Power Decoupling Method for Isolated DC to Single-phase AC Converter using Matrix Converter

Transcription

1 Pwer Decuplng Mehd fr Islaed DC Sngle-phase AC Cnverer usng Marx Cnverer Hrk Takahash, Nagsa Takaka, Raul Rber Rdrguez Guerrez and Jun-ch Ih Dep. f Elecrcal Engneerng Nagaka Unversy f Technlgy Nagaka, Ngaa, Japan hrk@sn.nagakau.ac.jp, nakaka@sn.nagakau.ac.jp, s39063@sn.nagakau.ac.jp, h@vs.nagakau.ac.jp Absrac Ths paper presens an slaed DC sngle-phase AC cnverer usng a marx cnverer fr HVDC (hgher vlage drec curren) pwer feedng sysem. The prpsed cnverer cmprses a full brdge nverer, a hgh frequency ransfrmer and a marx cnverer and des n use a bulky elecrlyc capacr. Then, n rder reduce a rpple cmpnen n a DC bus curren caused by he sngle-phase lad, hs paper als prpses a pwer decuplng mehd. The pwer decuplng mehd emplys a cener-apped ransfrmer and a small C fer nsead f addnal swches, whch ams acheve hgh effcency. Mrever, mdulan mehds f he full brdge nverer and he marx cnverer, and a cnrl sraegy f he pwer decuplng are descrbed. As an expermenal resul, he pwer decuplng mehd reduces he DC bus curren rpple /3. In addn, a valdy f a parameer desgn mehd f he prpsed cnrl s cnfrmed n smulans. eywrds marx cnverer; pwer decuplng; pwer rpple; I. INTRODUCTION Recenly, pwer cnsumpn f ICT (nfrman and cmmuncan echnlgy) equpmen n a buldng and a facry has been ncreasng drascally. As a slun fr pwer savng f a buldng, a HVDC (hgher vlage drec curren) pwer feedng sysem has been develped []. The HVDC pwer feedng sysem has a DC bus f 380 V n rder am a hgh effcency and lw cs because f reducng cnverers and cables, cmpared a cnvennal AC r a DC 48 V pwer feedng. Then, f an exsng pwer feedng sysem s replaced wh he HVDC ne, a DC-AC cnverer cnnec he DC bus and exsng sngle-phase AC equpmen s requred. In addn, he DC-AC cnverer needs slan beween he DC bus and he AC equpmen fr safey. Therefre, an slaed DC sngle-phase AC cnverer s requred. The slaed DC-AC cnverer requres dwnszng and hgh effcency. Then, a cnvennal cnverer cnsss f a full brdge nverer as a prmary cnverer, a hgh frequency ransfrmer and a secndary cnverer cmpsed f a dde recfer and an nverer. []. Hwever, he secndary cnverer uses a balky elecrlyc capacr smh DC-lnk vlage and resrcs dwnszng and hgh effcency. On he her hand, a marx cnverer has araced a l f aenns because a marx cnverer has n DC energy fer [3-4]. A marx cnverer prmses acheve hgher effcency, smaller sze and lnger lfe-me cmpared a cnvennal recfer-nverer sysem. Therefre, a marx cnverer s suable fr a secndary cnverer f he slaed DC snglephase AC cnverer. Hwever, a marx cnverer cann absrb pwer rpple whch s generaed by a sngle-phase lad because f n energy fer n s plgy. As a resul, DC bus curren ncludes a rpple cmpnen a wce f he AC lad frequency whch affecs a baery cnneced n DC bus fr back-up and elecrlyc capacrs n her cnverers adversely. Thus, a pwer decuplng capably usng small passve cmpnens s requred he slaed DC sngle-phase AC cnverer remve he rpple cmpnen. In pas wrks, sme crcu plges wh a pwer decuplng capably have been prpsed [5-6]. Hwever, hese papers emply n nly small passve cmpnens bu als mre swchng devces fr he pwer decuplng. In rder vercme hs prblem, a pwer decuplng mehd usng a cener-apped ransfrmer and a small C fer has been presened [7]. Ths mehd des n use addnal swches and suppresses he rpple cmpnen n he npu curren sgnfcanly. Hwever, [7] deals wh an slaed DC snglephase AC cnverer usng a dde recfer and a PWM nverer, n a marx cnverer. In addn, a parameer