Identifiction of Dynmic Model Prmeters for Lithium-Ion Btteries used in Hybrid Electric Vehicles Ciping Zhng 1, Jizhong Liu 2, S.M.Shrh 2, Chengning Zhng 1 (1. Ntionl Engineering Lbortory for Electric vehicle, School of Mechnicl nd Vehiculr Engineering, Beijing Institute of Technology, Beijing 181, Chin; 2. School of Engineering Sciences, University of Southmpton, Highfield, Southmpton, SO17 1BJ, UK ) Abstrct: This pper presents n electricl equivlent circuit model for lithium-ion btteries used for hybrid electric vehicles (HEV). The model hs two RC networs chrcterizing bttery ctivtion nd concentrtion polriztion process. The prmeters of the model re identified using combined experimentl nd Extended Klmn Filter (EKF) recursive methods. The open-circuit voltge nd ohmic resistnce of the bttery re directly mesured nd clculted from experimentl mesurements, respectively. The rest of the coupled dynmic prmeters, i.e. the RC networ prmeters, re estimted using the EKF method. Experimentl nd simultion results re presented to demonstrte the efficcy of the proposed circuit model nd prmeter identifiction techniques for simulting bttery dynmics. Keywords: Prmeters identifiction; dynmic bttery model; lithium-ion bttery; HEV; CLC number: TM912.8 Document code: A Article ID: 1. Introduction Lithium-ion btteries re incresingly used in portble electronics, utomotive nd erospce pplictions, s well s in bc-up power pplictions due to their high voltge, high energy density, none memory effect, nd low self-dischrge during storge. Recently there hs been fst growth in demnd for lrge lithium-ion btteries for direct power supply of electric vehicles (EV) nd hybrid electric vehicles (HEVs). Accurte modeling of bttery dynmics is importnt for ccurte simultion nd optimiztion, nd rel time energy mngement of EVs nd HEVs. An ccurte dynmic model of bttery usully involves the reltions of the terminl voltge to current, power, temperture, stte of chrge (SOC), the effects of self-dischrge, nd the effects of ging. Currently, there re three min types of model used to describe the reltionship between input nd output of bttery system. These re electrochemicl model [1, 2], rtificil neurl networ model [3, 4] nd electricl equivlent circuit model [5-7]. The electrochemicl bttery model describes the dynmic process of chemicl rections occurring on the electrodes bsed on mthemticl method, which cn integrlly reflect dynmic chrcteristics of the bttery. However, this model requires bttery chemicl prmeters nd detiled nowledge of the bttery construction nd mteril properties which is not normlly vilble to designers of vehicles. The rtificil neurl networs method hs dvntge of dptive lerning which cn be pplied to the system identifiction of bttery s nonliner chrcteristics during chrging nd dischrging. The rtificil neurl networs model hs be widely implemented for vrious bttery systems. However, this model requires lrge mount of dt for trining nd the ccurcy of these models
is ffected significntly by the trining dt nd trining method. Furthermore, the neurl networ model my not be suitble for simulting bttery chrcteristics of HEV since the bttery current fluctutes cutely nd rndomly s the power demnd vries during vehicle s driving cycles. Electricl equivlent circuit models re bsed on the opertionl principle of the bttery which simultes its dynmics with circuit networ composed of cpcitor, resistor, nd constnt voltge source etc. Equivlent circuit models hve been extensively reserched in recent yers due to its excellent dptbility nd simple reliztion. Severl equivlent circuit models such s RC model, Thevenin model nd Prtnership for New Genertion of Vehicles (PNGV) model hve been pplied to lithium-ion btteries in HEV. These models re used for simulting the dynmic chrcteristics nd estimting SOC of the bttery. The prmeters of equivlent circuit model for btteries re normlly determined by performing series of chrging nd dischrging tests t different SOC vlues with controlled current nd temperture. Vrious techniques hve been proposed to identify the model prmeters.. For exmple, the identifiction technique, bsed on experimentl dt coupled with chrcteristics of bttery model, is essentilly utilized for specifying the prmeters [8, 9]. However, it requires highly ccurte mesurement pprtus to obtin the resistnce nd time constnt of RC networ in the model. In ddition, it hevily relies on the experience of the resercher. The well nown Extended Klmn Filter (EKF) is recursive lgorithm for computing estimtes of sttes nd prmeters of nonliner system. It is prticulrly ble to optimlly estimte the sttes nd prmeters ffected by process nd mesurement noise [1]. It hs been pplied in wide rnge of pplictions such s stte observtion, prmeter estimtion nd stte prediction problems. In this pper, the EKF combined with the experimentl identifiction methods re used to obtin the circuit model prmeters of lithium ion bttery. 