Fault-tolerant Operation of Six-phase Energy Conversion Systems with Parallel Machine-side Converters

Faul - ole an Ope a ion o Six-phase Ene gy Con e sion Sys ems wi h Pa allel Machine-side Con e e s I. Gonzalez, M. J. Du an, H. S. Che, E. Le i, Fellow, IEEE, M. Be mudez, F. Ba e o, Senio Membe , IEEE Abs ac  The aul ole ance p o ided by mul iphase machines is one o he mos a ac i e ea u es o indus y applica ions whe e a high deg ee o eliabili y is equi ed. Aiming o ake ad an age o such pos - aul ope a ing capabili y, some newly designed ull-powe ene gy con e sion sys ems a e selec ing machines wi h mo e han h ee phases. Al hough he use o pa allel con e e s is usual in high-powe h ee-phase elec ical d i es, he aul ole ance o mul iphase machines has been mainly conside ed wi h single supply om a mul iphase con e e . This wo k add esses he aul - ole an capabili y o six-phase ene gy con e sion sys ems supplied wi h pa allel con e e s, de i ing he cu en e e ences and con ol s a egy ha need o be u ilized o maximize o que/powe p oduc ion. Expe imen al esul s show ha i is possible o inc ease he pos - aul a ing o he sys em i some deg ee o imbalance in he cu en sha ing be ween he wo se s o h ee-phase windings is pe mi ed. Index Te ms Mul iphase ene gy con e sion sys ems, aul ole ance, pa allel con e e s, ield o ien ed con ol. I. INTRODUCTION ne gy con e sion sys ems wi h ull-powe back- o-back (BTB) con e e s ha e ecen ly gained popula i y due o hei capabili y o handle bidi ec ional powe low wi h a good con ollabili y [1]. Compa ed o pa ial-powe opologies using doubly- ed induc ion gene a o s (DFIGS), he highe deg ee o con ol p o ided by ull-powe con igu a ions is cu en ly app ecia ed in wind ene gy indus y due o he igh e low- ol age ide h ough (LVRT) Manusc ip ecei ed Ma ch 9, 2015; e ised May 4, 2015; accep ed June 30, 2015. Copy igh (c) 2015 IEEE. Pe sonal use o his ma e ial is pe mi ed. Howe e , pe mission o use his ma e ial o any o he pu poses mus be ob ained om he IEEE by sending a eques o pubs- pe [email protected] g. This wo k was suppo ed by he Spanish Minis y o Science and Inno a ion unde P ojec s ENE2014-52536-C2-1-R and DPI2013-44278-R, and he Jun a de Andalucía unde P ojec P11-TEP-7555. I. Gonzalez-P ie o, M. Be mudez and F. Ba e o a e wi h he Depa men o Elec onic Enginee ing a he Uni e si y o Se ille, Spain, e-mail: [email p o ec ed] mbe mude[email p o ec ed] ba e [email p o ec ed]. M.J. Du an is wi h he Depa men o Elec ical Enginee ing a he Uni e si y o Malaga, Spain, e-mail: mjd[email p o ec ed]s. H. S. Che is wi h he UMPEDAC, Uni e si y o Malaya, Malaya, e- mail: [email protected] E. Le i is wi h he School o Enginee ing, Technology and Ma i ime Ope a ions, in he Li e pool John Moo es, Spain, e-mail: e.le [email p o ec ed] equi emen s o di e en g id-codes [2-3]. In addi ion, he BTB a angemen allows he con ol o bo h he powe deli e ed o he machine and o he g id, and his can be use ul in ac ion applica ions wi h egene a i e b aking. In his la e case he machine ope a es as a mo o bu he BTB opology allows he sys em o ans e he decele a ing kine ic ene gy in o he g id. Rega dless o he applica ion, he use o ull-powe BTB sys ems wi h an in e media e dc-link decouples he machine and g id sides, hus allowing he use o mul iphase machines connec ed o h ee-phase g ids [4]. Indus ial examples o mul iphase sys ems wi h ull-powe BTB con e e s a e he 1.1 MW nine-phase pe manen magne (PM) mo o d i e used in ul a-high speed ele a o s [5] (mo o ing) and he 5 MW wel e-phase PM synch onous gene a o used in wind ene gy u bines [6] (gene a ion). The combina ion o di e en numbe o phases and con e e a angemen s esul s in mul iple mul iphase opologies, including he use o independen BTB h ee-phase modules [5-6], he use o pa allel h ee-phase con e e s [7], and he se ies-connec ion o machine-side con e e s [8-11]. The li e a u e on mul iphase machines and d i es poin s ou di e en ad an ages o e s anda d h ee-phase machines, bu maybe he mos con incing one o indus y is he capabili y o p o ide aul ole ance wi h no ex a ha dwa e [12-13]. Among he di e en ypes o aul s ha may occu in a mul iphase d i e, he open-ci cui aul s (phase and line) ha e been he mos widely s udied cases because simple so wa e econ igu a ion su ices o ob ain sa is ac o y pos - aul ope a ion. When an n-phase machine is s a connec ed and supplied by an n-phase con e e , he open-ci cui aul implies ha he cu en can no longe low h ough he aul ed phase and he machine e ec i ely has only n-1 phases loca ed in an asymme ical manne . In such si ua ion, he aul needs o be i s ly de ec ed [14-15] and hen se e al modi ica ions need o be done o ob ain sa is ac o y pos - aul ope a ion, including he ecalcula ion o he cu en e e ences [16-17], he de a ing o he d i e [18] and he use o speci ic con ol schemes [19-25]. A g ea body o knowledge has been ecen ly epo ed in his ield o di e en numbe s o phases, using a ious machine and con e e ypes [12-25], bu conside ing single n-phase supply in all cases. Ne e heless, he use o single ol age sou ce con e e s (VSCs) in high-cu en applica ions is no possible due o he limi ed a ing o he IGBT-based con e e s. A good example