A comprehensive model for battery State of Charge prediction

Transcription

1 A ompehenive model fo battey State of Ce pedition Bat Homan, Gead J.M. Smit Compute Ahitetue and Embedded Sytem Univeity of Twente Enhede, the Netheland Rid P. van Leeuwen Ci enewable eney Saxion Univeity of Applied Siene Enhede, the Manix V. ten Kotenaa D Ten B.V. Wezep, the Netheland Abtat In thi pape the elatively imple model fo State of Ce pedition, baed on eney onevation, intodued in [] i impoved and veified. The model a intodued in [] i veified fo Pb-aid, Li-ion and Seaalt batteie. The model i futhe impoved to aommodate the ate apaity effet and the apaity eovey effet, the impovement ae veified with lead-aid batteie. Fo futhe veifiation the model i applied on a ealiti ituation and ompaed to meauement on the bevio of a eal battey in tt ituation. Futhemoe the eult ae ompaed to eult of the well-etablihed KiBaM model. Pedition on the SoC ove time done uin the popoed model loely follow the SoC ove time alulated fom meaued data. The eultin impoved model i both imple and effetive, makin it peially ueful a pat of mat ontol, and eney uae imulation. Index Tem Stoae, Peditive model, Smat id, Eney manaement I. INTRODUCTION Batteie ae an impotant pat of eveyday eney uae. Example inlude uin a battey fo blak-out ituation, uin a battey to toe eletiity eneated by pv-panel duin the day and fo uae duin the niht, and in an eleti vehile (EV). Simulation ae ued fo example to pedit weak point in exitin id [2] o to exploe the poibilitie of new type of id [3]. To auately imulate the eney uae in a id, auate model ae needed fo all devie onneted to the id. Thee ae many model available tt deibe the bevio of batteie [4], []. Some of the model, like the Dualfoil model [6] and the kineti battey model (KiBaM) [7] ae appliable fo only one type of battey. While othe model, like the Coulomb ountin model [8] ae ueful fo vaiou type of batteie. Some of thee model ae athe ompehenive and ompliated, and equie intimate knowlede of the battey. The Dualfoil model fo intane i eneally aepted a an exellent model fo Li-ion batteie, but it equie ove 0 input paamete, e.. the thikne of the epaato and the pooity of the athode, infomation tt i not eadily available fo eah battey. The Coulomb ountin model on the othe nd i athe imple and equie only few input paamete, but eneally yield a too ideal epeentation of battey bevio. So ome of the available model ae too omplex to be ued in eney-id imulation, while othe model ae imple but not auate enouh. A imple but effetive model wa oiinally developed fo themal toae but an be applied fo eleti toae a well [], [9]. Uin thi model it i poible to pedit the amount of eney tt an be died fom a battey, o ed into a battey at any iven tate of e (SoC). Thi model d ome dawbak, howeve, fo intane the apaity eovey effet and ate apaity effet ae not oveed. In thi pape, an extenion of the model fo battey SoC pedition, peented in [] i developed. II. METHODS A. Bai peditive battey SoC model The model to detemine the SoC of a battey duin diin and in, popoed in [] i baed on eney onevation, ombined with iniht fom expeimental data. The ovenin equation of the model i: S t = C t D t L t () In whih S t inifie the ne of toed eney, C t the ed eney, D t the demand and L t the eney lo, all within a time inteval t whih i the diete time inteval (t, t). D t = t P e,t = t I t U d,t (2) In whih P e,t the eleti powe onumption, I t the diin uent and U d,t the voltae output of the battey, both meaued at the invete. The SoC i alulated by equation 3. SoC t = S t S max, 0 SoC t (3) The toed eney S t i detemined by equation 4 and the maximum ed eney by equation. S t = S t + S t (4) S max = C U n = τ P,t t () In whih C i the battey apaity (o battey atin) in Ah, U n the nominal voltae and P,t the in powe fo time t whih inifie a time inteval duin a in yle, fo

