An FPGA Controller Based Real Time Implementation of a PMSM Drive

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A FIELD PROGRAMMABLE GATES ARRAY CONTROLLERBASED REAL TIME IMPLEMENTATION OF A

PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE

BySouvik Dasgupta

Registration No. 210606001 of 2006-07Roll No. 160606001

Under the Guidance of

Dr. Kaushik MukherjeeAnd

Dr. Mainak Sengupta

A thesisSubmitted in partial fulllment of the requirements for the degree of

Master of Engineering (Electrical Engineering)Specialization in Power Electronics and Drives

Department of Electrical EngineeringBengal Engineering and Science University,

ShibpurHowrah - 711 103

West Bengal, India


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BENGAL ENGINEERING AND SCIENCE UNIVERSITYHOWRAH-711103

FOREWORD We hereby forward the thesis entitled A FIELD PROGRAMMABLE

GATES ARRAY CONTROLLER BASED REAL TIME IMPLEMEN-TATION OF A PERMANENT MAGNET SYNCHRONOUS MOTORDRIVE submitted by Souvik Dasgupta (Registration No. 210606001of 2006-2007) under our guidance and supervision in partial fulllment of the requirementsfor the degree of Master of Engineering in Electrical Engineering (Specialization:Power Electronics and Drives) from this University.

(Dr. Kaushik Mukherjee) (Dr. Mainak Sengupta)Senior Lecturer Assistant Professor

Dept.of Electrical Engineering Dept.of Electrical EngineeringBengal Engineering and Science University Bengal Engineering and Science University

Howrah-711103 Howrah-711103

(Dr. S.P.Ray) ( Dr. M. Halder)Professor and Head Professor and Dean, FEAT

Dept.of Electrical Engineering Bengal Engineering and Science UniversityBengal Engineering and Science University Howrah-711103

Howrah-711103

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CERTIFICATE OF APPROVAL

The foregoing thesis entitled A FIELD PROGRAMMABLE GATESARRAY CONTROLLER BASED REAL TIME IMPLEMENTATIONOF A PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE

is approved as creditable study of an engineering subject carried out and presentedsatisfactorily to warrant its acceptance as a pre-requisite to the degree of Masterof Engineering in Electrical Engineering (Specialisation: Power Electronics andDrives ) of this University. It is understood that by this approval the undersigneddo not necessarily endorse or approve any statement made, opinion expressed orconclusion drawn therein, but approve the thesis paper only for the purpose forwhich it is submitted.

BOARD OF EXAMINERS

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ACKNOWLEDGEMENT

The author wishes to record his deep sense of gratitude to his supervi-sors, Dr. Kaushik Mukherjee and Dr. Mainak Sengupta, who have introduced thepresent area of work and guided in this work. The author also wishes to thankDr. Prasid Syem ,Prof. Debjani Ganguly for helping him with different sugges-tions. The author is also thankful to Prof. S. P. Ray for permitting him to usethe instruments of the department. The author is also indebted to his classmatesMr. Bhaskaran Barman, Mr. Prasanta Patra and NaMPET Project AssistantMr. Utpal Samanta and Mr. Avijit Ghosh for different constructive criticisms indifferent phases of the work .The author is also thankful to his seniors Mrs. Anin-dita Jamatia , Mr. Sudhin Roy, Mr. Pabitra Kumar Biswas for their criticismin different technical subjects and for their teachings in different power electronictools. The author also wishes to thank the NaMPET-FSS project for the fund-ing. Last but not the least, the author is strongly indebted to the almighty forpresenting him worlds best parents, who are not only supportive but also helpfulin different phases of his life.

(Souvik Dasgupta)Reg. No. 210606001Roll No. 160606001

Bengal Engineering and Science UniversityDate:

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Dedicated to my parents,Sri Sankar Dasgupta

and Smt. Mamata Dasgupta

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AbstractThis thesis is directed towards analysis, design, digital computer simulation

and practical implementation of a Permanent Magnet Synchronous Motor (PMSM)drive. The drive is suited for a low voltage ( 48V ) high current ( 20A) appli-cation.

A three phase permanent magnet synchronous motor, having three hall posi-tion sensors, as available in laboratory, is used for the PMSM drive experiments.The electrical parameters of this prototype machine is rst experimentally deter-mined. The adopted experimental method is deduced analytically on the basis of coupled circuit concepts initially and experimentation has been performed accord-

ingly.

Next, a basic PMSM drive, consisting of this machine and a self-commutatedIGBT based inverter, has been practically implemented. The inverter controlis done through eld programmable gate array (FPGA) in 120 0 conduction self controlled mode by processing of the three position sensor signals inside FPGAitself. A Detailed Numerical Model of this drive has been developed, by whichits starting, dynamic and steady-state performances are predicted. The steady-state performances are experimentally validated on the implemented prototype.Subsequently, an Averaged Dynamic Model, based on an averaging technique, ispresented, which has the simplicity of that of a conventional separately excited DC

motor with mechanical commutator. This Averaged Dynamic Model is capableof predicting both dynamic and steady-state behaviors of this drive. The perfor-mance as predicted by the Averaged Dynamic Model is validated experimentally,as also with the Detailed Numerical Model. They are found to match closely.

Subsequent section of the thesis deals with the position sensorless operation of the self controlled 120 0 conduction VSI fed the PMSM drive. Two schemes areproposed and simulated. One scheme uses two voltage and two current sensors tosense any two phase voltages and any two phase currents of the PMSM to derivethe rotor position information of the PMSM. This scheme is found to start themachine and operate at any speed. The main disadvantage of this scheme is that,

before starting the machine the rotor must be brought to a particular position.This scheme does not require almost negligible real-time computational effort. Thesecond scheme requires a Luenberger Observer realization in FPGA platformand information of DC link voltage and DC link current, that is one current sensorand one voltage sensor would be required for experimental implementation. Theobserver is realized on the basis of the Averaged Dynamic Model of the PMSM,derived earlier, in the work. The observer-based method can start the machinefrom any arbitrary rotor position and operate at any speed. The observer hasdigitally been programmed in FP GA platform.

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Next, vector control of a PMSM drive is studied through digital computersimulation. A Hysteresis Comparator based two-level voltage source inverter(VSI)-fed drive as well as a Sine PWM VSI-fed drive are simulated. A position sensorless vector controlled PMSM drive implementation is proposed and simu-lated.

Signicant control blocks for experimental implementation of a vector-controlledPMSM drive incorporating a two-level transistorized VSI are ultimately developedand tested in an FPGA environment and real time simulation of a rotor-positionsynchronized two-level VSI to feed a PMSM has been nally performed and tested.

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Contents

1 Introduction 1

1.1 General discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Operation of PMSM under Self control . . . . . . . . . . . . . . . . 21.3 Need of digital controllers in drives application . . . . . . . . . . . 61.4 Relevance of the work undertaken . . . . . . . . . . . . . . . . . . . 71.5 Outline of the present work . . . . . . . . . . . . . . . . . . . . . . 81.6 Organizations of the thesis . . . . . . . . . . . . . . . . . . . . . . . 8

2 Determination of electrical parameters of the PMSM 102.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Description of the test done in the laboratory . . . . . . . . . . . . 112.3 Test results of PMSM under test . . . . . . . . . . . . . . . . . . . 13

2.4 Merit of the process . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Development of PMSM drive operated through a three-phase,

1200 conduction voltage source inverter 153.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 System description . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.1 The machine . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.2 The power converter . . . . . . . . . . . . . . . . . . . . . . 163.2.3 Position sensors . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.4 Inverter controller . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 The basic PMSM drive performance . . . . . . . . . . . . . . . . . 183.4 Simulation studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4.2 Understanding the sensor position . . . . . . . . . . . . . . 203.4.3 Simulation of the PMSM . . . . . . . . . . . . . . . . . . . 213.4.4 System equations . . . . . . . . . . . . . . . . . . . . . . . . 223.4.5 Simulation results . . . . . . . . . . . . . . . . . . . . . . . 24

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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4 Development of an analytical Averaged Dynamic Model of a PMSMdrive operated with a 1200 conduction self-controlled inverter 334.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Development of Averaged Dynamic Model . . . . . . . . . . . . 344.3 Validation of the model with the help of Detailed Numerical Model 374.4 Experiments performed to obtain Speed-Torque characteristics of

the test PMSM fed with self-controlled 120 0 conduction inverter . 38

5 Study and simulation of schemes for position sensorless opera-tion of a PMSM drive fed from a 1200 conduction self-controlledinverter 425.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2 Description of the sensorless drive . . . . . . . . . . . . . . . . . . 425.2.1 Speed observer based position sensorless operation . . . . . 435.2.2 Back emf estimation based position sensorless operation . . 46

6 Study of FIELD ORIENTED CONTROL of PMSM drive 576.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.2 Understanding the Field Orientation of PMSM . . . . . . . . . . . 576.3 Simulation studies of different FIELD ORIENTATION processes . 61

