Seite - 248 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 616 Undermost circumstances, thedifferencesbetweenboth sides’DCbusvoltageare small and thehighest rotaryspeedsof themotor in thenon-flux-weakeningregion, triangleandindependent mode increase in theordernmY<nmΔ<nmD. Inaccordancewith this inequality,wedefineswitching fromstarmodeto trianglemode, fromtrianglemodeto independentmode,andfromstarmodeto independentmodeasupswitching; switchingfromindependentmodeto trianglemode, fromtriangle modetostarmode,andfromindependentmodetostarmodearedownswitching. Wewill beginwith theupswitchingstrategy. Duringmotorworkingperiod,parameters such asmagnetfluxandinductancefluctuatebecauseof rising temperature, followedbyfluctuationsof workingrangesofeachwindingmode. Toavoidfrequentswitchingwhentheworkingpointof the motorfluctuates, this paper proposes an algorithm to judge the saturation state of torque. When judgedaspositive,upswitching is triggeredtoensure theaccuracyof theswitchingboundary. This algorithm functionsduring theprocess of torque increasing fromzero to themaximum. It calculateswhen the expected torque is at amaximum, the timeperiod tint duringwhich torque increases fromzero to themaximumat this specificrotaryspeedin thecurrentwindingmode(staror triangle)as integration timeandintegrationofabsolute torqueerrorΔT (thedifferencebetweenactual torqueTl andexpectedtorqueT∗e )as threshold Ith in thisprocess. Then, it calculates integration Iof absoluteactual torqueerrorΔT from tint to thepresentandcompares itwith integration threshold Ith. If I≥ Ith, then themotor’s torque isalmost saturatedanddoesnotmatch theexpected torque. Thisalgorithmisbasedonwhether theoutput torqueagreeswith theexpectedtorque inaparticular periodtoeliminateuncertainties in thewindingmodes’workingrangebecauseoffluctuations in the motor’sparameters. Voltageequationsofmotor indqcoordinationareexpressed inEquations (6)and(7): ud=Rsid+Ld did dt −ωrLqiq (6) uq=Rsiq+Lq diq dt +ωr(Ldid+ψf). (7) Electromagnetic torque isshowninEquation(8): Te= p0iq[ψf+(Ld−Lq)id]. (8) Fromtheaboveequations,wecantell thatelectromagnetic torqueTe ismainlydeterminedbyaxis q’scurrent iq; thesmaller the inductancedifferencebetweenaxisdandq, thebigger theshare that iq determines.WhenLd=Lq=Ls themotor issurface-mounted;MTPAcontrol is id=0control. For the sakeof simplifyingcalculations, the integration timeof torque tint isderivedas id= 0control, and whenthedifferencebetweenLd andLq is small,MTPAcontrol is still accurateusing tint. Inaddition, because Lq ≥ Ld, the inertia of iq is higher and the change rate of iq is smaller if appliedwith the samevoltage,whichmakes thecalculated integrationtime tint isbiggerandthethresholdof torque saturation ishigher. Whenusing id= 0control, due to the currentof axisdbeing0, voltageequationsand torque expressionofmotor indqcoordinationhavechangedto: ud=−ωrLqiq (9) uq=Rsiq+Lq diq dt +ωrψf (10) Te= p0ψf iq. (11) Voltagevectorshave therelationship: u2s=u 2 d+u 2 q=(−ωrLqiq)2+(Rsiq+Lq diq dt +ωrψf) 2 . (12) 248