Decoupled Vector Control Scheme for Dual Three-Phase Permanent Magnet Synchronous Machines

Transcription

1 1 Decoupled Vecto Contol Scheme fo Dual Thee-Phase Pemanent Magnet Synchonous Machnes Juss Kattunen, Samul Kallo, Pas Peltonem, Pett Slventonen, and Oll Pyhönen. Abstact Dual thee-phase electc machnes have many advantages compaed wth conventonal thee-phase machnes. Howeve, the popetes of such machnes pesent challenges fo cuent contol that make t dffcult to poduce suffcent pefomance fo the electc dve. Ths pape ntoduces an mpoved vecto contol scheme fo dual thee-phase pemanent magnet synchonous machnes. The study ncludes detaled solutons fo key pats of the contol such as efeence fame tansfomatons, decouplng of the cuent contol loops, and modulaton. The pefomance of the suggested contol scheme s evaluated usng fnte-element analyses and expemental esults. The esults show that the scheme can poduce desed dynamcs fo the cuent contol and guaantees balanced cuent shang between the wndng sets. In addton, the poposed soluton s capable of educng cuent hamoncs poduced by the ntenal stuctue of the machne. Ths poblem s, howeve, only patly solved snce complete elmnaton of hamonc components s not acheved. Nevetheless, the suggested contol scheme ovecomes many of the dsadvantages found wth othe contol solutons. Impoved contol pefomance allows the full benefts of dual thee-phase dves to be utlzed even n demandng applcatons. Index Tems cuent contol, multphase, modulaton, voltage souce nvete M I. INTRODUCTION ULTIPHASE electc machnes have become a subject of sgnfcant nteest ove the last two decades [1], [2]. The nceased attenton among eseaches and ndusty to machnes wth moe than thee phases esults fom the possblty to acheve notable mpovements n vaous aspects of pefomance compaed wth the use of conventonal theephase electc machne dves. Sgnfcant advantages of multphase machnes nclude: educed toque pulsaton [3], educed hamonc content of the DC lnk cuent [4], potentally hghe effcency [3], [5], educed powe pe phase, and geatly mpoved elablty as a esult of hghe fault toleance [6], [7].. Manucscpt eceved Decembe 13, 212; evsed Febuay 22, 213 and Mach 28, 213; accepted May 21, 213. Copyght 213 IEEE. Pesonal use of ths mateal s pemtted. Howeve, pemsson to use ths mateal fo any othe puposes must be obtaned fom the IEEE by sendng a equest to pubs-pemssons@eee.og. The authos ae wth the Depatment of Electcal Engneeng, Lappeenanta Unvesty of Technology, 5385 Lappeenanta, Fnland (e-mal: juss.kattunen@lut.f). b 2 c 1 b 1 3 c 2 Fg. 1. Dual thee-phase pemanent magnet synchonous machne. Two sets of thee-phase wndngs spatally shfted by 3 electcal degees shae the same stato fame but ae galvancally solated fom each othe (sepaate neutal ponts). Roto angle θ efes to the angle between the dect axs of the oto and the magnetc axs of phase a 1. One of the most common multphase machne stuctues s the dual thee-phase machne [2]. Dual thee-phase machnes have two sets of thee-phase stato wndngs spatally shfted by 3 electcal degees wth solated neutal ponts. Fg. 1 shows ths confguaton, whch s also known n the lteatue as an asymmetcal sx-phase machne, a splt-phase machne o a double-sta machne. Dual thee-phase machnes offe a good compomse between addtonal complexty and potental benefts, and make ntegaton wth conventonal thee-phase technology elatvely smple, whch may explan the populaty of ths machne type. In addton to scentfc nteest, dual thee-phase machnes have also shown the effectveness n pactce. Dual theephase synchonous machnes have been successfully used n shp populson dves [8] and hgh-powe tubo-compessos [9]. It has been epoted that dual thee-phase pemanent magnet synchonous machnes (PMSM) ae a patculaly advantageous altenatve n wnd powe systems [1], [11] although much lowe powe applcatons as found n moe-electc a- θ a 2 a 1

2 2 caft [12] and electc vehcles [13] have also been poposed. These wde angng applcatons demonstate the pactcal value of eseach of dual thee-phase PMSMs and the contol. An effectve contol scheme s an essental pat of dual thee-phase PMSM dves and mpovements n contol can geatly beneft the pefomance of the dve and consequently the whole applcaton. Howeve, contol of dual thee-phase machnes s moe challengng than contol of conventonal thee-phase machnes because of the magnetc couplng between the wndng sets, whch complcates the dynamcs of the system. Futhe challenges ae caused by unbalanced cuent shang between the wndng sets [4], [14] and cuent hamoncs [15] [17]. Vaous contol schemes fo dual thee-phase machnes have been suggested n the lteatue. One appoach fo modelng and contol s a double d-q wndng epesentaton [2]. Ths appoach eplaces both thee-phase wndng sets wth equvalent d-q wndngs, esultng n two pas of d-q equatons. Many examples of vecto contol schemes usng the double d- q appoach can be found fo dual thee-phase nducton machnes (IMs) [4], [16] and PMSMs [18], [19]. Ou pevous study showed, howeve, that the double d-q appoach causes complex coss couplng between the two pas of d-q stato voltage equatons that s vey dffcult to elmnate n PMSM dves [2]. As a consequence, good dynamc pefomance s had to acheve usng such vecto contol schemes. An altenatve modelng and contol appoach s the vecto space decomposton (VSD) method [15], whch does not suffe fom such dffcult coss couplng poblems. Although VSD tself has poven to be extemely useful, the ognal VSD vecto contol scheme [15] has dawbacks such as the nablty to guaantee balanced cuent shang between the wndng sets. Snce ts ntoducton, VSD based vecto contol schemes wth dffeent modfcatons and mpovements have been suggested fo dual thee-phase IMs [14], [21] and PMSMs [1]. In [1], fo example, an addtonal pa of cuent contolles s added to the ognal VSD contol scheme, whch could n theoy solve the mbalance poblem [1]. Howeve, n the case dscussed, the soluton may not wok vey well n pactce because the added cuent contolles (PI) wee placed n the statonay efeence fame whee smple PI contolles cannot acheve zeo steady state eo fo the fundamental component. Othe suggested vecto contol schemes demonstate smla o othe lmtatons. Anothe potental way of ealzng hgh pefomance dve contol s dect toque contol (DTC). DTC schemes usng the VSD appoach have been pesented fo dual thee-phase IMs [22], [23] and, usng the double d-q appoach, fo synchonous machnes [8]. Howeve, hysteess based contol can poduce low-fequency voltage hamoncs, whch