On Thermal and State-of-Charge Balancing using Cascaded Multi-level Converters

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1 Joural of Powr Elcrocs Vol. 13 No. 4 July JPE hp:// dx.do.org/ /jpe O hrmal ad Sa-of-Charg Balacg usg Cascadd Mul-lvl Covrrs Fasal Alaf ars Johasso * ** ad Bo Egard * * Dp. of Sgal ad Sysms Chalmrs Uvrsy of chology Gohburg Swd ** Vkora Swdsh IC Gohburg Swd Absrac I hs sudy h smulaous us of a mul-lvl covrr (MC) as a DC-moor drv ad as a acv bary cll balacr s vsgad. MCs allow ach bary cll a bary pack o b dpdly swchd o ad off hrby ablg h poal o-uform us of bary clls. By xplog hs propry ad h brak rgrao phass h drv cycl MCs ca balac boh h sa of charg (SoC) ad mpraur dffrcs bw clls whch ar wo kow causs of bary war v whou rcprocag h coola flow sd h pack. h opmal corol polcy (OP) ha cosdrs boh bary pack mpraur ad SoC dyamcs s sudd dal basd o h assumpo ha formao o h sa of ach cll h schdul of rcprocag ar flow ad h fuur drvg profl ar prfcly kow. Rsuls show ha OP provds sgfca rducos mpraur ad SoC dvaos compard wh h uform us of all clls v wh u-drcoal coola flow. hus rcprocag coola flow s a rduda fuco for a MC-basd cll balacr. A spcfc corbuo of hs papr s h drvao of a sa-spac lcro-hrmal modl of a bary submodul for boh u-drcoal ad rcprocag coola flows udr h swchg aco of MC rsulg OP bg drvd by h soluo of a covx opmzao problm. Ky words: Hybrd lcrc vhcls Mul-lvl covrr Bars Cll balacg hrmal balacg Covx opmzao I. INRODUCION Alhough bary chology has volvd sgfcaly durg h las dcad bars of boh plug- hybrd lcrc vhcls (PHEVs) ad lcrc vhcls (EVs) corbu a larg prcag of h oal vhcl cos. Cosquly h succss of PHEVs ad of EVs dpds o h dvlopm of a bary ha wll o war ou prmaurly o avod addoal bary rplacm durg h xpcd lfspa of h vhcl. h bary pack (BP) of EVs/HEVs/PHEVs s bul from a larg umbr of small clls cocd srs ad paralll o m boh h raco powr dmad ad h lcrc rag rqurm. Dph of dscharg (DoD) s o of h mos mpora facors ha drm dgradao of bary clls such as bary oprao a hghr DoD shor h cycl lf ad vc vrsa [1]-[4]. hrfor h cycl lf of a bary s sgfcaly shor wh udrgos full charg-dscharg cycls as h cycl lf bcoms sgfcaly logr wh oly udrgos paral charg-dscharg cycls [5]. I a Mauscrp rcvd Ja ; rvsd May Rcommdd for publcao by Assoca Edor J Hur. Corrspodg Auhor: fasal.alaf@chalmrs.s l: Chalmrs Uvrsy of chology * Dp. of Sgal ad Sysms Chalmrs Uv. of ch. Swd ** Vkora Swdsh IC Swd pack wh sa of charg (SoC) ad capacy dvaos amog s clls som of h clls udrgo charg-dscharg cycls a hghr DoD ha ohrs. Cosquly hs clls may rach hr d-of-lf (EO) soor. hus maag a prfc balac bw SoC ad DoD of ach cll h bary pack s crucal prologg bary lf. hs balac ca b achvd by hr passv or acv balacg schms basd o varous opologs of swchd capacv ad rssv crcus as llusrad [6]-[9]. h ma prcpl of all acv balacg schms s o rasfr h charg from clls wh hghr SoC o clls wh lowr SoC by usg swchd capacors ha ac as rmda sorag baks. Passv balacg schms ypcally ulz dffrcs cll volag o bur xcss charg rssor baks. Asd from DoD cll mpraur s kow o hav a srog ffc o bary war such as hor clls dgrad mor quckly ha coldr clls [10]-[13]. Mor mporaly h prsc of a fw ovrhad clls ca war ou h r bary prmaurly. h mpraur mbalac bw clls s du o varao ral rssacs h mpraur grad h coola du o covcv ha rasfr sd h bary pack ad h o-uform xral local hrmal dsurbacs [13] [14]. h lfspa of a -Io cll s rpordly rducd by wo mohs for ach dgr cras oprag mpraur from 30 C o

2 570 Joural of Powr Elcrocs Vol. 13 No. 4 July C [15]. Howvr wh mpraur crass byod 40 C h cycl lf of a bary dcrass drascally. Forcd covco coolg s ypcally usd o maa bars wh h rcommdd mpraur rag. Howvr hs mhod cao compsa for h mpraur grad alog h coola flud sram. Clls ha ar closr o h ar l wll b coolr ha hos furhr dow h coola sram. Rcprocag ar flow (RF) was proposd [10] ad [14] as a ma o rduc h ffcs of h mpraur grad h coola sram. Howvr h prs sudy s show ha clls cou o suffr from o-uform local had spos h prsc of paramr varao ad local dsurbacs. Cosdrg h aformod causs of bary war h bary maagm u (BMU) should balac boh SoC ad mpraur dffrcs bw clls. hrfor hs papr vsgas h MC-basd acv cll balacg schm ha allows ho clls o b bypassd cosquly balacg boh SoC ad mpraur whou h d for RF. Cascadd MCs [16] [17] had b vsgad for lcrc drvs HEVs ad EVs [18] [19]. MC cosss of cascadd H-brdgs (HBs) wh a solad bary cll for ach HB. I hs papr h combao of HB ad a bary cll s rfrrd o as a powr cll (PC). MCs EV/HEV/PHEV applcao ar dd o rduc vrr losss ad oal harmoc dsoro h grad wavform for h lcrc mach. h usual swchg sragy moor drv applcaos of MCs s h phas-shfd puls wdh modulao (PS-PWM) chqu ha achvs h uform us of cascadd clls [16] [17]. Howvr MC prss a addoal advaag as h clls d o b uformly usd ovr a m wdow of o or svral volag wavforms. By o-uformly usg h clls ad by xplog h brak rgrao phass h drv cycl a MC cll balacr ca balac boh SoC ad mpraur dffrcs. I hs sudy h PS-PWM schm s rfrrd o as h uform duy cycl oprao (UDCO) as h opmal schm ha corols h duy cycl of ach PC o balac boh SoC ad mpraur s rfrrd o as opmal corol polcy (OP). h poal bf of usg MC o balac boh SoC ad mpraur of bary clls udr a u-drcoal flow (UF) has b horoughly vsgad ad compard wh ha of UDCO [0]. hus h ma corbuo of h curr sudy s o vsga OP udr RF ad h o compar h rsuls dal wh hos of OP udr UF. OP s calculad basd o h assumpo of prfc formao of h SoC ad h mpraur of ach cll as wll as of h fuur drvg. hs papr xams whhr OP provds mor sgfca mprovms compard wh UDCO udr UF ad RF ad whhr RF prss ay poal bfs for OP-basd acv cll balacg. For smplcy hs sudy mploys a DC mach as h lcrc mach ad modls h clls by rssv crcus. Morovr h smulao sudy focuss o a ar-coold bary Fg. 1. Block dagram of a sgl-phas cascadd HB MC. sub-modul (BSM) wh a srg of fv srs-cocd clls. h coola flow s assumd o b lamar wh kow l mpraur ad spd. I [1] oly o cofgurao of h fv-cll srg was sudd o valua h prformac of h MC-basd cll balacr. A smlar mhod was adopd h prs sudy. Howvr a mor horough aalyss was coducd o carfully assss h prformac of h cll balacr. For purpos of valuao wo dffr varas of h fv-cll srg wr sudd. I h frs vara h hghr rssac cll s locad a h d of h srg h dowsram of h coola flud. I h scod vara h hghr rssac cll s locad h mddl of h srg. h rssac of h hrmally xposd cll was assumd o b almos 50% hghr ha ha of ohrs clls wh comparg h prformac of UDCO ad OP udr boh UF ad RF. Bsds h smulao rsuls ad h valuao of MC as a cll balacr aohr mpora corbuo of hs papr s h dald drvao of a sa-spac lcro-hrmal modl of BSM udr h swchg aco of MC udr UF ad RF. h modl was formulad such a way ha a covx opmzao problm ylds OP udr a prfcly kow fuur drvg. hs modl ca b usd fuur rsarch dcdg h duy cycl a rcdg horzo modl prdcv corol schm [] basd o h bs avalabl prdco of fuur drvg. h papr s orgazd as follows. Sco II roducs h basc fuco of MC. Sco III prss h dald lcro-hrmal modlg of BSM udr h swchg aco of MC. h opmzao problm ad h umrcal soluo mhod ar dscrbd Sco IV. Sco V prss h smulao rsuls ad h comparso bw OP ad h UDCO schms udr boh UF ad RF. A dald dscusso o h smulao rsuls s provdd Sco VI. h coclusos ar gv Sco VII. II. MUI-EVE CONVERERS OVERVIEW hs sco provds a shor roduco o sgl-phas MC. I coras o wo-lvl covrrs ha coss of a sgl larg bary cocd wh a sgl HB MC as show Fg. 1 has svral srs-cocd PCs whch ach PC coas a HB ad h dpd bary cll. HB whch cosss of wo half-brdgs s a swch mod

