Coupling series two five-phase asynchronous machine powered by a single voltage inverter

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1 Leonaro Journal of Scences SS ssue 7, July-December p 9- Couplng seres wo fve-phase asynchronous machne powere by a sngle volage nverer Samr ABBAR *, Karm FELLAH, Foua BEKHORS Elecrcal Engneerng Deparmen, CEPS Laboraory, Djllal Labes Unversy, S Bel Abbes,, Algera E-mals: amrs8@yahoofr; mkfellah@yahoofr; mohame-fouabenkhors@unv-nanesfr Absrac Mul-phase machnes are presen n he fels of marne, ral racon, perochemcal nusry, avaon, auomove One of he benefs of hese kngs of machnes s he fac ha s possble o combne several seres machnes an orer nepenenly of he oher Ths arcle ams o sprea an equally mporan role n he suy of mul-sage machnes The suy leas o he rve sysem of machnes, her couplng moes, her feeng moe whch s que fferen an a prevew on her prncple of conrol Keywors Mul-phase conrol; Volage nverer; Asynchronous; nepenen conrol nroucon Snce he esgn of he frs mul-phase nucon machne (fve-phase n 969 [,] he neres of mulphase rve sysems powere by converers has rsen sharply [3-] An mporan propery of hs machne, s ha he new se of equaons conans only wo componens (, β; saonary -β axs Clark ransformaon, whch leas o couplng beween he saor an roor componens as he oher hree (x, y, o; zero sequence componens an he non-sequenal componens are no couple The suaon remans he same afer hp://ljsacaemcrecorg/ 9

2 Couplng seres wo fve-phase asynchronous machne powere by a sngle volage nverer Samr ABBAR*, Karm FELLAH, Foua BEKHORS applcaon of he roaonal ransformaon Ths ransformaon fallows a vecor conrol of he orque an flux wh he wo Componens only of he axs saor curren (, q; synchronous -q axs Park ransformaon, he oher wo componens; he axs (x, y s regare as egrees of aonal freeom Therefore, s possble o connec he saor wnngs of he wo machnes so ha fve-phase machne sees axs curren componen (, q an he oher axs of he curren componens (x, y an vce versa, woul become possble o compleely an nepenenly conrol he spee (poson, orque of he wo machnes wh he power of hese machnes s mae from a sngle volage nverer n smple erms, s possble o perform vecor conrol of hese wo machnes fe by a sngle volage converer prove ha he saor wnngs of boh machnes are connece n seres an an approprae ransposon of he phases s carre ou, so ha he fve curren proucng he roang magnec force n he frs machne, o no prouce roang magnec force n he secon [6-9] Ths suy leas o he rve sysem of he machnes, her moe of couplng, her feeng moe whch s que fferen an an overvew of her prncple of conrol Two-moor rve wh wo quas fve-phase For machne n-phases, he spaal splacemen beween wo consecuve phases s equal o / (where phase s number [ ] ( ( sn sn ( cos cos ( sn sn cos cos T ( where T Concora ransfer marx; phase s number; 3 r The ecouplng ransformaon marx for such a fve-phase machne s gven wh (: 3

3 Leonaro Journal of Scences SS ssue 7, July-December p 9- [ T ] cos( cos( cos( 8 cos( 8 6 cos( 6 cos( 8 cos( 8 6 cos( 6 The unerlyng ea of he concep of saor wnng seres connecon s ha flux/orque proucng currens of one machne mus be non-flux/orque proucng currens for all he oher machnes whn he rve sysem [;8] The possbly of achevng hs for a confguraon conssng of wo machnes of he srucure shown n Fgure s nvesgae nex s assume ha boh machnes operae n seay sae an ha he requre phase currens for flux/orque proucon are gven wh snusoal funcons ( / ( Fgure Asymmercal fve-phase machne s saor wnng To make he suy of hs moel easer, he choce of noe (A, B, C, D, an E nces volages a he oupu of he nverer, an (a, b, c,, an e he nces of volages an currens of he wo machnes (he nex '' means he frs machne an he nex '', he secon 3