can be ound in he wind ene gy indus y, whe e he use o low- ol age gene a o s in high powe u bines (10 MW) leads o he use o mul iple pa allel uni s [6]. Since edundan design is an e ec i e solu ion o main ain E pos - aul ope a ion and o hus educe he numbe o unexpec ed b eakdowns o sys ems, a ious powe con e e opologies equipped wi h edundan capabili y a e p oposed in [26]. The use o pa allel con e e s has been popula in h ee-phase ene gy con e sion sys ems [1], whe e he single swi ch aul no longe implies ha he cu en o he aul ed phase is ze o and all cu en s need o be de a ed o (m-1)/m o he a ed alue i m pa allel con e e s a e ope a ed. A simila concep can be ex ended o mul iphase d i es bu u he analysis is equi ed [27-28]. The edundancy ob ained using six-phase induc ion machines and pa allel con e e s has been ecen ly add essed in [28-29], whe e he enhancemen o he aul - ole an capabili y o ene gy con e sion sys em has been s udied by simula ions. This wo k ex ends he analysis and includes expe imen al esul s ha con i m he possibili y o educe he d i e de a ing by allowing an unequal cu en sha ing be ween he wo se s o h ee-phase windings. The main con ibu ions o his pape a e: i.The analysis o he aul ole ance o di e en mul iphase opologies ha include pa allel con e e s. P e ious in es iga ions on he aul ole ance o mul iphase machines ha e been ocused on opologies wi h single VSC supply, whe e con e e aul s lead o open- phase aul s. This implies in u n ha opologies wi h independen dc-links [5-6] need o disable he se o windings supplied by he aul y con e e , whe eas opologies wi h se ies connec ion o VSCs [8-11] canno con inue ope a ing. The si ua ion di e s in he scena io conside ed in his wo k because single con e e aul s only imply a educ ion in he pe -phase cu en . To ully exploi he aul - ole an capabili y o he sys em he machine needs o be asymme ically ope a ed, his being add essed o he i s ime in his pape . ii.The de i a ion o he x-y cu en e e ences o pe mi he unbalanced ope a ion o he d i e. Al hough he balanced ope a ion esul ing om he ope a ion wi h ze o x-y cu en s maximizes e iciency, he d i e de a ing in pos - aul si ua ion can only be educed by allowing he injec ion o non-ze o x-y cu en s in ce ain manne o comply wi h he pos - aul cu en es ic ions. This wo k de e mines he x-y cu en wa e o ms ha a e equi ed o maximize he achie able o que and also de ines he mos app op ia e e e ence ame o x-y cu en s o ease he design o he cu en con olle s. iii.The p oposal o an addi ional con olle o dynamically egula e he pos - aul cu en s. The asymme ical cu en sha ing be ween he mul iphase machine windings, discussed in i) and de e mined in ii), should be a iable in o de o maximize he pos - aul e iciency. In o he wo ds, he x-y cu en s should be injec ed only when needed o a oid he appea ance o ex a coppe losses. Fo his pu pose, his wo k sugges s he use o an addi ional con olle ha egula es he deg ee o imbalance and op imizes he cu en sha ing be ween windings. The pape is o ganized as ollows. Sec ion II desc ibes di e en mul iphase opologies ha use pa allel con e e s and analyzes hei aul - ole an capabili y. The pos - aul sys em capabili y is quan i ied in Sec ion III, whe e an imbalance in he cu en sha ing o he wo se s o h ee- phase windings is assumed. A new con olle o allow imbalance in he mul iphase sys em is p oposed in Sec ion IV, and he aul - ole an capabili y o he sys em is expe imen ally s udied in Sec ion V whe e s eady-s a e and dynamic es s a e shown o heal hy (p e- aul ) and pos - aul scena ios. Conclusions a e inally summa ized in he las sec ion. II. SIX-PHASE ENERGY CONVERSION SYSTEMS’ TOPOLOGIES Six-phase ene gy con e sion sys ems a e no mally based on asymme ical dual h ee-phase induc ion machines wi h wo isola ed neu als. This six-phase machine is a con inuous sys em which can be desc ibed by a se o di e en ial equa ions ha can be simpli ied in s a iona y coo dina es using he ec o space decomposi ion (VSD) app oach [30]. Using VSD, he o iginal six-dimensional space o he machine is ans o med in o h ee wo- dimensional o hogonal subspaces usually deno ed as 𝛼-𝛽, 𝑥-𝑦 and 0+-0−, whe e only 𝛼-𝛽 componen s con ibu e o he lux and o que p oduc ion. The 𝛼-𝛽 componen s ep esen he undamen al supply componen plus supply ha monics o he o de 12n±1 (n=1,2,3,…). The second s a o – o o pai o componen s ep esen s supply ha monics o he o de 6n±1 (𝑥-𝑦 subspace wi h n=1,3,5,…), while he ze o-sequence ha monic componen s can exis only i he e is a single neu al poin , in which case hey belong o he hi d pai o componen s. The asymme ical six-phase induc ion machine model, ob ained using VSD and he s anda d assump ions o he ac machine modeling (negligible i on losses, space ha monics, and magne ic sa u a ion), can be summa ized as ollows: 𝑣𝛼𝑠 =(𝑅𝑠+𝐿𝑠·𝑑 𝑑𝑡)·𝑖𝛼𝑠 +𝑀· 𝑑 𝑑𝑡𝑖𝛼𝑟 𝑣𝛽𝑠 =(𝑅𝑠+𝐿𝑠·𝑑 𝑑𝑡)·𝑖𝛽𝑠 +𝑀· 𝑑 𝑑𝑡𝑖𝛽𝑟 𝑣𝑥𝑠 =(𝑅𝑠+𝐿𝑙𝑠 ·𝑑 𝑑𝑡)·𝑖𝑥𝑠 𝑣𝑦𝑠 =(𝑅𝑠+𝐿𝑙𝑠 ·𝑑 𝑑𝑡)·𝑖𝑦𝑠 0=(𝑅𝑟+𝐿𝑟·𝑑 𝑑𝑡)𝑖𝛼𝑟 +𝜔𝑟·𝐿𝑟·𝑖𝛽𝑟 +𝑀· 𝑑 𝑑𝑡𝑖𝛼𝑠 +𝜔𝑟·𝑀·𝑖𝛽𝑠 0=(𝑅𝑟+𝐿𝑟·𝑑 𝑑𝑡)𝑖𝛽𝑟 −𝜔𝑟·𝐿𝑟·𝑖𝛼𝑟 +𝑀· 𝑑 𝑑𝑡𝑖𝛽𝑠 −𝜔𝑟·𝑀·𝑖𝛼𝑠 (1) whe e 𝐿𝑠=𝐿𝑙𝑠 +3·𝐿𝑚𝑠, 𝐿𝑟=𝐿𝑙𝑟 +3·𝐿𝑚𝑠, 𝑀=3·𝐿𝑚𝑠, 𝜔𝑟 is he o o elec ical speed (𝜔𝑟=𝑝·𝜔, 𝑝 being he pole pai numbe ), indices 𝑠 and 𝑟 deno e s a o and o o a iables