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53
Designo aSimple Ampe e‐Hou me e
Applica ioninS a e‐o ‐Cha geEs ima ioninLead‐AcidBa e ies h ougha
Mic ocon olle
LluísFa é*1,LluísClosas2,PauCasals3
Elec onicsEnginee ingDepa men ,Elec icalEnginee ingDepa men ,Facul a deNàu icadeBa celona,
Uni e si a Poli ècnicadeCa alunya–Ba celonaTECH.Ba celona,Spain.
*1[email p o ec ed]s;2lluis[email p o ec ed]du;[email protected]
Abs ac
Inanyapplica ioninwhichwo kingwi hba e iesisamus ,
heknowledgeo heba e ies’s a e‐o ‐cha ge(SOC)isa
undamen alpa ame e o anyone,soi de e mines he
emainingcapaci yin heba e y.The eexis se e al
me hods o hees ima iono hisSOCinLead‐acidba e ies;
howe e ,when he equisi eso hemeasu ingme hodmus
o e ,besidesp ecisionand eliabili y, hepossibili y o
in eg a e he esul sin oanau oma izedsys em, he
Coulomb’scoun e is heme hod ha p e ails.Thispape
p esen s, hen, hedesigno asimple Ampe e‐hou me e
basedlead‐acidba e ySOCes ima ingsys em.Suppo ed
byp e iouss udiesin he ieldo SOCes ima ioninHyb id
Elec icVehiclesandbyexpe imen al es sca iedou by he
esea che s, hemodellingo hesimple measu ingsys em
hasbeenpa ame e izedby ollowingPeuke ’sEqua ion,
anda e wa dsi hasbeenin eg a edin oada aacquisi ion
andp ocessingsys emdesigned h oughaCSNX25cu en
senso andalow‐cos andlow‐consume16F877
mic ocon olle .The undamen alconclusiono hispape is
ha ob aininganaccu a e esul whilees ima ing heSOCo
alead‐acidba e ywi hansimple Ampe e‐hou me e
de eloped h oughamic ocon olle basedsys emis
achie ablebu onlyi heusedmic ocon olle holdsenough
memo y oinclude hewholeda a ea men algo i hms.
Keywo ds
Ba e y;SOC;S a e‐o ‐Cha ge;Mic ocon olle ;Ampe e‐
Hou me e
In oduc ion
Inanyapplica ion ela ed oba e ies,p edic ing he
s a eo cha ge(SOC)isnecessa yino de o
de e mine he emainingcapaci yin heba e y.
Ine e yship,asinanyindus ial acili y,ba e ies
supply heeme gencypowe obackupsys ems.They
ep esen , hough,akeycomponen o he essel’s
engineandna iga ionsys ems.Ba e iesmus always
bewellmain ained, ullycha gedand eady o any
eme gencyoccu ing.Knowing heSOCo aship’s
ba e yis hebasiso anyba e ies’bankmain enance;
andachie inganau oma icme hod op edic his
SOCand oapplycon olledcha gingcycles o he
ba e ies, ul ils hewholeba e ymain enance
p oblem.
The ea ese e alme hods oes ima e heSOCinlead‐
acidba e ies[1][2][3][4]:elec oly e’sdensi y
measu ing, ol agemeasu ing,Coulombcoun ing,
in e nal esis ancemeasu ing…The i s o hese
me hods, heelec oly e’sspeci icg a i ymeasu ing,
is heonlyme hod ha canbenamedasanon‐
es ima ingme hodbecause heelec oly e’sdensi y
e lec s he ueSOCo helead‐acidba e y,soi
shows hea ailable a eo hechemicalsinside he
ba e y.On heo he hand, hisme hodwouldbe
annoying obein eg a edin oanau oma icsys em
due o heneed oacqui e,o e endesign,asui able
elec onicdensi ome e .Theo he h eemen ioned
me hods,despi ebeinges ima ingme hodswhich
onlylead oanapp oxima eSOC alue,a emo e
p one obeau oma ized.
Focusingon heCoulombcoun ingme hod,as
sugges edby ele an s udiesin he ieldo ba e y
SOCmeasu ing[5],speci icallyinHyb idElec ic
Vehicles(HEV)ba e y echnology[6][7][8], hispape
p esen s hede elopmen o anAmpe e‐hou me e
solu ion o hees ima iono heSOCinlead‐acid
ba e iesbydesigning hecomple es uc u eo he
SOCes ima o inamuchsimple way han he
p e iousci a ions;ob ainingamo e es ic edSOC
measu ing ool ha ,howe e , e eals hekey o a
u he de elopmen .
