Research Article New Multiphase Hybrid Boost Converter with Wide Conversion Ratio for PV System

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1 Inernaonal Journal of Phooenergy, Arcle ID 67468, 6 pages hp://dxdoorg/55/4/67468 Research Arcle New Mulphase Hybrd Boos Converer wh Wde Converson Rao for PV Sysem Ioana-Monca Pop-Calmanu and Folker Renken Appled Elecroncs Deparmen, Polehnca Unversy of Tmsoara, Tmsoara, Romana Power Elecroncs/Deparmen of Engneerng, Jade Unversy, Unversy of Appled Scences, 689 Wlhelmshaven, Germany Correspondence should be addressed o Ioana-Monca Pop-Calmanu; oanamoncapop@gmalcom Receved December ; Acceped March 4; Publshed Aprl 4 AcademcEdor:IsmalHAlas Copyrgh 4 I-M Pop-Calmanu and F Renken Ths s an open access arcle dsrbued under he Creave Commons Arbuon Lcense, whch perms unresrced use, dsrbuon, and reproducon n any medum, provded he orgnal work s properly ced A new mulphase hybrd boos converer, wh wde converson rao as a soluon for phoovolac energy sysem, s presened n hs paper To ensure ha all he phases of he converer operae a he same swchng frequency we use nerleavng opology The proposed converer can be used as an nerface beween he PV sysem and he DC load/nverer Ths mulphase converer has headvanageofreducedvalueandphyscalszeofhenpuandoupu capacor as well as he effor for he nducors To valdae he operaon of he converer we provde he analyses and he smulaon resuls of he converer Inroducon Phoovolac (PV) energy has araced neres as an energy source capable of solvng he problems of he energy crss Solar PV energy s becomng an ncreasngly mporan par of he renewable energy resources I s consdered one of he mos promsng energy resources due o s nfne power delvered drecly for free, and many oher advanages These nclude relably, avalably, zero polluon or desrucon of he land, reasonable nsallaon and producon cos, long lfe-span, and he capably of supporng mcrogrd sysems and connecng o elecrcal grds [ 5] One of he challenges n he case of grd connecon applcaons or hgh volage DC applcaons requremens s he low volage of he PV module For hs reason, many PV modules should be eher conneced n seres o mee hese applcaon requremens, or o use a sep-up DC/DC converer Ths ypeofconvererswdelyusednpvsysemstheorecally, a radonal sep-up converer can acheve a hgh sepupvolageganwhanexremelyhghduyraonearo % [6] The sep-up volage gan n pracce s lmed due o he effec of power swches, recfer dodes, he equvalen seres ressance of nducors and capacors, and he sauraon effecs of he nducors and capacors [7] Due o he fac ha hese radonal converers are no able o operae effcen wh a hgh duy rao near o %, scenfc leraure presens many opologes [8 ]ha provde a hgh sep-up volage gan whou an exremely hgh duy rao A very good revew of nonsolaed hgh sep-up DC/DC converers used n renewable energy applcaons s presened n [, ], where he advanages and dsadvanages of hese converers and he major challenges are summarzed In [4] he archecure of a hgh sep-up converer, whch conans seven pars ncludng a PV module npu crcu, a prmarysde crcu, a secondary-sde crcu, a passve regenerave snubber crcu, a fler crcu, a DC oupu crcu, and a feedback conrol mechansm, s presened The auhors from [4], for rasng he volage gan, are usng a coupled nducor wh a low-volage raed swch In [5]hreeypesof sep-up converers wh hgh-effcency by usng PV sysem wh reduced dode sresses sharng are proposed Through heemployofcouplednducorandswchedcapacor,he

