Modified Venturini Modulation Method for Matrix Converter Under Unbalanced Input Voltage Conditions

Transcription

1 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v Artcle odfed Venturn odulton ethod for trx Converter Under Unlnced Input Voltge Condtons Neerkorn Jrutus nd Yuttn Kumsuwn 2, *, 2 Deprtment of Electrcl Engneerng, Fculty of Engneerng, Chng Unversty, Chng, Thlnd nrk.jrt@gml.com * Correspondence: yt@eng.cmu.c.th; Tel.: ext. 44 Astrct: Bsed on Venturn method, t s n fvor of the modulton technque for controllng the mtrx converter due to only use of the comprson etween the duty cycles n tme domn nd the trngulr crrer wve for genertng the gtng sgnls nd the chevle voltge rto etween fundmentl output mgntude nd fundmentl nput mgntude to.866. However, even wth smple modulton method nd chevng mxmum fundmentl output mgntude, the possle nput voltge unlnce condtons ccordngly nfluence on the output performnces (more reducton nd dstorton). Thus, modfed Venturn modulton method s presented n ths pper, n order to solve the prolems of unlnced nput voltge condtons on the mtrx converter performnces. The proposed strtegy s to stsfy the desrle feture of the duty cycle modultng wves, s generted n the event of norml stuton. Up to ths pproch, t cn support ether sngle-phse condton or two-phse condton. Performnce of the proposed control strtegy ws verfed y the smulted mplementton n the ATLAB/Smulnk softwre wth showng good stedy-stte nd dynmc opertons. Keywords: Venturn method; mtrx converter; unlnced voltge condtons; crrer-sed pulse wdth modulton (PW).. Introducton Drect c-c mtrx converters were developed y Venturn nd Alesn [, 2], n 98. Accordng to ts unque mtrx structure conssted of nne -drectonl swtches, s drwn n Fgure, the ttrctve expedences, compred wth the ndrect mtrx converter, re the lck of lrge dc-lnk energy storge element, whch therefore leds to compct nd lghtweght sze of pckge, drectonl energy-flow lty, reducton n the voltge stress on ndvdul swtches, nd lso extend lfespn. By reson of ts ncluded cpltes of djustle output mgntude nd fundmentl frequency, t hs een used ovously n lterntve nd contnuous development, n vrous c electrcl utlty pplctons for ny ndustry, ncludng djustle speed drves for n c nducton motor [-5], unnterruptle power supples long wth mproved control strteges for enhncng the power qulty [6, 7] nd grd nterfcng converters n the renewle energy converson system [8, 9]. Regrdng the modulton methods of the mtrx converter, t s well known tht gretly relevnt nd powerful method s the Venturn modulton proposed n [] nd tht hs een frequently employed up to now [-5]. Wth ths method, whch s used s drect trnsfer functon, t cn e flexly used to provde the vrle-frequency nd -mpltude fundmentl output voltges from fxed-frequency nd -mpltude snusodl nput voltges. Ths cn e 28 y the uthor(s). Dstruted under Cretve Commons CC BY lcense.