3 Joural of Powr Elcrocs Vol. 13 No. 4 July dc-dc powr covrr [3] ha producs a four-quadra corollabl dc oupu usg four swchs amly S 1 S S ad 1 S as show Fg. 1. h MoSFEs ar ormally usd for hs swchs. o avod a shoo-hrough problm oly o of h swch pars ( S 1 S ) ( S S ) ( 1 S 1 S ) or ( S 1 S ) s swchd o a a m. ( S 1 S ) gras a posv oupu volag v from PC ( S S ) gras a gav 1 v ad boh ( S 1 S ) ad ( S 1 S ) gra v 0. hrfor h followg hr mods of oprao ca b dfd for ach PC dpdg o h swch par ha s swchd o: Mod -1 ( v > 0 ) Mod - ( v < 0 ) ad Mod - 3 ( v 0 ). o modl hs hr mods of oprao s j ( ) 1 s dfd as h ON-Sa ad s j ( ) 0 s dfd as h OFF-Sa of h swch corrspods o PC ad Î{ 1 } S j '' j dos o of h wo half-brdgs HB. hrfor h swchg fuco s () for Cll ca b dfd as ì 1 Mod -1 ï s ( ) s1( ) - s( ) í-1 Mod - ï î 0 Mod - 3 hus all hr mods of HB ca b dfd rms of s (). s ( ) s 1 ( ) s ( ) coas h h swchg vcor [ ] swchg fucos for all PCs sd MC. Wh h assumpo of a dal swch bhavor h ohmc ad h swchg losss ca b gord. hrfor h pu ad h oupu of HB ar rlad hrough h swchg fuco s () as show Fg.. hus h curr Cll s gv by B ( ) ( ) s ( ) () As a rsul of h srs coco h sam load curr passs hrough ach PC. Howvr h drco of h curr passg hrough Cll dpds o h slco of swchs ad o h drco of load curr. Smlarly h volag oupu from ach PC s dfd by v ( ) VB( ) s ( ). Hc h oal volag oupu from MC ca b wr as h sum of h volag oupu from ach v å v å 1 1 V B PC as gv blow. ( ) s ( ) (3) h umbr of volag lvls ha MC gras dpds o h umbr of PCs ad o h rmal volag V B of Cll. If h rmal volag of all clls s h sam MC ca h gra + 1 dffr volag lvls ( v ). Fg.. Swchg modl of HB. III. MODEING OF HE CE BAANCING SYSEM WIH RF h block dagram of h cll balacg sysm for RF ad for UF s show Fg. 3. MC s capabl of grag h sam oupu volag lvl v svral ways by usg dffr combaos of h hr mods for varous PCs provdg rdudacy grag h sam load volag hrough umrous possbl swch combaos. hs rdudacy adds a xra dgr of frdom (DoF) ha s ulzd hs papr o dsg h opmal corol sgal for Cll. Cosquly SoC ad mpraur dffrcs bw clls ar kp wh a cra zo whl sasfyg all ohr oprag rqurms. I hs sco a swchg modl ad a avragd sa-spac modl of a PC s drvd basd o h assumpo ha h load s a DC mach. Fally h compl sa-spac modl for PCs s dvlopd. A. Swchg Modl of a Powr Cll I hs subsco h lcro-hrmal modl of a swchd bary cll udr RF s drvd. Each PC s assumd o coa oly o Cll. h dyamcs of cll mpraur dpds o svral facors such as coola proprs cll maral proprs cll placm ad bary pack cofgurao. I [14] h forcd-covco coold bary pack was modld by h lumpd capacac hrmal modl ad by h flow work modl (FNM). I h sad sudy h bary pack was cofgurd as u ss pp ha rprss p paralll srgs wh ach srg calld a bary modul coag s clls cocd a srs. A suffc amou of fr spac s prs bw h clls o allow srams of lamar flow of h coola (ar). A cofgurao of h bary pack -Io clls ad h ar proprs adopd h prs papr ar smlar o hos [14]. Varous coffcs for h hrmal ad h physcal proprs of h cll ad of h ar usd hs sudy ar lsd abl I. Dals ar provdd [14]. C N [Ah] rprss h omal capacy of Cll ad R u [ KW ] rprss h covco hrmal rssac for Cll ha dpds o h gomry of h bary cll o h coola flud proprs ad o h -1

