1.A new battery model for use with battery energy storage systems and electric vehicles power systems

8/7/2019 1.A new battery model for use with battery energy storage systems and electric vehicles power systems

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A New Battery Model for use withBattery Energy Storage Systems and Electric Vehicles Power SystemsH.L. Chan, D.SutantoDepartment of Electrical Engineering,

The Hong Kong Polytechnic University,Hung Hom. Hong Kong.eesritantG3ii)oolvuedu hkFCZX:(852) 2330-1514

Abstract: This paper will initially present a review of the severalbattery models used for Electric Vehicles and Battery Energy StorageSystem applications. A model will be discussed which takes intoaccount the non-linear characteristics of the battery with respect tothe batterys state of charge. Comparisons between simulation andlaboratory measurements will be presented. The effects of highfrequency switching on the battery performance will also bediscussed. A strategy to reduce the high frequency charging anddischarging current will be proposed.Keywords: Battery Model, Battery Energy Storage Systems, ElectricVehicles, Battery Management.

I. INTRODUCTIONThe development o f electric vehicle has been accelerated bythe recent California Initiative which has required increasingproportions of new vehicles in Lo s Angeles area to be ZeroEmission vehicles. Similar legislation has now been passed inseveral other US states. This has impelled car manufacturersthroughout the world to have Electric Vehicles ready for themarket when the legislation is enforced. General Motors, forexample, has recently released the new EV 1 in USA. Thepossibility of large amounts of Electric Vehicles on the road,has also created interest in making better use of the sparebatteries that each Electric Vehicle must have. It has beensuggested that a Battery Chargin g station be made available bythe electric utilities, so that cars can come into the chargingstation and have they batteries replaced in a short time.While extensive research has been carried out to develop newtypes of batteriks and converters to convert the batteries outpu tinto useful work, very little work has been done in modelingthe battery itself. The fact that most power converters are nowswitched at relatively very high frequency (much higher than50Hz), will require new model of the batteries to take intoaccount the operation o f the battery under this high sw itchingmode. This paper will initially present the current state-of-theart of battery modeling for use in Elec tric Vehicles and B atteryEnergy Storage System. A new model will be introducedwhich takes into account the response of the batteries to highfrequency switching in the converter. Impact of batterychargers will be also be discussed. Comparisons betweensimulation and laboratory measurements will be presented.Some of the issues that will be considered are given below.

11. FACTORS DETERMINING BATTERY CAPACITYTo have better performance of EV, the energy utilization ofbattery capacity must be ensured. The following factors arecritical to determine battery capacity and must be consideredin any battery model:1 . Internal ResistanceSelf-discharge Resistance which takes account ofresistances in (a) electrolysis of water at high voltageand (b) slow leakage across the battery terminal at lowvoltage. This resistance is more temperature-sensitiveand inversely proportional to the temperature change.Resistances for Charge and Discharge: These are theresistances associated with electrolyte resistance, platesresistance and fluid resistance, however all theseresistances can be di f ferent in charging anddischarging.Overcharge and Overdischarge Resistance: When thebattery is overcharged or overdischarged, the internalresistance will be increased significantly due to theelectrolyte diffusion.2. Discharge Type:- - _Continuous Discharging: When battery continuouslydelivers energy to load without rest, and the batterycapacity is droppin g continuously.Intermittent Discharging: When a battery drives a loadfor a period and is disconnected from the load for sometime, then voltage recovery will be took place in thebattery to increase its voltage with so me amount. Whenthe battery is operating in this intermittent manner, itwill give a longer discharge time.3. Discharge Mode:Constant Load: When a battery delivers energy to aload of constant resistance, so the load current isdecreasing as battery voltage does.

