State of Charge Estimation for Lithium-Ion Batteries Using Neural Networks and Extended Kalman Filter

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1 State of harge Estmaton for Lthum-Ion Batteres Usng Neural Networs and Extended Kalman Flter Abstract--hs paper presents a method for modelng and estmaton of the State Of harge (SO) of lthum-on batteres usng neural networs and the Extended Kalman Flter (EKF). he neural networ s traned off-lne usng the data collected from the battery chargng process. hs networ fnds the model needed n the state space equatons of the EKF, where the state varables are the battery termnal voltage at the prevous sample and the SO at the present sample. Furthermore, the covarance matrx for the process nose n EKF s estmated adaptvely. he proposed method s mplemented on a lthumon battery to on-lne estmate the of the battery. Expermental results show good estmaton of SO and fast convergence of the EKF state varables. Index erms: Batteres, montorng, estmaton, Kalman flterng, neural networs. I. INRODUION SOME BAERIES are senstve to overcharge and/or deep dscharge, whch may lead to permanent damage to these devces. In the chargng process, t s usually desrable to charge the battery wth the hghest and safest current n order to reach the full State of harge (SO) as qucly as possble wthout enterng the overcharge regon [], []. herefore, t s necessary to measure the SO wth good accuracy for proper battery managements. Moreover, the State of Health (SOH) of batteres requres mantanng the SO wthn certan lmts at all tmes [], []. he SO defnton, n the smplest way, s the rato between the saved energy n the battery and the whole energy that can be saved n t []. he SO estmaton s not an easy tas and depends on the battery type and the applcatons for whch they are used. Generally, there are two categores for SO estmaton: ndrect methods and drect methods. In ndrect methods, the SO s estmated from some physcal propertes of the battery, such as the acd densty or the cathodc galvanostatc pulses. Estmatng these quanttes needs precse measurements and has several lmtatons n practce [], []. he other ndrect method s measurng the open-crcut voltage of the battery. In ths method, the battery must be relaxed for some tme to allow ts open-crcut voltage reach a steady-state condton. herefore, ths method s not practcal n applcatons where the battery s not allowed to be opened from the electrc crcut [], []. In other methods, SO s estmated usng the dscharge voltage of the battery []. Impedance spectroscopy s a commonly used ndrect method for electrochemcal processes such as batteres. hs method s used not only for the SO estmaton but also for the SOH estmaton as well [], []. However, ths approach requres some addtonal measurements that mae t sutable n laboratory tests, but not n practcal applcatons []. In [] the battery mpedance s measured drectly through varyng frequency to mprove the chargng process. In [], the electromotve force voltage s estmated, from whch the SO of the battery s determned. In ths wor, t s necessary to measure the battery mpedance wth ac current and voltage, whch seems to be sutable for laboratory tests. Some researchers have used fuzzy logc to model the relatonshp between the battery SO and ts parameters derved from mpedance spectroscopy measurements [], []. Among the drect methods for SO estmaton s the Ampere-hour countng technque. hs method needs the ntal SO, calculaton of the nternal consumptons by the battery, and accurate current sensors []. Artfcal neural networs have also been used by some researchers for the SO estmaton []-[]. In ths method, there s need for some nput-output data as the tranng set, whch must be obtaned by some other estmaton methods. he traned networ can then be used to estmate the SO. he Kalman flter s a powerful tool for the state estmaton of systems. Some researchers have used ths flter to estmate the open-crcut voltage or other parameters of batteres that have a drect relatonshp wth the SO [], []. In [] and [], the Kalman flter s employed to estmate some physcal quanttes, whch have drect effects on the SO. In some papers, the SO s defned as a model state and s estmated usng the Kalman flter [], []-[]. However, the Kalman flter needs a sutable model of the battery. Moreover, due to the use of feedbacs n ths flter, there s need for proper ntalzaton of states; otherwse, ts states may not converge. In ths paper, a state-space model of the SO s proposed that s approxmated usng a neural networ. hen, usng the Extended Kalman Flter (EKF) along wth the proposed model, the battery SO s estmated. he proposed method s mplemented and tested on a L-Ion battery. he expermental results show good accuracy and quc convergence for estmatng the SO of lthum-on batteres. hs paper s organzed as follows. Secton descrbes the battery model. Secton presents the proposed SO estmaton algorthm. Secton shows the expermental setups and results. Fnally, secton draws some conclusons and gves drectons for the future wor.