desgn mehd f s cnrl blck dagram has n been revealed. Ths paper prpses an slaed DC sngle-phase AC cnverer usng a marx cnverer n rder mprve he effcency and sze reducn. The prpsed sysem cnsss f a full brdge nverer, a cener-apped ransfrmer, a small C fer and a marx cnverer. The prpsed cnverer des n requre exra swchng devces fr he pwer decuplng, wng he cener-apped ransfrmer. In cnras, he marx cnverer s appled a PDM (pulse densy mdulan) whch s apprprae cnver a hgh frequency vlage a snusdal vlage a 50 Hz. Mrever, n rder yeld an nended cnrl perfrmance, hs paper clarfes a parameer desgn mehd f he pwer decuplng cnrl and an upu curren cnrl. Ths paper s rganzed as fllws; frsly, a crcu cnfguran f he prpsed DC-AC cnverer and a prncple f he pwer decuplng are descrbed; secndly, mdulan mehds and a cnrl blck dagram wh he desgn mehd are repred; fnally, fundamenal peran wavefrms and

2 ransen respnses f he prpsed sysem are evaluaed n smulans and expermens. II. CIRCUIT TOPOOGY Fg. shws a cnvennal slaed DC sngle-phase AC cnverer. The cnvennal crcu cmprses a full brdge nverer, a hgh frequency ransfrmer and a recfer-nverer sysem. The full brdge nverer upus a square vlage a a hgh frequency n rder reduce vlume f he ransfrmer. The secndary recfer cnvers he hgh frequency vlage a DC vlage and he PWM nverer cnrls an upu fler capacr vlage wh a feedback cnrl. When he lad curren s snusdal wavefrm and acheves he uny pwer facr, an nsananeus upu pwer p u s expressed by (). V bus I bus Full brdge Inverer N N dc C dc Dde recfer v u u u C u PWM nverer lad R lad v lad Fg.. A cnvennal slaed DC sngle-phase AC cnverer. The cnvennal cnverer uses a balky elecrlyc capacr C dc absrb he pwer rpple caused by a sngle-phase lad. p u V V lad lad I lad Ilad sn cs P cs sn ave where, V lad s he lad vlage (RMS), I lad s he lad curren (RMS), P ave s an upu average pwer and s he upu angular frequency. A rpple cmpnen shwn n he secnd erm f () shuld be bypassed n rder ban a cnsan DC curren f he DC bus. Hence, hs sysem has adp a balky elecrlyc capacr C dc absrb he pwer rpple. Fg. shws he slaed DC sngle-phase AC cnverer usng a marx cnverer and a small C fer whch s prpsed n hs paper. The marx cnverer s emplyed as a secndary cnverer n rder elmnae he DC-lnk capacr whch s used n Fg.. In addn, a cener-apped ransfrmer lnks he full brdge nverer he marx cnverer fr slan and he pwer decuplng whch resuls n reducng he DC bus curren rpple. A fer crcu ncludng a fer capacr C and a fer nducr s used absrb he pwer rpple. I shuld be ned ha a charge and a dscharge cmpensae he pwer rpple s mplemened a C. Fg. 3 shws a prncple f he pwer decuplng wh C. In rder yeld a DC bus curren whu he rpple, a relanshp amng he upu pwer p u, a DC bus pwer p bus and a charged pwer p s defned as () (4). p u p p bus Fg.. The prpsed slaed DC sngle-phase AC cnverer. The secndary cnverer s replaced wh a marx cnverer n rder elmnae a DC-lnk smhng capacr. In addn, a cener-apped ransfrmer and a small C fer are emplyed acheve a pwer decuplng whu addnal swchng devces. V bus I bus p bus V Cmax V Cmn v C p dscharge charge dscharge charge v lad 0 v lad p u lad lad V I lad lad sn sn p P cs p P bus u ave where, a plary f p s defned as psve when C s charged. I shuld be ned ha he used capacr s smaller han ne n he cnvennal cnverer because he pwer rpple s cmpensaed by varyng a fer capacr vlage v C n a large capacance. On he her hand, an nducr n he fer crcu s used fr a curren cnrl fr he pwer decuplng, whch s equvalen cnrl f p. The fer Inpu pwer p bus [W] Buffer pwer p [W] Oupu pwer p u [W] Fg. 3. A prncple f he pwer decuplng wh he fer capacr. A fer pwer cmpensae he pwer rpple s charged r dscharged a C. As a resul, a DC bus curren whu he rpple cmpnen s baned. curren cnrl s carred u by he full brdge nverer. The full brdge nverer upus a dfferenal mde vlage exce he ransfrmer and a cmmn mde vlage cmpensae he pwer rpple wh he C fer ndependenly, wng he cener-apped ransfrmer. Therefre, he prpsed cnverer des n requre addnal swchng devces fr he pwer

