CHAPTER 6 CONVENTIONAL SINGLE-PHASE TO THREE-PHASE POWER CONVERTERS. 6.1 Introduction

Transcription

1 CHAPTER 6 CONENTONAL SNGLE-PHASE TO THREE-PHASE POWER CONERTERS 6. troucto th chatr th aroach to covrt gl-ha owr to thr-ha owr utabl for owrg ac loa cu. Covtoal owr covrtr u for th covro of gl-ha ac voltag to thr-ha owr cu. Two covrtr toolog for th Covtoal Covrtr ar xla wth tal aaly. Th cotrol chm for th two covrtr toolog to cotrol th c voltag a to achv uty owr factor orato alo cu. A ucto mach wa u a a loa for th two covrtr toolog, whch wa mulat Matlab/Smulk to vrfy th fuctoalty of th covrtr. 6. Sgl-Pha To Thr-Pha Powr Covro Th ma fucto of th Thr-ha lctrcal qumt uch a thrha ac motor ar gfcatly mor ffct, coomcal a ay to cotrol th thr gl-ha coutrart. Th z of th thr-ha motor, for th am owr ratg a that of th gl-ha motor rlatvly mall. Thr-ha owr ot uually avalabl may of th rural or lght utral ara, u to th hgh cot of xtg th thr-ha rvc. So th oly avalabl owr may tac wll b gl-ha owr a o thr xt a for covrtr whch ca covrt 0

2 gl ha owr to thr ha owr kg m th corato of cot a goo rformac. 6...Covtoal Sgl Pha to Thr-Pha Powr Covrtr Crcut th clacal mtho of gl-ha to thr-ha covro th glha owr uly gv to th covrtr, whch ca thr b full, or half brg ty, caca wth a thr-ha vrtr wth a c lk caactor btw. Th gral coct of covtoal crcut a how Fg 6.. th covtoal covrtr th ac-to-c covro t from th c-to-ac covro. Th owr uly currt cotroll to b uoal by th full-brg ac-to-c covrtr, whl th ul-wth moulato vrtr cotrol th motor ut voltag. Th two cotrol acto ar t a a larg caactor rt btw th covrtr for coulg. Th work of th gl-ha vrtr to grat c voltag at t outut trmal a all that th thr-ha vrtr rqur c voltag wth lttl or o rl at t ut trmal. Th covrtr coct to th uly call th l covrtr a th o coct to th loa th loa- covrtr. Thu th covtoal toolog th cotrol of th l a th loa covrtr ar t. 03

3 -φ AC ac/c Covrtr vrtr MOTOR Fgur 6.: Coct of covtoal crcut. Two ty of covtoal gl-ha to thr-ha covro toolog ar cu th followg cto wth tal aaly of th mathmatcal mol Covtoal Full-Brg Toology Th covtoal full brg covrtr caabl of brctoal owr trafr, whch owr bg xchag btw th loa a th uly thr way. Th full brg toology a how Fgur 6. ha four wtch for th ac-toc covro. Th c voltag at th outut trmal of th covro roc f to a thr-ha vrtr whch rouc th thr ha balac voltag acro th loa. th toology Fgur 6. th owr trafr qut aart, that th gl ha uly al btw th two mot of th two covrtr lg a a bg caactor kt at th outut trmal, whch alo rv a a fltr. Th c voltag acro th caactor al to th thr-ha vrtr, whch ca b th oltag Sourc vrtr S, or th Currt Sourc vrtr CS toology whch th wtch ca b PWM orat or ormal thyrtor fr crcut. 04

4 AC-DC covrtr 3-ha vrtr - ha uly - L a b c Motor Fgur6.: Covtoal full-brg ac/c covrtr vrtr crcut. th abov xla crcut toology thr a ut ractor to ruc th rl th uly currt, whch ar u to th fact that th covrtr hav wtchg vc whch woul cotuouly b tur ON a tur OFF accorg to a rtrm attr lag to ulatg th ut currt Covtoal Half-Brg Toology Th half brg toology a how Fgur 6.3 mlar to a full brg o xct that a caactor lg wth utral accbl rlac o of th covrtr lg of th l covrtr, but th loa covrtr rma th am. Th toology char wh comar to th full brg ty a t volv l umbr of wtch but th z of th covrtr cra u to th caactor. 05

