Modelling of a Power Converter with Multiple Operating Modes

Transcription

1 Aricle Modellg a Power Converer wih Muliple Operag Mode Wang Feng ID uo Yuao * School Mechanical Auomoive Engeerg, Souh Cha Univeriy Technology, Guangzhou 564, Cha; xiaojwf@63.com * Correpondence: cyluo@cu.edu.cn; Tel.: Received: 7 May 8; Acceped: 8 May 8; Publhed: 5 June 8 Abrac: In order o achieve DC volage machg, onboard chargg, DC/AC verion, hree dependen converer are en needed radiional Dribued Power Converer (DPC) yem elecric vehicle (E): bidirecional DC/DC (BiDC/DC), AC/DC, DC/AC. requiremen elecronic device uch a powewiche, ducor, capacior make converer coly complicaed rucure. In h paper, a converer wih mulioperag mode (PCMM) preened. propoed PCMM can work BiDC/DC, AC/DC, DC/AC mode. aepace averagg model PCMM coniderg reance Inulaed Gae Bipolar Tranor (IGBT) ducor preened. Baed on h model, ranfer funcion yem derived conroller deigned. imulaion experimenal reul how ha PCMM can mee deign arge verify feaibiliy model. meauremen reul how ha weigh PCMM propoed h paper reduced by 5.% compared wih radiional rucure. Keyword: converer; bidirecional DC/DC; AC/DC; DC/AC. Inroducion Carbon dioxide (CO ) from vehicle exhau one ma caue greenhoue effec. Elecric vehicle (E) are conidered o be an imporan developmen direcion fuure auomobile dury becaue ir advanage reducg CO emion. In order o improve performance orage yem, a hybrid ource can be ued. []. In elecric vehicle (E), lihiumion baerie or fuel cell are en ued a primary poweource, which upplemened by a upercapacior pack or baery pack a auxiliary poweource o coniue a hybrid orage yem (HESS) []. A primary auxiliary poweource uually have differen volage level, a DC/DC converer needed o achieve volage machg [3]. Meanwhile, order o charge baery pack, a charger wih AC/DC funcion needed [4], which conver grid AC o DC. In addiion, when AC poweupply required for cae like oudoor aciviie, a DC/AC verer needed o conver baery DC o AC [5]. Simulaneouly, a DC/AC verer alo need o have grid connecion funcion, o ha baery level E can be fed back o grid afer verion when E i idle garage, reby playg a role grid peak hifg regulaion. DC/DC converer play an imporan role DC level converion orage yem, cludg hybrid orage yem [6], P yem [7,8], fuel cell yem [9], ec. Inerleaved one DC/DC opologie [9]. advanage h opology clude low oupu curren ripple high deniy []. erleaved DC/DC can be compoed wo phae [], hree phae [], or muliphae [3]. I ha grealy reduced volume weigh compared o radiional BiDC/DC. World Elecric ehicle Journal 8, 9, 7; doi:.339/wevj97

2 World Elecric ehicle Journal 8, 9, 7 7 To improve facor proce AC/DC converion, facor correcion (PFC) World Elecric ehicle Journal 8, 9, x FOR PEER REIEW 7 needed wih a pecial circui. radiional PFC mehod add a boo converer behd recifier bridge [4]. To Such improve a mehod require facor a recifier proce bridge AC/DC converion, a boo circui, which facor ha correcion dadvanage (PFC) low converion needed wih efficiency. a pecial circui. To improve radiional converion PFC mehod efficiency, add a boo reearcher converer have behd propoed a bridgele recifier PFCbridge circui [4]. opology Such a mehod ha doe require no require a recifier recifier bridge bridge a [5]. boo One circui, oluion which ha o add wo addiional dadvanage diode o low improve converion EMI efficiency. problem To improve [6]. Anor converion oluionefficiency, bridgele reearcher PFC wih have oem propoed a bridgele PFC circui opology ha doe no require recifier bridge [5]. One oluion pole opology [7]. Th opology doe no require addiional elemen. I only need o drive o add wo addiional diode o improve EMI problem [6]. Anooluion bridgele PFC wo wiche bridge dependenly. wih oem pole opology [7]. Th opology doe no require addiional elemen. I only re need are o drive hree wo ma wiche opologie bridge for DC/AC dependenly. verer [8]. One puhpull configuraion verer, which re are con hree ma fewopologie device for DC/AC verer eay[8]. o drive One [9]. However, puhpull configuraion due o rucural characeric verer, which con circui ielf, few puhpull device circui eay opology drive [9]. canno However, oupu due uoidal o rucural volage waveform, characeric which uiable circui forielf, low puhpull applicaion. circui opology Anorcanno oupu halfbridge uoidal opology volage verer, whichwaveform, ha few wichg which componen uiable for low a imple applicaion. rucure. Anor Neverle, halfbridge raedopology curren i verer, wich which wice ha ha few wichg componen componen a imple a fullbridge rucure. verer Neverle, circui, wih raed large curren curren i powewich wice ha componen a fullbridge verer circui, wih large re. hird one fullbridge verer, whoe oupu curren curren hrough wichg curren re. hird one fullbridge verer, whoe oupu curren curren hrough componen wichg are componen boh half are boh halfbridge half verer halfbridge circui. verer circui. drive circui drive circui fullbridge fullbridge complex verer han more wocomplex previou han opologie wo previou due o opologie preence due o four wichg preence device. four verer more Inwichg E wih device. hybrid orage yem, radiional Dribued Power Converer (DPC) cheme need In E a wih leahybrid hree dependen orage BiDC/DC, yem, AC/DC, radiional Dribued DC/ACPower converer. Converer When (DPC) an E begcheme driven, need buck a lea converer hree dependen boo BiDC/DC, converer AC/DC, are needed DC/AC o conver converer. When an beween E baery beg pack driven, buck auxiliary converer. boo An AC/DC converer converer are needed o needed conver o charge beween baery pack. baery pack auxiliary. An AC/DC converer needed o charge baery pack. A A DC/AC converer needed o upply AC o elecric appliance. opology h DC/AC converer needed o upply AC o elecric appliance. opology h yem hown Figure. Each converer need o be equipped wih eparae radiaor, which are yem hown Figure. Each converer need o be equipped wih eparae radiaor, which are hu rucurally hu rucurally complex complex coly. coly. Figure. Convenional dribued converer (DPC) opology. Figure. Convenional dribued converer (DPC) opology. Some reearcher have udied mulifuncional converer. convereyem Some egrag reearcher a moor have conrolleudied mulifuncional baery charger propoed converer. by JY ee e al. enabled converer AC/DC yem egrag converion a moohare conroller device baery a moor charger conroller propoed []. by Serkan JY ee Dumez e al. e al. enabled egraed AC/DC converion AC/DC o charger hare a baery on device ba a moor a DC/DC conroller converer []. by harg Serkan Dumez device e al. egraed a boo DC/DC converer [,]. TgChia Ou e al. propoed a mulipu converer o AC/DC charger a baery on ba a DC/DC converer by harg device achieve differen operaion mode [3]. a boo DC/DC Previou converer reearch on [,]. converer TgChia maly Ou e focue al. propoed on ir performance. a mulipu For egraion converer o achieve converer, differen operaion lieraure mode only menioned [3]. DC/DC AC/DC egraion. Compared wih Previou radiional reearch converer, h paper converer preen maly a novel focue egraed onmulifuncion ir performance. converer Forclude egraion Biconverer, DC/DC, AC/DC, lieraure DC/AC. only menioned Baed DC/DC opology AC/DC BiDC/DC, egraion. preened Compared PCMM add wih radiional only one converer, wich h an AC paper capacior preen o achieve a novel mulifuncion egraedoperaion. mulifuncion I hare converer ducor, clude BiDC/DC, capacior, AC/DC, IGBT module DC/AC. Baed fer hree on converion opologyfuncion BiDC/DC, reduced yem preened weigh. PCMM add only one wich an AC capacior o achieve mulifuncion operaion. I hare ducor, capacior, IGBT module fer hree converion funcion reduced yem weigh.