3 decuplng and number f devces f he prpsed cnverer s he same as ne f he cnvennal crcu. III. MODUATION METHOD A. Full Brdge Inverer Fg. 4 shws a mdulan mehd f he full brdge nverer. As menned abve, he full brdge nverer upus a dfferenal mde vlage v df exce he ransfrmer and a cmmn mde vlage v cm cmpensae he pwer rpple a he same me. Therefre, a dfferenal mde vlage reference v df and a cmmn mde vlage reference v cm are se as npu parameers n Fg. 4. I shuld be ned ha a gan f 0.5 s nsered a pah f v df nly because a reference penal f v df s dfferen frm ne f v cm. In rder ban he maxmum secndary vlage f he ransfrmer, v df s se p.u.. On he her hand, v cm s calculaed by a PI cnrller n he fer curren cnrl cmpensae he pwer rpple as menned n chaper IV. Fg. 5 shws peran mdes f he full brdge nverer. A hached gray lne ndcaes a urned ff swch and a black sld lne shws a curren pahway. Fg. 5 (a) and (b) llusrae he dfferenal mde ransfer he DC bus pwer. In hs mde, he ransfrmer s exced. In addn, a fer crcu vlage, whch s equvalen v cm, s cnsan f V bus /. On he her hand, Fg. 5 (c) and (d) shw he cmmn mde cnrl he fer curren n rder cmpensae he pwer rpple. In he cmmn mde, he ransfrmer s n exced because v df becmes zer. As a resul, he full brdge nverer cnrls v df and v cm ndependenly because he dfferenal mde changes v df nly and he cmmn mde changes v cm nly. Ths ndependence acheves ha he prpsed cnverer des n need addnal swches fr he pwer decuplng. B. Marx Cnverer Fg. 6 shws a cncep f a PDM mehd f he marx cnverer used as a secndary cnverer n he prpsed sysem. The PDM s apprprae fr a drec AC-AC cnverer whch prvdes a snusdal vlage a a cmmercal frequency frm a hgh frequency vlage, such as he prpsed sysem. The PDM reas an npu vlage wavefrm a hgh frequency as a pulse and synhesze an upu vlage wh a densy f he npu vlage pulses. In Fg. 6, a half cycle f he npu vlage pulses are used as he mnmum un f he upu vlage wavefrm. Then, he marx cnverer swches urn n zer vlage perd f he npu vlage wavefrm nevably. In cnsequence, he marx cnverer acheves a ZVS (zer vlage swchng) whch resuls n decreasng a swchng lss. Thus, he PDM s appled he marx cnverer n hs paper. Fg. 7 shws a blck dagram f he PDM. The blck dagram s cmpsed f a mdular, a swchng phase selecr and a synchrnzan wh a clck (C). Owng he swchng phase selecr, a full wave recfed sgnal f an upu vlage reference v u s used fr he PDM. The mdular generaes a gae pulse such as an analg-dgal cnversn. In addn, C synchrnze he gae pulse wh he zer vlage perd s baned by he cmmn mde f he full brdge nverer and a phase shfer easly. (a) Blck dagram (b) Defnn f v df and v cm Fg. 4. A mdulan mehd f he full brdge nverer. A dfferenal mde vlage reference v df s fr excng he ransfrmer and a cmmn mde vlage reference v cm s used cmpensae he pwer rpple wh he C fer. (a) Dfferenal mde. (b) Dfferenal mde. (c) Cmmn mde. (d) Cmmn mde. Fg. 5. Operan mdes f he full brdge nverer. IV. CONTRO STRATEGY AND PARAMETER DESIGN Fg. 8 shws a cnrl blck dagram f he prpsed cnverer. The blck dagram s cmpsed f a fer curren cnrl, a vlage cnrl f an upu fler capacr, a curren cnrl f an upu fler nducr and a cmpensan f a secndary vlage flucuan f he ransfrmer. These curren and vlage cnrls are mplemened by PI cnrllers. The fer curren cnrl s fr he pwer decuplng. The fler curren and vlage cnrl are prvde a sable lad vlage. In addn, he cmpensan f he secndary vlage flucuan f he ransfrmer s needed n rder elmnae a dsurbance f he fler curren cnrl caused by an npu vlage flucuan f he marx cnverer dependng n he