2 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 2 of 4 S Cc, S Cc trx Converter Power Crcut c Proposed control strtegy sed on Venturn method S Bc, S Bc S Ac, S Ac S C, S C S B, S B S A, S A S C, S C S B, S B S A, S A S Ac S A S Ac S A S A S Bc S B S Bc S B S B S Cc S C S Cc S C S C c R c R R L c L L n S A S B S C A B C A B C v B v C N Fgure.Structure of mtrx converter usng the proposed modfed Venturn modulton method. cheved hgh voltge gn, n terms of output voltge mgntude versus nput voltge mgntude, rechng.866, whch s the mxmum gn t ths tme. In ddton, s reported n [6], low-complexty nd good dynmc performnces of the Venturn modulton led to very convenent modulton method for the mtrx converter wth the reserch scope of fxed-frequency output voltge contruton. One mjor ssue of the mtrx converter system s the unlnce of the three-phse nput voltge condton, whch s cuse of the reducton nd/or dstorton n the output voltges (nd herey currents). To fgure out such prolem, the modfed nput current modulton strteges, sed on the spce vector modulton (SV) lgorthm, were proposed n [7-9] to mprove the qulty of the nput currents under unlnced voltge condtons. However, these strteges re needed the complcted rel-tmng vector clcultons tht lso depend on ll swtchng opertons of the mtrx converter. enwhle, the feedck compenston strteges v close-loop control, sed on the Venturn modulton method were presented n [2, 2]. However, t s dffcult to desgn feedck system long wth elorte mthemtcl trnsfer functons due to the exstence of unvodle non-lner prmeters, nd lso produce the tme dely. Another set of the soluton s the ddtonl element of the clmp crcut etween the nput nd output sdes of the mtrx converter, s ntroduced n [22, 2]. Ths leds to cumultve hrdwre component nd much more complexty of the control method sed on the relevnt prstc component desgn. Ths pper presents modfed Venturn modulton method for the mtrx converter under unlnced nput voltge condtons, whch s drwn n Fgure. The slent fetures of the proposed control strtegy re concsely clrfed s follows: It modfes the modulton strtegy sed on the Venturn method to regulte constnt duty cycle modultng wves despte of hvng unlnced nput voltge condtons. It smplfes the complexty of the nlytcl mthemtc model. Tht mens t does not rely on the mplementtons of the SV lgorthm nd the feedck closed-loop control. Any ddtonl hrdwre element s unnecessry to e nstlled for solvng the effects of the unlnced nput voltges, ledng to low cost soluton. The composton of ths pper to support the proposed control strtegy s orgnzed s follows. Secton 2 refly dscusses the scs of the Venturn modulton method long wth ts effects under the unlnced nput voltges. The theory of the proposed control strtegy to solve the prolem s susequently descred n Secton. Smulton results testfyng the proposed control strtegy performnce re demonstrted n Secton 4. Fnlly, ths pper s concluded n Secton 5.

3 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v of Overvew of Venturn ethod 2.. Structure nd Swtchng Operton of the trx Converter As shown n Fgure, the structure of the mtrx converter conssts of eghteen IGBTs n totl, where the swtchng sttes of ech leg re operted wthn two sc rules [, 2] s summrzed elow: No two drectonl swtches re turned on n the sme horzontl leg. Ths leds to short through n converter leg. All the swtches cnnot e turned off n the sme horzontl leg. Ths mght destroy the swtches n converter leg due to the overvoltge. On ccount of these two sc rules, there re swtchng sttes tht llow to operte n one leg of ths converter, s lsted n Tle. Wth these swtchng sttes, the swtchng sttes of leg nd leg c re lso smlr to leg, ut they re shfted y rd nd rd, respectvely. Hence, the 2 4 swtchng modes of the mtrx converter n three phses re totlng 27 modes, s clerly shown n Fgure 2. Tle. Swtchng Sttes per Leg (Leg ) of the trx Converter. Swtchng sttes S A Swtchng for Leg S B S C A On Off Off B Off On Off C Off Off On Phse output voltge v B v C v A A A A A A A A A B B B B B B B B B C C C C C C C C C c c c c c c c c c [A A A] [A A B] [A A C] [A B A] [A B B] [A B C] [A C A] [A C B] [A C C] A A A A A A A A A B B B B B B B B B C C C C C C C C C c c c c c c c c c [B B B] [B B A] [B B C] [B A A] [B A B] [B A C] [B C A] [B C B] [B C C] A A A A A A A A A B B B B B B B B B C C C C C C C C C c c c c c c c c c [C C C] [C C A] [C C B] [C A A] [C A B] [C A C] [C B A] [C B B] [C B C] Swtch turns on, Swtch turns off Fgure 2. Comnton of 27 swtchng modes of the mtrx converter. From whch, the reltonshp etween nput voltge ( v () t ) nd output voltge ( v () t ) cn e expressed n the swtchng functon pont of vew s follow: SA SB SC v ( t) SA SB S = C v o( t). () S Ac SBc S Cc Bsed on (), t s further lgorthm, whch s ntlly used to fnd the modultng functon n the Venturn modulton method for controllng the mtrx converter, s dscussed n the next susecton Prncple of the Venturn odulton Bsed on the Venturn modulton method, the ttnle gtng pulse generton for ech of the nne drectonl swtches s ntlly syntheszed from the nstntneous three-phse nput voltges ( v ( t)), s derved y: o