5 T S S S 3 - L T - - o a S S b S 3 c Motor Fgur 6.3: Covtoal Half-Brg Crcut. th half brg covrtr th c lk voltag wll b twc that a full brg covrtr, a o th wtchg vc mut wthta th cra voltag. But th toology uful wh th outut voltag ot too hgh, or for low owr alcato. Th quato whch crb th orato of th covrtr Fgur 6.3 ba o rchoff voltag law L, ar T T L 6. t S S S S a o 6. S b o 6.3 S 3 3 c o. 6.4 whr th voltag btw th utral ot of th loa a th mot of th o c-lk voltag. A th wtchg fucto for th two vc th am lg ar comlmtary th; T T

6 S S S S S 3 S Ag th Equato 6. to 6.4 togthr, Equato 6.9 obta DC S 3 S S3 S S S3 a b c o 6.9 By corg balac voltag, 0 a makg u of th a b c coto from Equato 4. to 4.3, Equato 4.7 bcom 6 DC S S S3 3 o 6.0 Subttutg for Equato 4.4 to 4.6, o 3 DC 3 3 DC DC S S S S S3 a 6. S S3 b 6. 3 S S c. 6.3 Ug th coto Equato from 6.5 to 6.8 Equato bcom T L 6.4 t S a o

7 S S b o c o. 6.7 Rlacg th wtchg fucto th abov quato wth th moulato gal th abov quato ar mof a gv Equato 6.8 to 6.. M tt L t 6.8 M a o 6.9 M a o 6.0 M 3 a o. 6. Th abov quato ca b wrtt th matrx form a, M M M 3 a b c o o o. 6. Traformg th abov matrx quato to th ychroou rfrc fram, cotat valu for moulato x ar obta whch mak th cotrol chm ml to b mlmt, a th cotrol of c varabl or quatt ot a comlcat a tho wth varyg quatt. 08

8 Thu by traformg th matrx quato 6.3, Equato 6.8 ar obta. m m m q o q /3 o 6.3 Thu, m q q 6.4 m 6.5 o m o Equato 6. th zro quc voltag ca b aum to b zro or om valu, whch la to cotuou PWM chm. th aaly that follow hr aum to b zro. Th c lk currt quato ca b wrtt a th um of ach of th loa currt a th uly currt a, C T S S 6.7 or quvaltly a b cs3 o C T am bm cm

9 Aly th ychroou rfrc fram traformato to th abov quato by makg u of th followg qualt, T qo [ ] abc T T T abc 6.9 T abc T qo T 6.30 Thrfor, th c lk currt ca b wrtt a C T T abc M3 6.3 T abc T whr [ ] a a b c M 3 M M M 3 Ug qo traformato for Equato 6.3 th quato for th c lk currt bcom, C T T T qo mqo 6.3 whr m qo [ mq m mo ] a T 3 0 0, Hc Equato 6.7 bcom, C T.5m.5m 6.33 q q or. 5m T C.5mqq 0

10 Th zro quc aum to b zro or othr wor th thr ha currt a u to zro. Equato 6.4 to 6.6 a Equato 6.36 cottut th bac quato for th cotrol of th mach. Th cotrol tratgy a th rcl of cotrol a xla th followg cto. 6.. Cotrollr Dg For Th Half-Brg Covrtr Th cotrol objctv for th l covrtr to achv uty owr factor for th uly voltag a th currt whl matag a cotat c bu voltag. Th way t o a xla, th c voltag cotroll to b cotat at a trm valu. Wh th loa currt cra or cra, t th gl ha uly whch houl comat for t, thu a th c magtu cotroll to b cotat th amout t vat from th actual valu roortoal to th amout of currt whch th uly ha to gv out, followg ay chag. Thu th magtu for th uly currt obta, th magtu, to b ha wth th uly voltag for whch a uoal wavform ychroou wth th owr uly obta by maurg th owr uly voltag a vg t by t ak valu. Th gv th rfrc for th uly currt. Th actual uly currt calculat a comar wth th rfrc a th chag accout by th l covrtr, by chagg th moulato x for th wtchg vc. Chagg th moulato ma th moulato x of

11 th wtchg gal cra or cra whch affct th amout th wtchg vc couct thu affctg th fuamtal currt comot Statoary Rfrc Fram cotrollr Th cotrollr tructur wth a P woul work ffctvly o for oly c quatt but ot wh th cotrol varabl a tm varyg quatty a th abov ca whr th zro quc currt ot a c quatty. Hc, th covtoal P cotrollr caot b u for t cotrol, thu a tatoary rfrc fram cotrollr mloy who tructur xla th block agram form outl Fgur 6.4 [3]. - j x θ j x θ q q q q j y θ j y θ a a Fgur 6.4: Structur of th Statoary Rfrc Fram Cotrollr Th rror of th currt ar frtly covrt to otv a gatv ychroou rfrc fram.., θ x a θ. Hc th outut of th traformato block : x q θ x 6.35 q θx 6.36