and subsc ip s 𝑙 and 𝑚 indica e leakage and magne izing induc ance, espec i ely. Model (1) can be used o s udy he pe o mance o he machine du ing he heal hy and aul y ope a ion o he en i e sys em. In heal hy ope a ion (neglec ing swi ching and dead- ime ha monics) only 𝛼-𝛽 componen s will exis . The addi ional deg ees o eedom ha become a ailable o con ol pu poses du ing he aul y ope a ion a e ela ed o he 𝑥-𝑦 subspace componen s, p o ided ha he con e e opology allows o his unc ionali y. Di e en opologies o six-phase ene gy con e sion sys ems wi h aul - ole an capabili y ha e been ecen ly analyzed by he scien i ic communi y. The i s opology uses independen BTB h ee-phase modules, each one supplying a di e en se o h ee-phase windings (Fig. 1a). Such an op ion has been indus ially implemen ed bo h in ac ion and wind ene gy applica ions using nine-, wel e- and eigh een-phase machines supplied om h ee, ou and six BTB h ee-phase modules, espec i ely [5-6, 31]. This opology has a simple and modula s uc u e, and is a na u al ex ension o he s anda d h ee-phase case. F om he aul ole ance poin o iew, his a angemen allows pos - aul ope a ion in he e en o a aul ei he in he machine, con e e , o dc-link. The p ocedu e o ob ain pos - aul ope a ion unde single open-ci cui aul is simple: he whole h ee-phase BTB aul ed module is disconnec ed and he machine ope a es wi h he emaining heal hy modules. Fo he speci ic case o a six-phase machine his s a egy is e med ‘single VSC’, and i implies ha he pos - aul α-β cu en capabili y is 50% a e single open-ci cui aul [7], esul ing in only 25% o p e- aul o que/powe o gi en slip and equency. A second op ion is o cascade he machine-side con e e s and connec he dc-link o a g id-side con e e (Fig. 1b), which can be mul ile el in o de o educe he ol age s ess o he IGBTs and imp o e he cu en quali y [8]. The main idea is o main ain low ol age on he machine-side bu ele a e he dc-link ol age o allow medium ol age a he g id-side [9-11]. This in u n educes he cu en a ing and he cable size o he gi en powe , hence gi ing a po en ial o e all capi al cos educ ion. This cascaded opology is pa icula ly sui able o mul i-MW wind ene gy applica ions, because he gene a o s ypically ope a e a low- ol age while he medium ol age on he g id-side allows ans o me less gene a ion [9-10]. The machine-side may ha e a dc-link midpoin connec ion o he g id-side (S1 closed in Fig. 1b) o lea e he dc-link midpoin isola ed (S1 open in Fig. 1b). The la e case allows a wo-wi e connec ion be ween machine and g id sides, which can be ad an ageous in he case o o -sho e wind a ms [4], bu equi es an addi ional con olle o he x-y cu en s o egula e he midpoin ol age [9]. I he dc-link midpoin is no isola ed, he ol age balancing ask can be pe o med om he g id-side, al hough he x-y con olle in he machine side is s ill desi able o imp o e he sys em dynamics [32]. In spi e o he ad an age o he se ies connec ion o gene a e a medium ol age, om he poin o iew o he aul ole ance he pos - aul ope a ion is no longe possible wi h he cascaded s uc u e shown in Fig. 1b. The eason is ha he six-phase machine needs o be ope a ed using wo isola ed neu als ( o p e en he low o ze o-sequence cu en s) and he open-ci cui implies ha he aul ed se becomes single-phase. Al hough he heal hy se o h ee- phase windings can s ill deli e a ed cu en , i is no possible o balance he dc-link ol ages (Vdc1 and Vdc2 in Fig. 1b) anymo e because o he powe oscilla ions caused by he single-phase (i.e. aul ed) se . To summa ize, he use o independen BTB modules p o ides limi ed aul - ole an capabili y (25% o p e- aul o que/powe o gi en slip and equency), whe eas he se ies connec ion o he VSCs has no aul - ole an capabili y a all. This scena io can be imp o ed i he six- phase machine is ed by ou h ee-phase wo-le el ol age sou ce con e e s (VSCs). In o he wo ds, each se o h ee- phase windings is connec ed o wo h ee-phase VSCs ope a ing in pa allel (Fig. 1c). In e acing induc o s a e placed a he ou pu o each VSC o acili a e pa allel ope a ion o he wo VSCs. Fo he pu pose o he discussion ha ollows, i is assumed ha he se o windings 𝑎1𝑏1𝑐1 is connec ed o VSCs 𝐴1𝐵1𝐶1 and 𝐴1 ′𝐵1 ′𝐶1′ (collec i ely e med as VSCs1), and he se o windings 𝑎2𝑏2𝑐2 is connec ed o VSCs 𝐴2𝐵2𝐶2 and 𝐴2 ′𝐵2 ′𝐶2 ′ (collec i ely e med as VSCs2). Due o he pa allel connec ion, he phase cu en is sha ed be ween he wo VSCs, so ha each VSC only needs o be sized o ake hal o he a ed phase cu en . This educ ion in he pe VSC cu en is adequa e in low- ol age high-powe d i es, whe e he use o only wo VSCs o d i e he six-phase machine is no easible due o he limi ed a ings o IGBT-based VSCs ( ypically a ound 1 MW). In addi ion, he edundancy p o ided by he pa allel con e e s p o ides enhanced aul ole ance. Simila ly o he case o h ee-phase gene a o s, he pa allel con e e s (Fig. 1c) a e no ole an o winding open-phase aul s bu hey p o ide addi ional aul ole ance agains con e e aul s, which a e mo e common and unp edic able han machine aul s [4]. The dc-links o VSCs1 and VSCs2 can hen be kep independen (Fig. 1a) o be cascaded in se ies o o m an ele a ed dc-link ol age (Fig. 1b). In he la e case he opology esul s in a