Page - 246 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 616 Thesynthesizedcurrentvector is showninEquation(2): is= √ 2 3 (iA+ iB+ iC)= √ 2 3 × 3 2 iej(ωst+φ1). (2) It can be observed that the amplitude of the synthesized stator current vector is √ 3/2 times thatof thephasecurrent. IfwetakeaxisAasareferentialaxis, thespaceangleof thecurrentvector correspondswith thephaseAcurrent in the timedomain. Instarandindependentmodes, the line current of the inverter is the phase current and the current capacity imax is themaximumof the phase current. In trianglemode, line currents i1, i2, and i3 andphase currents iA, iB, and iC have therelationship: i1= iA− iC, i2= iB− iA, i3= iC− iB. (3) Accordingto this relationship,whenmotorsare insteadystate, thevectordiagramsof lineand phasecurrents in the timedomainareasshowninFigure4. 6 S Bi Ai Ci 1i2i 3i Ci Figure4.Timedomainvectorof linecurrentandphasecurrent. This indicatesthat, intrianglemode, theamplitudeofthelinecurrent is √ 3timesthatof thephase current insteadystate.Consequently,whenthecurrentcapacityof the inverter is imax, themaximum of thephasecurrent in trianglemodeandthemaximumamplitudeof thesynthesizedstatorcurrent vector is1/ √ 3 times that instarandindependentmodes. Instar, independent,andtrianglemodes, the relationships betweenmaximumamplitude of current vector ismaxY, ismaxD, and ismaxΔ are as showninEquations (4)and(5): ismaxY= ismaxD= √ 6 2 imax (4) ismaxΔ= √ 6 2 × imax√ 3 = √ 2 2 imax. (5) Limitationsonvoltageandcurrentvectorsdetermine theworkingrangesofeachwindingmode. In star and trianglemodes, flux-weakening regions are not set. In independentmode, there are non-flux-weakeningandflux-weakeningregions. Innon-flux-weakeningregions, if thestatorvoltage increases to thesaturation threshold, themotorstartsworking in theflux-weakeningregiontoexpand thespeedregulationrange. In thenon-flux-weakeningregionofeachwindingmode, themotor is controlled by theMTPA (maximum torqueper ampere)method [25]. In flux-weakening regions, themotor iscontrolledbythedirectfluxcontrolmethod.Basedonthepresentmotor’sangularvelocity ωs, thealgorithmcalculates thespecificstator’smaximumflux,ψ∗s . Then,onthebasisof requested torqueT∗e , axisdandq’sexpectedcurrent i∗d, i ∗ q areworkedout [26]. TheOW-PMSMdrivesystem’sparametersareshowninTable1; theexternalcharacteristic curves controlledbytheabovecurrentstrategyaredemonstrated inFigure5. 246