Page - 310 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 10 In thisfigure,L1 andL4 are thematching inductorsofLS andLD,R1 andR4 are theirparasitic resistances. For high power applications, LS and LD are normally bulky, which make L1 and L4 bulky, and this is not beneficial for the objectives ofminiaturization and lightness. Thus the compensatingcapacitorsCS1 andCD1 are introducedtodecreaseL1 andL4. Still, theyshouldsatisfy the followingequations: CS1 “ 1 ωr2pLS´L1q, CD1 “ 1 ωr2pLD´L4q (6) ωr “ 1a L1CS “ 1? L4CD (7) Actually, LCL is a transformation of theLCparallel topology [18]. It iswell-known that the reflected impedanceof theLCparallel topologycontainsan imaginarypart [23], especiallywhenthe mutual inductanceandthe loadchangeonline,whichmakes the tuningprocessverycumbersome. Theadditional inductorof theLCLtopologycan justeliminate this imaginarypartwhether themutual inductanceandthe loadchangeornot.Usingamethodsimilar to that inSection2.1,wecanconclude that theLCL-LCLtopologyalsohasconstant-currentchargingcharacteristics. Theparasitic resistances areusuallysmalldueto theuseofLitzwires, thusneglectingtheparasitic resistanceswillnotaffect thesystemefficiencysharply,andinpractice that loss isverysmall comparedwith the losscausedby theHBridgeandrectifier, sowecanget thesimplifiedcalculationformulasof theLCL-LCLtopology as follows: iS “ VSjωrL1, i4 “ j MVS ωrL1L4 , iD “ VBjωrL4, i1 “ j MVB ωrL1L4 (8) Thetransferpowercanbewrittenas: PLCL´LCL “ MVSVB2ωrL1L4 (9) Equation(9) showsthat thechargingpowercanbeadjustedbyVS. UnlikeEquation(5), thereare twoadditionalpowerregulationfreedomsL1 andL4. 2.3. Comparisonbetween theLC-LCSeriesTopologyandLCL-LCLTopology The LC-LC series topology andLCL-LCL topology arewidely used in practice, as both can realize theconstant-currentchargingcharacteristics, theunity-power-factorcharacteristicsandeven bidirectionalpower transfercharacteristics. Their transferpowercharacteristicsarehoweverdifferent, for instance, the transferpowerof theLC-LCseries topology increaseswith the increasing transfer distancesaccordingtoEquation(5),andthetransferpoweroftheLCL-LCLtopologydecreaseswiththe increasingtransferdistanceaccordingtoEquation(9).However, their transferefficiencycharacteristics havenotbeencomparedbefore, thus thissectionaimstocompare themtoprovidesomesuggestions forpracticalengineeringdesign. Thechargingpowerandmagneticcoilsof the twotopologiesmust be identical, asonly thencan theefficiencycomparisonbemeaningful. Thechargingpowerof the LC-LCseries topologyequals to thatofLCL-LCLtopology, if theirchargingcurrentsaredesignedto be thesame,as theybothhavetheconstant-currentcharacteristic. BasedonEquations (4)and(8),we canwrite: VS ωrM “ MVS ωrL1L4 (10) FromEquation(10),onehasM2=L1L4. Thismeans that thechargingpowerof the twotopologies are the same if the product of two compensating inductors in the LCL-LCL topology equals the mutual inductanceM.Whenthe transferdistancesare10,15,20,25and30cm, themeasuredmutual inductancesbetweentwomagneticcoils (LS andLD) are107.155μH,66.66μH,42.538μH,28.125μH, 18.888μH,respectively.Normally, thedistancebetweenthechassisandgroundisaround20cm, thus thecorrespondingmutual inductanceM isaround42.538μH.AssumingthatL1 equalsL4, onehas 310