2 II. MODELING In ths paper, the SO s defned as an ndependent statespace varable and s modeled usng a Radal Bass Functon (RBF) neural networ []. A. SO as the state space varable he SO can be defned as the rato between the saved energy n a battery and the whole energy that could be saved n t [, ] t η () τ zt () = zt ( ) + dτ () where zt () s the SO, zt ( ) s the ntal SO, n s the nomnal capacty, t () s the nstantaneous current (postve for dscharge and negatve for charge), η s the olumbc effcency ( η = for dscharge and η = η for charge) []. In order to employ the Kalman flter, t s necessary to dscretze the model gven n (). Assumng that the samplng rate t s small enough and substtutng the ntegral wth the Euler approxmaton, Eq. () can be wrtten as η t z ( + ) = z ( ) + ( ) () n As Eq. () shows, the SO s defned as an ndependent state varable n the state space model. Other state varables and the output equaton wll be gven n the next secton. B. he proposed model t he SO of batteres has a nonlnear relatonshp wth ts termnal voltage and current []. It s usually not an easy tas to obtan ths nonlnear relatonshp. One way to fnd ths relatonshp s to analyze the chemcal reacton equatons, whch s very complcated. Fortunately, neural networs are unversal approxmators and can approxmate any nonlnear functon wth desred accuraces []. In ths paper, a RBF networ s used to fnd the requred nonlnear model. Fg. shows the structure of an RBF networ, where the nputs are the battery voltage at step -, the estmated SO at step, and the battery termnal current at step. he output of the neural networ approxmates the battery termnal voltage at step. In ths networ, the actvaton functons of neurons n the hdden layer are Green functons (e.g. Gaussan functons) n the followng form: ( ) G r t ϕ r = ( r t ) = exp, =,, σ M () where = [ ] r ( ) ( ) ( ) v z s the nput vector appled to the networ at the th step, t and σ are the center and the standard devaton of the Gaussan functon, respectvely, and M s the number of neurons n the hdden layer. In fact, the output of ths neural networ (.e. the battery termnal voltage at step ) s the sum of the weghted Gaussan functons as n v ( ) Fg.. Structure of the RBF neural networ for modelng. M F( r ) w w ϕ ( r ) () = + = where w ( =,, M) s the weght vector connectng the th z ( ) ( ) neuron n the hdden layer to the output layer and w s the bas weght for the lnear output neuron. he free parameters of ths networ are t, σ, w, and w, whch are defned durng the tranng phase of the networ usng algorthms such as the bac-propagaton and the least mean square []. onsderng the battery termnal voltage at step and the SO at step as the frst and the second state varables, respectvely, the state vector s defned as x( ) v ( ) x( + ) v ( ) x = : + x( ) = z ( ) x = = x( + ) z ( + ) () where v and z represent the termnal voltage and the SO of battery, respectvely. Usng the above defnton as the state vector, the state space model can be defned n the followng form: F( r) x( + ) ω( ) η t x( ) = + x( ) ( ) ω( ) + + n () y( ) F( r) υ( ) y( ) = + x( ) υ( ) where F ( r ) s a nonlnear functon, whch wll be approxmated by the RBF networ, vectors ω = [ ω ω] υ= υ υ are defned as the process and the and [ ] + measurement noses, respectvely, wth covarance matrces ϕ ϕ E[ ω ω ] = Q E[ υ υ ] = R Moreover, r (.e. the nput vector to the neural networ) s defned as v( ) () r = : x () where x s gven n (). Notce that, n the proposed model, the termnal voltage of battery at steps and, whch are shown n the output equatons as y ( ) and y ( ), respectvely, are used n the proposed model. ϕ Σ

