Battery Models
Battery Models
BatteryBasicTermsAmpere-hourCapacity.Ampere-hour(Ah)capacityisthetotalchargethatcanbedischargedfromafullychargedbattery.RatedWhCapacity=RatedAhCapacity×RatedBatteryVoltageC-rate.C(nominalC-rate)Fora1.6Ahbattery,Cis equaltochargeordischargethebatteryat1.6ACorrespondingly,0.1Cisequivalentto0.16A,and2Cforchargingordischargingthebatteryat3.2ASpecificEnergy.SpecificEnergy=RatedWhCapacity/BatteryMassinkgSpecificPower.SpecificPower=RatedPeakPower/BatteryMassinkgEnergyDensity.thenominalbatteryenergyperunitvolume(Wh/L).PowerDensity.thepeakpowerperunitvolumeofbattery (w/h).InternalResistance.Internal resistanceistheoverallequivalentresistancewithinthebattery.Itisdifferentforcharginganddischargingandmayvaryastheoperatingconditionchanges.Cut-offVoltage.Cut-offvoltageistheminimumallowablevoltagedefinedbymanufacturer1RemainingCapacitySOC=Stateof Charge(SoC).ASOC = SOC(t) -SOC(t )=-i(t)dtAhCapacityRatedCapacityDepthofDischarge(DoD).thepercentageofthetotalbatterycapacitythathasbeendischargedDOD=1-SOCStateof Health(soH).SOHcanbedefined astheratioofthemaximumchargecapacityofanaged batterytothemaximumchargecapacitywhenthebatterywasnew.SOH =-- Aged Energy CapacityRatedEnergyCapacity
Battery Basic Terms • Ampere-hour Capacity. Ampere-hour (Ah) capacity is the total charge that can be discharged from a fully charged battery. Rated Wh Capacity =Rated Ah Capacity ×Rated Battery Voltage • C-rate. C (nominal C-rate) For a 1.6 Ah battery, C is equal to charge or discharge the battery at 1.6 A. Correspondingly, 0.1C is equivalent to 0.16A, and 2C for charging or discharging the battery at 3.2 A. • Specific Energy. Specific Energy = Rated Wh Capacity/Battery Mass in kg • Specific Power. Specific Power = Rated Peak Power /Battery Mass in kg • Energy Density. the nominal battery energy per unit volume (Wh/L). • Power Density. the peak power per unit volume of battery (W/h). • Internal Resistance. Internal resistance is the overall equivalent resistance within the battery. It is different for charging and discharging and may vary as the operating condition changes. • Cut-off Voltage. Cut-off voltage is the minimum allowable voltage defined by manufacturer. • State of Charge(SOC). RatedCapacity RemainingCapacity SOC = t t0 1 SOC = SOC(t) − SOC(t0 ) = Ah Capacity i( )d • Depth of Discharge (DOD). the percentage of the total battery capacity that has been discharged. DOD = 1- SOC • State of Health (SOH). SOH can be defined as the ratio of the maximum charge capacity of an aged battery to the maximum charge capacity when the battery was new. SOH == Aged Energy Capacity Rated EnergyCapacity
BatteryCharge/DischargeProcessesLithiumcobaltoxideLithium-ion rechargeablebatteryPositive ElectrodeNegative ElectrodeDischargemechanismLoadElectronsCurrentSeparatorAnodeCathodeOxidationReductionSpecialtyCarbotLiCooIntercalationandde-intercalationofLitElectrolyteionsintoand outofthecathodeand(Polymerbattery:gelpolymerelectrolyte)@2006HowStuffWorksthe anodeRedox ReactionsOthercathodematerialLithiumironphosphate(LFP),Lithiummanganese(LMO)andLithiumnickelmanganesecobaltoxide(NMC)offerlowerenergydensity,butlongerlivesandinherentsafety
Oxidation Reduction Redox Reactions Intercalation and de-intercalation of Li+ ions into and out of the cathode and the anode Lithium cobalt oxide Other cathode material: Lithium iron phosphate (LFP), Lithium manganese (LMO) and Lithium nickel manganese cobalt oxide (NMC) offer lower energy density, but longer lives and inherent safety. Battery Charge/Discharge Processes
ElectrochemistryChargingCathod: LiCoO, -→ Li,-,CoO,+nLit +neLit = electrolyte =Anodee' = charging circuit = AnodeAnode: nLit +ne' + 6C → LiCXAnode: Li,C, → nLit +ne'+6CDischargingLit = electrolyte =Cathodee=loadcircuit=CathodeCathod: Li CoO +nLit +ne' →LiCoOCathod: LiCoO +Lit - Li +CoOOvercharging22IrreversibleLiCoO → Lit+Coor22Lithium cobalt oxide (LiCoO2)Li-ion batteries require overcharging protection circuits
Electrochemistry Charging Cathod: LiCoO2 → Li1−n CoO 2 +nLi+ +neLi+ electrolyte Anode e - charging circuit Anode Anode: nLi+ +ne- + 6C → Li C x 6 Discharging 2 Anode: Li C → nLi+ +nex 6 + 6C Li+ electrolyte Cathode e - load circuit Cathode Cathod: Li CoO +nLi+ +ne- →LiCoO 1−n 2 Overcharging Cathod: LiCoO +Li+ → Li +CoO 2 2 Irreversible or LiCoO → Li+ +CoO 2 2 Lithium cobalt oxide (LiCoO2) Li-ion batteries require overcharging protection circuits
Typical External Behavior ofCharge and Discharge Processes
Typical External Behavior of Charge and Discharge Processes
Open-Circuit VoltageduringBattery DischargeTypical DischargeCharacteristicsDischarge curveFullyChargedNominalareaExponentialExponentialareaNominalNom MaxExponentialCapacity (Ah)
Open-Circuit Voltage during Battery Discharge
Open-Circuit VoltageduringBattery ChargeTypical ChargeCharacteristicsMaximum()enNominalLead-AcidLi-lon600204080100120State-of-Charge (%)Typical ChargeCharacteristicsMaximum() onNominalNiMH&NiCD040602080100120State-of-Charge (%)
Open-Circuit Voltage during Battery Charge
BatteryResponseDynamicsTheresponsetimeofthebattery(at95%ofthefinalvalue)Thisvaluerepresentsthevoltagedynamicsand canbeobservedwhenacurrent step is applied:X:4196Battery Voltage(V)1.28Y: 1.271.26X:4130Y:1.2691.24X:4100Y.125405U410039003950400041504200Batterydischargecurrent(A)64203950400040504100415042003900Time
Battery Response Dynamics The response time of the battery (at 95% of the final value). This value represents the voltage dynamics and can be observed when a current step is applied:
Some Typical Battery Models
Some Typical Battery Models
Battery Model Structure 1:Voltage-ResistorModelsFirstorderlow-passfilterInternal0(Discharge)t)SelResistanceito+1 (Charge)battAExp(s)Sel(s)1/(B-i(t))·s+1ExpVbatt>ControlledEcharge=fi(it,i*,Exp,BattTpe)voltageEbattEdischarge=f2(it,i*,Exp,BattType)sourceSource:Mathworks,Inc
Source: Mathworks, Inc. Battery Model Structure 1: Voltage-Resistor Models