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Estimation of specific gravity and state of charge of lead acid battery

V.P.Labade, N. M. KulkarniDepartment of Electronic Science, Fergusson ollege, Pune!"##$$", %ndia

e!mail&'plabade(rediffmail.com, nmkulkarni#)*(+aoo.com

-bstract& Knowing the amount of energy left in a battery compared with the energy when it was full gives theuser an indication of how much longer a battery will continue to perform before it needs recharging. The

specific gravity of the rechargeable battery is very much important to understand capacity of the battery.

This is the customary way of determining the charge condition of lead acid batteries. It depends on measuring

changes in the weight of the active chemicals. As the battery discharges the active electrolyte, sulphuric acid,

is consumed and the concentration of the sulphuric acid in water is reduced. This in turn reduces the specific

gravity of the solution in direct proportion to the state of charge. The actual specific gravity of the electrolyte

indicates the state of charge of the rechargeable battery. During discharge, the specific gravity decreases

linearly with the ampere-hours discharged. The specific gravity measurements cannot be taen on sealed

lead-acid batteries hence open circuit voltage indicates the state of charge !"#$%. Determining the state of

charge of sealed batteries is under development. In this paper the attempt is made to measure the specific

gravity and state of charge !"#$%, depth of discharge !D#D% of sealed batteries using terminal voltage &'(.

"tate of $harge is e)uivalent of afuel gaugeof a battery electric vehicle!*E+%, hybrid vehicle!E+%,

or plug-in hybridelectric vehicle !E+% &(. The /ife e0pectancy of the battery measured in cycles. Thedepth of discharge has a ma1or affect on the life e0pectancy of a battery. The /ab+IE2 graphical

programming environment is used to develop the system for measurement the battery performance

parameters of the rechargeable battery. The /ab+IE2 and 3AT/A* tool are used to estimate battery

performance parameters of the rechargeable battery.

Ke+ords&"pecific gravity4 "tate of $harge !"#$%4 Depth of Discharge !D#D%4 /ab+IE2

I. I5T6#D7$TI#5

/e specific gra'it+ of te recargeable batter+ is 'er+ muc important to understand capacit+ of te batter+. /e

specific gra'it+ of solution depends on measuring canges in te eigt of te acti'e cemicals. -s te batter+

discarges te acti'e electrol+te is consumed and te concentration of te sulpuric acid in ater is reduced. /is in

turn reduces te specific gra'it+ of te solution in direct proportion to te state of carge. /e actual specific gra'it+

of te electrol+te indicates te state of carge of te recargeable batter+. 0enerall+ specific gra'it+ measurements

cannot be taken on sealed lead!acid batteries ence open circuit 'oltage as been used as an indication of te state of

carge. Determination of te state of carge of sealed batteries is under de'elopment . /e S1 and D1D can beestimated it te elp of terminal 'oltage of te batter+ for sealed lead acid batter+. /e results can be 'ar+ idel+

because it is depending on actual 'oltage le'el, temperature, discarge rate and te age of te cell and compensation

for tese factors must be pro'ided to acie'e a reasonable accurac+. /e energ+ contained in an electric carge is

measured in oulombs and is e2ual to te integral o'er time of te current ic deli'ered te carge.

Figure #& E3perimental setup of measurement of Specific 0ra'it+ and S1 and snap sot of te de'eloped s+stem
http://en.wikipedia.org/wiki/Fuel_gaugehttp://en.wikipedia.org/wiki/Fuel_gaugehttp://en.wikipedia.org/wiki/Battery_electric_vehiclehttp://en.wikipedia.org/wiki/Hybrid_vehiclehttp://en.wikipedia.org/wiki/Hybrid_vehiclehttp://en.wikipedia.org/wiki/Plug-in_hybridhttp://en.wikipedia.org/wiki/Plug-in_hybridhttp://en.wikipedia.org/wiki/Battery_electric_vehiclehttp://en.wikipedia.org/wiki/Hybrid_vehiclehttp://en.wikipedia.org/wiki/Plug-in_hybridhttp://en.wikipedia.org/wiki/Fuel_gauge