makes t less sutable fo dual thee-phase dves. Some DTC schemes have consequently suffeed fom majo poblems, especally wth cuent hamoncs [1]. Nevetheless, some vesons of pesented DTC schemes have demonstated feasblty even n commecal use [8]. Thus, whle DTC may not be the best altenatve fo all dual thee-phase machnes, some vesons clealy ae usable. Although vecto contol and DTC have tadtonally been the most commonly used contol schemes n PMSM dves, t s woth consdeng othe altenatves. Recently, utlzaton of pedctve cuent contol has been poposed fo dual theephase IMs [24], [25]. Pedctve stateges use a system model to pedct optmal swtchng states fo the convete. The pedcton eques ntensve computaton and eles heavly on the accuacy of the system model and ts paametes. Lack of toleance fo paamete eos and non-dealtes not coveed by the system model (e.g., back-emf hamoncs) can theefoe cause poblems n dual thee-phase PMSM dves. The above bef evew of contol schemes fo dual theephase machnes shows that mpovements ae equed n the aeas of dynamc pefomance, obustness, and contol of cuent balance and hamoncs. Thus, futhe nvestgaton s needed n ths feld and bette contol solutons should be developed. The am of ths pape s to develop an mpoved vecto contol scheme fo dual thee-phase PMSMs. The objectve of the contol scheme s to offe excellent dynamc pefomance and guaantee balanced cuent shang between the wndng sets. In addton, the contol scheme should educe (o pefeably elmnate) ntenally geneated cuent hamoncs caused by the PMSM tself and no addtonal low fequency cuent hamoncs should be poduced fom the convete sde. The study ncludes detaled solutons fo efeence fame tansfomatons, the machne model, model-based selecton of paametes fo cuent contol, decouplng of the cuent contol loops, and modulaton. The poposed contol scheme s based on a ecent machne model [26] that has not pevously been used fo contol puposes. Thus, ths pape takes nto account the latest developments n modelng of dual thee-phase PMSMs. The novelty of the contol scheme s to pefom the cuent contol and modulaton n dffeent efeence fames: the fst efeence fame (adopted fom [26]) esembles the VSD appoach and the second s a conventonal d-q fame. Ths soluton makes t possble to obtan hgh-pefomance cuent contol usng wellestablshed technques fo conventonal thee-phase PMSMs and, at the same tme, t povdes the means fo solvng chaactestc poblems of dual thee-phase machnes, such as balanced cuent shang and cuent hamoncs. The pefomance of the suggested vecto contol scheme s vefed by compehensve fnte-element analyss (FEA) and expemental studes. The est of ths pape s stuctued as follows: Secton II pesents the machne model that foms the bass fo the contol scheme. Secton III descbes the contol scheme. Secton IV povdes an analyss of the pefomance of the scheme usng the fnte-element method (FEM). Fnally, Secton V pesents expemental esults and Secton VI offes conclusons.

3 3 M q L q L q 1 Q 1 q2 q1 d-q efeence fames L d d1 L M d d2 d 1 D-Q efeence fames L Q 2 L D 1 D 2 Fg. 2. Conventonal d-q efeence fames (d 1-q 1 fo the fst wndng set and d 2-q 2 fo the second wndng set) compaed wth D-Q efeence fames used n ths pape. The D-Q appoach povdes much smple epesentaton of the machne whch can geatly beneft the contol. Mutual nductance tems M d and M q descbe the couplng between the fames n the d-q appoach. M q L q q 2 II. MACHINE MODEL Fom the pespectve of the contol scheme, the machne model should adequately descbe the dynamcs of the system as smply as possble. As was noted n the ntoducton, VSD type appoaches satsfy ths equement. Pevous VSD based vecto contol schemes fo dual thee-phase PMSMs [1] have used the ognal VSD appoach [15] to model the machne. Recently, howeve, mpovements have been made n the feld of modelng of PMSMs [26] that can beneft the contol. Theefoe, the machne model fo salent pole dual thee-phase PMSMs ntoduced n [26] s used n ths pape. The machne model s based on the followng tansfomaton matces: T DQ T ot (1) q1 q2 L d d2 M d cos sn sn cos T ot (2) cos sn sn cos whee θ s the oto angle (see Fg. 1). Snce zeo sequence components cannot flow, they ae neglected fom the tansfomaton. The tansfomaton matx (1) conssts of the statonay fame decouplng matx and the otaton matx (2). Usng (1) tansfoms the ognal phase-vaable pesentaton of the machne nto two decoupled two-axs synchonous efeence fames. Thus, applyng (1) to the phase cuents d1 d 2 T DQ a1 b1 c1 a2 b2 T c2 gves fou ndependent cuent components to be contolled n two sepaate efeence fames. These efeence fames ae called D 1 -Q 1 and D 2 -Q 2 n ths pape. Captal letteng s used to dstngush them fom conventonal thee-phase d-q efeence fames (.e., oto efeence fames). Fg. 2 clafes the dffeence between the efeence fames. It can be seen that the D-Q appoach povdes a much smple epesentaton of the machne. The tansfomaton matx (11) descbes mathematcally the connecton between the d-q and D-Q fames. Advantages of the D-Q appoach ae detaled below. Futhe nfomaton about both appoaches can be found n [2] and [26]. The D 1 -Q 1 and D 2 -Q 2 efeence fames ae totally decoupled wth espect to each othe, whch yelds a vey smple fom fo the machne equatons. It s assumed n the modelng that thee s no satuaton, that the machne stuctue s symmetcal, and that the wndng dstbutons ae snusodal. In addton, hghe ode hamoncs and on losses ae neglected. Unde these assumptons, the stato flux lnkage equaton s L L L L 3 whee L to L ae the synchonous nductances of the PMSM and ψ PM s the PM flux lnkage. A detaled descpton of calculaton of the paametes of the machne model can be found n [26]. It can be seen fom (4) that the nductance matx of the machne has no off-dagonal nductance tems, whch means that no couplng exsts between the efeence fames. In addton, couplng between the stato and oto occus only n the D 1 -Q 1 efeence fame. Thus, all the electomechancal enegy conveson must be descbed by ths efeence fame and cuent components n the D 2 -Q 2 efeence fame cannot affect the agap flux. On the othe hand, Fg. 2 shows that modelng the machne usng the double d-q appoach esults n both efeence fames (d 1 -q 1 and d 2 -q 2 ) havng couplng between each othe and between the oto and stato. These addtonal couplngs ae the fundamental poblem of the double d-q appoach. The tansfomaton matx (1) also has the popety that the fundamental component and the hamoncs of the ode (12n ± 1, n = 1, 2, 3 ) ae mapped nto the D 1 -Q 1 efeence fame and the hamoncs of the ode (6n ± 1, n = 1, 3, 5 ) ae mapped nto the D 2 -Q 2 efeence fame. Ths condton, howeve, holds only n a pefectly symmetcal stuaton. Any mbalance between the wndng sets causes the fundamental components and all the hamoncs to appea n both efeence fames. PM (3) (4)