3 III. ESIMAION ALGORIHM he estmaton algorthm, n ths paper, s based on the extended Kalman flter. he performance of Kalman flters depends on several factors, among them, dependency on an accurate state space model of the system, whch was proposed n the prevous secton. A. Extended Kalman flter he Kalman flter that s estmatng the states of a lnear tme-varyng model, whch approxmates the nonlnear model, s called the Extended Kalman Flter (EKF). Hence, f the system, whose states are to be estmated by the EKF, has a nonlnear model, then the nonlnear system must be lnearzed frst around the operatng pont wth a tme-varyng approxmaton. Even though the performance of EKF s not optmal, t wors fne for most applcatons []. For convenence, a summary of the EKF algorthm s gven n able. One mportant ssue n desgnng a Kalman flter s the proper selecton of covarance matrces for measurement and process noses. he covarance matrx of the measurement nose (R) can be determned from the battery data. he varances can be obtaned from the square of the root-meansquare (RMS) of nosy measurements on the battery termnal voltage. Moreover, t s assumed that the varances are ndependent and have Gaussan dstrbutons []. he covarance matrx of the process nose (Q) s estmated n ths paper usng the Maybec's estmator as [] K ˆ( ) Q = j j j j ( j j j j) N GvvG A P A P () j= N+ where matrces G, A and P are gven n able, N s the number of recent sample perods and v s the nnovaton vector calculated as v = y h xˆ, u () j j j B. Lnearzng the Proposed Model ( ) In order to apply the EKF to the proposed nonlnear model n (), the battery model must be lnearzed at samplng nstants. Let defne the nonlnear transton matrx functon fx (, u ) and the nonlnear measurement matrx hx (, u ) as F( r) F( r) fx (, u) = :, (, ) : x ( ) ( η t hx u = + n) x ( ) () Dfferentatng fx (, u) and hx (, u ) wth respect to x and then lettng x = x ˆ and x = x ˆ, respectvely, yelds F( r ) F( r ) A =, = () x= xˆ x= xˆ where F( r ) s the output of the RBF networ. Hence, M F( r ) ( ) w ϕ r t =, = () able : Summary of the EKF algorthm. State space model x+ = fx (, u) + ω y = hx (, u) + υ where ω and ν are ndependent, zero mean, Gaussan process and measurement noses wth covarance matrces Q =E[ ω ω ] and R =E[ ν ν ], respectvely. Defnton fx (, u) hx (, u) A =, = Intalzaton xˆ = E[ x ], x= xˆ x= xˆ ( )( ) P = E E[ ] E[ ] x x x x alculate for =,, me update State estmate propagaton xˆ ( ˆ = fx, u ) Error covarance propagaton P = A P A + Q Measurement update Kalman gan matrx G = P ( P + R ) State estmate update xˆ ˆ = x + G y ( ˆ hx, u ) Error covarance update P = ( IG ) P n whch, the dervatve of ϕ( ) can be found usng () as ( ) ϕ( ) r t wth respect to x ϕ r t r t r = () r hen, usng r = :[ x( ) x( ) ], t yelds r = () Moreover, assumng ϕ() s a Gaussan functon as n (), t gves ϕ ( r t ) r = ϕ( r t ) ( r t) σ Substtutng (), () and () nto () yelds M F( r) r = wϕ ( r t ) ( r t) σ = () ()

4 IV. IMPLEMENAION AND EXPERIMENAL SEUP he proposed SO estmator s tested on a lthum-on battery. Fg. shows the general structure of the expermental setup. he hardware conssts of a specal nterface crcut for samplng the current, the voltage, and the batter temperature. he sampled data are transferred to a computer va the seral port. he programmng language for data manpulaton and processng s Vsual ++. In addton, for acqurng data for tranng the RBF neural networ and for testng the proposed SO estmator, a battery charger has been ncluded that controls the on-off tme of chargng and dschargng the battery. he chargng technque s based on the reflex chargng method, whch s consdered as one of the most effectve chargng schemes []. In ths chargng method, the battery s frst charged wth a constant current for a small perod of tme, followed by dschargng for a very short tme and a relax nterval at the end. he entre chargng process can be vewed on the computer montor (Fg. ). Fg.,, and show the desgned crcuts for the samplng nterface, the sgnal condtonng, and the controllable charger, respectvely. As Fg. shows, mcrocontroller s used to transfer the sampled voltage, current, and temperature of battery to the computer. Moreover, ths mcrocontroller controls the on-off tme of chargng and dschargng by applyng the approprate nputs to the drver, based on the gven commands by the computer. For the temperature sensng, an LM sensor s used. hs sensor s calbrated n Kelvn and has mv/ scale factor. In the proposed method, the battery temperature plays no role n the chargng process. It s shown only for montorng purposes. he entre expermental setup s carred out at room temperature. For the current sensng, snce the maxmum current of the charger s set to about. A, a. ohm W resstor s used. Moreover, for voltage sensng, a dfferental amplfer s employed. For data samplng, the AD s used. hs chp has a resoluton of bt and can convert analog nputs to dscrete outputs n less than µs. For samplng, the analog nput n all channels must be n the range of to V. Hence, t s necessary to use a sgnal adaptor to match the sensors outputs wth the analog nputs of AD through the sgnal condtonng crcuts (Fg. ). Fg. shows the controllable charger, desgned for acqurng the data as well as testng the proposed technque for the SO estmaton. he charger conssts of a current source and a dschargng.