Analytical Modeling of Eccentric SPM Vernier Machine

Document Type : Original Article

Authors

1 Engineering department of the Shahrekord University

2 Engineering Department of the Shahrekord University

Abstract

In this paper the flux density components in the eccentric slotted surface mounted PM Vernier machine are obtained analytically at on-load and no-load conditions. In the modeling process some conformal transformations, including Schwartz Christoffel and bilinear transformations are applied. In addition, the Laplace solution is used to obtain the air gap flux density of the PMs and the armature reaction. To overcome the limitations of existing conformal transformation-based models, the concept of equivalent magnetization current and the uniqueness theorem are adopted. In the provided model, the air gap flux density, the machine cogging torque and the electromagnetic torque are obtained analytically. Finally, the obtained results are compared with the results of finite element analysis.  

Keywords


[1]      F. Zhao, T. A. Lipo and B. I. Kwon, “A novel dual-stator axial-flux spoke-type permanent magnet Vernier machine for direct-drive application,” IEEE Transactions on Magnetics, Vol. 50, No. 11, ID. 8104304, 2014.##
 
[2]      J. Li, K. T. Chau, J. Z. Jiang, C. Liu and W. Li, “A new efficient permanent-magnet Vernier machine for wind power generation,” IEEE Trans. Magn., Vol. 46, No. 6, pp. 1475-1478 2010.##
 
[3]      S. U. Chung, J. W. Kim, B. C. Woo, D. K. Hong, J. Y. Lee, and D. H. Koo, “A novel design of modular three-phase permanent magnet vernier machine with consequent pole rotor,” IEEE Transactions on, Magnetics, Vol. 47, No.10, pp.4215-4218, 2011.##
 
[4]      A. Rahideh, A. Vahaj, M. Mardaneh, and T. Lubin, "Two-dimensional analytical investigation of the parameters and the effects of magnetisation patterns on the performance of coaxial magnetic gears,” IET Electric Power Applications, Vol. 7, No.3, pp. 230–245, 2017.##
 
[5]      E. Spooner and L. Haydock, “Vernier hybrid machines” IEE Proc.-Electric Power Applications, Vol. 150, No. 6, pp. 655-662, 2003.##
[6]      B. Kim and T. A. Lipo, “Operation and Design Principles of a PM Vernier motor,” IEEE Transactions on Indastry Applications, Vol. 50, No. 6, pp. 3656-3663, 2014.##
 
[7]      A. Toba and T. A. Lipo, “Generic torque-maximizing design methodology of surface permanent-magnet Vernier machine,” IEEE Transactions on Indastry Applications, Vol. 36, No. 6, pp. 1539-1545, 2000.##
 
[8]      K. O. Okada, N. Niguchi, and K. Hirata, “Analysis of a Vernier motor with concentrated windings,” IEEE Transactions on Magnetics, Vol. 49, No. 5, pp. 2241-2244, 2013.##
 
[9]      L. Wu, R. Qu, D. Li and Y. Gao, “Influence of Pole Ratio and Winding Pole Numbers on Performances and Optimal Design Parameters of Surface Permanent Magnet Vernier Machines,” IEEE Transactions on Indastry Applications, Vol. 49, No. 5, pp. 2241-2244, 2013.##
 
[10]   G. Liu, S. Jiang, W. Zhao, and Q. Chen, “A New Modeling Approach for Permanent Magnet Vernier Machine With Modulation Effect Consideration,” IEEE Transactions on Magnetics, Vol. 53, No. 1, 2017.##
 
[11]   Y. Oner, Z. Q. Zhu, L. J. Wu and X. Ge, “Analytical sub-domain mo del for predicting open-circuit field of permanent magnet Vernier mach in e accounting for tooth tips,” Compel, Vol.35, No. 2, pp. 624-640, 2016.##
 
