Performance Improvement Technique for Induction Motor Driven by a Matrix Converter under Abnormal Input Conditions

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1 Junal f Autmatn an Cntl Engnng Vl. 1, N. 3, Sptmb 013 Pfmanc Impmnt chnu f Inuctn Mt Dn by a Matx Cnt un Abnmal Input Cntn Nguyn Khanh u am, Nguyn Van Nh, Huynh ha Hang, an Vu Duy Nhat Faculty f Elctcal & Elctnc Engnng, H Ch Mnh cty Unty f chnlgy 68 Ly hung Kt Stt, Wa 14, Dtct 10, H Ch Mnh Cty, VtNam Emal: tam_nguyn_bk@yah.cm Abtact Matx cnt (MC) an AC-AC pw cnt tplgy that ctly cnt ngy fm AC uc t an AC la wthut ung any ngy tag cmpnnt. hf, th tubanc n th nput ltag can ppagat nt th utput an ga n tat th pfmanc f mt la. h pap ntgat th bha f MC an t nflunc t th pfmanc f nuctn mt un unbalanc nput cntn. A f-fwa cmpnatn tchnu t lmnat th utput ltag ttn f MC an nu th pp patn f nuctn mt un unbalanc thn pp. Effctn an fablty f th cmpnatn mth ha bn mntat thugh mulatn ult. Inx m Matx cnt, nuctn mt, unbalanc, nl cntl I. INRODUCION h pha matx cnt ha c cnabl attntn n cnt ya [1]-[4], an m ha bn puc cmmcally. MC p hgh ualty pfmanc uch a na nual nput/utput wafm, ajutabl nput pw fact an cmpact ytm gn. hf, th nuctn mt f by matx cnt m aantagu t th cnntnal nt. Hw, u t th lack f th c-lnk tag cmpnnt, MC much m ucptbl t th nput ltag tubanc. If th nuctn mt u a a la f MC, any tubanc n th AC uc ltag wll b mmatly flct t th tat an thu unwant ppl wll appa n th lctmagntc tu. h wll la t th gaatn an n tatn f th ytm pfmanc. In t cp wth th pblm, al tchnu that uc th nflunc f abnmal nput ltag f MC ha bn pnt n m pap []-[4]. Pap [], [3] a ba n a ynamc mulatn f th ntantanu placmnt angl btwn nput ltag an cunt ct n th ct cnn chm. In Manucpt c Oct. 31, 01; Jan 8, 013. pap [4], th cnn pc fcttuly nt ctfcatn an nn tat, th cmpnatn tchnu ca ut by ajutng th ltag uc nt (VSI) mulatn nx m. In th pap, th nflunc f abnmal nput ltag t a ytm f nuctn mt f by MC wll b analyz n tal. h MC wll b cntll wth th am nct pac ct mulatn n [4], an a ffwa cmpnatn tchnu wth a mf nput placmnt fact (IDF) cntl pp. h IDF cntl tatgy, tgth wth th ajut mulatn nx, wll nu labl patn f th MC un unbalanc. A nl ct cntl utlz a th cntl algthm f th nuctn mt. mp th lw p patn pfmanc, th aapt full b wth hgh accuacy n tat flux, t p an tat tanc tmatn mply. h cntl chm can al b fun n [6]-[8]. h utput wafm f th MC an th ntantanu lctmagntc tu, p pn f th nuctn mt n uncmpnat an cmpnat ytm wll b hwn thugh mulatn t fy th ffctn f th f-fwa cmpnatn tatgy. II. MC CONROL SRAEGY A th pha t th pha matx cnt cnt f nn b-ctnal wtch whch allw any utput pha A, B, C t b cnnct t any nput pha, a hwn n Fg. 1. Fgu 1 a b c Aa Ab Ac Ba Bb Bc Ca Cb Cc S j( = A, B, C; j= a,b,c) A B C La h tplgy f th-pha t th pha matx cnt 013 Engnng an chnlgy Publhng : /jac