4 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 4 of where V denotes the mpltude of the nput voltges, sn ( ) ( ) ( ) va V t v ( t) v = B = V sn t 2, (2) v C V sn t 2 = 2 f denotes the fundmentl ngulr frequency of the nput voltges. Followng (2), t s dgnosed y ssumng the condton of the lnced three-phse nput voltges. Tkng nto consderton ths strtegy, the output voltges relted to the nput voltges wth the drect trnsfer functon cn e gven s: where () t ( v o ( t)) v ( t) =( t) v ( t), () o s the trnsfer mtrx of the mtrx converter, nd lso cn e defned s: ma mb mc () t = ma mb m C. (4) m Ac mbc m Cc Usng (4), the trnsfer mtrx conssts of the duty cycles for genertng the gtng pulses of nne -drectonl swtches. The comprehensve formul form for ll the duty cycles cn e ccordnglu expressed s: where j = A, B, C nd k =,, c. phse-to-neutrl output voltge. q c vv j k 2q m jk = 2qc sn 2 ( jt j ) sn ( jt), (5) V qm q v j denotes the phse-to-neutrl nput voltge. denotes the gn of.5. q m v k denotes the denotes the gn of denotes the modulton voltge rto, whch s n the lner modulton rnge of q c. Anlyzng () to (5), for gven, the mxmum mgntude of the fundmentl output q = c voltge cn e cheved y.866 of the nput voltge. For extendng the techncl clrfcton of the Venturn modulton method, much more detl cn e found n [, 2]. 2.. Sttement of Drwcks The exmple under oth lnced nd unlnced nput voltge condtons wth the Venturn modulton method t the modulton voltge rto q of s demonstrted n Fgure (), where the specfc prmeters lsted n Tle 2 re used. Before.2 s, the lnced nput voltge condton ffects the symmetrcl wveforms of pole voltges,, nd long wth the lne-to-lne output voltge v nd currents,, nd c c v N v N. Hence, s shown n Fgure 4() nd Fgure 5(), the fundmentl output voltge mgntudes pproch round.866 of nput voltges. In the contrry, t cn gn e oserved from Fgure () tht when the unlnced nput voltge condton (on phse A) occurred fter.2 s, the duty cycles n the only frst column of (4),.e., A n ths fgure, re reduced. Ths s why the output voltges result n symmetrcl wveforms, s t s evdent wth the purple dshed-lne orders. Ths consequently leds to further reducton nd dstorton n the output currents nd voltges, s nvestgted n Fgures 4 nd 5, respectvely. However, when the proposed control strtegy s ppled, s shown n Fgure t.2 s, the duty cycle hs ovously ncresed nd s equl to tht of the perod of the lnced nput voltge condton. Ths leds to the reducton of the prolems cused y the unlnced nput voltge condton, s cn e seen from the ncrementl fundmentl mgntudes of the output currents nd voltges long wth the reduced mgntudes of ther hrmoncs n Fgures 4(c) nd 5(c), respectvely. A

5 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 5 of Blnced nput voltge condton Unlnced nput voltge condton vc vb B A C v N Unlnced nput voltge condton Proposed control strtegy vc vb B A C v N - v N - v N (A) Tme (s) () c v (A) Tme (s) Fgure. A trnston from () lnced nput voltge condton to unlnced nput voltge condton wth the Venturn method nd unlnced nput voltge condton wth the Venturn method to unlnced nput voltge condton wth the proposed control strtegy. (Top to ottom) Wveforms of nput voltges va, vb, v C, duty cycles A, B, C, pole voltges vn, vn, v cn, lne-to-lne output voltge, nd output currents,, c. v c v gntude (A) gntude (A) gntude (A) Iˆ = 8.47A, I ˆ = 7.4 A, I ˆ = 8.A c,.5 THD =. 77% Hrmonc order Iˆ = 5.94A, I ˆ = 6.64 A, I ˆ = 6.45A c, ().5 THD = 4.84% THD = 4. 2% Hrmonc order Iˆ = 6.99A, I ˆ = 6.69 A, I ˆ = 7.29A c,.5 c THD = 4. 9% THD = 4.87% THD = 4. % 8 THD = 4. % Hrmonc order (c) c THD = 4. 45% THD = 4.86% Fgure 4. Hrmonc spectrum of output currents for the perod of () lnced nput voltge condton, unlnced nput voltge condton wth the Venturn method, nd (c) unlnced nput voltge condton wth the proposed control strtegy. c