3 World World Elecric Elecric ehicle ehicle Journal Journal 8, 8, 9, 9, 7 x FOR PEER REIEW World Elecric ehicle Journal 8, 9, x FOR PEER REIEW 3 7 Th Th paper paper preen preen a PCMM PCMM converer converer build build model model yem yem ug ug a aepace aepace averagg averagg modellg modellg mehod mehod [4]. [4]. Secion Secion roduce roduce model model converer converer each each operag operag mode. mode. Par Par 3 perform perform experimenal experimenal reul. reul. reul. Experimenal Experimenal evaluaion evaluaion evaluaion PCMM PCMM PCMM preened preened preened Secion Secion Secion Modellg Modellg Conrol Conrol Syem Syem PCMM PCMM propoed propoed h h paper paper ha ha hree hree workg workg mode. mode. opology opology hown hown Figure Figure. When.. When When workg workg BiDC/DC BiDC/DC mode, mode, wich wich K K K urned urned on on on wich wich K wich K K urned urned urned f. f. f. yem yem yem work work work buck buck buck mode mode mode or or boo boo or boo mode. mode. mode. In In AC/DC AC/DC In AC/DC mode, mode, mode, wich wich K wich K urned urned K urned on on on wich wich K wich K urned urned K f, f, urned f, yem yem work work yemwih wih work bridgele bridgele wih bridgele PFC PFC opology, opology, PFC opology, flow flow from from flow from grid grid o o gridbaery baery o ide. ide. baery In In DC/AC DC/AC ide. Inmode, mode, DC/AC wich wich K mode, K wich urned urned K on on urned wich wich K on K wich urned urned Kf. f. urned f. flow flow from from flow baery baery from ide ide baery o o AC AC ide ide ide o o o AC achieve achieve idedc DC o achieve o o AC AC converion. converion. DC o AC converion. AC AC ou ou AC AC ~ ~ DC DC K C C 3 3 K K 3 3 C DCH DCH Figure Figure.. Propoed Propoed opology. opology. A hown Figure 3, 3, when vehicle vehicle drivg, drivg, PCMM PCMM work work BiDC/DC BiDC/DC mode. mode. A hown Figure 3, when vehicle drivg, PCMM work BiDC/DC mode. conroller conroller dribue dribue for for baery baery auxiliary ource accordg o conroller dribue for baery auxiliary ource accordg o dem verer. auxiliary ource will provide when PCMM dem verer. auxiliary ource will provide when PCMM operae boo mode. PCMM deec DC bu volage, calculae reference curren operae boo mode. PCMM deec DC bu volage, calculae reference curren accordg o o ha auxiliary need o o repond wih. When auxiliary accordg o ha auxiliary need o repond wih. When auxiliary ource needed for for recovery, PCMM operae buck buck mode. PCMM deec ource needed for recovery, PCMM operae buck mode. PCMM deec volage auxiliary volage auxiliary calculae calculae arge arge curren curren accordg accordg o o o recovered recovered by by auxiliary auxiliary.. When When baery baery pack pack need need chargg, chargg, PCMM PCMM operae operae AC/DC AC/DC mode. mode. In In In conan conan curren curren chargg chargg age, age, conrol conrol objecive objecive PCMM PCMM oupu oupu curren. curren. In In In conan conan volage volage chargg chargg age, age, conrol conrol objecive objecive PCMM PCMM oupu oupu volage. volage. PCMM PCMM work work DC/AC DC/AC mode mode when when i i neceary neceary o o provide provide glephae glephae AC AC for for elecrical elecrical equipmen. equipmen. PCMM PCMM adop adop adop double double double loop loop loop conrol; conrol; conrol; curren curren curren ducor ducor ducor ner loop, ner ner loop, loop, oupu AC oupu oupu volage AC AC volage volage ouer loop, ouer ouer loop, loop, conrol arge conrol conrol arge arge oupu volage. oupu oupu volage. volage. Sar Sar Drivg? Drivg? No No Ye Ye Recycle Recycle Buck Buck Auxiliary Auxiliary Supply Supply Boo Boo Chargg? Chargg? Ye Ye AC/DC AC/DC AC upply? AC upply? Ye Ye DC/AC DC/AC Figure Figure Figure Flow Flow Flow char char char funcion funcion funcion needed needed needed E E E wih wih wih hybrid hybrid hybrid orage orage orage yem. yem. yem.