6.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 616.3.2 Different Vector Control strategies . . . . . . . . . . . . . . 626.3.3 Simulation of current control loop of vector control by hys-

teresis comparator . . . . . . . . . . . . . . . . . . . . . . . 626.3.4 Simulation of CURRENT CONTROL loop of VECTOR CON-TROL by SINE PWM Voltage Source Inverter . . . . . . . 66

6.3.5 Simulation of CURRENT CONTROL loop of POSITIONSENSORLESS VECTOR CONTROL by SINE PWM In-verter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.3.6 Simulation of SPEED CONTROL of PMSM by VECTORCONTROL with SINE PWM Inverter . . . . . . . . . . . 75

7 Advanced aspects related to real time simulation and implemen-tation of aspects of PMSM drive on FPGA platform 92

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.2 Real time simulation of RLC circuit and implementation of OB-SERVER in FPGA . . . . . . . . . . . . . . . . . . . . . . . . . . . 937.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 937.2.2 Simulating an RLC Circuit . . . . . . . . . . . . . . . . . . 937.2.3 Implementation of the Observer of PMSM . . . . . . . . . . 95

7.3 Towards the real-time implementation of VECTOR CONTROL WITH SINE PWM INVERTER of Permanent Magnet Synchronous Motor in FPGA environment . . . . . . . . . . . . . . . . . . . . . . . . . 987.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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7.3.2 Finding the performance of the encoder in running the PMSMin 1200 conduction algorithm under self control . . . . . . . 100

7.3.3 Experimental results . . . . . . . . . . . . . . . . . . . . . 1037.3.4 Development of modules required in the process of vector

control of PMSM drive . . . . . . . . . . . . . . . . . . . . . 1057.3.5 Testing of the different modules developed . . . . . . . . . . 1137.3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8 Conclusions and scope of future work 1268.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1268.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

appendices 129A 130

A.1 Parameters and specications of the machine . . . . . . . . 130

B Dynamic equations of the two operating modes of the PMSMunder 1200 conduction mode 131B.1 Basic a-b-c frame equations of the PMSM . . . . . . . . . 131B.2 MODE1 equations when two IGBTs and one freewheeling

diode D3 conduct . . . . . . . . . . . . . . . . . . . . . . . . . . 132B.3 MODE2 equations when two IGBTs conduct . . . . . . . . 132

C 133C.1 Matlab program to generate the look-up table of switching

pattern for encoder based 1200 conduction logic . . . . . . . 133

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List of Figures

1.1 Armature MMF and Field MMF Condition at zero starting for asynchronous machines . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Armature construction of PMSM . . . . . . . . . . . . . . . . . . . 41.3 Different axes of the Motor (abc - stationary, dq - synchronously

rotating) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Field under self control . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1 Power Circuit Of PMSM Drive . . . . . . . . . . . . . . . . . . . . 163.2 Hall pcb arrangement . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Experimental open circuit voltage of phase-C and three hall position

sensors output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Filter arrangement to eliminate unwanted glitches from position sen-

sor output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.5 FPGA program to generate control pulses of the switches under1200 conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.6 Position sensor signals and corresponding switching signals . . . . 213.7 The arrangement by which the DC link voltage of the inverter is

controlled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.8 Mechanical loading arrangement of the PMSM by a separately ex-

cited DC generator connected to the shaft of the PMSM . . . . . . 233.9 Experimental steady state waveforms of phase current and phase

voltage at V dc = 15V olts, no-load and sensor lead angle = 0 0 . . . 243.10 Experimental steady state waveforms of phase current and phase

voltage at V dc = 30V olts, no-load and sensor lead angle = 0 0 . . . 25

3.11 Experimental steady state waveforms of phase current and line volt-age at V dc = 15V olts, no-load and sensor lead angle = 0 0 . . . . . 263.12 Experimental steady state waveforms of phase current and line volt-

age at V dc = 30V olts, no-load and sensor lead angle = 0 0 . . . . . 273.13 Experimental steady state waveforms of phase current and phase

voltage at V dc = 25V olts, Viscous friction, f = 0 .0016Nm s/Rad ,Load Torque, T L = 1 .3Nm ,sensor lead angle = 0 0 . . . . . . . . . . 273.14 Experimental steady state waveforms of phase current and phase

voltage at V dc = 35V olts, Viscous friction, f = 0 .0016Nm s/Rad ,Load Torque, T L = 1 .5Nm ,sensor lead angle = 0 0 . . . . . . . . . . 28

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3.15 Conduction intervals for a particular phase for a particular sensorlead angle s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.16 Algorithm for simulating 120 0 conduction VSI fed PMSM . . . . . 293.17 Conduction modes for PMSM drive (a) Mode1 with T 1T 2 pair, (b)

Mode2 with T 1T 2 pair, (c) Mode1 with T 3T 4 pair and (d) Mode2with T 3T 4 pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.18 Simulated steady state waveforms of phase current and phase volt-age at V dc = 25V olts, Viscous friction, f = 0 .0016Nm s/Rad ,Load Torque, T L = 1 .3Nm ,sensor lead angle = 0 0 . . . . . . . . . . 31

3.19 Simulated steady state waveforms of phase current and phase volt-age at V dc = 35V olts, Viscous friction, f = 0 .0016Nm s/Rad ,Load Torque, T L = 1 .5Nm ,sensor lead angle = 0 0 . . . . . . . . . . 32

4.1 Simulated steady state waveforms of phase current and DC linkcurrent at V dc = 35V olts, Viscous friction, f = 0 .0016Nm s/Rad ,Load Torque, T L = 1 .5Nm ,sensor lead angle = 0 0 . . . . . . . . . . 35

4.2 Dynamic Equivalent circuit for PMSM . . . . . . . . . . . . . . . 364.3 Simulated waveforms of actual DC link current and averaged DC

link current at , Viscous friction, f = 0 .0016Nm s/Rad , LoadTorque, T L = 1 .5Nm ,sensor lead angle = 0 0 with step DC linkvoltage V dc = 35 V olts applied at t=0sec . . . . . . . . . . . . . . . 37

4.4 Simulated waveforms of actual DC link current and averaged DClink current at , Viscous friction, f = 0 .0016Nm

s/Rad , Load

Torque, T L = 1 .3Nm ,sensor lead angle = 0 0 with step DC linkvoltage V dc = 25 V olts applied at t=0sec . . . . . . . . . . . . . . . 38

4.5 Simulated waveforms of actual mechanical speed and averaged me-chanical speed at Viscous friction, f = 0 .0016Nm s/Rad , LoadTorque, T L = 1 .5Nm ,sensor lead angle = 0 0 with step DC linkvoltage V dc = 35 V olts applied at t=0sec . . . . . . . . . . . . . . . 39

4.6 Simulated waveforms of actual mechanical speed and averaged me-chanical speed at Viscous friction, f = 0 .0016Nm s/Rad , LoadTorque, T L = 1 .3Nm ,sensor lead angle = 0 0 with step DC linkvoltage V dc = 25 V olts applied at t=0sec . . . . . . . . . . . . . . . 40

4.7 Experimental MECHANICAL SPEED (in Rad/Sec)-LOAD TORQUE(in

Nm) characteristics of the PMSM, at different DC link voltage un-der self controlled 120 0 conduction algorithm . . . . . . . . . . . . 41

5.1 Schematic diagram of speed observer based position sensorless op-eration of the PMSM drive . . . . . . . . . . . . . . . . . . . . . . 43

5.2 Algorithm for simulating the observer based position sensorless op-eration scheme of 120 0 conduction VSI fed PMSM drive . . . . . . 48

5.3 Simulated waveforms actual rotor position and estimated rotor po-sition of PMSM under observer based sensorless operation, at V dc =48V olts, f = 0 .022Nm sec/Rad , T L = 0Nm . . . . . . . . . . . 49

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5.4 Simulated waveforms of phase-a current and corresponding phasevoltage of PMSM under observer based sensorless operation, atV dc = 48V olts, f = 0 .022Nm sec/Rad , T L = 0Nm . . . . . . . . 495.5 Simulated waveforms actual replica of DC link current and esti-mated DC link current of PMSM under observer based sensorlessoperation, at V dc = 48V olts, f = 0 .022Nm sec/Rad , T L = 0Nm 505.6 Simulated actual mechanical speed and estimated mechanical speedof PMSM under observer based sensorless operation, at V dc = 48 V olts,f = 0 .022Nm sec/Rad , T L = 0Nm . . . . . . . . . . . . . . . . . 505.7 Schematic diagram of back emf estimation based position sensorlessoperation of the PMSM drive . . . . . . . . . . . . . . . . . . . . . 51

5.8 Algorithm for simulating the back emf estimation based positionsensorless operation scheme of 120 0 conduction VSI fed PMSM drive 52

5.9 Simulated transient waveforms of phase-A back emf and phase-AZCD signal of PMSM under back emf estimation based sensorlessoperation from starting to few cycles, at f = 0 .022Nm sec/Rad ,T L = 0 Nm with the application of step DC link voltage V dc =48V olts at t=0Sec . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.10 Simulated transient waveforms of phase-B back emf and phase-BZCD signal of PMSM under back emf estimation based sensorlessoperation from starting to few cycles, at f = 0 .022Nm sec/Rad ,T L = 0Nm with the application of step DC link voltage V dc =48V olts at t=0Sec . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.11 Simulated transient waveforms of phase-C back emf and phase-CZCD signal of PMSM under back emf estimation based sensorlessoperation, at f = 0 .022Nm sec/Rad , T L = 0 Nm with the appli-cation of step DC link voltage V dc = 48 V olts at t=0Sec . . . . . . 54