4 4 Fo cuent contol, the most mpotant equatons of the machne ae the stato voltage equatons. Based on (4), the stato voltage equatons n the D 1 -Q 1 efeence fame ae u u R s R s L L and n the D 2 -Q 2 efeence fame u u R s R s L L d dt d dt d dt d dt L L L L 3 whee ω s the electcal angula speed of the oto and R s s the stato esstance. The fst set (5) s smla to the coespondng pa of stato voltage equatons fo a thee-phase PMSM. The second set (6) dffes fom (5) only by the mssng back-emf tem. Thus, the used modelng appoach offes smple dynamc equatons fo dual thee-phase PMSMs. Futhemoe, the smlates wth conventonal thee-phase equatons suggest that exstng contol solutons fo conventonal thee-phase PMSM dves may also be successfully used wth ths machne type. Last pat of the machne modelng s the toque equaton whch can be staghtfowadly deved usng a smla pocedue as fo conventonal thee-phase machnes [26]. The electomagnetc toque T e poduced by dual thee-phase PMSMs can be calculated fom T e p 3 PM L L whee p s the numbe of pole pas. A. Contol challenges PM (5) (6) (7) III. VECTOR CONTROL Smlaly to conventonal thee-phase machnes, the man dea of vecto contol fo dual thee-phase PMSMs s that the D 1 -axs stato cuent and the Q 1 -axs stato cuent can be contolled ndependently (povdng ndependent contol of flux and toque). In voltage souce nvete (VSI) fed dves, the stato cuent components ae contolled by contollng the stato voltage components of the machne. Howeve, coss couplng exsts between the stato voltage equatons (5), and consequently, the D 1 -axs voltage component u also affects and the Q 1 -axs component u affects. The D 2 -Q 2 efeence fame equatons (6) ae smlaly coupled. Theefoe, the stato voltage components u, u, u, and u and the coespondng stato cuent components cannot be consdeed as smple sngle-nput sngle-output systems. The stato cuents and can be ndependently contolled (so called decoupled cuent contol) by decouplng the stato voltage equatons. As a esult of the choce of the cuent contol efeence fame (1), ths coss couplng poblem s dentcal wth conventonal thee-phase PMSMs and can be easly solved [27]. Some poblems of dual thee-phase machnes ae not encounteed wth conventonal thee-phase dves. A good example s the challengng featue of easly occung lage stato cuent hamoncs [1], [14], [28]. The eason fo ths majo dawback s that the stato cuent hamoncs of the ode (6n ± 1, n = 1, 3, 5 ) ae lmted only by the vey small stato leakage mpedance [15], [16]. Theefoe, even small exctaton of these components can lead to sgnfcant coespondng cuent hamoncs. In an deal case, these hamoncs do not affect the a-gap flux and thus have no mpact on toque pulsaton. Howeve, they cause addtonal losses and consequently should be avoded [16], [28]. Dual thee-phase PMSMs have two man souces fo stato cuent hamoncs. The fst souce s the supplyng nvetes [15], [16], [28], [29]. VSIs can cause lage stato cuent hamoncs f the suppled voltage contans hamonc components of the ode (6n ± 1, n = 1, 3, 5 ). Thus, the modulated voltage wavefom should not contan unwanted low fequency voltage hamoncs. Such hamoncs ae usually neglgble f the modulaton method s wokng popely. The second souce s the ntenal stuctue of the PMSM tself [17], [2]. Pemanent magnets may not poduce pue snusodal flux dstbuton, and oto salency, pole shape and possble magnetc satuaton can cause hamoncs n the agap flux [17]. These non-dealtes can be a majo poblem n dual thee-phase PMSMs because they can easly poduce lage ntenally geneated cuent hamoncs. Ths ssue was clealy demonstated n ou pevous study [2]. Cuent hamoncs caused by non-snusodal a-gap flux can be educed by ntentonally feedng the ght combnaton of supply voltage hamoncs to the machne, as shown late n ths pape. Ths acton dffes fom the usual dese fo pefectly snusodal lne-to-lne supply voltage and eques that the modulaton scheme can poduce hamonc voltage components n the D 2 -Q 2 efeence fame. Voltage components n the D 2 -Q 2 efeence fame ae also necessay fo contollng the cuent shang between the wndng sets. The popetes of the wndng confguaton mean that the best toque qualty, stato MMF wavefom and effcency of a dual thee-phase PMSM ae acheved when equal cuents flow though both wndng sets. Howeve, small nheent asymmetes between the wndng sets and between the VSIs can cause unbalanced cuent shang [4], [18]. Ths poblem s well-known n the lteatue and ts establshed soluton s to use as many cuent contolles n the contol scheme as thee ae ndependent cuent components n the machne (fou n ths case) [1]. To gan the desed advantage fom fou cuent contolles, the modulaton method has to be able to poduce ndependent voltage vectos n both efeence fames (D 1 -Q 1 and D 2 -Q 2 ). In ths way, the wndng sets can be suppled wth voltages of dffeent magntudes and phase shft othe than 3 degees, a equement needed to compensate the asymmetes. Most of the challenges n contol of dual thee-phase ma-

5 5 T e,ef MTPA,ef =,ef =,ef +_,ef chnes ae elated to ssues wth cuent. Cuents ae dectly contolled vaables n vecto contol schemes and consequently can be effectvely manpulated. Ths popety povdes a vey effectve way to solve cuent-elated poblems and stongly suppots vecto contol as the ecommended contol method fo dual thee-phase machnes. B. Contol scheme and decouplng The contol scheme s based on a conventonal soluton of synchonous fame cuent contol usng smple PI contolles. Fg. 3 pesents the block dagam of the contol scheme. Fou cuent contolles ae used snce thee ae fou ndependent cuent components mapped nto two decoupled efeence fames: the man efeence fame D 1 -Q 1, whee toque poducton of the machne s contolled, and the hamonc efeence fame D 2 -Q 2, whee the balance between the wndng sets and cuent hamoncs s contolled. Snce D 2 -Q 2 s a synchonous efeence fame, any steady state mbalance wll be completely elmnated. Any cuent contol stategy such as maxmum toque pe ampee (MTPA, whch s the same as = fo non-salent pole machnes) can be used to calculate the efeence cuents n the D 1 -Q 1 fame. The stuaton s equvalent wth the calculaton of efeence cuents n vecto contolled thee-phase PMSM dves. In ths pape, the