12 whr, ; x0 x t θ θ 0 x θ - tal rfrc agl Th gal ar a through two cotrollr who trafr fucto ar gv by a. Hc th outut of th rgulator : 6.37 q θ x q θ x 6.38 Now th gal ar aga traform back to th abc rfrc fram wth om lay agl.., φ 0 0, φ θ θ φ θ θ x y x y t t. Hc th rultg gal from th traformato block ar: 6.39 θ θ j y x 6.40 θ θ j a a a y x Lt φ θ θ y x, th: 6.4 φ j φ j 6.4 Now ummg th two gal, to gt th outut of th cotrollr, whch aum to b qual to. ] [ ; φ φ φ φ j j j j By mlfyg th abov quato th trafr fucto of th ytm a: φ φ φ φ j j j j

13 th artcular ca lt u aum th cotrollr to b a P cotrollr who trafr fucto gv a k k k k 6.44 Hc, by ubttutg th abov trafr fucto 6.43 a mlfyg th ovrall trafr fucto bcom j[ k j k ] φ φ φ φ j[ k j k ] j[ k j[ k j k ] j k ] 6.45 For mlcty, f k k k ; k k k, th 3 k k coφ k coφ [k coφ coφ k coφ ] coφ k φ φ 6.46 gg th aramtr of th cotrollr, th omator of th trafr fucto comar wth Buttrworth Polyomal. Th Buttr-worth mtho locat th g valu of th trafr fucto uformly th lft half of th -la, o a crcl of rau o, wth t ctr at th org. Th Buttrworth olyomal for a trafr fucto wth a thr orr omator gv a: 3 3 w w w Hc by comarg th omator of th trafr fucto wth abov olyomal w 0 k ; coφ 0 k w ; coφ w / 3 0 coφ k φ 4

14 Th zro of th ytm ar fou by quatg th umrator of th trafr fucto to zro. Hc k coφ k coφ coφ k φ By olvg th quato th two zro of th ytm ar obta a: Z, Z k coφ ± 4k co φ 8k 4k coφ coφ k coφ φ For zro to b ral th followg coto ha to b atf: k > [ [ taφ ] / k k Th coto for zro to l th gatv half la, whch corro to markg th ytm to b mmum-ha wh th root ar ral, k > taφ Th coto for zro to b comlx umbr : k < [ [ taφ ] / k k Wh th root ar comlx umbr, th coto for zro to l th gatv half la, k k > 0 Now th trafr fucto of th cotrollr G AC to b fou. From Fg. 6.4 G AC ca b wrtt a G AC 6.49 [ φ φ j j] a

15 Lt k k k k Hc by ubttutg th trafr fucto of th P cotrollr a aumg k k k ; k k k a mlfyg th xro for GAC bcom, k coφ k coφ k coφ GAC 6.5 Hc aftr obtag th trafr fucto of th cotrollr, th k a k valu ar obta a xla abov a hc th cotrollr u to cotrol th currt Ovrall Cotrol Block Dagram Equato 6.5 to 6.6 cottut th bac quato for th cotrollr. Th cotrollr g ug th fback larzato xla Chatr 5. Equato 6.5 to 6.6 mol th loa. Th loa molg wa th ky coct of Chatr 5 a o t ot cu hr aga. For th l covrtr th moulato gal obta from Equato 6.8. Equato 6.8 ca b wrtt a, M tt L 6.5 whch th moulato gal for th fourth lg. Equato 6.34, th rouct of th trm T th rouct of two tm varyg gal of th am frqucy hc th rouct gv a fuamtal 6