4 Couplng seres wo fve-phase asynchronous machne powere by a sngle volage nverer Samr ABBAR*, Karm FELLAH, Foua BEKHORS 3 3 e E D c C b B a A (3 where a, b, c, an e : phase curren of he frs machne;, : Frs an secon machne source volage angular frequency, Le he nverer curren references are creae accorng o: 3 3 C e E B c D b A a ( where a, b, c, an e : phase curren of he secon machne an le he curren conrol be eal, so ha he nverer oupu currens may be aken as equal o he nverer curren references of equaon ( The nverer phase currens are encally equal o he phase currens flowng hrough machne [9] However, for he secon machne, ue o he phase ransposon nrouce n equaon (, he followng hols rue: a A * b D * c B * ( E * e C * where * reference value for conroller Two-moor rve wh a quas-fve-phase machne an a wo-phase machne s neresng o noe ha he phase roaon requre recly follows he Concora ecouplng sa ransfer marx s sep: The frs wo phases of he wo machnes are recly n seres, necessary for he 3

5 Leonaro Journal of Scences SS ssue 7, July-December p 9- mplemenaon phase s zero (whch follows he frs column of he ransfer marx Concora n sep: he phase "" (b of he frs machne s connece o he sage "3" (c of he secon phase roaon (secon column of he ransfer marx Concora 3 r sep: (c of he frs machne s connece o he "" phase (e of he secon, an he phase roaon s ( (hr column of he ransfer marx Concora h sep: ( of he frs machne s connece o he "7" phase of he secon bu, snce he machne s fve phase ajusmen has aken place an he phase '' of he frs wll be logge o he phase "" (7- (b of he secon, an he phase roaon Concora ransfer marx Ths follows he fourh column h sep: phase '' (e of he frs machne s connece o he "" phase ( of he secon, whch correspons o a phase roaon equal o ( From hs basc conseraon, s possble o consruc a connecon able as shown n Table The schema machng hese connecons s n Fgure Table Connecvy marx for he fve-phase case A B C D E M phase s 3 M phase s 3 M & M nexes correspon o he frs an secon respecvely Machne To verfy hs concep, eal snusoal currens were use Suppose ha he frs machne has prove a couple an a gven flow rae when powere by snusoal currens eals of effecve angular frequency equal o Smlarly, he secon machne wh he snusoal curren of angular frequency equal o [,-] Accorng o he connecon agram shown n Fgure, curren source smulaneously correspon o he phase currens of he frs machne (see Table 33

6 Couplng seres wo fve-phase asynchronous machne powere by a sngle volage nverer Samr ABBAR*, Karm FELLAH, Foua BEKHORS Table The wo-phase machne saor currens Curren componens M M β cos( cos( X Y cos( cos( O s Machne a n Machne a b b Source c c e e Fgure Connecvy of wo fve-phase machnes Couplng Seres Two fve-phase Asynchronous Machne Powere by a Sngle Volage nverer A mul-phase machne avanage s beng able o combne several machnes an for he seres nepenenly of each oher [3] Afer he couplng of wo machnes, powere by a suable nverer (Fg, uner hese conons, s possble o reconsruc he phase volages of he nverer, hs s menone n equaon (6 [6,] va vas vas vb vbs vcs vc vcs ves vd vs vbs (6 ν E ν es ν s where ν A, ν B, ν C, ν D, ν E volages o he oupu of he nverer; ν as, ν bs, ν cs, ν s, ν es : saor volages of he frs machne; ν as, ν bs, ν cs, ν s, ν es : saor volages of he secon machne 3