4 World Elecric ehicle Journal 8, 9, x FOR PEER REIEW 4 7 World Elecric ehicle Journal 8, 9, BiDC/DC Mode.. BiDC/DC Mode In buck mode BiDC/DC converer, equivalen circui yem a how Figure 4. In buck mode BiDC/DC converer, equivalen circui yem a how Figure 4. o C r r C R i Figure equivalen circui BiDC/DC mode. volage capacior v vc (), curren ducor i (), i () c (), curren ducor i (), i () are are eleced eleced a a ae variable yem. high ide volage v ae variable yem. high ide volage i () v i () eleced a pu variable, low eleced a pu variable, ide volage v o () low ide volage v () eleced a oupu variable. ae equaion oupu equaion o yem can be given a Equaion eleced () a oupu (). variable. ae equaion oupu equaion yem can be given a Equaion () (). i () i () i () i i() () = A i () B[v i ()] () i() A i () v v Bvi() c () c () () vc () vc () i () v o () = C i i () D[v () i ()] () vo() C v c () i () Dvi() () For bidc/dc converer operag an ducor conuou mode (CCM), coefficien vc () marix ae pace averagg equaion given a Equaion (3). For bidc/dc converer operag an ducor conuou mode (CCM), coefficien marix ae pace r averagg equaion given a Equaion (3). d A = r [ ],B = d r r d C C, C =, D = [] (3) R C where, r ernal reance rducor, r r d A, ernal B, reance C, IGBT, d duy D (3) cycle PWM. In eady ae, derivaive each ae variable zero, relaion beween eady ae oupu volage C pu volage C can RCbeexpreed by Equaion (4). where, r ernal reance ducor, R o = d ernal reance IGBT, d duy cycle PWM. R r r i (4) where, In Ready ae, derivaive each ae variable zero, relaion beween eady load reance. ae oupu average volage vecor pu yem volage can be can expreed be expreed a by um Equaion (4). eadyae value mall ignal value, hown Equaion (5). Rd o i (4) R r r i () T I i ˆ () where, R load reance. i () T = I ˆ i () (5) average vecor yem v c () can T be expreed c a vum ˆ c () eadyae value mall ignal value, hown Equaion (5).

5 World Elecric ehicle Journal 8, 9, In viciy eady ae, mall ignal model yem can be obaed by parial derivaive variable, aplace ranform can be ued a Equaion (6). i ˆ () i ˆ () = A vˆ c () i ˆ () i ˆ () B ˆv i () vˆ c () i i ˆ d() (6) Make ˆ d() =, ranfer funcion pu volage o each ae variable can be deermed via Equaion (7). G xvi = (SI A) B (7) Make ˆv i () =, ranfer funcion duy cycle o each ae variable can be calculaed a Equaion (8). G xd = (SI A) [ ] i T i (8) boo model buck model have dual ymmery, coefficien marix average ae pace equaion boo mode given by Equaion (9). A = r d r d C d d C R C,B =, C = [ ], D = [] (9) relaion beween eady ae oupu volage pu volage can be expreed a Equaion (). R o = ( d) ( d) i () R r ranfer funcion pu volage o each ae variable can be deermed by Equaion (). G xvi = (SI A) B () ranfer funcion duy cycle o each ae variable can be calculaed wih Equaion (). G xd = (SI A) [ c c I C I C ] T () conrol rucure BiDC/DC mode hown Figure 5. conroller con wo ner loop one ouer loop. In buck mode, ref reference volage low volage ide, ou oupu volage, d x duy cycle Q, d x duy cycle Q. In boo mode, ref reference volage high volage ide, ou oupu volage, d x duy cycle Q 3, d x duy cycle Q 4. PI x, PI x, PI x3 PI regulaor yem. Baed on model yem illuraed Equaion () (), parameer PI regulaor buck mode boo mode can be obaed eaily by oool oolbox MATAB.

6 oupu volage, dx duy cycle Q, dx duy cycle Q. In boo mode, ref oupu volage, dx duy cycle Q, dx duy cycle Q. In boo mode, ref reference volage high volage ide, ou oupu volage, dx reference volage high volage ide, duy cycle Q3, ou oupu volage, dx duy cycle Q3, dx duy cycle Q4. PIx, PIx, PIx3 PI regulaor yem. Baed on model dx duy cycle Q4. PIx, PIx, PIx3 PI regulaor yem. Baed on model yem illuraed Equaion () (), parameer PI regulaor buck mode World Elecric yem ehicle illuraed Journal 8, 9, Equaion 7 () (), parameer PI regulaor buck mode 6 7 boo boo mode mode can can be be obaed obaed eaily eaily by by oool oool oolbox oolbox MATAB. MATAB. AC AC dc dc ref ref ac ac K K C C ou ou C3 C3 PI x.5 PI x.5 Q Q Q Q K K C Q4 C Q4 Q3 Q3 d x PI x d x PI x d x PI PI x3 d x x3 Figure 5. conrol rucure BiDC/DC mode. Figure 5. conrol rucure BiDC/DC mode..... AC/DC Mode AC/DC Mode equivalen circui AC/DC mode how Figure 6. equivalen circui AC/DC mode how Figure dch dch r ac ac r r r r r C C o o R R r r Figure 6. equivalen circui AC/DC mode. Figure 6. equivalen circui AC/DC mode. Referrg o Figure 6, aume ha parameer four powewiche are ame. equivalen Referrg o circui ofigure Figure6, 6, aume negaive aumeha half ha cycle parameer parameer poiive four half four cycle powewiche wiche are e wave areame. are ame. equivalen ame. equivalen circui circui negaive negaive half cycle half cycle poiive poiive half cycle half cycle e wave e are wave refore, only poiive half cycle need o be analyzed. volage capacior C are ame. v c () refore, only poiive half, curren ducor i () cycle need, i () o be analyzed. volage capacior C vc () ame. refore, only poiive half cycle need o be analyzed. volage capacior C, v c (), curren curren are eleced a ae variable yem. AC ide volage v () ducor ducor i (), i i () (), are i eleced () are eleced a ae a variable ae variable ac eleced a pu variable, high ide volage v () yem. yem. AC AC ide volage o ide volage v () ac v ac () eleced a pu variable, high ide volage eleced a pu variable, high ide volage v () o v o eleced () eleced eleced a a a oupu oupu variable. variable. ae ae pace pace equaion equaion yem yem oupu equaion are expreed oupu variable. ae pace equaion yem oupu equaion are expreed Equaion () () (). (). coefficien marix average ae pace average equaion yem Equaion () (). coefficien marix average ae pace average equaion yem expreed expreed by by by Equaion Equaion (3). (3). (3). r r d r r r d d A = r d [ ],B = r r d d A C r r d B A, C =, D = [] (3) R C B (3) (3) In eady ae, d relaion beween eady d ae oupu C RC volage pu volage can be expreed a Equaion (4)., C, D, C RC, C, D, R o = ( d) ( d) i (4) R r