ω/w resstor used as a load. hese two crcuts are controlled by the SW and SW nputs, respectvely. Snce L-Ion batteres are very senstve to voltages above ther nomnal voltages, a voltage regulator s desgned to mantan the battery termnal voltage at.v. hs voltage regulator conssts of Q, Q, OP, and LM (Fg. ). A. Battery SO Estmaton As t was mentoned n Secton, the battery s modeled usng an RBF neural networ, whch s traned usng the data obtaned from the battery. Snce the SO of the battery s one of the nputs to the neural networ, t s necessary to measure Fg.. General structure of the proposed system. harger & Drver K ARRAY J Battery DB AP AP urrent sensor emperature sensor Y. Mhz XD uf Voltage sensor Dsplay U A P B P P AL P S P EO P OE P P uf IN IN EA/VP X X RESE RD WR U uf R IN R IN IN IN + - V+ V- GND MAXEWE() Interface crcut P P P P P P P P P P P P P P P P RXD XD ALE/P PSEN R OU R OU OU OU + - Seral port Fg.. Interfacng and samplng crcuts. uf RXD SW SW uf Vsual ++ program n computer the SO usng one of the avalable methods. For ths reason, the Ampere-hour countng technque, gven n (), s employed for collectng the tranng data. For calculatng η, the energy delvered by the battery durng dschargng s dvded by the rated energy (the nomnal capacty) of the battery n. Moreover, the samplng perod t s equal to. second for the SO estmaton. It should be mentoned that the samplng rate of the expermental setup s ms, whch s used for dsplay purposes, but the SO estmaton process s updated every ms. Fg. shows the data acqured from the expermental test on a. Ah lthum-on battery. hese data are used for tranng of the RBF networ. Although the battery temperature s measured and saved here, t s not used for the estmaton or chargng processes; the experments have been carred out at room temperature. he covarance matrx R s determned from the data n Fg., based on the square of the rms error between the actual and nosy termnal voltage, and s equal to R = dag... D LK SD D Z Q Q () v() v(-) msb lsb- EO ADD-A ADD-B ADD- ALE ENABLE SAR LOK ontroller SO estmator +v -v Z Z IN- IN- IN- IN- IN- IN- IN- IN- ref(-) ref(+) U L U SO AD xˆ P H-(A/D) H-(A/D) H-(A/D)

5 +V K K LMDZ() OU GND VS+ L -V + ontroled current source From controller R.ohm W R BAERY -V +V PO K ADAN () L K K emperature H-(A/D).... urrent(a) - -. emperature( o ) ohm.uf K K K Fg.. Sgnal condtonng crcut U LM Vn D N ADJ SW +Vout /R D N /R.V ohm/r uf/ uf/ Q /R B /R U OP N Q K ohm/r ohm/r Q B +V L -V Q BD Q N Q BD Q BD. ohm/r. ohm/r L-on.v BAERY urrent Voltage. ohm W/R RELAY +V N Q Fg.. ontrollable charger crcut (drver) wth voltage lmter /R D N /R H-(A/D) H-(A/D) he covarance matrx Q s determned adaptvely usng () wth ntal value equal to dag[..]. he varable N s selected equal to fve. It s mportant to menton that the proposed algorthm s not very senstve to the ntal value of matrx Q and the parameter N. hs s manly due to the fact that matrx Q s adaptvely adjusted to cope wth the changes. he data n Fg. are saved n the computer usng the developed software. In order to show how the varables n Fg. are varyng wth tme, seconds of Fg. s shown n Fg.. Snce the neural networ needs to be traned wth dfferent chargng condtons, the entre chargng cycle s dvded nto three parts: the frst part s performed wth % duty cycle, whle the second part s carred out wth % duty cycle, and the thrd part s performed wth % duty cycle. In order to avod overtranng of the NN, samples are selected out of samples (.e. samples out of every samples). he nputs to the neural networ are v ( ), ( ), and SO( ), whle the output s the battery termnal voltage at the present sample v ( ). here are neurons n the hdden layer wth σ =. ( =,,). hese SW.. estmated SO tme(sec.) Fg.. he expermental data obtaned from a full chargng cycle of a.ah L-Ion battery..... urrent(a) - emperature( o ). estmated SO. tme(sec.) Fg.. seconds of Fg.. numbers are usually defned wth tral and error []. At the end of the tranng phase, the performance ndex (.e. sum of the squared errors) for all data s almost equal to.. Next, the traned neural networ s used as a model n the EKF to estmate the same SO shown n Fg.. he bloc dagram of the estmaton algorthm s shown n Fg.. he result of the SO estmaton s shown n Fg.. he RMS error (between the and the estmated one) s equal to %, whch can be consdered as a good accuracy. Fg. shows how the elements of the estmated covarance matrx for the system nose are varyng durng the SO estmaton. B. Expermental ests Up to ths pont, tranng and testng of the RBF neural networ (n conjuncton wth the EKF) are performed offlne. Next, the desgned SO estmator s tested n the controlled and on-lne chargng processes for the same lthum-on battery. he results are shown n Fgs. -. Fg. shows the battery termnal voltage, the chargng current, the battery temperature, and the waveforms. For clarty, seconds of Fg. s depcted n Fg.. Fg.

6 Fg.. Bloc dagram of the mplemented estmaton algorthms. Z I Xˆ ˆ X F ( r ) Z I df ( r ) d xˆ yˆ F ( r ) y Σ + Q ˆ ( ),Eq.() A Qˆ Z I ˆ X State estmate update Xˆ Error covarance propagaton Z I P P G Error covarance update df ( r ) dxˆ G P P Kalman gan R x - - tme(sec.) Fg.. Varatons n the system nose covarance matrx Q usng the adaptve procedure Q Q Q Q.... estmated SO -. tme(sec.) Fg.. he desred SO measured by the Ampere-hour countng technque (dashed lne) and the estmated SO usng the proposed method (sold lne). shows the actual and the estmated SO durng the entre chargng process. he RMS error (between the and the estmated SO) s almost %. As Fg. shows, at the begnnng of the chargng process, the reflex chargng method has been used followed by the pulse chargng technque (at about SO=%), n whch the negatve pulses have been elmnated for the remanng chargng perod. Next, for testng the desgned estmator wth dfferent ntal condtons for the state varables, the battery s charged to about % of ts nomnal capacty. hen, t s separated from the charger and the charger s dsconnected from the power supply for about mn. Next, the process of chargng battery s resumed usng the same ntal condtons as f the battery were empty. he test results are shown n Fgs. -. As t s clear from Fg., the estmated SO converges qucly to the n less than. mn, whch shows that the proposed estmator s robust aganst dfferent ntal condtons. he RMS error s almost % for ths case. Fgs. and show the battery termnal voltage, the chargng current, the battery temperature, and the actual and the estmated SO waveforms. Fnally, Fg. shows the varatons n the elements of the covarance matrx Q. Varatons n Q at the begnnng are ndcatons of the quc reacton of the Kalman flter to reach the. he expermental setup s shown n Fg urrent(a) - emperature( o ). estmated SO tme(sec.) Fg.. ontrolled battery chargng usng the proposed estmator. V. ONLUSION AND DISUSSIONS A SO estmator for the lthum-on batteres usng neural networs and the extended Kalman flter wth adaptve covarance matrx for system nose was proposed n ths paper. he neural networ s of RBF type and was traned off-lne to fnd the approprate model needed n the extended Kalman flter, whch estmates the SO of the battery. he expermental results of the proposed estmator showed good accuracy and fast convergence to the actual state varables, ndependent of the chargng condtons and/or ntalzaton of the Kalman flter. One mportant pont s that the data for tranng the neural networ was collected from a brand new and healthy battery. Hence, the traned neural networ may not yeld acceptable output when the battery ages. hs problem can be resolved usng data gathered throughout the lfetme of the battery. he other soluton s to tran the neural networ adaptvely wth on-lne data. hese ssues and the effect of the battery temperature on the SO estmaton and the chargng current can gve drectons to the future wors.