2 whih: 0 t τ. The elation between the in time and powe i diplayed in fiue a. The maximum apaity S max may be a funtion of time due to deadation of the battey. Hene, the um of meaued in powe may be moe auate in patie tn the ate apaity. Cin powe (W) [Pb-aid / Seaalt] State of e Cin =me (min) Pb-aid Simula8on Pb-aid meauement Seaalt Simula8on Seaalt meauement Li-ion Simula8on Li-ion meauement (a) Meaued and pedited in powe v in time. Pb-aid Simula6on Pb-aid meauement Li-ion Simula6on Li-ion meauement Seaalt Simula6on Seaalt meauement ed Capaity (Ah) (b) Meaued and pedited SoC v die uent. Fi. : Meaued and pedited in and diin ateiti fo a Pb-aid, Li-ion and Seaalt battey. The ateiti fo eah battey ae ummaized in table I The amount of ueful eney tt an be upplied by the toae i detemined by S max and a minimum SoC value whih i detemined by the minimum ueful and afe to ue voltae of the battey. In [] an aveae die uent I av i intodued and alulated with equation 6. I av,τd,t = Cin powe (W) [Li-ion] τd,t D t τ d,t U d,t (6) Howeve, thi equation poven to intodue eo fo diontinuou diin poee involvin vaiou waitin peiod without diin. Alo, the auay of the aveae die uent onept in ae of dynami load vaiation i not yet invetiated. A new and bette method i developed in thi pape. The battey i uually not died beyond the minimum SoC, othewie it would be damaed. In the afe eion, expeiment how tt a linea elation exit between the deeae of the SoC and the total died apaity (in Ah) fom the battey. Thi elation i diplayed in fiue b. Fo the lope, equation 7 applie. SoC = (7) C D C The auay of the model deibed by equation -7 i poven with expeiment on vaiou battey type, deibed in table I, ubjeted to ontant die uent. TABLE I: Cateiti of the batteie ued fo veifiation Name Type U (V) I e (ma) C (Ah) Pb-aid Lead aid Li-ion Lithium-ion Seaalt Seaalt The Seaalt battey i an expeimental, tationay battey uently in development at the battey innovation ompany D. Ten. It i deined to be inheently afe and envionmentally fiendly. B. Model extenion fo diontinuou diin poee Mot batteie how two well known effet duin diontinuou diin: Rate apaity effet: Thi effet limit the eoveable SoC in elation to the diin uent. The hihe the die uent, the le SoC i eoveable fom the battey. Capaity eovey effet: Thi effet ou when a battey i died to a etain tate, followed by a etain amount of time without diin (the waitin peiod). Fo example, the battey an be died to it minimum ueful voltae, but when thi i followed by a waitin peiod, the voltae eove and it i poible to die the battey futhe. Thi effet i moe inifiant when peiod of hih die uent ae followed by a waitin peiod, while the ate apaity effet beome ininifiant fo elatively low diin uent. Thee two effet ae elated to eah othe. The apaity eovey effet i moe inifiant when the battey i died with elatively hih uent, i.e. when the ate apaity effet i alo inifiant. To deibe both effet, thee i ome analoy with a themal toae. When a themal toae i died by an outlet at the top and inlet at the bottom, old wate omin into the toae at the bottom mixe with wame wate within the toae in the bottom eion. Thi effet i influened by the die flow ate, the hihe the flow ate, the moe mixin will ou. A battey an be deibed imilaly, ee fiue 2. Geneally, when a battey i in, a eation take plae at one of the eletode (eletode ) eatin a ompound in whih the eney i toed (the blak ompound) When the battey i fully ed the ompound ontainin the eney i peent eveywhee in the battey (fiue 2a). When a battey i then died the ompound ontainin the eney to phyially move to the othe eletode (eletode 2) whee