appled MTPA stategy s based on a dect analytcal calculaton of optmal efeence cuents fo gven T e usng (7) and assumng constant nductance values. The cuent components n the D 2 -Q 2 fame ndcate ethe mbalanced opeaton o specfc cuent hamoncs. Thus, the efeence cuents fo the D 2 -Q 2 fame should always be zeo, as shown n Fg. 3, snce the am s usually balanced cuent shang and elmnaton of cuent hamoncs. Howeve, nothng n the contol scheme pevents the ceaton of desed mbalance and hamonc content by usng non-zeo efeences f some advantage s theeby obtaned. Pefomance of a smple PI contolle based cuent contol can be geatly mpoved by elmnatng the coss couplng effects n the stato voltage equatons. Ths decouplng pocedue eques that the followng decouplng voltage tems ae added to the output of the cuent contolles +_ +_ +_ PI PI PI PI u * u * u * u * ω u u u u D 1 -Q 1 D 2 -Q 2 d 1 -q 1 d 2 -q 2 u d1 u q1 u d2 u q2 d-q α-β θ d-q α-β u u u u decouplng decouplng decouplng decouplng L L L L 3 PM. (8) Decouplng can be done by feedng the decouplng tems (8) as postve feedback (measued quanttes ae used to calculate the decouplng voltage tems) o as feed-fowad (efeence values ae used to calculate the decouplng voltage tems) to the output of the cuent contolles. In both appoaches, the system should behave fom the pespectve of the cuent contol lke fou ndependent lnea fst ode systems, thus smplfyng the desgn of the cuent contolles. An altenatve way of decouplng the cuent contol s multvaable PI contol [3] (also known as vecto PI contol) whch uses ntegatos to calculate the decouplng tems. Ths method theoetcally poduces the same esult as (8) but s moe complex, and hence (8) s used hee. Based on the machne model, the decoupled system n the D 1 -Q 1 efeence fame has tansfe functons I U I U u α1 u β1 u α2 u β2 θ SV- PWM Decouplng SV- PWM ( s) ( s) R ( s) ( s) R S 1-6 S 7-12 D 1 -Q 1 D 2 -Q 2 a 1 b 1 c 1 a 2 b 2 c 2 1 L 1 L VSI VSI a1, b1, c1 a2, b2, c2 Fg. 3. Block dagam of the vecto contol scheme used to contol the VSIs. The cuent contol s made smultaneously n two decoupled efeence fames (D 1-Q 1 and D 2-Q 2) usng PI contolles. MTPA efes to the maxmum toque pe ampee opeatng pont. SVPWM s a conventonal thee-phase space vecto modulato. The electcal angula speed ω and the oto angle θ ae obtaned fom an angle encode. s. (9) Note that R s s eplaced n (9) by appaent D 1 - and Q 1 -axs esstance paametes R and R to gve bette match between the actual voltage-cuent behavo of the machne and the tansfe functons. In ths pape, the esstance and nductance paametes ae dentfed fom D 1 - and Q 1 -axs step esponses. Fo example, applyng U step to the machne whle cuent s kept at zeo should theoetcally poduce a fst ode esponse n cuent, as can be seen fom (5) and (9). The desed paametes can be detemned by notng the tme constant and steady state value of the esponse. Such a test can be easly pefomed usng the VSIs, the contol scheme and cuent measuements of the contol. Altenatvely, an dentfcaton method based on coss couplng voltage tems could be used. Thus, no specal θ s a 1 b 1 c 1 a 2 b 2 c 2

6 6 knowledge about the machne desgn s needed to obtan the paametes. Assumng that (9) adequately descbes the behavo of the system and machne paametes ae accuate, cuent contolle paametes can be easly desgned to gve the desed closed loop esponse. The model based method n [31] s used hee. Paametes fo the Q 1 -axs PI cuent contolle ae calculated fom K p ln9 ln9 L, K R (1) t t whee K p s the popotonal gan, K s the ntegal gan, and t s the desed se tme (fom 1 % to 9 %) of the esultng fst ode closed loop system. The paametes fo the othe cuent contolles ae calculated smlaly. The suggested contol scheme offes totally decoupled cuent contol whee the contolles see the machne as smple fst ode systems. Thus, vey good dynamc pefomance and smple cuent contolle desgn can be acheved. It should be noted that achevng the desed dynamc pefomance s stongly dependent on the accuacy of the machne paametes as can be expected fo such a model based method. Inaccuacy n the paametes causes a decease n the dynamc pefomance but has no effect on steady state opeaton. Because of the synchonous fame cuent contol, the contol scheme can povde zeo steady state eo n tems of constant cuent efeence tackng even wthout any knowledge of the paametes of the machne snce the ntegal acton elmnates the eo. Oveall, the sgnfcance of the accuacy of the machne paametes s smla to that n vecto contolled thee-phase PMSM dves, whee t appeas not to be a majo poblem. C. Modulaton The am of the modulaton s to synthesze the equed efeence voltage vectos n the D 1 -Q 1 and D 2 -Q 2 efeence fames usng a VSI. Thus, fou dffeent voltage vecto components (u, u, u, and u ) ae contolled smultaneously n two decoupled efeence fames. One possblty to acheve ths objectve s a VSD-type appoach. The ognal VSD space vecto PWM (SVPWM) stategy was ntoduced n [15]. Ove the last decade, mpoved vesons have been poposed, leadng to dffeent contnuous and dscontnuous 12-secto [28] and 24-secto [32] SVPWM stateges. Although some of these VSD SVPWM stateges have shown good pefomance [33], they all assume that a zeo aveage voltage vecto s always poduced n the hamonc efeence fame. As noted at the begnnng of ths secton, such a lmtaton clealy cannot be accepted n dual thee-phase PMSM dves. Thus, these methods cannot be used n the case dscussed n ths pape. Anothe soluton s that both wndng sets ae suppled by sepaate thee-phase VSIs whch ae ndependently modulated by conventonal thee-phase modulaton methods. Fo ths appoach, the lteatue contans examples usng cae [34] and SVPWM [35] based methods. Unfotunately, these papes suggest that efeence voltage vectos fo the modulatos always have equal magntude and phase shft of 3 degees. Ths estcton s analogous to the majo lmtaton of VSD SVPWM stateges that a zeo aveage voltage vecto s always poduced n the hamonc efeence fame. Thus, such a modulaton would lead to an nablty to educe cuent hamoncs and guaantee balanced cuent shang between the wndng sets. In the case of two ndependent thee-phase modulatos, thee s no compellng techncal eason to atfcally estct the modulaton ths way. Theefoe, thee-phase modulatos can be used to poduce any combnaton of voltage vectos wthn the lmts of avalable DC voltage, thus povdng a vey effectve modulaton stategy, as also noted n [36]. It s suggested n ths pape that two conventonal theephase SVPWM modulatos ae used fo