5.12 Simulated mechanical speed of PMSM from starting till steady stateunder back emf estimation based sensorless operation, at V dc =48V olts, f = 0 .022Nm sec/Rad , T L = 0Nm . . . . . . . . . . . 54

5.13 Simulated DC link current of PMSM from starting till steady stateunder back emf estimation based sensorless operation, at V dc =48V olts, f = 0 .022Nm sec/Rad , T L = 0Nm . . . . . . . . . . . 555.14 Simulated steady state waveform of phase-A current and phase-A voltage of PMSM under back emf estimation based sensorlessoperation, at V dc = 48V olts, f = 0 .022Nm sec/Rad , T L = 0Nm 56

6.1 Fixed stator windings magnetic axis and rotating rotor windingsmagnetic axis with rotor axis are rotating at electrical speed, r . 58

6.2 d-axis equivalent circuit of the wound eld synchronous motor ro-tating at electrical speed, r in rotor reference frame . . . . . . . 59

6.3 q-axis equivalent circuit of the wound eld synchronous motor ro-tating at electrical speed, r in rotor reference frame . . . . . . . 60

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6.4 Block diagram showing the torque production process in a Syn-chronous Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.5 Block diagram showing the torque production process in a Syn-chronous Motor at ids = 0 . . . . . . . . . . . . . . . . . . . . . . . 62

6.6 Steady State phasor diagram of the PMSM under true vector control(neglecting stator resistance r s ) . . . . . . . . . . . . . . . . . . . 63

6.7 Block diagram of current control method of VECTOR CONTROLby HYSTERESIS COMPARATOR . . . . . . . . . . . . . . . . . . 64

6.8 Internal structure of HYSTERESIS COMPARATOR controlled In-verter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.9 Internal structure of Permanent Magnet Synchronous Motor . . . . 656.10 Simulated transient waveforms (zooming the transient) of q-Axis

and d-Axis currents (in Amps) of stator in rotor reference frame of the PMSM under vector control with hysteresis controller in currentcontrol mode with Dc Link Voltage, V dc =48Volts, viscous dampingfriction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . 66

6.11 Simulated transient waveforms of q-Axis and d-Axis currents (inAmps) of stator in rotor reference frame of the PMSM under vectorcontrol with hysteresis controller in current control mode with DcLink Voltage, V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . . . . . . . . . . . . . 67

6.12 Simulated transient waveforms of Phase-A current(in Amps) andPhase-A back emf (in Volts) of the PMSM under vector control withhysteresis controller in current control mode with Dc Link Voltage,V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad, Pas-sive load torque, T L =0.56Nm . . . . . . . . . . . . . . . . . . . . . 68

6.13 Simulated transient waveforms of mechanical Speed (in Rad/Sec) of the PMSM under vector control with hysteresis controller in currentcontrol mode with Dc Link Voltage, V dc =48Volts, viscous dampingfriction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . 69

6.14 Simulated transient waveform of generated electromagnetic torque(in Nm) of the PMSM under vector control with hysteresis con-troller in current control mode with Dc Link Voltage, V dc =48Volts,viscous damping friction,f=0.0016Nm-sec/Rad, Passive load torque,T L =0.56Nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.15 Block diagram of current control method of VECTOR CONTROLby SPWM INVERTER . . . . . . . . . . . . . . . . . . . . . . . . 71

6.16 Internal structure of SPWM Inverter . . . . . . . . . . . . . . . . . 726.17 Simplied structure of q-axis stator winding for the design of cur-

rent PI controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

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6.18 Simulated transient waveforms (Zooming the transient) of q-Axisand d-Axis currents (in Amps) of stator in rotor reference frame of the PMSM under vector control with Sine PWM Inverter in currentcontrol mode with Dc Link Voltage, V dc =48Volts, viscous dampingfriction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . 74

6.19 Simulated transient waveforms of q-Axis and d-Axis currents (inAmps) of stator in rotor reference frame of the PMSM under vectorcontrol with Sine PWM Inverter in current control mode with DcLink Voltage, V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . . . . . . . . . . . . . 75

6.20 Simulated transient waveforms of Phase-A current(in Amps) andPhase-A back emf (in Volts) of the PMSM under vector control withSine PWM inverter in current control mode with Dc Link Voltage,V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad, Pas-sive load torque, T L =0.56Nm . . . . . . . . . . . . . . . . . . . . . 76

6.21 Simulated transient waveform of generated electromagnetic torque(in Nm) of the PMSM under vector control with Sine PWM in-verter in current control mode with Dc Link Voltage, V dc =48Volts,viscous damping friction,f=0.0016Nm-sec/Rad, Passive load torque,T L =0.56Nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.22 Simulated transient waveforms of mechanical Speed (in Rad/Sec) of the PMSM under vector control with Sine PWM inverter in currentcontrol mode with Dc Link Voltage, V dc =48Volts, viscous dampingfriction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . 78

6.23 Block diagram of current control method of POSITION SENSOR-LESS VECTOR CONTROL by SPWM INVERTER . . . . . . . . 79

6.24 Inside diagram of the block OBSERVER as mentioned in Fig.6.23 806.25 Simulated transient waveforms (Zooming the transient) of q-axis

actual and estimated currents (in Amps) of stator in rotor referenceframe of the PMSM under position sensorless operation of vector control with Sine PWM Inverter in current control mode with DcLink Voltage, V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . . . . . . . . . . . . . 81

6.26 Simulated transient waveforms of q-axis actual and estimated cur-rents (in Amps) of stator in rotor reference frame of the PMSM un-der position sensorless operation of vector control with Sine PWMInverter in current control mode with Dc Link Voltage, V dc =48Volts,viscous damping friction,f=0.0016Nm-sec/Rad, Passive load torque,T L =0.56Nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

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6.27 Simulated steady state waveforms of Phase-A current(in Amps) andPhase-A back emf (in Volts) of the PMSM under position sensor-less operation of vector control with Sine PWM Inverter in currentcontrol mode with Dc Link Voltage, V dc =48Volts, viscous dampingfriction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . 83

6.28 Simulated steady state waveforms of actual mechanical rotor po-sition (thm in Rad) and estimated electrical rotor position(thein Rad) of the PMSM under position sensorless operation of vector control with Sine PWM Inverter in current control mode with DcLink Voltage, V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad, Passive load torque, T L =0.56Nm . . . . . . . . . . . . . . 84

6.29 Simulated transient waveform of actual electromagnetic torque (Nm)of the PMSM under position sensorless operation of vector control with Sine PWM Inverter in current control mode with Dc Link Volt-age, V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad,Passive load torque, T L =0.56Nm . . . . . . . . . . . . . . . . . . . 85

6.30 Simulated transient waveform of actual mechanical speed (Rad/sec)of the PMSM under position sensorless operation of vector control with Sine PWM Inverter in current control mode with Dc Link Volt-age, V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad,Passive load torque, T L =0.56Nm . . . . . . . . . . . . . . . . . . . 86

6.31 Block diagram of speed control method of in a Vector ControlledPMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.32 Simplied structure of mechanical loop of PMSM under true vectorcontrol for the design of speed PI controller . . . . . . . . . . . . . 87

6.33 Simulated transient waveforms of mechanical speed (in Rad/sec)and electromagnetic torque (in Nm) of the PMSM under vectorcontrol with Sine PWM inverter in speed control mode with DcLink Voltage, V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad, passive load torque is changed from T L = 0 .56Nm toT L = 3Nm at time, t = 0 .5Sec . . . . . . . . . . . . . . . . . . . . . 88

6.34 Simulated transient waveform of phase-A voltage (in Volts) of thePMSM under vector control with Sine PWM inverter in speed con-trol mode with Dc Link Voltage, V dc =48Volts, viscous dampingfriction,f=0.0016Nm-sec/Rad, passive load torque, T L = 0 .56Nm . 89

6.35 Simulated steady state waveform of phase-A voltage (in Volts) of the PMSM under vector control with Sine PWM inverter in speedcontrol mode with Dc Link Voltage, V dc =48Volts, viscous dampingfriction,f=0.0016Nm-sec/Rad, passive load torque, T L = 3 Nm . . . 90

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6.36 Simulated steady state waveforms of phase-A current (in Amps)and phase-A back emf (in Volts) of the PMSM under vector controlwith Sine PWM inverter in speed control mode with Dc Link Volt-age, V dc =48Volts, viscous damping friction,f=0.0016Nm-sec/Rad,passive load torque, T L = 3Nm . . . . . . . . . . . . . . . . . . . . 91

7.1 FPGA Design le for real time simulation of RLC circuit usingEulers Integration method . . . . . . . . . . . . . . . . . . . . . . 94

