parameter identification of the lead-acid battery model

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tLI.&&~I- -('I Reec\a"";lhReacts IoI1th0 sulfuric ootd sulfate ;ons.c .c"'form 1 .... to form loade.e. s ulfato. Must sulfate. Pbs uppl y .lootronssupplios Iwend 10 Ionposlt1vepositive H 2SO 4 chergno end1 .... eloctrode""--- H2O 1. left ""---IIOQ8tiveFigure 1: Lead-acid battery [6].MODELING OF THE LEAD-ACID BATTERYThe lead-acid battery represents a fundamental and mainelement in the renewable energy systems and in thehybrid vehicles. Therefore, it is necessary to study themodeling of this type of batteries. In fact, very bigquantities of models exist, from the simplest, containingimpedance placed in series with a voltage source, to themost complex. In general, these models represent thebattery like an electric circuit composed of resistances,capacities and other elements, constant or variable(function of the temperature or the State Of Charge SOCthat gives an idea on the quantity of active substance)[7],[8].The simplified modelThe simplest model of a lead-acid battery is composed ofa voltage source placed in series with impedance (Fig. 2).,...Lr------Figure 2: Lead-acid battery simplest model.The main problem of this model is that the two elementsE(p) and Z(p) must be at least function of the State OfCharge (SOC) and of the battery's temperature e [9,10].The improvement of the simple model takes place whileadding a parasitic branch in parallel (Figure 3).I,... (C1SOC')Figure 3: Lead-acid battery general model.In fact, the parasitic branch represents the irreversiblereactions that take place in the battery as for example theelectrolysis of water that occurs at the end of the chargingprocess, especially in the case of overcharge. In thisbranch an Ip current circulates. The charge stocked in thebattery is only joined to 1m (current of the main branch, inamperes). A part of the total current I, which is the Ipcurrent, is a lost current and cannot be restored.The third order model [11]The model is consisted of two main parts: a main branchwhich approximated the battery dynamics under mostconditions, and a parasitic branch which accounted for thebattery behavior at the end of a charge. The main branchis formed of a R/C block placed in series with a resistance(Figure 4). All elements of figure 4 are functions of theState Of Charge (SOC), the charging/discharging currentsand the temperature of the electrolyte 9.EmNFigure 4: Lead-acid battery third order model.where:• Em was the main branch voltage,• R1 was the main branch resistance,• C1 was the main branch capacitance,• R2 was the main branch resistance,• I 01pn) was the Parasitic branch current,• Ro was the Terminal resistance.RO,...L+Main branch voltage (Em)Equation 1 approximated the internal electro-motive force(emf), or open-circuit voltage of one cell. The emf valuewas assumed to be constant when the battery was fullycharged. The emf varied with temperature and state ofcharge (SOC):Em = EmO - KE .(273 + 9)(1-SOC) (1)where:• Em was the open-circuit voltage (EMF) in volts,• Emo was the open-circuit voltage at full charge in volts,• KE was a constant in volts 1 DC,• 9 was electrolyte temperature in DC,• SOC was battery state of charge.Main branch resistance R1Equation 2 approximated a resistance in the main branchof the battery. The resistance varied with depth of charge,a measure of the battery's charge adjusted for thedischarge current. The resistance increased exponentiallyas the battery became exhausted during a discharge.v978-1-4244-1641-7/08/$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.
where:• R1 was a main branch resistance in Ohms,• R10 was a constant in Ohms,• DOC was battery depth of charge.(2)Main branch capacitance C1Equation 3 approximated a capacitance (or time delay) inthe main branch. The time constant modeled a voltagedelay when battery current changed.C 1 =l (3)RIwhere:• C1 was a main branch capacitance in Farads,• T1 was a main branch time constant in seconds,• R1 was a main branch resistance in Ohms.Main branch resistance R2Equation 4 approximated a main branch resistance. Theresistance increased exponentially as the battery state ofcharge increased.The resistance also varied with the current flowing throughthe main branch. The resistance primarily affected thebattery during charging. The resistance became relativelyinsignificant for discharge currents:Note that while the constant Gpo was measured in units ofseconds, the magnitude of Gpo was very small, on theorder of 10-12 seconds.I p =V PN. G po·exp + p (6)VpoSf[VPN /(t p .s+l) A (1-~)lwhere:• Ip was the current loss in the parasitic branch,• VPN was the voltage at the parasitic branch,• GpO was a constant in seconds,• Tp was a parasitic branch time constant in seconds,• Vpo was a constant in volts,• Ap was a constant,• 8 was the electrolyte temperature in DC,• 8t was the electrolyte freezing temperature in DC.Some definitionsExtracted charge QeEquation 7 tracked the amount of charge extracted fromthe battery. The charge extracted from the battery was asimple integration of the current flowing into or out of themain branch. The initial value of extracted charge wasnecessary for simulation purposes.tQe(t) = Qe_init + f-Im(t).dt(7)owhere:• R2 was a main branch resistance in Ohms,• R20 was a constant in Ohms,• A21 was a constant,• A22 was a constant,• Em was the open-circuit voltage (EMF) in volts,• SOC was the battery state of charge,• 1m was the main branch current in Amps,• 1* was the nominal battery current in Amps.(4)Total capacity CEquation 8 approximated the capacity of the battery basedon discharge current and electrolyte temperature.However, the capacity dependence on current was only fordischarge. During charge, the discharge current was setequal to zero in Equation 8 for the purposes of calculatingtotal capacity.C(I,9) = K,.C,' , {l-~)'1+(Kc-l~I~) Sf(8)Terminal resistance ROEquation 5 approximated a resistanceseen at the batteryterminals. The resistance was assumed constant at alltemperatures, and varied with the state of charge:Ro = Roo [1 + Ao(I-S0C)] (5)where:• Ro was a resistance in Ohms• Roo was the value of RO at SOC=1 in Ohms• Ao was a constant• SOC was the battery state of chargeParasitic branch current IpEquation 6 approximated the parasitic loss current whichoccurred when the battery was being charged. The currentwas dependent on the electrolyte temperature and thevoltage at the parasitic branch. The current was very smallunder most conditions, except during charge at high SOC.where:• Kc was a constant,• Co* was the no-load capacity at O°C in Amp-seconds,• 8 was the electrolyte temperature in DC,• I was the discharge current in Amps,• I" was the nominal battery current in Amps,• ~ and E were a constant.State Of Charge (SOC) and Depth Of Charge (DOC)Equations 9 and 10 calculated the SOC and DOC as afraction of available charge to the battery's total capacity.State of charge measured the fraction of charge remainingin the battery:SOC =1-Q eC(O,S)(9)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.
Page 1: PARAMETER IDENTIFICATION OF THE LEA
Page 5 and 6: The proposed thermal model is very

parameter identification of the lead-acid battery model

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