Seite - 228 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 410 3.4. BoundaryConductionMode Theboundarynormalized inductor timeconstantτL,B canbedefinedas: τL,B “ LsfswR (18) whereR is low-side inputequivalent resistance. Duringboundaryconductionmode(BCM), the inputcurrentBDCcanbederivedas: IL “ 4VLLsfswp1´Ddq (19) SubstitutingEquation(19) into (18), theboundarynormalizedtimeconstant inchargestatecan beexpressedas: τLd,B “4p1´Ddq (20) Similarly, indischargestate, the inputcurrentof thestudiedBDCcanbeobtainedas: IL “ 4VLLsfswDb (21) Theboundarynormalizedtimeconstant indischargestatecanbeexpressedas: τLb,B “4Db (22) Figure13showstheplotsofboundarynormalized inductor timeconstantcurvesτLd,BandτLb,B inchargeanddischargestates. TheBDCinchargestateoperates inCCMwhenτLd isdesignedtobe higher thantheboundarycurveofτLd,B. ThestudiedBDCindischargestateoperates indiscontinuous conductionmode(DCM)whenτLb is selectedtobe lower thantheboundarycurveofτLb,B. Figure13.Normalizedboundary inductances timeconstant inchargeanddischargestates. Figure14shows theboundary inductances curveof thestudiedBDCinchargeanddischarge states. If the inductance isselectedtobe larger thantheboundary inductance, thestudiedBDCwill operate inCCM.The studiedBDCcanoperatenotonly in charge statebut also indischarge state, theboundary inductancecanbederivedasbelowfromEquations (19)and(21), respectively. Ld,B “ 4p1´Ddqfsw V2L Pout (23) Lb,B “ 4Dbfsw V2L Pout (24) wherePout is theoutputpower. 228