Page - 166 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 5 7LPH V 7LPH V (a) (b) (c) (d) Figure5. (a)The loadcurrentprofileof theurbandynamometerdrivingschedule (UDDS) test; (b) the loadcurrentprofileof theworldwideharmonized lightvehicles testprocedure (WLTP) test; (c) the loadcurrentamplitudedistributionof theUDDStest; (d) the loadcurrentamplitudedistributionof theWLTPtest. 3.2.2.Determinationof theLengthof theFittedExperimentalDataset Thediffusionprocess,which is causedby thegradient in concentration, playsamajor role in the lowC-rate load current and rest cases. Since the electrochemical reactions occurring during the diffusion process are very complex, these reactions can be accurately modeled as infinite series-connectedRCnetworkswithawiderangeof timeconstants (τ1,τ2, . . . ,τj). Usually, thevalues of timeconstantsdependontheelectrodethicknessandthestructureof thebattery toagreatextent, andtypical timeconstantsare in therangeofseconds tominutes [45]. ThesecondorderRCnetwork canonlyapproximate thediffusionprocessbytwoparts: the fastdynamicspart (theshort-termRC networkwithτshort) andtheslowdynamicspart (the long-termRCnetworkwithτlong). In general, the values of the two time constants are closely related to the length of thefitted experimentaldataΔt.Whenonly the initial segmentof thevoltageresponse isemployedinparameter estimation, suchasPartAin thebottomsubfigureofFigure1, thevoltagesacross theshorter-term RCnetworkshave a largerdegree of variability,whichmeans that the shorter-termRCnetworks haveagreater impactonthe initial segmentof thevoltageresponse. This in turn leads to thesmaller estimated timeconstantsandsubsequently ignores theslowerdynamicsdiffusionprocess. Onthe contrary,after the initialphaseof therestperiod, suchasPartB in thebottomsubfigureofFigure1, thevoltagesacross theshorter-termRCnetworkshaveconvergedtozero; thus, thevoltagevariation causedbytheshorter-termRCnetworks isnegligible. Instead, thevoltagesacross the longer termRC networksmakearemarkablecontributiontothetotalvoltageresponse. Subsequently, itcanbeinferred that themeasureddatashowaslowervaryingcharacteristic,whichrepresent theslowerdynamics diffusionprocessandcanbemodeledbytheRCnetworkswith larger timeconstants.Hence, if the wholevoltageresponseof the longtimerestperiodisadopted,datawithslowervaryingvalueswill account fora largeportion,whichwill leadto therelatively largerestimatedtimeconstants.However, too large timeconstantswillmakethemodeloutputvoltageseverely lagbehindtheactual response andresult inapoordynamicperformance. 166