Engy an Pow Engining, 21, 1-17 oi:1.4236/p.21.213 Publih Onlin Fbuay 21 (http://www.cip.og/jounal/p) Th-Lvl Fiv-Pha Spac Vcto PWM Invt fo a Two Fiv-Pha Si Connct Inuction Machin Div N. R. ABJADI 1, J. SOLTANI 2, J. ASKARI 2, Gh. R. Aab MARKADEH 1 1 Dpatmnt of Engining, Shahko Univity, Shahko, Ian 2 Dpatmnt of Elctical an Comput Engining, Ifahan Univity of Tchnology, Ifahan, Ian Email: naviabjai@yahoo.com Abtact: Thi pap cib th coupl toqu an flux contol of a two i connct fiv-pha Inuction Machin (IM) iv that i uppli by a th-lvl fiv pha SVPWM invt, uing a wll known pha tanpoition in th i connction. At th fit, th coupl toqu an flux contoll i vlop ba on vaiabl-tuctu contol (VSC). Thn, a liing-mo (SM) flux obv in mploy to timat th tato flux; that u a two fnc fam which ult in liminating th p aaptation. Moov impl contol tatgy i intouc fo th-lvl SVPWM voltag ouc invt (VSI) that can b aily implmnt in pactic fo a two-i fiv pha IM iv. Finally, th ffctivn an capability of th popo contol mtho i vifi by comput imulation. Kywo: multipha ytm, multilvl VSI, liing mo contol 1. Intouction In lctical iv application, th-pha iv a wily u fo thi convninc. Howv, high-pha numb iv po val avantag ov convntional th-pha iv uch a: ucing th amplitu an incaing th fquncy of toqu pulation, ucing th oto hamonic cunt, ucing th cunt p pha without incaing th voltag p pha, an lowing th c-link cunt hamonic an high liability. By incaing th numb of pha, it i alo poibl to inca th toqu p m amp fo th am volum machin [1]. Multi-pha machin hav foun wi application in tanpot, txtil manufactuing an aopac inc fw ya [2 14]. Th cnt ach wok on multipha machin can b catgoiz into multi-pha pul with moulation (PWM) tchniqu fo multipha machin [2 14], hamonic injction to pouc mo toqu an to achiv btt tability [5], fault tolant iu of multi-pha moto iv [6], i/ paalll connct multi-pha machin [7 14]. Application involving high pow may qui multipha ytm, in o to uc t on th witching vic. Th a two appoach to upplying high pow ytm; on appoach i th u of multilvl invt upplying th-pha machin an th oth appoach i multilg invt up- plying multipha machin. Much mo wok ha bn on on multilvl invt. It i intting to not th imilaity in witching chm btwn th two appoach: fo th multilvl invt th aitional witching vic inca th numb of voltag lvl, whil fo th multilg invt, th aitional numb of witching vic inca th numb of pha [15]. In [16], Klly t al. alo vifi that an n-pha pac vcto PWM (SVPWM) chm can b cib in tm of th applying tim of availabl witching vcto on th bai of th pac vcto concpt. Howv, th pap only focu on how to aliz a inuoial pha voltag. A i wily known, mot multipha moto a ign to hav th noninuoial back-emf voltag. Hami A. Toliyat hav ma much ach on contol mtho an unning pfomanc aim at fiv-pha iv [1], but thi ubjct invtigat i th ytm fing with two lvl invt. Anoth ach wok ha bn on in [17] on a multipha two lvl noninuoial SVPWM. Th pow ating of th convt houl mt th qui lvl fo th machin an ivn loa. Howv, th convt ating can not b inca ov a ctain ang u to th limitation on th pow ating of miconucto vic. On olution to thi poblm i Copyight 21 SciR