16 comot a a co harmoc comot, o quatg trm o thr th co harmoc comot gt cacll a o Equato 6.34 ca b wrtt a C.5m. 5m 6.34 b q q Th ovrall cotrollr tructur how Fgur 6.5. Som of th quato Fgur 6.5 corro to Chatr 5 of th th, whch ar ot rwrtt hr to avo ulcato Smualto Rult Th Covtoal half-brg crcut Fgur 6.3 wa mulat ug a ucto mach a loa ug th cotrol tructur a how Fgur 6.5. Th mulato rult clu om ky aramtr for th loa a alo how th actual quatt follow th rfrc valu. Th rfrc th ca wa ram u from zro to th rat motor of 07.3 ra/c. Th aramtr for th mach loa ar gv Ax A. Fgur 6.6 to 6.9 how th mulato rult for th cu covrtr toology, wh tally th motor rug o o-loa a at a loa of 4N-m a o th mach a th ytm allow to ttl a th th loa wa rmov at 3. Fgur 6.6a how th c voltag rgulat to 700, t ca b that th voltag ruc lghtly wh th loa a but t graually bul u to b cotat at 700, 6.6b how th th rotor flux cotroll at a cotat valu how a ca b th actual valu follow th comma vry cloly. 7

17 r - P Eq 5.5 q - P Eq 5.49/ Eq 6.4 m q λ r r - P Eq 5.5 q - P Eq 5.50/ Eq 6.5 m T θ M M M 3 S PWM S... S3, T, T vrtor Motor c λ r - P S Eq6.34 b - G AC Eq 6.47 M tt Poto a S or c S t Eq 5.4 l Eq 6. Lmtr Fgur 6.5: Cotrol Block agram for th Covtoal Half-Brg Covrtr. 8

18 Fgur 6.7a a 6.7b how th motor frqucy a th rotor, followg ay chag t ca b that to k th rotor cotat th motor frqucy lghtly cra. Fgur 6.7 c a how th l a th lctromagtc torqu wh a loa torqu of 4 N-m a o to th mach. Fgur 6.8a th thr-ha loa currt ar lott agat tm wh th loa o th mach rt. Fgur 6.8b how th uly voltag a currt, whch ar almot ha wth ach othr. Th uly voltag cal by om factor o that both th voltag a currt ca b clarly. Fgur 6.8 c how th moulato gal for th four wtchg lg. Th moulato gal for th thr lg coct to th thr-ha ar balac, a th moulato gal for th fourth lg of th am frqucy a th uly. Fgur 6.9a th ufltr ha voltag ar lott agat tm whl Fgur6.9 b, c, th fltr loa voltag ar lott agat tm. a b Fgur 6.6: Rgulat c voltag a Th c lk voltag for a loa chag of 4 N-m, b th rotor flux lkag. 9

19 a b c Fgur 6.7: Loa chag. a Th motor frqucy ra/c, b Th rotor a th comma ra/c, c th l, th lctromagtc torqu of 4N-m. 0

20 a b c Fgur 6.8: O-loa of 4 N-m a loa currt, b uly voltag a uly currt, c th moulato gal M, M, M 3 a Mtt v tm

21 a b c Fgur 6.9: O loa of 4 N-m a Th thr ha ufltr loa voltag a, b, c a th zro quc voltag o, b Th thr-ha fltr loa voltag a, c b, c

22 6.3 Covtoal Toology wth Ruc Swtch Th co toology how fgur 6.3 a mofcato of th crcut aalyz cto 6.. Th vrtr ruc th cot by lmatg o of th lg th loa vrtr a o o of th ha rctly coct to th mot of th c lk caactor. L S T - a C a S b b S 3 c c Motor T - C S S 3 m Fgur 6.0: Covtoal Half-Brg toology wth ruc umbr of wtch. Wh comar to th covtoal half-brg covrtr th abov crcut mloy l umbr of wtch, thrby rucg th cot of th covrtr tu, but cotrol w o of th ha hr a coct to th c uly o th cotrol ha a lot. Th quato, whch govr th crcut toology, ar a follow: 3

23 L T T 6.53 t S S 3 S3 b S c o o whr o th voltag btw th utral of th loa a th mot of th c lk voltag a qual to th gatv of th ha voltag. a a o Ag th Equato 6.54, 6.55 a 6.56 togthr a kowg that th thr ha voltag ar to b balac that a b c th xro for o bcom o S S S S From th Fgur 6.3 t ca b obrv that th c lk voltag cotat though th voltag a may b ffrt; that th um of thr voltag qual to th c voltag a th ffrc th rl ovr th c voltag. σ Subttutg th wtchg fucto wth thr moulato gal Equato th moulato gal bcom, M tt σ L 6.6 t 4