2. Model formultion The power ssist unit in the hybrid electric vehicle described in this pper, is composed of 144 lithium-ion cells. Ech bttery module (bttery box) consists of 16 lithium-ion cells. Idelly, tests nd model identifiction need to be crried out on ech cell with lrge quntity of computtion. But this will be expensive nd time consuming. Alterntively, tests nd modelling could be bsed on one cell, nd then multiply by144 to obtin model of the whole bttery pc. But this my not be ccurte due to tolernce vritions between the bttery cells. As compromise the bttery module of 16 cells is regrded s the object for modelling, multiplying the mount of bttery modules s the totl bttery pc model. The electricl circuit model is used to describe the reltionship between the currents nd voltges mesured t the terminl of the bttery. The model used for the lithium-ion bttery comprises three prts, s shown in Fig. 1: 1) open-circuit bttery voltge V oc, which is composed of n equilibrium potentilve nd hysteresis voltge V h, 2) internl resistnce R i contins the ohmic resistnce R o nd the polriztion resistnce, where the polriztion resistnce hs two components nd R pc, where R p represents effective resistnce chrcterising ctivtion polriztion nd R p Rpc represents effective resistnce chrcterising concentrtion polriztion, 3) effective
cpcitnces, which consists two prmeters of C p nd C pc, these two prmeters re used to describe the ctivtion polriztion nd concentrtion polriztion, which re used to chrcterise the trnsient response during trnsferring power to/from the bttery. The electricl behviour of the circuit cn be expressed s following equtions: V V I & p p = (1) RpC p C p V V I & pc pc = (2) RpcC pc C pc V L = V V V V IR (3) e h p pc o C p C pc R o Ⅰ R p R pc V h R SD V L V e V oc Fig. 1 Proposed equivlent circuit model for the lithium-ion bttery 3. Prmeters estimtion 3.1 Open-circuit voltge The equilibrium potentil is the open circuit voltge mesured when the forwrd nd reverse rection rtes re equl in n electrolytic solution, thereby estblishing the potentil of n electrode. The equilibrium potentil of the bttery, which is determined by Nernst eqution, depends on the temperture nd the mount of ctive mteril left in the electrolyte. Fig. 2 illustrtes the open-circuit voltge (OCV) s function of SOC fter chrge nd dischrge t room temperture. In this experiment, the bttery ws first dischrged t constnt current of 3 A from fully chrged stte till 1 % of the nominl cpcity (1 A h) ws consumed. It ws subsequently left in open-circuit condition, while the open-circuit voltge ws observed. After one hour, the mesured voltge ws considered s equilibrium voltge since the rte of the increse of the open circuit voltge ws negligible nd hence the bttery ws ssumed to be got to stedy stte. The bttery ws subsequently dischrged by further 1 % of the nominl t the sme current nd the equilibrium voltge mesured fter witing for one hour, nd the procedure ws repeted to obtin the remining dt points on the dischrge curve in Fig. 2. The bttery ws then rechrged t the specified current, the equilibrium voltge fter chrge could be obtined every.1 SOC. From Fig. 2, we cn find tht the equilibrium voltge hs different vlues fter chrge nd dischrge
respectively t the sme SOC, which indictes tht the equilibrium potentil depends on previous tretment of the bttery nd the hysteresis phenomenon is observed during chrge nd dischrge. Thus, two SOC vlues exist for given equilibrium voltge. The hysteresis voltge needs to be considered when the open-circuit voltge is used to determine bttery s initil SOC.The hysteresis chrcteristics is thought to be due to the intercltion of lithium ions into crbon nd into LiMnO 2 electrodes for lithium-ion btteries s discussed in [11-14]. In this pper, in order to identify the model prmeters, we ssume SOC point is nown. Hysteresis will be neglected nd the verge open-circuit voltge of bttery V oc will be used. 66 Open circuit voltge / V 65 64 63 62 61 OCV fter dischrge OCV fter chrge Averge OCV 6 3.2 Ohmic resistnce 59.1.2.3.4.5.6.7.8.9 1 SOC Fig. 2 Open-circuit of bttery voltge s function of SOC t room temperture The totl Ohmic impednce of the bttery is the sum of the resistnce cross the solution nd the resistnce of the externl circuit, which depend on temperture nd SOC. The Ohmic resistnce of the bttery t the specified SOC nd temperture cn be determined experimentlly using pulse current chrging nd dischrging s illustrted in Fig. 3. 