Offline Battery Pack Model Optimization
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1 Offle Baery Pack Model Opmzao Laszlo TUROS D.E.., E.E..S. Traslvaa Uversy of Brasov Iulu SZEKELY Géza SERNÁTH Kaal GYÖRGY Absrac Accurae Baery Pack Modelg gas more ad more mporace may applcaos such as Hybrd Elecrc ehcles (HEs), Es [],[] ad small embedded UPS devces [8],[9]. A hgh fdely model gves formao of he dyamcs of he power delvery ad he Sae of harge (SO), whch s very mpora for esmag he rume of hese sysems. Keywords-compoe; SO, O, Baery Model, UPS I. INTRODUTION Baeres are raher complex sysems wh eral chemcal ad physcal processes ha are dffcul o model wh hgh fdely ad buld relaoshps bewee he appled posve or egave curre ad he volage. Lhum-Io baeres have ousadg properes comparso wh coveoal secodary baeres cludg N-d, ckel meal hydrde ad lead acd baeres. Oe of he ma feaures are hgh operag volage, hgh gravmerc ad volumerc eergy deses, o memory effec, low self-dscharge rae, operao a wde rage of emperaure [3]. For he elecrcal baery model exraco, here are wo ma mehods ha are used, he offle esmao of he parameers ope-loop model ad he ole esmao closed-loop model, whch are mosly based o he EKF (Exeded Kalma Fler) algorhm. The auhors [] descrbe he modelg seps by acpag he badwdh of he baery applcao ad he opmzg he badwdh of he baery pack model wh hs kowledge, bu do o descrbe he seps of model exraco algorhm deal. Based o hs arcle we ry o descrbe sysemacally he offle esmao of he baery model elecrcal parameers. The auhors [] descrbe he emperaure depedece of he baery model ad sudy he mpac of baery degradao afer several charge, dscharge cycles. The auhors [4] propose a baery model capable of reproducg lhum-o, ckel-meal hydrde, ad lead acd I- characerscs wh mmal model aleraos. The auhors [6] prese he elecro-hermal model ad he couplg bewee he elecrcal ad hermal model. They use a wo-sae hermal model o approxmae he core ad surface emperaures of he baery. The auhors [0] propose he ARX model o smulae he olear dyamcs of he baery, because of s dscree form ad sraghforward mplemeao could prove more suable for real applcaos, usg Kalma flers for SO esmao. Several leraures descrbe he ole esmao approach (such as []), where he auhors use coulomb coug correced every e mues wh he SO value predced by he smplfed EKF algorhm, whch reduces he compuaoal overhead ha s somemes s a requreme or cosra real-me evromes. Our approach s o use he offle esmaor ha has reduced complexy, bu sll acqure a hgh fdely baery pack model ad furher use offle smulao for sysem level desg. R R S R O Baery Model R SH=Ω Fgure. The measureme seup U Power Supply The expermeal measureme seup preseed Fg. hghlghs ha we use he dfferece bewee ad values o measure he baery volage, ad he value dvded by R SH o measure he curre. The osclloscope s capable of loggg daa S forma, drecly mporable MATLAB evrome for furher processg. II. THE MODEL PARAMETER EXTRATION Equao ad descrbe he proposed sysem as followg: 0 0 R () = I() R SO SO BAT = [ 0] + RS I() + O ( SO) () SO I Daa loggg Osclloscope
