Dynamic Modeling of PEM Fuel Cell Dedicated for transport Application

Transcription

1 e ème Séminire Interntionl r le Novelle et enovelle he nd Interntionl Seminr on New nd enewle Unité de eherhe Appliqée en enovelle Ghrdï Algérie et tore ynmi Modeling of EM Fel ell edited for trnport Applition BAU Zkri BENAIA Atllh AoSEE ortory Ammr elidji Univerity ghot Algeri z.rod@lgh-niv.dz.enli@mil.lgh-niv.dz Atrt thi pper propoe non-liner tte-pe dynmi model for plnr EM fel ell dedited for trnport pplition. he model i ed on oth thermodynmi nd eletril pet. hen n nlyi of thi model y hnging the prmeter like hydrogen flow rte prere nd memrne hmidity. he model imltion relt how the effet of thi of different prmeter. eyword EM fel ell hydrogen hydrogen flow rte memrne hmidity prtil prere I. INUIN Sine the deree of oil reerve de to the mive eploittion of the fel ell the domin of energy eome the fo of the pli interet. In ddition the environmentl polltion reqire the development of new tehnologie of energy []. In thi pper we tdy the proton ehnge memrne fel ell (EMF) whih i one of new energy nd it onidered the mot pproprite type of fel ell for repling internl omtion engine. It e olid polymer memrne eletrolyte nd lly work t verge tempertre (etween nd 9 ). ompred to other type of fel ell EMF i more ompt nd lightweight ee it generte etter volmi power nd power-denity. In ddition it operting tempertre i le thn llowing rpid trt-p. hee ft nd ility to rpidly hnge power otpt re ome of hrteriti tht mke EMF itle for tomotive power pplition. ther dvntge relt from the olid ntre of the eletrolyte ee with olid eletrolyte the eling of node nd thode ge i fr eier nd therefore le epenive to mnftre. It h lo le prolem with orroion whih men longer ell tk life []. here re everl tdie in the litertre relted to the EMF modeling. hee tdie im t ndertnding the phenomen orring in the fel ell in order to mke the pproprite ontrol. A nmer of mthemtil model hve een developed for thi prpoe t they re motly tedytte model whih re typilly ed for omponent izing [-] dynmi model [] hee model im t ndertnding the phenomen orring in the fel ell in order to mke the pproprite ontrol. We propoe in thi pper non-liner tte-pe dynmi model for ingle ell of plnr EMF trtre dedited for trnport pplition tht tke into ont the inflene of everl prmeter on the ytem ehvior. r model i ed on oth thermodynmi nd eletri pet. n the one hnd the diffion priniple whih i drwn from [] i ed to derie prere nd flow rte evoltion. n the other hnd the eletri priniple i ed to model the voltge nd the rrent. he dynmi ehvior of voltge rrent re tted with repet to g flow rte in g lk prtil prere nd hmidifition rte. he reminder of thi pper i orgnized follow: Setion eplin the EMF priniple nd tte ome nown relt nd remrk whih re needed in the eqent development. Setion preent wy to ild the dynmi model of ingle EM ell. Simltion relt nd nlyi re given in etion followed y onlion in etion. II. FUE E INIE A fel ell i n eletrohemil devie tht onvert the hemil of retnt (fel nd oidnt) diretly into eletriity energy. Wter nd het re the only y-pro if hydrogen i ed the fel ore. he priniple of EMF i hown in Fig. []. At the node the hydrogen molele i plit into hydrogen ion (proton) nd eletron. he hydrogen ion permete ro the memrne to the thode while the eletron flow throgh n eternl irit nd prode eletri power. ygen lly in the form of ir i pplied to the thode nd omine with eletron nd hydrogen proton to prode wter. Eletron irltion etween node nd thode throgh n eternl irit generte eletriity. he retion tht tke ple t the triple phe ondry zone (B). A typil EM fel ell h the following retion in []: Anode: e thode: e verll: eletriity het