7.2 FPGA Design le for real time simulation of RL circuit EulersIntegration method . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.3 Transient waveforms of per unit circuit current and per unit inputapplied voltage for a R-L circuit of R = 10, L = 20 mH for a step

voltage of, V g = 100V = 1 pu applied at t=0sec . . . . . . . . . . . 967.4 Transient waveforms of per unit capacitor voltage and per unit input

applied voltage for a R-L-C circuit of R = 10, L = 20 mH ,C =4uF for a step voltage of, V g = 100V = 1 pu applied at t=0sec . . 97

7.5 FPGA design le showing clock and ADC outputs for observer im-plementation for observer based sensorless operation . . . . . . . . 98

7.6 FPGA design le showing Eulers method to solve variables to beestimated for observer based sensorless operation . . . . . . . . . . 99

7.7 FPGA design le showing equation to estimate the DC link currentfor observer based sensorless operation . . . . . . . . . . . . . . . 100

7.8 FPGA design le showing equation to estimate the electrical speed

for observer based sensorless operation . . . . . . . . . . . . . . . 1007.9 FPGA design le showing equation to estimate the electrical rotor

position for observer based sensorless operation . . . . . . . . . . . 1017.10 FPGA design le showing equation method to generate switching

signals for observer based sensorless operation . . . . . . . . . . . . 1017.11 FPGA design les showing the digital inputs and outputs for the

program to evaluate the performance of the encoder . . . . . . . . 1027.12 FPGA design les showing two sets of switching signals which are

multiplexed to switch the IGBTs of the two level inverter . . . . . 1037.13 FPGA design les showing traditional programme segment to run

the motor under 120 0 conduction mode with hall sensor outputs. . 104

7.14 FPGA design les showing the changeover process from hall sensorto encoder mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.15 FPGA design les showing traditional programme segment to runthe motor under 120 0 conduction mode with single encoder output. 106

7.16 Switching signals are plotted individually with respect to the electri-cal rotor position when the PMSM was running under self controlled1200 conduction algorithm with encoder. . . . . . . . . . . . . . . . 107

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7.17 Experimental steady state waveform of phase current (in Amps)and respective phase voltage(in Volts) for the PMSM running underself controlled 120 0 conduction mode with hall sensors in actionat DC Link Voltage, V dc = 17V olts, viscous damping co-efficient,f = 0 .0016N sec/Rad and passive load torque, T L = 0 .56Nm . . 1087.18 Experimental steady state waveform of phase current (in Amps)and respective phase voltage(in Volts) for the PMSM running underself controlled 120 0 conduction mode with encoder in action at DCLink Voltage, V dc = 17 V olts, viscous damping co-efficient, f =0.0016N sec/Rad and passive load torque, T L = 0 .56Nm . . . . 109

7.19 FPGA design le showing the input and output of the control signal,generation block . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.20 FPGA design le showing the derivation of electrical rotor positionadd[10..0] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.21 FPGA design le showing the computation process of different in-stantaneous trigonometric functions of electrical rotor position, add[10..0]111

7.22 FPGA design le showing the computation process of two compo-nents of each phase control signals . . . . . . . . . . . . . . . . . . 111

7.23 FPGA design le showing the addition of all the components andgeneration of actual three phase control signals of SINE PWM . . 112

7.24 FPGA design le showing the generation of triangular wave for im-plementing Sine-triangle PWM strategy. . . . . . . . . . . . . . . . 113

7.25 FPGA design le showing the comparison of triangular wave witheach sine control signal for SINE PWM . . . . . . . . . . . . . . . 114

7.26 FPGA design le showing the blanking time between the upper andlower switching signals of each phase of SPWM INVERTER . . . . 115

7.27 Experimental waveform of phase-A control signal and vqcosr atmechanical speed of 1500rpm . . . . . . . . . . . . . . . . . . . . . 116

7.28 Experimental waveform of phase-A control signal and vd sin r atmechanical speed of 1500rpm . . . . . . . . . . . . . . . . . . . . . 117

7.29 Experimental waveform of electrical rotor position,theta[10..0] andphase-A control signal at mechanical speed of 270rpm . . . . . . . 118

7.30 Experimental waveform of electrical rotor position,theta[10..0] andphase-A control signal at mechanical speed of 750rpm . . . . . . . 119

7.31 Experimental waveform of shifted phase-A control signal and switch-ing signal of T1 as shown in Fig. 3.1, at mechanical speed of 1500rpm120



7.34 FPGA program les to simulate the switching process of the real-time-voltage source inverter . . . . . . . . . . . . . . . . . . . . . . 122

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7.35 FPGA program les to simulate the generation of phase voltages of the real-time-voltage source inverter . . . . . . . . . . . . . . . . . 123

7.36 Experimental steady state waveforms of Phase-A voltage (in PU)and Phase-B voltages (in PU) of the output of the real-time-voltagesource inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.37 Experimental steady state waveforms of Phase-A voltage (in PU)and Phase-C voltages (in PU) of the output of the real-time-voltagesource inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

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List of principal symbols

PMSM : Permanent Magnet Synchronous MotorT e : Electromagnetic torque, NmM a : Armature MMF, ATM f : Field MMF,ATvan , vbn , vcn : phase voltages of phase A, B, C respectively, Vi

a, i

b, i

c: phase currents of phase A, B, C respectively, Amps

r a : per phase resistance of the machine, OhmLs : per phase synchronous inductance, H0: Peak value of armature ux linkage due to permanent magnet, Wb-turnsr : Electrical speed of the machine, Rad/Secr : Electrical rotor position, Radm : Mechanical seed of the machine, Rad/SecP : Number of poles of the machinea : Total ux linkage of Phase A, Wb-turnsL ls : Leakage inductance of each phase of the motor, HLmd : Direct axis mutual inductance, H

Lmq : Quadrature axis mutual inductance,Hs: Sensor lead angle, Radt stop : Simulation time, Sect step : Step time of simulation,Seciapk : Peak of the fundamental armature current, Ampsi link : Dynamic value of the averaged DC link current, Ampsf : Viscous friction co-efficient, Nm-Rad/SecT L : Passive load torque, NmJ : Mechanical inertia of the machine, K g m2i link : Estimated value of the cyclic average value of DC link current, Amps

r : Estimated value electrical speed of the machine, Rad/sec

r : Estimated value of electrical rotor position, Radidc : Replica of DC link current only having the non-zero part, Amps

S a , S b, S c : Switching functions of phase A, B, C respectively pa , pb, pc: Zero Crossing Signals of phase A, B, C respectivelyV g : Per unit value of input applied voltage, puR: Per unit resistance, puL: Per unit inductance, pui: Per unit current, puV b: Base value of voltage, VI b: Base value of current, Amps

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Rb: Base value of Resistance, Ohmvc : Per unit capacitor voltage, puL ls : Leakage Inductance of the stator, HL lr : Leakage Inductance of the rotor referred to stator, HLdr : Self Inductance of d-axis damper referred to stator,HLqr : Self Inductance of q-axis damper referred to stator, HL f r : Self Inductance of main eld referred to stator, HLmd : d-axis Magnetizing Inductance, HLmq : q-axis Magnetizing Inductance, HLqs : Self Inductance of q-axis stator, HLds : Self Inductance of q-axis stator, Hr s : Per phase stator resistance, Hr r , r qr , r dr : Per phase rotor resistance referred to stator, Ohm

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Chapter 1

Introduction

1.1 General discussionsThe permanent magnet synchronous motor (PMSM)drive has several advantagesover other machines used as conventional servo-motors such as separately exciteddc motor, induction motor etc. As is well understood, the stator current of aninduction machine (IM) have to carry both the torque producing component of current and the magnetizing current. But in a PMSM, placing a permanent mag-net in the rotor relieves the stator from the need of carrying magnetising mmf producing currents. Hence for the same power output, PMSMs will operate ata higher power factor and its efficiency will be more than induction machines,as currents owing through the stator reduces. It may also be relevant to notethat conventional cylindrical rotor synchronous motor (SM) has a DC excitationin the eld, which requires brushes and slip rings in the rotor eld winding. Thesebrushes and slip rings require regular maintenance and also produce extra lossesfor their presence. The key reason for developing this PMSM was [1] to replacethe disadvantageous features of SM by placing a permanent magnet in the ro-tor. Hence PMSM has sinusoidal EMF distribution with respect to space andrequires sinusoidal input stator (armature) currents to produce steady ripple-freetorque. On the other hand, BLDC (Brushless DC Motor) has trapezoidal EMFdistribution with respect to space and requires trapezoidal input stator (armature)currents to produce steady ripple-free torque [2]. For this PMSM has become themost attractive competitor to other ac and dc drives for adjustable speed high per-formance drive applications[3, 4]. It may however be important to point out thatthis advantage comes at the cost of a small but crucial disadvantage. One mayrecall that the SM eld gets weakened due to demagnetising armature ampere-turns when operating at leading power factors and magnetised when operating atlagging power factors. In a wound-eld SM this is not a problem as there is noscope for the permanent demagnetization of the eld. In a PMSM this processmay cause irreversible demagnetisation of the permanent magnet. Hence one has

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technically to incorporate schemes to ensure that demagnetising ampere-turns donot cause such damage.

