Direct Energy Converter Controllers for Switched Reluctance Motor Operation Andrew Simon Goodman, MEng(Honours) SubmittedtotheUniversityofNottinghamforthedegreeofDoctorofPhilosophy,April 2007. Abstract Thereisincreasingdemandforsimplemotordrivesofferinghighreliabilityandfaulttoler- anceinapplicationssuchastheaerospaceactuatorindustry,withthedevelopmentof‘more electricaircraft’. Thisthesispresentsamotordriveemployingaswitchedreluctancemotor,thenovelsingle sidedmatrixconverter,andanoveldoublebandhysteresisbasedcontrolschemeforcontrol oftheconverter,implementedusingafieldprogrammablegatearray(FPGA). The single sided matrix converter is a direct energy converter, capable of supplying unidi- rectional currents from a multiphase AC voltage source. It is suitable for driving motors such as the switched reluctance motor and trapezoidal permanent magnet direct current (PMDC) machine. The use of a direct energy converter removes the DC link energy stor- age element usually found in switched reluctance motor drives, making practical imple- mentation possible without the use of electrolytic capacitors. This is a requirement for applicationsintheaerospaceindustry. Controllerimplementationwithouttheuseofadig- ital signal processor (DSP) makes application of the converter in the aerospace industry easyasspecificDSPapprovalisnotrequired. Simulationsoftheconverteroperationarepresented,followedbyadescriptionoftheprac- tical implementation of the novel converter and control schemes. Practical results demon- strate the reliable operation of the converter, driving both switched reluctance and trape- zoidalPMDCmachines. The work has been published in three conference papers, presenting both the topology of thedriveandtheappliedcontrolschemes,aswellasanalysingthefaulttolerantcapabilities ofthedrive. i ii Acknowledgements I would like to thank Dr Keith Bradley for his wide ranging expertise, encouragement and trusting belief in me throughout this PhD. I would also like to thank Dr Pat Wheeler for his assistance with the hardware design, Xiaoyan Huang for her help with the PMDC machine, and Kevin Last, Colin Blackburn, Matt Cooper and the other workshop staff for the mechanical and electrical help needed in producing and testing the single sided matrix converterandsettingupthemotorloadingsystem. I also have to thank my friends both within and outside the Electrical and Electronic En- gineering Department of the University of Nottingham, especially Paul Robson, Graham Stabler,RoderickMacKenzie,EdwardChristopher,RalphFeldman,LeeEmpringham,Lil- iana de Lillio, Adam Docherty, Ashley Dobson and Ruth Staniforth, for their friendship, supportandvitaltechnicalassistancethroughoutthedifferentstagesofthisresearch. ThanksalsototheEPSRCforfundingme,andtoSwitchedReluctanceDrivesfortheloan oftheswitchedreluctancemotorusedinthefinalstagesoftheSSMCtesting. Finally, but most importantly i’d like to thank my family. Firstly my parents, Richard and Rosemary Goodman, for providing me with a loving, stable and stimulating upbringing, and for supporting me in many ways throughout my PhD. I could never have dreamt of reaching this stage in my education without them. I am also very greatful to my sister, EmilyGoodman,andherFiance´ SimonTalksfortheirsupport. iii KeytoAcronyms,Abbreviations&Terminology Notation Meaning ω RotationalSpeed θ Angularposition (V,I)A,B,C InputPhase(Voltages,Currents) (V,I)u,v,w,x,y OutputPhase(Voltages,Currents) A,B,C,U RequiredInputPhaseConnections (A,B,C)withpolarity(U) A/D AnaloguetodigitalConverter AC AlternatingCurrent CARAD