4 57 Joural of Powr Elcrocs Vol. 13 No. 4 July 013 ABE I DEFINIION OF BAERY PARAMEERS Nussl umbr whch ur dpds o h Ryolds umbr. h coffc Cs r sc psvs[ JK ] rprss ha capacy (amou of ha rgy rqurd o ras h mpraur of Cll by 1 Klv) -1 r s s h dsy c ps s h spcfc ha capacy (ha capacy pr u mass 3 of bary) ad V s [ m ] s h volum of Cll. h -1 coffc c r c V& [ WK ] s hrmal coducac of f f pf f h coola flud. All ohr quas ar show Fg. 4. I hs papr oly o submodul (of h bary modul) ha cosss of srs-cocd bary clls s sudd. Frs h hrmal modl s drvd sparaly for h coola flow ach drco. h wo modls ar h combd o cra h modl for RF. I hs sudy boh RF ad UF ar xamd ad compard. Hc h cas of forward flow (.. from lowr o hghr cll dx) s dsgad as UF for as of rfrc. h hrmal modl proposd [14] dos o cosdr ay powr lcroc swchg of h bary clls. hus powr lcroc swchg mus b corporad o h curr framwork. h prvous modl was modfd by mbddg h swchg fuco s () ad subsquly combg wh h hacd hv quval lcrcal modl show Fg. 4 o drv h swchg lcro-hrmal modl of PC. For forward flow h dyamcs of h surfac mpraur s [K] of Cll rms of () ad () afr subsug h valu of B () from quao () o h modl proposd [14] s gv by h & " { 1 } (4) s -ass + bss + asf-1 s rprss h saaous ohmc powr losss o Cll ad f- [ ] s h mpraur of 1 K mpraur od ' -1' (of h flud lm modld by FNM) aachd o Cll a upsram drco. Equao (4) s o ha rsg rms of corol dsg bcaus xplcly dpds o h flud od mpraur f-1 for s Fg. 3. Cocpual block dagram of a bary cll balacg sysm wh RF. s (0) s a vcor coag h al mpraur of all clls ξ(0) s a vcor coag h al SoC of all clls P d s h dmadd powr for load wh h kow volag ad curr profl ad f 0 f rprs mpraurs of mpraur-ods of h coola flud. h subsysm sd h blu box rprss BSM bg balacd ad h gr boxs coa h swchg fucos for h corrspodg cll. Cll ha s o drcly kow. hrfor hs quao mus b modfd o rmov hs xplc dpdcy. For corol dsg purpos h mpraur dyamcs of ach cll ca b mor appropraly modld rms of bary curr s ad of h mpraur Î { } of h B coola flud a h l. o achv hs f-1 s lmad from quao (4) as follows. Accordg o [14] h mpraurs of h ods ' -1' ad '' ar rlad by a ad ( s + bf-1) a f " f f 0 f (5) b ar dfd abl I. Gv ha f 0 s a kow quay h by forward rcurso of quao (5) ay f ca b xprssd as a fuco of h l flud mpraur f 0 ad of h mpraurs s1 o s of h bary clls such as f 1 f f 3 æ 1 ç è a1 s1 æ b ç è a1a s1 æ bb3 ç è a1a a3 æ b1b b3 + ç è a1a a3 æ b1 + ç è a1 æ 1 + ç è a s1 f 0 f 0 s æ b3 + ç è aa3 æ b1b + ç è a1a s f 0 æ 1 + ç è a3 ad so o. hrfor h gral quao for ay wr as follows: f f1 s1 + a fs + + a fs b f f 0 s3 (6) f s a + (7)

5 Joural of Powr Elcrocs Vol. 13 No. 4 July a fj æ 1 æ 1 ç Õ ç a b k bk f f " ³ 1 (8) è a è Õ k 1ak æ ç Õk ( j+ 1) bk " > j a ç fj 0 " < j (9) è Õk j ak Usg quao (7) (4) h hrmal dyamcs of h bary clls ca b rwr as follows: & a + + a + b s + b (10) : s 1 s1 s s f 0 a s a - " ³ 1 (11) æ ( -1) k ( j 1) k a ç Õ + b j a ç ( 1) s " > j a - j 0 " < j è Õk j ak æ ( -1) k 1 k b ç Õ b a ç ( -1) è Õk 1 ak s " ³1 (13) Aalogous o h forward flow cas h hrmal dyamcs of Cll s drvd for h rvrs coola flow (.. from hghr o lowr cll dx). h rsul s gv blow & a b (14) s () () 1 s a s + bss + () f s h mpraur of h l flud rg BSM from h Cll sd. h ohr coffcs ar dfd as follows: () () ( -+ 1) a a " ³ 1 b b " ³ 1 (15) () () aj aj " < j aj 0 " > j f (16) h lcrcal quval modl of a bary cll s show Fg. 4. hs modl s a hacd hv modl wh wo m cosa bhavors [4] [6]. h dyamc modl for hs crcu s gv by V & -a V + b s (17) V & -a V + b s (18) & x -b s (19) 3 V (x - b s (0) B f ) -V1 -V r B s h curr flowg hrough Cll ad ormalzd SoC of Cll. Î[ 0 1] V 1 ad x s h x s a u-lss quay. V ar h volags across capacors C 1 ad C rspcvly ad V B s h oupu volag of Cll. h SoC-dpd op crcu volag s gv by V f x ) oc ( Fg. 4. Elcrcal modl of a bary cll. f : 0 1 Â 0 s a fuco of SoC. Equaos (10) o (0) dscrb h swchd bhavor of h bary udr h [ ] + swchg aco of MC rms of h load curr () ad of h swchg fuco s (). hrfor hs modl ca b cosdrd as a swchg modl of B. Avragd Sa-Spac Modl of PC PC. Cll balacg ca b formulad as a opmzao problm usg wo approachs. I h frs approach cll oprao s opmzd by drcly usg h swchg fuco s () as a opmzao varabl for Cll. h swchg fuco s () quao ca oly aa valus from h dscr s { }. Hc h compud opmal corol s a dscr-valud sgal. I hs cas h sysm s ormally modld as a swchd sysm wh varous mods of oprao ad h opmzao problm hrfor bcoms combaoral ha s ormally dffcul o solv bcaus of s o-covx aur. Howvr h am of hs sudy s o valua OP whch cssas a modl wh a ral-valud corol sgal bcaus such modls ar far asr o hadl opmzao problms ha hos wh dscr-valud sgals. Hc h scod corol approach s usd sad u Î -1 1 whch s h avrag of h h bary duy cycl [ ] swchg pu fuco s () s usd as opmzao varabls for Cll. h opmzr compus a corol vcor sgal u ha coas duy cycls Î[ -1 1] u for ach PC. No ha h gav duy cycl mas oprao Mod -. h compud corol u s h fd o h modulao block M whch h gras a appropra swchg fuco s Î s() for ach PC. Gv ha h swchg modl (10) (0) volvs dscr-valud sgals s () hs sgals mus b rasformd o ral-valud avragd sgals o modfy h sysm modl (10) (0) accordgly. h us of avragg s jusfd by h fac ha mos cass h swchg frqucy F s sd h modulaor M s sgfcaly hghr ha h badwdh of h sysm. hus by assumg ha s f F >> f ad by mployg h wo-m scal sparao prcpl [7] h cocp of avragg ca b mployd [8] [9]. I ohr