hyb id se ies-pa allel opology simila o he one sugges ed in [27-29] and he me i s a e in be ween ha o a pu e se ies and pu e pa allel connec ion: ele a ed dc-link ol age wi h some deg ee o aul ole ance. Addi ional ea u es o he opologies o Fig. 1a and Fig. 1b include lowe d /d o he common-mode ol age (CMV), which is known o be a main cause o leakage cu en s in high powe applica ions and lowe ol age a ing o he powe con e e s. In any case, he mos ele an cha ac e is ic, compa ed o he case o single VSC supply, is he imp o ed aul ole an capabili y, which is explo ed nex . III. POST-FAULT SYSTEM CAPABILITY The case o a single open-ci cui aul is analyzed he ea e , whe e one o he con e e legs is disconnec ed om he machine winding due o a aul . Wi hou lack o gene ali y, i is assumed u he on ha leg-𝐴1 ′ o he VSCs1 is aul ed. Due o he pa allel connec ion o he con e e s 𝐴1𝐵1𝐶1 and 𝐴1 ′𝐵1 ′𝐶1′, phase-𝑎1 is s ill ed wi h leg-𝐴1 o VSCs1, and consequen ly he cu en can s ill low. Howe e , maximum phase cu en 𝑖𝑎1 is now jus hal o he a ed phase cu en due o he limi a ion on he VSCs cu en a ing. In he s udy o he sys em capabili y i is i s assumed ha he oscilla ion o he dc-link ol age in no pe missible. To ensu e non-oscilla ing dc-link ol age, he ac i e powe lowing in each o he wo se s o h ee-phase windings should be cons an . Since he machine is no damaged by he aul , his implies ha he h ee-phase cu en s (ei he in VSCs1 o VSCs2) need o be balanced, i.e. wi h same ampli udes and 120 deg ees o phase shi . The cu en ampli udes o VSCs1 a e limi ed o hal he a ed alue due o he limi a ion on he aul ed phase, so he maximum s eady-s a e cu en s a e: 𝑖𝑎1 =0.5∙𝐼𝑛·cos(𝜔·𝑡) 𝑖𝑏1 =0.5∙𝐼𝑛·cos(𝜔·𝑡−120𝑜) (2) 𝑖𝑐1 =0.5∙𝐼𝑛·cos(𝜔·𝑡−240𝑜) whe e 𝜔 is he angula equency o s a o phase cu en s and 𝐼𝑛 is he peak alue o he a ed cu en . Fo he same eason o a oiding oscilla ing powe , he phase cu en s in winding 2 should also ha e he same magni ude and 120 deg ees o phase sepa a ion. Howe e , since he VSCs2 emain heal hy, he cu en in each winding can go up o he a ed alue. To ep esen a gene al case which acili a es u he s udy, he phase cu en s can be w i en as: 𝑖𝑎2 =𝑘·𝐼𝑛·cos(𝜔·𝑡−30𝑜) 𝑖𝑏2 =𝑘·𝐼𝑛·cos(𝜔·𝑡−150𝑜) (3) 𝑖𝑐2 =𝑘·𝐼𝑛·cos(𝜔·𝑡−270𝑜) whe e k ep esen s a cons an 0<𝑘<1, which can be op imized. By applying he powe -in a ian Cla ke decoupling ans o ma ion [6]: [𝑇]=1 √3 [ 1 −1/2 −1/2 √3/2 −√3/2 0 0 √3/2 −√3/2 1/2 1/2 −1 1 −1/2 −1/2 −√3/2 √3/2 0 0 −√3/2 √3/2 1/2 1/2 −1 ] (4) o he phase cu en s o (2)-(3), he s a o α-β and x-y cu en s can be ob ained: 𝑖𝛼𝑠 =√3·𝐼𝑛·(0.25+0.5·𝑘)·cos(𝜔·𝑡) (5) 𝑖𝛽𝑠 =√3∙𝐼𝑛∙(0.25+0.5∙𝑘)∙sin(𝜔·𝑡) 𝑖𝑥𝑠 =√3∙𝐼𝑛∙(0.25−0.5∙𝑘)∙cos(𝜔·𝑡) 𝑖𝑦𝑠 =√3∙𝐼𝑛∙(−0.25+0.5∙𝑘)∙sin(𝜔·𝑡) Ze o sequence cu en s a e omi ed om he analysis because he machine is con igu ed wi h wo isola ed neu al poin s ha p e en hei low. Since cu en s in bo h windings a e a se o balanced h ee-phase cu en s, x-y cu en s a e ela ed o α-β cu en s by he k ac o : 𝑖𝑥𝑠 =0.5−𝑘 0.5+𝑘𝑖𝛼𝑠 𝑖𝑦𝑠 =−0.5−𝑘 0.5+𝑘𝑖𝛽𝑠 (6) This means ha x-y cu en s ha e he same equency and phase ela ion as he α-β cu en s, wi h he di e ence only in hei ampli udes. The ela ionship de i ed in (6) is impo an o con ol pu poses and will be used in sec ion IV o build a con olle ha pe mi s he unbalanced ope a ion de ined in (2)-(3) wi h 𝑘>0.5. F om (5) i can be obse ed ha he α-β cu en magni ude inc eases wi h he alue o k. This implies ha inc easing k will inc ease he lux and o que, which in u n inc eases he o que/powe . Ne e heless, changing he alue o k will also cause he low o x-y cu en s, which in oduces addi ional coppe losses in he s a o windings and educes he ac ual o que/powe ob ained om he machine. No dis o ion o he ai gap lux and o que is expec ed by he appea ance o x-y cu en s because he six- phase induc ion gene a o is conside ed o ha e dis ibu ed windings and consequen ly spa ial ha monics a e negligible. Fig. 1: Mul iphase ene gy con e sion opologies: a) Independen BTB VSC modules, b) Se ies connec ion o VSCs and c) Pa allel connec ion o VSCs. Fo he speci ic case o k = 0.5, all phase cu en s o m a balanced se o asymme ical six-phase signals wi h ampli udes o 𝐼𝑛2 ⁄. Since he cu en s a e balanced, x-y cu en s a e ze o. E en hough his s a egy minimizes losses by ha ing ze o x-y cu en s, he maximum α-β cu en magni ude is only hal o he a ed alue, which diminishes he maximum achie able powe . In o de o analyze he s eady-s a e achie able powe o inc easing alues o k, he cu en s can be exp essed in complex o m as: 𝑖𝛼𝛽𝑠 =(𝑖𝛼𝑠 +𝑗∙𝑖𝛽𝑠) 𝑖𝑥𝑦𝑠 =(𝑖𝑥𝑠 +𝑗∙𝑖𝑦𝑠) (7) 𝑖𝛼𝛽𝑟 =(𝑖𝛼𝑟 +𝑗∙𝑖𝛽𝑟) Six-phase Machine G id VSCs 1 VSCs 2 dc-link 1 dc-link 2 G id Midpoin connec ion S1 3-ph Vdc1 Vdc2 Six-phase Machine VSCs 1 VSCs 2 a1b1 c1 a2b2c2 a1b1 c1 a2b2c2  VSCs 1 a1b1 c1a1b1 c1 A1B1 C1 A1’ B1’C1’ dc-link dc-link BTB module #1 BTB module #2 dc-link 1 dc-link 2 Vdc2 Vdc1 Idc1 Idc2 Idc1 Idc2 a) b) c) F om he equi alen ci cui o a squi el cage induc ion machine [28], i is possible o calcula e he powe balance and ob ain he ou pu powe (neglec ing mechanical and i on losses): 𝑃𝑜𝑢𝑡 =𝑃𝑖𝑛−𝑃Cu−𝛼𝛽𝑟 −𝑃Cu−𝛼𝛽𝑠 −𝑃Cu−𝑥𝑦𝑠 𝑃𝑜𝑢𝑡 =1−𝑠 𝑠∙𝑅𝑟∙|𝑖𝛼𝛽𝑟|2 𝑃Cu−𝛼𝛽𝑟 =𝑅𝑟∙|𝑖𝛼𝛽𝑟|2 (8) 𝑃Cu−𝛼𝛽𝑠 =𝑅𝑆∙|𝑖𝛼𝛽𝑠|2 𝑃Cu−𝑥𝑦𝑠 =𝑅𝑆∙|𝑖𝑥𝑦𝑠|2 whe e s a o and o o cu en s a e hose de ined in (7). 