CivilAircraftandTechnologyDemonstration D CurrentDirectionofChange DB DoubleBand DC DirectCurrent DSP DigitalSignalProcessor DTI DepartmentofTradeandIndustry EHA ElectrohydraulicActuator EMA ElectroMechanicalActuator EMF ElectroMotiveForce EPSRC EngineeringandPhysicalSciencesResearchCouncil FPGA FieldProgrammableGateArray I,i Current IC Integratedcircuit IGBT InsulatedGateBipolarTransistor IPC AssociationConnectingElectronicsIndustries L Inductance LinearSRM MagneticallyLinear,NonSaturating, RotatingSwitchedReluctanceMotor MOSFET MetalOxideSemiconductorFieldEffectTransistor PCB PrintedCircuitBoard ContinuedonNextPage... iv Notation Meaning PMDC PermanentMagnetDirectCurrent PWM PulseWidthModulation R Resistance RL ResistiveandInductive rms RootMeanSquare rpm RevolutionsperMinute SAa,SBa,SCa SSMCOutputCurrentHighSideSwitchesconnectingto inputphaseA,B,Crespectively SAb,SBb,SCb SSMCOutputCurrentLowSideSwitchesconnectingto inputphaseA,B,Crespectively SATOW SurfaceActuationofThinandOptimisedWings SB SingleBand sec Seconds Scope Oscilloscope SR SwitchedReluctance(Motor) SSMC SingleSidedMatrixConverter SVM SpaceVectorModulation t Time U1,U2,U3,U4 OutputCurrentwithrespecttoHysteresis BandLogicSignals V Voltage V+3,V+2,V+1 PositiveInputVoltageLevelBands V0 VoltageLevelzero V-1,V-2,V-3 NegativeInputVoltageLevelBands V1,V2,V3 RequiredVoltageLevel(withoutpolarity) VHDL Very-High-SpeedIntegratedCircuit HardwareDescriptionLanguage X,Y,Z,A,B,C InputVoltageStateLogicSignals x-x SwitchedReluctanceMotorPoleNumbers Contents 1 Introduction 1 1.1 ThesisStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 PowerElectronicConvertersincludingtheMatrixConverter 6 2.1 PowerElectronicConvertersOverview . . . . . . . . . . . . . . . . . . . . 6 2.1.1 ThePWMCurrentSourceRectifier . . . . . . . . . . . . . . . . . 8 2.2 DirectPowerConverters(ACInput) . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 TheCycloconverter . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 TheMatrixConverter . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 TheConventionalMatrixConverter . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 CircuitStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.2 MathematicalModelandModulationStrategies . . . . . . . . . . . 14 2.3.2.1 TheModulationProblemandBasicSolution . . . . . . . 18 v CONTENTS vi 2.3.2.2 TheOptimumAmplitudeAlgorithm . . . . . . . . . . . 20 2.3.2.3 ScalarModulationApproach . . . . . . . . . . . . . . . 22 2.3.2.4 SpaceVectorModulationApproach . . . . . . . . . . . . 24 2.3.2.4.1 SpacePhasors . . . . . . . . . . . . . . . . . . 24 2.3.2.4.2 MatrixConverterOutputSpacePhasors . . . . 25 2.3.2.4.3 SelectionofSwitchingStates . . . . . . . . . . 25 2.3.2.5 IndirectModulationApproach . . . . . . . . . . . . . . 30 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3 SingleSidedMatrixConverterDCDrive 33 3.1 TheSingleSidedMatrixConverter . . . . . . . . . . . . . . . . . . . . . . 33 3.1.1 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.1.2 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1.2.1 ControlPlatform . . . . . . . . . . . . . . . . . . . . . . 35 3.1.2.2 ControlApproach . . . . . . . . . . . . . . . . . . . . . 37 3.1.2.2.1 SingleBand . . . . . . . . . . . . . . . . . . . 37 3.1.2.2.2 DoubleBand . . . . . . . . . . . . . . . . . . 37 3.1.3 AdvantagesoverotherPowerConverters . . . . . . . . . . . . . . 40 3.2 SuitableMotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 CONTENTS vii 3.2.1 SwitchedReluctance . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.2 TrapezoidalPermanentMagnetDC . . . . . . . . . . . . . . . . . 