Development of Real Time Simulation Models of Solid Oxide Fuel Cells for use in Hardware-in-the-Loop Systems

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1 Ffth LACCEI Internatnal Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy (LACCEI 007) Develpng Entrepreneural Engneers fr the Sustanable Grwth f Latn Amerca and the Carbbean: Educatn, Innvatn, Tenlgy and ractce 9 May 1 June 007, Tampc, Méxc. Develpment f Real Tme Smulatn Mdels f Sld Oxde Fuel Cells fr use n ardware-n-the-lp Systems Denver F. Chedde Flrda Internatnal Unversty, Mam, Fl, USA, dedde@yah.cm Nrman D.. Munre Flrda Internatnal Unversty, Mam, Fl, USA, munren@fu.edu ABSTRACT A dynamc mdel f a sld xde fuel cell (SOFC) s presented. Ths ne-dmensnal mdel s based n the transprt and electremcal phenmena ccurng nsde the cell. The mdel s desgned fr rapd cmputatns, thus enablng ts mplementatn n real tme smulatn systems, su as hardware-n-the-lp (IL) envrnments. It was determned that a 1D mdel utlzng 1 cmputatnal ndes gves the best balance between cmputatnal speed and accuracy. Ths mdel s able t predct the transent thermal and vltage respnse f the fuel cell t anges n lad current. At a base cell current f 340 A, a steady state cell vltage f V s predcted. The steady state annel temperature ncreases are predcted t be 70 K at the ande and 90 K at the cathde. Based n the thermal nerta f the cell, steady state cndtns are reaed n apprxmately 10 mnutes. Keywrds: Real tme, IL, SOFC, smulatn 1. INTRODUCTION The cncept f a hydrgen ecnmy has generated tremendus nterest n recent years. A hydrgen ecnmy s ne where hydrgen s the man energy vectr. There are varus reasns fr ths nterest. Frstly, the emssn f green huse gases frm hydrgen systems s cnsderably less than fssl fuel cmbustn, and thus hydrgen energy s less deleterus t the envrnment. Secndly, the USA s seekng t aeve energy ndedence frm Mddle Eastern l. Thus pltcs s als a majr drvng frce tward a hydrgen ecnmy. Because f the renewed nterest n hydrgen energy, fuel cell tenlgy has emerged as a majr pwer surce f the future. Fuel cells are electremcal devces wh cnvert the ptental energy resdent n a fuel and xdant t electrcal energy wthut drect cmbustn. If hydrgen and xygen are used as fuel and xdant respectvely, then the nly emssns wuld be water and heat. If hydrcarbns are used as fuels, then there wll be emssn f carbn dxde durng the refrmatn prcess, but ths emssn s stll less than cmbustn prcesses. Sld xde fuel cells (SOFC) are partcularly attractve fr stand alne pwer generatn r cgeneratn. SOFCs perate at hgh temperatures ( C), therefre prduce useful heat as well as electrcal pwer. Because f the hgh temperature, SOFCs can be used n cnjunctn wth ther pwer systems. Fgure 1 shws a sematc f a SOFC gas turbne hybrd pwer plant. The SOFC wrks tgether wth a regular gas turbne t prduce addtnal electrcal pwer and heat. Su systems are very useful fr stand alne pwer generatn. Fuel cell mdelng and smulatn are mprtant tls n the develpment f fuel cell tenlgy. Effectve and cmprehensve mdelng can preclude the hgh csts f prttype develpment and testng. It can als save tme and expedte resear and develpment. The hardware-n-the-lp (IL) cncept s used t nvestgate the feasblty f varus pwer generatng systems nvlvng fuel cells. IL systems nvlve a fuel cell mdel, peratng n real tme, fully nteractng wth real cmpnents f a pwer plant. Fgure shws a Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-1

2 sematc f a IL setup fr the SOFC gas turbne hybrd shwn n Fgure 1. Su a system s advantageus because t avds the need fr havng an actual SOFC. It can test the feasblty f the hybrd pwer generatng cncept wth actually havng the fuel cell, thus avdng the cst f develpment and prttypng. Fgure 1: Sematc f a SOFC Gas Turbne ybrd wer lant Fgure : ardware-n-the-lp Sematc Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-