Fi s o all, hema hema icalpa h, ollowed o
de e mine heSOC,willbep esen ed.Then, he
designo heelec onicci cui sneeded oacqui e he
da a om heba e ies,besidessomelabo a o y es
esul s,willbedesc ibed.Thenex poin will ocuson
hede elopmen o heso wa ep og ammedin he
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mic ocon olle .Toconclude hispape ,ac i ical
e isiono he esul sob ained om hep o o ype’s
es ingin helabo a o y,willbep esen ed.
The Ma hema hical Model
In1897,W.Peuke exposed he esul so his
in es iga ionsonlead‐acidba e ies.In hepublished
pape ,i was e ealed ha his es shadledhim oan
empi icalequa ionwhichlinked hedischa geo he
ba e ieswi h hei eala ailablecapaci y[9].
This o mulaisknownas hePeuke ’sEqua ion:
IC n
(1)
BeingC he ealdischa gedcapaci y,I hedischa ge
in ensi y, hedischa ge imea heI a eandn he
Peuke numbe .
ThePeuke ’sEqua iono e ed hepossibili y owo k
wi hama hema icalmodelwhich ollows he
beha iou o ba e iesinadischa gecycleclose han
hedi ec ex apola ion omjus Iand .Thisn
numbe , hen,isacoe icien ,unique o eachba e y
andsligh ly a iable h oughi sli ingand
en i onmen alcondi ions,whichb eaks he aux
linea i yin heba e y’smodelandapp oachesi s
beha iou oamo eexponen ialwo k.
Following hePeuke ’sEqua ion,so,i becomes
possible oob ainane alua iono heSOCjus bya
eweasycalculuss eps.
Knowing, i s o all, ha hee iciency(E)o aba e y
is unc iono C and heu ilecapaci y(C)[3]:
n
nn
I
I
I
I
I
C
C
E
1
(2)
Then, heSOC o adischa gingcyclecanbepu on
he o mulae:
m
n
o
m
o
C
IC
C
CC
SOC
100100
(3)
Inpe cen age.BeingCm hemaximuma ailable
capaci y om heba e yandCo hecapaci ybe o e
s a ing hedischa ge.
Whe easinacha gingcycle, hesamepa hmus be
ollowedbu makinga ewaddi ionalconside a ions.
IECECca )2())1(1( (4)
So he ea econside ed hecha ginglosesdu ing he
p ocess.
m
o
m
ca o
C
CEC
C
CC
SOC )2(
100100
m
o
C
IEC
SOC )2(
100
(5)
BeingCo,in hisequa ion, hecapaci ybe o es a ing
hecha gingp ocess.
Finally, hen, hemainequa ions ocalcula e heSOC
incha ginganddischa gingp ocesses h ough he
de elopmen o hePeuke ’sEqua ionha ebeen
ob ained.Recapi ula ing heSOCshows obein
unc iono I, ,n,Cm,CoandE.
Andbymeasu ingandcalcula ing hesepa ame e si
ishow heSOC aluewillbe oundin hispape .
Howe e ,i shouldbewa ned ha n,asanumbe ha
pa ame e izes hechemicalbeha iou o heba e y,is
s onglydependen o en i onmen alcondi ionsas
empe a u e,aswellaso heagingo heba e y.So,
anaccu a ecalculuso heSOCshouldinclude
co ec ing ac o s o ,a leas , empe a u eandaging
[3][10][11][12][13].
Due o echnicalbounda ies, heseco ec ionswillno
inallybeimplemen edin hisdesign.nwillbe, hen,
calcula ed o eachoneo heba e iesand ea edasa
cons an .Howe e ,wha hee ec so empe a u e
andba e yagingin ol eshouldalwaysbepu in o
conside a ion.
The Ha dwa e Design
I isassumed, hen, ha o eachaSOC alue he
ope a ingpa ame e sin(3)and(5)mus bep e iously
known,and hekeyp ocess oachie e hee alua ion
o heSOCis hep ocedu eo measu eand
calcula iono hesepa ame e s.
I hea en ionis ocusedon(3),i canbeeasily ound
ha bo hCmandncanbeconside edasgi en
cons an s o aspeci icba e y,whe easCoisadi ec
esul o heimmedia elyp e ious
cha ging/discha gingp ocess.Then, heonly wo
pa ame e swhichdo eallymus bemeasu eda eI
and .
Whilee alua ing(5), he inalconclusionbecomes he
sameasabo e.