Constant Current: Current drawn from a battery is keptconstant to a load that continuously reduces i tsresistance, the discharge duration in this mode isshorter due to the average current is higher. Thevoltage drops more faster than that in constant load.Constant Power: A constant electrical power is drawnby load from a battery, such that the load current willbe increasing to compensate for the decreasing batteryvoltage. This mode has the shortest disc harge time.0-7803-5935-6/00/$10.00 (c) 2000 IEEE 470


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4. Rate of Charge/Discharge: To extend the service life ofbattery the rate of charge and discharge can not be toohigh. Excessive overcharging and over-discharging canreduce battery life. Further, the frequency of switchingneeds to be taken into account, particularly now when theEV or BESS batteries are subjected to high switchingfrequency associated with the converters in the controlsystem.

111. BATTERY MODELIn the following section, six battery models will be describedbriefly. One of these is found to be simple and yet representsmany of the important features of the EV batteries.A. Simple Battery ModelThe most commonly used battery model is shown in Figure 1.This model consists of an ideal battery with open-circuitvoltage Eo and a constant equivalent internal series resistanceESR. Vo is the terminal voltage of battery.

ESR'--i.-4I v0-- Eo0Figure I . Simple Battery Model

Vo can be obtained from the open circuit measurement andESR can be obtained from both the open circuit measurementand one extra measurement with load connected at theterminal when the battery is fully charged. While this modelhas been extensively used, it does not take into account thevarying characteristic of the internal imp edance of the batterywith the varying state of charge, electrolyte conc entration andsulfate formation. Such a model is only applicable in somecircuit simulations where the energy drawn out of the batteryis assumed to be unlimited or where the state of charge is oflittle importance. Clearly, fo r electric vehicle applications, thismodel is not appropriate.B.Modified B attery ModelJean Paul Cun [ I ] proposed an improved battery model basedon the configuration given in Figure 1. In this battery model,the battery's state of the charge is taken into account, bymaking the ESR of battery no longer constant, but varies i naccordance with its state of charge. A common formula is tose t ESR = Ro/Sk, where Ro = initial battery internal resistancecalculated when the battery is full charged and S = 1 - Ah/Clo,where C lo is the ten-hour capacity (Ah) at the referencetemperature (this value varies as the battery ages). S variesfrom 0 (battery discharged) to 1 (battery charged). k is acoefficient that is a function of the discharge rate, calculatedon the basis of kl, k2,and k3. kl. k2 and k3 are coefficientsdetermined using the curves provided by the manufacturers.They correspond to three discharge rates.

This model has been used by many battery manufacturers forbattery monitoring purposes.C.Thevenin Battery Model

The other commonly used model is the Thevenin batterymodel, which consists of an ideal no-load battery voltage (Eo),internal resistance (R), capacitance (CO) and overvoltageresistance (Ro). CO represents the capacitance of the parallelplates and Ro represents the non-linear resistance contributedby the contact resistance of plate to electrolyte.CO

I "OFigure 2. Thevenin Battery Model

The main disadvantage of the Thevenin battery model is thatall the elements are assumed to be constant, but in fact all thevalues are functions of battery conditions.D. Dynamic Battery Model [7-91An empirical mathematical model is developed in [7,8] tomodel lead-acid trac tion battery: K

e t b = - (Rb +=litbwhereetb = battery terminal voltageV, = charge dependent open circuit voltageRI, = battery terminal resistor, typ ically OAohmK = polarization constant, typically 0.1 ohmi,b = battery discharge current, ampsSOC = state of chargeThe improvement of this model is to account for the non-linear characteristic of both the open circuit voltage andinternal resistance represented by the WS OC component.E. Fourth O rder Dynamic Model [ 1 I ]Giglioi [ I I ] proposed a dynamic model shown in Figure 3.The battery model is comprised of two parts: (a) current I pflowing through RP(electro lyte reaction) , Rd (Ohm ic effect)and its associated leakage capacitance Ca and RW (waste ofenergy) and its associated leakage capacitance CW;(b) currentIs flowing through RS(self discharge).Although this model is sophisticated and accurate forsimulation purpose, it still has some drawbacks in that: (a) alonger time is required for computation due to the high orderof model; and (b) modeling procedure is too complicatedbecause it involves a lot of empirical data.

