Directtorquecontrolofdouble Star Permanentmagnetsynchronousmachine

DirectTorqueControlofDouble Star permanentmagnetSynchronousMachine

B.NAAS1,2,B.NAAS1,L.NEZLI1,M.ELBAR1,2,M.O.MAHMOUDI,M.SBOUCHERIT.

,,,

1ProcessControlLaboratory,NationalPolytechnicSchool,Algiers,Algeria

2ElectricalEngineeringDepartment,ZianeACHOURUniversity,Djelfa,Algeria

Abstract—Inordertoincreasetheavailabilityoftheembarked actuators onesolutionistoequipthemwithdouble-star machines.Toincreasetheircompactnessthepermanentmagnet synchronousmachines(PMSM)areusuallypreferred.

ThisstudydescribesthecontrolofdoublestarPMSM,using

Direct Torque Control(DTC). TheimplementationoftheDTC appliedtoadoublestarsynchronousmachineisvalidatedwith simulated results. Inthispaperamethodformodeling and simulationofsynchronous motordrivesusing MALAB/SIMULINK.

B. Assumptions

Thestudypresentedinthispaperisbaseduponhefollowing assumptions:

- Thetwostarsareidenticalshiftedupanangle.

- Therotorusnon-salient.

- Thethreewindingsofeachstarareshiftedbyθ=1200.

- The magnetomotrice forces in the air-gap have a sinusoidalrepartition;

- Thesaturationoftheironinthemachineisneglected.

Index Terms—direct torque control (DTC), Double star synchronousMachine(DSPMSM),andinverter.

I. INTRODUCTION

Since,years80,doublearmaturesynchronousmachine

DSSMsuppliedbypowerelectronicconverterarewidely

b2 ib2

Vb2

Vb1

Φf

Va2

ia2

usedformarineapplications [1],[4],[6].Duetotheir compactnessandnopowerlossesintherotorsynchronous

machines permanentmagnet(PMSM)areincreasingly used inembeddedsystems.Innumberofapplications, suchas actuatorsusedinthe fieldofaeronauticsorcars[13],[14].

Nowadays,theactualdevelopment ofpowerelectronics devicesallowssupplyingDSSMbyPWMinverter[5],[7].In theotherhand,thevectorcontroltechnique [8],[9]allows improvingperformancesofthisspeeddrive.

ThedifficultytocontroltheDS-PMSMsuppliedbystrong couplingis duetothestrongmagneticcouplingbetween.

Vc1

ic1

Vc2

γ θ

ic2

Va2

Va1

ia1

II. ELECTRICALDRIVE SCHEME

Theelectrical driveconsideredwiththisstudy isshownin figure(1).Itiscomposed ofdoublestarsynchronous machinesuppliedoftwoinverters.

III. MODELOFDOUBLESTARSYNCHRONOUS MACHINE

Fig.2Electricalwindingsdoublestarpermanentmagnet

synchronousmachine

C.Electricalequationswith(α.β)frames

ByapplyingtheConcordiatransformationto eachstar, the(α,β)modelofdoublestarpermanentmagnet synchronousmachineisobtained[11],[12].Thus,the machinewindingscanbesubstitutedbyanequivalent schemeinthe(α,β)frameasshowninfigure(3):

A. Description

Aseveryrotatingelectricalmachine,thedoublestar permanentmagnetsynchronousmachineiscomposedofa statorandrotor.Asshowninfigure(2),thestatorisatwo three-phasewindings,socalledstar,shiftedupbyanangle γ=300.

Controlofinverter

D D2 D3

T11

T12

T13

R C

D1 D2 D3

T’12

T’22

T’12

T11

T12

T13

DSPMSM

T’12

T’22

T’32

Controlofinverter

Fig.1Electricaldrivescheme

Vβ1

Vβ2

iβ1

iβ2

Indoublestarmachine

(10) (11)

Vα2

iα2

Vα1

iα1

IV. DIRECTTORQUECONTROLPRINCIPLE

Thedirecttorquecontrol ofadoublestarpermanent magnetsynchronous machineisbasedonthedirect determination ofthesequencecontrolusedtoswitcha voltageinverter.

