Fuzzy Controlled Lithium-Ion Battery Equalization with State-of-Charge Estimator

Yuang-Shung Lee Chii-Wen Jao

Department of Electronic Engineering

Fu-Jen Catholic University

Hsin-Chuang, Taipei(24205), Taiwan

E-mail: lee@ee.fiu.edu.tw

Keyword: Baaey equahtion, iimhrm-ion battery, bidirectional CU-convater, SOC ed", fizzy logical control

1. Introduction

Due to the popularity of mobile phone and portable q w , the issue of battery for the pomble d i i i e s becomes "&able [ I f . For the ansideration env?" t populatios a mumble and recbatgeable battay as the second battery is more popularly and ampable [3]. For the Limitr of voltage and storage capacity of signal cell of battery, baaaies m series

the mostavai!able. Because the reaction of elechuchmid and intad

impclewe of eachbaaayisnotahvays the same[4], so the overdarge and deepdischarse pmblem ofcm happens m saies connectedbatteries shing. 'Ihe ovadmge anddeqxlkhatge uill cause the risk of pamanent damage and shorten the life cycle of baaay [3,4]. For impravinS the M o n descn'bed above, we often use battery qualiz" systw to reduce ih

connected for ma"g the supply of voltage and capacity is

unbalancing of cell voltage and extend the life cycle of banaies shing. In recent yeag lea&acid battery, alkaline baaery and

Iithkmion baaery are commonly used for portable utilities and electric vehicles [SI. As for lithium-ion battery, it has the goodness of non-memoly e€&, high w o w cell voltage, low pqndatim low se l fdkhge rate, and high power densay m vohnne and high energy awsity of weight The density of p o ~ ~ f m ~ ~ ~ - i o n b a t t a y i s ~ l e a s f o r l ~ - ~ d b a t t e r y , one and half for alkaline ones, so the lithium-ion battery bearmesthenewtopicofresearchforthe~ndbattery[6l. But for lihim-ion battery, overcharge will cause vaporized in the intemal of battery, which increase the pressure and Ouse explore damage, deepdxharge will damage the intend brine, which harms the battayor make the battery short So the colmol method for cbargingclida&g and protecfion of the lithium ion bathies string is vay important

The proposed battery equahtion scheme is designed by using bidiwtional C&-cmvate(7ll, The CU-cmverter is a buck-boost awater, controlling the owff states of the switch to hme the duty cycle, which can mate the fimhnal abiity of buck or boost recharge. In h i s way the equalization system will have the bidirectional a b i i m the fuu duty cycle. Therefore the proposed bid i red id equalvation has m a y advantages such as hi& equalLation &ciw, enagy t r a m f d o n dkctionismmUableandmdular&ignapmach [SI.

?he methodto evaluak the chatgekhatge efficiency, which is universal accepted for most mearcha, is the State+f<harge (soc) method as the refewce forthe dua!ion ofrecharge efficiency. There are two ways to decide the SOC value, the coul~untingdcdandmtetnal impendencem&od[9].

From the charge and ddmge anve of the Mium-ion baaay . The &ciencyof&qd"ge is also a f f e c b e d by the hq", between batteries and the dmtion of charge.'-. To predict the equalkd mnml faaors is vay complicate, by applymg the limy "I method, the mml ~ c a n b e ~ t h e f m y c o n t r o l ~ i s p m p e r f o r ~ ~ t h e l K m l i n e a r k ~ m o f b a a a y e q . d l a i q d u e t o ithasmoreadaptiveandmdbetta~ciencyf~nonlinearmnml. In this papa, fizzy logical meMod is used to edmate me

SOC value of each- and @ke the Sheprd's model of

* 0-7803-7952-7/03/$17.00 0 2003 IEEE. 4431

baaay to decide the in ted of each batterY[lO]. Daive the satespace equations of the b i d i t d i d e q a l m ~ o n scheme as the control plant Applins the estirrated SOC value and voltage Merence between banaies as the two control input h%m, and he coniml plant adjust the duty cycle d o of the switching, to me the c w e and d w h g e rate, the voltages and SOC of each battery can be eqnalm m balance, d e n the voltage & of baaeries comes the same,' the equalizatlonprocgs will stop, the result shows that the SOC and voltage of each baaay are al l inbalance and at qual vaiue, so it is a biditdional and bigb efficiency esualimfion system

The PIU@ mnhul methcd has the advan- of bidirectional e n q y bansformation of cells, quickly charghg rate m the beginnin& stably s" to the final average value and without ovmhatge or nuder discharge. It e" that the voltage of each battery during the chargmg pnress is ahvayx in safetyrange.