24 M M 3 σ b o 6.6 a σ c o 6.63 a Makg u of th coto Equato 6.56 th Equato 6.6 a a 6.63 a ca b rwrtt a M M 3 σ b a 6.6 b σ c a 6.63 b Th c lk caactor currt a th rl ar gv Equato 6.64 a 6.65, C T b S c S Th trm T qual to M TT C σ b c 6.65 th q a - ax comot th abov quato ca b wrtt a v C 5 v q q T Th rouct of th trm T th rouct of two tm varyg gal of th am frqucy hc th rouct gv a fuamtal comot a a co harmoc comot, o quatg trm o thr th co harmoc comot gt cacll a o Equato 6.66 ca b wrtt a v v q q C

25 Th cotrol chm for th covrtr mlar to th half-brg, but u to th lack of cotrol o ha a, t voltag trm by th voltag of ha b a c b, c. Th quato whch ar uful gg th cotrollr tructur ar 6.6, a Th cotrol chm ca b brfly crb a follow; th loa that th ucto mach cotroll to mata a cotat a rotor flux. Th comma a th flux comma gv th rfrc for th q-ax a th -ax tator currt rctvly from whch th q-ax a th -ax tator voltag ar fou whch ar th outut of th cotrollr, that th valu of v q a v ar th rfrc voltag to b ythz by th vrtr. Th voltag a ar covrt back to abc fram ug th frqucy whch calculat by ag th rotor a th l. Th gv th thr ha voltag v q a, b v, from whch th moulato gal for th to c a th bottom wtchg vc ar fou. Th wtchg gal ar u to calculat th c lk voltag, whch comar wth th rfrc to outut th magtu of th ut uly currt whch ajut to ay chag th loa. For th uly voltag to b ha wth th uly currt, th currt multl by th ha of th uly voltag, whch comar wth th actual uly currt, th ffrc rgulat to gv th moulato gal for th l covrtr. Thu mlmtg th abov cotrol, a flux cotrol of th ucto mach a uty owr factor from th uly achv. Th cotrollr agram a how Fgur

26 r λ r c - P r - P Eq 5.5 q - P Eq 5.5 λ r Eq 6.67 S c - q - - P P G AC q Eq 5.49 Eq 5.50 Eq 6.6 q T θ a b c Eq 6.6, 6.63 M M 3 M tt S, T S, S3, S3 T, S PWM vrtor Motor Poto a S or S t Eq 5.4 l Eq 6. Lmtr Fgur 6.: Cotrol chm block agram for Covtoal Half-Brg toology wth ruc wtch 7

27 6.3.. Smulato Rult Th covtoal half brg covrtr wth ruc umbr of wtch mulat for a ucto mach. Th mulato how th tm ro for th varou quatt a wa o ur o-loa coto o th motor a aftr th motor ttl to th rat, a loa of 4 N-m wa a at a th th mach wa allow to ttl bfor th loa wa rmov. Fgur 6. a th rgulat c voltag how, t ca b that th c voltag ro wh th loa a but graually bul u to almot th rfrc valu a Fgur 6. b th rotor flux alog wth t comma valu lott agat tm. Fgur 6.3 a th loa currt wh a loa of 4 N-m wa a lott agat tm a Fgur 6.3 b th uly voltag a currt ar urmo o ach othr wh th loa wa a how, th uly voltag wa cal ow by a factor to clarly how that th currt a voltag ar arly ha wth ach othr. Fgur 6.4 a to how th motor frqucy, th rotor cotroll to th rfrc, th l a th lctromagtc torqu wh a loa of 4 N-m a ar lott agat tm. Fgur 6.5 how th ufltr a th fltr loa voltag lott agat th tm ar how. Fgur 6.9 how th moulato gal for th wtch ach of th lg, that for th ha b, ha c a th for th lg coct to th uly voltag T a T. 8

28 a b Fgur 6.: Rgulat c voltag a Th c lk voltag for a loa chag of 4 N-m b th rotor flux lkag. a b Fgur 6.3: O-loa of 4 N-m a loa currt, b th uly voltag a th uly currt. 9

29 a b c Fgur 6.4: Loa chag a th motor frqucy ra/c, b th rotor a th comma ra/c, c th l, th lctromagtc torqu of 4N-m. 30

30 a b c Fgur 6.5: O loa of 4 N-m a th thr-ha ufltr loa voltag,, b th thr-ha fltr loa voltag a, c b, c a, b c 3

31 Fgur 6.6: O-loa of 4 N-m a M, b M, c M 3 th chatr two covtoal crcut wr mol a a cotrol chm wa t forth for ach o of thm. Smulato rult a tal aaly of th cotroll ytm cofrm th fablty of th covrtr to ur uty ut owr factor whl cotrollg th motor. 3