7 mall ignal value, a hown Equaion (5). ^ i () () i T I ^ i () I i () T World Elecric ehicle Journal 8, 9, 7 ^ 7 7 () v c T c v () c In average viciy vecor eady yem ae, can be mall expreed ignal a model um yem eadyae can be obaed value by mall parial ignal derivaive value, a hown variable, Equaion (5). aplace ranform carried ou wih Equaion (6). i () T I i ˆc () ^ ^ i () T = I i ˆ i () i() () (5) ^ v c () T ^ c ^ v ˆ () ^ c i() Ai() Bvi() d() (6) ^ ^ In viciy eady vae, mall ignal model yem can be obaed by c() vc() I parial derivaive variable, aplace ranform carried ou wih Equaion (6). C i ˆ () i ˆ () c ^ i ˆ () = A i ˆ Make d (), ranfer funcion () pu volage B ˆv i () o each cae d() variable ˆ can be deermed (6) a Equaion (7). vˆ c () vˆ c () I C Make d() ˆ G xvi SI A B (7) =, ranfer funcion pu volage o each ae variable can be deermed ^ a Equaion v(7). Make i (), ranfer funcion duy cycle G xvi = (SI A) o each ae variable can be calculaed a B (7) Equaion (8). Make ˆv i () =, ranfer funcion duy cycle o each ae variable can be calculaed a T Equaion (8). c c I Gxd SI A G xd = (SI A) [ ] T (8) c c C I C (8) conrol rucure AC/DC mode hown Figure 7. (5) e ac C3 K Q Q dc K Q4 C dch C Q3 ac d PI PI ref / rm RMS Figure 7. conrol rucure AC/DC mode. Figure 7. conrol rucure AC/DC mode. loop compoed an ner curren loop an ouer loop. oupu regulaor PI PI ouer ouer loop loop pu pu volage volage v vacare are muliplied, muliplied, o o ha ha oupu oupu curren curren proporional proporional o o pu pu volage. volage. In order In order o keep o keep oupu oupu conan when conan pu when volage pu durbance, volage RMS value pu volage added a feed forward. ignal calculaed by muliplier ued a a reference curren loop, curren loop adjued by regulaor PI o oba duy cycle PWM..3. DC/AC Mode wave form oupu DC/AC mode a uoidal form, re no DC eady ae operaion po. I a ypical large ignal nonleayem, equivalen circui DC/AC mode hown Figure 8.

8 .3. DC/AC Mode wave form oupu DC/AC mode a uoidal form, re no DC eady ae operaion po. I a ypical large ignal nonleayem, equivalen circui DC/AC mode hown Figure 8. World Elecric ehicle Journal 8, 9, ac Z C r r a b dc Figure equivalen circui DC/AC mode. vc () C curren ( i (), i () ) (, volage v c () capacior C curren (i (), i ()) ducor (, ) are ) eleced are eleced a a ae ae variable variable yem. yem. volage volage v ab () vbeween ab () beween wo po wo po a a b aken a pu variable, oupu volage v ac () b aken a pu variable, oupu volage v () ac aken a oupu variable. Becaue aken a oupu variable. Becaue i () = i i() (), equaion circui can be expreed a Equaion (9) (). i(), equaion circui can be expreed a Equaion (9) (). ( di () ) di () = r i d () v c () v ab () (9) ri ( ) vc( ) vab( ) (9) d ( ) di () = r i () v c () v d ab () () di () ri( ) vc( ) vab( ) () dv c d () C = i d () v c() () Z dvc() vc() C v ac () = iv c () () () () d Z coefficien marix ae pace equaion hown Equaion (3). vac () vc () () r /( ) [ ] A = coefficien marix ae pace equaion hown Equaion (3). r,b = /( ), C =, D = [] (3) C r Z C volage v ab () a dconuou ignal, r which can be averaged over a wichg period o oba i average A ae. For unipolar modulaion, when /( modulaion ) wave v re f () = re f (ω) (3) carrier ampliude, average value B volage v /( ) ab () one period can be expreed a Equaion (4). C ZC, C, D re f (ω), v ab () T = dc (4) v volage () ab Subiug Equaion (4) a dconuou o ae ignal, equaion which can yem, be averaged relaed over characeric a wichg period can be o vref () ref ( ) derived. oba i average ernal ae. reance For unipolar wo modulaion, ducorwhen defed modulaion a r, n wave ranfer funcion yem can be expreed by Equaion v () carrier ampliude, (5). average value volage ab one period can be expreed a Equaion (4). G xvi = (SI A) B (5) ref ( ) conrol rucure DC/ACvmode ab () T hown dc (4) Figure 9. conrol yem compoed an ner loop an ouer loop. reference volage ( re f ) oupu volage a uoidal wave wih required frequency. Regulag by regulaor (PI ), reference curren loop obaed, duy cycle PWM oupu by regulaor (PI ).

9 be derived. ernal reance wo ducor defed a r, n ranfer funcion yem can be expreed by Equaion (5). xvi G SI A B (5) World Elecric ehicle Journal 8, 9, conrol rucure DC/AC mode hown Figure 9. AC ac Q Q C3 K dc K Q4 C dch C Q3 ac ref PI PI d Figure Figure conrol conrol rucure DC/AC mode..4. imiaion conrol Propoed yem Model compoed an ner loop an ouer loop. reference volage ( ref ) oupu volage a uoidal wave wih required frequency. Regulag by regulaor (PI), PCMM model eablhed h paper ha followg limiaion. reference curren loop obaed, duy cycle PWM oupu by regulaor Firly, model baed on average ae variable eablhed by average ae pace (PI). model. ae variable model reflec average value variable a wichg cycle. Th model canno effecively reflec decripion wich deail..4. imiaion Propoed Model Secondly, model a mall ignal model, which reflec mall ignal durbance characeric PCMM model yem eablhed neaeady h ae. paper When ha yem followg durbed limiaion. by a large ignal, uch a arup, Firly, hor circui, model oudden baed break, on average yemae characeric variable eablhed canno beby accuraely average decribed. ae pace model. To reflec ae variable yem characeric model reflec more accuraely, average a nonlear value variable modelg mehod a wichg needed. cycle. However, Th model canno yemeffecively model obaed reflec bydecripion nonlear wich modelg deail. mehod rar complex, which will brg Secondly, difficulie model o conroller a mall deign. ignal Th model, model which can ue reflec claical conrol mall ignal ory durbance o deign a conroller characeric for PCMM. yem I can quickly neaeady deign ae. a conroller When ha yem mee durbed engeerg by a large requiremen. ignal, uch a arup, hor circui, oudden break, yem characeric canno be accuraely decribed. 3. Simulaion To reflec yem PCMMcharaceric more accuraely, a nonlear modelg mehod needed. However, Accordg yem o deign model requiremen obaed by anonlear cera vehicle modelg model, mehod PCMM rar need complex, o achieve which DC will converion brg difficulie beween o uper conroller capacior deign. bankth model lihiumion can ue claical baeryconrol pack, converion ory o deign from glephae a conroller for ACPCMM. o lihiumion I can quickly baery deign pack, a conroller converion ha mee from engeerg lihiumion requiremen. baery pack o glephae AC. performance requiremen PCMM are hown Table. 3. Simulaion PCMM Accordg Table. o Deign deign parameer requiremen converer a cera wih vehicle mulioperag model, mode PCMM (PCMM). need o achieve DC converion beween uper capacior bank lihiumion baery pack, converion from Parameer alue glephae AC o lihiumion baery pack, converion from lihiumion baery pack o glephae AC. performance High iderequiremen volage range PCMM 35 4 are hown Table. ow ide volage range 3 olage AC pu or oupu Rm 8 4 Table. Deign parameer converer wih mulioperag mode (PCMM). AC frequency 5 Hz Oupu Parameer AC 3 kw alue Raed ducor curren 5 A High ide volage range 35 4 ow ide volage range 3 In order o mee olage requiremen AC pu or curren oupu ripple volage Rm 8 4 ripple differen mode, capaciance ducance need AC o frequency be mached wih PCMM deign 5 parameer Hz [5]. reul Oupu AC 3 kw obaed by parameer machg how ha ducance 69 uh, AC filer Raed ducor curren 5 A capacior C 3 3 µf, high ide filer capacior C 94 F, low ide capacior C F. Malab/Simulk wa ued foimulaion ma circui imulaion model hown Figure.