N. R. ABJADI ET AL. 11 Figu 1. Two fiv-pha machin iv uppli by a ingl invt uing multi-lvl invt wh witch of uc ating a mploy to vlop high pow lvl convt. Th avnt of invt f moto iv alo mov th limit of th numb of moto pha. Thi fact ma it poibl to ign machin with mo than th pha an bought about th incaing invtigation an application of multi-pha moto iv [18,19]. In [2], Qingguo Song, intouc a mtho to upply a ingl fiv-pha pmannt magntim ynchonou moto (PMSM) with a th lvl SVPWM VSI. But th mtho i not capabl to contol mo i connct multipha machin o poucing noninuoial voltag. Spac-vcto moulation (SVM) i an avanc tchniqu fo th gnation of output voltag o cunt in invt ba on th patial viualization of thi vaiabl. In th convntional appoach of thi tchniqu, th invt i untoo a a whol, allowing full contol ov th witching qunc of th witch an achiving maximum u of th c-link voltag. Th fiv-pha inuction moto iv hav many mo pac voltag vcto than th th-pha inuction moto iv. Th inca numb of vcto allow th gnation of a mo laboat witching vcto tabl in which th lction of th voltag vcto i ma ba on th al-tim valu of th tato flux an toqu vaiation. In thi pap, a fiv-pha 3 lvl SVPWM algoithm i vlop to contol a two i IM iv ytm. Rcognizing th VSC mit an th avantag of uing th SVM, thi pap pnt a VSC-DTC olution fo i-connct inuction moto iv. Dict toqu an flux contol i achiv by man of VSC. cunt a givn a: va va1 va2 vb vb1vc2 vc vc1v2, vd v1vb2 ve v1v2 i i i i i i i i i i i i i i i A a1 a2 B b1 c2 C c1 2 D 1 b2 E 1 2 Each machin i uppo to hav it own paamt. Uing th coupling Clak tanfomation, th oiginal pha vaiabl a colat to nw ( ) vaiabl a f C f abc, wh C i th pow-invaiant tanfomation matix: C 1 co co 2 co 3 co 4 in in 2 in 3 in 4 2 x 1 co 2 co 4 co6 co8 5 y in 2 in 4 in 6 in8 1/ 2 1/ 2 1/ 2 1/ 2 1/ 2 (1) (2) Th (, ) an ( x, y ) voltag an cunt of th fiv-pha VSI a obtain a: v INV v va 1 v A a2 v 1 v x2 v INV vb v b1 v c2 v 1 v y2 INV vx C v C C vc1 v (3) 2 vx1 v2 v INV y v D v 1 v b 2 v y 1 v 2 v INV ve v 1 v 2 2. Dciption an Moling of th Div Sytm Th iv conit of two fiv-pha quil cag inuction machin. Rfing to Figu 1 th fiv-pha tato wining of th two machin a connct in i, with an appopiat pha tanpoition [19]. Th twomoto iv ytm i uppli fom a ingl fiv-pha VSI. Fom Figu 1 th lationhip btwn voltag an Figu 2. Fiv-pha IM quivalnt cicuit of on machin Copyight 21 SciR