3 on multiple die yle tatin at the maximum SoC, diin with vaiou uent, on eah battey. TABLE II: α value fo the invetiated battey type. Battey α (0 4 V/A) Pb-aid.79 +/ Li-ion / Seaalt 2.3 +/- 0. (a) (b) () Fi. 2: Shemati epeentation of the ate apaity effet in a battey. a) The battey i fully ed. b) The battey i diin lowly. ) The battey i diin fat. d) The battey i fully died. anothe hemial eation take plae eatin anothe ompound (the white ompound) while eleain the eney. The onentation of the blak ompound at eletode 2 epeent the voltae of the battey. So in othe wod if the battey i died, the onentation of the blak ompound, and thu the voltae dop until thee i too little of the blak ompound left at eletode 2 to ontinue diin, then the battey i died (ee fiue 2d). If the battey i died lowly (i.e with low die uent) the white ompound i well mixed with the blak ompound. When 0% of the blak ompound been ued, (ee fiue 2b) the onentation of the blak ompound at eletode 2, and thu the voltae, i lowe then when the battey i fully ed. If the battey i died fat (i.e with hih die uent) the blak ompound i ued fate tn the mixin ou (ee fiue 2), eatin a laye of the white ompound tt limit ae to eletode 2 fo the blak ompound. When 0% of the blak ompound been ued in thi ae, the onentation of the blak ompound at eletode 2, and thu the voltae, i muh lowe tn when the battey wa died lowly. Mathematially, the edued voltae i theefoe deibed a a funtion of the diin uent, whih an be any funtion but it i loi to popoe the implet poible, linea elation iven in equation 8 (d) U d,t = U d,t α I d,t (8) Whih elate the die voltae at time t to the die voltae at the peviou time inteval and a fato α multiplied with the diin uent at time t. With thi equation it i poible to deibe the ate apaity effet beaue a hihe die uent, aue a fate dop of the die voltae tn a lowe uent, whih i the eene of the ate apaity effet. Thi equation i applied with ue on eult of the expeiment on the thee battey type (ee table I) deibed in fiue. The value of α fo the thee battey type ae lited in table II, the value in table II wee detemined on multiple batteie of the ame type, and The value of α appea to be ontant fo vaiou die uent in one battey, and fo multiple batteie of the ame type. It i likely, howeve, tt the value of α i influened by the open iuit potential, eney ontent, ize and eomety of a battey. In othe wod fo eah battey to be inluded in imulation uin the popoed model, two o moe meauement on tt battey ve to be done to detemine the value of α. It hould alo be noted tt the value of α i likely to be dependent on the deadation (o aein) of the battey, beaue the ove-all pefomane of the battey deeae ove time [0]. Howeve, the influene of the battey deadation on the value of α not been invetiated. Fo the apaity eovey effet thee i no analoy between eleti and themal eney toae. One mixed, the wate in a themal toae doe not eove bak to hihe tempeatue. Fiue 3 how a hemati epeentation of a battey duin the poe of eovey. (a) (b) () Fi. 3: Shemati epeentation of the eovey effet in a battey. a) The battey i fully ed. b) The battey i died fat to 0% of it apaity, but the voltae dopped to the minimum allowable ondition. ) The battey i allowed to et fo a peiod of time, thi eult in a editibution of the blak ompound. d) The battey i fully died. Fiue 3a how the battey fully ed, and fiue 3b how the battey died; the onentation of the blak ompound at eletode 2 i low and thu the voltae i low. Note tt the onentation of the blak ompound nea eletode 2 (in the ey aea) i lowe tn the onentation of the blak ompound elewhee in the battey. If the battey i then allowed to et fo a peiod of time (ee fiue 3) the blak and white ompound ae popely mixed aain, and the (d)

