CJEE

Chinese Journal of Electrical Engineering ›› 2024, Vol. 10 ›› Issue (2): 44-58.doi: 10.23919/CJEE.2024.000057

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Analytical Solution of a Fractional-slot Double-layer-winding Open-slot Vernier Permanent Magnet Machine with Tooth Tips

Weibing Wang1,*, Ming Cheng2   

  1. 1. School of Electric Power Engineering, Nanjing Institute of Technology, Nanjing 211167, China;
    2. School of Electrical Engineering, Southeast University, Nanjing 210096, China
  • Received:2023-10-13 Revised:2024-01-11 Accepted:2024-02-17 Online:2024-06-25 Published:2024-07-01
  • Contact: * E-mail: weibingwang@njit.edu.cn
  • About author:Weibing Wang was born in Jiangsu, China. He received the B.Sc. degree from the College of Computer and Information Engineering, Hohai University, Changzhou, China, in 2002, and the Ph.D. degree in Electrical Engineering from the School of Electrical Engineering, Hohai University, Nanjing, China, in 2008.
    Since 2008, he has been with Nanjing Institute of Technology, where he is currently an Associate Professor with the School of Electric Power Engineering and a Researcher with the Key Laboratory of Active Distribution Network of Jiangsu Province. His teaching and research interests include the analysis and control of electrical machines.
    Ming Cheng (M’01-SM’02-F’15) received the B.Sc. and M.Sc. degrees from the Department of Electrical Engineering, Southeast University, Nanjing, China, in 1982 and 1987, respectively, and the Ph.D. degree from the Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China, in 2001, all in Electrical Engineering.
    Since 1987, he has been with Southeast University, where he is currently a Chair Professor at the School of Electrical Engineering and the Director of the Research Center for Wind Power Generation. From Jan. to Apr. 2011, he was a Visiting Professor with the Wisconsin Electric Machine and Power Electronics Consortium, University of Wisconsin, Madison, WI, USA. His teaching and research interests include electrical machines, motor drives for EV, and renewable energy generation and servo motor systems. He has authored or co-authored more than 400 technical papers and 5 books and is the holder of 130 patents in these areas.
    Prof. Cheng is a Fellow of the Institution of Electrical and Electronics Engineers, a Fellow of the Institution of Engineering and Technology. He has served as the Chair and Organizing Committee Member for many international conferences. He was a Distinguished Lecturer of the IEEE Industry Applications Society in 2015/2016.

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Abstract: An analytical solution (ANA) for a fractional-slot double-layer-winding open-slot vernier permanent magnet (VPM) machine with tooth tips is presented. Magnetic vector potential equations are analytically solved using the technique of variable separation in four subdomains in a two-dimensional polar coordinate system. Based on the solved magnetic vector potential, the flux density distribution, torque, flux linkage, inductance, electromotive force (EMF) and power factor are analytically developed. An 18-slot/32-rotor-pole prototype is analyzed, and the results match well with the finite element analysis (FEA), which validates that the ANA consumes less time than FEA. Therefore, the tooth tips are optimized using the ANA to improve the average torque. Moreover, the ANA can be used to evaluate the demagnetization withstand capabilities of permanent magnets. The material utilization, slot-filling factor, EMF, and torque are compared between the models with three and four subdomains. Finally, an experimental prototype is constructed and tested, and the results validate the ANA.

Key words: Analytical solution, magnetic field, vernier permanent magnet machine, subdomain, optimization, demagnetization