ANALYSIS OF REGENERATIVE BRAKING IN ELECTRIC MACHINES A Thesis Presented to The Academic Faculty by Aravind Samba Murthy In Partial Fulfillment of the Requirements for the Degree Master of Science in the School of Electrical and Computer Engineering Georgia Institute of Technology May 2013 ANALYSIS OF REGENERATIVE BRAKING IN ELECTRIC MACHINES Approved by: Professor David G Taylor, Advisor School of Electrical and Computer Engineering Georgia Institute of Technology Professor Thomas G Habetler School of Electrical and Computer Engineering Georgia Institute of Technology Professor Yorai Wardi School of Electrical and Computer Engineering Georgia Institute of Technology Date Approved: 3 April 2013 To my mother and grandmother iii ACKNOWLEDGEMENTS This dissertation would not have been possible without the guidance and the help of several individuals who inonewayoranothercontributed andextended theirvaluable assistance in the preparation and completion of this study. Firstandforemost, myutmostgratitudetomyadvisor, Dr.DavidGTaylor, whose continuousguidanceandsupporthasbeeninvaluabletome. Hispatience, motivation, enthusiasm, and immense knowledge has helped me during the research and writing of this thesis. I could not have imagined having a better advisor and mentor and it was certainly a pleasure working with him. I have been greatly influenced by his discipline and dedication to his work and look up to him as a role model. I would like to thank Dr. Thomas G Habetler and Dr. Yorai Wardi, for taking valuable time out of their busy schedules to serve on my thesis reading committee and provide their invaluable suggestions. I would like to acknowledge support from the Department of Energy under Award Number DE-EE0002627. I would also like to thank Dr. Michael J Leamy from the Woodruff School of Mechanical Engineering who is an integral part of the project which funded this research. Last but not the least, I would like to thank the ones closest to my heart, my family and my fianc´ee. I thank my mother who has single-handedly supported me since my father’s passing away nine years ago, I owe her my everything. I would like to thank my grandmother and sister who have been tremendous emotional supports throughout my life. I would also like to thank my aunts for always being there for my family. I would like to thank my fianc´ee, Rajatha Bhat, for always being there to cheer me up whenever I was dejected due to the hurdles I faced during the course of my research. iv TABLE OF CONTENTS DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . iv LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 II REGENERATIVE BRAKING IN DC MACHINES . . . . . . . . 4 2.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Separately Excited DC Machine . . . . . . . . . . . . . . . . 9 2.3.2 Permanent Magnet DC Machine . . . . . . . . . . . . . . . . 11 2.4 Symbolic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.1 Neglecting Core Loss Resistance, R . . . . . . . . . . . . . . 12 c 2.4.2 Including Core Loss Resistance, R . . . . . . . . . . . . . . . 16 c III REGENERATIVEBRAKINGINPERMANENTMAGNETSYN- CHRONOUS MACHINES . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3.1 IPM-A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.2 IPM-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.3 SPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Symbolic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.1 Neglecting Core Loss Resistance, R . . . . . . . . . . . . . . 35 c 3.4.2 Including Core Loss Resistance, R . . . . . . . . . . . . . . . 38 c v IV APPLICATION IN AN ELECTRIC VEHICLE . . . . . . . . . . . 43 4.1 Loss Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.1 Electrical Subsystem Losses . . . . . . . . . . . . . . . . . . . 44 4.1.2 Mechanical Subsystem Losses . . . . . . . . . . . . . . . . . . 49 4.2 Braking Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 V CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 vi LIST OF TABLES 1 Separately Excited DC Machine Parameters Used for Numerical Opti- mization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Permanent Magnet DC Machine Parameters Used for Numerical Op- timization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Interior Permanent Magnet Synchronous Machine (Star-Connected) Parameters Used for Numerical Optimization (IPM-A) . . . . . . . . 30 4 Interior Permanent Magnet Synchronous Machine (Star-Connected) Parameters Used for Numerical Optimization (IPM-B) . . . . . . . . 31 5 Surface Permanent Magnet Synchronous Machine (Delta-Connected) Parameters Used for Numerical Optimization . . . . . . . . . . . . . 33 6 Braking Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 7 Vehicle Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 8 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 vii LIST OF FIGURES 1 4-quadrant motoring and braking operations in the torque-speed plane. 