2 Inernaonal Journal of Phooenergy U In D L L D D S D O U Ou U Ou /U In 5 4 Hybrd boos converer Tradonal boos converer Fgure : Sngle-phase hybrd boos DC/DC converer proposed converers aan hgh sep-up converson rao whou operang a exreme duy rao Very ofen n he leraure s presened hgh sep-up DC/DC converer ha ulzes a leas one coupled nducor One of hese srucures s presened n [6] where he operang prncple and seady sae analyses are dscussed n deal, and a prooype of he crcu s mplemened Anoher confguraon of sepup converer wh coupled nducor s presened n [7] Ths converer acheves a hgh sep-up volage converson rao, whou exreme duy raos and he numerous urn s raos of a coupled nducor The leakage nducor energy of he coupled nducor s effcenly recycled o he load Oher hgh sep-up DC/DC converers wh coupled nducor are presened n [8 ] In hs paper s presened and analysed he srucures of he sep-up hybrd boos converer [7, ], or as named n some papers swched nducor boos ype One of he man dsadvanages of hs crcu s ha he effor for he npu and oupu capacor, n he case of a sngle-phase DC/DC converer s very hgh Ths s he same wh he effor of he nducors Based on he srucure of he hybrd boos converer bul n mulphase desgn, we presen a mehod for reducng hs dsadvanage hrough a new mulphase hybrd boos converer d (U Ou /U In ) = (d + )/(d ) (U Ou /U In ) = /(d ) Fgure : Converson rao of a hybrd boos and radonal boos DC/DC converer U In U In D L I In ID D O OP I Ou D IC S OC C I L D S u S CO Fgure : Sngle-phase hybrd boos DC/DC converer S U Ou U Ou Swched-on sae Sngle-Phase Hybrd Boos Converer Fgure shows he sep-up hybrd boos converer whch was nroduced n [] The hybrd boos DC/DC converer consss of a classcal boos converer n whch s nsered an L-swchng srucure The L-swchng srucure consss of wo nducors and hree dodes We can smply say ha he npu nducor from a classcal boos converer was replaced byhewonducorsnhenewhybrdconvererthsypeof converer provdes hgh gan and hgh effcency and s used for many applcaons such as solar cell energy converson sysems [7], fuel cell energy converson sysems, baery backup sysems for unnerrupble power supples, and hgh nensy dscharge lamp ballas for auomoble head lamps [] The gan of he hybrd boos converer s hgher han he radonal boos converer by a facor of (d + ) Fgure shows a comparson beween he gan of he hybrd boos converer and he radonal boos converer U In S U Ou Swched-off sae Fgure 4: Curren flow n swched-on and swched-off sae of he hybrd boos DC/DC converer To ensure a beer undersandng, hs secon connues by presenng and dscussng he power par of he hybrd converer, whch s presened n Fgure Thepowerparconsssofannpuneworkwhwo nducors and hree dodes, a sep-up crcu wh he power swch S and dode D O,aswellasaDC-lnkcapacora henpuandoupusdeofheconvererbasedonlyon he crcu srucure, we can observe ha he energy can be ransferred only n one drecon from npu o oupu

3 Inernaonal Journal of Phooenergy L = L = L I L AV Δ L L = L = L I L AV Δ L I In IP OP I Ou on off IC on off OC T P T P T P T P T P T P Fgure 5: Curren waveforms a he npu of a sngle-phase hybrd boos DC/DC converer (d = ) Fgure 8: Curren waveforms a he oupu of a sngle-phase hybrd boos DC/DC converer (d = ) 7 P In /P In R (U Ou /U In ) = 5 (U Ou /U In )= (U Ou /U In )=9 I OC /I L AV d Fgure 6: Maxmum power ransfer n case of fxed oupu volage Δ L max = 5 I L AV Δ L max = d 7 Fgure 9: RMS curren n he oupu capacors of a sngle-phase hybrd boos DC/DC converer 6 I IC /I L AV 5 4 Δ L max = 5 I L AV Δ L max = d Fgure 7: RMS curren n he npu capacors of a sngle-phase hybrd boos DC/DC converer For operaon of he converer we use a pulse conrol mehod Fgure 4 shows he curren flow n he crcu n he swched-on and he swched-off sae In he swched-on sae he nducors are conneced n parallel and he curren of boh nducors flows n he npu phase and n he swch elemen For hs reason durng he swched-on sae he curren n he oupu phase OP s zero (Fgure 8)Inheswched-offsaehenducancecurren flows n seres hrough he nducors and he oupu dode In hs momen he nducors are conneced n seres, whle he npu phase curren IP and oupu phase curren OP are he same as he nducor curren The expecaon beng ha only he average value of he npu phase curren would flow n he converer npu curren, I In, whle he AC-curren componen