2 Junal f Autmatn an Cntl Engnng Vl. 1, N. 3, Sptmb 013 h nput pha ltag un nmal cntn can b xp a: () c( ) a t t ph( t) b ( t) V m c( t 10 ) (1) c () t c( t 10 ) wh V m an a pctly th ampltu an nput angula funcy f th nput pha ltag. In t btan th abl nual aag utput ln ltag,.g., c( ) AB t () ( t) BC 3V m c( t 10 ) CA c( t 10 ), a typcal tanf functn f MC xp n (3) c( t) c( t ) (3) M ( t) m. c( t 10 ). c( t 10 ) c( t 10 ) c( t 10 ) wh 0m 1 th mulatn nx an abtay angl. A claly p n [1], th tanf functn mtat a VSR-VSI cnn, a hwn n Fg. a a VSR VSI b c A B C CA b c AB BC pa pb pc p p Ap Bp Cp na nb nc Fgu n pn An Bn Cn Emulatn f VSR- VSI cnn V n Fg. a fcttu c-lnk ltag whch pn calculat a V Vc 3 Vm c (4) pn A a ult f th tanf functn mulatn, th ampl alu f th utput ln ltag pac ct an nput pha cunt pac ct fn by V V I. I ( ) j t j L m L ( ) j t j m m can b ynthz by tw ajacnt wtchng tat ct an z ct n th pct hxagn ung PWM tchnu a llutat n Fg. 3. Im b I(b, c) BC V (p, p, n) S 3 S S 3 S I (b, a) 3 I (a, c) 1 V3(n,p,n) V1 (p, n, n) S 4 I0 a S 4 V0 L AB θ c R θ R S 1 S 1 (c, a) I6 (a, b) V4 (n, p, p) V6(p, n, p) S 5 S 6 S 5 S 6 c I 5 (c, b) CA V5 (n, n, p) I 0 (a, a) (b, b) (c, c) V 5(n, n, p) (n, n, n) I (p, n) V (a, b, c) Fgu 3 VSR hxagn (a) an VSI hxagn (b) h multanu utput ltag an nput cunt SVM can b btan by cmbnng th tw mulatn tatg n bth pat VSI an VSR f MC. Dpnng n lcatn f th tw tatng fnc pac ct L an n ct f th pct hxagn, an apppat t f wtchng cmbnatn whch ntm a tmn a Im (5). /. ( ). ( c),. ( ). ( ),. ( ). ( ), m.m n 60 n 60 c. / m.m n n 60 c c. / m.m n 60 n c c. / m.m. n( ). n( c), c 0 1,, wll b lct. wh m th VSR mulatn c nx an chn a 1 f mplcty. m th VSI mulatn nx whch fn th ltag tanf at fm th DC lnk t th pak utput ltag (6) 0 m 3. V / V 1 (7) m c III. INDUCION MOOR CONROL ALGORIHM A. Inuctn Mt Ml h gnal nuctn mt ml n abtay fnc fam cb a fllw u R / t j 0 R / t j( ) (8) L L m L L m 3 Lm P L Im{ } wh u, u,, tat an t ltag an cunt ct, tat an t flux lnkag ct L, L, L m tat, magntzng an t nuctanc angula lcty f th t fl wth pct t th tat angula lcty f th t lctmagntc tu xp n tm f pac ct B. Pncpl f Fl-Ont Cntll h man bjct f th RFOC t npnntly cntl th tu an flux. h n by lctng th p f th fnc fam ual t th p f tatn f t flux pac ct. Un th cntn, th t flux pac ct bcm a pu al aabl nc an 0 (9) h tu uatn n (8) thn xp n th fllwng fm: 3 Lm (10) P L Wth an aumptn that th patn un cntant flux gn, th - cmpnnt f tat ltag, can b mplf t R L / t L (11) R L / t L wh 1 L / ( L L ) m C. Snl Vct Cntl Ung Aapt Ml In t ach hgh accuacy n t p, flux, an tat t tmatn, an aapt b that ff g pfmanc n a lag p ang 187

