Model-based State-of-energy Estimation of Lithium-ion Batteries in Electric Vehicles

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1 Avlble onlne t ScenceDrect Energy Proced E5-Aled Energy Symoum nd Summt 5: Low crbon cte nd urbn energy ytem Model-bed Stte-of-energy Etmton of Lthum-on Bttere n Electrc Vehcle Yuje Wng, henbn Zhng, Zongh hen * Dertment of Automton, nverty of Scence nd Technology of hn, Hefe 7, P hn Abtrct Wth the ncreng lcton of lthum-on bttere, the functon of bttery mngement ytem BMS come to be more ohtcted. The tte-of-energy SOE of lthum-on bttere crtcl ndex for energy otmton nd mngement n electrc vehcle. The conventonl ower ntegrl method re ey to cue ccumulted error due to current or voltge drft of enor. Therefore the EKF method emloyed n th tudy. A dt-drven model etblhed to decrbe the reltonh between the oen-crcut voltge OV nd SOE bed on the exermentl dt of LN / o / Mn / O bttery. The dynmc urbn drvng chedule of Wuhu cty n hn h been conducted on the lthum-on bttery to verfy the ccurcy of the rooed method. The reult how tht ccurte SOE etmton reult cn be obtned by the rooed method. 6 5 The Author. Publhed by Elever by Elever Ltd. Th Ltd. n oen cce rtcle under the BY-N-ND lcene htt://cretvecommon.org/lcene/by-nc-nd/4./. Selecton nd/or eer-revew under reonblty of E Peer-revew under reonblty of the orgnng commttee of E 5 Keyword: Electrc vehcle; Bttery modelng; Stte-of-energy; EKF.. Introducton Wth the growng concern on the deleton of energy reource nd globl wrmng roblem cued by conventonl nternl combuton engne vehcle, electrc vehcle hve drwn more nd more ttenton. The bttery the ey to the develoment of electrc vehcle. Lthum-on bttere fetured by hgh energy denty, low elf-dchrge rte, long cycle lfe nd envronmentl frendlne hve found wde lcton n the re of electrc vehcle ower uly ytem []. The lthum-on bttery trong nonlner nd tme vrblty ytem for t comlcted electrochemcl roce. The etmton * orreondng uthor. Tel.: E-ml ddre: chenh@utc.edu.cn The Author. Publhed by Elever Ltd. Th n oen cce rtcle under the BY-N-ND lcene htt://cretvecommon.org/lcene/by-nc-nd/4./. Peer-revew under reonblty of the orgnng commttee of E 5 do:.6/j.egyro.6.6.5