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/e remaining capacit+ in a cell can be calculated b+ measuring te current entering 4carging5 or lea'ing

4discarging5 te cells and integrating 4accumulating5 tis o'er te time. /e designed s+stem utili6es a dataac2uisition card of manufacturer National %nstrument 4N%5 along it LabV%E7 tool to read batter+ parameters. /e

S1 of te batter+ determines te a'ailable capacit+ of te batter+ and is e3pressed as a percentage of some

reference, sometimes its rated capacit+ but more likel+ its current capacit+. For estimation of S1 coulomb counting

tecni2ue is used and accurate 'alues of ampere our is displa+ed 8"9. /e dept of discarge as a ma:or effect onte life e3pectanc+ of a batter+. /e e3perimental setup for measuring batter+ parameters are gi'en in te block

diagram figure#./si block diagram consists of batter+, signal conditioning unit, electrical load to discarge te

batter+. /e student 'ersions of LabV%E7 and M-/L-; tool are used effecti'el+ to estimate some of te batter+

parameters.

II. S


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%f single cellBopen circuit 'oltage is ).#*' ten specific gra'it+ ill be #.)?C. /e specific gra'it+ of a full+

carged industrial batter+, or traction batter+, is generall+#.)?C, depending on te manufacturer and t+pe. Some

manufacturers use specific gra'ities as ig as #.*)$ in an attempt to gain additional - capacit+, but at te cost of a

sorter c+cle life.

III."TATE #8 $A69E !"#$%

/e S1 is defined as te a'ailable capacit+ e3pressed as a percentage of some reference, sometimes its rated

capacit+ but more likel+ its current capacit+. =sing te analog+ of a fuel tank in a car, State of arge 4S15

estimation is often called te 0as 0auge or Fuel 0auge function. /e preferred S1 reference sould be te rated

capacit+ of a ne cell rater tan te current capacit+ of te cell. /is is because te cell capacit+ graduall+ reduces

as te cell ages. /emperature and discarge rate effects reduce te effecti'e capacit+ e'en furter. /e difference in

reference points is important if te user is depending on te S1 estimation as e ould in a real gasgaugeapplication in a electrical 'eicle 8#9. =nfortunatel+ te S1 measurement reference is often defined as te

current capacit+ of te cell instead of te rated capacit+. %n tis case a full+ carged cell, nearing te end of its life,

could a'e an S1 of #$$ but it ould onl+ a'e an effecti'e capacit+ of ?$ of its rated capacit+ and ad:ustment

factors ould a'e to be applied to te estimated capacit+ to compare it to its rated ne capacit+. =sing te current

capacit+ rater tan te rated capacit+ is usuall+ a design sortcut or compromise to a'oid te comple3it+ of

determining and alloing for te age related capacit+ ad:ustments ic are con'enientl+ ignored.

/e accurate estimation of te remaining carge in te batter+ is re2uired te ageing and en'ironmental factors must

be taken into account. %n electrical 'eicle applications te S1 is used to determine range 8>9. %t is an absolute

'alue based on capacit+ of te batter+ en ne, not a percentage of current capacit+ ic could result in an error

of )$ or more due to batter+ ageing. -utomoti'e fuel gauges are notoriousl+ imprecise so an S1 accurac+ of C,

if it could be acie'ed, ould probabl+ be satisfactor+ for suc applications. %n +brid electrical 'eicle te S1determines en te engine is sitced on and off. /e S1 is measured using different metods i.e. direct metod,

specific gra'it+, 'oltage and current metod or coulomb counting metod. /e data of manufacturer is fitted usingcubic spline metod and constant coefficients are calculated for specific gra'it+ and state of carge of te batter+.

/e 'alues coefficients are P#, P), P*, P", P", PC, P> and P are gi'en belo. /e e2uations are in terms of open

circuit 'oltage is gi'en belo in e2uation number # and ).