4 4 Inernaonal Journal of Phooenergy would flow n o he capacor C I and he average value of he oupu phase curren would flow n he converer oupu I Ou Forcalculaons,weassumedhaallelemensofhe converer would work whou losses, he volage and currens a he npu and oupu were deally DC-values, and he converer would be conrolled wh pulse wdh modulaon [4] Wh hese requremens n he converer swchng saes, he volage a he nducors can be deermned by applyng he volage-second balance on he nducor as follows: off : on : u L =U In, u L = U Ou U In, where u L s he nducor volage, U In s he npu volage, and U Ou s he oupu volage As we can see from he above formulas, he volage a he nducors s posve n he swched-on sae and negave n he swched-off sae In crcu operaon he posve and negave volage-me-area a he nducors mus always be he same Wh hs condon he converson rao of he hybrd boos DC/DC converer can be calculaed Consder U Ou = +d d U In () wh d= on T P, d = off T P () DC/DC Converer Inpu Crcu In Fgure 5 he curren waveformsahenpuofhehybrdboosconverers presened The frs waveform shows he currens n boh nducors,andwecanseehaheyarehesamethenducor curren rses n swched-on sae and fall n swched-off sae, so ha a rangular shape curren s generaed The mddle waveform presens he npu phase curren IP,and he lower waveform presens he npu capacor curren IC The average curren I L AV depends on he duy cycle d Consder I L AV = I In +d () In order o calculae he requred nducance and capacance n he crcu we needed o fx condons for he crcu operaon We frs needed o know he raed oupu volage, as well as he mnmal npu volage a raed power whch should be ransferred Wh hese condons he converson rao of he crcu for raed npu power P In R ransfer s fxed In hs operaon pon he DC-npu curren and he average curren I L AV n he nducors can be calculaed I s assumed ha hs average curren I L AV s he maxmum DC-value n he nducances Fgure 6 shows he possble power ransfer dependen on he duy cycle for hree dfferen converer desgns The nducvy mus be calculaed for he maxmum nducor volage-me-area whn he pulse perods and he maxmum accepable curren varaon durng hs me In he swched-on sae on,henpuvolageu In s conneced a he nducors The volage U In s descrbed n formula (5) as a funcon of he oupu volage and he duy cycle Consder L =L = U In on Δ L, (4) L =L = U Ou T P Δ L d ( d) +d (5) Consderng he full duy cycle range, he volage-mearea whn he pulse perods reaches s maxmum for a duy cycle of approxmaely 4% For hs duy cycle n general he converer nducance s specfed The maxmum accepable curren varaon Δ L max s chosen normally beween % and % of he raed average nducance curren I L AV R These nducances can be realzed as ndvdual or muual coupled nducances L =L = U Ou T P ( ) Δ L max wh Δ L max = ( ) I L AV R We connue wh he calculaon of he capacy of he npu sde We begn wh he wors case scenaro whch could happen when he converer npu curren s an deally average valueandheoverallac-currenofhenpuphaseflowsn he capacor (seefgure 4) Ths AC-curren n he capacor produces an AC-volage a he npu ha s overlad wh he DC-npu volage For hs reason he maxmum accepable volagevaraonahecapacormusbechosendurnghe capacy dmenson Consder C I = C on Δu C, C I = I L AV T P Δu In max d ( d) The curren-me-area depends on he duy cycle havng s maxmum a 5% and a he raed nducance curren I L AV In pracce, he accepable sac volage varaon a he converer npu s chosen smaller han % of he raed npu volage U In R C I = I L AV R T P wh Δu 4 Δu In max U In R (8) In max InhenpuofheDC/DCconverers,elecrolyccapacors are ofen used [5] The man desgn crera for hese capacors are he RMS curren loads The RMS curren n he npu capacor s calculaed as a funcon of he duy cycle for an average nducance curren I L AV and a maxmum curren varaon Δ L max Consder I IC =I L AV d ( d) +( Δ L max d ( d) (+ d) ) I L AV (+d) ( ) (6) (7) (9)