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F. Over-Current Battery Model [ IO]Figure 4 shows a SPICE battery model. It has a variablecurrent source, a variable voltage sources, a variable resistorand a capacitor.

L I .Figure 3. Fourth Order Dynamic Modelt+- IT J E m LGb EvbA* -

vbY4-Figure 4. Over-Current Battery Model

whereGb =variable current source to m odel the battery current andis defined by Peukert relationship: Battery Capacity,

EV b = variable voltage source to model the battery voltage andis defined by Nernstian relationship: Battery Voltage,

ERI,= variable voltage sou rce characterizing voltage dropacross the battery, it is actually modeled as the internalresistance, RR = internal resistance including R I, R2 and RsR I= resistance of grid, group bar and lug material, which is aconstant AIR2= resistance of electrolyte=Az/CR3 = resistance of plate surface sulfation=AJ*(l-C)Cb =capacitor, the voltage across Cb which is scaled to 1Vwhen 100% of SO C and OV when 0% of SOCVb =curren t sensor of zero voltage for SPIC E simulationA,-, are constants and obtained by experiments.

C = A ~x I*'

VOC=Ad+As+log(C)

This model provides a good representation of both variableinternal drop in the battery and changes in the output voltagedue to the state of charge. H owever one of i ts drawbacks isthat too many parameters are required.

G. Improved Battery Model [2,4]Figure 5 shows a battery model that we believe is the simplestand at the same time meets all the requirements for a goodbattery model. It takes into account most nonlinear batteryelements characterist ics both during charging and duringdischarging a s well as their dependence on the state of chargeof th e battery. fiji CurrentSensorI I 1 ' 2

BatteryVoltage

Figure 5 . Improved Battery ModelAll the elements included in this model are functions of theopen-circuit voltage of battery, which in turn relates to state ofcharge. The characteristic of these elements are described asbelow:

Self-Discharge Resistance (Rp): It takes account ofresistances in (a) electrolysis of water at high voltage and(b) slow leakage across the battery terminal at low voltage.This resistance is a function o f the open circuit voltage.Resistances for Charge and Discharge (Rc and Rd): Theseare the resistances associated with electrolyte resistance,plates resistance and fluid resistance, however all theseresistances can be different in charg ing and discharging.Overcharge and Overdischarge Resistance (Rc o and Rdo):When the battery is overcharged or overdischarged, theinternal resistance will b e increased significan tly due to theelectrolyte diffusion.Battery Capacity (Cb): A battery delivering or storingenergy behaves as a large capacitor. However, it i smodeled as a voltage source, VOCin SPICE model whichis function of state of charge.

The following table tabulates the relationships of the batteryelements described above as VOCchanges and extracted from[2] and manufacturer's data.Because the model takes into account the variation of theelements with the open circuit voltage. and these relationshipsare obtained either from measurements or data sheet, themodel is very accurate, and errors between actual tests andsimulation will be minimised. Therefore, i t provides arelatively simple but accurate structure.

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Table I . Parameters of Battery Elements-3%0.0005.4505.7005.8IO6.I876.4066.7183.437

--

voc I R p n voc I Rc I voc I Rd I soc,O.OOoc( 195.d O.OO@ 0.1164 4.0000( 4 . 0 4 0.d

poood 0.d I IIV. SIMULATION

To test the model, a PSPICE simulation program using theimproved battery model was carried out and the results arecompared with the laboratory experiment. In the laboratory, a6V sealed lead-acid battery is used and is subjected to (a) 1.5hours of constant current discharge at 1.5A. then (b) 15minutes of rest, and (c) another 1.5 hours of constant currentcharge at 1.5A. The experimental set-up is discussed in thenext Section. The results from the simulation are shown in Fig.6. The non-linear characteristics of the battery terminalvoltage during charging and discharging can be clearlyobserved.

