Page - 245 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 616 1 1 2 dc V 1 1 2 dc V 2 1 2 dc V 2 1 2 dc V Amu Bmu Cmu nmu Figure2.Schematicdiagramofmid-pointvoltage. 1 2 dc V 1 2 dc V 1 2 dc V dcV dcV 1 2 2 dc dcV V 1 2 2 dc dcV V 1 2 2 dc dcV V (a) Star mode (b) Triangle mode (c) Independent mode Figure3.Synthesizingvoltagevectorofeachwindingmode. Theamplitudesofbasicvoltagevector instar, triangle,andindependentmodesusbY,usbΔ and usbD canbeobtainedfromFigure3as √ 2/3Vdc, √ 2/3×√3Vdc, and √ 2/3(Vdc1+Vdc2), respectively. In these equations, √ 2/3 is the equal-power conversioncoefficient. Wecansee thatwhen thebus voltage isVdc, theamplitudeof thebasicvoltagevector in trianglemode is √ 3 times that instarmode. In independentmode,whenbusvoltageVdc1=Vdc2=Vdc, theamplitudeof itsbasicvoltagevector is twice that instarmodeand2/ √ 3 times that in trianglemode. Ithas tobenotedthat theabovebasic voltagevectorsaredistributedwithanπ/3angle interval, and ineachwindingmodetherearesix equal-amplitudebasicvoltagevectors formingavoltagevectorhexagon in themotorvectorplane. It is likely thatvoltagevectormaynotequal theamplitudeofahexagonvertex’svoltagevector inany angle.Hence, theamplitudeof thevoltagevector in themotor’sappropriate linear range is supposed tobe theradiusof the inscribedcircleofahexagon √ 3/2times theamplitudeofbasicvoltagevectors when the switch status are as above. Then, themaximumamplitudeof the voltage vector at any angle instar, triangle, andindependentmodesusmaxY,usmaxΔ, andusmaxD are:Vdc/ √ 2, √ 6Vdc/2,and (Vdc1+Vdc2)/ √ 2, respectively. Nowwewilldiscuss the stator current’s limitationsonwindingmodes. Becauseofwindings’ inductancecharacteristics, thephasecurrentof themotorhas inertiaandcannotabruptlychange like voltage. Therefore, insteadystate, thewaveformsof the three-phasecurrent in the timedomainare equal-amplitudesinusoidwith2π/3phasedifference. Three-phasecurrentvectorsaredemonstrated inEquation(1): ⎧⎪⎨ ⎪⎩ iA= icos(ωst+φ1)ej0 iB= icos(ωst+φ1− 2π3 )ej 2π 3 iC= icos(ωst+φ1− 4π3 )ej 4π 3 . (1) 245