Fig.3Representationoffictitiouscoilsdiphasicin (α,β)

frame

Theelectricalequationin(α,β)frame:

(1) (2)

(3)

(4) Thefluxequation

(5)

(6) (7) (8)

Electromagnetictorque

(9) (10)

Thischoice isusually basedonuseofhysteresis comparators whosefunctionistocontrolthesystemstate, namelythe amplitudeof stator flux and electromagnetic torque.AVoltage Inverterdeliverstwelvedistinctpositions (figure4)intheplanphase.

DTCinsingleinverterutilizesthe(23=8) eightpossible statorvoltage vectors,twoofwhicharezerovectors,to controlthestatorfluxandtorquetofollow thereference valueswithinthehysteresis bands. Thevoltage spacevector ofathree-phasesystemisgivenby:

(12) (13)

Thecontrolsequencesofthetwoinvertersisdoneinaway thatwill havethevoltage vectorsattheexitofthesecond inverteroffsetbyanangleof300,thevectorsofvoltageatthe outputoffirstinverterfigure1.

(14)

Fig.4Voltagespacevector

A combinatorialanalysis of switch states of the two

Thisangleshiftbetweenthetwostarsofthemachines,which

invertersgives(2

=64)switchingmodes,ie64different

is equalπ/6.

V4 V3

vectorsVS possible.Hencethere are sixty four possible

combinations for controlling the switches of the two

inverters.TableI.

Wewillthereforeamongthesixty-foursequences,twelve activesequences.Thesevectorsdefinetwelvevoltageat the outputofbothinvertersVSi(i=1,2,..,12),andfoursequences (Si=000000,000111,111000,111111)aresequencesof freewheelinganddefinefourzerovoltagevectors.Thetruth tablefortheactivesequencescanbesummarizedin the followingtable:

TheorderbytheDTCofDSSMcanberepresentedby figure5.

V9 V1

ࢣs*

ࢣs

φs*

ࢣ

Truth

Table

Sa1b1c1

ia1b1c1

DS-PMSM

Sa2b2c2

φs

ીs

ia2b2c2

Torque

Estimator

φsαβ

FluxEstimator Voltage

Estimator

Va1b1c1

Va2b2c2

isαβ

Vsαβ

Concordia

Transformation

Fig.5DirecttorquecontrolofDSPMSM

J=0.005N.m2/s,Mfd=1.518H,if=1A, fr=0.001N.s/rad.

V. NUMERICALSIMULATIONRESULTS

ThepaperdescribesaMATLAB SIMULINK that providesfacilitiesforinvestigationofalgorithmsforsolving directtorquecontrolproblems ofdoublestarsynchronous machine.

B.Parametersforthe DoubleStarSynchronousmachine:

Motordetails:5kW,3phase,50Hz,1pole,200v, Rs=2.35Ω,Ld=0.1961H, Md=0.185H,

Lq=0.1105H,Mq=0.1005H,γ=300,

0.14

StatorFlux

VI. CONCLUSION

0.12

0.1

0.08

0.06

0.04

0.02

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Temps(s)

TrajectoryoftheStatorFlux

Inthispaper,wepresentedthedirectcontrolofthetorque ofthesynchronous doublestarmachinesuppliedbytwo voltageinvertersattwolevels.

Thisstudypresents acontrolstrategy foradouble stator thepermanent magnetsynchronous machinebasedonthe direct control torque (DTC) using an PI regulator. The

simulationresultsshowthattheDTCis anexcellentsolution forgeneral-purposeDSSMdoublestarsynchronousmachine

0.15

0.1

0.05

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-0.1 -0.05 0 0.05 0.1 0.15

phialfa1(Wb)

ElectromagneticTorque

drives.Inverywidepowerrange.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

drives for electrical propulsion,” IEE: 9

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ZoomElectromagneticTorque

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0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6

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