4 cmmn mde vlage reference v cm. A desgn mehd f hese cnrls s descrbed frm he nex secn. I shuld be ned ha he fler vlage cnrl s n descrbed because he vlage cnrl s n a echncal ssue n hs paper and can be seleced n he prevus sudes. dvc Pave cs 0 C d Vbus Pave sn 4 C A. Calculan f Buffer Curren Reference In rder absrb he pwer rpple caused by he snglephase lad, a fer curren reference shuld be calculaed frm p u and a chargeable energy f C. Frs f all, he fer capacr energy W C s presened by (5). W C v C 0 dvc d v C C d 0 d I shuld be ned ha P ave s calculaed by a lad ressance. Therefre, he pwer rpple s cmpensaed by usng he fer curren cnrl wh he curren reference as shwn (9). B. Buffer Curren Cnrl Fg. 9 shws a blck dagram desgn he PI cnrller fr he fer curren cnrl and a fler F (s) fr a ple-zer cancelan. A plan mdel s he C fer crcu. In addn, p_ s a prprnal gan and T _ s an negral me f he fer PI cnrller. Then, a clsed lp ransfer funcn f where, s a fer curren and 0 s a sar me f peran. In cnras, W C s als expressed by usng p. WC p d Pave cs 0 d By usng (5) and (6), v C s calculaed as fllwng. 0 P ave v V sn sn C C 0 C 0 where, V C0 s an nal vlage f C and V C0 s V bus /. If 0 s zer, (7) s rewren as (8). Fg. 6. A cncep f a PDM mehd f he marx cnverer. The PDM reas a half cycle f an npu vlage wavefrm as a pulse and synhesze an upu vlage wh a densy f he npu vlage pulses. V P 4 C bus ave v sn C Fnally, s derved by usng an upu pwer reference P ave. Fg. 7. A blck dagram f he PDM. The PDM s based n mdular. V bus Fg. 8. A cnrl blck dagram f he prpsed cnverer. A fer curren cnrl s fr he pwer decuplng. A vlage cnrl f an upu fler capacr and a curren cnrl f an upu fler nducr s prvde sable lad vlage. A cmpensan f he secndary vlage flucuan f he ransfrmer s requred fr an nended cnrl perfrmance.

5 Fg. 9 excep F (s) s expressed by (0). p _ st _ C T _ T _ p _ p _ s s p _ C C T PF In rder ransfrm (0) n a sandard frm f a secnd rder ransfer funcn, F (s) s defned as () and a clsed lp ransfer funcn ncludng F (s) s presened by (). F T _ ( s) st _ p _ C _PF v s +st _ F (s) p_ st _ s PI cnrller C C fer crcu Fg. 9. A blck dagram desgn he PI cnrller fr he fer curren cnrl and a fler F (s) fr a ple-zer cancelan. By usng hs mdel, an nended cnrl respnse f he pwer decuplng s baned. u F u (s) u_pf p_u +st _u st _u PI cnrller v u s u Fler nducr u p s _ C s p _ T _ C p _ T _ Fg. 0. A blck dagram desgn he PI cnller fr he curren cnrl f an upu fler nducr and a fler F u (s) fr a ple-zer cancelan. Then, p_ and T _ are calculaed by usng an nended naural angular frequency n_ and a dampng facr f a sandard frm f a secnd rder ransfer funcn. T p _ n n _ n _ C Hence, he pwer decuplng wh an nended cnrl perfrmance s acheved by (3) and (4). C. Curren Cnrl f Oupu Fler Inducr Fg. 0 shws a blck dagram desgn he PI cnrller fr he curren cnrl f he upu fler nducr and a fler F u (s) fr a ple-zer cancelan. A plan mdel s a fler nducr. In addn, p_u s a prprnal gan and T _ u s an negral me f he fler curren PI cnrller. Then, f F u (s) s defned