𝑃𝑖𝑛 is he powe p o ided by he p ime mo e (gene a o ) o he elec ical supply (mo o ). 𝑃𝑜𝑢𝑡 is he elec ical powe gene a ed by he sys em (gene a o ) o he mechanical powe on he sha (mo o ), and 𝑃𝐶𝑢 a e he coppe losses associa ed wi h he di e en cu en s lowing in he machine. F om he equi alen ci cui [28] and (5), he o o α-β o o cu en s can be exp essed as a unc ion o he pa ame e k: |𝑖𝛼𝛽𝑟|=√3∙𝑋𝑚·(0.5∙𝑘+0.25)∙𝐼𝑛 √(𝑋𝑚+𝑋𝑙𝑟)2+(𝑅𝑟 𝑠)2 (9) Pos - aul o que/powe wi h k = 0.5 is 25% (simila ly o he case wi h single VSC supply) o he p e- aul alue o a gi en slip and equency, as i could be expec ed because he α-β cu en s a e hal o he p e- aul alue and o que/powe inc eases wi h he squa e o he cu en (0.52=0.25). Simila ly, pos - aul o que/powe wi h k = 1 (maximum alue o k wi h pa allel VSC supply) is 56.25% o he p e- aul gene a ed powe . This is again expec ed since he α-β cu en s a e 75% o he p e- aul alue (0.752=0.5625). Consequen ly, o he same equency and slip, inc easing he alue o k ele a es he achie able o que/powe by 225% (56.25/25=2.25) compa ed o single VSC supply, i a p ope imbalance s a egy is designed o he pa allel connec ion o Fig. 1c. In a gene al case he slip and equency do no emain cons an and he achie able powe depends on he a io o he d-q e e ence cu en s (𝑖𝑑𝑠 𝑖𝑞𝑠 ⁄) [7,29]. In any case, he s eady s a e analysis shows ha he capabili y o inc ease he α-β cu en s esul s in a ele an gain o he pos - aul achie able o que/powe . All he analysis de eloped so a is common o he opologies o Fig. 1a and 1b because he cu en con ol is no a ec ed by he a angemen o he indi idual dc-links. Ne e heless, he imbalance ha esul s om ope a ing he d i e wi h 𝑘>0.5 has a di e en impac on he dc-link ol ages o independen and cascaded opologies. In he case o Fig. 1a he powe ex ac ed om dc-links 1 and 2 is di e en in pos - aul ope a ion (𝑃1≠𝑃2), bu he dc- cu en s can also be di e en (𝐼𝑑𝑐1≠𝐼𝑑𝑐2) allowing unbalanced cu en ope a ion wi h cons an dc-link ol ages (𝑉𝑑𝑐1=𝑉𝑑𝑐2). Ne e heless, in he case o he cascaded opology o Fig. 1b wi h no dc-link midpoin connec ion o he g id-side (S1 open in Fig. 1b), he dc-cu en s a e o ced o be equal (𝐼𝑑𝑐1=𝐼𝑑𝑐2) causing an imbalance in he dc-link ol ages: 𝑉𝑑𝑐1 𝑉𝑑𝑐2=𝐼𝑑𝑐2 𝐼𝑑𝑐1∙𝑃1 𝑃2 <1 (10) The deg ee o dc-link ol age imbalance depends on he cu en imbalance, de ined by k, and he machine impedances. Fu he de ails and an analy ical de i a ion can be ound in [29]. The ol age imbalance can be sol ed in he cascaded opology i he dc-link midpoin is connec ed o he g id side (S1 closed in Fig. 1b), because he es ic ion 𝐼𝑑𝑐1=𝐼𝑑𝑐2 does no apply in his case. IV. PROPOSED FAULT-TOLERANT CONTROLLER The gene al s uc u e o he p e- aul con ol s a egy is shown in Fig. 2. The scheme is an indi ec o o ield o ien ed con ol (IRFOC) wi h an ou e speed loop and inne cu en loops o d-q and x-y cu en s. Only ou phase cu en s (ia1, ib1, ia2 and ib2) need o be measu ed because he emaining phase cu en s can be ob ained om he condi ion o ha ing wo isola ed neu al poin s. Measu ed phase cu en s a e con e ed in o α-β cu en s using he Cla ke ans o ma ion [𝑇] o (4) and d-q cu en s a e ob ained om he o a ion o α-β cu en s in he o wa d (synch onous) di ec ion using he Pa k ans o ma ion: [𝐷]=[𝑐𝑜𝑠𝜃𝑠𝑠𝑖𝑛𝜃𝑠 −𝑠𝑖𝑛𝜃𝑠𝑐𝑜𝑠𝜃𝑠] (11) whe e he angle 𝜃𝑠 o he o a ing e e ence ame is ob ained om he measu ed speed 𝜔 and he es ima ed slip: 𝜃𝑠=∫( 𝑖𝑞𝑠 ∗ 𝑇𝑟𝑖𝑑𝑠 ∗+𝑃·𝜔)𝑑𝑡 (12) whe e P is he numbe o pole pai s and T he o o ime cons an . The machine is luxed by se ing a alue o 𝑖𝑑𝑠 ∗ ha co esponds o he a ed lux o he machine, while he o que is egula ed by he ou e speed con ol loop ha p o ides he e e ence o he quad a u e cu en 𝑖𝑞𝑠 ∗. The ou pu o he d-q cu en con olle s and he decoupling e ms eds and eqs [12] p o ide he e e ence ol ages 𝑣𝑑𝑠 ∗ and 𝑣𝑞𝑠 ∗. The second inne cu en con ol loop co esponds o he x-y cu en componen s. Con ol can be pe o med in he s a iona y e e ence ame using he Cla ke ans o ma ion [𝑇], in he synch onous ame using he Pa k ans o ma ion [𝐷], o in he an i-synch onous ame using he in e se o he Pa k ans o ma ion [𝐷]−1[33]: [𝐷]−1 =[𝑐𝑜𝑠𝜃𝑠−𝑠𝑖𝑛𝜃𝑠 𝑠𝑖𝑛𝜃𝑠𝑐𝑜𝑠𝜃𝑠] (13) In he p e- aul si ua ion, and conside ing he independen BTB opology o Fig. 1a, he x’-y’ cu en e e ences 𝑖𝑥𝑠 ′∗ and 𝑖𝑦𝑠 ′∗ a e ze o (Fig. 2a) and he x-y cu en con ol can s ill be pe o med in he s a iona y ame. Howe e , o he cascaded opology o Fig. 1b, 𝑖𝑦𝑠 ′∗ is ob ained om a dc-link ol age balancing con olle (Fig. 2b) ha ensu es simila 𝑉𝑑𝑐1 and 𝑉𝑑𝑐2 alues by p ope injec ion o y’-cu en o di e he ac i e powe om VSCs1 o VSCs2 o ice e sa [9]. In his case he x-y cu en componen s need o be o a ed in he an i-synch onous di ec ion [33] ( e med 𝑖𝑥𝑠 ′,𝑖𝑦𝑠 ′ in Fig. 2) o acili a e he con ol o he ac i e powe om he y-cu en con ol loop, he ou pu o he x-y cu en con olle s p o ides he x’-y’ ol age e e ences 𝑣𝑥𝑠 ′∗ and 𝑣𝑦𝑠 ′∗ in an i-synch onous e e ence ame, and he d-q and 𝑥′-𝑦′ e e ence ol ages a e ans o med in he in e se di ec ion using he Pa k ([𝐷] and [𝐷]−1) and Cla ke ([𝑇]) ma ices o p o ide he phase ol age e e ences (𝑣𝑎1 ∗𝑣𝑏1 ∗𝑣𝑐1 ∗𝑣𝑎2 ∗𝑣𝑏2 ∗𝑣𝑐2 ∗), which a e inpu s o he ca ie -based six-phase PWM [7,9] ha gene a es he swi ching signals o VSCs1 and VSCs2. The aim in pos - aul si ua ion is o d i e he