6 574 Joural of Powr Elcrocs Vol. 13 No. 4 July 013 words h sysm rspos s assumd o b drmd prdomaly by h duy cycl ( ) Î[ -1 1] u or h avrag of h swchg pu fuco s (). I addo carful drvao s rqurd gv ha h swchg modl volvs cra blar ad quadrac rms. I hs sco h avragd modl s drvd dal by avragg ach sgal ovr o swchg cycl. h followg assumpos ar mad drvg h avrag quas: Assumpo 1: h swchg fuco ca oly aa valus hr from s { 0 1} or from { 1} 0 - durg ay swchg cycl of prod s. hs assumpo mpls ha s o allowd o charg ad o dscharg h bary cll durg h sam swchg cycl. Assumpo : h load curr () rmas farly cosa durg ay swchg cycl. hs assumpo s jusfd basd o h dscusso abov. Assumpo 3: All ral lcrcal sas V 1 V1 V V ad x x as wll as rmal volag V B rma farly cosa durg h swchg cycl. Basd o hs assumpos h avrag of h swchg fuco s () whch s also calld h duy cycl s gv by 1 o u ( ) s ( ) s ± ò ( ) d s -s o s h ON m of a swch durg ay swchg rval. hs quaos shows ha u () ca aa ay couous ral valu h rval [ 1 1] valu of s - dpdg o h o. All ohr avragd sgals ca b dfd rms of u () ad () as follows: B( ) u Br u () v x ) u - b u (3) ( f ( ) -V1 -V B s h avrag curr flowg hrough Cll durg rval s Br s h roo ma squar (RMS) curr ha curs quval ohmc loss across Cll durg o swchg cycl ad v s h avrag oupu volag from PC durg prod s of ay swchg cycl. [0] prss h dald drvao of all h avragd varabls. Usg h avragd quas h avragd modl of follows: & s 1 a + + a s1 & s + b s V1 -a1v 1 + b1 r PC s wr as u + b u f (4) (5) & V -av + b u (6) & x -b 3 u (7) V (x - b u (8) B f ) -V1 -V r s 1 ad s dsga h forward ad h rvrs coola flow rspcvly ad { } f Î s h kow flud mpraur o of h wo ls dpdg o h drco of h coola flow. Gv ha o couously dffrabl u ad f 0 f u (4) s u ar dfd rms of wo w corol varabls u 1 ad u dfd as 1 max{ 0 u} Î[ 0 1] u max{ 0 - u } [ 0 1] u ( u - u ) Î[ 1 1] ad ( u + u ) [ 0 1] 1 - ha ar u ad Î rspcvly. hus u 1 Î. u1 ca h b rprd as h duy cycl for Mod-1 as u ca b rprd as h duy cycl for Mod-. I hs w cox u 1 ad u cao b boh ozro smulaously (cf. Assumpo 1) a ay m for safy rasos whch f volad ca caus a shoo-hrough problm. Basd o hs wly dfd corol sgal h hrmal subsysm of bary Cll for rcprocag coola flow s gv by X & a + b (9) 1 X a X + gˆ ( x ) uˆ X Î Â ˆ ( x ) [ b x b x ] Â s s s g ˆ [ u u ] f u 1 Î ad x. Smlarly h lcrcal subsysm of Cll s gv by X & A X + gˆ ( x ) uˆ (30) [ ] 3 1 X X 3 Î Â X X wh X 1 V1 X V ad X x 3 A dag( -a1 - a 0) 3 3 Î Â ad ˆ 3 ( x ) [ bx - bx ] Î Â [ b b ] b g wh b C. Compl Avragd Sa-Spac Modl of -Cll MC A -cll MC ca b rprsd varous sa-spac modls dpdg o h umbr of clls ad o h cofgurao whch hy ar cocd sd ach PC. I hs modl ach PC s assumd o coa oly o Cll. Usg quaos (9) ad (30) as basc buldg blocks h sa-spac sysm for h hrmal subsysm of clls ca b wr as follows:

7 Joural of Powr Elcrocs Vol. 13 No. 4 July X + G ˆ ( x) uˆ ( + W s ) X & A Y C X (31) (s ) A Î Â f s h sysm marx whch h lowr ragular marx wh coffcs A s a j dfd by quaos (11) ad for forward coola flow () ( A A ) s h uppr ragular marx wh coffcs () a j dfd by quaos (15) ad (16) for rvrs coola flow ˆ ( x ) dag( gˆ 1 ( x ) gˆ ( x )) Î Â G s h load curr-dpd pu marx for h hrmal subsysm W ( ) [ b b ] Î Â s 1 wh coffcs (s ) b dfd by quao (13) for s 1 ad quao (15) for s s h scalg vcor for h l flud mpraur C I Î Â s h oupu marx X [ X X ] Î Â 1 s h hrmal sa vcor [ uˆ1 uˆ ] Î Â uˆ s h pu vcor Î Â s h kow flud mpraur ( f 0 or f f ) o of wo ls dpdg o h drco of h coola flow ad Y Î Â s h oupu vcor. Smlarly h lcrcal subsysm of h -clls s gv by X & A X + Gˆ ( x ) uˆ (3) 1 A) 3 3 A dag( A Î Â s h sysm marx ˆ 3 ( x ) dag( gˆ 1 ( x ) gˆ ( x )) Î Â G s h load curr-dpd pu marx for h lcrcal subsysm X 3 [ X X ] Î s h lcrcal sa vcor 1 Â ad uˆ Î Â s h pu vcor. Subsquly h wo subsysms ca b combd dagoal form. é X& ù éa ê X 1 & ú ê ë û êë 0 0 ùé X ù égˆ ( x ) ù é W ù uˆ úê ú + ê A X Gˆ ú + ê ú úû ë û êë ( x ) úû ê 0 ú 143 ë û X& A X ( ) Gˆ s ( x ) W ˆ ) f X& A ( X + G( x ) uˆ + W s Y CX (33) A 4 4 Î Â s h sysm marx f ˆ 4 ( x ) Î Â s h load curr-dpd pu marx for h compl 4 sysm [ ] C 0 Î Â s h oupu marx C s h sa vcor 4 G X Î Â 4 uˆ Î Â s h pu vcor ad W Î Â s h scalg vcor for h l flud mpraur. h avragd sa-spac lcro-hrmal modl udr RF as show quao (33) s a pc-ws aff sysm. Rmark 1: h corol sgal h mods of ''. h mod whch HB ad Cll sd ach u ca b usd o drm HB sd ay PC a ay m PC s oprag ca b drmd by algorhm 1. Smlarly algorhm ca b usd o drm h mod of Cll (.. whhr s chargg or dschargg) sd ay PC. IV. OPIMIZAION PROBEM I hs sco a opmzao problm s formulad for h OP schm o achv cll balacg rms of boh mpraur ad SoC. h avragd sa-spac modl drvd h prvous sco s usd alog wh a objcv fuco ad cra cosras as dscrbd blow. A. Dfo of h Objcv Fuco h objcv of hs sudy s o qualz SoC of all clls a h fal m ad o maa boh SoC ad mpraur dvaos amog h clls wh a cra zo durg h r drv cycl. hs objcvs wll b spcfd as cosras h x subsco. Aohr am s o mmz mpraur dvaos amog h bary clls as spcfd h followg objcv fuco: f J ( Y ) ( Y1 - Y ) + + ( Y -1 - Y ) d ò (34) 0 o rasform J (Y ) o h quadrac form X 1 1 Q C Q Q C s dfd wh ( -1) 1 dag( q1 q -1 ) ÎÂ Q q [ 1-1]. hrfor h objcv fuco (34) ca b rwr as h followg sadard quadrac form:

8 576 Joural of Powr Elcrocs Vol. 13 No. 4 July 013 f B. Dfo of Cosras ò J ( X ) X QXd (35) 0 hr ar som hard (opraoal safy ad balacg) cosras ha d o b rspcd by OP. h objcv of balacg SoC s dfd rms of h followg zo ad rmal cosras. Durg ru-m SoC of all clls mus say wh a cra zo from ach ohr as gv by - DSoC ( X 3( ) - X j3( )) DSoC " " j Î 1 (36) { } ad a h fal m SoC of all clls should b qual: { 1 } X 3( f ) X j3( f ) " j Î (37) I addo SoC of Cll mus say wh followg zo: { 1 } 0 X 3( ) 1 " " Î (38) o sur gh hrmal balacg addo o mmzg h dvaos of cll mpraurs a hard cosra maas mpraur dvaos amog h clls h followg zo: { 1 } - Ds ( s ( ) - sj ( )) Ds " " j Î (39) Morovr a safy cosra o h maxmum oprag mpraur of ach cll s prs. { 1 } s ( ) s max " " Î (40) s max s h maxmum oprag mpraur allowd for Cll. h objcv o rack h dmadd load volag ( v d ) ca b wr as h followg cosra v d å[ f ( X 3 ) - X 1 - X ) u - br u x ] 1 ( (41) v d s ormally provdd by h hghr suprvsory block calld rgy maagm sysm (EMS) h cox u 1-1 uˆ rprss h duy cycl of Cll. I of HEVs. [ ] hs sudy f ( X 3) s assumd o b cosa whl X 1 ad X ar glgbl whch ar ormal assumpos dvlopg EMS for (P)HEVs [30]. hs assumpos prsrv h covxy of h problm. Morovr a cosra s dfd o h maxmum curr ha ach bary cll ca supply. [ ] x u Î (4) B m B max B m ad B max ar h mmum ad h maxmum bary curr lms rspcvly. Cra cosras ar also prs o h corol sgal u ˆ u [ u u ] Î Â 1 whch ar gv by [ 1] u Î[ 0 1] u ( u + u ) [ 0 1] 1 Î 0 1 Î ad ( u - u ) Î[ 1 1] u (43) 1 - Basd o h dfos of u 1 ad u h prvous sco hs valus cao b ozro smulaously o avod a shoo-hrough problm. hus h followg cosra s mposd o sur safy: u 0 (44) 1 u Howvr h las cosra s o-covx ad mus b rmovd o prsrv covxy of h problm. C. Dfo of h Opmzao Problm h opmzao problm ca subsquly b wr as follows: J 0 f ò m X QXd subjc o uˆ 0 ˆ ) ì ( s X & A X + G( x ) uˆ + W f ï ícosras (36) - (44) ï x ( ) f ad s ar kow a ach m sp. î (P-I) h opmzao problm (P-I) s o-covx bcaus of h o-covx cosra u 0. I h x subsco 1 u cra assumpos ar formulad o rsor covxy ad o smplfy h problm. D. Solvg h Opmzao Problm Usg CVX h problm (P-I) was solvd by CVX whch s a MAAB-basd packag for spcfyg ad for solvg covx programs [31] [3] ad uss a dscpld covx programmg ruls [33]. CVX rasforms MAAB o a modlg laguag allowg cosras ad objcvs o b spcfd usg sadard MAAB xprsso syax. h o-covx cosra ( u 0 ) mus b rmovd 1 u pror o sablshg h opmzao problm (P-I) CVX. I hs sudy cll balacg s achvd by assumg ha h mods of all PCs blog hr o s {Mod 1 Mod 3} or o {Mod Mod 3} bu o o {Mod 1 Mod } a ay m sa. I ohr words s o allowd a ay m sa o charg ad o dscharg clls smulaously. Basd o hs assumpo h sg of u 1 ca b pr-dcdd basd o h sg of a kow dmadd load volag ( v d ). hrfor a v ³ 0 u 0 ad u ( u - u ) 0. d 1 ³ Ohrws u 1 0 ad cosquly u 0. hrfor h o-covx cosra ( u 0 ) d o b spcfd. h 1 u sysm was dscrzd usg Eulr s approxmao a samplg m h 1sc. h smulao paramrs ar show abl II

9 Joural of Powr Elcrocs Vol. 13 No. 4 July ABE II SIMUAION PARAMEERS R s s h omal valu of srs rssac R s of ay Cll N s h prdco (or drvg) horzo dscr m ad s h rcprocao prod or h prod whch h coola compls o cycl of uform forward ad rvrs flows. V. SIMUAION RESUS A fw varabls mus b roducd bfor h smulao rsuls ar prsd. hs varabls ar llusrad plos 1 N for mor clary. X å X ( k) s dfd as h N k 0 avrag mpraur of Cll o h r drvg horzo N 1 ad X b å X s h avrag mpraur of BSM. 1 Smlarly h ormalzd avrag powr loss pr u ohm across ay Cll o h r drvg horzo s gv by I max j 1 N æ 1 ç è N N åk å Br 1 N k 1 ( ( k) ou Br j ( k)) (45) ou Br j s h RMS curr hrough Cll j for OP udr UF as dfd by quao (). h suprscrps o ad u dsgush h sgals of OP from UDCO as h suprscrps u ad r rprs UF ad RF rspcvly. Fg. 5 shows h drv cycl daa comprsg h dmadd powr volag ad curr profls usd h smulaos. I h followg scos h smulao rsuls of wo dffr cll cofguraos ar prsd o horoughly valua h ffcvss of h proposd OP. I cofgurao-1 h cll wh 50% hghr rssac s assumd o b h las dowsram cll (Cll 5 ) h fv-cll srg as cofgurao- h cll wh hghr rssac s assumd o b cocd h mddl (.. a poso of Cll 3 ) of h srg. Boh srg cofguraos ar dscussd sparaly blow o show h mplcaos of OP. A. Cofgurao-1: Dowsram Cll 5 has hghr rssac I hs subsco h prformacs of UDCO ad OP udr boh UF ad RF ar valuad. Cll 5 s assumd o hav Fg. 5. Drv Cycl: Dmadd Powr Volag ad Curr Profl. wo shor durao hgh powr paks xs: aroud 10 scods ad () aroud 350 scods. Fg. 6. rackg of dmadd oupu volag. h fgur shows ha OP racks h dmadd oupu volag wh sgfcaly small rror. h rackg prformac s h sam for srg cofguraos 1 ad. almos 50% hghr srs rssac bcaus of agg or of som ohr ffc. h mpraur ( X ) SoC ( x ) ad h ormalzd avrag pr u powr loss ( I ) ar plod for ach cll. No ha h assumpo abou 50% cras ral rssac s o uralsc as accordg o [34] h bary ral rssac may vary sgfcaly as a fuco of s cycl-lf. h smulao rsuls ar show for boh OP ad UDCO Fg. 7 for RF ad Fg. 8 for UF. OP vrsus UDCO udr RF: Fg. 6 shows h oupu volag grad by MC ad h good rackg prformac wh a sgfcaly small rror for OP. h mpraurs of all clls udr RF ar show for OP Fg. 7(a) ad for UDCO polcy Fg. 7(b). h mpraur of Cll 5 udr RF for h UDCO polcy s sgfcaly hghr ha ha of OP.

10 578 Joural of Powr Elcrocs Vol. 13 No. 4 July 013 (a) Opmal mpraur of ach cll for OP udr RF. Dsp R s5 bg 50% hghr OP succssfully achvd hrmal balacg amog all clls. (b) mpraur of ach cll for UDCO udr RF. Rd: Hos Cll gh Gr: Colds Cll. Cll 5 suffrs from hrmal ru away as show rd. (c) Opmal SoC of ach cll for OP udr RF. h plo shows ha OP has smulaously achvd SoC ad hrmal balacg show Fg. 7(a). Fg. 7. Cofgurao-1 udr RF: Smulao rsuls ad comparso bw OP ad UDCO for RF wh h mos dowsram Cll 5 havg 50% hghr rssac. h plos show ha OP sgfcaly prforms br ha UDCO udr RF. h uform us of clls s aurally o opmal hs suao bcaus h rssac ( R s5 ) of Cll 5 s 50% hghr ha ha of h ohrs. h plos also show ha usg RF s o hghly hlpful for UDCO udr paramr varao. RF oly hlps o rduc mpraur dvao h clls wh omal rssac whl clls wh hghr rssac sll suffr from hrmal ru away. (a) Opmal mpraur of ach cll for OP udr UF. Dsp Rs5 bg 50% hghr OP has succssfully achvd hrmal balacg amog all clls. (b) mpraur of ach cll for UDCO udr UF. Rd: Hos Cll gh Gr: Colds Cll. Cll 5 suffrs from hrmal ru away as show rd. (c) Opmal SoC of ach cll for OP udr UF. h plo shows ha OP has smulaously achvd SoC ad hrmal balacg show Fg. 8(a). Fg. 8. Cofgurao-1 udr UF: Smulao rsuls ad comparso bw OP ad UDCO for UF wh h mos dowsram Cll 5 havg 50% hghr rssac. h plos show ha OP sgfcaly prforms br ha UDCO udr UF. h uform us of clls s aurally o opmal hs suao bcaus h rssac ( R s5 ) of h Cll 5 s 50% hghr ha ha of ohrs. Fg. 7 ad 8 show ha OP xhbs smlar prformac udr UF ad RF. hus RF s rduda for a MC-basd acv cll balacg sysm wh oprad usg OP. (a) Opmal ormalzd avrag powr loss pr u ohm across Cll for OP udr UF. h dashd horzoal black l shows ormalzd u powr loss across Cll for UDCO. (b) Opmal ormalzd avrag powr loss pr u ohm across Cll for OP udr RF. h dashd horzoal black l shows ormalzd u powr loss across Cll for UDCO. (c) Opmal saaous duy cycls for ach cll durg hgh curr rvals for OP wh RF. h plo shows ha durg hgh curr rvals OP las uss Cll 5 compard wh ohr clls. Fg. 9. Cofgurao-1 UF vrsus RF: Opmal powr loss dsrbuo udr UF ad RF. hs plos show ha durg hgh curr rvals OP las uss Cll 5 compard wh ohr clls. hus Cll 5 provds lss curr durg hgh curr rvals ad cosquly has lss losss as show Fg. 9(b). hs s aurally opmal as losss ar quadrac curr. Morovr OP achvd good hrmal balacg whl maag h mpraurs of all clls wh ± C ad SoC wh ±10% from ach ohr as show Fg. 7(c). SoC for h UDCO polcy s o show. Howvr a uform dcay s assumd for ach cll. Fg. 9(b) shows h ormalzd avrag u powr loss I for ach cll udr RF. h horzoal dashd black l llusras h avrag u powr loss ur I