3 Junal f Autmatn an Cntl Engnng Vl. 1, N. 3, Sptmb 013 mply. Euatn f tat tmatn n th tatnay fam xp a: x ˆ Ax ˆ ˆ Bu ( ˆ G ) t ˆ 11 A 1 1 ˆ B x u ( ˆ G ) ˆ O 1 A (1) wh xˆ [ ˆ ˆ ˆ ˆ ] : tmat alu f tat cunt an t flux n tatnay fam u u u, : tat ltag an cunt Rˆ L I a I ( / ( ) (1 ) / ( )) L / ( L L )((1/ ) I ˆ J ) a I a J 1 m 1 1 ( L / ) I a I 1 m 1 ( 1/ ) I ˆ J a I a J I, J, B (1/ L ) I, O th t tm cntant, ˆ th tmat p G th fback gan f th b, G lct that th pl lcatn f th b k tm ( k 1) pptnal t th mt pl [5]: wh g1 g g3 g4 G g g1 g4 g3 g1 ( k 1)( aˆ ˆ ˆ 11 a ), g ( k 1) a g ˆ ˆ 3 ( k 1)( a1 a11) g1, g4 g ( L L Lm ) / Lm h aapt chm f p an tat tanc tmatn a cb a Fgu 4 p R K K t p PI K K t PI PI l ˆ ˆ ˆ aapt b nct SVM Gat abc nput ltag a matx cnt Sytm cnfguatn f nl ct cntl f nuctn mt n by matx cnt IV. PERFORMANCE OF SYSEM OF MARIX CONVERER FED INDUCION MOOR UNDER ABNORMAL INPU CONDIION A. Matx Cnt Opatn un Abnmal Input Vltag h c-lnk ltag cb n (4) uppl ctly t th VSI pat n th VSR-VSI cnn llutat n Fg.. Whn utlzng th SVM f th VSI pat, un nmal cntn f nput ltag, th c-lnk ltag alway cn t b a cntant alu. hu, any aatn f th ltag wll b flct t th utput f th SVM mply wthut any cmpnatn tchnu. A b B IM c C analyz th c-lnk ltag aatn u t th abnmal nput ltag, a m gnal uatn pp Vpn Vc 3 3 c( ) c (13) wh th magntu f nput pha ltag pac ct, th gnalz nput placmnt fact. In nmal nput cntn, ha a cntant magntu an tat at a cntant angula lcty. Snc V m (14), (13) an (4) a thu ualnt. Hw, un abnmal cntn n tm f nput unbalanc, nn-nual nput ltag an ht tm ltag ag, magntu an angula lcty f a n lng cntant an (14) n lng atf. In th ca, (13) p an accuat ult f c-lnk ltag aatn whl (4) alway puc a cntant alu a n nmal cntn. h la t th wng patn f MC nc (4) u t th SVM f VSI pat f th magnay VSR-VSI n Fg.. llutat th pfmanc f MC un nmal an abnmal nput cntn, mulatn ult f tw ca a gn: Ca 1: Balanc an nual nput ltag whch magntu an funcy a 0Vm an 50 Hz pctly. Ca : Abnmal nput ltag cat by ang 10% f th hamnc an 0% f ffth hamnc n ach pha f th ltag n ca 1. In bth ca, th abl IDF z. Fg. 5a an 5b llutat pctly th aatn n magntu f nput pha ltag pac ct n ca 1 an ca. It cla that th magntu cntant n ca 1 an tm-a n ca. Angula lcty f nput pha ltag an cunt pac ct an th atn a b n th am cp a hwn n Fg. 6a f ca 1 an 6b f ca. h atn xpct t b ual t th IDF whch t at z n bth ca. Hw, a claly hwn n Fg. 6a an Fg. 6b, th atn nly ual t z n ca 1 whl cllatng aun z n ca. h alu f th c-lnk ltag calculat by (4) an (13) a thn pltt n th am gaph a hwn n Fg. 7a an Fg. 7b. It can b n that th c-lnk ltag calculat by (13) jut ual t whch calculat by (4) n ca 1 whl ffnt n ca. (a) Ca 1 (b) Ca Fgu 5 Magntu aatn f nput pha ltag pac ct un nmal nput ltag (Ca 1) an abnmal nput ltag (Ca ) 188

an (13) un nmal nput ltag (Ca 1) an abnmal nput ltag (Ca ) B. Inuctn Mt Dn by Matx Cnt Opatn un Abnmal Input Vltag h ytm cnfguatn f nl ct cntl f nuctn mt n by matx cnt cb n Fg. 4.