2 Yuje Wng et l. / Energy Proced of cell tte rmeter, uch the oen-crcut voltge OV, tte-of-chrge SO nd vlble energy, ly n mortnt role n enurng vehcle tblty nd relblty. In recent yer, tude n etmton of redul energy hve ncreed n lterture [-5], mong whch the mot drect lgorthm the ower ntegrl method. However through the ntegrl method, the etmton error ncree concuouly due to the ccumulted error ntroduced by current or voltge drft of enor. Therefore model-bed etmton method hve been develoed. The bttery model ued n electrc vehcle cn be dvded nto three tye, the electrochemcl model, the neurl networ model nd the equvlent crcut model. The electrochemcl model bed on the electrochemcl mechnm of the bttery cn ccurtely reflect the chrctertc of the bttery. The neurl networ model cn multe the hgh nonlnerty of lthum-on bttere, but requre lrge number of trnng mle. Bed on the dynmc chrctertc nd worng rncle of the bttery, the equvlent crcut model develoed by ung retor, cctor, nd voltge ource to form crcut networ. Th er rooe method for SOE etmton of lthum-on bttery bed on EKF. Snce there tll not n cceted model for SOE, A dt-drven model etblhed to decrbe the reltonh between the oen-crcut voltge OV nd SOE bed on the exermentl dt. The er orgned follow: In Secton, the defnton of SOE frt ntroduced. Then dt-drven model for SOE etmton rooed bed on the rel dt of lthum-on cell. At lt, the EKF mlementton reented. In Secton, we frt ntroduced the bttery tet bench, then exerment under dynmc current condton re conducted to verfy the ccurcy of the rooed method. The reult how tht ccurte SOE etmton reult cn be obtned by the rooed method. Fnlly, the concluon of the tudy re gven n Secton 4.. Model Bed SOE Etmton.. Defnton of SOE el-tme etmton of the vlble energy of the bttery crucl need n the growng feld of electrc vehcle lcton. The SOE reflect the redul energy of bttery, nd defned the rto of the remnng energy to the totl energy. The SOE cn be exreed the followng equton: t P d t SOE t SOE t E N where SOEt the SOE vlue t tme t, SOEt the SOE vlue t ntl tme t, E N rereent the nomnl energy whch cn be obtned by the meurement verge of multle bttery tet, Pτ rereent the ower t tme τ... Model for SOE etmton The equvlent crcut model h been wdely ued n vrou tye of modelng nd multon for t hgh ccurcy. Deendng on dfferent lcton nd the requred ccurcy, dfferent tye of cell model hve been develoed n lterture. Among whch, the Thevenn equvlent crcut model n effectve model to rereent the bttery dynmc. A hown n Fg., the Thevenn equvlent crcut model nclude n oen-crcut voltge ocv whch ued to rereent the voltge ource nd decrbe the ttc chrcter of the cell, erl retnce

3 Yuje Wng et l. / Energy Proced whch ued to decrbe the cell ohmc nternl retnce, networ whch decrbe the cell olrton effect comoed by olrton retnce nd olrton cctnce. ocv t Fgure Bttery model Bed on the electrc crcut nly, the electrcl behvor of the cell model cn be exreed : ocv t / / where rereent the lod current negtve for chrge, otve for dchrge, ocv rereent the oencrcut voltge, t rereent the termnl voltge, rereent the olrton voltge over the networ, rereent the ohmc nternl retnce, nd rereent the olrton retnce nd olrton cctnce, reectvely. The electrcl behvor of Thevenn model n Eq. cn be rewrtten n the frequency domn follow: / ocv t The trnfer functon G of Eq. cn be wrtten follow: G 4 A blner trnformton method hown n Eq. 5 emloyed for the dcretton clculton of G nd the reult hown n Eq. 6: T 5 where the dcretton oertor nd T the mle ntervl. Heren, T. G 6 where 7

4 Yuje Wng et l. / Energy Proced Then the dcretton equton cn be wrtten follow: t, ocv, t, where, nd re the coeffcent. The ttc reltonh between ocv nd the SOE n Eq. 8 nonlner whch nfluence the comlexty of the etmtor. Snce there tll not n cceted model for SOE, dt-drven model etblhed to decrbe the reltonh between ocv nd SOE. onderng the ocv -SOE curve of LN / o / Mn / O bttery from the exermentl dt hown n Fg., the dt-drven model cn be exreed Eq. 9: t SOE t SOE t ocv SOE t / SOE t 4 5 ln SOE t 6 ln SOE t where ocv rereent the oen-crcut voltge t tme t, SOEt rereent the SOE t tme t nd β =,,,, 4, 5, 6 re model coeffcent whch cn be dentfed by the let-qure method. OVV EKF bed SOE etmton SOE%. Fgure ocv-soe curve of LN /o /Mn /O bttery 8 9 The ytem model n tte-ce form cn be wrtten : Χ AΧ Bu, w Υ X Du, v where, Χ t x, Υ,, u, P, u, ex t / A ex t / B t / N ocv x, D / Then the EKF lgorthm cn be led for the tte etmton.. Exerment nd Anly