modulaton. Ths soluton eques that the efeence voltage vectos n the D 1 -Q 1 and D 2 -Q 2 efeence fames ae tansfomed nto conventonal thee-phase d-q efeence fames. The vaables n the D 1 -Q 1 and D 2 -Q 2 efeence fames have a staghtfowad connecton to coespondng vaables n conventonal d-q efeence fames (hee d 1 -q 1 fo the fst wndng set and d 2 -q 2 fo the second wndng set) u u u u d1 q1 d2 q u u 1 u u. (11) The voltage vectos can easly be tansfomed fom one efeence fame to anothe usng (11). In ths way, modulaton becomes a smple task snce voltage vectos n conventonal d-q efeence fames ae tval to synthesze usng any well-known thee-phase modulaton method. The suggested modulaton stategy togethe wth the whole contol scheme s llustated n Fg. 3. The combnaton of the tansfomaton (11) and the two ndependent thee-phase SVPWM modulatos has many advantageous popetes. The most obvous one s the ease of mplementaton. Exstng algothms and tested thee-phase modulaton methods can be effectvely utlzed, whch can save tme and touble. It also makes the method computatonally effcent snce yeas of extensve study and wde usage have made space vecto modulaton a vey smple task. Futhemoe, the suggested contol scheme does not eque much computng powe because, n addton to modulaton, the scheme contans only smple PI contolles and tansfomatons between efeence fames. Most mpotantly though, the poposed modulaton method allows fully ndependent and exact contol of all the equed voltage vecto components (u, u, u, and u ) unlke many othe solutons pesented n the lteatue. IV. FEM RESULTS Pefomance of the suggested contol scheme was fst analyzed usng FEM-Smulnk cosmulaton. In ths cosmulaton, FEM (Cedat Flux 2-D ncludng skewng) was used to model the dual thee-phase PMSM and the contol scheme was mplemented n Smulnk. The nput vaables of the FEM based machne model wee the oto speed and lne-to-neutal volt-

7 7 ages gven by Smulnk. Fom these values, FEM calculated the electomagnetc toque and stato cuents, whch wee etuned to the contol scheme n Smulnk, thus closng the contol loops. VSIs wee modeled n ths case as deal voltage souces because of the sample tme lmtatons caused by FEM. The FEM machne model tself was based on the same desgn as the test machne of the expemental setup used n ths pape (see Table I fo paametes). The FEM model was thooughly vefed aganst the eal machne. Thus, the pefomance of the contol scheme can be elably evaluated takng nto account the eal behavo of the machne but avodng all the pactcal poblems n the mplementaton of the contol scheme. Note that the FEM model was used only as a vefcaton tool and teated fom the pespectve of the contol scheme smlaly as a eal machne. No nfomaton about the machne desgn whch cannot be known wthout the FEM model was utlzed n ths pape. In the followng cases, the otatonal speed of the machne s the nomnal speed 35 /mn unless othewse stated. The machne s opeated n most of the cases as a geneato because of the lmtatons of the expemental setup. Howeve, the contol scheme opeates equally well n both (moto and geneato) modes snce they dffe only by the sgn of the efeence cuents. Thus, all the esults pesented hold fo moto and geneato opeaton of the machne. Opeatng condtons n all the cases wee selected to coespond wth the expemental tests pesented n the next secton. A. Cuent hamoncs As mentoned eale, the ntenal stuctue of the dual thee-phase PMSM can be a majo souce of cuent hamoncs. These hamoncs can be educed by poducng compensatng hamonc voltage components n the D 2 -Q 2 efeence fame. The ntoduced dea s that cuent hamoncs poduced by the machne tself can be elmnated usng the D 2 -Q 2 fame cuent contol. To demonstate the ssue, the uppe cuve of Fg. 4 shows the case whee cuent contol n the D 2 -Q 2 efeence fame s omtted. In ths case, a zeo aveage voltage vecto s always poduced n the D 2 -Q 2 efeence fame, as pesented n many papes. Lage cuent hamonc components can be seen because of the nablty of the contol to compensate the effect of the non-snusodal a-gap flux. As a compason, Fg. 4 also shows the case (lowe cuve) whee cuent contol n the D 2 -Q 2 efeence fame s opeatng as suggested n ths pape. A majo educton can be seen n the magntude of the cuent hamonc components (ffth hamonc educes 72 % and seventh 77 %). The contol scheme s poducng substantal voltage components n the D 2 -Q 2 efeence fame to educe the cuent hamoncs. The esult shows that ntentonal feedng of supply voltage hamoncs to the machne can be used to compensate the effect of the nonsnusodal a-gap flux, and the basc concept of hamonc elmnaton s thus vefed T me [ms] T me [ms] Fg. 4. Phase cuent wth (lowe cuve) and wthout (uppe cuve) cuent contol n the D 2-Q 2 efeence fame. Lage cuent hamonc components can be seen when omttng cuent contol n the D 2-Q 2 efeence fame. Usng the suggested contol gves a majo educton n hamonc components. Both cuves have equal fundamental component. The D 1-Q 1 fame efeence cuents ae n ths case,ef = A and,ef = -4 A. It s evdent that the cuent s not pue snusodal n the lowe cuve of Fg. 4. Thus, the cuent contolles ae able to educe the effect of ntenal non-dealtes but not completely emove them. Ths outcome s as expected snce fxed gan PI contolles have lmted ablty to compensate the effect of snusodal dstubances. Wthout ths lmtaton (e.g., usng esonance contolles), pue snusodal phase cuent could be poduced wth ths contol scheme. An example of usng esonance contolles fo stato cuent hamonc contol of double fed nducton geneato can be found n [37]. Snce the fequences of the majo hamoncs (5 th and 7 th ) ae always known, a smla appoach could be appled n the case of ths pape. Howeve, extensve analyss of the soluton would be equed, and thus t s left fo a futue wok. B. Balance Cuent contol n the D 2 -Q 2 efeence fame s also esponsble fo contollng the balance between the wndng sets. The suggested contol scheme can n theoy guaantee balanced cuent shang between the wndng sets. Pefomance of the balance contol was tested by ntentonally ceatng asymmety n the system by nceasng the esstance of one wndng set. A esstance of 4.4 Ω was added, whch ceated vey sevee asymmety. Fg. 5 pesents the cuents of phases a 1 and a 2 wth and wthout cuent contol n the D 2 -Q 2 efeence fame. It can be seen that the ceated asymmety leads to sevee mbalance f cuent contol n the D 2 -Q 2 efeence fame s not used. Use of cuent contol n the D 2 -Q 2 efeence fame, on the othe hand, esults n symmetcal loadng.