5 Inernaonal Journal of Phooenergy 5 The resul can be spl no wo One s dependen on he average curren I L AV and he oher s dependen on he rangle curren varaon n he nducances In Fgure 7, hecurrennhermscapacorsshownthemaxmum valueofhecapacorcurrenshgherhanhehalfaverage nducance curren I L AV Thecurrenvaraonhas,however, only a small nfluence on he oal RMS curren n he capacor DC/DC Converer Oupu Crcu Fgure 8 shows he curren and volage waveforms a he oupu of he hybrd boos DC/DC converer The frs waveform n Fgure8 shows he curren n boh nducors The mddle waveform presens he oupu phase curren OP The lower waveform shows he AC-curren n he oupu capacor Ths curren can be calculaed by subracon of oupu phase curren OP and oupu curren I Ou We connue wh he calculaon for he capacy of he oupu sde We begn wh he wors case scenaro whch wouldhappenwhenheconvereroupucurrensandeally average value and he overall AC componen of he oupu phase curren flows n he capacor (see Fgure 8) Ths ACcurren n he capacor produces an AC-volage a he oupu ha s overlad wh he DC-oupu volage For hs reason he maxmum accepable volage varaon a he capacor mus be chosen durng he capacy dmenson The currenme-area n he capacor whn he pulse perods can be descrbed as a funcon of he oupu curren and he duy cycle Consder C O = I Ou T P Δu Ou max d, C O = I L AV T P Δu Ou max d ( d) () The curren-me-area depends on he duy cycle wh s maxmum a 5% and a raed nducance curren I L AV In pracce, he accepable sac volage varaon s chosen smallerhan%ofhenomnaloupuvolageu Ou Consder C O = I L AV R T P wh Δu 4 Δu Ou max U Ou R () Ou max Also on he oupu sde of he hybrd boos converers, elecrolyc capacors are ofen used For desgn of he capacors, he RMS curren n he oupu mus be calculaed In he nex formula he RMS curren s deermned as a funcon of he duy cycle for an average nducance curren I L AV and a maxmum nducance curren varaon Δ L max Consder I OC =I L AV d ( d) +( Δ L max d ( d) ) I L AV (+d) ( ) () The resul can also be spl no wo: one s dependen on he average nducor curren I L AV, and he oher s dependen on he rangle curren varaon n he nducances In Fgure 9, he curren n he RMS capacor s shown The maxmum value s more han he half average nducance curren I L AV Thecurrenvaraonalsohasonlyasmall nfluence on he oal RMS curren n he capacor The effor for he npu and oupu capacor n he case of a sngle-phase DC/DC converer s very hgh In he nex secon a mehod for reducng he capacor currens s presened Wh hs mehod, he effor for he nducors can also be reduced Mulphase DC/DC Converer Several soluons and her conrol were presened n he leraure for nerconnecon of he converers [6 ] Mulphase confguraon s one of hem [ 5] Alhough he physcal connecon of he mulphase looks exacly he same lke parallel connecon, he man dfference beween hem s he mehod of how hey me/conrol her man swches The parallel confguraon s operaed by havng he swchng sgnals for man swches concde wh each oher (eg, when swch from frs power converer urns on, so does he swch from he second power converer and vce versa) The man advanage of parallel confguraon s ha he conrol crcu mus only provde a sngle swchng sgnal In mulphase converer each swch operaes a a dfferen me wh a phase shf beween he swch gae drvers [6] buwhcommonfrequencytheresulofhephasedelay allows mulphase confguraons o exhb hgher overall effcency due o rpple cancelaon, smaller oupu fler requremens, and smaller oupu volage rpple [7 4] Theoupuvolagerpplesreducedbecauseheoupu frequency s ncreased by he number of phase mes of he ndvdual swch frequency Hgher oupu frequency makes he oupu rpple easer o fler whch allows smaller componens and furher ncrease n effcency [6] In [4] s presened anoher wo-phase boos converer opology, whch due o he fac ha he mulphase confguraon, a he oupu he crcu, wll have jus a sngle capacor andheoupuvolagewllhaverpplecomponenwce he operang swchng frequency of each ndvdual boos converer The frequency mulplcaon effec also occurs a he npu sde of he converer and wll reduce he npu flersandwllmprovehequalyofhenpucurren [4] The hybrd boos DC/DC converer presened n hs paper can also be bul n mulphase desgn Therefore he dfferen phases are conneced a a common npu and oupu capacor The oal curren s subdvded n he dfferen phases By nerleavng swchng opology he AC-currens n he npu C I and oupu capacor C O can be reduced clearly In addon he frequency of he capacor currens s ncreased Wh suable crcu desgn he effor of he nducances can be decreased Fgure shows a DC/DC converer n wo-phase desgn

6 6 Inernaonal Journal of Phooenergy I In IC U In C I L D O D IP IP OP OP I Ou D S OC L D S u S C O U Ou Phase I IC /I L AV phase phase IP D L D S D O OP phase L Phase D S u S 4 d 6 8 Δ Ln max = 5 I Ln AV Δ Ln max = Fgure : Two-phase hybrd boos DC/DC converer Fgure : RMS curren n he npu capacors of a one-, wo-, and hree-phase hybrd boos DC/DC converer L = L I Ln AV Δ Ln L = L I Ln AV Δ Ln on off IP on off OP L = L I Ln AV Δ Ln L = L I Ln AV Δ Ln T P / on off IP T P / on off OP IP I In OP I Ou IC OC T P T P T P Fgure : Curren waveforms a he npu of a wo-phase hybrd boos DC/DC converer (n =, d = ) T P T P T P Fgure : Curren waveforms a he oupu of he wo-phase hybrd boos DC/DC converer (n =, d = )