Many schemes have been proposed for the control of PMSM drive. Amongthem one of the most attractive control scheme is the VECTOR CONTROLscheme[5]. It is more suitable for PMSM drive as its control is totally throughstator side and there is no provision for rotor eld excitation control. By thisvector control we can make such an arrangement that it can be operated in a samemanner as DC machine.

In the forthcoming chapters it is discussed, how PMSM can be used in con- junction with proper inverter switching congurations, to act just like a separatelyexcited DC motor.

1.2 Operation of PMSM under Self controlIt is well known that a conventional synchronous motor has no starting torque.At starting speed if we excite the synchronous motor armature (Stator) with abalanced three phase supply of rated frequency the armature rotating magneticeld will make an angle with rotor (eld) magnetic eld, which is time varying.Therefore no net average torque is produced as shown in Figure 1.1 So, at this

condition the average dc torque: T e = K 20 M a M f sin d = 0

A PMSM has a balanced 3-phase winding in the stator and a permanent magnetas its rotor. The rotor permanent magnet eld distribution is designed such thatits distribution is almost sinusoidal in space. The armature windings are also sodesigned that the armature MMFs also vary almost as pure sinusoids in space.

The basic construction of a PMSM is shown in Figure1.2. This Figure 1.2 isshowing the three armature windings (phases), i.e. a, b and c with their axesmarked, along with the d-axis, which is the axis of the permanent magnet eld(rotor). Positive direction of rotation of the rotor is assumed anti-clockwise. Theq (quadrature)is an axis, assumed to be 90 0 ahead of the rotor d-axis and therotor position is dened as an angle r , as shown in Fig. 1.2. r is the anglesubtended between the stator (armature) a phase axis and the q-axis of therotor. It is positive in the counter clock wise direction, i.e. in powitive directionof rotation ( r ).

With the above assumptions, The cylindrical rotor PMSM machine armaturevoltage equations (assuming machine neutral are isolated) are as follows:

van = r a ia + Ls pia + 0r cos r (1.1)

vbn = r a ib + Ls pib + 0r cos(r 2/ 3) (1.2)

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Figure 1.1: Armature MMF and Field MMF Condition at zero starting fora synchronous machines

vcn = r a ic + Ls pic + 0r cos(r + 2 / 3) (1.3)

where, van , vbn , vcn are three phase voltages, ia , ib, ic are three phase currents, 0 isthe peak value of armature ux linkage due to permanent, r a and Ls are per phaseresistance and per phase synchronous inductance of the motor, p = ddt operator. ris the electrical speed of the machine and the machine being synchronous is alwaysrelated to its mechanical rotor speed m by the expression shown in equation 1.4.

r = P 2

m (1.4)

where, P = Number of pole in the machine and m = mechanical rotor speed of the motor.

Brushless DC Motors and / or PMSMs are generally analyzed in a-b-c or rotord-q reference frame [6]. Fig. 1.3 shows these two frames. The a,b and c axes arexed on the plane of the paper (stationary a-b-c frame) and the q-d axes (d-axisis assumed the rotor permanent magnet eld axis), maintaining quadrature witheach other, rotates with the rotor electrical speed r . Counter clock wise rotationis assumed positive and at t=0, the q-axis is assumed to be aligned with the a-phase axis.Now, if it can be arranged by rotor position feedback that voltages feeding thearmature phases of the PMSM have the fundamental component of the phasevoltages which are function of electrical rotor position of the motor r ,then one

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Figure 1.3: Different axes of the Motor (abc - stationary, dq - synchronouslyrotating)

where, s = tan 1[ V m sin( z )V m cos(z ) 0 r)]tan 1[r L sr a ] , I m =maximum value of phase cur-rents and V m = maximum value of phase voltages .

If now three phase to two phase transformation [6] is applied, it is seen that theq andd axis components of armature MMF space phasor, M aq and M ad are asshown in equation 1.11:

M aq

M ad= (

2

3)K cos(r ) cos(r 2/ 3) cos(r + 2 / 3)

sin(r ) sin(r 2/ 3) sin(r + 2 / 3)iaibic

(1.11)

Where, k = per phase number of turnsIf equations 1.8, 1.9, 1.10 are substituted in equation 1.11 it is obtained as:

M aqM ad

= I m K cos(s)

sin(s) (1.12)

So, the armature MMF space phasor, Ma can be written as:

M a = Im.k [sin(s) + j cos(s)] (1.13)

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The eld (rotor) MMF space phasor, Mf can be written as:

Mf = [ Mf + j 0] (1.14)

Figure 1.4: Field under self control

Now, from equation 1.13 and 1.14 it can be noted that, under this circum-stances, armature(stator) MMF, Ma makes a time invariant angle = 2 + swith the eld (rotor) at all the speeds as shown in gure 1.4. So, motor will developan average (DC)torque at all the speeds. So, motor will also develop DC torque atzero speed also. So, by this rotor position feedback control strategy, synchronousmotor can be started without the help of a pony or auxiliary motor. This methodis called Self Control [7] of synchronous motor. It can be noted that under self control rotor speed will be always in synchronism with stator supply frequency,starting from zero speed, because here, the stator current and voltage is made tofollow a frequency dictated by the rate of change of rotor position by having rotorposition feedback

1.3 Need of digital controllers in drives ap-plication

Now, it is understood that, to maintain the self-control principle, motor phasevoltages are to be dictated by the pattern of rotor position. Different such self-control processes are available, viz. Self- Controlled 120 0 conduction algorithm,Self-Controlled 180 0 Conduction algorithm, Vector Control.In actual PMSM

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drive, equations 1.1, 1.2, 1.3 are implemented by feeding the motor through aninverter with self commutated devices say IGBT. Now, generating the switchingsignals depending on the rotor position feedback is a computation oriented work.In most of the cases these computational works are done with the help of some highperformance processor. Previously Digital Signal Processors (DSP) were used forthis purpose [8]. But, as VLSI technology is improving, many more high perfor-mance controllers are emerging. Subsequently, the need of variable-architecture-processor is felt in the eld of drives research. The most successful variable-architecture-processor came out with the name FIELD PROGRAMMABLE GATES ARRAY (FPGA) . The main advantage of this FPGA is that, this processor can bearranged like the processor of our choice depending upon the computational burdenrequired in the specic derives application.The modern day embedded controllerscan perform online complex computation very fast. This has become a require-ment in power electronic applications, where a decision making is often to be madevery fast depending on a faster online mechanical computation and accordingly apower device is ultimately to be turned on or off based on the information. Thiscalls for a digital environment which can solve differential equations with very highfrequency. This invariably needs a processor, which processes in parallel way of computation. An FPGA is a suitable platform for implementing such systems.The basic advantage of an FPGA is that it can be programmed to process datain parallel. Thus the implementation of system equations on an FPGA, results invery short execution time. The controller model in equation form is realized as acombination of sequential and combinational logic elements. This digital circuit isthen programmed in to FPGA.

1.4 Relevance of the work undertakenInduction motors (IM) are widely used in variable speed electric drives due totheir ruggedness mainly. On the other hand, DC machines, although not thatrugged, present most ideal characteristics amenable to easy control. Amongst ACmotors IM continued to hold sway over the synchronous motor (SM) due to in-herent absence of starting torque. To the user who is always in search of best of

all world type of solutions therefore a machine with the practical advantages of the AC machines and ease of control of DC machines would be ideal. The PMSMwith a shaft mounted position sensor is one such machine. It is fundamentally asynchronous machine without the starting problems and on the other hand ap-pears like a DC separately excited machine with constant excitation as far as itscontrol is concerned. To top it all, the presence of high energy permanent magnets(instead of eld winding as in case of the conventional SM) in the rotor, reducesits size and weight. Thus a lot of work in the area of adjustable speed drivesnow center around this particular machine. Interestingly one such machine wasdesigned and fabricated in the Power Electronics laboratory of this institute dur-

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ing a previous post-graduate thesis work. The present author could hardly resistthe temptation to work in the area of PMSM drives with such a machine alreadyavailable. Hence this work. One permanent magnet synchronous motor was de-signed and made during one of the previous ME thesis works [9]. The motor wasdesigned to be Sinusoidal Permanent Magnet Rotor Flux Distribution .The ratings of the motor, based on which theoretical design was done, are as fol-lows: Input Inverters DC Link Voltage, V dc =48 Volts, Maximum Output Power Rating, P out =1kW, Maximum Mechanical Speed, N r =3000rpm .The motor was designed to drive one electric bi-cycle. During the design of themachine, the temperature aspects and ux aspects of the machine were solved byANSY S software and the results were compared with that found from differentempirical formulae.

1.5 Outline of the present workThe PMSM existing in the Power Electronics Laboratory is essentially a lowvoltage( 48V olts) and high current( 20Amp) motor. So, the speed response of the motor is very fast. In the present scope of work, different control algorithmsare simulated and some of them are validated experimentally. Before character-izing the motor, electrical parameters also have been experimentally found out.Simulation studies uses these electrical parameters, as an input. The results foundin different stages are presented in few chapters.