12 N. R. ABJADI ET AL. i INV i 1 ix2 i INV i 1 iy2 (4) i INV x ix 1 i 2 i INV y iy 1 i 2 Th toqu quation of th two i-connct machin a givn a follow Tk Pk Lmk( ikik ikik) (5) h k=1,2 an P k a pol pai. Fom th quation an (4), on can not that th toqu pouction cunt of th fit moto ( i 1, i 1 ) a qual to non poucing toqu cunt of th con moto ( ix2, iy 2). A a ult, th two moto can b contoll inpnntly though a ingl VSI. Th tato voltag quation of ach machin a vk Rkik ( Lki Lmki ) t k k vk Rkik ( Lki k Lmki k) t vxk Rkixk ( Llkixk) t vyk Rkiyk ( Llkiyk) t wh k=1,2. Th oto voltag quation of ach machin a Rkik 1( Lkik Lmkik) ( Lki k Lmki k) t Rkik k( Lkik Lmkik) ( Lki k Lmki k) t wh k=1,2. In Figu 2 th fiv-pha IM quivalnt cicuit of on machin i hown. 3. Sliing-Mo Contoll Block iagam of th vaiabl-tuctu ict toqu contoll iv (VSC-DTC) un coniation i hown in Figu 3. A can b n fom thi figu, fo ach moto th contol quantiti a th tato flux magnitu an toqu. A fnc tato voltag, v j v v, i obtain q at th output of th VSC, wh v i gnat by th flux contol law an v q by th toqu contol law. Th (6) (7) Figu 3. Block iagam of th VSC-DTC contol law i of th Rlay with contant gain typ [21], 1 v ( )gn( ) K P K I S (8) v ( K )gn( ) ˆ ˆ PT K IT S (9) 1 q q K wh =/t, gn i th ignum function,, P K, I K an PT K a th PI contoll gain, IT S S j S i th liing ufac, an upcipt ^ q tan fo timat quantiti. In o to acclat th voltag pon uing p tanint, th toqu contol law contain a ffowa compnation fo th ynamic lctomotiv foc (EMF). Th PI contoll hlp to uc th chatting aociat with VSC an fin th ytm bhavio whn it i not in th liing mo (uing th aching pha). Th liing ufac i ign o a to nfoc SM opation with fit-o ynamic, S S S c c j q j ( T T ) T (1) ˆ ˆ T T T ; c an c T a wh ign contant. In th liing mo, th contol law (8) an (9) tict th ytm tat onto th ufac, an it bhavio i xcluivly govn by S [21]. 4. Sliing-Mo Obv In [21,22], an inhntly nol SM obv ha bn vlop. It u two fnc fam allow liminating th p aaptation. Thi fatu i ignificant in iv that o not n th p timation fo contol (toqu-contoll iv) an it i xpct to pouc btt ult than convntional obv. An SM obv fo IM i t ˆ R i ˆ v K i i ˆ j gn( ) 1 (11) L (12) K ˆ 2 i i L ˆ ˆ Lm i 2 (13) m 1 ˆ ˆ ( j( )) ˆ t LT T gn( ) L In o to liminat th oto p aaptation, th tato Equation (11) i implmnt in tato fnc Copyight 21 SciR
N. R. ABJADI ET AL. 13 Figu 4. Schm of a fiv-pha th-lvl invt oto flux fam (upcipt ), which otat with oto flux p, ˆ R i v K gn( ˆ ) 1 i i (14) t 1 ˆ Lm ˆ ( j( )) ˆ t LT T K gn( ˆ ) 2 i i (15) Taking into coniation that th oto flux i align with th fnc fam, th oto mol (15) tun out to b impl: 1 ˆ Lm ˆ ˆ t LT T (16) ( K gn( ˆ )) 2 i i ˆ q (17) It can b hown that th obv i tabl if it gain a lag nough [21]. 