parameter identification of the lead-acid battery model

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Depth of charge measured the fraction of usable chargeremaining, given the average discharge current. Largerdischarge currents caused the battery's charge to expiremore prematurely, thus DOC was always less than orequal to SOC.where:• SOC was battery state of charge,• DOC was battery depth of charge,• Qe was the battery's charge in Amp-seconds,• C was the battery's capacity in Amp-seconds,• a was the electrolyte temperature in °c,• lavg was the mean discharge current in Amps.Estimate of Average CurrentThe average battery current was estimated as follows inEquation 11.(10)lavg = 1m (11)(t l ·s+l)where:• lavg was the mean discharge current in Amps,• 1m was the main branch current in Amps,• T1 was a main branch time constant in seconds.Thermal modelSEquation 12 was modeled to estimate the change inelectrolyte temperature, due to intemal resistive lossesand due to ambient temperature. The thermal modelconsists of a first order differential equation, withparameters for thermal resistance and capacitance.Gpo, Vpo,Ap.- The capacitance parameters used in equation 8:Kc,Co,E,O.- The thermal parameters used in equation 12:Ca,Ra ·Main branch parameters identificationAll parameters are calculated experimentally through veryappropriate tests. The most adequate test is illustrated infigure 5."'0 J)J'oltopJ114Cummtr "'31Figure 5: Test serving in determining the parameters of themain branch of the third order lead-acid model.To identify Emo and KE, one needs two equations, theseequations are obtained while measuring the voltage in thebeginning and at the end of the test, Vo and V1 (they areequal to the emf at the beginning and at the end). For Thevalues of the load state, SOCbeginning and SOCend, they canbe known easily.It is sufficient one equation to identify R10. This equationwas obtained by making the following difference, (V1-V4),which is due to the presence of the resistance R1.The main branch resistance is neglected R2.Where:• a was the battery's temperature in °c,• aa was the ambient temperature in °c,• aini! was the battery's initial temperatureto be equal to the surrounding ambient temperature,• P s was the 12R power loss of Ro and R2 in Watts,• Re was the thermal resistance in °c 1 Watts,• Ce was the thermal capacitance in Joules 1°C,• T was an integration time variable,• t was the simulation time in seconds.(12)in °c, assumedSame test is applied as for the emf parameters. Roo and Aoare identified while measuring the instantaneous dropvoltage following the application of the current I.Parasitic branch parameters identificationThe identification of the constants GpO, Vpo and Ap isobtained by making tests when the battery is completelyfull. In this case, 1m is supposed to be neglected and thetemperature of the electrolyte can be estimated from theambient temperature.PARAMETERS IDENTIFICATIONThe mentioned equations of the lead-acid third ordermodel contain constants that must be determinedexperimentally by tests in the laboratory. These constantsor parameters can be divided in four categories:- The main branch parameters used in equations 1 to 5:EmO,KE ,RIO,R20,A21' A22 ,Roo,Ao·- The parasitic branch parameters used in equation 6:Capacitance parameters identificationThis identification needs four equations. To do that, twomethods can be used. The first one is based on the datagiven by the manufacturer and the second one is based onthe experimental test.Thermal parameters identification978-1-4244-1641-7/08/$25.00 ©2008 IEEEAuthorized licensed use limited to: GOVERNMENT COLLEGE OF TECHNOLOGY. Downloaded on December 31, 2009 at 04:54 from IEEE Xplore. Restrictions apply.
The proposed thermal model is very simple. It is formed ofthermal resistance Re and of thermal capacitance CeoThese two parameters are determined experimentally orare given by the manufacturers of batteries.It should be noted that, contrary to all others parameters,the thermal resistance depends on the site where thebattery is placed.SIMULATIONThe presented third order model of the lead-acid batteryusing its identified parameters is used in Matlab/Simulinksoftware in order to validate its functioning. The linearity ofthe model is due to the omission of the parasitic branch inthe general model.Charging stateWith regard to the discharging phase of the accumulator,several initial conditions are taken into consideration. Infact:- The accumulator is supposed to be completely charged,- The initial charge extracted is zero (Qe_init = 0),- The ambient temperature is supposed equal to 25°C,- The initial values of SOC and DOC are equal to 0.8.The phase of the discharge is presented in figure 7.oCum'".1': ~ .: :! :'.!': :I!'::::.... :::....: ::~.'.'.:::'.:::'.-""""""':""""""'["""·······················:············1··:::······:::····:::··:::····::i·25L-_-L-_---'-__-L-_--'-_---"'--_-'-_---'-_----'Voltage•. ,:::: :.i:I~:::::::·:: ~.!.. :::.::: :'.~To simplify the modeling of the chosen accumulator, thetemperature of the electrolyte is supposed equal to theambient temperature. In addition:- The accumulator is supposed to be empty,- The initial extracted charge is negligible (Qe_init = 0),- The ambient temperature is supposed equal to 25°C,- The initial values of the SOC and DOC are equal to 0.2.The model functioning in the charging state is illustrated infigure 6. In fact, before the beginning of this phenomenon,the current in the model was zero, the voltage is equal to1.95 V and the SOC is set to be 0.2. The charging of themodule of the studied accumulator takes place withconstant current equal to 20 A. The duration of thetransient state is about 5000 seconds. During this period,the voltage across the model terminals increases in alinear way as far as reaching its maximal value Erno whichis equal to 2.22 V. Same, the SOC increases linearly. Afterthe accumulator's charging, the voltage becomes equal to2.15 V and the SOC approaches to 0.8. This means thatthe accumulator will be able to continue charging as theSOC didn't reach the unity value.Figure 7: Battery discharging.In general, before the accumulator's connection with aload, the voltage across its terminals is equal to 2.15 V.When the load is placed, the accumulator begins toprovide current. This one is supposed constant. Theduration of this phase is supposed to be equal to 5000seconds. During this period, the voltage across the modelterminal decreases in a linear way as far as reaching itsminimal value. In the same way, the SOC decreaseslinearly. After the accumulator's discharge, the voltagebecomes equal to 1.95 V and the SOC approaches to 0.2.CONCLUSIONThe electric lead-acid batteries are devices that providethe electric energy from chemical one. These are electrochemicalgenerators. They store the energy that theyrestore according to the needs. They can be rechargedwhen one reverses the chemical reaction; it is whatdifferentiates them from the electric batteries.Discharging stateFigure 6: Battery chargingThese accumulators are used in several applications, forexample, they serve to supply electrically the cars, theheavy weights, the planes, etc.. One uses them likestationary batteries, assuring the lighting and the workingof the embarked devices.Seen their interests in the daily life, the electric lead-acidbatteries are studied in this paper. The principle of workingand the battery's modeling are discussed.978-1-4244-1641-7/08/$25.00 ©2008 IEEEAuthorized licensed use limited to: GOVERNMENT COLLEGE OF TECHNOLOGY. Downloaded on December 31, 2009 at 04:54 from IEEE Xplore. Restrictions apply.
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