11 Joural of Powr Elcrocs Vol. 13 No. 4 July across ach cll for h UDCO polcy as h colord vrcal bars llusra h avrag u powr loss or I across ach cll for h OP schm. h ral rssac R s5 of Cll 5 s almos 50% hghr ha ha of ohr clls. hus as show Fg. 9(b) h aurally opmal polcy s h las us of Cll 5 compard wh ohrs ad Cll 1 udr bs hrmal codos should b usd mos. OP vrsus UDCO udr UF: h mpraurs of all clls ar show for OP Fg. 8(a) ad for UDCO polcy Fg. 8(b) udr UF. Fg. 9(a) shows h ormalzd avrag u powr loss for ach cll udr UF. OP aga prforms br ha h UDCO polcy as dmosrad h fgur. Smlar o h RF cas OP smulaously achvd good hrmal ad SoC balacg by usg Cll 5 whch s h mos dowsram cll wh 50% hghr rssac las compard wh h ohrs as Cll 1 s usd mos. [0] prss a mor dald comparso bw OP ad UDCO udr UF. Opmal Powr oss Dsrbuos for UF ad RF: Fg. 9(a) ad 9(b) dmosra h ormalzd avrag u powr loss for UF ad RF cass rspcvly. hs fgurs dmosra h ffc of h coola flow schm o opmal dcsos of OP. h dffrc bw h avrag u powr loss UF ad ha RF should b od parcularly h dffrc bw h opmal powr loss dsrbuos for Cll 5 h wo cass. I h RF cas h Cll 5 ha s o logr a dowsram cll ca bf from coola rcprocao. hus OP dcds o us almos 10% mor ( rms of losss) ha ha of h UF cas. Alhough h opmal powr loss dsrbuo s dffr boh cass h mpraur cras of h clls s h sam as show Fgurs 8(a) ad 7(a). hs smlary dcas ha OP auomacally hadls h coola flow schm ad dcds o h opmal powr loss dsrbuo ovr ach cll accordgly. OP lkws hadls hrmal mbalacs causd by rssac varao ad by h mpraur grad h coola. Fg. 9(a) shows ha h UF cas opmal powr loss dsrbuo bw wo adjac clls dffrs by almos 10% du o h mpraur grad h coola. h dffrc powr loss dsrbuo bw wo clls s almos 0% bcaus of h rssac varao. hs fdg dcas ha alhough h powr loss dffrc du o rssac varaos s larg powr loss du o h coola mpraur grad s also o glgbl. hus acv hrmal balacg s sll cssary o compsa for h mpraur grad h coola hough o rssac varao occurs h bary srg. I rcollco o dcso s ad hoc hr vryhg s hadld sysmacally by solvg h modl-basd opmzao problm (P-I). B. Cofgurao-: Mddl Cll 3 has hghr rssac I hs subsco h prformacs of UDCO ad OP udr boh UF ad RF ar valuad for cofgurao- of h fv-cll srg. I hs cas h mddl Cll 3 sad of Cll 5 s assumd o hav almos 50% hghr srs rssac. h mpraur ( X ) SoC ( x ) ad h ormalzd avrag pr u powr loss ( I ) ar plod for ach cll. Smulao rsuls ar show for boh OP ad UDCO Fg. 10 for RF ad Fg. 11 for UF. h drv cycl daa s h sam as hos prsd prvously (Fg. 5). OP vrsus UDCO udr RF: Fg. 10(a) ad 10(c) show h mpraurs ad SOC of all clls for OP udr RF. Fg. 10(b) xhbs h mpraur for h UDCO polcy udr RF. h mpraur of Cll 3 for h UDCO polcy s sgfcaly hghr udr RF ha ha of OP hs cofgurao. Morovr OP smulaously achvd good hrmal ad SoC balacg whl sasfyg all cosras. Fg. 1(b) shows h ormalzd avrag u powr loss I ha s opmally dcdd by OP for ach cll. h ral rssac R s3 of Cll 3 s almos 50% hghr ha ha of ohr clls. hus h aural OP las uss Cll 3 compard wh ohr clls ad Cll 1 ad Cll 5 udr h bs hrmal codos for h RF cas ar usd mor. OP vrsus UDCO udr UF: Fg. 11(a) ad 11(b) show h mpraurs of all clls for OP ad for h UDCO polcy rspcvly. Fg. 1(a) prss h ormalzd avrag u powr loss for ach cll udr UF. As show h fgurs OP prforms br ha UDCO. Smlar o ha h RF cas OP smulaously achvd good hrmal ad SoC balacg for hs cll cofgurao by usg Cll 3 las ad Cll 1 h mos compard wh ohr clls as show Fg. 1(a). Opmal Powr oss Dsrbuos for UF ad RF: Fg. 1(a) ad 1(b) dsplay h ormalzd avrag u powr loss for UF ad for RF cass rspcvly. hs fgurs dca h ffc of h coola flow schm o h opmal dcsos of OP. h opmal powr loss dsrbuos for Cll 3 hs cofgurao ar rlavly smlar boh UF ad RF cass. Gv ha Cll 3 s h mddl cll rcprocao has a slgh fluc o h opmal powr loss dcso of OP for hs cll. VI. DISCUSSION I hs sco som mpora mplcaos of h smulao rsuls ar dscussd. A. Bfs of Rcprocag Ar Flow

