Page - 251 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 616 3.1. CurrentModulationMethod inStarandTriangleModes Starmoderequiredendsof three-phasestatorwindingsconnectedtoonepoint,whichcouldbe accomplishedbymakingall lowerarmsof the idle inverter’sbridges turnedonat thesametimein dual invertersconfigurationwhile theother inverterwasworkingtocontrol the three-phasecurrent. BasedonexpectedtorqueT∗e ,wecouldgetcontrolvariables i∗d and i ∗ q throughtheabovementioned MTPAandflux-weakeningstrategy. Then,withdq0toABCcoordinationtransformation,expected phase currents i∗A, i ∗ B and i ∗ C were obtained;meanwhile, actual phase currents iA, iB, and iC were acquiredvia thecurrent sensor. Phasecurrenterror representedthedifferencebetweeneachphase expectedcurrentandtheactualcurrent,which isdemonstratedbyfollowingformula: ΔiA= iA− i∗A,ΔiB= iB− i∗B,ΔiC= iC− i∗C. (20) Fromeachphasecurrent’serror,wecouldcontrol the three-phasecurrent.Giventhehalf-width of thecurrent’shysteresisband, theacceptablecurrenterror ish.WhenonephasecurrenterrorΔi≥ h, theupperarmof thisphase’s inverterbridgewasturnedoffandthe lowerarmwasturnedon,making themidpointvoltageof thisphase−Vdc/2, a lowervoltage, and thephase current errorΔiof this phasedecreasing.WhenphasecurrenterrorΔi≤−h, theupperarmof thisphase’s inverterbridge wasturnedonandthe lowerarmwasturnedoff,makingthemidpointvoltageof thisphaseVdc/2, a lowervoltage,andthephasecurrenterrorΔiof thisphase increasing. Trianglemode requires theheads and tails of three-phase statorwindings tobe connected in a circle, which is completed by shutting downone power source and turning on triangle circuit switch. Theother side’s inverterwasworking to control themotor’s current. Whatwasdifferent fromstarmodewasthat trianglemode, insteadofcontrolling themotor’sphasecurrent iA, iB, and iC directly, controlledmotor’s line current i1, i2, and i3 to controlmotor’s phase current indirectly. The relationshipof trianglemode’sphase current and line current is shown inEquation (3). With Equation(3),wecantransformphasecurrent’sexpectedvalue i∗A, i ∗ B, and i ∗ C to linecurrent’sexpected value i∗1, i ∗ 2, and i ∗ 3, thendetermine line current’s errorΔi1,Δi2, andΔi3 to have each line current hysteresiscontrolledrespectively. If ignoringzero-sequencecurrent in trianglecircuit,wegot iA+ iB+ iC=0,andthenwecould get thephasecurrentexpression, representedbythe linecurrentasEquation(21)viaEquation(3): iA=(i1− i2)/3, iB=(i2− i3)/3, iC=(i3− i1)/3. (21) If theacceptable linecurrenterrorwashl, thehalf-widthof thehysteresisbandof i1, i2washl, andtheacceptableerrorof i1− i2was2hl, thenwecouldcalculate theacceptableerrorofphasecurrent iA = (i1− i2)/3as 2hl/3. Thus, itwas clear that if the acceptable error ofphase current stayedat h, the line currenthysteresis comparator’s acceptable current errorwas required tobe set at 3h/2, sowehad: hl=3h/2. (22) At thispoint, if ignoring thezero-sequence current, the trackingerrorof thephase current in trianglemodewasthesameas that instarmode.However,note that the topologyof trianglemode is different from that of starmode andDCbusvoltagewasdirectly loadedon thephase current. Ineverycombinationof inverterswitchingstates, therearefivepossiblephasevoltages instarmode: −2Vdc/3,−Vdc/3, 0,Vdc/3, 2Vdc/3. In trianglemode, there are threepossiblephasevoltageswith higheramplitude:−Vdc, 0,Vdc. Therefore, if thehalf-widthof thehysteresisbandwasdetermined accordingtoEquation(22), eventhoughtheacceptable trackingerrorof thecurrent in trianglemode wasthesameas that instarmode, thecurrentsawtoothfluctuation in trianglemodeismoredrastic than that in starmodeand the switching frequencyof inverters, alongwith the core lossofmotor, wouldbegreater thanthose instarmode. 251