45 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4 SingleSidedMatrixConverterSimulation 52 4.1 SwitchedReluctanceMotorModel . . . . . . . . . . . . . . . . . . . . . . 53 4.2 TrapezoidalPMDCMotorModel . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 SingleBandControllerModel . . . . . . . . . . . . . . . . . . . . . . . . 61 4.4 DoubleBandControllerModel . . . . . . . . . . . . . . . . . . . . . . . . 65 4.5 Inductive/ResistiveLoad . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.5.1 PulsedOutputCurrent . . . . . . . . . . . . . . . . . . . . . . . . 69 4.5.2 ContinuousOutputCurrent . . . . . . . . . . . . . . . . . . . . . . 72 4.5.3 FourierAnalysisofPulsedCurrentinRLLoad . . . . . . . . . . . 74 4.5.3.1 SingleBandControl . . . . . . . . . . . . . . . . . . . . 75 4.5.3.2 DoubleBandControl . . . . . . . . . . . . . . . . . . . 83 4.5.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.5.4 DeviceLossEstimationandComparison . . . . . . . . . . . . . . 91 4.6 SwitchedReluctanceMotorLoad . . . . . . . . . . . . . . . . . . . . . . 92 4.6.1 Speed-530rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 CONTENTS viii 4.6.2 Speed-3080rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.7 PMDC(SATOW)MotorLoad . . . . . . . . . . . . . . . . . . . . . . . . 101 4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5 PrototypeDrive-ConstructionandControlImplementation 107 5.1 ConverterHardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.1.1 FPGAControllerPCB . . . . . . . . . . . . . . . . . . . . . . . . 109 5.1.2 ResolverInterfacePCB . . . . . . . . . . . . . . . . . . . . . . . . 111 5.1.3 CurrentMirrorsPCB . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.1.4 VoltageTransducersandClampPCB . . . . . . . . . . . . . . . . 114 5.1.4.1 ClampVoltageMonitoringCircuit . . . . . . . . . . . . 115 5.1.5 MatrixPowerPCB . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.1.5.1 HighVoltage/HighCurrentAreas . . . . . . . . . . . . . 117 5.1.5.1.1 HighVoltageImplications . . . . . . . . . . . 121 5.1.5.1.2 HighCurrentImplications . . . . . . . . . . . 122 5.1.5.1.2.1 CopperAreaRequired . . . . . . . . . 123 5.1.5.2 GateDriveCircuit . . . . . . . . . . . . . . . . . . . . . 126 5.1.5.3 LowVoltageControlandMeasurementSignals . . . . . 128 5.1.5.4 MechanicalConsiderations . . . . . . . . . . . . . . . . 128 CONTENTS ix 5.2 FPGAControllerDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.2.1 FPGADesignConsiderations . . . . . . . . . . . . . . . . . . . . 130 5.2.1.1 DataValidity . . . . . . . . . . . . . . . . . . . . . . . . 131 5.2.1.2 NumericalManipulation . . . . . . . . . . . . . . . . . . 131 5.2.1.3 StateMachines . . . . . . . . . . . . . . . . . . . . . . . 132 5.2.2 ControlStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2.2.1 TransducerDataAcquisitionandProcessing . . . . . . . 134 5.2.2.2 InputVoltageStateDetermination . . . . . . . . . . . . 136 5.2.2.3 Resolver Data Processing, Filtering and Current Refer- enceCreation . . . . . . . . . . . . . . . . . . . . . . . 136 5.2.2.4 PhaseCurrentControllers . . . . . . . . . . . . . . . . . 139 5.2.2.4.1 SingleBandCurrentController . . . . . . . . . 140 5.2.2.4.2 DoubleBandCurrentController . . . . . . . . 143 5.2.2.5 TripHandling . . . . . . . . . . . . . . . . . . . . . . . 145 5.2.2.6 DataExtraction . . . . . . . . . . . . . . . . . . . . . . 146 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6 PrototypePracticalResults 149 6.1 BasicControlDataRequiredforBothControlSchemes . . . . . . . . . . . 149