5. Th Lvl Spac Vcto Pwm Figu 5. Th witching vcto on α-β an x-y plan fam, an th oto Equation (12) i implmnt in In [2], a tchniqu of vcto pac contol of th-lvl voltag ouc invt f fiv-pha machin wa pnt. Uing th am ia cib in [2], in thi pap a SVPWM voltag ouc i vlop which i capabl of upplying th two moto iv ytm with iffnt oto p. Th SVPWM chm i ign to gnat an abitay fnc voltag pac vcto which contitut th moto main fqunci 1 an 2. Figu 4 how th chm of a fiv-pha th-lvl invt. Th a 243(3 5 ) voltag vcto; th magnitu an itibuting of voltag vcto a fa mo complx than fiv-pha two-lvl invt. Howv, not all of vcto a uitabl to vcto ynthizing. Coni voltag vcto with magnitu V L.6472V DC, VM.6156 VDC, VS.3236V DC an zo voltag vcto a fficint woking vcto. Th a 43 fficint vcto in ach plan, incluing 3 non-zo vcto, 1 unant an 3 zo vcto, a hown in Figu 5. Th cimal numb in Figu 5 not th witching mo. Whn ach cimal numb i convt to a fiv igit numb in ba 3, th 2' in thi numb inicat that th two upp witch in th coponing witching am a on an th 1' in thi numb inicat that th two mil witch a on, whil th ' inicat th on tat of th low witch. Th MSB (mot ignificant bit) of th numb pnt th witching tat of pha a, th con MSB fo pha b, an o on. A hown in Figu 5, lct woking voltag vcto qually ivi th cagon into tn ction 1, 2,..., 1. Fom th avag vcto concpt uing on ampling Copyight 21 SciR
14 N. R. ABJADI ET AL. V b V a V n Figu 6. Rfnc vcto an witching vcto in ction 1 of α-β plan Figu 7. Flowchat to aliz fnc voltag vcto pio, th fnc voltag vcto on th α-β an x-y plan can b aliz by ajuting th applying tim of 3 vcto. Figu 6 how ach ction can b ivi into fou mall tiangl gion, an th fnc voltag vcto i fom by th apical voltag vcto in thi tiangl [2]. Fo xampl if th fnc vcto i btwn vcto 218 an 216 in α-β plan (cto 1), an moov it i locat in gion C, a hown in Figu 6, th activ witching vcto a 217, 216, 18 (o 229). To contol 2 i-connct moto, in half of ach witching pio, th α-β fnc vcto, in α-β plan, i u a th fnc vcto an in half oth, th x-y fnc vcto, in x-y plan, i u to tmin th witching vcto. Thi tatgy can b pat in all of th cto an hown in flowchat of Figu 7. It i wothwhil to not uing th witching vcto fo xampl in α-β plan, by abov uggt mtho, th x-y componnt a ngligibl an vic va. In thi way, both α-β fnc vcto an x-y fnc vcto a aliz. It i btt to nomaliz vcto by VS.3236V DC, thn ach witching vcto cooinat bcom intg a hown in Figu 6. Fom Figu 6, th cooinat of fnc vcto a obtain a follow o V (c tg ctg36 )in a V (18) n in (19) V b ov n in 36 wh i th angl btwn fnc vcto an a-axi in ach ction. Th pac vcto PWM tatgy i accomplih by th following quation V EaT E V FaT F V GaT G V at (2) V EbT E V FbT F V GbT G V bt T E T F T G T wh T E, in ach tiangl gion; an T F an T G a th apical witching vcto T i half of th witching pio. Fo implicity th witching tim fo all of th gion a calculat in Tabl 1. 6. Simulation Rult Th popo contol chm i implmnt in a block iagam hown in Figu 8. In thi figu, only contol of IM1 i illutat (om ubcipt a omitt fo th ak of bvity), th am can b appli to IM2. Notic that th SM contoll an obv gain a obtain by tial an o. Similaly th cofficint of p PI contoll a obtain a k p 1, ki 1.1. Simulation ult a obtain fo a two iffnt fivpha quil cag IM with paamt hown in Tabl 2. Th IM p an tato flux contol ult a obtain an