7 x urrent(a) x emperature( o ) x.. estmated SO tme(sec.)..... x Fg.. seconds of Fg emperature( o ). urrent(a) estmated SO tme(sec.) Fg.. ontrolled battery chargng usng the proposed estmator estmated SO -. tme(sec.) Fg.. he actual and the estmated SO durng chargng process, usng the proposed estmator urrent(a) - emperature( o ).... estmated SO tme(sec.) Fg.: he frst seconds of Fg... estmated SO x - - x - Q Q.. - x - Q. tme(sec.) Fg.. estng the proposed SO estmator wth dfferent ntal condtons for state varables of EKF (dsconnectng the power supply for mn.). - x - - tme(sec.) Fg.. Varatons n the system nose covarance matrx Q usng the adaptve procedure Q

8 Fg.. he expermental setup REFERENES [].R. rompton, Battery Reference Boo, Newnes Publshng o., Oxford. [] S. Pller, M. Perrn, and A. Jossen, Methods for state-of-charge determnaton and ther applcatons, J. Power Sources, vol., pp.-,. [] E. Messner and G. Rchter, Vehcle electrc power systems are under changed! Implcatons for desgn, montorng and management of automotve batteres, J. Power Sources, vol., pp. -,. [] P. J. Blood and S. Sotropoulos, An electrochemcal technque for state of charge (SO) probng of postve lead acd battery plates, J. Power Sources, vol., pp. -,. [] G.. Hseh, L. R. hen, and K. S. Huang, Fuzzy-controlled l on battery charge system wth actve state-of-charge controller, IEEE rans. Ind. Electron., vol., no., pp. -, June. [] A. H. Anbuy and P. E. Pascoe, VRLA battery state-of-charge estmaton n telecommuncaton power systems, IEEE rans. Ind. Electron., vol., no., pp. -, June. [] F. Huet, A revew of mpedance measurements for determnaton of state-of-charge or state-of-health of secondary batteres, J. Power Sources, vol., pp.-,. [] S. Rodrgues, N. Munchandraah, and A.K. Shula, A revew of stateof-charge ndcaton of batteres by means of ac mpedance measurements, J. Power Sources, vol., pp.-,. [] L. R. hen, Desgn of an optmal battery pulse charge system by frequency-vared technque, IEEE rans. Ind. Electron., vol., no., pp. -, Feb.. [] M. oleman,. K. Lee,. Zhu, and W. G. Hurley, State-of-charge determnaton from EMF voltage estmaton: usng mpedance, termnal voltage, and current for lead-acd and lthum-on batteres, IEEE rans. Ind. Electron., vol., no., pp. -, Feb.. [] A. J. Salnd,. Fenne, P. Sngh,. Atwater, and D. E. Resner, Determnaton of state-of-charge and state-of-health of batteres by fuzzy logc methodology, J. Power Sources, vol., pp. -,. [] P. Sngh,. Fenne, and D. E. Resner, Fuzzy logc modelng of stateof-charge and avalable capacty of ncel/metal hydrde batteres, J. Power Sources, vol., pp.