Florida State University Libraries Electronic Theses, Treatises and Dissertations

The Graduate School

2014

Real-Time Switched Reluctance Machine Emulation via Magnetic Equivalent Circuits Fletcher Fleming

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FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING

REAL-TIME SWITCHED RELUCTANCE MACHINE EMULATION VIA MAGNETIC

EQUIVALENT CIRCUITS

By FLETCHER FLEMING

A Dissertation submitted to the Department of Electrical and Computer Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Summer Semester, 2014

Fletcher Fleming defended this dissertation on July 17, 2014. The members of the supervisory committee were:

Chris S. Edrington Professor Directing Dissertation

Juan Ordonez University Representative

Simon Foo Committee Member

Uwe Meyer-Baese Committee Member

Mark H. Weatherspoon Committee Member

The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements.

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ACKNOWLEDGEMENTS First off I’d like to give a big thanks to my advisor, mentor and friend Dr. Chris Edrington. I’ve learned a lot from you over my MS, PhD programs and CAPS career. You’ve kept me afloat technically, financially and mentally throughout whatever shenanigans come my way. I’ve learned how to approach new problems and teach/manage others how to best contribute, the payoff of a good plan, professionalism, superior technical writing and presentation skills, to be both self-critical and efficient in finishing a task and much more. I can’t count the number of times that you’ve been there for me to troubleshoot and bounce ideas back and forth. With your support, I’ve attended over twenty conferences (both domestic and international) with a presentation and/or publication at each. Thanks for being a great advisor, keeping me focused on my finishing up my dissertation research. Between my parents’ support and Dr. Edrington’s consistent funding stream, I’ve managed to escape graduate school debt free. For that I’m extremely grateful, thanks. Thanks to my family for asking the routine question of, “Fletcher, when are you going to finish?” only to get the answer, “Probably in about two more years…” Whew, did I ever get some mileage out of that answer. I wouldn’t have made it this far without y’all; you’ve always loved and supported me, being there should I need anything. Love y’all. As for my friends; thanks for not worrying about that sliding two year window. You’ve constantly kept me sane and entertained in some form or fashion. Work hard, play hard. Thanks to Florida State University and The Department of Computer and Electrical Engineering. I’ve been in nearly every ECE professor’s office or class at some point with an issue needing their attention. Thanks to Dr. Meyer-Baese for trusting me with an expensive FPGA to play with and ultimately implement my research on. Without your expertise and guidance, RT-MEC would be missing the RT. Furthermore, thanks to my committee for flexibly meeting with me whenever necessary. Finally, thanks to the Energy Conversion and Integration Group and the Center for Advanced Power Systems. Jesse Leonard, one of the smartest and most selfless guys I know. It’s been a pleasure working alongside you. Thanks to everyone involved with the switched reluctance machine test bed over the years, especially Troy Bevis and his outstanding work ethic

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which was crucial in bringing it to life. All the post-docs, students, scientists and full-time staff have taught me so much and taken care of me however necessary. Thanks everyone.

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TABLE OF CONTENTS LIST OF FIGURES ....................................................................................................................... vii LIST OF TABLES .......................................................................................................................... x LIST OF ABBREVIATIONS ........................................................................................................ xi ABSTRACT................................................................................................................................. xiii CHAPTER 1 INTRODUCTION .................................................................................................... 1 1.1

NGIPS Motivation............................................................................................................ 1

1.2

Electromagnetic Device Modeling and Simulation Methods .......................................... 3

1.3

Hardware-in-the-Loop ...................................................................................................... 7

1.4

8/6 Switched Reluctance Machine ................................................................................... 9

1.5

Literature Review: SRM MEC and Real-time Machine Modeling Methods................. 11

1.6

Problem Statement and Contribution ............................................................................. 12

CHAPTER 2 SRM THEORY AND MODELING ....................................................................... 15 2.1

SRM Fundamentals and Test Bed .................................................................................. 15

2.1.1

SRM History and Theory of Operation .................................................................... 15

2.1.2

SRM Drives Overview .............................................................................................. 17

2.1.3

SRM Experimental Test Bed .................................................................................... 19

2.2

FEA Modeling ................................................................................................................ 22

2.3

ODE Modeling ............................................................................................................... 24

2.4

MEC Modeling............................................................................................................... 27

2.4.1

Constant Permeance: Slot Leakages ....................................................................... 29

2.4.2

Parametrically Nonlinear Permeances: Air gap ..................................................... 31

2.4.3

Inherently Nonlinear Permeances: Core ................................................................. 33

2.4.4

Initial SRM MEC Model .......................................................................................... 35

2.4.5

Nodal SRM MEC Mathematic Representation ........................................................ 38

2.4.6

Iterative MEC Solution: Gauss-Seidel ..................................................................... 43

CHAPTER 3 REAL-TIME IMPLEMENTATION ...................................................................... 45 3.1

Real-time MEC Model ................................................................................................... 45

3.1.1

Real-time Solution Method ...................................................................................... 45

3.1.2

Differentiating the MEC .......................................................................................... 47

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3.2

Model Reduced RT-MEC .............................................................................................. 51