4 onentation of blak ompound in the ey aea and thu the voltae i ineaed. Note tt the ove-all onentation of the blak ompound in the battey not ned duin the waitin time. Now the battey an aain be died (ee fiue 3d). At the end of the eond die the onentation of blak ompound in the ey aea and thu the voltae i a low a it wa in fiue 3b but the ove-all onentation of the blak ompound i lowe. Futhe eovey i not poible. In fiue 4a it i hown tt the eovey effet of the voltae depend on the waitin time. Initially, a fit ode ytem appoximation fo the voltae wa aumed with a ontant time ontant but eult wee unatifatoy. When the time ontant itelf i made a funtion of the waitin time, the auay of the eult ineae onideably. A emaked, the eovey effet i deibed a a fit ode effet, equation 9. t τt (9) Ud,t = Ud,t0 + Ud,max Ud,t0 e Wa i t me 0mi n e( 4A) e2( A) (a) Meaued voltae duin two oneutive die tep, uin the Pb-aid battey, with vaiou waitin time. Point A-E indiate the die endpoint, fo thee point the SoCmin i alulated (ee table III) In whih Ud,t the ineain die voltae duin the waitin time t fom an initial voltae Ud,t 0 at the tat of the waitin time. Ud,max i the maximum voltae of the battey at fully ed ondition. τt i the fit ode time ontant whih i a funtion of the waitin time. Fo the time ontant τ the followin linea elation i intodued whih pove uffiient auay, equation 0. τt = β t + γ (0) It i deied to ue an altenative, linea deiption fo the eovey effet iven in equation 9. Fo thi, the exponential funtion i lineaized uin the fit tem of a Taylo expanion, whih yield an appoximately equal auay, equation. t Ud,t = Ud,t 0 + Ud,max Ud,t 0 () τt III. R ESULTS (b) Pedited SoCmin fo the Pb-aid battey, validated with meauement on two Pb-aid batteie. Point A-E indiate the meaued SoCmin fo expeiment A-E (ee table III). A. Veifiation of the model fo the Capaity eovey effet To veify the method outlined in etion II-B pedition made uin equation 8 and wee ompaed to the eult of die expeiment on the Pb-aid battey. Fiue 4a how the battey voltae a a funtion of time, duin two oneutive die of the Pb-aid battey and the waitin time between the two oneutive die wa vaied. In thi aph point A-E ae the end-point of the expeiment. Fo eah expeiment the minimal tate of e (SoCmin ) wa detemined and ummaized in table III. e( 4A) e2( A) () Voltae and SoC, pedited with equation fo two oneutive die tep on a Pb-aid battey, with a 60 min waitin time (ee expeiment D in table III and IV). Fi. 4: Compaion between pedited and meaued voltae and SoC uin the Pb-aid battey. TABLE III: Expeiment ettin and meaued SoCmin Expeiment A B C D E Id (A) 4 Uend (V) tet (min) SoCmin (-) Fiue 4b how the pedited SoCmin fo the Pb-aid battey a a funtion of die ate, validated with die expeiment. The SoCmin fo point A i pedited oetly, but the SoCmin of point B-E deviate fom thei pedited value. The deviation fom the pedited value eem to be dietly elated to the waitin time between oneutive die. In fiue 4 the die uent, waitin time, pedited die voltae, and pedited SoC, and SoCmin ae hown fo expeiment D. The die voltae i alu-

5 lated with equation 8 duin diin with ontant uent and with equation duin the waitin time peiod, the appopiate value of α, β and γ ae inluded in table IV. The SoC i alulated with equation, 2 and 3. Similaly the voltae, SoC and SoC min wee pedited fo expeiment B,C and E, the eult of thee pedition ae ummaized in table IV. TABLE V: Settin fo imulation done uin the popoed model and the KiBaM model Popoed KiBaM α V/A C Wh β.8 - C tat,9 Wh γ.8 min E max Wh k SoC tat SoC tat TABLE IV: Simulation ettin and eult Expeiment α β γ SoC min SoC min (0 4 V/A) (-) (min) Pedited Meaued A B C D E In eah ae the auay of the value fo SoC min, i exellent. Beide tt, the linea dop of die voltae and exponential ineae with ineain time ontant duin the waitin time i ealiti. The only dawbak of uin equation in patie, i tt it i neeay, fo the detemination of the elation between the time ontant and