1.

voltage of the battery, the constant current supply and provideconstant current discharging of battery.

MicrocomputermLoad i [ . l .......... , ,

Constant Chen t

Figure 7. Battery Testing SystemThe results obtained from laboratory measurement are shownin Figure 8which is identical to that in Fig. 6. This can beexpected as the variations of the model with the state of chargeare now well represented both from measurements andmanufacturer's data sheet.However, it should be noted that the battery tests carried out inboth simulation and experiment are under constant DCcondition. in order to verify the battery performance underhigh frequency switching condition, a possible application ofEV battery as an active filter and power factor correction issimulated, first using the ideal battery model with constantvoltage and then wi thth e proposed battery model.

'I

*mm 0" ,mm I" 2" *"Tine

Figure 8. Experiment Result

VI. BESS PROVIDING ACTIVE FILTERING ANDPOWER FACTOR CORRECTIONV. EXPERIMENTThe experimental set-up is shown in Figure 7.It comprises amicrocomputer, a constant current supply. a constant currentload de mand, circuit selector, current and voltage sensors. Themicrocomputer is used to control and record the current and0-7803-5935-6/00/$10.00 ( c )2000 IEEE 47 3

A PSPICE simulation of an active filter using a BatteryEnergy Storage system is shown in Figure 9.


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.............................................. 8Active FilterFigure 9. Active Filtering System

The current drawn from the non-linear load contains a lot ofharmonics, it will definite ly de grad e the pow er factor ofelectricity supply if the active filter is not installed. TheBattery energy. storage system is used to provide alternatingpositive and negative current to ensure that the input currentsource will have a perfect sinusoidal waveform and in-phasewith the supply vo ltage. Th e circuit configuration is shown inFigure 9.The Capacitor in parallel with the battery is intendedto provide fi l tering in that i t will take most of the highfrequency component of the switching devices allowing theba t te ry t o expe r i enc e l ow f requ ency cha rg ing anddischarging. . The ac t ive f i l te r was implemented wi thhysteresis control strategy[3], wh ere the input source current iscontrolled within a tolerance band or hysteresis band. Theswitching frequency is as high as several kHz.Two studies were carried out for comparison, the first caseusing an ideal battery as energy storage and the second onemade use of the improved battery model. Both tw o cases weresimulated using PSPICE.

VII. ACTIVE FILTER USING IDEAL BATTERYFigure 10.a shows the supply current ( I s ) , load current ( I L ) andactive filter current (IF). The non-linear load demanded acurrent containing high harmo nics and the active filter currentwas controlled by referencing the ideal sinusoidal supplycurrent, such that the actual supply current is IS = I t - IF.However, it can be seen from Figure 1O.b that the batteryvoltage remains constant and no current flows through thecapacitor. The high frequency component is absorbed by thebattery, a very undesirable situation as this will shorten thebattery life.Clearly such a result is not realistic and does not reflect thetrue performance of the battery.

0 I . ' I , 0 1 , * .Ti m (nu)

Figure 10.a Active Filter U sing Ideal Battery

I I

------+4

4 10 2 . ' I

Tinu!(nu)

Figure 10.bActive F ilter Using Ideal BatteryVJII. ACTIVE FILTER USING IMPROVED BATTERYMODEL

Using the improved b attery model instead of the ideal model,the PSPICE simulation generated quite a different resultillustrated in Figure 1 1 .a and 1 1.b.Nevertheless, the battery voltage and capacitor current shownin Figure 10.b are not the sam e as those shown in Figure 10.b.The capaci tor now absorbs most of the high f requencycomponent and the battery only needs to absorb or generatethe low frequency component.

IX. CONCLUSIONThe paper has presented a review of several battery modelsused in the industry. One particular model was found to bestrepresent the non-linear characteristic of the battery elementswith respect to the state of charge very well . The batterymodel is then used to simulate the application of BESS as anactive filter. Super-capacitor was used to take care of the highfrequency component. The use of the proposed model of th ebattery allows a better understanding o f the battery behaviourwhen used in conjunction with Electric Vehicle or BatteryEnergy Storage System.