6 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 6 of gntude gntude gntude V ˆ = 44V,THD = 6.8%, v Hrmonc order () V ˆ = 86.7V,THD = 65.8%, v Hrmonc order V ˆ = 97.V,THD = 62.4%, v Hrmonc order (c) Fgure 5. Hrmonc spectrum of lne-to-lne output voltge for the perod of () lnced nput voltge condton, unlnced nput voltge condton wth the Venturn method, nd (c) unlnced nput voltge condton wth the proposed control strtegy.. Proposed Control Strtegy for trx Converter Solvng the unlnced nput voltge nfluences, the use of the proposed control strtegy y modfyng the modulton of Venturn method n order to regulte the desrle modulton voltge rto, resultng n keepng the desrle duty cycles to e constnt. Bsed on the duty q c cycle clculton n (5), to mke n nlyss wth regrd to lnced nd unlnced nput voltge condtons, the desred reference voltges of the three-phse nput voltges re ntlly gven s: where * v j, ref ( ) v, = V, sn t, (6) * j ref j ref j j denotes the desred reference voltges of the three-phse nput voltges n the norml stuton. Susequent to the check of lnced nd unlnced nput voltges, the men functon ( ) of the three-phse nput voltges cn e determned s: v men ( ) v = v v v. (7) men A B C Consderng (7), f the three-phse nput voltges re lnced, the men functon ecomes. Otherwse, t wll led to tngle ppernce. Accordngly, the error ( e j v men ) etween the desred nput voltge reference nd the men of the three-phse nput voltges cn e clculted y e = v v. (8) * rj j, ref men Usng (6) to (8), the proposed modfed duty cycle clculton sed on the Venturn method cn e formulted s ( ) vmen e j vk 2q jk = 2qc sn 2 ( jt j ) sn ( jt). (9) V q m Accordng to (9), the proposed control strtegy sed on the Venturn method modfes the duty cycle clculton n the terms of the nput voltges for regultng t n order to not e vred followng the unlnced nput voltges. Lter on, these duty cycles re entered nto the process of gtng pulse generton for drvng ll the swtches of the mtrx converter, referrng to Fgure 6.

7 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 7 of 4 * * *, ref v B, ref v C, ref v B v C v men / e ra e rb e rc va vb v C Duty Cycle Clculton (9) 9 Gtng Pulse Generton S A, S A S B, S B S C, S C S A, S A S B, S B S C, S C S Ac, S Ac S Bc, S Bc S Cc, S Cc Proposed control strtegy sed on Venturn method Fgure 6. Schemtc dgrm of the proposed control strtegy. 4. Smulton Results Smultons of the proposed control strtegy y modfyng the Venturn modulton method for the mtrx converter (see Fgures nd 6) re crred out on the convenent softwre of ATLAB/Smulnk envronment n order to verfy the theoretcl nlyss nd the proposed control performnce. Herey, the specfc prmeters ndcted n Tle 2 re lso employed. Tle 2. Prmeters Used for Smulton. Prmeters Symols Vlues Three-phse nput voltges Input frequency va, vb, vc f s f o 22 V 5 Hz Output frequency 5 Hz Three-phse resstve lods R, R, R c Three-phse nductve lods L, L, L c mh Swtchng frequency odulton voltge rto f sw q c.5 2 khz Fgure 7 shows the smulted results of the proposed control strtegy wth the modulton voltge rto of.5 under the % step-sg commnd for sngle-phse unlnced nput voltge q c condton on phse A. As shown n Fgure 7(), the men functon v men results n V for the perod of the lnced nput voltge condton, s theoretclly clculted from (7). Hence, the proposed control lgorthm s drectly mplemented on the Venturn modulton prncple. On the contrry, snce the phse-a nput voltge sgs to 28 V, the proposed control strtegy s crred out for regultng the duty cycles t of.5 wth mgntude of the men functon t. V. As the results, the ptterns of the pole voltges q c v v N, N, nd produce the lnce nd stlty for the lne-to-lne output voltges ( wth the proposed control strtegy v for the fgure), s well s the three-phse output currents,, nd, s drectly confrmed y the spectrum of output currents shown n Fgure 7. The mgntudes of the output voltges cn e clculted such tht ther fundmentl components re equvlent to round 5% of the nput voltges, whch s greele nd correspondng to theory of the Venturn method. Smlrly, the unlnced nput voltge condton of the 5% step-sg commnd s demonstrted n Fgure 8. Wth Fgure 8(), the ppernce of the men functon v n the sg c durton resemles tht of Fgure 7(), wheres ts mgntude further up to round 5.55 V. Tht mens the dsturnce of unlnced nput voltges s more ntense n comprson to the cse of Fgure 7. As expected, the duty cycle modultng wves keepng wth the constnt modulton voltge rto q of.5 led to stle nd good qultes of the output voltges nd currents. c Referrng to Fgure 8, the cceptle hrmonc spectrum of output currents s cheved wthout the reducton n the mgntudes of ther fundmentl components, ncludng the dstorton of the men