IV. $76+E 8ITTI59

ubic spline metod of cur'e fitting used to point boundar+ 'alue problem and integral e2uation. /e data fitting

b+ means of pol+nomial as been considered in mecanical splines. /e resulting appro3imation is called as spline

appro3imation or cubic spline. /is metod is used to fit a uni2ue cur'e it gi'en data of batter 'oltage, S1 andSpecific gra'it+ of te batter+. /e folloing e2uation 4#5 and 4)5 deri'ed and relation of specific gra'it+ and S1

is ritten in terms of batter+ 'oltage

Specific 0ra'it+A P# 4;atter+ Voltage5* G P) 4;atter+ Voltage5)G P* 4;atter+ Voltage5 G P" BBBBBBBBBBBBBBB 4#5

7ere P#, P), P* and P" are constant coefficients.i.e.P#A H$.$$*I)>, P)A$.$C??C*, P*A$.C$#?*, P"AH>.C>)#

State of argeA PC 4;atter+ Voltage5* G P> 4;atter+ Voltage5)G P 4;atter+ Voltage5 G P? BBBBBBBBBBBBBBB 4)5

7ere PC, P>, P and P? are constant coefficients i.e.PCA HC.$??", P>A##C.>), PAH"#?.*>, P?AH)?#C.)

Direct Measurement ould be eas+ if te batter+ could be discarged at a constant rate. /e carge in a batter+ is

e2ual to te current multiplied b+ te time for ic it floed. =nfortunatel+ tere are to problems it tis. %n all

practical batteries, te discarge current is not constant but diminises as te batter+ becomes discarged, usuall+ in

a non!linear a+. -n+ measurement de'ice must terefore be able to integrate current o'er time. Secondl+, tismetod depends on discarging te batter+ to kno o muc carge it contained 8*9. %n most applications e3cept

peraps in 2ualification testing, te user 4or te s+stem5 needs to kno o muc carge is in te cell itout

discarging it.

%t is not possible eiter to measure directl+ te effecti'e carge in a batter+ b+ monitoring te actual carge put into

it during carging. /is is because of te oulombic efficienc+ of te batter+. Losses in te batter+ during te carge

! discarge c+cle mean tat te batter+ ill deli'er less carge during discarge tan as put into it during carging.

/e oulombic efficienc+ or carge acceptance is a measure of o muc usable energ+ is a'ailable during


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discarging compared it te energ+ used to carge te cell. arge efficienc+ is also affected b+ temperature and

S1

S1 can be estimated from 'oltage of te batter+ or cell as te basis for calculating S1 ./e results can 'ar+

depending on actual 'oltage le'el, temperature, discarge rate and te age of te cell and compensation for tese

factors must be pro'ided to acie'e a reasonable accurac+. /erminal 'oltage is te 'oltage of batter+ terminals it

te load applied. /e terminal 'oltage 'aries it state of carge and carge@discarge current. /e 'oltage beteente batter+ terminals itout load applied is open circuit 'oltage. /e open circuit 'oltage depends on te batter+

state of carge and increases it state of carge.

/e energ+ contained in an electric carge is measured in oulombs and is e2ual to te integral o'er time of te

current ic deli'ered te carge. /e remaining capacit+ in a cell can be calculated b+ measuring te current

entering 4carging5 or lea'ing 4discarging5 te cells and integrating 4accumulating5 tis o'er te time. /e

calibration reference point is a full+ carged cell, not an empt+ cell, and te S1 is obtained b+ subtracting te net

carge flo from te carge in a full+ carged cell. /is metod, knon as oulomb counting, pro'ides iger

accurac+ tan most oter S1 measurements since it measures te carge flo directl+. Joe'er it still needscompensation to allo for te operating conditions as it te 'oltage based metod. urrent sunt, Jall Effect and

0M magneto resisti'e sensors for current sensing purpose. oulomb counting depends on te current floing from

te batter+ into e3ternal circuits and does not take account of self discarge currents or te oulombic efficienc+ of

te batter+.