machine ensu ing ha he cu en s in he aul ed VSCs1 a e below hal he a ed alue (𝑚𝑎𝑥|𝑖𝑎1𝑏1𝑐1|≤𝐼𝑛2 ⁄). This a ge can be achie ed by using a cons an deg ee o imbalance (e.g. se ing k=1 o all ope a ing poin s), bu his esul s in a subop imal solu ion because e iciency would be dec eased due o unnecessa y injec ion o x-y cu en s. In he low- o que egion o example, he limi o VSCs1 is no eached and consequen ly he machine can be symme ically ope a ed as in p e- aul si ua ion (Fig. 2a o Fig. 2b) wi h no need o se k > 1 and gene a e addi ional coppe losses. Howe e , when he o que is such ha he cu en s in VSCs1 each he pos - aul limi (𝑚𝑎𝑥|𝑖𝑎1𝑏1𝑐1|=𝐼𝑛2 ⁄) o k = 0.5, he sys em can no longe inc ease he gene a ed o que/powe unless some imbalance in he powe sha ing o VSCs1 and VSCs2 is pe mi ed. A his momen , he con olle o Fig. 2c is ac i a ed. This con olle is de ised o p o ide a iable x-y cu en injec ion (i.e. a iable k) o gene a e only he minimum deg ee o imbalance ha is equi ed o comply wi h cu en limi s. The designed s a egy in u n a o s he e icien ope a ion by minimizing coppe losses and also limi s he imbalance in he dc-link ol ages o cascaded opologies. The con olle ha egula es he imbalance is de eloped so ha when he modulus o he d-q cu en s is abo e hal he a ed alue, his excess is aken as he inpu o a p opo ional- in eg al (PI) an i-wind-up con olle whose ou pu is he k pa ame e . As he load o que inc eases, mo e q-cu en is equi ed and a highe alue o k is demanded. Acco ding o (6), he alue o k de e mines he amoun o x-y cu en s ha need o be injec ed, in o de o p o oke he equi ed imbalance o he sys em. Ne e heless, i is impo an no only o de e mine he op imal amoun o x-y cu en s bu also o selec a p ope e e ence ame o simpli y he con ol scheme. I he x-y con ol is pe o med in he s a iona y e e ence ame, as i is a common p ac ice in mul iphase d i es in heal hy ope a ion [34], i is necessa y o egula e sinusoidal cu en s and he limi ed bandwid h o PI con olle s will esul in a poo pe o mance [33]. Fo he pu pose o egula ing a ying x-y cu en s i has been ecen ly sugges ed o use dual PI o esonan con olle s [35-36]; his howe e complica es o some ex en he con olle s uc u e and uning. Fo una ely, in his case i is possible o pe o m he con ol in a e e ence ame whe e x-y cu en s become cons an . I can be no ed om (6) ha he equi ed x-cu en is p opo ional o α-cu en while he equi ed y-cu en is in e sely p opo ional o he β-cu en . This implies ha he α-β cu en ec o o a es in synch onous di ec ion whe eas he x-y cu en ec o o a es in an i-synch onous di ec ion. I ollows ha he o a ion o x-y cu en s in backwa ds di ec ion leads o x-y cu en s ( e med x-y in he o a ing e e ence ame) becoming p opo ional o d-q cu en s: 𝑖𝑥𝑠′=0.5−𝑘 0.5+𝑘𝑖𝑑𝑠 𝑖𝑦𝑠′=−0.5−𝑘 0.5+𝑘𝑖𝑞𝑠 (14) Consequen ly, he choice o his an i-synch onous e e ence ame p o ides cons an x’-y’ e e ences om (14) ha allow he use o s anda d PI con olle s. The use o esonan con olle s (PR), which is a common p ocedu e in aul - ole an con ol schemes wi h ime- a ying x-y cu en e e ences [7, 21, 36], is hen no necessa y. In he case o independen opologies o Fig. 1a he alue o k is sa u a ed o 1 o ensu e ha he maximum cu en o he heal hy VSCs2 co esponds o he a ed cu en , and he same applies o he cascaded opology wi h dc-link midpoin connec ion (S1 in Fig. 1b). When he dc-link midpoin o he cascaded opology is isola ed, he alue o k may be se o a lowe alue in he ange [0.5,1] depending on he pe missible dc-link ol age imbalance due o he a ings o he sys em (IGBTs and dc-link capaci o ol age capabili y) [29]. Fo he pu pose o analysis in his wo k i is assumed ha k can go up o 1, so ha he maximum deg ee o unbalance is ob ained. V. EXPERIMENTAL RESULTS To e alua e he p ope ies o he p oposed aul - ole an con olle , i has been implemen ed in a labo a o y-scale p o o ype. The es bench and expe imen al esul s a e p esen ed nex . A. Tes Bench A h ee-phase induc ion machine has been ewound o ob ain he asymme ical six-phase induc ion machine, shown wi hin he es bench illus a ion in Fig. 3. Pa ame e s o he cus om-buil six-phase machine ha e been de e mined using con en ional, AC- ime domain and s and-s ill es s wi h in e e supply [37-38], p o iding s a o and o o esis ances o 4.2 and 2 , s a o and o o leakage induc ances o 4.2 and 55 mH, and mu ual induc ance o 420 mH. The six-phase machine is d i en by con en ional h ee-phase powe con e e s om Semik on (SKS22F modules) ha co espond o VSCs1 and VSCs2 in Fig. 1. The con e e s a e connec ed o a dc powe supply sys em as in Fig. 1a and he con ol ac ions a e pe o med by a TI TMS320F28335 digi al signal p ocesso . The con ol uni is p og ammed h ough JTAG and TI p op ie a y so wa e Code Compose S udio. Cu en and speed measu emen s a e aken wi h ou hall-e ec LEM LAH 25-NP senso s and a GHM510296R/2500 digi al encode , espec i ely. The load o que is p o ided by a DC-machine whose a ma u e is connec ed o a a iable esis i e-induc i e load. The ull scheme o he es bench is depic ed in Fig. 3. B. Expe imen al Resul s Di e en expe imen al es s ha e been applied se ing a lux e e ence ids* = 1A, a a ed q-cu en o 8A, a swi ching equency o 10 kHz and dc-link ol ages o Vdc1 = Vdc2 = 300V. The h eshold o he ac i a ion o he con olle in Fig. 2c is se o idqs = 4A, which co esponds o hal he a ed alue. The ansi ion om p e- o pos - aul si ua ion is i s ly es ed o e i y he capabili y o he sys em o wi hs and an open-ci cui aul in leg-𝐴1 ′ o he VSCs1. The sys em is ope a ed in p e- aul si ua ion using he p oposed a) b) c) Fig. 2: Field o ien ed con ol (FOC)o he six-phase induc ion machine wi h synch onous d-q cu en con ol and an i-synch onous x-y cu en con ol (le ) and x’-y’ cu en e e ence calcula ion ( igh ) in a) P e- aul si ua ion wi h independen BTB opology (Fig.1a), b) P e- aul si ua ion wi h cascaded opology (Fig. 1b) and c) Pos - aul condi ion o ei he independen BTB o cascaded opologies. Applies o he case o pa alleled con e e s o each h ee-phase winding a he machine’s side. con ol scheme wi h 62.5% o he a ed cu en (iqs*= 5A) and a e e ence speed  * = 800 pm (Fig. 4a). Du ing p e- aul si ua ion (un il = 10s) he alue o k is 0.5 (Fig. 4b), indica ing an equal cu en sha ing in bo h se s o h ee- phase windings (a1,b1,c1 and a2,b2,c2). Acco ding o (6) his implies ha he x-y cu en e e ences a e se o ze o (𝑖𝑥𝑠 ′∗ = 𝑖𝑦𝑠 ′∗ = 0) as indica ed in he s a egy o Fig. 2a. To each he balanced ope a ion obse ed in Fig. 4e, x-y cu en s a e egula ed o ze o as i is shown in Fig. 4d. Consequen ly, he p e- aul phase cu en s o he wo se s o h ee-phase windings ha e equal ampli udes and a phase shi ing o 30º. The d-q cu en s, esponsible o he o que p oduc ion, a e success ully con olled o hei e e ence alues (Fig. 4c) and his in u n implies ha he machine speed is egula ed o he e e ence speed (Fig. 4a). Now, when he aul occu s ( = 10s), he x’-y’ e e ences a e no longe se o ze o bu ob ained om he con olle shown in Fig. 2c. Since he modulus o he d-q cu en s is o e he h eshold alue (idqs = 4A), k is quickly inc eased by he con olle , as i can be obse ed in Fig. 4b. The new alue o k implies ha x’-y’ e e ences a e no longe se o ze o bu o alues ha a e p opo ional o d-q cu en e e ences (14). In ou case, x’-y’ cu en s ack new non-ze o e e ences (Fig. 4d), o cing he imbalance in he phase cu en s depic ed in Fig. 4e. No ice ha he an i-synch onous e e ence ame selec ed o he x’-y’ componen s esul s in cons an cu en e e ence alues in he pos - aul si ua ion, a o ing he acking p ocess using PI con olle s. No ice also ha he unbalanced ope a ion in pos - aul si ua ion is cha ac e ized by a educ ion (an inc ease, espec i ely) in he phase cu en o he aul y (heal hy) h ee-phase winding (a1,b1,c1 and a2,b2,c2, espec i ely). Then, pos - aul d-q cu en s a e main ained a hei espec i e p e- aul e e ences (Fig. 4c) and he machine speed is egula ed o he e e ence alue (Fig. 4a). The ansi ion om p e- o pos - aul ope a ion is done wi hou any impac on he d-q cu en s o he mo o speed, his being one o he bene i s o he p oposed con olle ha egula es he unbalanced ope a ion be ween h ee-phase windings. The abili y o he en i e sys em o ope a e in pos - aul si ua ion is a second bene i o he p oposed unbalanced ope a ion con olle . In he case o balanced pos - aul ope a ion (k = 0.5), he maximum q-cu en is iqs* = 3.9A, indica ing an insu icien cu en p oduc ion o main ain he machine speed a e he aul . The conclusions ob ained om his es can be summa ized as ollows: i) he p oposed pos - aul x-y cu en e e ences esul in an unbalanced ope a ion ha allows p ese ing he pos aul cu en a ings (𝑚𝑎𝑥|𝑖𝑎1𝑏1𝑐1|≤𝐼𝑛2 ⁄ and 𝑚𝑎𝑥|𝑖𝑎2𝑏2𝑐2|≤𝐼𝑛), ii) he non-ze o x’-y’ cu en e e ences in pos - aul si ua ion a e acked by simple PI con olle s due o he selec ed an i- synch onous e e ence ame ha esul s in cons an x’-y’ cu en alues, iii) he ansi ion om he p e- o he pos - aul si ua ion is smoo hly pe o med, and i ) highe d-q cu en s a e ob ained using he unbalanced ope a ion, which allows main aining he p e- aul d i e pe o mance in a wide ange o ope a ion. Pos - aul ope a ion is analysed nex using he p oposed con olle in s eady and ansien s a es. Fig. 5 shows he p e- aul pe o mance wi h a change in he speed e e ence om 800 o 600 pm a = 14s. Since he load o que is p o ided by a dc-machine whose powe / o que is p opo ional o he squa e o he speed, he decele a ion implies a educ ion o he load o que. The q-cu en is dec eased acco dingly (Fig. 5b) and he mo o speed ollows i s e e ence alue (Fig. 5a). The d-cu en is sa is ac o ily Six-phase Machine VSCs 1 VSCs 2 ∗ PI Ou e speed con ol − ∗ PI Inne d-q cu en con ol ∗ ∗ ∗ ∗ ∗= PI Inne x-y cu en con ol ′∗ ′∗ ′∗ ′∗ ′ ′ ∗ ∗ − PWM ∗ ∗ ∗ ∗ ∗ ∗ PI ′∗ ′∗ = ′∗ = ′∗ = PI ∗0.5 Sa u a ion [0.5,1] k(4) ′∗ ′∗ ′∗ ′∗ ′∗ ′∗ +_++ +_ +_ +_++ +_ a) b) c) a) b) c) kep close o 1A du ing he whole es and he x’-y’ cu en s a e d i en o ze o by he p e- aul con olle . The same es is epea ed bu wi h a aul ins iga ed a = 10s (Fig. 6). The imbalance is hen egula ed by he con olle o Fig. 2c, causing an inc ease o k up o app oxima ely 0.82 a e he aul occu ence (Fig. 6d). Since he modulus o he d-q cu en s is educed du ing he ansien , he alue o k is also educed because a lowe deg ee o imbalance is equi ed a 600 pm. Compa ed o he heal hy case shown in Fig. 5, he mo o speed (Fig. 6a) and d-q cu en s (Fig. 6b) a e ound o be e y simila in p e- and pos - aul si