10 capaciance ducance need o be mached wih PCMM deign parameer [5]. reul obaed by parameer machg how ha ducance obaed by parameer machg how ha ducance 69 uh, AC filer C 69 uh, AC filer capacior 3 C C 3 μf, high ide filer capacior C capacior 3 C 94 F, low ide capacior 3 μf, high ide filer capacior C 94 F, low ide capacior F. Malab/Simulk wa ued foimulaion ma circui imulaion model hown World Elecric F. Malab/Simulk Figure ehicle. Journal 8, wa 9, 7 ued foimulaion ma circui imulaion model 7 hown Figure. Figure. Ma circui imulaion model. Figure. Ma circui imulaion model. 3.. Bidirecional DC/DC Mode Bidirecional Bidirecional DC/DC DC/DC Mode Mode In buck mode, a hown Figure, ducor curren drive ignal are obaed for an pu In In volage buck buck mode, mode, 35 a a, hown hown oupu volage Figure Figure,,, ducor ducor oupu curren curren drive drive 3 kw. ignal ignal Durg are are obaed obaed operaion, for for an an wo pu pu IGBT volage volage urn on alernaely,, oupu oupu volage volage each phae lag,, by 8 oupu oupu degree o reduce 3 3 kw. kw. Durg oupu Durg curren operaion, operaion, ripple. In wo wo Figure IGBT IGBT, urn urn on on alernaely alernaely each each phae phae lag lag by by 8 8 degree degree reduce reduce oupu oupu curren curren ripple. I I are curren waveform wo ducor. I um I I. ripple. In Figure, I I are curren waveform wo ducor. I um I curren In Figure ripple, I I. I I55. are A. Becaue curren waveform erleaved rucure, wo ducor. oupu I curren umi reduced I Io. curren ripple I 55. A. Becaue erleaved rucure, oupu curren I 3.8 curren A. ripple I reduced o 55. A. Becaue erleaved rucure, oupu curren I reduced o A. A. 5 5 I. I..8 PWM PWM I.8 PWM PWM I I.6 I () () Figure Figure.. Inducor Inducor curren curren waveform waveform bidirecional DC/DC DC/DC mode. mode. Figure. Inducor curren waveform bidirecional DC/DC mode. Inducor curren(a) In boo mode, for pu volage, oupu volage 35, load 3 kw, In boo mode, for pu volage, oupu volage 35, load 3 kw, oupu volage repone a hown Figure a. oupu volage repone a hown Figure a. In buck mode, for pu volage 35, oupu volage, load 3 kw, oupu In buck volage mode, repone for pu proce volage a hown 35, oupu Figure volage b., load 3 kw, oupu 36 oupu volage volage repone reached proce a eady a hown ae Figure m b. 8 m boo mode buck mode, repecively. oupu volage error reached oupu a volage eady ae le han m % m conroller boo deigned mode baed buck on mode, preened repecively. model error accurae. oupu volage le han %. conroller deigned baed on 3 preened model accurae. 8 World Elecric ehicle Journal 8, 9, x FOR PEER REIEW 7 dch () 3 8 dc () 6 PWM PWM () () 3.. AC/DC Mode Figure Figure.. Oupu Oupu volage volage waveform: waveform: boo boo mode; mode; buck buck mode. mode. In AC/DC mode, imulaion udie were carried ou for pu volage 8 4, repecively. For oupu volage DC 4, load reance 6 ohm, oupu.667 kw a eady ae, pu volage curren are a hown Figure 3. In h mode,

11 34 dch () 3 3 World Elecric ehicle Journal 8, 9, In buck mode, for pu volage 35, oupu 4 volage, load 3 kw, oupu volage repone proce a hown Figure b. () () oupu volage reached a eady ae m 8 m boo mode buck mode, repecively. error oupu volage le han %. conroller deigned baed on preened model accurae. Figure. Oupu volage waveform: boo mode; buck mode. 3.. AC/DC Mode In AC/DC mode, imulaion udie were carried ou for pu volage 8 4, repecively. For oupu volage DC 4, load reance 6 ohm, oupu.667 kw a eady ae, pu volage curren are are a a hown hown Figure Figure In h In h mode, mode, PCMM PCMM recified recified AC AC poweupply upply realized realized facor facor correcion. correcion. dc () ac I ac_rec ac ac ac I ac I ac 4 I ac I ac I ac_rec ac() Iac(A) () Figure 3. Oupu volage curren waveform. ac A hown Figure 3, ac waveform for pu volage RMS value 8, I ac pu pu curren curren waveform. waveform. ac waveform waveform for for pu pu volage volage RMS RMS value value 4 4,, I ac I correpondg pu curren waveform. In conra, I ac_rec ac I pu curren wihou _ correpondg pu curren waveform. In conra, ac rec facor correcion. Wih facor correcion, pu curren change proporionally pu curren wih wihou pu volage, facor correcion. circui Wih how a reive facor load characeric. correcion, pu curren facor change greaer han proporionally.996. wih pu volage, circui how a reive load characeric. facor greaepecrum han.996. pu curren analyzed, differen order harmonic are hown Table. oal pecrum harmonic dorion pu curren (THD) analyzed, pu differen curren (I order harmonic are hown Table. h ) 6.6% for AC 8. For AC 4, oal harmonic THD dorion pu curren (THD) (I pu curren (Ih) 6.6% for AC 8. For AC 4, h ) 8.%, which mee requiremen Cla A equipmen THD pu IEC63 curren (Ih) ard 8.%, (I which mee requiremen Cla A equipmen h ). I h_rec harmonic pu curren wihou IEC63 ard (Ih). Ih_rec facor correcion. harmonic pu curren wihou facor correcion. Table. Harmonic pu curren. I ac Harmonic Order I h_rec (A) I h (A) I h (A) I h (A) Harmonic Order I h_rec (A) I h (A) I h (A) H (A)

