOR I r 1 POO r (17) (16) SECOR I SECOR SECOR I m,mx = 1 OOP r r 6 5 POP Modultion rnge: m 1 (18) 5/15/15 PEGCRES 15

31 Spce ector Modultion Sector Simulted Weforms I I I III II I I II III I AB d AO d / i A 5/15/15 PEGCRES 15 1 f 1 = 6Hz, f sw = 9Hz, m =.696, s = 1.1ms

32 Spce ector Modultion Weforms nd FF AB d HD =8.% AO d / HD =8.% i A HD =8.7% n / AB d..1. AB d HD =8.% 5/15/15 PEGCRES n

33 SPWM Modified SinePWM 5/15/15 PEGCRES 15

34 SPWM Modified SinePWM 5/15/15 PEGCRES 15 4

35 SPWM Modified SinePWM 5/15/15 PEGCRES 15 5