3.3

Real-time Implementation .............................................................................................. 55

3.3.1

Platform Selection .................................................................................................... 55

3.3.2

Real-time Implementation Optimizations ................................................................ 57

3.3.3

Resource Utilization and Performance .................................................................... 60

CHAPTER 4 RESULTS AND ANALYSIS................................................................................. 63 4.1

SRM Torque and Flux Linkage Characteristics ............................................................. 63

4.2

Startup Speed Characteristic .......................................................................................... 67

4.3

Speed Control Application ............................................................................................. 69

4.4

Response to Torque Load............................................................................................... 71

CHAPTER 5 CONCLUSIONS AND FUTURE WORK ............................................................. 73 5.1

Challenges, Assumptions and Limitations ..................................................................... 73

5.2

Impact and Applications................................................................................................. 75

5.3

Conclusion...................................................................................................................... 75

5.4

Future Work ................................................................................................................... 76

APPENDIX A

VARIOUS TRANSFORMER MEC SOLUTIONS ........................................ 79

A.1

Nodal Analysis of a Twin Winding MEC ...................................................................... 79

A.2

Mesh Analysis of a Twin Winding MEC ....................................................................... 84

A.3

Nodal Analysis of a 5-Node Twin Winding MEC ......................................................... 86

A.4

Iterative Nodal Analysis of a Twin Core, Twin Winding MEC .................................... 88

APPENDIX B

SUPPLEMENTAL SRM DATA..................................................................... 93

B.1

SRM Characteristics and Supplemental Data ................................................................ 93

B.2

SRM Base Speed and Single Pulse Current Mode......................................................... 96

REFERENCES ........................................................................................................................... 100 BIOGRAPHICAL SKETCH ...................................................................................................... 107

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LIST OF FIGURES Figure 1-1: Notional MVDC ship system design [2] ...................................................................... 2 Figure 1-2: CHIL system flow diagram - generic example ............................................................ 8 Figure 1-3: PHIL system flow diagram - voltage drive example ................................................... 9 Figure 2-1: Cross sectional view of the 8/6 SRM ......................................................................... 16 Figure 2-2: Asymmetric bipolar bridge converter ........................................................................ 17 Figure 2-3: Experimental 8/6 SRM............................................................................................... 19 Figure 2-4: 8/6, 1kW 4-phase SRM motor stand .......................................................................... 19 Figure 2-5: SRM drive test bed..................................................................................................... 20 Figure 2-6: Experimental flux linkage and inductance profiles.................................................... 22 Figure 2-7: SRM FEA model ........................................................................................................ 23 Figure 2-8: FEA model, flux linkage and inductance profiles...................................................... 23 Figure 2-9: Aligned, midway and unaligned inductance polynomial fits ..................................... 27 Figure 2-10: ODE Fourier series model, flux linkage and inductance profiles ............................ 27 Figure 2-11: Flux tube definition .................................................................................................. 28 Figure 2-12: Slot leakage partitioning .......................................................................................... 29 Figure 2-13: Stator slot measurements ......................................................................................... 31 Figure 2-14: Pole overlap for various rotor positions ................................................................... 31 Figure 2-15: Air gap permeance and angular derivative between stator and rotor teeth .............. 33 Figure 2-16: Calculation of INP ................................................................................................... 34 Figure 2-17: 8/6 SRM MEC topology .......................................................................................... 37 Figure 2-18: MEC nodal analysis, upper node, u1 vector ............................................................. 39 Figure 2-19: MEC nodal analysis, middle node, u1 vector ........................................................... 39

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Figure 2-20: MEC nodal analysis, bottom node, u1 vector ........................................................... 39 Figure 2-21: MEC tooth excitation, branch circuit depiction ....................................................... 41 Figure 2-22: Code flow for Gauss-Seidel iterative MEC solution ............................................... 44 Figure 3-1: Code flow for unique system of differential equations .............................................. 47 Figure 3-2: Differential SRM MEC, flux linkage and inductance profiles .................................. 51 Figure 3-3 Model reduced SRM RT-MEC ................................................................................... 52 Figure 3-4: Model reduced SRM RT-MEC, flux linkage and inductance profiles ...................... 55 Figure 3-5: Terasic DE4 FPGA development board..................................................................... 57 Figure 4-1: Experimental SRM, torque vs. rotor angle and current ............................................. 64 Figure 4-2: Torque-angle comparison at 15A ............................................................................... 65 Figure 4-3: Flux linkage-angle comparison at 15A ...................................................................... 67 Figure 4-4: SRM drive control diagram........................................................................................ 68 Figure 4-5: Startup speed characteristic comparison .................................................................... 68 Figure 4-6: SRM closed-loop speed control ................................................................................. 70 Figure 4-7: Zoomed to represent difference in speed controllers ................................................. 70 Figure 4-8: Torque response under 300 rpm speed control reference .......................................... 71 Figure A-1: Single node, twin winding, O-core transformer MEC .............................................. 79 Figure A-2: Flux tube intersection example ................................................................................. 80 Figure A-3: Nodal twin winding MEC, case I, equal windings.................................................... 83 Figure A-4: Nodal twin winding MEC, case II, V2