7 Inernaonal Journal of Phooenergy 7 DC/DC Converer Inpu Crcu In Fgure he curren waveformsahenpuofawo-phasehybrdboosconverer are shown Frs, he currens n boh nducances and he npu curren of phase one are shown Represened underneah n green are he same currens of phase wo The rangle shaped nducance currens of he wo phases areshfedwhabouahalfpulseperodaswched-on me he npu curren of each phase s wce as small as he nducance curren from a sngle-phase converer Bu n hs crcu he overall npu phase curren I IP consss of he sum of all he npu phase currens The overall npu phase curren I IP, wh he DC-componen I In s shown n Fgure Alsofor hscrcusassumedhaonlyhedc-currensflowng n he crcu npu Wh hese condons, for mulphase converers, he funcon beween he npu curren I In and he average nducance curren of he ndvdual phases I Ln AV can be calculaed Consder I Ln AV = I In n (+d) () The oal AC-componen of he overall npu phase curren I IP flows n he npu capacor (Fgure ) Ths curren s clearly smaller n comparson o a sngle-phase hybrd boos converer In addon, he frequency of he capacorcurrensdoubledforhesereasonsheflereffor s reduced We connue wh he calculaon of he nducances and capacors of a mulphase hybrd boos converer The same echncal condons for a sngle-phase converer are appled and he calculaon of nducances for an n-phase desgn can be accomplshed n he same way as for sngle-phase crcus Takng no accoun he npu curren whch s subdvded no he dfferen phases, he maxmum curren varaon n he nducances mus be based on he maxmum DCcurren a raed power n he ndvdual phases For desgn, he maxmum curren varaon s seleced beween % and % of he phase DC-curren n he nducances a raed power Consder L n =L n = U Ou T P ( ) Δ Ln max wh Δ Ln max = ( ) I Ln AV R (4) Theampludeofheranglecurrenvaraonnhe nducors s dependen on he duy cycle of he converer Because he duy cycle n all phases has he same value, he curren varaons n all nducors are equvalen Consder Δ Ln = (d) ( d) (+d) ( ) Δ L n max (5) The necessary npu capacy of he mulphase hybrd boos converer wll now be calculaed Compared o a snglephase desgn, he capacor curren s reduced and he curren frequency s ncreased by he number of phases As a consequence he curren n he capacor has a volage varaon a he npu For he capacor desgn, he permssble sac volage varaon n general s seleced smaller han % of he raed npu volage Consder C I = T P I Ln AV 4 n Δu In max wh Δu In max u In R (6) In hese DC/DC converers, elecrolyc capacors are used ofen A man desgn creron of hese capacors s he RMS curren load For hs reason, for mulphase DC/DC converers he RMS curren n he npu capacor C I wll be calculaed Therefore he swchng processes n he phases are assumed as deal Moreover, s acceped ha he curren n he npu s an deal DC-curren The wors case scenaro wll happen when he capacor s loaded wh he oal ACcurren componen The npu capacor curren for wo-phase converers s represened n Fgure In he case of closer nspecon he capacorcurrencanbesplnowodfferencomponens: a recangle par and a rangle par The RMS curren of hese wo componens has been calculaed The RMS resul of he recangle poron for mulphase converers s shown n he formula below: I IC Π = I L n AV n (d n ) ( n d) I L n AV n (d n ) ( n d) I L n AV n (d n ) ( n d) f n d n f n d n f n d n IL n AV n (d n n ) (n n d) f d n n n n (7) In hs formula s necessary o consder ha he average nducance curren I Ln AV becomes smaller wh an ncreasng number of phases For example, he average nducance curren I Ln AV n a wo-phase converer s only half as bg as n a sngle-phase converer Wh hs fac n mnd he recangle componenofhenpucapacorcurrencanclearlybe reduced wh a mulphase desgn In addon, he RMS curren of he rangle has been calculaed The nex formula shows he RMS resuls for a mulphase crcu desgn Consder

8 8 Inernaonal Journal of Phooenergy 7 I OC /I L AV phase phase phase d Δ Ln max = 5 I Ln AV Δ Ln max = Fgure 4: RMS curren n he oupu capacors of a one-, wo-, and hree-phase hybrd boos DC/DC converer Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 5 m m 44 m Sgnal Sgnal Fgure 5: Inpu volage Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 47 m 5 m m 5 m m 6598 m m 875 m Fgure 6: PWM pulse appled o swch one (pnk sgnal), respecve swch wo (red sgnal) 76 76

9 Inernaonal Journal of Phooenergy Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 5 m m 4694 m m Fgure 7: Inpu curren of phase one, IP Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 5 m m 489 m m 64 Fgure 8: Inpu curren of phase wo, IP Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 5 m m 495 m m 8 Fgure 9: Overall npu phase curren, IP

10 Inernaonal Journal of Phooenergy L L Tme (ms) Trace y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac () L 5 m m 959 m m () L 5 m m 959 m m L Fgure : Curren hrough nducors L and L, L, L Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 44 m m m 968 m m Fgure : Curren hrough nducor L, L Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 5 m 577 μ m 65 m m 7 Fgure : Oupu curren of phase one, OP