1.6 Organizations of the thesisThe report is organized in six chapters.After the introductory chapter, Chapter 2 is devoted to experimental determi-nation of the electrical parameters of the PMSM available in the laboratory.

Chapter 3 presents the Development of PMSM drive operated througha three-phase, 1200 conduction voltage source inverter . The details of thesimulation and subsequently the experimental validation of those simulated resultsare presented here.

Chapter 4 presents the development of the Averaged Dynamic Model of a PMSM drive operated through a three-phase, 1200 conduction voltagesource inverter . This averaged model is also validated in this chapter.

Chapter 5 presents simulation of different position sensorless operation schemesof PMSM drives operated under 120 0 conduction mode. Two such schemes aresimulated in this chapter.

Chapter 6 presents different vector control strategies and their simulation. Cur-rent and voltage controllers for those drives are also presented in this chapter.

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Chapter 7 presents the development of real-time codes for different signicantfunctional blocks required for experimental implementation of a vector controlledPMSM drive incorporating a sine PWM voltage source inverter.

Chapter 8 indicates the concluding comments on the work done so far and workthat can be taken up in future are also discussed in this chapter.

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Chapter 2

Determination of electrical

parameters of the PMSM

2.1 IntroductionThe PMSM drive is efficiently used in different servo drive application. Thosedrives are essentially vector controlled and the torque is highly dependent onproper eld orientation. But, if the process of vector control is concerned, itcan be seen that the process needs a very accurate mathematical model of thesystem. To determine the mathematical model, it is required to know the exactexperimental and true value of electrical and mechanical parameters of the PMSM.Several methods are proposed but many of them are not even realistic from themagnetic circuit point of view of the PMSM.

PMSM is essentially a special kind of synchronous motor. So, scientists tried rstArmature Short Circuit test [10] on PMSM for its electrical parameter determi-nation. But during this process, the armature MMF has a tendency to totallydemagnetize the rotor permanent magnet. The parameters of the PMSM can alsobe determined by measuring the torque or power output by some torque transduceror dynamometer [11]. But, this process will give inaccurate results if iron losseshave to be taken into account, especially in high cupper resistance motors, such

as low power motors. In many papers [12], some parameter identication methodis utilized to determine the parameters of the PMSM. In those papers an ANNbased or KALMAN lter based adaptive model is developed for the PMSM. Sub-sequently, those adaptive models are trained based on known results (say torque,power etc) of some tests done in different load conditions. This method can notbe used for very fast vector controlled motors as these training methods are verytime consuming exercises.

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2.2 Description of the test done in the labo-ratory

The general voltage-current equation (Fig. 1.2 and 1.3) of Phase -A of a PMSM[6] is:

van = r a ia + pa (2.1)

Where a = Total ux linkage of Phase-A Expression of a can be written as interms of ia , ib and ic :

a ={L ls + LA LB cos(2r )}ia+ {0.5LA LB cos 2(r 23 )}ib+ {0.5LA LB cos 2(r +

23 )}ic+ 0 sin(r )

(2.2)

Where,L ls = Leakage inductance of each phase of the motor.Lmd = 32 (LA + LB )= Direct axis mutual inductance.Lmq = 32 (LA LB )= Quadrature axis mutual inductance.Differentiating equation 2.2 with respect to time and putting r = pr it is foundthat:

pa =

{L ls + LA LB cos(2r )} pia+{

0.5LA

LB cos2(r

2

3 )

} pib

+ {0.5LA LB cos2(r + 23 )} pic+2 LB r [ia sin(2r ) + ib sin 2(r 23 ) + ic sin 2(r + 23 )]+ 0r cos(r )(2.3)

Now, analytical ndings of these equations applied to certain experimental condi-tions as follows

CASE 1:A small DC voltage is applied in Phase-A terminals (i.e. terminals a-n of Fig 1.2and Fig 3.1). Such that phase-A and main eld (d-axis) aligns with each other.Now, the DC is withdrawn without disturbing the rotor position. A single phase

variable AC source is connected across phase-A (a-n), a small voltage is appliedand phase-A current is checked. So, this condition can be analytically stated asfollows:

r = 0r = 2ib = pib = 0ic = pic = 0

(2.4)

Using equation 2.3 and conditions of equations 2.4,

van = r a ia + ( L ls + LA + LB ) pia (2.5)

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Say, frequency of the AC source is = s rad/sec, Then at steady state it is notedthat:

V an = [r a + j s (L ls + LA + LB )]I a (2.6)

Where, all uppercase quantities are representing the RMS value of the correspond-ing quantities.CASE 2:Now, A.C. supply from phase-A(a-n) is removed without changing rotor position.A small voltage is applied across phase-B(b-n). Phase B current and open circuitvoltage at phase A(a-n) is noted. This condition can be analytically stated asbelow:

r = 0r =

2ia = pia = 0ic = pic = 0

(2.7)

Using equation 2.3 and conditions of equations 2.7,

van = [(LA + LB

2 )] pib (2.8)

So, at steady state:

V an = [ j s (LA + LB

2 )]I b (2.9)

CASE 3:

Now, A small DC voltage is applied across phase-B (b-n), so that Phase-B axisgets aligned with that of main eld axis (d-axis). Now, the same AC single phasevoltage source is applied across phase-C and open circuited voltage of Phase- A isnoted and current of Phase-C is also noted. So, analytically this condition can bestated as follows:

r = 0r = 76ia = pia = 0ib = pib = 0

(2.10)

Using equation 2.3 and conditions of equations 2.10 it is obtained:

van = [L

A2 + LB ] pic (2.11)

So, at steady state:

V an = [ j s (LA 2LB

2 )]I c (2.12)

CASE 4:A small DC voltage is applied across phase-A (a-n) keeping other phases are keptopen and machine rotor eld aligns with phase-A axis. Motor will not rotateunder this condition. The phase-A DC voltage and phase-A DC current is notedand their ratio ( van /i an ) gives the motor phase resistance.

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With the noted experimental readings of V an , I a , V an , I b, V an , I c , equations2.6,2.9, and 2.12 are solved to get the values of LA , LB and L ls of the PMSM.

2.3 Test results of PMSM under testRUN 1:The following table reects the test results of CASE 1 as mentioned in the previoussection. All the voltage and current data are taken from digital storage oscillo-scope (Phase B and C kept open circuited):

Sl. No. Van(in mV) Ian(in Amps)1. 220.4 2.02

2. 354.1 3.19

RUN 2:The following table reects the test results of CASE 2 as mentioned in the previoussection. All the voltage and current data are taken from digital storage oscillo-scope (Phase A and C kept open circuited):

Sl. No. Van(in mV) Ibn(in Amps)1. 24.46 1.812. 28.76 2.08

RUN 3:

The following table reects the test results of CASE 3 as mentioned in the previoussection. All the voltage and current data are taken from digital storage oscillo-scope (phase A and B kept open circuited):

Sl. No. Van(in mV) Icn(in Amps)1. 16.06 1.232. 28.87 2.11

RUN 4:The phase-A is excited with DC voltage and following data at the machine termi-nal are found by oscilloscope (Phase B and C were kept open circuited):

Sl. No. Van(in mV) Icn(in Amps)

1. 2.45 3.692. 1.99 3.04

From results of RUN 4, the DC resistance of per phase of the motor is as follows:r a = 0 .0655ohm . Due to skin effect ar 50 Hz , r a (a.c. ) = 1 .1r a = 0 .07205ohm .

Now, putting this value of per phase ac resistance and results of RUN 1, RUN2 and RUN 3 ( at 50 Hz single phase AC source) in equations 2.6, 2.9 and 2.12respectively it is found that the electrical parameters of the PMSM are as follows:

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Stator Leakage Inductance= L ls = 1 .771

104H

LA = 8 .63 105H LB = 0 .06 105H =negligible i.e the machine is almost non-salientStator magnetizing Inductance= Lmd = Lmq = 32 LA = 1 .304 104H Per phase resistance= r a = 0 .0655ohmRUN 5:The PMSM is rotated anticlockwise at no-load at different speeds with the help of a prime-mover and hence the PMSM acts as a generator. Line Voltage rms ( V ab )is noted along with its electrical frequency ( f r ) with an Oscilloscope. The resultsare listed below:

SL NO. V ab (in Volts) f r (in Hz)

1. 13.832 33.232. 13.192 31.253. 11.96 28.104. 10.74 25.195. 9.35 21.866. 8.00 18.747. 6.30 14.77

A best-t curve is drawn and its equation is found as:

V ab = 0 .41f r + 0 .3 0.41f r (2.13)from the theory of PMSM, is concerned, the line voltage, in terms of peak perma-nent magnet rotor ux linkage and electrical frequency can be written as:

V ab = (2 0 3/ 2)f r (2.14)Now, solving equations 2.13 and 2.14, peak of permanent magnet rotor ux linkageis found to be:

0 = 0 .0533wb turnsIt is to be mentioned here that, the designed value of 0 of the test machine wasreported as 0 = 0 .06wb turns [9].