65 64.5 Chrge Bttery voltge / V 64 63.5 63 V IR loss Puse 62.5 Dischrge V1 62 1 2 3 4 5 6 Time Fig. 3 Bttery voltge response t the pulse current As shown in Fig. 3, the instntneous bttery voltge is dropped t the condition of pulse current which cn be expressed s:
V= V 1 V (4) The ohmic resistnce cn be given by: Where I is the chrge/dischrge current through the bttery. V R o = (5) I The Ohmic resistnce ws found to be independent of the bttery current. But it ws found to be function of SOC shown in Fig. 4. It cn be seen tht the resistnce vries with SOC, nd hs high vlues t lower SOC nd lso hs high vlue t SOC=1. 15 Ohmic resistnce /m Ω 14.5 14 3.3 Identifiction of dynmic behviour prmeters 3.3.1 The extended Klmn filter The Klmn filter is mthemticl technique tht provides n efficient recursive mens for estimting the sttes of process, in such wy so s to minimize the men of the squred error [15]. The filter hs been pplied extensively to the field of liner estimtion including stte estimtion, prmeters estimtion nd dul estimtion. The extended Klmn filter (EKF) is nonliner version of Klmn filter tht linerizes bout the current men nd covrince of the stte. It cn be described s follows [16] : the system of interest is continuous-time dynmics with discrete-time mesurements given by: where u(t) is the control input; w(t) x& = f( x, u, wt, ) y wt () v = h ( x, v ) ~ ~ (, Q) (, R ) (6) represents process noise which is ssumed to be continuous-time Gussin zero-men white noise with covrince of Q ; v represents mesurement noise which is ssumed to be discrete-time Gussin white noise with zero men nd covrince R. The procedure for using the EKF for optiml stte nd prmeter estimtion cn 13.5.1.2.3.4.5.6.7.8.9 1 SOC Fig. 4 Ohmic resistnce of the bttery s function of SOC t room temperture
be summrised s follows: Step I : Initilistion The initil estimtion of x before ny mesurement is modelled s Gussin rndom vector with men X nd covrince P, which is expressed by: P = E[ x ] = E[( x )( x T ) ] (7) Step II: time updte (from time ( 1) to time ( ) ) The time updte phse uses the stte estimte nd its covrince from the previous time step ( 1) to produce n estimte of the stte t the current time step ( s follows: ) x & ˆ = f (, u,, t) P& = AP PA T Q (8) Where A is prtil derivte Jcobin mtrix evluted t the current stte estimte which cn be given s: f A= (9) x x=ˆ x In this step, the integrtion is processed with = 1 nd P = P 1. At the end of the integrtion, we hve = nd P = P. With reference to eqution (8), the estimted stte nd its covrince propgtes from time ( 1) to time () bsed on the previous vlues, system dynmics, the control input nd the errors of the ctul system [17]. Step III: mesurement updte In this phse, the mesurement informtion t time is processed to refine the estimte of x to rrive t more ccurte stte estimte. The resulting estimte of x is denoted, nd its covrince is denoted P. Performing the mesurement updte of the stte estimte nd estimtion error covrince, the mesurement updte eqution cn be described s follows: K P = Where K is Klmn gin mtrix; which is given by: T = P C ( C P K ( y C T R ) = ( I K C ) P ( I K C ) h (,, t )) 1 T T K R K C is the prtil derivtive of h x, v ) ( (1) with respect to x,
C h = x x= (11) It should be noted tht nd re both estimtes of the sme quntity; nd re both estimtes of x. However, is the estimte of x before the mesurement y is ten into ccount, which is clled priori estimte, nd is the estimte of fter the mesurement y is ten into ccount, which is clled posteriori estimte. 