12 In an dependen verer mode, oupu AC volage curren phae do no need o rack phae grid volage. A volage conroller ued o regulae oupu volage. For DC volage 4 oupu volage RMS value, oupu volage curren are hown Figure 4. World Elecric ehicle Journal 8, 9, 7 7 For oupu volage RMS wih load 5 W, 3 kw,.5 kw, volage ac, ac, ac 3 are hown Figure 4. Iac, Iac, Iac3 are curren waveform for 5 W, 3 kw, 3.3. DC/AC Mode.5 kw operaion. In an oupu dependen curren verer analyzed mode, by frequency oupupecrum, AC volage each curren order phae harmonic do no hown need o rack Table phae 3. Ih, Ih, grid Ih3 are volage. harmonic A volage conroller Iac, Iac, ued Iac3, repecively. o regulae oupu THD volage. pu Forcurren DC volage 9.% 4 5 W,.53% oupu 3 volage kw ( RMS ), value.8%.5, kw oupu ( ) volage mode, repecively. curren are I can hown mee Figure requiremen 4. Cla A equipmen accordg o IEC63 ard. 4 3 ac ac ac3 I ac I ac3 6 4 ac () Iac I ac () Figure 4. Oupu volage curren waveform. Figure 4. Oupu volage curren waveform. Table 3. Harmonic oupu curren. For oupu volage RMS wih load 5 W, 3 kw,.5 kw, volage ac, ac, Harmonic order Ih (A) Ih (A) Ih3 (A) H (A) Harmonic order Ih (A) Ih (A) Ih3 (A) H (A) ac3 are hown Figure 4. I.. ac, I.3 ac, I ac3 are curren waveform for 5 W, 3 kw, kw operaion oupu curren.4 analyzed.4 by. frequency.8 pecrum, 3 each.5 order.68 harmonic.85 hown Table 3. I h, I 4 h, I.7 h3 are harmonic I ac, I ac, I 5 ac3, repecively. THD pu curren 9.% W,.53%.66 3 kw.44 (.4 ),.8% 6.5 kw.4 ( ).94 mode,.44 repecively..5 I can mee requiremen 6.9 Cla.7 A equipmen..3 accordg o7 IEC ard Table 3. Harmonic oupu curren Harmonic Order I h (A) I h (A) I h3 (A) H (A) Harmonic Order I h (A) I h (A) I h3 (A) H (A) Experimenal In order o reduce ducor volume,, 69 uh/5 A. In AC/DC DC/AC mode, are conneced erie wih an ducor for value. mh/ A. Filer capacior C 3 employ a 3 uf/6 capacior, filer capacior C employ wo 47 F/5 alumum elecrolyic capacior, filer capacior C employ a F/4 alumum elecrolyic capacior. four wich ube are made up wo MITSUBISHI PMDA IPM module. curren ampled by a HAS EM curren enor. volage enor ue EM 5P volage enor o olae ample. experimenal e bench hown Figure 5.

13 wich ube are are conneced made up erie wo MITSUBISHI wih an ducor PMDA for value IPM module.. mh/ A. curren Filer capacior ampled C3 employ by a HAS a 3 uf/6 EM curren capacior, enor. filer capacior volage C enor employ ue wo EM 47 5P F/5 volage alumum enor elecrolyic o olae capacior, ample. filer experimenal capacior C e employ bench a hown F/4 Figure alumum 5. elecrolyic capacior. four wich ube are made up wo MITSUBISHI PMDA IPM module. curren ampled by a HAS EM curren enor. volage enor ue EM 5P volage enor o olae ample. experimenal e bench hown Figure 5. World Elecric ehicle Journal 8, 9, Figure 5. Experimenal e bench. Accordg o acual meauremen experimenal prooype, elecronic componen weigh 8.7 kg, while acceorie, uch Figure a Experimenal encloure e bench. wire, weigh 7.4 kg, reulg a oal prooype weigh 6. kg. If BiDC/DC, DC/AC, AC/DC converer are alled dependenly, Accordg o o acual oal weigh meauremen will be 33 kg. Comparaively, experimenal PCMM prooype, can reduce elecronic weigh componen by 5.%. weigh 8.7 kg, while acceorie, ucha a encloure wire, wire, weigh weigh kg, kg, reulg reulg a oal a oal prooype 4.. BiDC/DC prooype weigh Mode weigh kg. kg. If If BiDC/DC, DC/AC, AC/DC converer are alled dependenly, be 33 pu volage oal weigh will oupu be 33 volage kg. Comparaively, BiDC/DC PCMM model are canhown reduce Figure weigh 6a,b. by 5.%. In figure, pk curve are high ide volage. blue curve are low ide volage. 4.. BiDC/DC Mode In boo mode, for an pu volage, oupu volage 35, load reance 3 Ω, pu volage oupu volage volage BiDC/DC are a hown model are Figure hown 6a durg Figure 6a,b. iiaion In figure, converion. pk curve converion are efficiency high ide reache volage. 96.4%. blue curve are low ide volage. In boo mode, for an pu volage, oupu volage 35, load reance 3 Ω, pu volage oupu volage are a hown Figure 6a durg iiaion converion. converion efficiency reache 96.4%. Figure Figure Inpu Inpu volage volage oupu oupu volage volage boo boo mode, mode, buck buck mode. mode. In buck mode, for an pu volage 35, oupu volage, load reance 3 In boo mode, for an pu volage, oupu volage 35, load reance 3 Ω, Ω, pu volage Figure 6. Inpu oupu volage volage are oupu a hown volage Figure boo 6b mode, durg buck iiaion mode. converion. pu volage oupu volage are a hown Figure 6a durg iiaion converion. converion efficiency 96.%. converion In buck mode, efficiency for an reache pu volage 96.4%. 35, oupu volage, load reance 3 Ω, In pu buck mode, volage for an oupu pu volage volage are 35 a hown, oupu Figure volage 6b durg, iiaion load reance converion. 3 Ω, converion pu volage efficiency oupu 96.%. volage are a hown Figure 6b durg iiaion converion. converion efficiency 96.%. 4.. AC/DC Mode AC volage connec a 3 ka ranformer o adju grid volage for pu PCMM. DC oupu conneced o a reance load. In abence facor correcion, four revere diode form a recifier bridge, circui operae unconrolled recifieae. pu volage curren AC ide are hown Figure 7a. facor.57, oupu volage unconrollable.