[12]   Y. Oner, Z. Q. Zhu, L. J. Wu, X. Ge, H. Zhan and J. T. Chen, “Analytical On-Load Subdomain Field Model of Permanent-Magnet Vernier Machines,” IEEE Transactions on Indastrial Electronics, Vol.63, No. 7, pp. 4105-4117, 2016.##
 
[13]   Y. Yang, G. Liu, X. T. Yang, and X. Wang, “Analytical Electromagnetic Performance Calculation of Vernier Hybrid Permanent Magnet Machine,” IEEE Transactions on Magnetics, Vol. 54, No. 6, 2018.##
 
[14]   D. Li, R. Qu, J. Li, L. Xiao, L. Wu, and W. Xu, “Analysis of Torque Capability and Quality in Vernier Permanent-Magnet Machines,” IEEE Transactions on Indastry Applications, Vol. 52, No. 1, pp. 125-135, 2016.##
 
[15]   D. Thyroff, C. Hittinger, I. Hahn, “Analytic Power Factor Calculation for Vernier Machines with Concentrated Windings,” IEEE IEMDC, pp. 21-24, 2017.##
 
[16]   D. Thyroff, and I. Hahn, “Optimization of the Flux Modulation Poles for Vernier Machines with Concentrated Windings,” IEEE WEMDCD, pp. 20-21, 2017.##
 
[17]   D. Zarko, D. Ban and T. A. Lipo, “Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance,” IEEE Transactions on Magnetics, Vol. 42, No. 7, pp. 1–8, 2006.##
 
[18]   K. Boughara, D. Zarko, R. Ibtiouen, O. Touhami, and A. Rezzoug, ‘Magnetic Field Analysis of Inset- and Surface- Mounted Permanent Magnet synchronous motors using Schwarz-Christoffel transformation’, IEEE Transactions on Magnetics, Vol. 45, No.8, pp. 1828-1837, 2009.##
 
[19]   T. C. O. Connell, and P. T. Krein, “A Schwarz–Christoffel-Based Analytical Method for Electric Machine Field Analysis,” IEEE Transactions on Energy. Conversion, Vol.24, No. 3, pp. 565-577, 2009.##
 
[20]   K. J. Binns, P. J. Lawrenson, C. W. Trowbridge, “The Analytical and Numerical Solution of Electric and Magnetic Fields,” John Wiley, 1998.##
 
[21]   S. T. Boroujeni, P. Jalali, N. Bianchi, “Analytical modeling of no-load eccentric slotted surface mounted PM machines: cogging torque and radial force,” IEEE Transactions on Magnetics, Vol. 30, No. 2, pp. 754–760, 2015.##
 
[22]   U. Kim and D. K. Lieu, “Magnetic Field Calculation in Permanent Magnet Motors with Rotor Eccentricity: With Slotting Effect Considered,” IEEE Transactions on Magnetics, vol. 34, no. 4, pp. 2253-2266, 1998.##
 
[23]   P. Jalali, S. T. Boroujeni, and N. Bianchi, “Analytical modeling of slotless eccentric surface-mounted PM machines using a conformal transformation,” IEEE Transaction on Energy Conversion, Vol.32, No. 2, pp.    658-666, 2017.##
 
[24]   S. T. Boroujeni and H. Bagheri, “Analytical modeling and prototyping a slotless PM-inset machine,” IET Electric Power Applications, Vol. 11, No. 3, pp. 312–322, 2017.##
 
[25]   S. Taghipour, M. H. Hajare, “Cogging torque optimization in SPM machines using segmented block PMs,” Journal of Applied Electromagnetic, vol.2, no.4, pp. 31-38, 2014.##
 
[26]   M. Alizade, V. Zamani, “Multi-objective optimization of the rotor geometry in SPM machines,” Journal of Applied Electromagnetic, vol.2, no.2, pp. 21-32, 2014.##
  • Receive Date: 27 September 2019
  • Revise Date: 16 November 2019
  • Accept Date: 03 February 2020
  • Publish Date: 09 May 2020