11 Inernaonal Journal of Phooenergy Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 88 5 m 575 μ m 658 m m Fgure : Oupu curren of phase wo, OP Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 47 m 88 5m m 5m m 6 R Fgure 4: Overall oupu phase curren, OP Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 47 m 5 5m m 448m m Fgure 5: Oupu curren, I Ou

12 Inernaonal Journal of Phooenergy R Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 47 m 5 5m m 448m m Fgure6:Zoomonoupucurren V[ 9] Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 47 m 9 5m m V[ 9] Fgure 7: Oupu volage, V Ou Tme (ms) y MnX MaxX MnY MaxY Mean RMS Peak-peak Abs mean RMS ac Inegral Rpple Rpple fac Harmonc Form fac 47 m 9 5m m Fgure8:Zoomonoupuvolage,V Ou

13 Inernaonal Journal of Phooenergy I IC Δ Δ L n max n [[ (n+) d] (d /n) + [ (n+) d] (/n d) ] ( ) (+d) f n d n = Δ L n max n [[4 (n+) d] (d /n) + [ (n+) d] (/n d) ] ( ) (+d) f n d n ΔL n max n [[6 (n+) d] (d /n) + [4 (n+) d] (/n d) ] ( ) f (+d) n d n ΔL n max n [[ n (n+n) d] (d (n )/n) + [( n ) (n+n ) d] (n/n d) ] ( ) f n d n (+d) n n (8) The curren varaon Δ Ln max n hs formula s seleced nrelaonoheraedaveragenducancecurreni Ln AV durng he crcu dmenson Ths wll mean ha wh he same crcu dmenson and ncreasng number of phases, he curren varaon s reduced The geomercal addon of recangle and rangle RMS componens resuls n he oal capacor curren for an nphase hybrd boos DC/DC converer Consder I IC = I IC Π +I IC Δ (9) Fgure shows he RMS curren n he npu capacors of mulphase DC/DC converers The curren load of he capacordecreaseswhhencreasngnumberofphases The nfluence of he recangle RMS componen s clearly domnan (doed lnes, Ln max =) The maxmum capacor curren componen produced from he recangle poron s smaller by a facor of /n for n-phase converers The rangle capacor curren s no dependen on he converer power andhas,forallloads,hesamevalueincaseofraedpower he addonal load from he rangle curren n he capacors s small DC/DC Converer Oupu Crcu Fgure shows he curren waveforms a he oupu of a wo-phase hybrd boos DC/DC converer Frs, he currens n boh nducors and heoupucurrenofphasearerepresenedinhemddle he curren of phase s shown The rangle nducance currenofhewophasessshfedwhnabouahalfpulse perod of each oher A swched-off mes, he nducors are connecednseresandhecurrenflowsoheoupuphase, jus as n a sngle-phase converer However, n hs crcu, he overall oupu phase curren I OP consss of he sum of all heoupuphasecurrenstheoveralloupuphasecurren I OP wh he DC-componen I Ou s shown Fgure Is assumed ha only he DC-curren s flowng n he crcu oupu; he oal AC-componen of he overall oupu phase curren I OP flows n he oupu capacor In comparson o asngle-phasehybrdboosconvererhscurrensclearly smaller In addon, he frequency of he capacor curren has been doubled The necessary oupu capacy of he mulphase hybrd boos converer wll nex be calculaed Compared o a sngle-phase desgn, he oupu capacor curren s reduced and he curren frequency s ncreased by he number of phases As a consequence he curren n he capacor has a volage varaon a he oupu For he capacor desgn he permssble sac volage varaon n general s seleced a less han % of he raed oupu volage Consder C O = T P I Ln AV wh Δu 4 n Δu Ou max u Ou R Ou max () The RMS curren n he oupu capacor C O wll nex be calculaed for mulphase hybrd boos DC/DC converers Theoupucapacorcurrenforawo-phaseconverers represened n Fgure Lke he npu capacor, he oupu capacor curren can also be spl no a recangle and a rangle componen The RMS curren of he recangle poron for mulphase converers s shown n he formula below: I OC Π = I L n AV n (d n ) ( n d) I L n AV n (d n ) ( n d) I L n AV n (d n ) ( n d) f n d n f n d n f n d n IL n AV n (d n n ) (n n d) f d n n n n () The oupu capacor RMS curren, ha s, produced by he recangle componen s exacly he same as ha n