2.4 Merit of the processThe description of the process suggests that, this process is very simple. Thereis no chance of demagnetization of the permanent magnet in this test and yetthe signicant machine inductance are found out. The calculations are also verysimple. The values of the parameters, thus obtained, would be in future used forsimulation and also for developing controllers for a complete PMSM drive. Theonly demerit is that it can not account for the parameter uncertainties, which mightprove to be important while developing complex online indirect implementationstrategies viz. vector control , if based on value of a particular machines parameter.

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Chapter 3

Development of PMSM drive

operated through athree-phase, 120 0 conductionvoltage source inverter

3.1 Introduction

This chapter is devoted to simulation studies, implementation details and experi-mental waveforms of the basic PMSM drive when the laboratory prototype PMSMis fed from a self-controlled transistorized three-phase inverter operated under 120 0

conduction of its devices. Initially each building block of the implemented drivehas been discussed. Afterwards the experimental results are presented and in thelast section some simulation details, to understand the signicance of the observedphenomena, are discussed.

3.2 System descriptionA self-controlled, three phase permanent magnet synchronous motor driven by aself-commutated IGBT inverter is investigated in this report. The power circuitdiagram of the implemented drive was shown earlier in Fig. 3.1.

The PMSM has a permanent magnet as its rotor. The three-phase armatureof the synchronous machine is fed by a self-commutated inverter under 120 0 con-duction. The inverter is switched according to the rotor position signals of threehall position sensors. The switching of the devices of the inverter is controlledby the block marked as Inverter Controller as shown in Fig. 3.1. This block is

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Figure 3.1: Power Circuit Of PMSM Drive

implemented inside a Field Programmable Gate Array(FPGA) based developmentboard available in the laboratory.

3.2.1 The machineThe PMSM prototype used here is existing in the laboratory and has armature inthe stator and eld in the rotor. The eld is made of a permanent magnet. Theparameters of the machine were experimentally determined and checked throughrigorous experiments. The machine is essentially a high current (20 Amps) andlow voltage (48 Volts) design. The parameters and the ratings of the machine areprovided in Appendix A.

3.2.2 The power converterThe power converter panel used in the experiment is essentially a rectier-inverter

assembly (Semikron make MD B6CI 600/415-10F stack). The rectier is made of three phase diode-bridge. The rectier is fed from a three-phase transformer. Theoutput DC of the rectier is terminated on a capacitor bank and the capacitoris feeding the inverter. The panel needs to be supplied with a 15 Volts supplyfrom outside only. The control signals of the six- devices are given at six controlterminals of the inverter.

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3.2.3 Position sensorsThree Hall position sensors are connected in the stator. A +15 V olts regulatedDC power supply is needed to power up the PCB containing the sensors.Eachsensor produces a binary signal, high for 180 0 and low for the remaining 180 0.Each sensor signal is shifted from the other by 120 0 as shown in Fig. 3.2, whenthe PMSM is run as a generator by an external prime-mover (i.e. by the shaftconnected DC machine acting as motor as shown in Fig. 3.8), at a constant speed,the hall effect position sensor outputs and the PMSMs armature induced phase(C-phase) voltage are shown in Figure 3.3. If the position sensor signals are

Figure 3.2: Hall pcb arrangement

noted carefully, it can be observed that the mutual electrical phase shifting of theposition sensor signals are not exactly 120 0 . This is most probably due mechanicalinaccuracies at the time of mounting of the position sensor. It is reected in thecurrent waveform of the machine, as well, as will be discussed later.

3.2.4 Inverter controller

The inverter-controller shown in Fig. 3.1 is totally implemented inside FPGA .Three position sensor signals are rst fed to wave-shaping-cum-lter circuit whichis made of 555 timer as shown in Fig 3.4, to eliminate the unwanted glitches inthe position sensor output. The X ,Y and Z signals are crude signals which areproduced by the position sensors and X1 , Y1 and Z1 are signals which are freeof glitches and are respective complements of X ,Y and Z signals. These are nowfed to the FPGA development board for processing. Now, the switching signalsfor each IGBT of the inverter are generated from these X1, Y1 and Z1 signalsand fed to the gate terminals of the inverter IGBTs. The program is shown inFig. 3.5. The logic that is implemented inside FPGA is such that as soon as

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Figure 3.3: Experimental open circuit voltage of phase-C and three hallposition sensors output

the phase induced emf of a particular phase passes from its positive zero crossing,the IGBT of the inverter, that is connected to that phase and the positive DCbus will be gated just 30 0 electrical after that, viz at r = 900, the positivezero crossing of phase-A induced emf comes and IGBT T1 is gated at r = 600.Under this circumstances the phase induced emf and the fundamental current of that phase becomes co-phaser. This is called switching algorithm for Sensor LeadAngle=Zero degree. This fact is validated in the subsequent sections. In Fig.3.5, p ,q and r are respectively X1 ,Y1 and Z1 signals. Output signal of 555Timer is the inverted version of the corresponding input signal. To nullify thisinversion these signals are again inverted inside FPGA. In Fig. 3.5, s1 ,s2 ,s3 , s4 ,s5 , s6 are the six switching signals as per generated truth-table, but to nullifyunwanted glitches, which may be generated due to FPGA interfacing card layout,each switching signals are ANDed with one of the position sensor signals or itsinverted version, whose low to high going edge coincides with that of the switchingsignal. The timer outputs and the switching signals are interfaced through digitalpins of FPGA. These signals are shown in Fig. 3.6.

3.3 The basic PMSM drive performanceWhile powering up, the DC link voltage, V dc (Fig. 3.1) is slowly increased, andsystem is kept under no-load condition and PMSM is started. The DC link voltageis increased or decreased by changing the three phase voltages V R , V Y and V B withthe help of a three phase variac as shown in Figure 3.7. The DC link voltage isfurther increased to test the conditions of the drive at higher speeds. Subsequently,the PMSM is loaded with generator loading arrangement as shown in Figure 3.8.

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Figure 3.4: Filter arrangement to eliminate unwanted glitches from positionsensor output

The DC generator eld current I f dcgen is controlled by controlling the eld voltageand the load torque is controlled by controlling the load resistance R load as shownin Figure 3.8.

The experimental waveforms of important variables like phase voltage, correspond-ing phase currents and typical line voltages are presented in the report. The no-load waveforms are shown in Fig. 3.9, Fig. 3.10, Fig. 3.11 and Fig. 3.12. Theexperimental waveforms of the drive under loaded conditions are shown in Fig.3.13 and Fig.3.14.

The experimental results are quite satisfactory except at some parts of the wave-forms. In one particular 120 0 electrical conduction cycle of a particular phase,two consecutive 60 0 conduction cycles are not symmetrical. The reason may be(as already explained earlier) and are validated in Fig. 3.3, i.e. the Hall positionsensors outputs mutually are not exactly 120 0 electrical apart. If the steady stateexperimental waveforms are noticed carefully, it can be noted that the phase an-gle between the fundamental armature phase current and corresponding armaturephase back emf appears to be 0 0. This is true irrespective the DC Link Voltageand loading conditions applied, as expected in the sensor lead angle 0 0 condition.

3.4 Simulation studies

3.4.1 IntroductionThe drive reported in this chapter is PMSM drive fed by an VSI inverter under1200 conduction of switches. If the switching pattern of 120 0 is concerned, it can

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Figure 3.5: FPGA program to generate control pulses of the switches under1200 conduction

be noted that, sometime two devices (two IGBTs) and sometimes three devices(Two IGBTs and one freewheeling diode) are conducting. Hence all the threephase voltages of the machine can not be predicted under this operating conditionat a time. So, d q axis modeling of the drive is difficult here. So, a Detailed Numerical Model is developed. In this model the a-b-c frame equations of alltwelve switching (as will be described later) combinations are numerically solvedand the performance of the drive is predicted. In short, this Detailed NumericalModel requires better insight of the drive under all possible switching conditions.

3.4.2 Understanding the sensor positionThe sensor lead angle is dened by the variable, s. The denition and innermeaning of sensor lead angle is described in previous section. These denitionsare depicted in Fig 3.15. Here 120 0 conduction VSI fed PMSM is considered. Anti-

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Figure 3.6: Position sensor signals and corresponding switching signals

clockwise rotation of the rotor is considered positive and stator phases are xed inspace. If the denition of sensor lead angle, given in previous section is considered,for a specic sensor lead angle s the conduction pattern of a particular phase willbe as shown in Fig. 3.15. When q -axis coincides with OS + line, positive currentconduction starts in the phase (as top switch connected to that phase is given

gate signal) and when q -axis coincides with OE + line, positive current conductionapproaches to end (as gate signal of top switch connected to that phase is withdrawn). After 60 0 electrical rotation of eld, when q -axis coincides with OS line,negative current starts in the phase (as bottom switch connected to that phaseis given gate signal) and when q -axis coincides with OE line, negative currentapproaches to end (as gate signal of bottom switch connected to that is withdrawn). This process repeats cyclically for all three phases. The sensor positioncan be adjusted by locating the rotor position sensor properly with respect to thestator frame. It is observable here that, sensor angle is coming out to be the anglebetween phase induced e.m.f. and phase current.