8 Voltage [V] Speed [pm] T me [ms] T me [ms] Fg. 5. Cuents of phases a 1 and a 2 when system has asymmety. Cuent contol n the D 2-Q 2 efeence fame s omtted n the uppe cuve. The lowe cuve shows the esult usng the contol scheme. The suggested method povdes balanced cuent shang. Both cases poduce same aveage electomagnetc toque. Refeence cuents ae,ef = -3.5 A and,ef = -3 A. A futhe test of the contol scheme unde asymmetcal condtons s pesented n Fg. 6. In ths case, the constant toque efeence gvng nomnal cuent of the machne s equested fom the contol. Rotatonal speed of the machne s changed fom 35 /mn to -35 /mn lnealy dung a 1 s peod. The machne opeates the fst half of the test as a moto and the second half as a geneato. Fg. 6 shows that constant toque s poduced unde the contnuous speed tansent state despte asymmetes. It can be seen that balanced cuent shang s acheved though the whole speed ange. Voltage commands fo modulatos show that the VSIs supply the fst and second thee-phase wndng sets wth sgnfcantly dffeent voltages to compensate the asymmety. The tests show that the suggested contol scheme can offe balanced cuent shang unde a wde ange of opeatng condtons. C. Dynamc pefomance The dynamc pefomance of the suggested contol scheme was tested usng step esponses of the cuent. Dung ths test, the cuent was kept at zeo and the cuent efeence was changed fom zeo to -3 A. Paametes of the cuent contol wee dmensoned usng (1) to gve fst ode esponses wth se tmes t fom 5ms to 2 ms. It can be seen fom the esults gven n Fg. 7 that the closed loop step esponses ae as desed. Responses have the shape of the fst ode system and they accuately follow the se tme specfcaton of the cuent contol. Thus, the decouplng scheme wth model based desgn of the contol paametes clealy woks as ntended. It should be noted that the DC lnk voltage level of the VSIs, T me [s] T me [s] T me [s] 4 u d1 u q1 u d2 u q T me [s] Fg. 6. Rotatonal speed, D 1 and Q 1-axs cuents, a 1 and a 2 phase cuents, and voltage commands n conventonal d-q efeence fames gven to the SVPWM modulatos when the system has asymmety. The suggested method povdes balanced cuent shang though whole speed ange. Note that balanced cuent shang does not mean that cuents of phases a 1 and a 2 should be equal at standstll ( pm,.5 s). the swtchng fequency of the VSIs, and the sample tme of the contol loops set lmtatons fo the speed of the esponse. Nevetheless, the esults wth dffeent se tme specfcatons show that when these lmtatons ae not exceeded, the contol scheme can poduce the desed dynamcs fo the cuent contol. Usng a maxmum toque pe ampee (MTPA) cuent contol stategy wth salent pole machnes as pesented n Fg. 3 causes both cuents ( and ) to change smultaneously dung toque changes. Because of the decouplng between the cuent contol axes, - and -cuents can n theoy be contolled ndependently, thus enablng fast smultaneous cuent changes wthout dstubances between axes. Good dynamc pefomance also ncludes that changes n otatonal speed do not cause substantal changes n cuents and toque. Opeaton of the contol scheme unde these condtons s pesented n Fg. 8, whch shows the - and -cuents and a1 a2

9 Toque [Nm] t = 5 ms 15 t = 1 ms 1 t = 15 ms 5 t = 2 ms T me [ms] Fg. 7. Step esponse of the cuent wth dffeent se tme t specfcatons of cuent contol. Actual se tmes of the cuents (4.8 ms, 1.2 ms, 15.2 ms, and 2.4 ms) coespond well wth the specfcatons. In addton, esponses have the desed shape of the fst ode system. The dashed lne epesents the efeence cuent. In the fgue, the sgn of the cuents s evesed fom the actual values (geneato opeaton) T me [ms] T me [ms] Fg. 8. Toque step gvng nomnal cuent of the machne. Pesented toque s gven by FEM. The contol scheme uses the MTPA cuent contol stategy. Dynamc pefomance emans good despte smultaneous change of both cuents. Toque qute accuately has the dmensoned 1 ms se tme (actual value 9.7 ms). Afte the step (t = 1 ms), the otatonal speed of the machne s halved fom the nomnal value. Ths majo speed change causes only mno changes n cuents and toque. The dashed lnes epesent the efeence cuents. In the fgue, the sgn of the cuents and toque s evesed fom the actual values (geneato opeaton) toque of the machne. In Fg. 8, the contol scheme s fst fed by the toque efeence step gvng the nomnal cuent of the machne. Afte the step, the otatonal speed of the machne s halved (lnealy dung a 1 ms peod) fom the nomnal value. The contol scheme agan shows desed pefomance snce the toque esponse usng the MTPA cuent contol stategy s only slghtly faste (t = 9.7 ms) than the dmensoned value (t = 1 ms) and only mno dstubances can be seen when the otatonal speed changes. Note that dffeent contol paametes wee used compaed wth Fg. 7 because of changes n the machne paametes caused by satuaton. V. EXPERIMENTAL RESULTS The expemental setup conssted of two thee-phase VSIs wth a common DC lnk, a commecal actve font end (AFE), a 25 kw salent pole dual thee-phase PMSM, and a 18 kw DC machne dve fo loadng the PMSM. Table I pesents the paametes of the PMSM. The VSIs opeate at a 5 khz swtchng fequency. The setup ncludes an encode fo the oto angle feedback. Contol of the VSIs s mplemented n a dspace platfom. In addton, a DSP/FPGA cad s used fo T e AFE DC lnk VSI S 1-6 VSI S 7-12 G M Use PC DSP/ dspace nteface FPGA S 7-12 Fg. 9. Schematc of the expemental setup. The dual thee-phase PMSM opeates as a geneato otated by the DC machne dve. Two thee-phase VSIs supply the dual thee-phase PMSM. The VSIs have a common DC lnk and ae contolled by the dspace platfom. The AFE feeds the geneated powe back to the gd. TABLE I MACHINE PARAMETERS Nomnal powe P n 25 kw Nomnal cuent I n 22.5 A Nomnal voltage U n 38 V Nomnal speed n n 35 pm Numbe of pole pas p 4 Slots pe pole pe phase q 1 Stato skewng 1 slot Stato esstance R s.53 Ω PM flux lnkage ψ PM 2.6 Wb L, L, L, L, 31 mh, 42 mh, 7 mh, 8 mh sgnal pocessng. Fg. 9 pesents the schematc of the expemental setup. The pefomance of the suggested contol scheme was expementally vefed by epeatng the FEM-Smulnk cosmulaton cases (cuent hamoncs, balanced cuent shang, and dynamc pefomance) wth the setup. In addton, t was nvestgated how asymmety n the system affects decouplng of the cuent contol