4 Junal f Autmatn an Cntl Engnng Vl. 1, N. 3, Sptmb 013 (a) Ca 1 (b) Ca Fgu 6 Angula lcty f nput ltag an cunt pac ct an th atn un nmal nput ltag (Ca 1) an abnmal nput ltag (Ca ) V c V c Vc (a) Ca 1 Vc (b) Ca Fgu 7 Dc-lnk ltag calculat by (4) an (13) un nmal nput ltag (Ca 1) an abnmal nput ltag (Ca ) B. Inuctn Mt Dn by Matx Cnt Opatn un Abnmal Input Vltag h ytm cnfguatn f nl ct cntl f nuctn mt n by matx cnt cb n Fg. 4. h nct ltag f t flux nt cntl algthm appl t th chm. h pncpl f th p cntll t mantan a cntant alu f th -ax cunt whl ntantanuly changng th -ax cunt. A claly hwn n (10), whn th t flux hl cntant, th lctmagntc tu pptnal t th alu f -ax cunt. Snc th ltag-f ml u, th utput f th cntl ytm a th tat - ax ltag fnc. h - ax cmpnnt f th fnc ltag a cb a fllw (15) wh (, ) a th ynchnu fnc ltag whch th tw PI cunt cntll puc, (, ) ( L, L ) a tw cuplng ltag. h fnc ltag (, ) a thn tanfm nt ax cmpnnt whch a ctly u t th abl magntu an angula lcty f th utput ltag pac ct. Supp that th fnc utput pha ltag pac ct, at an ntant f amplng, ha magntu f Vm an angula lcty f a xp n (16) V (16) j m. Ung (4) an (7), th VSI mulatn nx tmn a c m m m 3. V V m m V 3V c (17) Hw, a puly mntn n IV.A, un abnmal nput cntn, th c-lnk ltag n lng cntant an ay accng t (13). Aumng that alu f th c-lnk ltag gat than alu f th abl utput ln ltag magntu V 3. V (18), thn wth m calculat by (17), th actual alu f utput pha ltag magntu that MC can puc c m Vm 1.c m. V V c m 3 V c m KV. m (19) h angula lcty f th utput pha ltag pac ct cntll npnntly f t magntu. hf, xactly btan gal f th clnk ltag aatn. A a ult, th utput pha ltag pac ct that MC can btan a j j V. K. V (0) (16) an (0) claly hw that m m ual t th fnc pac ct n ca f nmal nput cntn whl ffnt n magntu n ca f abnmal nput cntn. Fgu 8 Illutatn f actual - ax cmpnnt f a ctan fnc ltag un abnmal nput cntn. Fg. 8 u t th latnhp btwn utput pha ltag pac ct aatn an th aatn f - ax cmpnnt f th fnc ltag. It can b n fm Fg. 8 that th - ax cmpnnt aatn pptnal t a fact fn a K 1 (1) Hnc, th actual alu f - ax cmpnnt f th fnc ltag a btan a K K () () claly p that wth th nput fnc ltag cmpnnt f (, ) n - ax, f (18) atf, th actual alu that MC can btan un abnmal nput cntn a K(, ). h ualnt t patn f MC un nmal cntn whn atnal cmpnnt f (, ) a nt t th fnc cmpnnt. A puly mntn, th fnc ltag n - ax u t cat apppat tu t cntl th 189

Junal f Autmatn an Cntl Engnng Vl. 1, N. 3, Sptmb 013 nuctn mt p. h tu, a cb n (10), pptnal t bth t flux an -ax cunt whch a pctly cntll by -ax an -ax fnc ltag cmpnnt.

F-Fwa Cmpnatn Statgy A cu n ctn IV, th c-lnk ltag a ung patn f MC un abnmal nput cntn. h aatn pnnt n th ntantanu magntu f nput pha ltag pac ct an th placmnt fact a cb n (13).

h gnalz IDF whch a wth hl cntant by mfyng th cntllabl angula lcty f nput cunt pac ct n VSR pat a fllw (3) Hnc, alway atf ung abnmal cntn.

Othw, t wul la t th mulatn an th cmpnatn tchnu pp n (3), (4) n lng atf. hf, t nu th ffctn f th cmpnatn mth, a gnal cntant pp a mn( V ) max( 3. V ) (5) c V.