3.4.3 Simulation of the PMSMFrom the basic knowledge of 120 0 conduction VSI fed load, the total electricalconduction period can be divided into six conduction intervals. Each conductioninterval can be subdivided into two modes. In MODE 2 two switches, one fromthree switches connected to positive DC bus and one from three switches connectedto negative DC bus, conduct. MODE 2 contributes to the maximum time of thatconduction period. Now, MODE 1 lasts for a very small time before MODE2, when three devices (two of which are the switches already conducting andwill continue to do so in the incoming MODE 2 and one diode which is the

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Figure 3.7: The arrangement by which the DC link voltage of the inverter iscontrolled

freewheeling diode connected to the phase which is leaving conduction, not tosuddenly stop the conduction of the phase). Two such MODE1 and two such

MODE2 are shown in Figure 3.17. This MODE 1 is present when conduction isswitching from previous conduction interval to present conduction interval. ThisMODE 1 is called Commutating Mode or Inter-switch Mode . MODE 1lasts for the time up to which current through the phase which is outgoing persistsand free wheeling diode is on. When this current is zero operation is switchedto MODE 2 . So, it is clear that throughout one complete electrical cycle thereare six MODE 1 and six MODE 2 , which occur depending upon electrical rotorpositions. These six MODE 1 equations are similar but differ only w.r.t. somefunctions relating electrical rotor position. The same can be told for six MODE2 equations. The algorithm for simulating such drive is shown below in Fig.3.16. In the algorithm shown the system equations are solved by FOURTH

ORDER RUNGE KUTTA method. And the variables like voltages, currents,torque, and speed are updated in regular interval in each time step iteration. Thismodel is called DETAILED NUMERICAL MODEL [13] of PMSM drive. Atypical C code implementation of the above algorithm is done. The results of the simulation is shown in subsequent sections.

3.4.4 System equationsTwo Mode 1 and two Mode 2 conditions are shown in Fig. 3.17. Four moresimilar Mode 1 and Mode 2 conditions exist. In Mode 2 , only one loop current

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Figure 3.8: Mechanical loading arrangement of the PMSM by a separatelyexcited DC generator connected to the shaft of the PMSM

ows and all phase currents can be expressed in terms of this current only. InMode 1 , an extra loop current, icom exists. Given below are Mode 1 equationswhen T 1, T 2 and D 3 conduct and Mode 2 equations when T 1 and T 2 conduct.

Mode 1 equations when T1, T2 and D3 conduct:

Basic equations of this mode are as below:

ian = im + icomibn = imicn = icomV dc = van vcnvan = vbn

(3.1)

Now, putting equation 3.1 in equations 1.1, 1.2 and 1.3 and using torque balanceequations it is found that the dynamic equations of Mode1 can be arranged as

follows: pim = f 11 (im , icom , r , r ) picom = f 21(im , i com , r , r ) pr = f 31(im , icom , r , r ) pr = f 41(r )

(3.2)

Where, currents im , icom are the currents as shown in Figure 3.17 and the functionsare discussed in Appendix B. These equations 3.2 are used to get the solution of variables specied in Mode1 in the simulation.

Mode 2 equations when T1and T2 conduct:

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Figure 3.9: Experimental steady state waveforms of phase current and phasevoltage at V dc = 15V olts, no-load and sensor lead angle = 0 0

ian = imibn = 0icn = imV dc = van

vcn

(3.3)

Now, putting equation 3.3 in equations 1.1, 1.2 and 1.3 and using torque balanceequations it is found that the dynamic equations of Mode2 can be arranged asfollows:

pim = f 51(im , r , r ) pr = f 61(im , r , r ) pr = f 41(r )

(3.4)

Where, currents im , icom are the currents as shown in Figure 3.17 and the functionsare discussed in Appendix B. These equation 3.4 are solved to get the variablesspecied in Mode2 in the simulation.

3.4.5 Simulation resultsThe algorithm for the DetailedNumericalModel is tested for different operatingconditions and DC link voltages. The steady-state simulated results are shownin Fig. 3.18 and Fig. 3.19. The results are closely tallying with that of theexperimental ones. The simulated results also verifying that, at sensor lead angle00, the phase angle between the fundamental component of armature phase currentand corresponding phase induced emf is 0 0. In detailed numerical model the beck

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Figure 3.10: Experimental steady state waveforms of phase current and phasevoltage at V dc = 30V olts, no-load and sensor lead angle = 0 0

emf prole of the machine is assumed to be sinusoidal as shown in equations 1.1,1.2 and 1.3. But, in the designed experimental lab prototype PMSM, the inducedemf prole is at-topped with the atness span of around 54 0 electrical as foundexperimentally (seen from Fig. 3.3). Hence, when the PMSM is run as a motor

with self controlled 1200

conduction VSI, this is reected as the less sharp peakphase voltages as shown in Fig. 3.13 and Fig. 3.14. The two consecutive 60 0

electrical conduction intervals of machine phase are not exactly symmetrical. Thiscan be explained from Fig. 3.3, which reects that the position sensor outputs arenot exactly 120 0 electrical apart mutually, due to slight misalignment of the halleffect based position sensors, as discussed before.

3.5 ConclusionIt can be noted that the operation of the PMSM that is explained in this chapteris mainly under self controlled 120 0 conduction mode. Now, for BLDC modeof operation of PMSM drive the switching sequence of the inverter is that of the 120 0 conduction mode of the switches of a VSI. As a result, as explainedany two switches at a time conduct (if inter-switch transients of each mode areneglected)causing the same current to ow through the conducting phases. Inactual DC motor due to the presence of brush segments, the armature currententers into the pseudo stationary coil through one brush and the same currentleaves the pseudo stationary coil through other brush. As DC motor rotates,the terminals of the same pseudo-stationary coil are formed with different set of actual armature coil. In 120 0 conduction mode VSI fed PMSM, the armature

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Figure 3.11: Experimental steady state waveforms of phase current and linevoltage at V dc = 15V olts, no-load and sensor lead angle = 0 0

MMF phasor producing coil (at a time two phase coils are connected to formthe equivalent pseudo-stationary coil) set is changed as motor rotates due to thepresence of inverter. Other than this some extra advantages are also gained in1200 conduction VSI fed PMSM. The main advantage of this is that, here as

soon as switch T 1 (Ref. Figure 4.14 starts conducting, the positive part of phase-A current will start building. Hence, if this start of conduction point of T 1 isdelayed or advanced, ia can be made to lead or lag the induced emf of phase A,0r cos(r ) . Thus the internal power factor (power factor w.r.t angle betweenback emf and the corresponding phase current )of PMSM can be controlled directlyin 1200 conduction VSI conguration. The start of conduction point of T 1 can becontrolled by changing s which is a constant of equation 1.8. In further analysisit is shown that this s = sensor angle of 120 0 conduction VSI fed of PMSM.Analytically speaking this implies that, in this 120 0 conduction VSI the angle s(Ref equation 1.8) which is the internal power factor angle (neglecting commutationoverlap), can be directly controlled, though it is a voltage source inverter. In effect

it can be seen that change on s can shift the space angle of armature MMF,M a (Ref.Figure 1.4). This is analogous to the space angle control of armatureMMF by brush shifting in conventional DC machine.

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Figure 3.12: Experimental steady state waveforms of phase current and linevoltage at V dc = 30V olts, no-load and sensor lead angle = 0 0

Figure 3.13: Experimental steady state waveforms of phase current and phasevoltage at V dc = 25V olts, Viscous friction, f = 0.0016Nm s/Rad , LoadTorque, T L = 1.3Nm ,sensor lead angle = 0 0

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Figure 3.14: Experimental steady state waveforms of phase current and phasevoltage at V dc = 35V olts, Viscous friction, f = 0.0016Nm s/Rad , LoadTorque, T L = 1.5Nm ,sensor lead angle = 0 0

Figure 3.15: Conduction intervals for a particular phase for a particularsensor lead angle s

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Figure 3.16: Algorithm for simulating 120 0 conduction VSI fed PMSM

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Figure 3.17: Conduction modes for PMSM drive (a) Mode1 with T 1T 2 pair,

(b) Mode2 with T 1T 2 pair, (c) Mode1 with T 3T 4 pair and (d) Mode2 withT 3T 4 pair

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Figure 3.18: Simulated steady state waveforms of phase current and phasevoltage at V dc = 25V olts, Viscous friction, f = 0.0016Nm s/Rad , LoadTorque, T L = 1.3Nm ,sensor lead angle = 0 0

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Figure 3.19: Simulated steady state waveforms of phase current and phasevoltage at V dc = 35V olts, Viscous friction, f = 0.0016Nm s/Rad , LoadTorque, T L = 1.5Nm ,sensor lead angle = 0 0

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Chapter 4

Development of

An FPGA Controller Based Real Time Implementation of a PMSM Drive

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Transcript of An FPGA Controller Based Real Time Implementation of a PMSM Drive