The e o e, hedesigno heSOCe alua o mus
ollow wopa hso de elopmen :Ononeside,a
de icewhichisable omeasu e he alueso Iand ;
On heo he side,ap ocesso whose askwillbe he
in eg a iono all hegi encons an sandmeasu ed
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55
aluesin o heequa ionso SOCcalcula ion,(3)and
(5).
To ul il he i s o hesegoals,i becomesnecessa ya
sensingde ice.Ino de op ocessall hesignalsand
da a alues, he eisacompulso yneedo a
mic ocon olle .
PIC16F877
ThePIC16F877isalow‐cos andlow‐consume
mic ocon olle [14] ha caneasilybein eg a edin oa
sys emlike his.
Wi hi sco espondingde elopmen boa d,i can
ecei eand ansmi da a,soi hasa8ga es
Analogical/Digi al(A/D)con e e ,aLCDcon olling
po andapo ocon olex e nalin e up ions.
ThePIC16F877can, hen,de elop hemaindesi ed
asks.Jus by ecei ing heda ao I h oughi sA/D
module,i could heo e icallybep og ammed o
calcula ein e nally heelapsed ime, ,while he
measu ingp ocessoccu s.Then,allnecessa y
measu edda acanbeob ained.
CSNX25
Ino de omeasu e hecu en and ansmi heIda a
o hemic ocon olle , he eisaneed ouseacu en
sensingde ice.
In hisspeci icdesign, hechosensenso is he
CSNX25[15][16],abidi ec ionalmagne o esis i e
senso ha deli e sanou pu cu en p opo ional o
ameasu edIup o25A.A angewhichgoes om–25
o+25Aisadesi ed ange o ap o o ype e siono
hedesign,and hebidi ec ionali yo hesenso sui s
pe ec ly oaSOCcalcula ingp ocedu ewhich
seg ega es hecha gingcycle om hedischa ge.
The16F877A/Dmodule,howe e ,onlywo kswi h
posi i e ol agesignal alues,soi u nsnecessa ya
i s con e sion om hep opo ionalcu en signal
emi edby heCSNX25 oap opo ional ension alue.
By ollowing heda ashee indica ions[15], his i s
s epcanbedonejus byin eg a inga esis ance
be ween heou pu pinso hesenso .
Knowing ha wi hapa allelconnec iono he
p ima ypinso hesenso , henominalou pu cu en ,
wi h25Ain hep ima y,willbeINou =12.5mA, hen
wi h hesugges ed80Ω esis ance, heou pu ension
alue eaches1V.
Howe e , hisonlysol espa o hep oblem.The
bidi ec ionali yo hesenso iss illap oblem,soi
gi esanou pu angeo –1 o+1V.Andnega i e
aluescanno bep ocessedby he16F877.
Ino de oob ainaposi i e esponse oall he
measu edcu en alues,i isnecessa y he
de elopmen o asignalp ocessingci cui able oadd
a ol agele el o heCSNX25 ensionou pu .
SignalP ocessingCi cui
Theincompa ibili ybe ween heou pu signalso he
cu en senso and heanalogicalinpu so he
mic ocon olle has es ic ed hedesign’s
bidi ec ionalope a ion.Howe e , hisbounda ycan
beb okenby hein eg a iono anin e media esignal
p ocessingci cui able ocon e heCSNX25
emissionsin oa aluableinpu o he16F877.
Due o hemainp oblemwhichis henega i e alues
o ensionwhileusing hesenso omeasu enega i e
cu en s, hesolu ionis headdi iono a ol agele el
o his ensionou pu ha makesall heou pu s
posi i e.
Ino de oob ain hissignalp ocess, hemo esui able
ci cui isanins umen a ionampli ie wi ho se on
heg ound.Byadjus ing hiso se alue o he
desi ed,wo kingwi hnonega i e alueson he
ou pu becomespossible.Mo eo e , hegain(G)o he
ins umen a ionampli ie canbealsoadjus ed o
inc ease heou pu esolu ion.
So,i hedesi edmaximumou pu angeis ixed
be ween0and5V, heidealo se becomes2.5V.
os VGVV
5.2 (6)
Andbyknowing,as oldbe o e, ha heo iginal
ensionou pu aluewasup o1V, hen,Gcanbese
up o2, oob ainawo king ange om0.5 o4.5V.
FIG.1SIGNALPROCESSINGCIRCUIT
2
3
1
12
2
1R
R
R
R
VV
V
G
G
s
(7)
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56
2
20
102
1
5.2
12
k
k
VV
V
VV
V
G
o
ss
No ice ha a ollowe o he2.5V e e ence ol age
hasalsobeenincluded.