5 Junal f Autmatn an Cntl Engnng Vl. 1, N. 3, Sptmb 013 nuctn mt p. h tu, a cb n (10), pptnal t bth t flux an -ax cunt whch a pctly cntll by -ax an -ax fnc ltag cmpnnt. Hw, a tw cmpnnt ay accng t () un abnmal cntn, th actual tu appl t th nuctn mt by MC wll b K tm pptnal t th fnc tu. C. F-Fwa Cmpnatn Statgy A cu n ctn IV, th c-lnk ltag a ung patn f MC un abnmal nput cntn. h aatn pnnt n th ntantanu magntu f nput pha ltag pac ct an th placmnt fact a cb n (13). h a f th pp f-fwa cmpnatn tatgy t calculat th ntantanu alu f th c-lnk ltag an thn ajut th VSI mulatn nx m t an apppat alu. h gnalz IDF whch a wth hl cntant by mfyng th cntllabl angula lcty f nput cunt pac ct n VSR pat a fllw (3) Hnc, alway atf ung abnmal cntn. h cmpnatn VSI mulatn nx m thn ajut accng t th c-lnk ltag alu n (13) m 3V V m m V 3 c c (4) Hw, a cb n (18), th utput ln ltag hul nt xc th c-lnk ltag alu. Othw, t wul la t th mulatn an th cmpnatn tchnu pp n (3), (4) n lng atf. hf, t nu th ffctn f th cmpnatn mth, a gnal cntant pp a mn( V ) max( 3. V ) (5) c V. SIMULAION RESULS In t cnfm th ffctn f th ffwa cmpnatn mth, m mulatn tu ung MALAB/Smulnk t pctly mulat th cnntnal cntl tatgy, an f-fwa cmpnatn tatgy un nput ltag cntn whch cntan 10% th hamnc an 0% ffth hamnc. mplmnt th ml f p nl IFOC cntl f IM n by MC, a tana.kw, tw pl, 380V, 50hz nuctn mt u. h nuctn mt ha th fllwng paamt alu: R =1.79, R =1.8, L =0.0853H, L = H, L = m H. h ynamc pn f th ytm tt wth fnc t p chang an la aatn. h fnc p t at 60 a/ n th ft cn, at 1 a tp chang happn t t th fnc p at 10 a/. La tu ntally t at z, tp chang n m la a appl at 0.5 an 1.5 wth alu f 3Nm an 7Nm pctly. Un th am gn patng cntn, pfmanc f IM n by MC wthut any cmpnatn tchnu an wth f-fwa cmpnatn tatgy a llutat n Fg. 9-Fg. 11. Fg. 9a play btwn 1.4: 1.6 th tat cunt n uncmpnat ytm. h tat cunt n cmpnat ytm wth hamnc ttn uc cnably a hwn n Fg. 9b. Effctn f th pp cmpnatn tatgy al mntat thugh mpmnt n utput tu an p pn f IM. A llutat n Fg. 10a an Fg. 11a, tt tat cunt ult n hgh ppl lctmagntc tu an thu untabl p f t. Fg. 10b an Fg. 11b claly hw th mpmnt wth y lw ppl tu an tabl t p whn th cmpnatn tatgy appl. Fgu 9 (a) uncmpnat ytm (b) cmpnat ytm Stat cunt n uncmpnat ytm an cmpnat ytm (a) uncmpnat ytm (b) cmpnat ytm Fgu 10 Output tu n uncmpnat ytm an cmpnat ytm (a) uncmpnat ytm (b) cmpnat ytm Fgu 11 Rt p n uncmpnat ytm an cmpnat ytm VI. CONCLUSION h pap ha analyz th nflunc f abnmal nput ltag t th ytm f an nuctn mt n by a matx cnt. h p nl IFOC mply a th p cntl ml f nuctn mt. mp th ytm pfmanc un abnmal 190

Junal f Autmatn an Cntl Engnng Vl. 1, N. 3, Sptmb 013 nput cntn, a f-fwa cmpnatn tatgy pp. Output ualty f uncmpnat an cmpnat ytm ha bn hwn t cnfm th ffctn f th pp mth. REFERENCES [1] L. Hub an D.

Mattn, Cmpan f tw cunt mulatn tatg f matx cnt un unbalanc nput ltag cntn, IEEE an, l. 49, n., pp. 89-96, Apl 00. [3] D. Caa, G. Sa, an A.