8 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 8 of 4 sg (pu.) v men vc vb 5-5 en.5 A B C v N - v N (A) gntude (A) Tme (s) Iˆ =.74A, Iˆ =. A, I ˆ =.6A c,.5 () Hrmonc order c v THD = 2. 6% THD = 2. 5% THD = 2.88% Fgure 7. Smulton results wth the condton of % step-sg sngle-phse unlnced nput voltge. () (Top to ottom) Wveforms of step-sg commnd nd error, three-phse nput voltges, duty cycle modultng wves, three-phse pole voltges, lne-to-lne output voltge, nd three-phse output currents. Three-phse output currents hrmonc spectrum for unlnced nput voltge durton. wveforms. Ths cn uthentcte the proposed control strtegy performnce nd ts theoretcl vldty. A set of the smulted results for the % step-sg commnd on phses A nd B re shown n Fgure 9. Consderng.2 s to.24 s (see Fgure 9()), owng to the sme level of unlnced nput voltge sg, the men functon v results n the sme mgntude s tht of the sngle-phse men unlnced nput voltge condton (see Fgure 7()), except tht ts phse ngle s led y 9. c

9 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 9 of 4 sg (pu.) v men vc vb 5-5 en.5 A B C v N - v N (A) gntude (A) Tme (s) Iˆ =.46A, Iˆ =.85 A, I ˆ =.92A c,.5 () Hrmonc order c v THD = 2. 78% THD = 2.98% THD = 2. 7% 2 Fgure 8. Smulton results wth the condton of 5% step-sg sngle-phse unlnced nput voltge. () (Top to ottom) Wveforms of step-sg commnd nd error, three-phse nput voltges, duty cycle modultng wves, three-phse pole voltges, lne-to-lne output voltge, nd three-phse output currents. Three-phse output currents hrmonc spectrum for unlnced nput voltge durton. Even though oth phse-a nd phse-b nput voltges unntentonlly fll to round 28 V, the output voltges nd currents cn cheve recognzle qultes nd mgntudes for the whole durton. In Fgure 9, t s evdent tht the output voltges nd currents re stll kept three-phse lnced feture wth the performnce of the proposed control strtegy. c

10 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v of 4 sg (pu.) v men vc vb 5-5 en.5 A B C v N - v N (A) gntude (A) Tme (s) Iˆ =.46A, Iˆ =.4 A, I ˆ =.4A c,.5 () Hrmonc order c v THD = 2. 62% THD = 2.82% THD = 2. 8% 2 Fgure 9. Smulton results wth the condton of % step-sg two-phse unlnced nput voltges. () (Top to ottom) Wveforms of step-sg commnd nd error, three-phse nput voltges, duty cycle modultng wves, three-phse pole voltges, lne-to-lne output voltge, nd three-phse output currents. Three-phse output currents hrmonc spectrum for unlnced nput voltge durton. Susequent to nvestgton of the proposed control strtegy performnce under the two-phse unlnced nput voltge condton, the pplcton of the 5% step-sg commnd on phses A nd B s lso chllenged n Fgure. As t cn e seen n the sg perod of the nput voltges, the men functon v of ths cse s found to e round 5.55 V (see Fgure ()), t hs the sme men mgntude s tht of Fgure 8(). A chnge n the dul-phse (A nd B) nput voltges does not ffect c