3 wever, t s essental that the fuel cell mdel be accurate and fast. It must accurately smulate the fuel cell behavr t prperly nteract wth the ther cmpnents. And t must d s quckly enugh t perate n real tme. Dedng n the settng, the cmpressr valve n the turbne system may and clse every 5 mllsecnds. S t s mperatve that the fuel cell mdel perfrm tme dedent cmputatns n less tme than 5 ms. The Appled Resear Center (ARC) f Flrda Internatnal Unversty (FIU) s wrkng tgether wth the US Department f Energy (DOE) Natnal Energy Tenlgy Center (NETL) n Mrgantwn, WV t mprve the fdelty f ther SOFC mdels. The NETL s nvestgatng a SOFC gas turbne hybrd pwer plant, by utlzng the IL cncept. Ther present fuel cell mdels perate n zer dmensns (0D) usng lumped system dmans. Su mdels apply the gvernng dfferental equatns ver lumped dmans, and hence determne transent nput/utput behavr. Because f ther smplcty, they perfrm rapd cmputatns. Unfrtunately, because f ther smplcty, thse cmputatns are f lw fdelty r lw accuracy. FIU s seekng t mprve the fdelty f ther systems by develpng 1D SOFC mdels. 1D mdels dvde the fuel cell dmans nt numerus cntrl vlumes, dedng n the number f cmputatnal ndes used. As su, they mprve the accuracy f cmputatns, especally thse nvlvng temperature varatns wthn the cell. Fgure 3 shws the mass and energy balance acrss ne ndal cntrl vlume. The prblem wth 1D mdels s that they requre lnger cmputatnal tmes than 0D mdels. The gal f the present wrk s t develp a 1D dynamc (transent) mdel f an SOFC, wh s capable f perfrmng tme dedent cmputatns, s less than 5 ms, thus enablng ther utlzatn n real tme IL systems. Fgure 3: Cntrl Vlume eat and Mass Balance Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-3

4 . MODEL DEVELOMENT The present mdel entals ar (xygen and ntrgen) flwng n the cathde, and refrmed hydrgen (hydrgen, carbn dxde and water vapr) flwng the n the ande. The ande gases enter the cell at 1100 K and atmspherc pressure, whle the cathde gases enter at 1073 K and atmspherc pressure. The ntrgen and carbn dxde are electremcally nert. Oxygen dsscates nt xygen ns and electrns, whle hydrgen gas reacts wth thse ns t prduce water. The flw f electrns results n an electrcal current, whle the electrde ptental dfference prvdes the cell vltage. Equatns 1 and shw the half cell reactns ccurrng at the ande and cathde respectvely. O 4 e O (1) O 4 e O () The reversble cell ptental can be cmputed frm the temperature and partal pressure f the reactant gases. 0.5 R T = O E E 0 ln (3) 0. 5 F O atm 4 E0 = (.904 x 10 ) T (4) The vltage drps r verptentals can be determned based n the hmc resstance f the varus cell cmpnents and the actvty f the electrdes (Aguar et al, 005). ref R T an 1 1 η act = snh ln (5) F O O ref 0 ref ref O O R T ca 1 η act = snh (6) F x η ( ) ( ) ( ) hm = 6.78 x 10 exp exp T (7) T The actual cell vltage s equal t the reversble cell ptental less the verptentals. The gvernng equatns f mass, speces, mmentum and energy transprt are shwn belw. ( ρ u) x x = ( c ) = ρ t T A m L cell ( ρ u) ( ρ u ) t x A m L u cell 4 f Re µ N A ( ρ u c T ) A T m ctnt ( T Tnt ) nt nt nt ρ p = knt (10) nt t x Ant x Ant Lcell ( c ) cell u ( T T ) T m ct Qgen T nt ρ p = k (11) t x A L (8) (9) Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-4

5 ω ( ρ u ω ) ( ρ ω ) m ρ = D (1) t x x A Lcell The gvernng equatns are appled ver the cntrl vlume shwn n Fgure 3. The tme dedent dfferental equatns are then slved n Matlab/Smulnk usng a 4 th rder Runge-Kutta methd. All ther numercal values, cnstants and cell dmensns are the same as thse n Lese et al (006). 3. RESULTS AND DISCUSSION The number f ndes used n the mdel must be sen t aeve the best balance between speed and accuracy. Fgure 4 shws the steady state cell vltage at a cell current f 340 A fr varus number f ndes. It s fund that fr ths prblem, steady state cndtns are aeved wthn 600 secnds. Fgure 5 shws the varatn f steady state utlet temperatures as the number f ndes ncrease. Fgure 6 shws the cmputatnal tme requred t perfrm ea cmputatn. These fgures shw that as the number f cmputatnal ndes ncreases, the accuracy f the results mprve. The temperature ncreases acrss the cell frm nlet t utlet because the gas streams pck up heat, wh s generated n the cell. Ths temperature ncrease hwever s verestmated when a small number f ndes s used. As the number f ndes ncreases, there s a levelng f ff the utlet temperatures. The same thng s true f the cell vltage. Fgure 6 shws that the cmputatnal tme ncreases as the number f ndes ncreases, as expected. As the number f ndes ncreases, the mdel s requred t perfrm mre cmputatns. Fgure 4: Steady State Cell Vltage vs. Number f Ndes S the number f ndes must be sen t aeve the best balance between speed and accuracy. It can be seen that the mprvement n accuracy frm 3 ndes t 1 ndes s great, whereas the mprvement frm 1 ndes t 51 ndes s mnmal. Essentally the accuracy des nt mprve mu abve 1 ndes. wever, the cmputatnal tme cntnues t ncrease. 1 ndes requre 3.5 ms f cmputatnal tme fr ea tme teratn, whle 51 ndes requre 13.8 ms. Snce 5 ms s the crtcal tme value, a mdel usng 51 ndes cannt be used fr real tme systems. The mdel wth 1 ndes s clearly the best ce. Its accuracy s nt mu dfferent frm the Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-5