the waitin time, to meaue the die voltae uve of one battey fo at leat thee diffeent waitin time, to detemine the value of β and γ (a) Applied uent and eultin voltae of the Pb-aid battey, both meaued and alulated with the popoed model. Poitive uent epeent in tep, neative uent epeent diin tep. B. Veifiation in a ealiti ituation To detemine the appliability of the popoed model fo mat id ontol appliation, a ealiti tet wa done. The lead-aid battey a deibed in table I wa ed and died with vaiou uent, tatin fom vaiou tate of e, mimikin ondition tt ould ou when uin a battey in eal life. Thi meauement wa ompaed to a imulation of the bevio of a lead aid battey unde the ame ondition uin the popoed model. The bevio of the battey wa alo imulated uin the well etablihed kineti battey model (KiBaM), fit popoed by Manwell and MGowan [7] and lealy explained by Joneden and Havekot []. The KiBaM model epeent a battey a two ommuniatin well of e, the bie of the two well an fill the malle one, while the malle well an be died. The ate apaity effet and the apaity eovey effet ae epeented by equalization effet between the two well. The KiBaM model equie the detemination of thee paamete, in addition to a tatin SoC and the maximum eney ontent (E max ) of the battey. Applyin the model yield dietly the tate of e. The main diffeene in it appoah between the popoed model and the KiBaM model i tt in the popoed model the battey voltae i alulated, and fom the voltae the SoC i detemined; the KiBaM model make no ue of the battey voltae and alulate the SoC dietly. The paamete ued fo the imulation of the battey bevio ae lited in table V. (b) Reultin SoC of the Pb-aid battey, alulated baed on meauement, and imulated with the popoed model and the KiBam model. Fi. : Meauement data and imulation eult of the uae of Pb-aid battey in a ealiti ituation. The meauement data and the eult of the imulation ae peented in fiue. In fiue a the applied uent and eultin / alulated voltae ae diplayed. The pedited voltae follow ouhly the ame patten a the meaued voltae. Howeve, the pedited voltae deviate tonly fom the meaued voltae in the intane whee the battey i bein died deeply, (i.e. died to voltae below,v). Thi i aued by limitation of the popoed model, the model wa deined to pedit the pat of the in and diin poe tt ae motly linea with epet to time, wheea the pat whee the battey i bein deeply died ae definitely not linea with epet to time. The voltae i alo not pedited oetly at intane whee the battey tat in afte a peiod whee the battey wa not bein ued (i.e. at +/- 0 minute). Thi ou beaue

6 thee i a diffeene between the open iuit potential OCP tt i meaued when the battey i not ued, and the in voltae tt i bein meaued when the battey i ed. The model doe not (yet) aount fo thi diffeene. Howeve the main pupoe of the popoed model i not to ive an auate pedition of the battey voltae ove time, but to ive an auate pedition of the SoC ove time. The SoC ove time, alulated fom the meaued data, and pedited uin the popoed model and the KiBaM model i diplayed in fiue b. In ontat to the voltae, the SoC pedited with the popoed model follow the meaued SoC loely. In the ae whee the pedited SoC deviate fom the meaued SoC, the pedited SoC i lowe. The deviation fom the meaued SoC i unde % ove all, and about 0 % in the wot ae (aound 800 minute). The laet deviation ou at aound 30 minute, and aound 800 minute, thee intane oinide with the intane wee the battey wa deeply died, and whee the battey voltae wa pedited pooly. The SoC pedited with the KiBaM model alo follow the meaued SoC loely. Ove-all the deviation between the meaued SoC and the SoC pedited with the KiBaM model ae between % and 0%. In the intane whee the SoC pedited with the popoed model howed the laet deviation (i.e. the low point in the