as (5), a clsed lp ransfer funcn f Fg. 0 s presened by (6). F u ( s) st p _ u T _ u u u _ u u p u _ p _ u s s u ut _ u Fg.. A relanshp beween he cmmn mde vlage reference v cm and he full wave recfed wavefrm f he secndary vlage. In rder cmpensae he secndary vlage flucuan, v u s dvded by v s_rec. Therefre, p_u and T _u are desgned by usng an nended naural angular frequency n_u and a dampng facr u n he same way wh he fer curren cnrl as (7) and (8). p _ u un _ u u u T _ u n _ u D. Cmpensan f Secndary Vlage Flucuan In rder ban an nended respnse f he fler curren cnrl regardless f a secndary vlage f he ransfrmer, a cmpensan f a secndary vlage flucuan f he ransfrmer s needed. Then, he secndary vlage depends n V bus, v cm and a urn ra f he ransfrmer N /N. By he way, he PDM deals wh a half cycle f he secndary vlage pulses as he mnmum un, regardless f a plary f he secndary vlage. Thus, he cmpensan s cnsdered wh a full wave recfed wavefrm f he secndary vlage v s_rec. Fg. shws a relanshp beween he cmmn mde vlage reference v cm and v s_rec n a smulan. Ths smulan s carred u wh Fg. 4 (a) nly. Therefre, he fer curren cnrl s n appled and he marx cnverer s n cnneced. These wavefrms are nrmalzed wh he DC

6 bus vlage V bus. The urn ra f he ransfrmer s :. Frm Fg., v s_rec s synchrnzed wh v cm and s presened as (9). TABE I. SIMUATION CONDITION. N vs _ rec Vbus vcm N Therefre, n rder cmpensae he secndary vlage flucuan, v u s dvded by v s_rec as shwn n (9). V. SIMUATION AND EXPERIMENTA RESUTS A. Smulan Resuls n Seady Sae Table shws a smulan cndn verfy a fundamenal peran f he prpsed cnverer. I shuld be ned ha he fler capacr and he lad ressance s replaced wh a vlage surce f 00 V rms, 50 Hz fr smplcy. Thus, he vlage cnrl f he upu fler capacr s n used. Fg. shws he npu and he upu wavefrms n a seady sae. Fg. (a) shws a resul whu he pwer decuplng mehd and (b) shws a resul wh he mehd. A DC bus curren s flered wh a PF wh a cu-ff frequency f khz n rder remve a swchng rpple. Frm Fg. (a), he DC bus curren has a rpple cmpnen a 00 Hz caused by he sngle-phase lad. Then, he rpple cmpnen a 00 Hz s 03% wh reference an average curren n (a). In cnras, he rpple cmpnen s reduced n (b), wng he pwer decuplng mehd. As a resul, he rpple f he DC bus curren s suppressed by 9.5%. In addn, a fler nducr curren THD (al harmnc dsrn) s less han %. B. Evaluan f Cnrl Perfrmance In rder verfy he prpsed desgn mehd f he cnrl parameers descrbed n chaper IV, ransen respnses f he fer curren cnrl and he fler curren cnrl are evaluaed n hs secn. I shuld be ned ha hese smulans are mplemened wh a DC mdel n rder evaluae he cnrls wh an versh and an versh me. Fg. 3 shws an ndcal respnse f he fer curren cnrl. Frm Fg. 3, he acual fer curren fllws he reference rgh afer a sep npu. In addn, he acual curren cnfrms an deal respnse f based n Fg. 9. Then, a percenage versh f he deal respnse s 4.60% and an versh me f he deal respnse s ms. These resuls crrespnd her desgned values based n he naural angular frequency and he dampng facr n Table I. I shuld be ned ha he desgned percenage versh PO and he versh me T are calculaed by fllwng equans. (a) Whu he pwer decuplng mehd. (b) Wh he pwer decuplng mehd. Fg.. Inpu and upu wavefrms n a seady sae. The prpsed pwer decuplng mehd reduces he DC bus curren rpple by 9.5%. PO 00[%] exp Fg. 3. An ndcal respnse f he fer curren cnrl. The verh and he versh me crrespnd he desgned values. T n_ Fg. 4. An ndcal respnse f he fler curren cnrl. The verh and he versh me crrespnd he desgned values.