hown in Figu 9(a) an Figu 9(b) pctivly. Th ult obtain fo an xponntial fnc oto p fom zo to 8 a/ fo machin 1 an an xponntial fnc oto p fom zo to 4 a/ fo machin 2. Th amplitu of tato flux a Tabl 1. Calculation of witching tim in ach gion V V T V T (, ) (,) Ea Eb F a Rgion A: V ( V, ) (1,) Fa V Fb T G V bt (, ) (,1) Ga Gb Rgion B: Rgion C: V V T T T T E F G V V T V T (, ) (,1) (1 ) Ea Eb E a ( V, ) (1,) (1 ) Fa V Fb T F V b (, ) (1,1) Ga Gb T G E F V V T T T T V V T V V T (, ) (,1) (2 ) Ea Eb E a b ( V, ) (1,1) Fa V Fb T F V at (, ) (,2) Ga Gb V V T T T T G E F V V T V V T (, ) (1,) (2 ) Ea Eb E a b Rgion D: ( V, ) (2,) Fa V Fb T G V bt (, ) (1,1) Ga Gb V V T T T T F E G Copyight 21 SciR
N. R. ABJADI ET AL. 15 Tabl 2. Im paamt Machin 1 [23]: Pn1 3hp f 5Hz P 1 3 R 1.78 R 1.66 L 1 33.15mH L 1 33.15mH m1 L 29.7mH Machin 2 [19]: Pn2 7.5hp f 5Hz P 2 2 R 2 1 R 2 6.3 L 2 46mH L 1 46mH L m2 42mH Etimat Stato Flux1 <Wb> Etimat Stato Flux2 <Wb>.5.4.3.2.1.5 1 1.5 2 2.5 3 3.5 4.5.4.3.2.1.5 1 1.5 2 2.5 3 3.5 4 Tim <> (c) 2 T1 <N.m> 1-1.5 1 1.5 2 2.5 3 3.5 4 w1, w1 <a/> w2, w2 <a/> Stato Flux1 <Wb> Stato Flux2 <Wb> 1 5-5 Figu 8. Div ytm block iagam -1.5 1 1.5 2 2.5 3 3.5 5-5.5 1 1.5 2 2.5 3 3.5 Tim <>.5.4.3.2.1 (a).5 1 1.5 2 2.5 3 3.5 4.5.4.3.2.1.5 1 1.5 2 2.5 3 3.5 4 Tim <> (b) T2 <N.m> 15 1 5-5 -1.5 1 1.5 2 2.5 3 3.5 4 Tim <> ia1 <A> 15 1 5-5 -1 () -15.5 1 1.5 2 2.5 3 3.5 4 Tim <> () Figu 9. a) Roto p; b) Stato flux; c) Etimat tato flux; ) Moto toqu; ) Moto pha a cunt kpt contant (.4 Wb fo both IM). Copyight 21 SciR
16 N. R. ABJADI ET AL. Th p an flux tack thi fnc with a goo ynamic. It i vint fom th Fig. that th flux of th IM2 main unaffct uing th tanint of th p of IM1 an vic va, moov th p a alo almot unaffct. Th ult vify th ability of th popo contol an SVPWM tchniqu uing p tat up an p val. In aition, th moto tato flux timat ult a hown in Figu 9(c). Finally th toqu an pha a cunt of IM a hown in Figu 9() an 9() pctivly. Th invt pha a cunt ( ia 1 ) inclu two fqunci to un both IM. 7. Concluion Thi pap ha icu a two fiv-pha i-connct IM iv which i uppli by a 3 lvl fiv-pha SPWM VSI. An SM contoll i u that i capabl of contolling th tato flux an toqu of ach moto paatly. Th popo contoll in thi pap i capabl to tack th p fnc an th flux fnc in pit of moto itanc mimatching. In aition, th tanint ynamic of th moto tato flux an toqu i pcily gulat by th ign of SM contoll. Moov an algoithm i uggt to pouc α-β an x-y voltag componnt with a 3 lvl SVPWM VSI. Th ffctivn an valiity of th popo contol mtho i vifi by imulation ult. REFERENCES [1] H. A. Toliyat, Analyi an imulation of fiv-pha vaiabl-p inuction moto iv un aymmtical connction, IEEE Tanaction on Pow Elctonic, Vol. 13, No. 4, pp. 748 756, July 1998. [2] D. Dujic, G. Gani, M. Jon, an E. Lvi, A pac vcto PWM chm fo multifquncy output voltag gnation with multipha voltag-ouc invt, IEEE Tanaction on Inutial