2 where BAT represes he baery volage measured bewee ermals ad ad (=..) s he volage drop across he paralleled R - compoes he elecrcal model, SO s he sae of charge of he baery. Equao 3 descrbes he mahemacal model (eq. ad eq.) sae-space represeao form: x ( ) = A( θ ) x( ) + B( θ ) u( ) y( ) = x( ) + D( θ ) u( ) + f ( x) where we used followg oaos: θ = [ R ] T s R R represeg he parameers vecor (hese values eed o be esmaed); [ ( ) ( ) SO ( ] T x ( ) = c c ) s he sae space vecor, where y( ) = BAT ( ) s he baery ermal volage oupu sgal ad s value s parameer depede u ( ) = I ( ) s he curre pu sgal f (x) - s a sae depede olear fuco. For parameer esmao process, we ca defe he followg cos fuco (4). J ( θ ) = E(, θ ) d = ( y p ( ) y(, θ )) d (4) Ths fuco s formed as he cumulave square error bewee he expermeally measured oupu value y p () (baery ermal volage) ad he smulaed model oupu value y(,θ). The boh oupus were obaed for smlar pu sgal. Ths cos fuco ca be wre dscree me form: = 0 (3) J ( θ ) = ( y ( ) y(, θ )) (5) p We have o fd a mmzg algorhm of he cos fuco. The grade updae rule ca be used parameer esmao problem. The followg recursve expresso s he basc relaoshp esmao process: < k + > < k > θ = θ Γ J ( θ ) (6) where Γ s he cosa seps marces, ad he grade of he J(θ) s he dreco vecor: T J ( θ ) J ( θ ) J ( θ ) J ( θ ) = (7) 5 The elemes of hs vecor ca be approxmaed by J ( θ ) J ( θ + h v ) J ( θ ) (=..5) (8) h where v s he -h colum of he 5 order dey marx. u() (I) f (x) Parameerzed mahemacal model Physcal Sysem Baery Model R R R O θ y p () Mmzao Fgure. Schemac represeao of he esmao heory The schemac represeao of he esmao heory s show Fg.. The model exraco algorhm s ma seps are: offle measureme of he expermeal daa calculao of he al SO value from he O value choose he al value of he parameer vecor ad he cosa seps marces Γ The erao flow volves he followg sub-seps:. Smulae he proposed model.. alculae he roo mea square error value ( J (θ ) ), whch also ses oe of he soppg crera of he model exraco algorhm. 3. alculae he roo mea square error value of he slghly modfed model by addg a small amou o he parameer vecor ( J ( θ + h j v j ) ), where he h j are scaled depedg of he parameer ype. 4. alculae he grade vecor J (θ ). 5. Sep he ew parameers vecor wh he cosa sep < k + > grade mehod θ. 6. Lm he ewly acqured parameers o posve values oly, sce ressor ad capacor values cao have egave values. 7. The algorhm sops f reaches he maxmum erao umber or he roo mea square error bewee expermeal baery value ad he model oupu s lower ha a predefed value. III. SO-O PROFILE EXTRATION For SO-O profle exraco a pulse charggdschargg cycle ca be used []. For expermes, we use a 500mAh raed, IFP-8650 LfePO4 baery. + y E(, θ ) ()
3 Fg.3 preses he O-SO profle of he LFePO4 baery cell 5% SO seps ad he polyomal ha erpolaes hese pos, used furher he baery model smulaos. The resuled polyomal s a 8-order polyomal ha has a low roo mea square devao from he expermeal resuls. Icreasg he polyomal order furher Fgure 3. The erpolaed O-SO Profle of a LFePO4 baery cell does o have sgfca mpac o he overall precso of he resulg fuco. Depedg o he PU memory/speed cosras he resuled polyomal ca be ulzed as a fuco SO=f(O) or a lookup able ca be geeraed o oba he al SO value. Ths s a very mpora sep f we ed o use ole exraco algorhm mplemeed a mcrocoroller. Fg.4 preses he geeraed ad expermeally measured baery charge curre profle, values used as he pu daa for he sysem model. Fgure 5. Relao bewee he expermeally deermed baery volage (durg charge profle), he al model ad he opmzed model oupu cosas usg more paralleled R- crcus seres wh he exsg oes. The obaed parameers wh he proposed algorhm are: R =8mΩ, R =48mΩ, =00.8F, = F, R S =0.8Ω The followg equao deermes he evoluo of he SO durg charge profle: SO( ) = SO( 0 ) + ( ) d (9) 0 where he al SO( 0 ) value s deermed based o he O volage descrbed he SO-O profle exraco seco. Fg.6 preses he chage SO value durg he charge profle preseed Fg. 4. Fgure 4. The expermeally measured baery charge curre profle Fg.5 preses he expermeal baery volage whe chargg wh he curre Fg.4, he al model oupu ad he model oupu wh opmzed parameers afer 00 eraos of he model exraco algorhm. Should hgher fdely model s eeded he algorhm ca be easly exeded for 3 or 4 me Fgure 6. Evoluo of he SO value durg charge profle