2 2 Steady-state equivalent circuit diagram of a DC machine (field circuit not shown). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Schematic diagram showing the connection of the DC machine to the DC source through the DC-DC converter. . . . . . . . . . . . . . . . 7 4 Steady-state equivalent circuit diagram of an electrochemical battery pack which is used as the DC source. . . . . . . . . . . . . . . . . . . 7 5 Numerical optimization solutions for seperately excited DC machine. 10 6 Numerical optimization solutions for permanent magnet DC machine. 13 7 Regenerative braking boundaries and maximum regenerative braking current curve for a permanent magnet DC machine neglecting core loss resistance, R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 c 8 Regenerative braking boundaries and maximum regenerative braking current curve for a permanent magnet DC machine including core loss resistance, R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 c 9 Cross-section of a two pole interior permanent magnet synchronous machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 10 Schematic of a star-connected AC machine connected to the DC source through a DC-AC converter. . . . . . . . . . . . . . . . . . . . . . . . 23 11 Steady-stateequivalentcircuitmodelsinthedandq axesofaninterior- permanent-magnet synchronous machine. . . . . . . . . . . . . . . . . 23 12 Abstracted block diagram of the DC source, DC-AC power converter and electric machine in terms of d and q variables in the rotor frame of reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 13 Numerical optimization solutions of the interior permanent magnet synchronous machine IPM-A. . . . . . . . . . . . . . . . . . . . . . . 31 14 Numerical optimization solutions of the interior permanent magnet synchronous machine IPM-B. . . . . . . . . . . . . . . . . . . . . . . 32 15 Numericaloptimizationsolutionsofthesurfacepermanentmagnetsyn- chronous machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 16 Regenerative braking boundaries and maximum regenerative braking current curve for a surface permanent magnet synchronous machine neglecting core loss resistance, R . . . . . . . . . . . . . . . . . . . . . 37 c viii 17 Regenerative braking boundaries and maximum regenerative braking current curve for a surface permanent magnet synchronous machine including core loss resistance, R . . . . . . . . . . . . . . . . . . . . . 40 c 18 Contours of constant losses of the electrical subsystem plotted on the torque-speed plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 19 Contours of constant efficiency of the electrical subsystem plotted on the torque-speed plane. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 20 Resistance forces associated with a vehicle traveling along an inclined road. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 21 Sample operating points in the braking quadrant of the torque-speed plane used to explain the braking strategies. . . . . . . . . . . . . . . 51 22 Comparison of braking strategies for the UDDS drive cycle . . . . . 57 ix SUMMARY All electric machines have two mechanical operations, motoring and braking. The nature of braking can be regenerative, where the kinetic energy of the rotor is con- verted into electricity and sent back to the power source or non-regenerative, where the source supplies electric power to provide braking. This thesis investigates several critical issues related to regenerative braking in both DC and AC electric machines, including the determination of boundaries in the torque-speed plane defining the re- generative braking capability region and the evaluation of operating points within that capability region that result in maximum regenerative braking recharge current. Electric machines are used in the powertrains of electric and hybrid-electric ve- hicles to provide motoring or braking torque in response to the driver’s request and power management logic. Since such vehicles carry a limited amount of electrical energy on-board their energy storage systems (such as a battery pack), it is impor- tant to conserve as much electrical energy as possible in order to increase the range of travel. Therefore, the concept of regenerative braking is of importance for such vehicles since operating in this mode during a braking event sends power back to the energy storage system thereby replenishing its energy level. Since the electric machine assists the mechanical friction braking system of the vehicle, it results in reduced wear on components within the mechanical friction brake system. As both mechanical friction braking and electric machine braking are used to provide the requested vehicle braking torque, braking strategies which relate to splitting of the braking command between the two braking mechanisms are discussed. The reduction in energy consumption of a test vehicle along different driving schedules while using different braking strategies is also studied. x