11 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v of 4 sg (pu.) v men vc vb 5-5 en.5 A B C v N - v N - 5 v -5 2 c (A) gntude (A) Tme (s) Iˆ =.4A, Iˆ =. A, I ˆ =.49A c,.5 () THD = 2. 79% Hrmonc order THD = 2.98% THD = 2. 6% Fgure. Smulton results wth the condton of 5% step-sg two-phse unlnced nput voltges. () (Top to ottom) Wveforms of step-sg commnd nd error, three-phse nput voltges, duty cycle modultng wves, three-phse pole voltges, lne-to-lne output voltge, nd three-phse output currents. Three-phse output currents hrmonc spectrum for unlnced nput voltge durton. the duty cycles wth the proposed control strtegy. Ths s why there re not more dstortons n the output voltges nd currents, s cn e vewed from the correspondng hrmonc spectrum n Fgure. For dscusson, t s noteworthy tht the proposed control strtegy s not workle for cse of much more thn 5% two-phse unlnced nput voltge condton. Tht mens t s unservcele for the extreme sngle-phse nd two-phse unlnced nput voltge condtons, ncludng the three-phse unlnced nput voltge condtons. c

12 THD of output current (%) V V Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 2 of Accordng to the dsgreele output profles under 5%-sg unlnced nput voltge condton of the proposed control strtegy, s nvestgted n the prevous secton, t s consequently evluted wth only % sg of sngle-phse unlnced nput voltge condton. To dstnctly confrm the performnce of the proposed control strtegy, t s lso compred wth the conventonl Venturn method n the pont of vew of the fundmentl output mgntude nd the output current qulty, s shown n Fgures () nd. The evluton of Fgure () shows tht the proposed control strtegy cn mprove the output mgntude of the mtrx converter from the conventonl Venturn method under the sme condtons s unlnced nput voltges lthough t produces lower output mgntude, when compred to tht of the norml stuton, wth modulton ndex of greter thn.5. As the hve een llustrted n Fgure, t s ponted out tht the THD proposed control strtegy not only cn mprove the output mgntude of the mtrx converter, ut lso cn develop the output current qulty from the conventonl Venturn method, when t s operted under unlnced nput voltge condton. oreover, t lso provdes the sme THD tendency, s operted under the non-unlnced nput voltge condton (norml stuton). Ths could confrm the performnce of the proposed control strtegy for the mtrx converter under unlnced nput voltge condtons. ˆ ˆ, (pu.) AB, (Blnced) NormlStuton %Sg of phse A(Venturn method [, 2]) %Sg of phse A(Proposed control strtegy) odulton voltge rto ( ) () NormlStuton %Sg of phse A(Venturn method [, 2]) %Sg of phse A(Proposed control strtegy) q c odulton voltge rto ( ) Fgure. Performnce evluton of the proposed control strtegy for the mtrx converter compred wth the conventonl Venturn method ([, 2]). 5. Concluson A control strtegy y modfyng the Venturn modulton method for mtrx converter under unlnced nput voltge condtons s presented n ths pper. It s not necessry to consume ny ddtonl energy storges, hrdwre devces, nd complcted control lgorthms. In the proposed q c