12 580 Joural of Powr Elcrocs Vol. 13 No. 4 July 013 (a) Opmal mpraur of ach cll for OP udr RF. (b) mpraur of clls for UDCO udr RF. Cll 3 has hghr mpraur. (c) Opmal SoC of ach cll for OP udr RF. Fg. 10. Cofgurao- udr RF: Smulao rsuls ad comparso bw OP ad UDCO for RF wh mddl Cll 3 havg 50% hghr rssac. h plos show ha OP sgfcaly prforms br ha UDCO udr RF. h Fg. 10(b) shows ha usg RF s o vry hlpful for UDCO udr paramr varaos. (a) Opmal mpraur of ach cll for OP udr UF. (b) mpraur of ach cll for UDCO udr UF. (c) Opmal SoC of ach cll for OP udr UF. Fg. 11. Cofgurao- udr UF: Smulao rsuls ad comparso bw OP ad UDCO for UF wh mddl Cll 3 havg 50% hghr rssac. h plos show ha OP sgfcaly prforms br ha UDCO udr UF as wll. (a) Opmal ormalzd avrag powr loss pr u ohm across Cll for OP udr UF. (b) Opmal ormalzd avrag powr loss pr u ohm across Cll for OP udr RF. (c) Opmal saaous duy cycls for ach cll durg hgh curr rvals for OP wh RF. Fg. 1. Cofgurao- UF vrsus RF: Opmal powr loss dsrbuo udr UF ad RF. hs plos show ha durg hgh curr rvals OP las uss Cll 3 compard wh ohr clls. hus Cll 3 ss lss curr durg hgh curr rval ad cosquly has lss losss as show Fg. 1(b). hs s aurally opmal as losss ar quadrac curr. I hs sco UF ad RF ar compard for boh OP ad UDCO. h mpraurs of h clls for h UDCO polcy udr UF ar show Fg. 8(b) for cofgurao-1 ad Fg. 11(b) for cofgurao-. h mpraurs of h clls for h UDCO polcy udr RF ar xhbd Fg. 7(b) for cofgurao-1 ad Fg. 10(b) for cofgurao-. Smlarly h mpraurs of h clls for OP udr UF ar show Fg. 8(a) for srg cofgurao-1 ad Fg. 11(a) for srg cofgurao-. h mpraurs of h clls for OP udr RF ar show Fg. 7(a) for srg cofgurao-1 ad Fg. 10(a) for srg cofgurao-. hs fgurs clarly show ha OP has o sgfca ga wh usg RF parcularly for shor srs-cocd bary srg. h ma purpos of RF s mrly o achv mpraur uformy. Usg RF wh h UDCO polcy mmzs mpraur dvaos amog clls wh omal rssac. Howvr s o ha usful for Cll 5 or Cll 3 ha has 50% hghr rssac. hs fgurs clarly dca ha RF whou OP ca brg mpraur uformy oly h srg havg clls wh sam rssacs. Morovr h mpraur grad h coola udr RF s glgbl oly for shor srgs of clls. For log srgs RF grally cao rmov hs grad complly. hus RF alo cao solv h mpraur o-uformy problm bary packs of EV/HEV/PHEV bcaus hs bary packs ormally hav log srgs of clls wh hgh possbly of havg rssac dffrcs.

13 Joural of Powr Elcrocs Vol. 13 No. 4 July Howvr h mpraur uformy udr sad codos ca b achvd by opmally shfg h powr losss amog h clls usg MC-basd OP v udr UF. hus h prsc of OP RF s a rduda fuco. B. Cofgurao-1 vrsus Cofgurao- I hs subsco h opmal powr loss dsrbuo for wo srg cofguraos s compard. Fg. 9(b) ad 1(b) show ha chagg h poso of h hghr rssac cll h srg has slgh fluc o h powr loss dsrbuo h RF cas. Howvr h fluc may b mor ocabl logr bary srgs. I h cas of UF chagg h poso of h hghr rssac cll always fluc opmal dcsos o powr loss dsrbuo. hs fdg ca b valdad by comparg h opmal powr loss dsrbuos of Cll 5 ad of Cll 3 Fg. 9(a) ad 1(a). h dffrc powr loss compsas for h mpraur grad h coola for h UF cas. A dffrc ca b obsrvd h mpraur dyamcs for h wo cofguraos udr h UDCO polcy as llusrad Fg. 11(b) ad 8(b). hs dffrc s du o hghr rssac Cll 3 h mddl of h srg for cofgurao- hrby grag mor ha ha rsuls hghr mpraur dffral bw Cll ad Cll 3. Mawhl mpraurs of Cll 1 o Cll 4 for cofgurao-1 ar dsrbud a sarcas fasho bcaus of uform mpraur grad h coola. Howvr h mpraur voluo of h wo cofguraos s almos h sam udr OP as show Fg. 11(a) ad 8(a). C. Workg of OP a ushll OP achvs hrmal balacg by las usg Cll 5 (or Cll 3 ) compard wh ohr clls durg hgh curr rvals as show Fg. 9(c) (or Fg. 1(c)). hus Cll 5 (or Cll 3 ) has lss ohmc losss. hs polcy s aurally opmal as losss ar quadrac curr. I a ushll OP achvs hrmal balacg by avodg h us of hghr rssac clls durg pak powr rvals ad by usg h cll mor frquly durg low powr rvals. Morovr smlars ca b obsrvd bw h opmal duy cycls of h swchs wo dffr srg cofguraos as show Fg. 9(c) ad 1(c). VII. SUMMARY AND CONCUSIONS hs arcl vsgad h poal bf of opmally usg h xra DoF of MC for smulaous balacg of SoC ad mpraur of clls udr UF ad RF. A compl sa-spac lcro-hrmal modl was dvlopd ad a cosrad covx opmzao problm was formulad ad solvd basd o h assumpo ha h sa of ach cll ad h schdul of rcprocag ar flow ar prfcly kow. h smulao rsuls showd ha a 50% cras ral rssac of ay cll OP opmally uss h xra DoF of MC sgfcaly rducg mpraur dvao amog h clls compard wh h ad hoc uform duy cycl oprao. I a ushll OP achvs hrmal balacg by opmally shfg h powr losss amog h clls dpdg o hr rssac ad posos h srg. hus OP ca also achv mpraur uformy udr paramr varaos v wh UF as RF cao maa mpraur uformy such crcumsacs whou OP. hs sudy shows ha usg RF has o sgfca bf wh usg a MC-basd OP. hus RF s cosdrd a rduda fuco wh a MC-basd acv cll balacg sysm s oprad usg OP. ACKNOWEDGMEN h auhors would lk o hak Nkolc Murgovsk Adrs Graurs Oskar Josfsso ad orbjr hrgr for all h posv dscussos whl dvlopg hs work. hs work was suppord by h Chalmrs Ergy Iav. REFERENCES [1] B. I. Bloom J. S. Col S. Jos E. Polz V. Baagla G. Hrks C. Moloch R. Rchardso. Uklhausr D. Igrsoll ad H. Cas A acclrad caldar ad cycl lf sudy of l-o clls Joural of Powr Sourcs Vol. 101 No. p Oc [] B. Kuh G. Pl ad P. Kr Elcrcal proprs ad qualzao of lhum-o clls auomov applcaos Vhcl Powr ad Propulso 005 IEEE Cofrc p. 5 Sp [3] S. ukc J. Cao R. Basal F. Rodrguz ad A. Emad Ergy sorag sysms for auomov applcaos IEEE ras. Id. Elcro. Vol. 55 No. 6 pp Ju [4] K. Smh. Markl K. G-Ho ad A. Psara Dsg of lcrc drv vhcl bars for log lf ad low cos Acclrad Srss sg ad Rlably (ASR) IEE Workshop o Oc [5]. Rddy d s Hadbook of Bars 4h Edo 4h d. McGraw-Hll Profssoal [6] W. C. D. Drury ad P. Mllor Comparso of passv cll balacg ad acv cll balacg for auomov bars Vhcl Powr ad Propulso Cofrc (VPPC) 011 IEEE pp. 1-7 Sp [7] J. Cao N. Schofld ad A. Emad Bary balacg mhods: A comprhsv rvw Vhcl Powr ad Propulso Cofrc 008. VPPC 08. IEEE pp. 1-6 Sp [8] W. Bly Cll balacg cosdraos for lhum-o bary sys-ms Bary Cofrc o Applcaos ad Advacs h Aual pp. 3-6 Ja [9] P. Kr Bary maagm for maxmum prformac plug- lcrc ad hybrd vhcls Vhcl Powr ad Propulso Cofrc 007. VPPC 007. IEEE pp. -5 Sp [10] C. Park ad A. Jaura Rcprocag bary coolg for hybrd ad ful cll vhcls ASME Iraoal Mchacal Egrg Cogrss ad Exposo