2 e ème Séminire Interntionl r le Novelle et enovelle he nd Interntionl Seminr on New nd enewle Unité de eherhe Appliqée en enovelle Ghrdï Algérie et tore B. rrent otpt Negleting the trnit dynmi of the retion the reltion etween rrent nd retion n e epreed [9]: i F F F () Where perript repreent the g flow into the oter rfe of diffion lyer or wter vpor proion rte t thode. he mimm rrent tht ell n otpt i limited y retnt pply rte the re where retion tke ple nd ioni onivity of eletrolyte. Fig.. EM fel ell priniple A. Voltge otpt In the idel ittion (reverile) eletril work i eql to the Gi free energy releed g [9] f g f FE () he eletromotive fore or reverile open irit voltge E of the hydrogen fel ell i given E E ln F () Where nd re retnt prtil prere E i lo lled Nernt voltge. Irreveriilitie rede the ell voltge. hey re minly tivtion lo ohmi lo nd onentrtion lo. he voltge i lly modeled in the tedy tte form []: i i V E io Aln B ln () i il Where i i the rrent proded y the ell. o i the inherent reitne of the fel ell. i i the ehnge rrent n importnt prmeter of weighting the tivity of tlyt retion. i l i the limiting rrent t whih the fel i ed p t rte eql to it mimm pply rte. A nd B re oeffiient. he eond term in the eqtion repreent the ohmi lo the third term i tivtion lo nd the forth term repreent the onentrtion lo. III. MEING AA hi pper del with modeling the dynmi performne of fel ell foing on oth eletril nd diffion pprohe. he dynmi of the EMF will e repreented y non-liner differentil eqtion trnformed into n eqivlent mthemtil formltion: the tte pe repreenttion. he method of tte pe domin ehiit gret dvntge epeilly in the tdy of ontrol prmeter etimtion nd optimiztion. Beide it preent powerfl tool for imltion. A mentioned in etion we re intereted on the plnr fel ell geometry. hi trtre i ilt y tking together mltiple ingle ell. ene the fel ell tk i eletrilly eril onnetion of thee ell. It i illy thi ft whih motivte to fo on ingle ell modeling ine in eril onnetion the ingle ell voltge i dded p []. In ddition we onider tht the fel ell lie in meoopi le. For thi reon we my onider ingle ell lmped volme of the tk. hi enle to me n niform vrition of the tempertre inide the ingle ell. Aording to thee hypothei we tdy model ed on diffion nd eletril priniple. he EMF modeling proe will e divided into three prt. In the firt prt we etlih reltion etween prere nd flow rte ording to onentrtion nd diffion lw. hen we et eletril reltionhip etween voltge nd rrent in the eond prt. he third prt i devoted to the tte-pe formltion. he firt inpt i the hydrogen flow rte into the oter rfe of diffion lyer inflene the rrent otpt nd o ffet the retion. ther inpt re prtil prere of retnt in g lk. hey ffet the diffion proee well the Gi free energy nd th the voltge nd rrent otpt. he fifth inpt i the hmidifition rte relted to wter mngement. It role i to mintin the memrne hmidity nd to lne wter geonmption in the ytem. Indeed on one hnd if the hmidifition level of the memrne i too low the proton trnporttion throgh the memrne will eome diffilt nd thi will led to higher internl reitne. Another inpt tht inflene the hmidifition reitne i the tempertre whih together

3 e ème Séminire Interntionl r le Novelle et enovelle he nd Interntionl Seminr on New nd enewle Unité de eherhe Appliqée en enovelle Ghrdï Algérie et tore with hmidifition rte inflene the ohmi loe. hi eventlly ffet voltge nd rrent otpt. Finlly the otpt vrile re voltge rrent. we define in tle I the inptotpt vrile. ABE I INU AN UU VAIABE Inpt hydrogen flow into the oter rfe of the prtil prere of hydrogen in node g lk the prtil prere of oygen in thode g lk the prtil prere of wter in thode g lk midifition rte Fel ell tempertre tpt y V Voltge otpt y i rrent otpt A. iffionl pproh In thi prt we re going to e the diffion priniple in order to etlih the epreion of g prtil prere t B nd g onmption rte t B with repet to oth g onmption rte t g lk nd. Indeed in or plnr geometril model we determine the diffion fl de to the onentrtion differene etween g lk nd B zone ording to Fik firt lw: () Where i the onentrtion grdient. he low diffion lyer thikne nd the poro hrteriti of the eletrode llow to me tht ge diffe in one dimenion (in the diretion; ee Fig. ene the epreion of the diffion fl Eq. () eome: () he diffion oeffiient in poro mteril n e llted ording to Givzzi-gno implified eqtion: 9r () M In order to ompte we e Fik eond lw whih provide the vrition of the onentrtion with repet to time: () t For the oltion of thi eqtion in [] we e the ple trnform whih pper to e more itle for the tte-pe repreenttion. Indeed the ple trnform of Eq. () i given y : With the following ondry ondition: A (9) () () ene the oltion of Eq. (9) with repet to thee ondry ondition i follow: ep ep ep A ep ep ep () n the rfe of the diffion lyer m flow rte hve: A ep ep efore eqtion () we ep A ep ep ep () he derivtive epreion of onentrtion in zone B i: ep A ep () ep ep hen: ep ep A ep ep ()