3.3.2 Implementtion This section presents the implementtion for estimting sttes nd prmeters of the dynmic bttery model. For the electricl circuit model, the output voltge of the bttery is bsed on eqution (3) which cn be rerrnged by V Vp = Voc [ 1 1] [ Ro I (12) Vpc L ] where V oc represents the verge voltge of the bttery open-circuit voltge. The current flowing out of the bttery is ssumed positive for this study. Ting time derivtive of output voltge of the bttery nd ssuming dv oc / dt, di / dt (the rte of chnge of open-circuit voltge nd terminl current between smpling time is negligible) gives: R o V& 1 1 1 1 1 1 L = VL V p I Voc (13) RpcC pc RpC p RpcC pc RpcC pc C pc C p RpcC pc In this study, the prmeters R p, C p, R pc, C pc re considered s constnt t specified SOC. The prmeters considered s sttes re dded to the stte vribles. Combing equtions (1), (2), (12) nd (13), the system cn be expressed s follows: x& = f ( x, u) (14) y = h ( x ) 1 1 1 1 T where x = [ Vp Vpc VL ], R C R C u= I, h ( x ) = VL. T ( x, u) = [ f1 f2 f3 f4 f5 f6 f7 f ] nd = x x x x u ; p f1 1 4 5 5 f2 = x2x6x7 x7u; f3 x6x7x3 ( x4x5 x6x7 ) x1 ( Rox6 x7 x5 x7 ) u x6x7v oc f 4 = ; f 5 = ; f 6 = ; f 7 =. = ; p pc pc
Then we cn clculte the mtrices of the system by f A = x x = = 11 31 22 33 14 34 15 35 26 36 27 37 Where 11 = x4x5, 14 = x1 x5, 15 = x1x4 u 22 = x6x7, 26 = x2x7, 27 = x2x6 u 31 = x4x5 x6x7, 33 = x6x7, 34 = x5x1, 35 = x4x1 u, 36 = x7x3 x7x1 Ro x7u Vocx7, 37 = x6x3 x6x1 Ro x6u u Vocx6. C = [ 1 ] Fig. 5 shows the estimting results with EKF lgorithm for the sttes nd prmeters of the model t the point of 1 % SOC. In this cse, the covrince mtrices Q, P nd R selected re given by:.1.1.1 Q =.1,.1.1.1 1 P = 2, 1E 6 1E7 1E 4 R = 1. Fig. 5 () nd (b) shows the behviour of the estimted voltges chrcterising bttery polriztions. Fig. 5 () shows tht the voltge of cpcity chrcterising bttery ctivtion polriztion reches stedy-stte within 4 seconds, which suggests tht time constnt of the RC networ is smll. However, the voltge of cpcity chrcterising bttery concentrtion polriztion in Fig. 5 (b) tes much longer time to get stedy stte. In Fig. 5 (c), (d), (e) nd (f), the estimted prmeters hve got to constnt vlues within 4 seconds. Fig. 5 (g) represents the behviour of estimted voltge nd mesured voltge of the bttery. There is resonble
greement between the estimted voltge nd the mesured voltge; the mximum estimte error is within.3 V, s shown in Fig. 5 (h). This suggests tht the extended Klmn filter cn be effectively implemented to estimte the prmeters of bttery model. Vp / V Rp / Ω).15.1.5 2 4 6 8 1 () 1 x 1-3 1 1 1 2 4 6 8 1 (c) Vpc / V.25.2.15.1.5 Cp / F 2 4 6 8 1 (b) 1 998 996 994 992 99 2 4 6 8 1 (d) Cpc / F Terminl voltge / V 1 8 6 4 2 2 4 6 8 1 (e) 66.5 66 65.5 65 Estimted Mesured 64.5 2 4 6 8 1 (g) Rpc / Ω Estimte error / V 1 x 1-3 8 6 4 2 2 4 6 8 1 (f).3.2.1 -.1 2 4 6 8 1 (h) Fig. 5 Estimting results of sttes nd prmeters for the bttery model with EKF lgorithm (SOC=1.) 4. Simultion nd vlidtion The DST driving cycles [7] ws pplied for vlidting the dynmic model of the bttery. The initil bttery SOC ws set to 1.. The model prmeters obtined for SOC of 1., nd ssumed to be constnt during the simultion. This is not strictly true, s the prmeter will chnge with the
chnge of SOC. But for short opertion time, it my be resonble pproximtion. The mesured nd estimted terminl voltge of the bttery is illustrted in Fig. 6. From Fig.6, it is shown tht the bttery model with the estimted prmeters cn effectively simulte the bttery dynmics, nd the bttery terminl voltge error shown in Fig. 7 is pproximtely round 3 %. It is cler tht the error will increse with time, nd it is necessry to updte the prmeters to mintin smll error. Fig. 6 suggests tht the prmeters need to be updted t lest every 2 seconds. This will be implemented in the future. Terminl voltge / V 75 7 65 6 55 Simulted Voltge 5 1 2 3 4 Fig. 6 The simulted nd mesured voltge of the bttery for DST cycle (SOC =.1) Mesured Voltge 1.5 Simultion error / V 1.5 5 1 15 2 25 3 35 4 Fig. 7 The simultion error for the bttery 5. Conclusions This pper presented n equivlent circuit model with two RC networs chrcterising bttery ctivtion nd concentrtion polriztion process. The extended Klmn filter ws used to estimte the coupled prmeters reflecting bttery polriztion chrcteristics. The prmeters chrcterising bttery equilibrium potentil nd ohmic resistnce were determined experimentlly. Simultion results using proposed model with the identified prmeters, were found to gree stisfctorily with the experimentl results. Future wor will focus on using EKF to estimte bttery sttes (for exmple SOC nd stte of helth) nd for online model prmeters identifiction. References [1] Bumby J R nd et l. Computer modelling of the utomotive energy requirements for interntionl
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