Elctonic, Vol. 55, No. 5, pp. 1943 1955, May 28. [3] E. Lvi, D. Dujic, M. Jon, an G. Gani, Analytical tmination of DC-Bu utilization limit in multipha VSI uppli AC iv, IEEE Tanaction on Engy Convion, Vol. 23 No. 2, pp. 433 443, Jun 28. [4] V. Olchuk, F. Pofumo, an A. Tnconi, Analyi of opation of ymmtical ual th-pha convt with hybi chm of ynchoni PWM, Intnational Rviw of Elctical Engining (IREE), Vol. 2, No. 6, Dcmb 27. [5] M. J. Duan, F. Sala, an M. R. Aahal, Bifucation analyi of fiv-pha inuction moto iv with thi hamonic injction, IEEE Tanaction on Inutial Elctonic, Vol. 55, No. 5, pp. 26 214, May 28. [6] R. Kianinzha, B. Nahi-Mobaakh, L. Baghli, F. Btin, an G.-A. Capolino, Moling an contol of ix-pha ymmtical inuction machin un fault conition u to opn pha, IEEE Tanaction on Inutial Elctonic, Vol. 55, No. 5, pp. 1966 1977, May 28. [7] N. R. Abjai, J. Soltani, an J. Akai, Nonlina liing-mo contol of a multi-moto wb wining ytm without tnion no, IEEE Intnational Confnc on Inutial Tchnology (ICIT 28), pp. 1 6, Apil 21 24, 28. [8] E. Lvi, S. N. Vukoavic, an M. Jon, Vcto contol chm fo i-connct ix-pha two-moto iv ytm, IEE Pocing-Elctonic Pow Application, Vol. 152, No. 2, pp. 226 238, Mach 25. [9] M. Jon, S. N. Vukoavic, E. Lvi, an A. Iqbal, A ix-pha i-connct two-moto iv with coupl- ynamic contol, IEEE Tanaction on Inutial Application, Vol. 41, No. 4, pp. 156 166, July Augut 25. [1] K. K. Mohapata, R. S. Kanchan, M. R. Baiju, P. N. Tkwani, an K. Gopakuma, Inpnnt fil-oint contol of two plit-pha inuction moto fom a ingl ix-pha invt, IEEE Tanaction on Inutial Elctonic, Vol. 52, No. 5, pp. 1372 1382, Octob 25. [11] M. Jon, S. N. Vukoavic, an E. Lvi, Paalll-connct multipha multiiv ytm with ingl invt upply, IEEE Tanaction on Inutial Elctonic, Vol. 56, No. 6, pp. 247 257, Jun 29. [12] E. Lvi, M. Jon, S. N. Vukoavic, an H. A. Toliyat, A fiv-pha two-machin vcto contoll inuction moto iv uppli fom a ingl invt, Jounal, Vol. 14, No. 3, pp. 38 48, Augut 24. [13] K. K. Mohapata, M. R. Baiju, an K. Gopakuma, Inpnnt p contol of two ix-pha inuction moto uing a ingl ix-pha invt, Jounal, Vol. 14, No. 3, pp. 49 62, Jun Augut 24. [14] M. Jon, E. Lvi, an A. lqbal, A fiv-pha iconnct two-moto iv with cunt contol in th otating fnc, 35th Annual IEEE Pow Elctonic Spcialit Confnc, Aochn, Gmany, pp. 3278 3284, 24. [15] J. W. Klly, E. G. Stanga, an J. M. Mill, Multipha pac vcto pul with moulation, IEEE Tanaction on Engy Convion, Vol. 18, No. 2, pp. 259 264, Jun 23. [16] J. W. Klly, E. G. Stanga, an J. M. Mill, Multipha invt analyi, Pocing of IEEE Intnational Elctic Machin Div Confnc (IEMDC), pp. 147 155, 21. [17] H.-M. Ryu, J.-H. Kim, an S.-K. Sul, Analyi of multipha pac vcto pul-with moulation ba on multipl -q pac concpt, IEEE Tanaction on Pow Elctonic, Vol. 2, No. 6, pp. 1364 1371, Novmb 25. Copyight 21 SciR
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