14 4 Inernaonal Journal of Phooenergy he npu capacor I s necessary o also consder ha he average nducance curren I Ln AV becomes smaller wh he ncreasng number of phases The nex formula shows he oupu capacor RMS componen produced by he rangle par of mulphase converers Consder Δ L n max n d [(n ) (d /n) + (n ) (/n d) ] ( ) (+d) f n d n Δ L n max n d [(n ) (d /n) + (n ) (/n d) ] ( ) (+d) f n d n I OC Δ = ΔL n max n d [(n ) (d /n) + (n ) (/n d) ] ( ) (+d) ΔL n max n d [(n n) (d (n )/n) + [n (n )] (n/n d) ] ( ) (+d) f n d n () f n n d n n The geomercal addon of recangle and rangle RMS componens resuls n he oal capacor curren for n-phase converers Consder I OC = I OC Π +I OC Δ () In Fgure 4 he RMS curren n he oupu capacors of mulphase DC/DC converers s shown The curren load of he capacor decreases wh he ncreasng number of phases If neglecng he curren varaon (Δ Ln max =,doed lnes), he maxmum curren n he oupu capacor C O s smaller for n-phase converers by a facor of /n compared o a sngle-phase desgn The load n he oupu capacors produced by he rangle curren s fxed by he nducance converer desgn Ths capacor curren s no dependen on he convered power If he converer s operaed wh raed oupu power, hs curren has only a small nfluence on he overall capacor curren In he fgure, he oupu capacor curren s represened wh a curren varaon of Δ Ln Nmax = 5I Ln AV The nfluence of he rangle curren a he oupu capacors s smaller han a he npu sde of he converer The calculaons ndcae ha he rangle curren load n he npu and oupu capacor for mulphase converers s clearly reduced Pung hs knowledge no pracce, he rangle curren n he nducances can be seleced more largely [4, 4]ThedynamcsofhehybrdboosDC/DC converer can be mproved and beyond ha he nducance andcapacorefforofhecrcucanbereducedsubsanally Besdes he calculaed curren n he capacors also s flowng harmoncs curren produced by swchng processes of he phases [44] Ths curren has been examned n [45 47] for dfferen converers In consequence, hese resuls can also be used for a hybrd boos converer The addonal curren can conrbue subsanally o he oupu capacors, heang uphecapacorsdurnghesmallloadofheconverer However, wh hgher power he calculaed capacor curren domnaes A saemen for all semconducor ypes canno be made Beyond ha, hs addonal curren s dependen on he pulse frequency of he converer Smulaon of he Two-Phase Hybrd Boos DC/DC Converer We made hs smulaon of he wo-phase hybrd boos DC/DC converer n CASPOC smulaon program wh a power source, no wh a PV module The followng parameers are used for smulaon: P In = W, U In =6V, I In = 5A, L = L = L = L = 855 μh, C I = 565 μf, C O = 58 μf, and f s =5kHz In prevous Fgures 5, 6, 7, 8, 9,,,,, 4, 5, 6, 7, and 8 are presened he resuls of smulaon Fgure 6 presens he PWM pulses appled o swch, correspondng o frs phase of he converer, respecve he PWM pulses appled o swch, correspondng o he second phase of he converer Fgure 7 show he npu curren of phase, Fgure 8 showhenpucurrenofphase,andhe overall npu phase curren whch consss of he sum of all he npu phase currens, n our case phase one and phase wo s presened n Fgure 9 IsobvousfromFgure ha he currens of phase one hrough nducors L and L ( L, L ) are equal The currens of phase wo hrough nducors L and L ( L, L ) are equal, bu here s represened jus one of hem n Fgure Oupucurrenofphase,respecve, and he overall oupu phase curren whch consss of he sum of all he oupu phase currens, n our case phase one and phase wo, are presened n Fgures,,and4Inhe las fgures are presened he oupu curren and volage, and herppleofhem 4 Concluson Begnnng from a sep-up hybrd boos converer whch was nroduced n [], afer analyses hs crcu and seeng f