The statespace equation of bidirectional baaay esualjzer with the Sb@s battery model is derived for d"g the battery eqaluahon conimller m section 2. Io sec t id , the limy logical coniml of SOC estimator is designed using the volhge and cbarge anrent of each battery to establish the membership functions, with these functious ad f m y d e base ,we can predict the SOC value of each banery dming the equalirmg process. Section 4 presen~ the comparison between the theoretical S i o n and expimenlal resulo; and d y s i s the efficiency ofthis lnoposed system

2. State-space model of battery equalization

ICE2

Fg.1 a l g e systan of baaay string with the battery equahtion

Fig.1 shows the charged configuAon of the stack battery with the ICE (individual cell equakm). The I= eqnalm the cell voltages bztwem two battery cek, it can balaace the voltage Mmce behveen cells and insure all the bgaery wo&ing m safety and manage &e enwin the shing.

lllae are many types of equaljzas, for the sa* enagy 'e t lpeofequahm o " p i o n ma-

is most p r e f d for engineas The nond&@iiive eq" can be classified mto two types the lmidirediod and

. .

bidirectional, the latter has many advantages such as a higb e q n a k a h efficiency non-dm@ive anrent d i v e , bidirdonal energy t"afiw capability, and a mcdular

The j m b i d i t d i d baaay equalmr p"kd as m Fig.2, the fimaion of bud-bost can create by wntrohg the dof f

approach

stateofMOSFET~Qi and@.

4%

I

!=

Fig. 2 Bidirectional COK converter

Assume that the bansistors and diodes io F i g are all ideal devices and the bidirectional converta is d e s i i for wo&ing in oontinuous i n d n c b r ~ t modeL ne equivalmi circuit of bidirectional battery equaliza for V,>Vwl can be represented as Fig.3, while the Tm state, it means Qlis tumed on and Q is med 0% at the Ta state means the Qlis med off and @ is turned OIL

Fig. 3 Equivaleut circuit of a bidirecfid equakm forV,,>V,

The confinuous of icdudm -t will cause 4 hnn on Tuning the TJT.,,, state opedon, w l m the voltage of V, is high= than V,,, the energy of &onger cell V, can be

4432

h a o d d to the weak cell V, that is the buck convertm W o n ; on the con-, when the voltage of V,, 1s lugher than V, the e n q y of shunga cell V,, can be transferred to

The dynamic equation for the equivalent circuit for codtion v, that is the boost converter hctiolL

as V, ZV,, &Ton state can he expmsed as:

(3)

forj=l,2,. . .p

Smlarly, the dynamic equations for the equivalent circuit at T,state canbe expresedas:

(9

Take Shephds model of battery into consideratioq the tRminal voltage ofbaaery during ch;nging can be eqn-esd as:

Vbj = E , + IJRbj -i jRbj forj=lJ, ...p (9)

Vbj = E, + ISRb - i,R,

Vbj+l = E,,, + I,Rbj+, - ibj+lRbj+l

Using Eq.(9) to replace the V, and V,, while

(10)

(11)

and

To set the switchmg operator variable U , while at T, condition U =I and at Ta condition U -0 then the dil€erena form equalions above of Eq.(l)-(3) and Eq.(4)-(6) can be combined together. Ifreplace the presentaton of V,, and V, m above equations,

then the new *space equation with extRnal CLment source of bidinxiid Wfay quaker M e V,,>V, can be eqmwd as:

Where V, ,Fsj &,R, andlqare the baminalvoltage, spenfied intemal voltage, chgddischarge m t mtemal “e, and p ! a r i d ~ o f t h e ~ c e U , ~ e l y . ’ l h e S C € , i s t h e siateof.charge of the jth cell. setting a new resistmce variable of

thebaaqwhm R, = ( R j +kj-)forj=1,2,...~

nerefore€Gq.(7)0nberewrittenas:

1 socj

Vbj =E,. -ibjRbj fork1 ,Z,...p (8)

If applied e x t e d cllrrent source to cb;uge the bamay while the ament is,& adding this cwent source in@@), then the tRminalvo~ofthechalgingbaaeryonbeorpressedas

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By the same pceduz, the equivalent Circuit of bi.directional baaay equakm for Vb<Vwl can be plotted as Fig.4. S m , the siatespace quaiion with exmnal anrent soulce of b i d i m f i d Cijk-cmv& while Vb4w, can be expmsed as:

x = A , * + E , (13) where

A , =

and

t J for j=l,2,. . .p

et i is also the switchmg operator variable for the equivalent circuit of bidimtional battery e q d m for Vbcwl in Fig. 4, at the T, condition U =1, at the Tflndkion U 4. Here the tumid voltage of the bauery of V, and Vwl are dehdas

-

V, = E, + I , R, + i j , Rbj (14)

= "sRbj+l + i j2Rbj+l (15)

compared Fig. 3 withFig. 4, It is clear to see thatwhile inFig 3 at T, condition, it is the T& ooditicm for Fig 4 m the "e. So the switch operatorvariable ofeach circuit has the re- that is u=(~-ii), with the relationship, finding that the element &for(i#j) in @d A& & ( i # j ) in [A&~.w has a rek&msbip that for &= &, ( i# j ) , an*Bb

F m the res&, cleariy Eq.( 12) and Eq.( 13) has the bi-hear relaiionslnp. By applied the sign fimc!ion, the termioal voltage of chargins battery m the two conditions V d v , or Vb<Vw,, Eq.(lO),(ll) and Eq.(l4),(15) can be d x e into the compact form like

A =

- and

B =

mnditions are opposite, so Eq.(l8) &lied for both c w g conditions as forV,,>V, orVbl<v,

For this paper analysis there are three batkxies stack in series(n=3), the --space equations present^ as the compact form:

I. J

I o

i o

0

-s,%, r, c,

-s,%, r,

--U -

0

-@-U)

r, - 0

0

0

0

-s,%,

0

0

0

-(l-w)

s -

--w -

4434

B =

L4 0 J wbete Si=S!P f?bi-vd and &@ &-vt~)

Here must be notice that the expression of the taminal voltage Of the second bamvbz, betweea the first and thinl b a q will be changed into the new @on as by using the KVL

'b2 = 's2 + ' S R ~ Z - S,ib2Rb2 -s2ib3'b2 (20)

That'sbecausethemiddlebatte~~willcharge/~behveen the first and third battery

As the remit, Eq.(19) is the slatespace equalion for b id i r ed id equaliza with extemal m t s o w as qudimtion system for baaaieS &k m Series acd suiiable for all voltages inequality mditim in consideration.

3. Fuzzy logic controlled SOC estimator

Inhis paper, by using the bidkdonal baaety equaliza for the battery shings, to coniml the duty cycle and tune ihe chargddishge rate. During the equalidng process, the voitage ofeach cell is mtinuous changmg and the charge rate must go with the changing voltage. Ihe voltage value is related to the value SOC, the SOC is the state index of-, which means theamountofemgyinsidethetnitery

Once the SOC is meamrd, the scite of- is known, and thechargingratembetunewahthepredctedSoc.

To measure the exact battery Soc is vaydifl id especiauY for an electrochardcal device. Based on this amcept, chose tbe f k y logical c a n t r o l o d d t o estimate the SOC will be ahstandandprogermemodasmnpamlwithotherdcds.

?he Fu: consists of the rule base, inferem engine, and de- Inhis paper, tbe FLC input

variables are the measLDiog voltage and the chargmg ament. Ihe SOC is related to these two qualities ofthebattery [I 11.

FUU"Ore, the two decisive inputs for the FLC, voltage is more dominant for the SOC it is clear to see that limn the c w m e characteristl 'a a w e of MRIATRI lOAHWium-ionbaaery [12].