7 Fg. 4 shws an ndcal respnse f he fler curren cnrl. Frm Fg. 4, he acual fler curren u fllws he reference u rgh afer a sep npu. In addn, he acual curren cnfrms an deal respnse f u based n Fg. 0. Then, a percenage versh f he deal respnse s 4.60% and an versh me f he deal respnse s.46 ms. These resuls crrespnd her desgned resuls calculaed n he same manner wh (0) and (). Therefre, he prpsed desgn mehd acheves an nended cnrl perfrmance. C. Expermenal Resuls n Seady Sae An expermenal seup s demnsraed valdae he prpsed sysem,. I shuld be ned ha a fer capacr f 50 F, a fer nducr f mh, a lad nducr f mh and a ransfrmer f he urn ra f / are used, and a C fler s nsered n he DC bus sde. Mrever, he PDM mehd based n he mdulan n Fg. 7 s replaced wh a PDM dscussed n [8] because f an expermenal lman. In addn, he cnrl parameers are adjused fr he expermen. Fg. 5 shws expermenal wavefrms f he prpsed cnverer wh V bus f 350 V, v u f 80.8 V rms and an R- lad f 594 W. Fg. 6 (a) shws a resul whu he pwer decuplng mehd and (b) shws a resul wh he mehd. Frm (a), he fer capacr vlage des n vary because he full brdge nverer des n upu he cmmn mde AC vlage. As a resul, he DC bus curren has a pwer rpple cmpnen a 00 Hz. In cnras, he prpsed pwer decuplng mehd prvdes he cmmn mde AC vlage flucuae he fer capacr vlage. In cnsequence, he pwer rpple cmpnen n he DC bus curren s decreased. Then, he upu vlage THD n (b) s 5.9% because f a reslun prblem f he used PDM mehd. Fg. 6 shws a harmnc analyss f he DC bus curren. I shuld be ned ha he harmnc number s based n he upu frequency a 50 Hz. Frm he resul whu he pwer decuplng mehd, he pwer rpple cmpnen a 00 Hz s 65.5% wh reference an average curren. In cnras, he prpsed mehd reduces he 00-Hz cmpnen 43.3% because he fer capacr vlage flucuan absrbs he pwer rpple a 00 Hz. As a resul, he prpsed mehd reduces he pwer rpple /3. The DC bus curren dsrn wll be reduced mre by mprvng he upu vlage qualy wh he PDM mehd based n he mdulan and he fer curren cnrl perfrmance. VI. CONCUSION Ths paper presens an slaed DC sngle-phase AC cnverer usng a marx cnverer. The prpsed cnverer elmnaes a bulky elecrlyc capacr because a marx cnverer s emplyed as a secndary cnverer. Ths paper als descrbes he pwer decuplng mehd reduce a rpple cmpnen n a DC bus curren caused by a sngle-phase lad. In addn, desgn equans f he pwer decuplng cnrl and an upu curren cnrl are prpsed. As a smulan resul, he prpsed pwer decuplng reduces he DC bus curren rpple by 9.5%. In addn, an expermenal resul verfes he prpsed pwer decuplng mehd reduces he 00-Hz cmpnen caused by he pwer rpple /3. (a) Whu he pwer decuplng mehd. (b) Wh he pwer decuplng mehd. Fg. 5. Expermenal wavefrms n a seady sae. Fg. 6. Harmnc analyss f he DC bus curren. The prpsed pwer decuplng mehd reduces a 00-Hz rpple n he DC bus curren /3. REFERENCES [] T. Babasak, T. Tanaka, Y. Nzak, T. Tanaka, T. Ak, F. urkawa: "Develpng f Hgher Vlage Drec-Curren Pwer-feedng Prype Sysem", Prc. 3s INTEEC 009, (009) [] S. Jung, Y. Bae, S. Ch, H. m: "A lw cs uly neracve nverer fr Resdenal Fuel Cell Generan", IEEE Trans. Pwer Elecrn., Vl., N. 6, pp (007) [3] P. W. Wheeler, J. Rdrguez, J. C. Clare,. Emprngham: "Marx Cnverers: A Technlgy Revew", IEEE Trans. Ind. Elecrn., Vl. 49, N., pp (00) [4] J. Rdrguez, M. Rvera, J. W. lar, P. W. Wheeler: "A Revew f Cnrl and Mdulan Mehds fr Marx Cnverers", IEEE Trans. Ind. Elecrn., Vl. 59, N., pp (0) [5] T. Shmzu, S. Suzuk: "A sngle-phase grd-cnneced nverer wh pwer decuplng funcn", Prc. IPEC 00, pp (00) [6]. H. Cha, P. T. Cheng: "Pwer Decuplng Mehds fr sngle-phase hree-ples AC/DC cnverers", Prc. ECCE009, pp (009) [7] J. Ih, F. Hayash: "Rpple Curren Reducn f a Fuel Cell fr a Sngle-Phase Islaed Cnverer Usng a DC Acve Fler Wh a Cener Tap", IEEE Trans. Pwer Elecrn., Vl. 5, N. 3, pp (00) [8] Y.Nakaa, J.Ih: "A Fundamenal Verfcan f a Sngle-phase Three-phase Marx Cnverer wh a PDM Cnrl based n Space Vecr Mdulan", Prc. IPEC 04, N. 9P-, pp (04)