loops. A test wth speed contol coveng a wde ange of opeatng ponts was also conducted. Reducton of cuent hamoncs s pesented n Fg. 1. The esults ae agan shown wth and wthout cuent contol n the D 2 -Q 2 efeence fame to clealy demonstate the dffeence. Lage cuent hamonc components can be seen when a zeo aveage voltage vecto s poduced n the D 2 -Q 2 efeence fame, and a notable educton (ffth hamonc educes 6 % and seventh emans the same) s acheved by usng the cuent contol. The educton s much smalle than wth FEM snce the cuent contolles have lowe gans at the hamonc fequences because of lmtatons n the expemental setup. To vefy the balance contol, asymmety had to be ntentonally ceated because the expemental setup does not nheently have asymmetes that would lead to sgnfcantly unbalanced cuent shang between the wndng sets. The asymmety needed was ceated by addng esstances (4.4 Ω, the lowest avalable opton n the laboatoy) between the machne and the VSI of the second wndng set. Fg. 11 pesents the cuents of phases a 1 and a 2 wth and wthout cuent contol n the D 2 -Q 2 efeence fame. It can be seen that even sevee mbalance can be coected wth the suggested contol scheme. a2,b2,c2 a1,b1,c1 θ S 1-6

10 Rotatonal speed [pm] T me [ms] T me [ms] Fg. 1. Phase cuent wth (lowe cuve) and wthout (uppe cuve) cuent contol n the D 2-Q 2 efeence fame. Lage cuent hamonc components can be seen when omttng cuent contol n the D 2-Q 2 efeence fame. Use of the suggested contol scheme esults n a notable educton n hamonc components. Both cuves have equal fundamental component. The D 1-Q 1 fame efeence cuents ae n ths case,ef = A and,ef = -4 A T me [ms] T me [ms] Fg. 11. Cuents of phases a 1 and a 2 when the system has asymmety. Cuent contol n the D 2-Q 2 efeence fame s omtted n the uppe cuve. The lowe cuve shows the esult usng the contol. The suggested method povdes balanced cuent shang. Both cases poduce the same aveage electomagnetc toque. Refeence cuents ae,ef = -3.5 A and,ef = -3 A. The dynamc pefomance was evaluated usng the step esponse of the cuent. A zeo efeence was gven fo the cuent and -3 A fo. Cuent contolles wee agan dmensoned to gve fst ode esponses wth se tmes t t = 5 ms 15 t = 1 ms 1 t = 15 ms 5 t = 2 ms T me [ms] Fg. 12. Step esponse of the cuent wth dffeent se tme t specfcatons of cuent contol. Actual se tmes of the cuents (3.2 ms, 8.3 ms, 13. ms, and 19.1 ms) coespond adequately wth the specfcatons and esponses have the desed shape of the fst ode system. The dashed lne epesents the efeence cuent. In the fgue, the sgn of the cuents s evesed fom the actual values (geneato opeaton) T me [s] Fg. 13. Step esponses of the,,, and cuents when the system has asymmety. The dashed lne epesents the efeence cuent. Sevee asymmety causes mno couplng between the cuent contol axes. The dstubances between the axes ae quckly elmnated by the cuent contol thus enablng nealy ndependent contol of the cuents even n asymmetcal condtons T me [s] T me [s] Fg. 14. Rotatonal speed and D 1-Q 1 efeence fame cuents of the machne n the speed contol test case. The dashed lne shows the efeence speed cuve. Acceleaton speed s lmted by the cuent lmt as can be seen. Load toque s 17 Nm. In ths case, the machne opeates most of the tme as a moto. A shot peod of geneato opeaton can be seen dung the deceleaton phase. The contol scheme povdes fast and accuate cuent contol ndependent fom otatonal speed.

11 11 fom 5 ms to 2 ms. Fg. 12 shows the esults. The contol scheme pesents good dynamc pefomance, although the actual se tmes of the cuents ae somewhat shote than the specfed values. Devaton fom the desed pefomance s caused by ssues such as the ncease n the DC lnk voltage level (AFE s not able to mantan constant DC voltage because of the fast ncease n powe geneaton) whch ae not taken nto account n the modulaton. In addton, the DC machne dve s not capable of mantanng constant otatonal speed dung apd toque changes. As a esult, the speed deceases 1 % 2 % dung the steps n Fg. 12. These poblems mpa pefomance compaed wth the pefect esult n the FEM-Smulnk cosmulaton and ae also the eason why the sze of the step s lmted to 3 A. Obvously, the desed se tme specfcatons could have been acheved pecsely, despte the pactcal poblems, by fne-tunng the contol paametes. Howeve, ths was not done hee (o wth the FEM esults) because the man am s to demonstate dect use of (1) n the desgn of cuent contolles. The esults clealy show that the suggested method woks satsfactoly. Pevous esults have shown that the contol scheme povdes fully decoupled cuent contol wth the desed dynamc pefomance when the machne paametes ae accuately known and the system has no asymmety. Howeve, an asymmety caused by, fo example, the dffeence n the stato esstances of the wndng sets esults n addtonal coss couplngs between the cuent contol axes. The machne model does not take nto account such couplng whch must thus be actvely elmnated by the cuent contolles. The consequences of ths ssue ae llustated n Fg. 13 whch pesents the dynamc pefomance of the contol scheme when system has asymmety. Note that the asymmety was vey sevee (see Fg. 11) and contol paametes of a symmetcal case wee used. It can be seen n Fg. 13 that a apd change n the cuent of one axs causes a mno change n the cuent of anothe axs. The dstubances between the axes ae elatvely small and they ae quckly elmnated by the cuent contol. In addton, t can be seen that the asymmety causes a decease n the dynamc pefomance: the actual se tmes of the cuents ae appoxmately doubled fom the specfed values (5 ms) whch s not a majo concen. Thus, suffcent pefomance s acheved and the contol scheme povdes nealy ndependent contol of the cuents even n asymmetcal condtons. Fo the fnal test pesented n Fg. 14, an oute speed contol loop (PI contolle) was added to the contol scheme. The efeence speed cuve shown was gven fo the speed contolle to test the dynamc pefomance of the scheme unde a wde ange of opeatng ponts. The speed efeence tackng s accuate but somewhat slow because of the lage moment of neta of the axs compaed to the maxmum avalable toque. Nevetheless, the esults demonstate agan the good dynamc pefomance of the toque contol, whch s the man objectve. It can be seen that the cuent contol