To enme a safe region for the voltage specification during esualidng process of the baitery skin& the allowable balancing

baaey isde6nedlimn2.8Vto 4.N 'Ihe second decisive IC@,

equali?ing current is c"dy small, the safe range for the

voltage inkml lirrdtttion for the MRulTRI l0Ah MiulE-b

cimgeh/discharge m t is abut0.lAto 4.0A ?he first step ofFLC p" is to fuzz@ the iaputs and

create the "I+ fimctions, for exanrple as for the first bat&ay V,, is shom in Fig. S(a) and Fig.S(b),and the membership iimaion of o w SOC is sbm in Fig. 6.

In Fig S(a) and S(b),the "ring voltage V, and b a are divided into five subsets and described each adsets using live lingujstic variables, ie. VL(vq h e ) , L&w)"ediWX.=Qs0, and VWJ~IY and defined the degxe of for each subset in Gaussian "bershp, won .Fig@) shows the mRnbership fimction of the esthrafing ou@a SOC,

Ihereaun to use g"ftype is to avoidodatbnbuse it's a rmre s" disaibution method to define the degree of

memory for the defim@ pcocess, which on speed-up the

fimdon pmduce m tk same &deration, but it needs notice here,Wbytakingabsolutelyvalueofi+therieedsfor"ny alsocankreduced

"hip wcq another reasDLl is mat it needs less

e s t i m a t i n g s o c w a h F L c p r a p s s . s o Q e s ~ ~ ~

4435

................................................................................................... Fig. 7 Block diagram of the FLC SOC estimator

The FLC consis@ of the d e base, inference +e, M d o n , and delizdicaiion, as shown in Fig. 7. n e steps to create aispvalue of SOC value withFLC SOC estimator is: ( l )Topu t theV,and~ in tOthe l i zd ie rmge tUB~)and

(2) To use the d e base and inference engine to get the U&). (3) To ob& the defwjlier U&) and getling niSp value of SOC

The estimating d e base of the FLC SOC estimator for linguistic variable is shown in Table I .

UA(x),rqx!ively.

value.

Table 1 le

In this FLC SOC csdmator, h m are (5x5) t i m y conml rules ~n the d e basc for e3ch SK,, as mn chwk hum Table I , thc K& rules m premed 3s follows:

&: IfV, lsVL and iw is VS hen SG€, isVL for-12,. . .,m

The algorithm used for the infmce en@ and dch& in this proposed FLC SOC csrimator is the m - m m composition and the center of gravity mhal The s y t m d c design p " s and resulb for thepmposed FLC SOC ewimaWr are SUmmarGal as follows: Stcpl . Ob& the nue d u e w, for be ith mput mcmbmhip

b d m for x and the jth mput membership function for Y ""g

w,= min {pAt (x). pB, ( y ) } fori=lJ, 5 and j=lJ, 5 (21)

~tepz. calculate the fuzzy output value, pou (z) using w,

and the km output m a n b h p fi" according to

& d e , pok(z)

poy(z) = min{a,,,pok(z)} fork=IJ. ... (22)

step3. DetRmine b e fuzzy set foroutput& pou, (z) uskg

1 1

R , = ( R , + k . - SOC ,

And the mult of SOC " t e d v a h i e cauk displaiedwith a& or the fuzzy surface. Fig. 8 is the result of t imy surface of soq.

. . : ,....) ..., . . i . .

Fig. 8 Fuzzy surface of SOC, w& respecttov, and 4

Fig. 9 shows the miavpnx" based battery management system @MS) in this siudied The seos01 senses the cell voltages and battery chatging idischarge CLmenf which is the V, and & and " f e r these dah to the FLC SOC estimator mat infmduced in this sedim, to mate the SOC value of ea& battery, and use the SOC vaiue applied to the hi-4 battery qualidm system to get the V h of%, also hansfer mev, ofeachbattery ceU to me qdi" syst~n in orderto decide the witch opaator variable U , to create a PWM control signal which lune the charge/&hge rate.

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q " o n process is a safety and to prevent damage to the battery. The SOC plot of !his simulation process is also shown in Fig. 13

I........ ..................................... F*d Microprocessor BhS

.................................................