Andso, he inal esul so hesensingci cui ,as es ed
in helabo a o y,lead o he ollowingg aph.
FIG.2SENSINGCIRCUITCHARACTERIZATIONGRAPH
Whichshowslinea i ybe ween–20A o20Aby
ollowing henex equa ions:
63.33735.1 sp ima y VI (8)
79.328314,1
_ snega i ep ima y VI (9)
I isonlynecessa y obeconside ed ha (9) esul
mus bealways ea edasaposi i e alue,becauseo
16F877,asin he endingshownbelow:
FIG.3SENSINGCIRCUITCHARACTERIZATIONGRAPHIN
PIC16F877
Becoming(9), hen,in he o hcomingcalculus:
79.328314.1
_ snega i ep ima y VI (10)
The Mic ocon olle ’s P og am
P esuming ha hemeasu emen o Ihasbeensol ed
h ough hedesigno hep esen edmeasu ingci cui ,
henex s ep obe akenis oob ain hemissing alues
osol e(3)and(5).
Recapi ula ingCmandna especi iccons an alues
o anyba e y,Comus becalcula edinsi ua e a
cha gingo adischa gingcycle,whileEiscalcula ed
h ough(2)and, inally, is obeob ained h ougha
in e nalmic ocon olle calculusbyusinganin e nal
ime o he16F877[14].Onceall hese aluesha e
beenei he acqui edo eadascons an sin he
mic ocon olle sp og am, heya ebeingope a edin
o de oob aina inal esul whichleads oaSOC
alue eadable o heope a o .
Thesea e hemain askso hep og am,asshownin
he ollowing able:
TABLE1MICROCONTROLLER’SPROGRAMMAINTARGETS
ANDTASKS
Objec i es Ac ion
Recei e ol ageinpu signal
h oughanalogicalinpu s
Ac i a eApo
Iden i yoneApo ’spinas
analogicalinpu
Ac i a e ime cycle
De inecons an alues
Da ap ocess
In e nalp og amo he
mic ocon olle
Show esul s h oughLCD
Ac i a eDpo
Iden i you pu pins odeli e
ou pu message
Theseac ions obe akenino de oachie e he
objec i esmus beincludedin hedesigno he
so wa ep og ammedin he16F877.Ino de o
de elop hisp og ammingdesign,i isused he
so wa e o isualp og ammingo mic ocon olle s
Niple 5.2.[17],whichallowsa isualde elopmen o
hesolu ion h ough lowdiag amsp io o he
con e sion oassemble code.
A lowdiag amschemeo hep og amisp esen ed
nex :
FIG.4MICROCONTROLLER’SPROGRAMBASICSCHEME
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No ice ha somein e media eac ionsha ebeen
addedino de oapp oach hescheme o he eal
s uc u eo hep og am.Oneo hemos impo an
poin sis hecalculuso Insoi mus bedone h ough
Taylo se iesin hemic ocon olle :
...
!3
ln
!2
ln
ln1 32
InIn
InIn
(11)
And he e o e he emus alsobecalcula ed alues o
heseloga i hms.Howe e ,in hiscase, hechoice
madeis oassign aluesinama ix ype ableo
a iables o di e en alueso Ibe ween he
ope a ing ange.
Thep og am, hen,mus es ima e he alueo Inby
usingadoubleapp oachcalculus:Fi s o all,aTaylo
de elopmen ,wi hsix e ms;secondly,loga i hm
alueswhichdon’ i exac ly he ue alues.These
es ima ionsnecessa ilylead oane o on heSOC
calcula ion.
Mo eo e ,aswellas he16F877canno calcula e
loga i hms,o wo kwi hnega i enumbe ss o edin
a iables,i alsocanno p ocessdecimals,sowo king
wi hmul ipleso hedesi ednumbe sbecomes
necessa yino de oachie eaminimum esolu ion.
Howe e , hesenumbe scanno be oohigh,ei he ,in
o de o i egis e s.Fo ins ance, heIcalculusasa
esul o (8)and(10)becomes he ollowing:
100004063.33735.13090 ssp ima y VVI (12)
100004079.32831.13090 _ ssnegp ima y VVI (13)
Ano he ocuso e o .
Resul s and E o Analysis
In hep e iouspoin so hispape , hedi e en pa s,
o modules,o heSOCes ima o ha ebeenp esen ed.