loops povde fast and accuate contol ndependent of the otatonal speed o the opeaton mode of the machne. VI. CONCLUSION Ths pape pesented a vecto contol scheme fo dual theephase PMSMs. Dscusson of the scheme coveed efeence fame tansfomatons, the machne model, decouplng of the cuent contol loops, model-based selecton of cuent contol paametes, and modulaton. The pefomance of the suggested contol scheme was evaluated usng FEM and an expemental setup. The esults clealy demonstated that the dynamcs of the cuent contol can be accuately specfed (wthn the lmts of the system) usng the scheme and the pesented model based methods. Consequently, the contol scheme can be easly appled to a vaety of applcatons havng dffeent equements and lmtatons fo the se tme of toque. Compaatve tests wth and wthout the suggested synchonous fame cuent contol n the D 2 -Q 2 efeence fame clealy showed the mpotance of ths featue neglected n many othe papes. The esults vefed that ths contol can completely elmnate steady state mbalance even unde vey sevee asymmety. Thus, balanced cuent shang can be acheved despte the dffeences between the wndng sets and the VSIs. In the poposed scheme, cuent contol n the D 2 -Q 2 efeence fame s esponsble also fo educng the cuent hamoncs. Only a modeate esult was obtaned n ths case. The contol scheme was able to educe the magntude of the cuent hamoncs but not completely elmnate them. Ths fndng s to be expected snce fxed gan PI contolles ae not capable of completely compensatng the effect of snusodal dstubances. Nevetheless, the suggested contol scheme povdes a bass fo appoachng ths ssue usng moe advanced contol solutons. Futue wok ams to show that when the lmtaton of the PI contolles s emoved, pue snusodal phase cuent can be poduced wth the poposed contol scheme. All n all, the suggested scheme povdes an excellent contol soluton fo dual thee-phase PMSM dves. Oveall pefomance s good, although the scheme stll has poblems wth cuent hamoncs. Othe well-known ssues n contol of dual thee-phase PMSMs appea to have been adequately addessed. Futhemoe, the smple stuctue usng conventonal thee-phase SVPWM modulatos makes mplementaton easy and computatonally effcent, thus mnmzng the equed effot to utlze ths hgh-pefomance contol scheme. ACKNOWLEDGMENT The authos would lke to thank D. R. Pöllänen and M. T. Knuutla fom The Swtch Dve Systems Oy fo the valuable deas and comments. REFERENCES [1] E. Lev, Multphase electcal machnes fo vaable-speed applcatons, IEEE Tans. Ind. Electon., vol. 55, no. 5, pp , May 28. [2] E. Lev, R. Bojo, F. Pofumo, H.A. Tolyat, and S. Wllamson, Multphase nducton moto dves a technology status evew, IET Elect. Powe Appl., vol. 4, no. 1, pp , 27.

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Wu, and X. Jang, Novel flte fo stato hamonc cuents educton n sx-step convete fed multphase nducton moto dves, IEEE Tans. Powe Electon., vol. 28, no. 1, pp , Jan [3] B. Bahan, A. Kam, B. Rey, and A. Rufe, Decoupled dq-cuent contol of gd-ted voltage souce convetes usng nonpaametc models, IEEE Tans. Ind. Electon., vol. 6, no. 4, pp , Ap. 213 [31] L. Hanefos and H.-P. Nee, Model-based cuent contol of AC machnes usng the ntenal model contol method, IEEE Tans. Ind. Appl., vol. 34, no. 1, pp , Jan./Feb [32] K. Maouan, L. Baghl, D. Hadouche, A. Khelou, and A. Razzoug, A new PWM stategy based on a 24-secto vecto space decomposton fo a sx-phase VSI-fed dual stato nducton moto, IEEE Tans. Ind. Electon., vol. 55, no. 5, pp , May 28. [33] J. Peto, E. Lev, F. Baeo, and S. Toal, Output cuent pple analyss fo asymmetcal sx-phase dves usng double zeo-sequence njecton PWM, n 37 th Annu. Conf. IEEE Industal Electoncs Socety (IECON 211), Melboune, 211, pp [34] R. Bojo, A. Tencon, F. Pofumo, G. Gva, and D. Matnello, Complete analyss and compaatve study of dgtal modulaton technques fo dual thee-phase AC moto dves, n 22 IEEE 33 d Annu. Powe Electoncs Specalsts Conf., Cans, 22, vol. 2, pp [35] D. Yazdan, S. Khajehoddn, A. Bakhsha, and G. Joós, Full utlzaton of nvete n splt-phase dves by means of a dual thee-phase space vecto classfcaton algothm, IEEE Tans. Ind. Electon., vol. 56, no. 1, pp , Jan. 29. [36] G. Gand, G. Sea, and A. Tan, Space vecto modulaton of a sxphase VSI based on thee-phase decomposton, n Int. Symp. Powe Electoncs, Electcal Dves, Automaton and Moton (SPEEDAM 28), Ischa, 28, pp [37] C. Lu, F. Blaabjeg, W. Chen, and D. Xu, Stato cuent hamonc contol wth esonant contolle fo doubly fed nducton geneato, IEEE Tans. Powe Electon., vol. 27, no. 7, pp , Jul Juss Kattunen eceved the B.Sc. and M.Sc. degees n electcal engneeng fom the Lappeenanta Unvesty of Technology, Lappeenanta, Fnland, n 21 and 211, espectvely, whee he s cuently wokng as a Reseache towad the D.Sc. degee. Hs eseach nteests nclude powe electoncs and electcal dves.

13 13 Samul Kallo eceved the M.Sc. degee n electcal engneeng fom the Lappeenanta Unvesty of Technology, Lappeenanta, Fnland, n 28. He s cuently wokng towad the D.Sc. degee at the same unvesty. Hs eseach nteests nclude modelng of electcal machnes and powe electonc convetes especally n the feld of enewable enegy. Pett Slventonen s a Pofesso (Electoncs) wth Lappeenanta Unvesty of Technology (LUT). He eceved hs Doctoal n 21, Lc. Tech n 1997, and M.Sc. n 1993 n Electcal Engneeng. Dung hs caee at LUT, he has had seveal eseach and teachng postons snce 199, funded by the Natonal Technology Agency of Fnland (TEKES) and seveal Fnnsh companes. Pas Peltonem (M 9) was bon n 1978 n Fnland. He eceved hs M.Sc and D.Sc degees n electcal engneeng fom Lappeenanta Unvesty of Technology,Fnland n 25 and 21, espectvely. Hs aeas of nteests nclude dstbuted geneaton n mcogds, contol of gd-connected convetes and electc dves and passve flteng solutons. Oll Pyhönen eceved the M.Sc. and D.Sc. degees n Electcal Engneeng n 199 and 1998 fom Lappeenanta Unvesty of Technology (LUT), Fnland. He has been Pofesso n Appled Contol Engneeng snce 2 at LUT. In 21 he eceved futhe teachng and eseach esponsblty n the wnd powe technology at LUT. He has ganed ndustal expeence as a R&D Engnee at ABB Helsnk n and as a CTO of The Swtch n He has publshed about 8 papes n the contol of electcal dves, powe electoncs and othe ndustal and enewable enegy applcatons.