4 e ème Séminire Interntionl r le Novelle et enovelle he nd Interntionl Seminr on New nd enewle Unité de eherhe Appliqée en enovelle Ghrdï Algérie et tore A in [] ine i rond zero the e of ylor erie epnion ot nd pplition of ple inver trnform we rrive t: A () Now me tht ge re idel. hen we hve: N V N () V Where N i the nmer of mole of g preent on the volme V. At B we hve = (ee Fig. ).thi infer tht ( ) () he differentil eqtion etween m flow rte nd prere of different g t B nd g lk : A (9) Eq. () i derived with repet to time i otined : () By mltiplying Eq. () per () nd tking into ont with Eq. () nd Eq. () it i then: A () he tittion of Eq. () in Eq. (9) give: A A () B. Eletril pproh he eletrohemil phenomen proded inide the fel ell omponent re modeled y eqivlent irit. It repreent the loe nd it dynmi hrteriti ffet the dynmi ehvior of voltge nd rrent. More preiely it i ompoed of three type of reitne repreenting the ohmi reitne m the tivtion reitne t t nd the onentrtion reitne t t nd two hrge pitie de to the dole lyer dl dl phenomen nd one geometril pity geom etween the eletrode. A typil eqivlent irit whih tke into ont ll thee omponent we otin the eqivlent irit of the EMF hown in Fig. where i i the rrent of the geometril pity[]. Fig.. Eqivlent irit of one ell et Ve V V from the eqivlent irit i follow: Where: A i t t ln it io dv V i e e t t t dl () B i on ln it i it F F F hi implie tht: dv e V e () ln e F F F F Where nd dl io ioil dl With: Vo it o Where: m o A ep herefore the voltge nd rrent otpt re llted follow: Vot E Ve Vo () dvot i it i F geom () h the rrent otpt i eome: d i F G Fgeom o G () t l

5 e ème Séminire Interntionl r le Novelle et enovelle he nd Interntionl Seminr on New nd enewle Unité de eherhe Appliqée en enovelle Ghrdï Algérie et tore Where: dv d F G e geom ln d d G geom m. Stte-pe repreenttion In thi prt we preent the model ed on diffionl nd eletril pprohe in the tte-pe form. We onider then we preent the diffionl model: ) ydrogen onmption rte : () And it prtil prere in the viinity of node t B: (9) Where. A A ) oygen onmption rte: B () And it prtil prere in the viinity of thode t B: () Where. A A ) wter onmption rte: () And it prtil prere in the viinity of thode t B: () Where. A A he ove eqtion how tht ge onmption rte depend on inpt derivtive.thi ft i generlly negtive ee the derivtive mode n mplify the otpt noie. herefore we e low-p filter to eliminte the noie inreing in derivtive mode. oneqently the firt order derivtive of the inpt vrile n e pproimted y the following eqtion []: ) ( ) ( U U () Where i n pproimtion ftor greter thn. et e n iliry inpt define ) ( U.th: () () ene fter introding the intermedite vrile to the model we define the tte-pe vetor follow: e V hi together with ll the ove eqtion led to following tte-pe model: 9 9 ln he otpt eqtion re preented follow: i y V y ot IV. SIMUAIN ESUS In thi etion we will preent the imltion relt tht demontrte the effet of the hydrogen flow rte the g prere hnge nd the effet of hmidifition.

6 rrent otpt(v) rrent otpt (A) Voltge otpt (V) Voltge otpt (V) ydrogen flow rte (mole) ydrogen prtil prere () e ème Séminire Interntionl r le Novelle et enovelle he nd Interntionl Seminr on New nd enewle Unité de eherhe Appliqée en enovelle Ghrdï Algérie et tore We will imlte the model ording to the prmeter of []. Mot of thee re tken from [].he imltion relt repreent the dynmi ehvior for one ell of EMF. A. Effet of the hydrogen flow rte: he hydrogen flow rte in g lk i lly impoed y the onor of engine. owever we onider it i very importnt inpt in order to view the effet of it hnge on the otpt. We will preent it effet y imlting the repone to ple hydrogen flow rte hnge well the effet of the ditrne fig (-). - emp ().9. Fig. le hydrogen flow rte hnge B. Effet of prtil prere : Ully the ontrol of the fel ell ytem i not ed on retnt prere tion ee thi prmeter doe not hve ig inflene on the otpt. hi ft will e hown in thi prt where we imlte the effet of hydrogen nd wter prere y imlting the otpt repone to rmp prere hnge. he effet of oygen prtil prere i the me with the effet of hydrogen prtil prere. he imltion relt in fig (-)..... emp () Fig. rmp hydrogen prtil prere hnge emp () Fig. Voltge repone to ple hydrogen flow rte hnge... emp () Fig. rrent repone to ple hydrogen flow rte hnge ne n immeditely oerve tht the vrition of the voltge i oppoite to the vrition of the hydrogen flow rte while the otpt rrent hnge i proportionl to it. emp () Fig. Voltge repone to rmp hydrogen prtil prere hnge... emp () Fig. rrent repone to rmp hydrogen prtil prere hnge