13 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v of lgorthm, the duty cycle clculton sed on the Venturn method s modfed y mthemtcl nlyses on the men functon of the mesured three-phse nput voltges nd the error clcultons n order to stsfy the desrle stle nd lnced output voltges, long wth the desrle mgntudes of fundmentl components. Among the results, the proposed control strtegy s le to elmnte the low-order hrmoncs of the output voltges nd provde s the lnced wveforms under sngle- nd two-phse unlnced nput voltge condtons. Among these resons, t cn lso confrm the vldty of the theoretcl prncple nd the uthentcty of the proposed control strtegy performnce. Unfortuntely, ths strtegy s unworkle for mssve sg voltge condtons of more thn 5% nd three-phse unlnced nput voltge condtons. References.. Venturn. A new sne wve n, sne wve out converson technque whch elmntes rectve elements. Seventh Ntonl Sold-Stte Power Converson Conference, Sn Dego, Clforn, rch 24-27, 98; pp. E_-E_ Venturn; A. Alesn. The generlsed trnsformer: A new drectonl snusodl wveform frequency converter wth contnuously djustle nput power fctor. IEEE Power Electroncs Speclsts Conference, Atlnt, Georg, June 6-2, 98; pp , DOI.. P. Nelsen; F. Bljerg; J. K. Pedersen. New protecton ssues of mtrx converter: Desgn consdertons for djustle-speed drves. IEEE Trns. Ind. Applct., 999, vol. 5, no. 5, pp. 5-6, DOI. 4. C. Klumpner; P. Nelsen; I. Bolde; F. Bljerg. A new mtrx converter motor (C) for ndustry pplctons. IEEE Trns. Ind. Electron., 22, vol. 49, no. 2, pp. 25-5, DOI. 5. D. Orser; N. ohn. A mtrx converter rde-through confgurton usng nput flter cpctors s n energy exchnge mechnsm. IEEE Trns. Power Electron., 25, vol., no. 8, pp , DOI. 6. H.. Nguyen; H. Lee; T. Chun. Input power fctor compenston lgorthms usng new drect-sv method for mtrx converter. IEEE Trns. Ind. Electron., 2, vol. 58, no., pp , DOI. 7. T. Sh; Y. Yn; H. An;. L; C. X. Improved doule lne voltge synthess strteges of mtrx converter for nput/output qulty enhncement. IEEE Trns. Ind. Electron., 2, vol. 6, no. 8, pp. 4-46, DOI. 8. H. Hojr; H. okhtr; L. Chng. Rectve power control of permnent-mgnet synchronous wnd genertor wth mtrx converter. IEEE Trns. Power Del., 2, vol. 28, no. 2, pp , DOI. 9. S. ond; D. Ksth. Improved drect torque nd rectve power control of mtrx converter-fed grd-connected douly fed nducton genertor. IEEE Trns. Ind. Electron., 25, vol. 62, no. 2, pp , DOI.. J. Rodrguez; E. Slv; F. Bljerg; P. Wheeler; J. Clre; J. Pontt. trx converter controlled wth the drect trnsfer functon pproch: Anlyss, modelng nd smulton. Int. J. Electron., 25, vol. 92, no. 2, pp. 6 85, DOI.. P. Wheeler; J. Rodrguez; J. Clre; L. Emprnghm; A. Wensten. trx converters: A technology revew. IEEE Trns. Ind. Electron., 22, vol. 49, no. 2, pp , DOI. 2. S. Bernet; S. Ponnlur; R. Techmnn. Desgn nd loss comprson of mtrx converters, nd voltge-source converters for modern AC drves. IEEE Trns. Ind. Electron., 22, vol. 49, no. 2, pp. 4 4, DOI.. J. Rzs. Cpctor clmped multlevel mtrx converter controlled wth Venturn method. th Interntonl Power Electroncs nd oton Control Conference, Poznn, Polnd, Septemer -, 28; pp , DOI. 4. Y. e; L. Hung. Improved swtchng functon modulton strtegy for three-phse to sngle-phse mtrx converter. IEEE 6th Interntonl Power Electroncs nd oton Control Conference, Wuhn, Chn, y 7-2, 29; pp , DOI. 5. S. Lopez Arevlo; P. Znchett; P. Wheeler; A. Trentn; L. Emprnghm. Control nd mplementton of mtrx-convertersed AC-ground power-supply unt for rcrft servcng. IEEE Trns. Ind. Electron., 2, vol. 57, no. 6, pp , DOI. 6. J. Rodrguez;. Rver; J. W. Kolr; P. W. Wheeler. A revew of control nd modulton methods for mtrx converters. IEEE Trns. Ind. Electron., 22, vol. 59, no., pp. 58-7, DOI.

14 Preprnts ( NOT PEER-REVIEWED Posted: 22 y 28 do:.2944/preprnts v 4 of F. Bljerg; D. Csde; C. Klumpner;. tten. Comprson of two current modulton strteges for mtrx converters under unlnced nput voltge condtons. IEEE Trns. Ind. Electron., 22, vol. 49, no. 2, pp , DOI. 8. X. Wng; H. Ln; H. She; B. Feng. A reserch on spce vector modulton strtegy for mtrx converter under norml nput-voltge condtons. IEEE Trns. Ind. Electron., 22, vol. 59, no., pp. 9-4, DOI. 9. X. L;. Su; Y. Sun; H. Dn; W. Xong. odulton strteges sed on mthemtcl constructon method for mtrx converter under unlnced nput voltges. IET Power Electron., 2, vol. 6, ss., pp , DOI. 2. K. Sun; D. Zhou; L. Hung; K. tsuse. Compenston control of mtrx converter fed nducton motor drve under norml nput voltge condtons. IEEE Industry Applctons Conference, Settle, WA, USA, Octoer -7, 24; pp. 62-6, DOI. 2. H. Krc; R. Akky. Control of Venturn method sed mtrx converter n nput voltge vrtons. Interntonl ultconference of Engneers nd Computer Scentsts, Kowloon, Hong Kong, rch 8-2, 29, DOI.