aph, aound 30 and 800 minute), the deviation between the meaued SoC and the SoC pedited with the KiBaM model ae notieably malle. Howeve, the laet deviation ou a the battey eahe a hihe SoC, aound 20 and 60 minute, at thee time the popoed model how little o no deviation. A poible explanation fo thee deviation i tt the KiBaM model i le uitable to pedit the SoC of batteie tt ve uffeed deadation. To aount fo battey deadation in the popoed model, one an ne the E max to eflet the edued maximum eney ontent of the deaded battey. IV. CONCLUSIONS A ompehenive model fo battey SoC pedition, laely baed on ealie wok [], [9] by the autho of thi pape i veified and expanded upon. The model i deined to be both auate and imple enouh to be ued a pat of mat ontol, and eney uae imulation. Peviouly the model wa veified with data on lead-aid batteie, ed and died with ontant uent. Fitly, the model i futhe veified with meauement on lithium-ion batteie, a well a the expeimental eaalt battey. In all expeiment on thee batteie, peented in fiue, the SoC ould be pedited auately. Seondly, the model i expanded to aommodate the ate apaity effet and apaity eovey effet. The model i expanded with two linea elation (equation 8 and ) with whih the influene of thee two effet on the battey SoC an be pedited. To ue thee elation in the SoC pedition the paamete α, β and γ ve to be detemined fom battey die expeiment; meauement fo eveal die uent ae equied to auately detemine the paamete. The expanded model wa veified uin meauement on leadaid batteie, peented in fiue 4. In all intane the SoC of the battey ould be auately pedited uin the model. Thidly, the model i veified in a ealiti ituation: a lead-aid battey i ed and died with vaiou uent, and with vaied waitin time between e and die tep. A pedition of the SoC duin the ame equene of event i alo made uin the popoed model. The ame pedition i alo made uin the well-etablihed KiBaM model. The meauement and pedition ae diplayed in fiue. The voltae pedited with the popoed model follow the meaued voltae only ouhly, howeve, the pedited SoC loely follow the meaued SoC, deviatin le then % ove all. It i demontated tt the popoed model i both auate and eay to ue; fou meauement on a patiula battey ae equied to pedit the battey bevio auately. V. FUTURE WORK Futue wok i dediated to invetiate appliation of the expanded model fo moe battey type, inludin the expeimental Seaalt battey and to ompae moe thoouhly with the KiBam appoximation. Anothe poblem to adde i to impove the model to take into aount the diffeene between OCP and e voltae, a diued in etion III-B. Othe futue wok i aimed at inteation of the model into the Tiana mat id imulato [] whih i ued fo imulation tudie and a bae fo embedded mat ontol ytem. ACKNOWLEDGEMENTS The autho tnk the Duth national poam TKI Swith2Smatid (pojet Smat Gid Evolution) and the duth oanization RVO fo thei uppot. REFERENCES [] B. Homan, R. P. van Leeuwen, L. Zhu, J. B. de Wit, and G. J. M. Smit, Validation of a peditive model fo mat ontol of themal and eletial eney toae, in IEEE Eneyon206. [2] G. Hooteen, A. Moldeink, J. L. Huink, G. J. M. Smit, F. Shuin, and B. Kootta, Impat of peak eletiity demand in ditibution id: A te tet, in IEEE Poweteh 20. [3] K. X. Peez, M. Baldea, T. F. Eda, G. Hooteen, R. P. van Leeuwen, T. van de Klauw, B. Homan, J. Fink, and G. J. M. Smit, Soft-ilandin a oup of houe thouh hedulin of hp, pv and toae, in IEEE Eneyon 206. [4] W.-Y. Cn, The tate of e etimatin method fo battey: a eview, ISRN Applied Mathemati, vol. 203, 203. [] M. R. Joneden and B. R. Havekot, Whih battey model to ue? Softwae, IET, vol. 3, no. 6, pp , [6] M. Doyle, T. Fulle, and J. Newman, Modelin of alvanotati e and die of the lithium/polyme/inetion ell, J. 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