Fig.9 'The pmposedbattery equahmwith mieop~lcessorbased

battery""

4. Simulation and experimental results

In order to venfy the designed d t s discussed above, a computa s i " and expimmts are performed for a bell battery stack with the proposed qAiza!ion scheme W i m t h e S O C e s t i m a t O r l h e c k u i t c o n i i ~ o n o f ~ t is sham m Fig. 10, Qe ICE meaDs w d n a l and mteuigm cell equalization system, the B.MS is composed of mi- 8052 which ccoltain FLC and equalize contml si& generator

T- ~~~~~j v., =

M SPt- II

c.4 - sava

Vu-=

Fig IO Fqm"l installation

The battery for !his experha is the MRVITRI IOAH lihim-ion battery, the M a l voliages of the batteries are

Applied the des&@ FLC SOC esthnator and b i d k h a l bamxy qAiza!im system we proposed use the Matkb S i , the simulation resvlt of cells voltage mjjeaolv is shownmFig. 1I.Theexpimenbl~isshovininFig. 12. 'The s W o n result is very close tothe experimentaIss.&s, t h e e n d r e s u l t F o f t h e b a t t e r y v o ~ e m j ~ i s ~ ~ e v ~ t o ~ e average value ofthe t h e cells vohge, and when it reach at the average- the equalidon process will came to stop, so it's a betlerwayto avoid0Vach;nge orlmdacharge and mm the

vbl4.oy vbl=3.8y andv&2.9v,

"I/ m 1.9

I I

TWMSSC) 1 .o 2.0 3.0 4.0 5.0

Fig. 12 FxpenmentaI resultF

505 OF --E-"

\ - - ~._.ZO" i .... --~ y-.\-

..-. . 0 8 .........

3 0s 0 1

,..,- 0 - ..... 0 2 "

0 - 0 D 1 0 2 01 0 . 0 5 0 s 0 ,

Fig13 SOCsofBatteydmingeqdizing

FmmFigll and Fig 13, whi& show that the change trendy of cell voltage and SOC for e v q battery is the same, it implied this FLC SOC, estimator is a very acclllitcy med~cd for esthratioghe SOC. Ha, musZ mtice that the Vu curve and SOGcurvemFigll andFig.l3,haspiecewiSeflatperiod,the reason is the eqdzingprocess, when the energy m vb, is h a n s f d to vb, ,ad at the same tine, the enetgv mV, is also M e n d to Vu, but the diffaence value of voltage behueen vb, andv, is small as comprnedwith the d i J € m value of voltage between Vu and V,, which forced V, g m down alter aperid of flat

To prove the FLC SOC estimata equahmion systan is bidkectiod, exchauge the voltage value of for

result is shown m Fwl5 No w&, it's a bi-dktiod epIhtb"asmmparedFig. 1SwithFig 11.

Inboth dimtiom of charging pmcesg the propaties of each

TIUEISES,

v b 1 = 2 . w p 3 . 8 v and V&.o\! and simulafon again the

4437

equah direcfion are the same, a c h imply it's a stable and ouManding ecrualizafion system, eqxdly for nonlinear elechic device.

_r- 3 ,/-

D 0 1 0 2 (13 0 . 0 5 0 6 0 7 0 8 0 s 2 8

TlMElSEC,

Fig. 1 5 Cell voltage f+ctory of batteries dming equabhg

5. Conclusions

A battery &tion scheme with the limy controlled SOC esfimator was proposed for bidiredonal baaehy ecrualizafion of a series c o n n d battery $zing to extend the cycle life and gu;nantee the cbrpgidischasging safety opaating of ihe lithium-ion batteries. A state-space model of the h i d i r e d d baaRy on scheme wiih the battery model was derived for designed the f u z y SOC ' s d m k x A novel approach was perfonned to design the baaery equahAon system wiih the inteuigent soc esfimator. CoMputer SimULzon and expimental results show the advantage of.the intelligent predicted equalldns perf- of the lifhim-ion baitay string.

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[q K.S.shau5, L.RChen, ICS.Wong, LS.Chen:' Fuzzy

Equaljzing converter for serial ch;nging of Long Badery

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[7].2 Zhang, S. Cin: ,"A High E5ciency 1.8kW Baaay !3qdi"', Applied Power Elechunics conference and ExpositioI& APEC 93, Cod- Roceedmgs, IEEE Eighth Annul, pp221 -227,1993.

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