14 4.. volage AC/DC unconrollable. Mode Wih AC volage facor connec correcion, a 3 ka ranformer oupu o adju volage grid DC volage 35, for pu pu PCMM. curren DC proporional oupu conneced o pu o volage. a reance load. pu In volage, abence pu curren, facor oupu correcion, DC volage four are revere hown diode Figure form 7b. a recifier By bridge, facor correcion, circui operae facor unconrolled creaed o recifier.988. ae. converion pu I World volage efficiency Elecric ehicle curren 96.4%, Journal 8, hd AC 9, 7 ide 5.68%, are hown oupu Figure volage 7a. poweable facor under.57, regulaion oupu 4 7 volage regulaor. unconrollable. Wih facor correcion, for an oupu volage DC 35, pu curren proporional o pu volage. pu volage, pu curren, oupu DC volage are hown Figure 7b. By facor correcion, facor creaed o.988. converion I efficiency 96.4%, hd 5.68%, oupu volage able under regulaion regulaor. Figure Figure olage olage curren curren AC/DC AC/DC mode: mode: wihou wihou facor facor correcion; correcion; wih wih facor facor correcion. correcion DC/AC Mode Wih facor correcion, for an oupu volage DC 35, pu curren proporional o In pu DC/AC volage. mode, for pu an pu volage, volage pu curren, DC 35, oupu volage DC volage RMS are hown, load Figure reance 7b. By 54 Figure Ω, facor 7. frequency olage correcion, curren 5 Hz, AC/DC wave facor mode: form creaed wihou oupu o.988. volage, facor converion correcion; pu curren, efficiency wih DC 96.4%, ide volage I hd facor are 5.68%, correcion. a hown Figure oupu8a. volage pk able curve under DC regulaion high ide volage, regulaor. blue curve oupu volage, yellow curve oupu curren. THD oupu curren 5.893% 4.3. DC/AC efficiency Mode 96.7%. In DC/AC mode, for an pu volage DC 35, oupu volage RMS, load reance 54 Ω, Ω, frequency 5 Hz, wave form oupu volage, pu curren, DC ide volage are a hown Figure 8a. pk curve DC high ide volage, blue curve oupu volage, yellow curve oupu curren. THD oupu curren 5.893% efficiency 96.7%. Figure 8. Oupu volage, oupu curren, oupu volage DC/AC converer. Waveform wih moor load. In order o verify performance verer wih a moor load, a 9 W AC moor load wa uddenly applied o reance load. reulg waveform hown Figure 8b. Durg Figure Figure Oupu Oupu volage, volage, oupu oupu curren, curren, oupu oupu volage volage DC/AC DC/AC converer. converer. Waveform wih wih moor moor load. load. In order o verify performance verer wih a moor load, a 9 W AC moor load wa In order o verify performance verer wih a moor load, a 9 W AC moor load uddenly applied o reance load. reulg waveform hown Figure 8b. Durg wa uddenly applied o reance load. reulg waveform hown Figure 8b. Durg load change, oupu 8 W wih a converion efficiency 96.7%, oupu aympoically able. 5. Concluion Th paper preen a PCMM converer wih hree differen workg mode for E applicaion. propoed PCMM can work BiDC/DC, AC/DC, DC/AC mode. In upercapacior & baery

15 World Elecric ehicle Journal 8, 9, hybrid orage yem for E applicaion, BiDC/DC mode conver beween baery upercapacior; AC/DC mode charge baery, DC/AC mode provide an AC ource o elecrical equipmen. Mamaical repreenaion aepace averagg model PCMM coniderg reance IGBT ducor preened. Baed on h model, relaionhip beween eady ae oupu volage pu volage given. In order o decribe yem characeric undemall ignal perurbaion, mall ignal model PCMM ranfer funcion yem are derived. Ug eablhed PCMM model, conroller wa deigned. imulaion experimenal reul how ha PCMM can mee deign arge feaibiliy model verified. PCMM converer reduce co lighen yem weigh by harg ducor, IGBT, capacior, or componen. meaured reul how ha, compared wih a radiional vehicle converion yem, PCMM rucure propoed h paper reduce weigh by 5.%. model preened h paper reflec characeric yem undemall ignal durbance. In fuure reearch, repone characeric yem undeae wichg will be udied baed on nonlear modelg. Auhor Conribuion: uo Yuao conceived udy. Wang Feng planned experimen. uo Yuao Wang Feng wroe manucrip. All auhor ubmied commen, read approved fal manucrip. Fundg: Th reearch wa funded by Major Reearch Developmen Projec Guangdong Science Technology Deparmen, gran number 6B3. Conflic Inere: auhor declare no conflic ere. Nomenclaure E PFC DC DCH K K K 3 Q,Q Q 3,Q 4, C C C 3 v c () v o () i ˆ () i ˆ () vˆ c () PCMM THD v ac () i () i () R o Elecric vehicle Power facor correcion ow ide volage () High ide volage () Swich DC/AC Swich AC/DC Swich DC/DC IGBT fir phae IGBT econd phae Inducor (H) Capacior low ide (F) Capacior high ide (F) Capacior AC ide (F) olage capacior () Oupu volage () Curren mall ignal (A) Curren mall ignal (A) Small ignal capacior () Power converer wih mulioperag mode Toal harmonic dorion olage AC ide () Curren ducor (A) Curren ducor (A) load reance (Ω) Average oupu volage eady ae ()