-,. [] K. Kutluay, Y. Çadýrcý, Y. S. Özazanç, and I. Çadýrcý, A new onlne state-of-charge estmaton and montorng system for sealed lead acd batteres n telecommuncaton power supples, IEEE rans. Ind. Electron., vol., no., pp. -, Oct.. []. Yamaza, K. Saura, and K. I. Muramoto, Estmaton of the recharge capacty of sealed lead-acd batteres by neural networ, n Proc. IEEE Int. elecommus. Energy onf, San Francsco,, pp. -. [] J. Peng, Y. hen, and R. Eberhart, Battery pac state of charge estmator desgn usng computatonal ntellgence approaches, n Proc. IEEE Annual Battery Applcatons onf., Long Beach, U.S.A.,, pp. -. []. H. al, D. Du, Z. Y. Lu, and H. Zhang, Artfcal neural networ n estmaton of battery state-of-charge (SO) wth nonconventonal nput varables selected by correlaton analyss, n Proc. IEEE Machne Learnng and ybern., Bejng,, pp. -. []. a, D. Du, Z. Lu, and J. Ge, State-of-charge (SO) estmaton of hgh power NI-MH rechargeable battery wth artfcal neural networ, n Proc. IEEE Neural Inform. Proces., Sngapore,, pp. -. []. H. a, D. Du, and Z. Y. Lu, Battery state-of-charge (SO) estmaton usng adaptve neuro-fuzzy nference system (ANFIS), n Proc. IEEE Int. onf. Fuzzy Syst., St. Lous, pp.-,. [] W. X. Shen,.. han, E. W.. Lo, and K.. hau, Adaptve neurofuzzy modelng of battery resdual capacty for electrc vehcles, IEEE rans. Ind. Electron., vol., no., pp. -, June. [] S. Pang, J. Farrell, J. Du, and M. Barth, Battery state-of-charge estmaton, n Proc. A, Arlngton,, pp. -. [] B. S. Bhangu, P. Bentley, D. A. Stone, and. M. Bngham, Nonlnear observers for predctng state-of-charge and state-of-health of lead-acd batteres for hybrd-electrc vehcles, IEEE rans Veh. echnol., vol., no., pp. -,. [] A. Vaseb, S.M.. Bathaee, and M. Partovbahsh, Predctng state of charge of lead-acd batteres for hybrd electrc vehcles by extended Kalman flter, Energy onverson and Management, vol., pp.-,. [] O. Barbars, F. Vasca, and L. Glelmo, State of charge Kalman fllter estmator for automotve batteres, ontrol Eng. Practce, vol., pp.-,. [] J. Lee, O. Nam, and B. H. ho, L-on battery SO estmaton method based on the reduced order extended Kalman flterng, J. Power Sources, vol., pp. -,. [] S. Santhanagopalan and R. E. Whte, Onlne estmaton of the state of charge of a lthum on cell, J. Power Sources, vol., pp.-,. [] G. L. Plett, Extended Kalman flterng for battery management systems of LPB-based HEV battery pacs, part : modelng and dentfcaton, J. Power Sources, vol., pp. -,. [] G. L. Plett, Extended Kalman flterng for battery management systems of LPB-based HEV battery pacs, part : state and parameter estmaton, J. Power Sources, vol., pp.-,. [] G. L. Plett, Kalman-flter SO estmaton for LPB HEV cells, n Proc. th Int. Battery, Hybrd and Fuel ell for Electrc Veh. Symp. & Exhbton (EVS), Bousan,, pp. -. [] S. Hayn, Neural Networs: a omprehensve Foundaton, Prentce Hall, New Jersey,. [] S. Hayn, Kalman Flterng and Neural Networs, Wley/Inter-Scence, New Yor,. [] P. S. Maybec, Stochastc Models, Estmaton, and ontrol, vol., Academc Press,. [].. Hua and M. Y. Ln, A study of chargng control of lead-acd battery for electrc vehcles, n Proc. IEEE Int. Symp. Ind. Electron., Puebla, Mexco,, vol., pp. -.