7 Leonaro Journal of Scences SS ssue 7, July-December p 9- Afer applyng he ransformaon o he Concora ransfer marx (equaon (, he oban componens (, β, (x, y an zero-sequence ha are compleely ecouple (equaon 7 [ v ] [ R ][ ] [ L ] [ ] L [ P( θ ][ ] βs s βs xys s βs vos Rs os Los cs [ v ] [ R ][ ] [ L ] [ ] L [ P( θ ][ ] cs s βs xys m m βr βr where: L cs an L os are respecvely he cyclc an he homopolar nucance These componens (,β an (x, y s compleely nepenen, possble o apply wo fferen frequences o each of he wo roaons subses: s, beng he angular frequency of he saor magnues of he frs machne s ha of he secon [], such ha: (7 θs θ θr θs θ θr s r s r (8 where θ: Elecrcal angle beween he frs phase o he frs phase saor an he roor vs Rs s Lcs s qs Lcs s slm qr Lm r vqs Rs qs Lcs s s Lcs qs s Lm r Lm qr v ps Rs ps Lcs s ps Lcs ps s Lm qr Lm r vzs Rs zs Lcs s ps Lcs zs s Lm r Lm qr vos Rs Los (9 Moel for smulaon Ths moel shows ha of fve-phase Machne scusse n preceen paragraph The fference les n he value ressors, nucors, an frequency of roaons [8] Are he saor flux of he frs an he secon machne respecvely (equaon gven n & : ψ s Lcs s Lm r ψ qs Lcs qs Lm qr ψ ps Lcs ps Lm r ψ zs Lcs zs Lm qr ( 3

8 Couplng seres wo fve-phase asynchronous machne powere by a sngle volage nverer Samr ABBAR*, Karm FELLAH, Foua BEKHORS vs Rs s s ψ qs ψ s vqs Rs qs s ψ s ψ qs v ps Rs ps s ψ ps ψ ps vzs Rs zs s ψ ps ψ zs vos Rs Lo ( Gven he uraon of sar-up of he wo machnes, he smulaon s one as follows: he wo machnes are fe a me, empy o be followe by he applcaon of a loa of m 9s on he frs an 3 nm a 8s on he Fgure 3 Fgure 3 Dagram of couplng smulaon seres of fve-phase wo asynchronous machnes Resuls an scusson Fgure sar smulaon resuls of fve-phase wo asynchronous machnes couple n seres an powere by a sngle volage nverer Fgure, show he resuls of he smulaon of 36

9 Leonaro Journal of Scences SS ssue 7, July-December p 9- he loa sarng process asynchronous moors powere by a volage nverer, followe by applyng a loa of m a me 9s on he frs an 3m he secon me n 8s Cem M Cem M Cem M 3 Cem M 3 Torque (m 3 m Torque ( - 3 Tme (s Tme (s a Torque b Zoom n 3 3 wm M Spee(rpmwmM 3 ( Tme (s c Spee Fgure Seres wo fve-phase asynchronous machne powere by a sngle volage nverer smulaon resuls The ea here s o show ha s possble o couple n seres an conrolle nepenenly of he oher wo machnes, whch are powere by a sngle nverer [9,] Elecromagnec orques of boh machnes s compleely nepenen of one anoher Each machne behaves as f was powere by an nepenen source an works alone Afer applyng a loa on he frs machne, oes no surb he secon whch was sll n ranson Conversely he applcaon of a loa on he secon machne oes no surb he 37

10 Couplng seres wo fve-phase asynchronous machne powere by a sngle volage nverer Samr ABBAR*, Karm FELLAH, Foua BEKHORS operaon of he frs, whch was seay [,8] Curren (A Tme (s Tme (s Saor phase a curren e Zoom n 8 6 Volage (V Tme (s f nverer volage ou pu Fgure (connuaon A zoom shows he elecromagnec orque low orque pulsaons a he frequency of KHz As has been pone a he moel level, he essenal fference beween he wo machnes s n he power supply The curren an volage curves clearly show he sum of wo snusos of fferen amplue an frequency [9,-] Ths work allowe us o ge a clear ea alreay operang an one of he properes of fve-phase asynchronous machne n general Ths prelmnary work wll enable us o suy power of hs machne wh a non-perfec source, o suy he consequences of he choce of a parcular nverer [] However, he resuls presene solely from calculaons an smulaons, s 38