16 World Elecric ehicle Journal 8, 9, i c I,I r Average pu volage eady ae () Average capacior volage eady ae () Average curren ducor eady ae (A) Inducor reance (Ω) IGBT reance (Ω) Inpu volage () Duy cycle v i () d v re f () reference volage () v c () T Average volage capacior one cycle () i () T Average curren one cycle (A) i () T Average curren one cycle (A) Reference. Ou, T.C.; Hong, C.M. Dynamic operaion conrol microgrid hybrid poweyem. Energy 4, 66, [CroRef]. Khaligh, A.; i, Z.H. Baery, Ulracapacior, Fuel Cell, Hybrid Energy Sorage Syem for Elecric, Hybrid Elecric, Fuel Cell, PlugIn Hybrid Elecric ehicle: Sae Ar. IEEE Tran. eh. Technol., 59, [CroRef] 3. Pahlevanezhad, M.; Drobnik, J.; Ja, P.K.; Bakhhai, A. A oad Adapive Conrol Approach for a ZeroolageSwichg DC/DC Converer Ued for Elecric ehicle. IEEE Tran. Ind. Elecron., 59, [CroRef] 4. Pahlevanezhad, M.; Da, P.; Drobnik, J.; Ja, P.K.; Bakhhai, A. A ZS Inerleaved Boo AC/DC Converer Ued Plug Elecric ehicle. IEEE Tran. Power Elecron., 7, [CroRef] 5. Sreeraj, E.S.; Chaerjee, K.; Byopadhyay, S. OneCycleConrolled SgleSage SglePhae olagesenorle GridConneced P Syem. IEEE Tran. Ind. Elecron. 3, 6, Oadi, A.; Kazerani, M. A Comparaive Analy Opimal Sizg BaeryOnly, UlracapaciorOnly, BaeryUlracapacior Hybrid Energy Sorage Syem for a Ciy Bu. IEEE Tran. eh. Technol. 5, 64, [CroRef] 7. Ou, T.C.; Sciubba, E. Deign a Novel olage Conroller for Converion Carbon Dioxide o Clean Fuel Ug Inegraion a anadium Redox Baery wih Solar Energy. Energie 8,, 54. [CroRef] 8. Gradii, G.; Adolfi, G.; Ta, G.M. Phoovolaic opimizer boo converer: Temperaure fluence elecrormal deign. Appl. Energy 4, 5, 4 5. [CroRef] 9. Wen, H.; Su, B. Hybridmode erleaved boo converer deign for fuel cell elecric vehicle. Energy Conver. Manag. 6,, [CroRef]. Pavlovky, M.; Guidi, G.; Kawamura, A. Aemen Coupled Independen Phae Deign Inerleaved Muliphae Buck/Boo DCDC Converer for E Power Tra. IEEE Tran. Power Elecron. 4, 9, [CroRef]. Shah, A.; Haje, M.; Mar, J.P.; Pierfederici, S.; Rael, S.; Dava, B. High olage Raio DC DC Converer for FuelCell Applicaion. IEEE Tran. Ind. Elecron., 57, [CroRef]. Urciuoli, D.P.; Tipon, C.W. Developmen a 9 kw bidirecional DCDC converer for dene applicaion. In Proceedg IEEE TwenyFir Annual Applied Power Elecronic Conference Expoiion (APEC 6), Dalla, TX, USA, 9 3 March 6; p Garcia, O.; Zumel, P.; de Caro, A.; Cobo, J.A. Auomoive DCDC bidirecional converer made wih many erleaved buck age. IEEE Tran. Power Elecron. 6,, [CroRef] 4. Zhang, W.; Feng, G.; iu, Y.F.; Wu, B. A digial facor correcion (PFC) conrol raegy opimized for DSP. IEEE Tran. Power Elecron. 4, 9, [CroRef] 5. Cho, Y.; ai, J.S. Digial PlugIn Repeiive Conroller for SglePhae Bridgele PFC Converer. IEEE Tran. Power Elecron. 3, 8, De Souza, A.F.; Barbi, I. High facor recifier wih reduced conducion commuaion loe. In Proceedg Inernaional Telecommunicaion Energy Conference (INTEEC 99), Copenhagen, Denmark, 9 June 999; pp. 8 9.

17 World Elecric ehicle Journal 8, 9, Su, B.; Zhang, J.; u, Z. ToemPole Boo Bridgele PFC Recifier wih Simple ZeroCurren Deecion FullRange ZS Operag a Boundary DCM/CCM. IEEE Tran. Power Elecron., 6, [CroRef] 8. Dagupa, S.; Sahoo, S.K.; Pa, S.K. SglePhae Inverer Conrol Technique for Inerfacg Renewable Energy Source wih Microgrid Par I: ParallelConneced Inverer Topology wih Acive Reacive Power Flow Conrol along wih Grid Curren Shapg. IEEE Tran. Power Elecron., 6, [CroRef] 9. Chen, A.; Shao, D.; Chunhui, D.U.; Zhang, C. Highfrequency DC lk flyback gle phae verer for gridconneced phoovolaic yem. In Proceedg nd IEEE Inernaional Sympoium on Power Elecronic for Dribued Generaion Syem (PEDG), Hefei, Cha, 6 8 June ; pp ee, J.Y.; Song, H.S.; Yoo, I.P.; Jang, K.Y.; Sh, S.; Joo, J.H. Syem for Rechargg PlugIn Hybrid ehicle Conrol Mehod for Same. Unied Sae Paen Applicaion 4983, March.. Dumez, S.; Chen, C.; Khaligh, A. A reducedpagle age direc AC/DC Onboard charger for auomoive applicaion. In Proceedg IEEE 3 TwenyEighh Annual Applied Power Elecronic Conference Expoiion (APEC), ong Beach, CA, USA, 7 March 3; pp Dumez, S.; Khaligh, A. A ChargeNonlearCarrierConrolled ReducedPar SgleSage Inegraed Power Elecronic Inerface for Auomoive Applicaion. IEEE Tran. eh. Technol. 4, 63, 9 3. [CroRef] 3. Ou, T.C.;, W.M.; Huang, C.H. A mulipu converer for hybrid renewable generaion yem. In Proceedg IEEEPES/IAS Conference on Suaable Alernaive Energy (SAE 9), alencia, Spa, 8 3 Sepember Sun, J.; Michell, D.M.; Greuel, M.F.; Kre, P.T.; Ba, R.M. Averaged modelg PWM converer operag dconuou conducion mode. IEEE Tran. Power Elecron., 6, Manikala, S. Swichg Power Supplie A o Z; Newne: Newon, MA, USA,. 8 by auhor. icenee MDPI, Bael, Swizerl. Th aricle an open acce aricle dribued under erm condiion Creaive Common Aribuion (CC BY) licene (hp://creaivecommon.org/licene/by/4./).