ua ions. Howe e , he egula ion o k in pos - aul si ua ion esul s in non-ze o x’-y’ cu en s (Fig. 6c) ha gua an ee ha he d i e ope a es wi hin he cu en limi s in bo h VSCs1 and VSCs2. In he nex es he six-phase machine is d i en a 700 pm and is loaded by he dc-machine in p e- aul si ua ion (Fig. 7). A = 15s he dc-machine is disconnec ed esul ing in a sudden unloading o he six-phase induc ion mo o . The load emo al causes a sho o e shoo o he mo o speed (Fig. 7a), bu he quick dec ease o he q-cu en (Fig. 7b) decele a es he machine and e u ns he speed o he e e ence alue. The d-cu en is main ained a 1 A and he x’-y’ cu en s a e con olled o ze o (Fig. 7c), showing a good decoupling wi hou any o he sudden unloading. The same es is epea ed bu including he aul occu ence con ol a = 10s (Fig. 8). The es shows ha he alue o k is ini ially inc eased in pos - aul si ua ion because he modulus o he d-q cu en s is o e he h eshold se in he con olle (idqs = 4A). Ne e heless, when he machine is unloaded ( = 15s) he unbalanced ope a ion is no longe needed because he balanced ope a ion can gene a e he equi ed o que. A his poin he alue o k is quickly educed o 0.5 o ope a e in balanced mode (Fig. 7d). This is e lec ed in he x’-y’ cu en e e ences ha a e egula ed back o ze o when he machine is unloaded and he imbalance is no longe needed (Fig. 7c). I mus be emphasized he e ha he unbalanced ope a ion is only desi able when he balanced ope a ion is no easible, because he non-ze o x’-y’ cu en s ha a e equi ed o p o oke he imbalance esul in highe coppe losses. Figs. 4 and 8 show ha he pos - aul unbalanced ope a ion can be ob ained bo h in he s eady-s a e and ansien si ua ions. The con olle o Fig. 2c egula es he deg ee o imbalance k o allow balanced ope a ion when possible (low- o que egion) and g adually inc eases he unequal cu en sha ing when he addi ional o que is equi ed (up o he limi se by he a ed cu en a k=1). VI. CONCLUSION This wo k has analyzed di e en opologies o ull-powe mul iphase ene gy con e sion sys em using pa allel con e e supply. The aul - ole an capabili y in unbalanced mode o ope a ion has been add essed o he i s ime in his wo k, de i ing he pos - aul cu en e e ences and p oposing a new con olle ha keeps machine cu en s wi hin pos - aul a ings. The main conclusion om his s udy is ha i is possible o ob ain addi ional o que/powe in six-phase ene gy con e sion sys ems wi h pa allel con e e s i some deg ee o imbalance in he cu en sha ing be ween he wo se s o h ee-phase windings is allowed. This cu en sha ing can be egula ed by p ope con ol o he x-y cu en s, inc easing he α-β cu en by 50% ha esul s in 225% addi ional o que/powe in he elec ical d i e o a gi en slip and equency The egula ion o hese non-ze o x-y cu en s can be pe o med by simple PI con olle s in a e e ence ame wi h an an i-synch onous o a ion ha e en ually esul s in cons an alues o he x’-y’ e e ences. The con olle ha egula es he deg ee o imbalance pe mi s balanced ope a ion in he low- o que egion and a iable deg ee o imbalance when he o que is inc eased, hus achie ing minimum coppe losses and low dc-link ol age imbalance in cascaded opologies. The imbalance o ced by he sugges ed con olle se s an uppe limi o ensu e ha he cu en s a e wi hin accep able alues in bo h he aul ed and heal hy se s o h ee-phase windings. The sugges ed aul - ole an mode o ope a ion is easible in opologies wi h independen BTB modules as well as in cascaded opologies wi h a se ies connec ion o he machine-side con e e s and a single g id-side con e e . REFERENCES [1] B. Wu, Y. Lang, N. Za ga i, and S. Kou o, “Powe con e sion and con ol o wind ene gy sys ems,” IEEE P ess - John Wiley and Sons, Hoboken, NJ, 2011. [2] M. Lise e, R. Cá denas, M. Molinas, and J. Rod íguez, “O e iew o mul i-MW wind u bines and wind pa ks,” IEEE T ans. on Indus ial Elec onics, ol. 58, no. 4, pp. 1081–1095, 2011. [3] F. Blaabje g and K. Ma, “Fu u e on powe elec onics o wind u bine sys ems,“ IEEE Jou nal o Eme ging and Selec ed Topics in Powe Elec onics, ol. 1, no. 3, pp. 139-152, 2013. [4] H.S. Che, W.P. Hew, N.A. Rahim, E. Le i, M. Jones, and M.J. Du an, “A six-phase wind ene gy induc ion gene a o sys em wi h se ies-connec ed DC-links,” in P oc. IEEE Powe Elec . o Dis ibu ed Gene a ion Sys ems PEDG, pp. 26-33, 2012. Fig. 3: Tes bench used o he expe imen al esul s. a) b) c) d) e) Fig. 4: Expe imen al esul s in he p e- o pos - aul ansi ion a 800 pm. F om op o bo om: mo o speed, deg ee o unbalance k, d-q cu en s, 𝑥′-𝑦′ cu en s and phase cu en s. a) b) c) Fig. 5: Expe imen al esul s in he es wi h a speed change om 800 o 600 pm (p e- aul ). F om op o bo om: mo o speed, d-q cu en s and 𝑥′-𝑦′ cu en s. 0 5 10 15 20 600 800 1000 1200 Time (s) Speed ( pm) *  0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Time (s) k k 0 5 10 15 20 -2 0 2 4 6 Time (s) Cu en (A) ids *ids iqs *iqs 0 5 10 15 20 -2 0 2 4 Time (s) Cu en (A) ixs ´* ixs ´iys ´* iys ´ 9.9 9.95 10 10.05 10.1 -5 0 5 Time (s) Cu en (A) |In/2| -|In/2| 0 5 10 15 20 600 800 1000 1200 Time (s) Speed ( pm) *  0 5 10 15 20 -2 0 2 4 6 Time (s) Cu en (A) ids *ids iqs *iqs 0 5 10 15 20 -2 0 2 4 Time (s) Cu en (A) ixs ´* ixs ´iys ´* iys ´ P e- aul Pos - aul