11 Leonaro Journal of Scences SS ssue 7, July-December p 9- mporan o complee hs suy by he praccal mplemenaon of hs suy n hs manuscrp, exensve smulaon sues Couplng seres wo fve-phase asynchronous machne powere by a sngle volage nverer were presene Moellng an smulaon of wo nepenen of he wo machnes was scusse The resuls obane emonsrae he possbly for nepenen conrol of wo machnes pursung a sngle nverer There ecouplng he sensvy of he algorhm o change n he me consan of he machne has been analyse Appenx The machne s consere a four-pole machne whose smulaon parameers are as follows: Componens Frs Machne M Secon Machne M Vs: volage phase V 3 V F: frequency Hz 6 Hz Rs: he saor ressance Ω Ω Rr:he roor ressance 63 Ω 63 Ω J: momen nera 3 3 coeffcen of vscous frcon *-3 *-3 Saor cyclc -nucance 6 mh 6 mh Dsperson -coeffcen References Wllamson S Pulsang Torque an Losses n Mulphase nucon Machnes, nusry Applcaons Conference, Thry-Sxh AS Annual Meeng Conference Recor of he EEE,, p -6 Sngh G K, Mulphase nucon Machne Drve Research, Elecrc Power Sysems Research,, 6(, p Bhak M J, Mmukul C C, Two-moor sngle-nverer fel-orene nucon machne rve ynamc performance, Sahana,, 39(, p 39-7 Tolya H A, Harer H, Prelmnary nvesgaon of nverer fe Fve phase nucon Moor, Proc EEE, 969, 6(6, p Jones M, Vukosavc S, Lev E, nepenen vecor conrol of a sx-phase seresconnece wo moor rve, Proceeng of he Secon nernaonal Conference on Power 39

12 Couplng seres wo fve-phase asynchronous machne powere by a sngle volage nverer Samr ABBAR*, Karm FELLAH, Foua BEKHORS Elecroncs, Machnes an Drves, Lverpool John Moores Unversy, Enburgh, UK;,, p Lev E, Jones M, Vukosavc S, Tolya H A, A fve phase wo machne vecor conrolle nucon moor rve supple a sngle nverer, h European Conf on Power Elecroncs an Applcaon, EPE 3 Toulouse, CD-ROM, Paper o 7 Tolya H A, Xu H, A ovel Drec Torque (DTC Meho for Fve-Phase nucon Machnes, Proc APEC Conf,,, p Lev E, Jones M, Vukosavc S, Even phase mul moor vecor conrolle rve wh sngle nverer supply an seres connecon of saor wnngs, EEE Proc Elecr Appl, 3,, p Jones M, Lev E, Vukosavc S, Tolya H A, nepenen vecor conrol of sevenphase hree-moor Drve Sysem supple from a sngle Volage Source nverer, Proc EEE Power Elec Spec Conf PESC, 3, Acapulco, Mexco, pp 86-87, Faha M, Charpener J F, Semal E, An Ecen Conrol of a Seres Connece Two- Synchronous Moor -Phase wh on Snusoal EMF Supple by a Sngle-leg VS: Expermenal an Theorecal nvesgaons, Elecrc Power Sysems Research,, 9, p -9 Abja R, Solan J A, Askar J, Markaeh, G R A, Three-Level Fve-Phase Space Vecor PWM nverer for a Two Fve-Phase Seres Connece nucon Machne Drve, Journal of Energy an Power Engneerng,, p -7 Lev E, Jones M, Vukosavc S, qbal A, Tolya H A, Moelng, Conrol, an Expermenal nvesgaon of a Fve-Phase Seres-Connece Two-Moor Drve Wh Sngle nverer Supply, nusral Elecroncs, EEE Transacons, 7, (3, p Bouscayrol A, Delarue P, Fornel B D, Francos B, Hauer J P, Meboy-Tabar F, Monmasson E, Perzak-Dava M, Razk H, Semal E, Benkhors M F, Conrol srucures for mul-machne mul-converer sysems wh several couplngs by crera mergng, European Conference on Power Elecroncs an Applcaons, Dresen,, 9pp