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4 1 ID , . . I W I I ~ .

Tinw(mr)

Figure 1 1.a Active Filter Using Imp roved ModelThe supply current, load current and filter current in Figure10.a follows s imilar pattern as before.

rm- i mt-

0 2 4 . , m * 2 , . 7 6T k (m)

Figure 1 I .b Active Filter Using Improved ModelX.ACKNOWLEDGMENTS

The authors gratefully acknow ledge the financial contributionsof the Hong K ong U niversity Grants Comm ittee and the HongKong Polytechnic University to the project and to Mr. JimMcDowall, Chair, PES Stationary Battery Committee for hiscommen ts on the abstract of the paper.

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XI. REFERENCES[ I ] Jean Paul CUN, Jean No FIORINA, MichaelFRAISSE, Henri MABBOUX, "The Experience of a

UPS Company in Advanced Battery Monitoring",MGE UPS Systems, Grenoble, France,'http://www-merlin-gerin.eunet.fr/news/techpap/tp02us.ht'

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Ziyad M. Salameh, Margaret A. Casacca and WilliamA. Lynch, "A Mathematical Model for Lead-AcidBatteries", IEEE Trans. on Energ y Conversio n. Vol. 7,No. 1, March 1992C. E. Lin, M. T. Tsai, Y. S. Shiao and C. L. Huang,"An Active Filter for Reactive and HarmonicCompensation Using Voltage Source Inverter", IE EInt'l Confe rence on Ad vances i n Power Sys t emC o n t ro l , O p e r at io n a n d M a n a g e m e n t , N o v e m b e r1991, Hong Kong .M a r g a r e t A. C a s a c c a a n d Z i y a d M . S a l a m e h ,"De te rmina t ion o f Lead-Ac id Ba t t e ry Capac i tyVia Ma thema t ica l Mode l ing Techn iques" , IEEETrans. on Energy Conversion. Vol . 7, No. 3, Sept.1992"Rechargeable Bat ter ies Appl ica t ions Handbook",T K 2 9 4 I .R43 1991 , Techn ica l Marke t ing S t a f f ofGates Energy Products , Inc .Dav id L inden , "Handbook of Bat ter ies" SecondEdi tion, TK29 0 1 .H36 1994, McGraw -Hil l , 1994J a y n e , M .G . , a n d M o r g a n , C., "A Ne wMathema t i ca l Mode l of a Lead Acid Bat tery forElec tric Vehicles", Eig hth Int 'l Elect ric Veh icleConference , Washington, D.C. , O ctober 1986.S i m s , R.I., Carnes, J .C. , Dziec iuch, M.A. andFenton, J .E. , "Computer Mod el ing of Automot iveLead Acid Bat ter ies", Ford Research Labora tor iesTechnica l Report SR-90- 154, Sept. , 25, I990Jayan ths , M.S., H a y h o e , G.F., and Henry, J .J . ,"Model ing and D igita l Com pute r Simula t ion of anElectric Vehicle", Technical Report , PennsylvaniaT r a n s p o r t a t i o n In s t i t u t e , P e n n s y l v a n i a S t a t eUniversity , Universi ty Park Pennsylvania , August ,1979.R o b b i n s , T.; Hawkins , J . "Ba t t e ry mode l forO v e r c u r r e n t P r o t e c t i o n S i m u l a t i o n of D CDist r i bu t ion S y s t e m S", I N T E L E C . S i xt een t hI n t e rn a t i o n al T e l e c o m m u n i c a t i o n s E n e r g yConference , p307- 14.Giglioli R.,Cerolo P., "Charge and Discharge FourthOrder Dynam ic Model of the Lead Battery", 10IhInt'lElectric Vehicle Symposium, Hong Kong, 1990, p. 1-9.

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1.A new battery model for use with battery energy storage systems and electric vehicles power systems