6 51 nde mdel, but ts tme requrements are mu less. The remander f the results wll be based n the 1 nde mdel. Fgure 5: Steady State Outlet Channel Temperatures vs. Number f Ndes Fgure 6: Cmputatnal Tme vs. Number f Ndes Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-6

7 Fgure 7: Transent Vltage Respnse Fgure 8: Transent Thermal Respnse Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-7

8 Fgure 7 shws the transent vltage respnse when the current ncreases frm 0 A t 340 A at tme = 100 secnds. In fuel cells, the vltage decreases as the current ncreases. Fgure 7 shws an nstantaneus decrease n vltage when the current anges. wever, ver tme the vltage slwly ncreases and levels ff at V. Fgure 8 shws the crrespndng plt fr ande and cathde utlet temperature and average EN temperature. It shws that the temperatures gradually ncrease t ther steady state values. At 340 A, there s mre heat beng generated n the cell than at 0 A, hence the ncrease n all the temperature values. As the EN temperature ncreases, the reversble cell vltage ncreases, whle the hmc and actvatn verptental decrease. Bth f these cntrbute t the ncrease n cell vltage ver tme fllwng the nstantaneus drp (Fgure 7). It s als seen that steady state cndtns are nly reaed after nearly 10 mnutes, due t the hgh thermal nerta f the system. 4. CONCLUSIONS A ne-dmensnal mdel was develped fr a SOFC, wh s desgned fr use n IL systems. It s fund that emplyng 1 cmputatnal ndes allws fr hgh accuracy and fast cmputatnal tmes (3.5 ms). Ths mdel can be used fr real tme smulatn f SOFC, whle mprvng the fdelty ver exstng lumpedparameter mdels. The present mdel s able t predct the transent vltage and thermal respnse t anges n lad current. As su t can effectvely nteract wth real cmpnents n a IL system. 5. ACKNOWLEDGMENTS The authrs wuld lke t express ther grattude fr the supprt frm the NSF CREST Supplement Grant (Award N. RD ) n cnductng ths wrk. 6. NOMENCLATURE Arabc Symbls A Area cp Specfc heat capacty F Faraday cnstant f Frctn factr eat transfer c-effcent k Thermal cnductvty m Mass flw rate N Number ressure Q eat R Unversal gas cnstant Re Reynlds number T Temperature t Tme u Velcty x Dsplacement n the drectn f the gas annel Greek Symbls Dynamc vscsty Densty Mass fractn Subscrpts and Superscrpts 0 Reference state act Actvatn an Ande Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-8

9 atm ca gen nt hm Atmspherc Cathde Channel Generated Speces Intercnnect Ohmc stve-electrlyte-negatve REFERENCES Aguar,., Adjman, C.S., and Brandn, N.. (005). Ande-Supprted Intermedate-Temperature Drect Internal Refrmng Sld Oxde Fuel Cell II. Mdel-Based Dynamc erfrmance and Cntrl. Jurnal f wer Surces, Vl. 147, N. 1, pp Lese, E.A., Gemmen, R.S., Smth, T.., and aynes, C.L. (006). A Dynamc Bulk SOFC Mdel Used n a ybrd Turbne Cntrls Test Faclty. GT , Barcelna, Span. Authrzatn and Dsclamer Authrs authrze LACCEI t publsh the paper n the cnference prceedngs. Nether LACCEI nr the edtrs are respnsble ether fr the cntent r fr the mplcatns f what s expressed n the paper. Tampc, Méxc May 9-June 1, th Latn Amercan and Carbbean Cnference fr Engneerng and Tenlgy 7B.1-9