7 rrent otpt (A) rrent otpt (A) Voltge otpt(v) Voltge otpt (V) Memrne hmidifition rte (%) Wter prtil prere() e ème Séminire Interntionl r le Novelle et enovelle he nd Interntionl Seminr on New nd enewle Unité de eherhe Appliqée en enovelle Ghrdï Algérie et tore.... emp () Fig. 9 rmp wter prtil prere hnge.... emp () Fig. Voltge repone to rmp wter prtil prere hnge relt in Fig (-) how the otpt repone to the Sinoidl hmidifition rte hnge etween nd %. ne n how tht the voltge ehve proportionlly to the hmidifition rte. hi de to the ft tht the memrne reitne m i onverely proportionl to m. 9 emp () Fig. Sinoidl hmidifition rte hnge emp () Fig. rrent repone to rmp wter prtil prere hnge Aording to Nernt eqtion we ee in Fig ( ) tht the voltge repone i proportionl to hydrogen prere evoltion t i onverely proportionl to the wter prere.. Effet of memrne hmidifition rte: he effet of the memrne hmidity i importnt ee it inflene the lo ehvior. Indeed the memrne hmidity ffet it reitne vle whih i the min element tht determine the hmi lo. he imltion. emp () Fig. Voltge repone to inoidl hmidifition rte hnge... emp () Fig. rrent repone to inoidl hmidifition rte hnge V. NUSINS In thi work the dynmi model of EM fel ell dedited for trnport pplition re preented with fo on the diffionl nd eletril pprohe. We hve nlyzed the inflene of fel ell operting prmeter

8 e ème Séminire Interntionl r le Novelle et enovelle he nd Interntionl Seminr on New nd enewle (hydrogen flow rte prtil prere nd memrne hmidifition rte) on fel ell performne we hve fond tht hydrogen flow rte h lrge effet on otpt voltge the otpt rrent i generlly ffeted y the hydrogen flow rte owever the memrne hmidity nd prtil prere doe not hve ig inflene on the otpt. Unité de eherhe Appliqée en enovelle Ghrdï Algérie et tore EFEENES [] A. ddd. Boyekhf A. Modni et l. ynmi modeling of roton Ehnge Memrne Fel ell:he effet of tempertre nd memrne hmidity IEEE Emerging tehnology nd ftory tomtion jnry pge 9-. [] A. Beih. Zmohe Modeling nd prmeter etimtion of prmetre of proton ehnge memrne fel ell ytem Interntionl onferene on eletril engineering nd tomti ontrol etif. [] Y. o G. Wn et l. tedy tte performne modeling of fel ell engine vehilr eletroni nd fetyieee interntionl onferene on. []. th S. Vidhy et l ning of EM fel ell model prmeter for predition of tedy tte nd dynmi performne nder vrio operting ondition interntionl jornl of hydrogen energy (). [] Y. Qi B. nd.. hng dynmi modeling of loid oide fel ell: the effet of diffion nd inherent impedne ornl of power ore () -. [] Y. Zho E. itikopolo ynmi modeling nd prmetri ontrol for the polymer eletrolyte fel ell ytem ornl of power ore () -. [] F. i. hoikh et l. ynmi modeling of EM fel ell with tempertre effet ornl of power ore () -. []. Spigel EM fel ell Modeling nd imltion ing MAAB Ademi pre [9]..krhpn Modeling nd ontrol of fel ell ytem nd fel proeor h.. theiuniverity of Mihign Ann Aror Mihigin(). [] M. tt ptimition et getion d énergie por n ytème hyride : oition pile à omtile et Sperondenter h.. thei niverité de tehnologie Belfort Montélird(). [] A. ddd. Boyekhf A. Modni et l. Non-liner dynmi modeling of proton ehnge memrne fel ell ornl of power ore () -. [] A. ddd Modélition dynmiqe non linéire de l pile à omtile d type EM : pplition à l régltion de l hmidité dn l memrne eletrolytiqe h.. theiniverité de tehnologie Belfort Montélird().