Finally,in hislas i em,i is obeshown he unning
beha iou o heassembledp o o ypedu ing he es s
ca iedou on helabo a o ybyusingaschemesuch
as his:
FIG.5SOCESTIMATORWORKINGSCHEME
In his ealcase,whilede eloping helas s ageso he
16F877’sp og am, he i s bounda yis ound:a
memo ylimi which o cesalimi in henumbe o
p og amlines.Thisp oblemisdue o he
mic ocon olle ’scons uc ion,bu i couldbesol ed
byusingap og ammingso wa ewhichallowed
p og ammingbyin e up ions.Ra he han heNiple
5.2case.
Themainconsequenceo hismemo ylimi is
obse edin hecalculuso Inand,mo es ongly,in
heapp oxima iono heloga i hms.Asi hasbeen
exposed, hesema hema icalope a ionsneedlo so
ac o s oob ainanes ima ed alueclose o he eal
one.Andwi hamemo ylimi i becomesimpossible
ode elop hecalculus.
Keepingupwi h helabo a o y es s, hen, o a95A∙h
ba e y,wi hn=1.26, he esul sob ainedin he
in e nalcalculuso hemic ocon olle o SOC e eal
he ollowingwo kingg aph o adischa gecycle:
FIG.6SOCERRORINADISCHARGECYCLE
No ice ha hee o g owsas he imeo unning
inc easesdue o headdi iono hee o in he
calculuso hein e media ecapaci ies;aswellasi
g ows o highe cu en alues,whichisaeasy
p edic able esul .
Andin heg aph o acha gecycle:
FIG.7SOCERRORINACHARGECYCLE
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58
Again,e o sappea ,bu wi hlowe aluesin his
case,due o hena u eo (3)and(5).I isobse ed ha
in(3)Inhasamo e ele an unc ionwhilein(5)i s
weigh isligh enedbyo he ac o s.
Ino he wo ds,by ocusing helab es son hee ec s
o hisIne o ,i is ound ha i hasa ema kable
incidencein hecalculuso heC (1)bu lesse inCca
(4).Incompa isonwi h hee o sinI,InandC and
Cca , espec i ely, hekeye idence ocomp ehend his
w ongbeha iou o heSOCcalcula o ’sp o o ypeis
ound.
FIG.8COMPARISONBETWEENINTERMEDIATEERRORS
No ice ha he eisaninsigni ican e o in he
calculuso I h ough(12)and(13),ane o which
meansalmos no hing illi isope a edin(11) o
ob ainIn h oughalimi edapp oach.
Top o e hishypo hesis,asolu iono hemain
p ecisionp oblemis oundjus byexecu ing es sin
which heIncalculuse o is educed oan
insigni ican aluebyinducinganequi alen da a
signal o hemic ocon olle .
FIG.9SOCERRORINADISCHARGECYCLE.SOLUTION
APPLIED.
Thee o isalmos elimina ed o in ensi ieslowe
han10A,andi pe o msp edic ablysoi couldbe
co ec ed.
Inacha gingcycle, he esul sa ealsoposi i e,
educing hee o inSOC alue:
FIG. 10 SOCERRORINACHARGECYCLE.SOLUTIONAPPLIED.
P o ing ha wi hou such es ic i ebounda iesin he
numbe o p og amlines, heSOCes ima o pe o ms
ina e yposi i eway.
Conclusions
Tes esul swhichha ebeenp esen edin hispape
show ha i ispossible ode elopasimple SOC
es ima ingsys embydesigninganAmpe e‐hou me e
baseds uc u e h oughamic ocon olle which
con olsbo hada aacquisi ionandada ap ocessing
sys em.
Howe e ,ino de oachie egoodaccu a e esul sin
hisSOCes ima o ,i becomesnecessa y he
de elopmen o no onlyanaccu a eda aacquisi ion
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59
sys em,by hechoiceanddesigno a obus cu en
sensingci cui ,bu alsoada ap ocessingsys em
whichallows henecessa yin e nalma hema ical
ope a ionsneeded oob ainanonco up ed esul .
Ob aininganaccu a e esul o alead‐acidba e y’s
SOCwi hanAmpe e‐hou me e basedsys emsuchas
hep esen edin hispape isonlypossiblei heused
mic ocon olle holdsenoughmemo y oinclude he
o ali yo heneededp og amlines.Agoodmemo y
ese oi woulde enpe mi a u u eimp o emen o
hep esen ed esul s,by headdi iono co ec ing
ac o s o unbalancingdis u bancessuchas he
men ionedIcalcula ions, he empe a u ee ec on he
ba e yo heageing.
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