15 Inernaonal Journal of Phooenergy 5 s suable for a PV sysem, we realze ha one of he man dsadvanages of hs crcu s ha he effor for he npu and oupu capacor, n he case of a sngle-phase DC/DC converer, s very hgh Ths s he same wh he effor of he nducors A mehod for reducng hs dsadvanage was based on he same srucure of he hybrd boos converer bu bul n a mulphase desgn To ensure ha all he phases of he converer operae a he same swchng frequency and wh phase-shf beween hem, we used nerleavng swchng sraegy Afer we analyze hs new mulphase hybrd boos converer, made he heorecal calculaon, and skech he waveform, our presumpon became rue The effor of he nducors, of he npu and oupu capacor, s decreased and ahesamemeherszesreducedthefrequencyofhe capacorcurrenssncreasedwhhenumberofphaseto valdae and confrm our heorecal calculaon, we smulae hs crcu n CASPOC [48] smulaon program Therefore, how s obvous from heorecal calculaon and waveforms assocaed o, compared wh he smulaon waveforms, we can see a very good accordance Based on hs, nex sep wll be o pu hs crcu no pracce Conflc of Ineress The auhors declare ha here s no conflc of neress regardng he publcaon of hs paper Acknowledgmens Ths work was parally suppored by he sraegc Gran POSDRU 7/5/S/7765, nsde POSDRU Romana 7 cofnanced by he European Socal Fund Invesng n People References [] A Campocca, L Dusonche, E Telare, and G Zzzo, Comparave analyss of dfferen supporng measures for he producon of elecrcal energy by solar PV and Wnd sysems: four represenave European cases, Solar Energy,vol8, no, pp 87 97, 9 [] T Andrejašč, M Jankovec, and M Topč, Comparson of drec maxmum power pon rackng algorhms usng en 55 dynamc es procedure, IET Renewable Power Generaon,vol5,no4,pp8 86, [] SSWWalker,NKSooryaarachch,NDBLyanage,PAG S Abeynayake, and S G Abeyrane, Comparave analyss of speed of convergence of MPPT echnques, n Proceedngs of he 6h Inernaonal Conference on Indusral and Informaon Sysems (ICIIS ), pp 5 56, Kandy, Sr Lanka, Augus [4] 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16 6 Inernaonal Journal of Phooenergy [] B Axelrod, Y Berkovch, and A Ionovc, Swchedcapacor/swched-nducor srucures for geng ransformerless hybrd DC-DC PWM converers, IEEE Transacons on Crcus and Sysems I: Regular Papers, vol55, no, pp , 8 [] L Huber and M M Jovanovc, Desgn approach for server power supples for neworkng applcaons, n Proceedngs of he 5h Annual IEEE Appled Power Elecroncs Conference and Exposon (APEC ), pp 6 69, February [4] F Renken and V Karrer, DC/DC converers for auomove board-ne srucures, n Proceedngs of he Inernaonal Power Elecroncs and Moon Conrol Conference (EPE-PEMC 4), Rga, Lava, Sepember 4 [5] F Renken, Hgh emperaure elecroncs for fuure hybrd drve sysems, n Proceedngs of he h European Conference on Power Elecroncs and Applcaons (EPE 9),pp 7,Barcelona, Span, Sepember 9 [6] L Huber and M M Jovanovc, Desgn approach for server power supples for neworkng applcaons, n Proceedngs of he 5h Annual IEEE Appled Power Elecroncs Conference and Exposon (APEC ), pp6 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Thesarergeneraor sysems, funcons and componens, n Proceedngs of he h FISITA World Auomove Congress, Barcelona, Span, May 4 [4] V Karrer and F Renken, Power elecroncs for he negraed sarer generaor, n Proceedngs of he Opmzaon of he Power Tran n Vehcles by Usng he Inegraed Sarer Generaor (ISG ), pp 47, Haus der Technk e V, Munch, Germany, [44] F Renken, Analyc calculaon of he DC-lnk capacor curren for pulsed sngle-phase H-brdge nverers, European Power Elecroncs and Drves Journal, vol,no4,pp 9, [45] F Renken, Analyc calculaon of he DC-lnk capacor curren for pulsed sngle-phase H-brdge nverers, European Power Elecroncs and Drves Journal, vol,no4,pp 9, [46] F Renken, Analyses of he DC-lnk curren n dsconnuous modulaed hree-phase nverers, n Proceedngs of he h Inernaonal Power Elecroncs and Moon Conrol Conference (EPE-PEMC 6), Pororož, Slovena, Augus-Sepember 6 [47] F Renken, DC-lnk curren n pulsed H-brdge nverers, n Proceedngs of he Inernaonal Exhbon & Conference for Power Elecroncs, Inellgen Moon and Power Qualy (PCIM 9), Nürnberg, Germany, May 9 [48] CASPOC Smulaon program, hp://wwwcaspoccom/

17 Inernaonal Journal of Medcnal Chemsry Phooenergy Inernaonal Journal of Organc Chemsry Inernaonal Inernaonal Journal of Analycal Chemsry Advances n Physcal Chemsry Inernaonal Journal of Carbohydrae Chemsry Journal of Quanum Chemsry Subm your manuscrps a Journal of The Scenfc World Journal Journal of Inernaonal Journal of Inorganc Chemsry Journal of Theorecal Chemsry Specroscopy Analycal Mehods n Chemsry Chromaography Research Inernaonal Inernaonal Journal of Elecrochemsry Journal of Journal of Caalyss Journal of Appled Chemsry Bonorganc Chemsry and Applcaons Inernaonal Journal of Chemsry Specroscopy