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Third Harmonic Utilization in Permanent Magnet Machines


Table of contents

About this book


This book investigates the utilization of harmonics in the permanent magnet (PM) or rotor shape to improve the torque density of PM brushless AC machines including three-phase inner rotor and outer rotor machines, five-phase machines, dual three-phase machines, linear machines, by means of analytical, finite element analyses, and as well as experimental validation. 

The torque density can be improved while the torque ripple remains low in PM shaping utilizing the 3rd harmonic. In this book, the analytical expression of output torque is derived for PM machines with rotor shape using the 3rd harmonic, and then the optimal 3rd harmonic for maximizing torque is analytically obtained. 

The book compares the PM shape in surface-mounted PM (SPM) machines and the rotor lamination shape in interior PM (IPM) machines utilizing the 3rd harmonic, and it becomes clear that their shaping methods and amount of torque improvement are different. 

In a five-phase PM machine, the 3rd harmonic can be utilized in both the current waveform and PM shapes to further improve the output torque. For the dual three-phase SPM machines without deteriorating the torque more than 30% when the optimal 3rd harmonic into both the current and PM shape are injected.

The harmonics in airgap flux density have significant influence on the cogging torque, stator iron flux distribution, and radial force between the rotor and stator. These effects has been investigated as well in this book.


Permanent magnet machines Third harmonic Torque density PM shaping Harmonic current injection Torque ripple

Authors and affiliations

  1. 1.Department of Electrical EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Department of Electronic and Electrical EngineeringThe University of SheffieldSheffieldUK

About the authors

For internal use only:
Professional Experience
2015-present Professor, Phd supervisor
Nanjing University of Aeronautics and Astronautics
2014-2015 Research and Development Engineer, Ansys Inc., PA, USA
2013-2014 Research associate Siemens Sheffield University Wind Power Research Centre, UK
2010-2013 Research associate, Sheffield University, UK
2009-2010 Post-doctoral researcher, Memorial University, Newfoundland, Canada
2010-2013 Ph.D in Electrical Engineering, Sheffield University, UK
2004-2009 Ph.D in Electrical Engineering, Zhejiang University, Hangzhou, China.
2000-2004 B.S. in Automation, China Jiliang University, Hangzhou, China
2014-2015 Co-simulation between Maxwell and Matlab
2013-2014 PM machine design for wind power
2010-2013 PM machine design for high performance EPS applications
Demonstrator for the undergraduate student in Sheffield University
2009-2010 High efficiency line-start PM motor design and IPM generator design for wind power
2007-2009 Inverter and DSP controller for high speed sensorless control systems.
Technical support of MagneForce motor design software
2007.7-2007.9 Internship position of PM motor design in TECO 
2006-2007 Optimization and development of high-speed sensorless permanent magnet motors
2005-2006 Finite element analysis of three-dimension artificial heart pump motor
PM machine design for high performance EPS applications
Serial DC motor design for electrical machine tools (Bosch Company)
2004-2005 Optimization design of high speed generator for micro-gas turbine

2014-present IEEE Senior member
2012 Best paper awards in international conference and exhibition on ecological vehicles and renewable energy
2009-2010 Excellent plan for Ph.D thesis of Zhejiang Univeristy Excellent graduate student of Zhejiang University
2007-2008 First-Class Scholarship for Excellent Student of Zhejiang University
“TECO” Enterprise Scholarship of Zhejiang University
“MPS” Enterprise Scholarship of Zhejiang University
“Wang Guosong” Scholarship of Zhejiang University
Award of Excellent Leadership of Graduate Student of ZhejiangUniversity
Award for paper published on Journal of Applied Physics
2000-2004 Excellent Graduate Student of China Jiliang University
First-Class Scholarship for Excellent Student of China Jiliang University (4 times)

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