Page - 309 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 10 InFigure1,LS andLD represent themagneticcoils,CS andCD represent theresonantcapacitors, RS andRD represent theparasitic resistances, andM is themutual inductancebetweenLS andLD. Whenthesystemworks in theresonantstate,onehas:# VS “ iSRS´ jωrMiD jωrMiS “ iDRD` jVB (1) where iS and iD are the resonant currents in theprimaryandsecondarycoils, andωr is thesystem resonant frequency. BysolvingEquation(1),wehave:$’’’’’’’’’’’&’’’’’’’’’’’% |iS|“ VS` ωrMVBRD RS` pωrMq 2 RD |iD|“ ωrMVS RS ´VB RD` pωrMq 2 RS (2) Equation(2) showsthat thechargingcurrent iDdependsonωr,M,RS,RD,VS andVB.Normally, VBmaychangewhilecharging,as it increaseswith thestateofcharge(SOC)of thebattery. Because ωr=2πfr isupto100kHz,M is from20μHto100μH,RS is in themilliohmlevel, andVS isusually larger thanVB,wehave: ωrMVS RS "VB (3) BysubstitutingEquation(3) intoEquation(2),wecanfindthat iD remainsunchangedduringthe wholechargingprocess,whichrealizesaconstant-currentchargingfunction.As theproductofRS and RD is smaller thaneitherof them,Equation(2) is furthersimplifiedinto:$’&’% |iS|“ VBωrM |iD|“ VSωrM (4) It isworthmentioningthat thecurrentsourcecharacteristicofLC-LCseries topologyis tenable onlywhenthechargingobjectsarebatteriesorsomeothercapacitive load. BasedonEquation(2), the transferpowercanbeexpressedas: PLC´LC “|iD| ¨VB “ ωrMVS´VBRSRDRS`ωr2M2 ¨VB (5) 2.2. LCL-LCLTopology Similarly, thesimplifiedLCL-LCLtopology[18,29–31] is showninFigure2. Figure2.LCL-LCLtopology. 309