14 58 Joural of Powr Elcrocs Vol. 13 No. 4 July 013 (IMECE003) Washgo DC USA pp Nov [11] Dyamc hrmal modl of -Io bary for prdcv bhavor hybrd ad ful cll vhcls SAE rasacos Vol. 11 No. 3 pp [1] ras ha rasfr of 4 V N-MH bars for a HEV applcao Fuur Car Cogrss 00. [13] A. Psara ad B. S. Vlahos A hrmal prformac of EV ad HEV bary moduls ad packs Procdgs of h 14h Iraoal Elcrc Vhcl Symposum Orlado Florda Dc [14] R. Mahamud ad C. Park Rcprocag ar flow for l-o bary hrmal maagm o mprov mpraur uformy Joural of Powr Sourcs Vol. 196 No. 13 pp Jul [15] C. Moloch J. Chrsophrs J. Bl R. Wrgh G. Hu. aramlla H. Hasks ad. Mllr Hgh-powr bary sg procdurs ad aalycal mhodologs for HEV s SAE [16] J. Rodrguz. Fraqulo S. Kouro J. o R. Porllo M. Pras ad M. Prz Mullvl covrrs: A ablg chology for hgh-powr applcaos Procdgs of h IEEE Vol. 97 No. 11 pp Nov [17] M. Malowsk K. Gopakumar J. Rodrguz ad M. P adrz A survy o cascadd mullvl vrrs IEEE ras. Id. Elcro. Vol. 57 No. 7 pp Jul [18]. olbr F. Z. Pg ad. Hablr Mullvl co vrrs for larg lcrc drvs IEEE ras. Id. Appl. Vol. 35 No. 1 pp Ja./Fb [19] O. Josfsso A. dskog S. udmark ad. hrgr Assssm of a mullvl covrr for a PHEV charg ad raco applcao Elcrcal Machs (ICEM) 010 XIX Iraoal Cofrc o pp. 1-6 Sp [0] F. Alaf. Johasso ad B. Egard Evaluag h poal for cll balacg usg a cascadd mul-lvl covrr usg covx opmzao IFAC Workshop o Eg ad Powrra Corol Smulao ad Modlg 01 Oc. 01. [1] F. Alaf. Johasso ad B. Egard Prformac valuao of mullvl covrr basd cll balacr wh rcprocag ar flow Vhcl Powr ad Propulso Cofrc (VPPC) 01 IEEE pp Oc. 01. [] J. Rawlgs uoral ovrvw of modl prdcv corol IEEE Cor. Sys. Vol. 0 No. 3 pp Ju [3] N. Moha. M. Udlad ad W. P. Robbs Powr Elcrocs: Covrrs Applcaos ad Dsg 3rd d. Joh Wly & Sos 003. [4] F. Codca S. Savars ad G. Rzzo O bary sa of charg smao: A w mxd algorhm Corol Applcaos 008. CCA 008. IEEE Iraoal Cofrc o pp Sp [5] M. Ch ad G. Rco-Mora Accura lcrcal bary modl capabl of prdcg rum ad -v prformac IEEE ras. Ergy Covrs. Vol. 1 No. pp Ju [6] H. H R. Xog X. Zhag F. Su ad J. Fa Sa-of-charg smao of h lhum-o bary usg a adapv xdd kalma flr basd o a mprovd hv modl IEEE ras. Vh. chol. Vol. 60 No. 4 pp may 011. [7] H. Khall Nolar sysms. Prc Hall NJ 00. [8] J. Kassaka M. Schlch ad G. Vrghs Prcpls of Powr Elcrocs. Addso-Wsly [9] S. Srsukprasr h modlg ad corol of a cascadd-mullvl covrr-basd SACOM PhD hss Vrga ch 004. [30]. Guzzlla ad A. Scarra Vhcl Propulso Sysms. Sprgr 005. [31] M. Gra ad S. Boyd CVX: Malab sofwar for dscpld covx programmg vrso 1.1../../cvx Apr [3] Graph mplmaos for osmooh covx programs Rc Advacs arg ad Corol sr. cur Nos Corol ad Iformao Sccs V. Blodl S. Boyd ad H. Kmura Eds. Sprgr-Vrlag md 008 pp hp://saford.du/ boyd/graph dcp.hml. [33] S. Boyd ad. Vadbrgh Covx Opmzao. Cambrdg Uvrsy Prss 006. [34] D. Adra Bary Maagm Sysms for arg hum Io Bary Packs 1s d. Arch Hous Fasal Alaf was bor Abboabad Paksa. H rcvd hs BE dgr Mcharocs 004 from h Naoal Uvrsy of Sccs & chology (NUS) Paksa ad hs M.Sc. dgr Sysms Corol ad Robocs 011 from h KH Royal Isu of chology Swd. From 004 o 008 h workd as a Corol Dsg Egr for a radar projc h Elcrcal Egrg Dparm a NUS. Hs rdscplary rol a am cludd dsgg svral lcroc corol crcus ad lcromchacal compos for a compl sysm. From 010 o 011 h was a Rsarch Egr a h Auomac Corol aboraory KH Swd. H s currly a PhD sud h Auomac Corol dvso of h Chalmrs Uvrsy of chology Swd ad s volvd a projc o hybrd lcrc vhcl sysms wh h Chalmrs Ergy Iav sc 011. Hs ma aras of rs clud modl-basd corol dsg covx opmzao ad opmal corol ad hr applcaos o powr lcroc-swchd sysms for acv cll balacg EV/HEV/PHEVs for prformac opmzao of bary maagm sysms. ars Johasso rcvd hs M.Sc. dgr Auomao ad Mcharocs ad hs Ph.D. Auomac Corol from h Chalmrs Uvrsy of chology Gborg Swd 004 ad 009 rspcvly. H has b wh h Elcromobly group a h Vkora Swdsh IC sc 011 h s prsly coducg a rsarch o powrra corol wh h Chalmrs Ergy Iav. Hs ma rsarch rss ar opmal corol of hybrd ad plug- hybrd lcrc vhcls corol of auxlary sysms rucks acv cll balacg ad sysm suds of hybrd vhcls. H s a mmbr of IEEE.

15 Bo Egard rcvd hs M.Sc. dgr Elcrcal Egrg ad hs Ph.D. Auomac Corol from h ud Isu of chology ud Swd 1974 ad 1979 rspcvly. Durg 1980 h was a Rsarch Assoca a h Iformao Sysms aboraory Saford CA. From 1981 o 1989 h was wh Asa Brow Bovr h was havly volvd h roduco of adapv corol h procss dusry. I 1989 h was appod Profssor of Auomac Corol a h Chalmrs Uvrsy of chology Gborg Swd. Hs ma aras of rs clud adapv ad hybrd corol as wll as applcaos of corol h auomov ara. H has b a Assoca Edor of h IEEE rasacos o Corol Sysms chology ad h Europa Joural of Corol. H s a mmbr of h doral board for h Iraoal Joural of Adapv Corol ad Sgal Procssg. H s a Fllow of IEEE. Joural of Powr Elcrocs Vol. 13 No. 4 July