4 I order o aalyze he frequecy behavor of he acqured sysem wh he exraced ad opmzed parameers for he baery model whou (O) s smulaed. Equao (0) shows he resuled rasfer fuco. H ( s) s + s + 3 = (0) ds + d s + d3 The followg equaos gve he ad d parameers: ( R R R ) = () S ( R R + R R + R R R R ) = ( S S + ( R + R ) + = R S 3 (3) ( R R ) ( R R ) d = (4) d = + (5) d = 3 (6) Furher research ad developmes are progress for real evrome usg a embeddable D-D UPS u (descrbed deals a earler arcle [9]) developed by he auhors. Fg.9 shows he D-D UPS u. Fgure 9. The D-D UPS u Fgure 7. ad 8. plos he correspodg Bode ad Nyqus dagram for he rasfer fuco descrbed eq.8. ONLUSION The proposed baery model shows hgh fdely wh he badwdh doma of eres ad he resuls of he model opmzao algorhm are sasfacory. The cumulave square error bewee he smulao ad expermeal resuls are less f he algorhm sars wh a good esmao of he al SO value. Ths s accepable sce s a offle esmao mehod. Good esmao of he al SO value ca be acqured f he baery ress log eough bewee es scearos. AKNOWLEDGEMENT The Secoral Operaoal Programme Huma Resources Developme (SOP HRD), ID34378, faced from he Europea Socal Fud ad by he Romaa Goverme, suppors hs paper. Fgure 7. The Bode dagram of he rasfer fuco Fgure 8. The Nyqus dagram of he rasfer fuco REFERENES [] Jawe L, Mchael S. Mazzola, Accurae baery pack modelg for auomove applcaos, Joural of Power Sources, olume 37, Sepember 03, Pages 5-8, ISSN [] Mhe-Popa, L.; amacho, O.M.F.; Norgard, P.B., "hargg ad dschargg ess for obag a accurae dyamc elecro-hermal model of hgh power lhum-o pack sysem for hybrd ad E applcaos," PowerTech (POWERTEH), 03 IEEE Greoble, vol., o., pp.,6, 6-0 Jue 03 [3] Gafraco Psoa, Lhum-Io Baeres Advaces ad Applcaos,Frs Edo, Elsever, 04, ISBN: [4] Kroeze, R..; Kre, P.T., "Elecrcal baery model for use dyamc elecrc vehcle smulaos," Power Elecrocs Specalss oferece, 008. PES 008. IEEE, vol., o., pp.336,34, 5-9 Jue 008 [5] Hura, T.; eraolo, M.; Gazzarr, J.; Jackey, R., "Hgh fdely elecrcal model wh hermal depedece for characerzao ad smulao of hgh power lhum baery cells," Elecrc ehcle oferece (IE), 0 IEEE Ieraoal, vol., o., pp.,8, 4-8 March 0
5 [6] Hecor E Perez, Jaso B Segel, Xfa L, Y Dg, ad Mahew P asaer. Parameerzao ad valdao of a egraed elecrohermal LPF baery model. ASME Dyamc Sysems orol oferece, Oc 0. [7] hrsopher D. Rah, hao-yag Wag, Baery Sysems Egeerg, Joh Wley & Sos Ld., Frs Edo, ISBN: , 03 [8] Géza seráh, László Turos "Embeddable, smar, D operaed UPS for small ad md szed baery backup applcaos," Opmzao of Elecrcal ad Elecroc Equpme (OPTIM), 0 3h Ieraoal oferece o, IEEE,vol., o., pp.567,574, 4-6 May 0 [9] László Turos, Géza seráh, Iulu Szekely, Eergy Effce Oupu Regulao wh Adapve Behavour a D-D UPS, Elsever Proceda Techology, olume, 04, Pages 34-4, ISSN -073, [0] Shfe Yua, Hogje Wu, heglag Y Sae of harge Esmao Usg he Exeded Kalma Fler for Baery Maageme Sysems Based o he ARX Baery Model [] Hura, T., eraolo, M., Gazzarr, J., ad Jackey, R., "Smplfed Exeded Kalma Fler Observer for SO Esmao of ommercal Power-Oreed LFP Lhum Baery ells," SAE Techcal Paper , 03, do:0.47/03-0-5
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