During te cell carge ! discarge c+cles te composition of te acti'e cemicals in te cell canges as te

cemicals are con'erted beteen te carged and discarged states and tis ill be reflected in canges to te cell

impedance. /us measurements of cell internal impedance can also be used to determine S1 oe'er tese are not

idel+ used due to difficulties in measuring te impedance ile te cell is acti'e as ell as difficulties in

interpreting te data since te impedance is also temperature dependent 8*9. /e resistance itin te batter+,generall+ different for carging and discarging, also dependent on te batter+ state of carge. -s internal resistance

increases, te batter+ efficienc+ decreases and termal stabilit+ is reduced as more of te carging energ+ iscon'erted in to eat.

/e Life e3pectanc+ of te batter+ measured in c+cles, or o man+ times te+ can be discarged and recarged

before te+ ill no longer take a full carge. /e dept of discarge 4D.1.D.5 as a ma:or effect on te lifee3pectanc+ of a batter+ ! discarging onl+ ?$ of te total capacit+ of te batter+ ill t+picall+ gi'e )C more

c+cles tan total discarges 8*9. /e discarging of te same batter+ up to )$ of te total capacit+ of te batter+ill make te batter+ last essentiall+ fore'er.

V. 6E"7/T A5D $#5$/7"I#5

/e softare is ritten in LabV%E7 and data taken from te recargeable batter+ troug data ac2uisition card

=S; >$$?. /e e3pected and obser'ed 'alues of S1 and specific gra'it+ are gi'en in te fig.*. /e obser'ed

'alues of soc and specific gra'ities are nearb+ same te eac oter itin te some e3perimental error. /e snap

sot of te LabV%E7 front panel is gi'en belo fig).

/e s+stem also gi'es oter electrical parameter of te batter+ i.e. open circuit 'oltage and temperature of te

recargeable batter+. /e temperature is important factor ic affects te life of te batter+. Jence tis parameter

is added and son in te result


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Figure *&E3pected and obser'ed 'alues of te Specific 0ra'it+ and S1

A$K5#2/ED93E5T

/e autors of tis paper ould like tank to acknoledge Dr.-.D.Saligram, Jead of Electronic Science

Department, =ni'ersit+ of Pune and Principal Dr..0.Pardesi, Prof..V.Kedkar, Fergusson ollege, Pune for

promoting and moti'ating te researc en'ironment of te department.

6E8E6E5$E

8#9 ames Larminie 413ford ;rookes uni'ersit+ o3ford =K5, on Lor+ 4-centi Designs Ltd., =K5, Electric

Veicle /ecnolog+ E3plained, ;+ Publication on 7ile+ and sons, Ltd.

8)9 ob+n -. acke+ - simple, effecti'e lead!acid batter+ modeling process for electrical s+stem component

selection 8)$$!$#!$?9

8*9 - 0uide to =nderstanding ;atter+ Specifications, M%/ Electric Veicle /eam, December )$$?

8"9V.P.Labade, N. M. Kulkarni and -. D. Saligram %ntelligent ;atter+ Jealt Monitoring S+stem for

=ninterrupted Poer Suppl+ NS%!*> 4)$!)), 1ctober )$##, ;areill+, =P5 ournal of te %nstrument Societ+ of %ndia%SSN $I$!II?* Vol."# No." pp)#*!)#>4)$##5

8C9 V.P.Labade, N. M. Kulkarni and -. D. Saligram Design of eal!/ime Monitoring S+stem for Measurement of

;atter+ Parameters of Electric Veicle 8ecent /rends in -lternate Energ+ /-E )$##, N%/ Ko6ikode

4alicut5,Kerala, P!P **, I!#$un )$##9

8>9 Modeling of J+brid Electric Veicle ;atteries b+ am andra Maddala, ;.E. a tesis in electrical engineering

Plug!in J+brid Electric Veicle ontrol Strateg+ Parameter 1ptimi6ation -+meric ousseau, S+l'ain Pagerit

-rgonne National Laborator+ I$$ S ass -'e, %L >$"*I, =S-

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