Pn, Spac ct mulat matx cnt wth mnmz numb f wtchng an a f-fwa cmpnatn f nput ltag unbalanc, IECON, l., pp. 833-839, Jan 1996. [5] H. Kubta, K. Matu, an.

6 Junal f Autmatn an Cntl Engnng Vl. 1, N. 3, Sptmb 013 nput cntn, a f-fwa cmpnatn tatgy pp. Output ualty f uncmpnat an cmpnat ytm ha bn hwn t cnfm th ffctn f th pp mth. REFERENCES [1] L. Hub an D. Bjc, Spac ct mulat th-pha t th-pha matx cnt wth nput pw fact cctn, IEEE an. IA, l. 31, pp , N/Dc [] F. Blaabjg, D. Caa, C. Klumpn, an M. Mattn, Cmpan f tw cunt mulatn tatg f matx cnt un unbalanc nput ltag cntn, IEEE an, l. 49, n., pp , Apl 00. [3] D. Caa, G. Sa, an A. an, Ructn f th nput cunt hamnc cntnt n matx cnt un nput/utput unbalanc, IEEE an, l. 45, n. 3, pp , Jun [4] P. Nln, F. Blaabjg, an J. K. Pn, Spac ct mulat matx cnt wth mnmz numb f wtchng an a f-fwa cmpnatn f nput ltag unbalanc, IECON, l., pp , Jan [5] H. Kubta, K. Matu, an. Nakan, DSP-ba p aapt flux b f nuctn mt, IEEE anactn n Inuty Applcatn, l. 9, n., pp , Ma./Ap [6] K. B. L an F. Blaabjg, Imp nl ct cntl f nuctn mt f by a matx cnt ung nnlna mlng an tubanc b, IEEE an. Engy Cn., l. 1, n. 1, pp. 5 59, Ma [7] K. B. L an F. Blaabjg, Ruc- xtn lunbg b ba nl ct cntl n by matx cnt wth nnlnaty cmpnatn, IEEE an, l. 53, n. 1, Fb [8] M. Mntana, S. M. Paa, C. R, an A. ll, Sp nl cntl f nuctn mt ba n a uc- aapt b, IEEE an, l. 15, n. 6, N Nguyn Khanh u am c h bachl g n Autmatc Cntl Engnng fm th H Ch Mnh Cty Unty f chnlgy, Vtnam n 010. H cuntly a ach n Faculty f Elctcal an Elctnc Engnng, H Ch Mnh Cty Unty f chnlgy. H ach ntt manly nclu aanc cntl f lctcal machn an pw lctnc. Nguyn Van Nh c h M.S. an PhD. g n Elctcal Engnng fm th Unty f Wt Bhma, Czch Rpublc n 1988 an 1991, pctly. Snc 007, h ha bn an acat pf f Faculty f Elctcal an Elctnc Engnng at H Ch Mnh Cty Unty f chnlgy, Vtnam. H wa a ptctal at KAIS, Ka n 001 an wa a tng pf n H ach ntt nclu mlng an cntl f ac mt, act flt, an PWM tchnu. H a mmb f th Inttut f Elctcal an Elctnc Engn (IEEE). Huynh ha Hang wa bn n Vtnam, n H c th M.S. an PhD. g n Elctcal Engnng fm H Ch Mnh Cty Unty f chnlgy, Vtnam n 1999 an 005, pctly. Snc 1996, h ha bn wth Dpatmnt f Elctcal an Elctnc Engnng, H Ch Mnh Cty Unty f chnlgy, Vtnam, wh h cuntly a Vc Dan. H wa wth Unty f Haut Alac a a pt-c fllw f n ya n 007. H ach ntt a n th aa f ntllgnt cntl an cmput n. 191

Applications of Lagrange Equations

Applications of Lagrange Equations Applcaton of agang Euaton Ca Stuy : Elctc Ccut ng th agang uaton of oton, vlop th athatcal ol fo th ccut hown n Fgu.Sulat th ult by SIMI. Th ccuty paat a: 0.0 H, 0.00 H, 0.00 H, C 0.0 F, C 0. F, 0 Ω, Ω