Estimation of Fourier coefficients of flux density
for Surface Mounted Permanent Magnet (SMPM)
Generators by Direct Search Optimization

Mamidi Ramakrishna Rao

doi:https://doi.org/10.14445/22315373/IJMTT-V67I7P518

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 7 | Year 2021 | Article Id. IJMTT-V67I7P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I7P518

Estimation of Fourier coefficients of flux density for Surface Mounted Permanent Magnet (SMPM) Generators by Direct Search Optimization

Mamidi Ramakrishna Rao

Citation :

Mamidi Ramakrishna Rao, "Estimation of Fourier coefficients of flux density for Surface Mounted Permanent Magnet (SMPM) Generators by Direct Search Optimization," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 7, pp. 150-157, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I7P518

Abstract

— For Surface Mounted Permanent Magnet (SMPM) generators, it is essential to predict its performance to analyze the magnet’s air gap flux density wave shape. The flux density wave shape is neither a pure sine wave or square wave or combination. This is due to variation of air gap reluctance between stator and permanent magnets. The stator slot openings and the number of slots make the wave shape more complicated. In order to reduce the analysis complexity, approximations are done to the wave shape, and Fourier analysis is used. Instead of usual integration method, the Fourier coefficients, an and bn, are obtained by direct search method optimization. The wave shape with optimized coefficients gave wave shape close to the desired wave shape. Harmonics amplitudes are worked out and compared with initial values. It can be concluded that direct search method can be used for estimating Fourier coefficients for irregular wave shapes

Keywords

Fourier analysis, Flux plot analysis, Direct search, SMPM generators, Optimization

References

[1] Alexandre Marx, An in-depth comparative study of direct drive versus gear box wind turbines, KTH School of Industrial Engineering and Management. Master of Science Thesis, Stockholm, Sweden. FULLTEXT01.pdf (diva-portal.org) 1-67
[2] F.Libert and J. Soulard, DESIGN STUDY OF A DIRECT-DRIVEN SURFACE MOUNTED PERMANENT MAGNET MOTOR FOR LOW SPEED APPLICATION, Department of Electrical Machines and Power Electronics, Royal Institute of Technology (KTH), Stockholm, Sweden.pages, 1-6. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.532.197&rep=rep1&type=pdf
[3] Amuliu Bogdan Proca, Ali Keyhani, Ahmed EL, Analytical Model for Permanent Magnet Motors with Surface Mounted Magnets, IEEE Transactions of energy conversion, 18(3) (2003) 386-391
[4] Dmitriv Sergeevich Nikitin Fouriers Analysis Lecture 8:, Tomsk Polytechnic University NikitinDmSr@yandex.ru
[5] Mamidi Ramakrishna Rao, Estimation of parameters for Induction motor’s analytical model by Direct search method, 2008 International Conference on Electrical Machines and Systems Wuhan, China, Conference date, IEEE Xplore (2nd Feb 2009), (2008) 17-20.
[6] R Ramarathnam, Optimization of Polyphase Induction Motor Design, Dissertation, Indian Institute of Technolgy, (1969). Appendix-II
[7] Wei-Ta Chu,One -Dimensional Search Methods, https://web2.qatar.cmu.edu/~gdicaro/15382/additional/one-dimensional-search-methods.pdf Spring (2014).
[8] Professor Erik Cheever,The Fourier Series, Department of Engineering, SwarthmoreCollege, https://lpsa.swarthmore.edu/Fourier/Series/WhyFS.html