5 Yuje Wng et l. / Energy Proced Tet bench In order to mle the meurement dt uch current, voltge, temerture, chrge/dchrge Amhour Ah nd Wtt-hour Wh etc., the bttery tet bench bult n lbortory, hown n Fgure., whch cont of n TEK bttery tet ytem BTS6KW5VA for lodng the bttery wth rogrmmble current, BMS for rotecton of crcut nd hot comuter for dt recordng. The meured dt trnmtted to the hot comuter through TP/IP. Bttery tet ytem Lto Bttery c BMS Servce wtch Progrm downloder Fgure Lbortory bttery tet bench.. Exerment Anly In order to verfy the lcblty of the etmtng lgorthm bed on EKF, bttery electrc vehcle roduced by hery Automoble o., Ltd. teted n the exerment. The nomnl ccty nd the nomnl energy of the bttery ytem re 76 Ah nd Wh. The cut-off voltge of chrge nd dchrge re 4. V nd. V, reectvely. Fg.4 how the dynmc urbn drvng chedule n Wuhu, hn. Fg.4 b how the omron of model nd meured voltge of cell n c. A cn be een n the fgure, the generl he of the model nd meured voltge re lmot the me. The SOE etmton reult nd the SOE etmton error re hown n Fg.5 nd Fg.5 b, reectvely. The root-men qure error nd mxmum bolute etmton error re clculted to e nd the etmted erformnce of the rooed lgorthm. The reult how tht the rooed EKF bed SOE etmton roch h mxmum bolute etmton error of.89% nd root-men qure error of.469%.

6 Yuje Wng et l. / Energy Proced urrenta -5 - b VoltgeV Tme te Meured Model Tme te Fgure 4. Dynmc urbn drvng chedule of Wuhu cty n hn. b. omron of model nd meured voltge of cell n c. SOE% True tte EKF b SOE etmte error% Tme te Tme te Fgure 5. SOE etmton reult. b. SOE etmton error.

7 4 Yuje Wng et l. / Energy Proced oncluon The SOE of lthum-on bttere crtcl ndex for energy otmton nd mngement n electrc vehcle. Th er rooe SOE etmton method for lthum-on bttery bed on EKF wth dtdrven model develoed by the the rel exermentl dt of LN / o / Mn / O bttery. The dynmc urbn drvng chedule ued for verfyng the ccurcy of the rooed method. The exerment reult how tht ccurte SOE etmton reult cn be obtned by the rooed method. 5. oyrght Author ee full coyrght over er ublhed n Energy Proced Acnowledgement Th wor uorted by the Ntonl Nturl Scence Fund of hn Grnt No nd the Fundmentl eerch Fund for the entrl nverte under the contrct of WK5. eference [] Lu L, Hn X, L J, et l. A revew on the ey ue for lthum-on bttery mngement n electrc vehcle. J Power Source ; 6: [] Yuje Wng, henbn Zhng, Zongh hen. A method for jont etmton of tte-of-chrge nd vlble energy of LFePO4 bttere. Al energy 4; 5: 8-7. [] Stocr S, Mrno V, nov M, et l. Energy-otml control of lug-n hybrd electrc vehcle for rel-world drvng cycle. IEEE Trn Vehculr Technol ; 67: [4] Mmdou K, Lemre E, Dellle A, et l. Defnton of tte-of-energy ndctor SoE for electrochemcl torge devce: lcton for energetc vlblty forectng. J Electrochem Soc ; 598: A98 7. [5] Lu XT, Wu J, Zhng B, et l. A method for tte of energy etmton of lthum-on bttere t dynmc current nd temerture. J Power Source 4; 7: 5 7. Zongh hen receved h BS nd MS degree from nverty of Scence nd Technology of hn ST n 988 nd 99 reectvely. He h erved on the fculty of ST from 99. Snce 998, he h been rofeor of ST. He w gned tnt to the redent of ST from to, n chrge of the technology ndutry. He n exert tht enjoy the ecl government llownce of the Stte ouncl of Peole eublc of hn. He h more thn refereed ublcton. H reerch focued on the modelng, multon nd control of comlex ytem, nformton cquton nd control, robotc nd ntellgent ytem. He h rovncl nd mnterl rogre re n centfc nd collectve technology.