finite element method; electrical machines; harmonics; magnetic devices
Abstract :
[en] An original and easy-to-implement method to take into account movement (motion) in the 2D harmonic balance finite element modelling of electrical machines is presented The global harmonic balance system of algebraic equations is derived by applying the Galerkin approach to both the space and time discretisation. The harmonic basis functions, i.e. a cosine and a sine function for each nonzero frequency and a constant function 1 for the DC component, are used for approximating the periodic time variation as well as for weighing the time domain equations in the fundamental period. In practice, this requires some elementary manipulations of the moving band stiffness matrix. Magnetic saturation and electrical circuit coupling are considered in the analysis as well. As an application example, the noload operation of a permanent-magnet machine is considered. The voltage and induction waveforms obtained with the proposed harmonic balance method are shown to converge well to those obtained with time stepping.
Dular, Patrick ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Vandevelde, Lieven
Melkebeek, Jan
Oliveira, Ana Margarita
Kuo-Peng, Patrick
Language :
English
Title :
Two-dimensional harmonic balance finite element modelling of electrical machines taking motion into account
Publication date :
2003
Journal title :
COMPEL
ISSN :
0332-1649
eISSN :
2054-5606
Publisher :
Emerald Group Publishing Limited, Bradford, United Kingdom
Volume :
22
Issue :
4
Pages :
1021-1036
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
BELSPO - Politique scientifique fédérale [BE] F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE] CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico [BR]
De Gersem, H. and Hameyer, K. (2002), "Air-Gap flux splitting for the time-harmonic finite-element simulation of single-phase induction machines", IEEE Trans. Magn., Vol. 38 No. 2, pp. 1221-4.
Gyselinck, J., Dular, P., Geuzaine, C. and Legros, W. (2002a), "Harmonic balance finite element modelling of electromagnetic devices: a novel approach", IEEE Trans. Magn., Vol. 38 No. 6, pp. 521-4.
Gyselinck, J., Geuzaine, C., Dular, P. and Legros, W. (2002b), "Multi-harmonic modelling of motional magnetic field problems using a hybrid finite element - boundary element discretisation", Proceedings of the Second International Conference on Advanced Computational Methods in Engineering (ACOMEN02), Liège, Belgium, 28-31 May, on CDROM.
Gyselinck, J., Dular, P., Geuzaine, C. and Legros, W. (2002c), "Two-dimensional harmonic balance finite element modelling of electromagnetic devices coupled to nonlinear circuits", Proceedings of the XVII Symposium Electromagnetic Phenomena in nonlinear Circuits (EPNC2002), 1-3 July, Leuven, Belgium, 11-4 (accepted for COMPEL).
Ida, N. and Bastos, J.P.A. (1997), Electromagnetics and calculation of fields, Springer-Verlag, New York, NY.
Lombard, P. and Meunier, G. (1992), "A general method for electric and magnetic coupled problem in 2D and magnetodynamic domain", IEEE Trans. Magn., Vol. 28 No. 2, pp. 1291-4.
Lu, J., Yamada, S. and Bessho, K. (1991), "Harmonic balance finite element method taking account of external circuits and motion", IEEE Trans. Magn., Vol. 27 No. 5, pp. 4024-7.
Luomi, J., Niemenmaa, A. and Arkkio, A. (1986), "On the use of effective reluctivities in magnetic field analysis of induction motors fed from sinusoidal voltage source", Proceedings of the International Conference on Electrical Machines (ICEM86), 8-10 September, München, Germany, pp. 706-9.
Oliveira, A.M., Kuo-Peng, P., Sadowski, N., Andrade, M.S. and Bastos, J.P.A. (2002), "A non-a priori approach to analyze electrical machines modeled by FEM connected to static converters", IEEE Trans. Magn., Vol. 38 No. 2, pp. 933-6.
Saad, Y. (1996), Iterative Methods for Sparse Linear Systems, PWS Publishing Company.
SPARSKIT: a basic tool-kit for sparse matrix computations (2003), http://www.cs.umn.edu/Research/arpa/SPARSKIT/sparskit.html
Yahiaoui, A. and Bouillaut, F. (1985), "Saturation effect on the electromagnetic behaviour of an induction machine", IEEE Trans. Magn., Vol. 31 No. 3, pp. 2036-9.
Yamada, S. and Bessho, K. (1988), "Harmonic field calculation by the combination of finite element analysis and harmonic balance method", IEEE Trans. Magn., Vol. 24 No. 6, pp. 2588-90.
