Analytical hybrid Flux switching permanent magnet machines
model
Citation for published version (APA):
Ilhan, E., Gysen, B. L. J., Paulides, J. J. H., & Lomonova, E. (2010). Analytical hybrid Flux switching permanent
magnet machines model. In Proceedings of the 11th Joint MMM-Intermag Conference, January 18-22, 2010,
Washington D.C. (pp. 1625-1625). Institute of Electrical and Electronics Engineers.
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Published: 01/01/2010
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Analytical Hybrid Flux Switching Permanent Magnet Machines Model. E. llhan, B. Gysen, J. Paulides, E. Lomonova
Electrical Engineering, Eindhoven University of Technology, Eindhoven, Netherlands 1) INTRODUCTION
The conservation of energy and the development of energy-efficient products at minimum costs is a critical challenge facing the world today. A recently introduced class of machine, the flux switch ing permanent magnet machine (FSPM) [1], could play a pivotal role in answering some of these issues for the automotive and energy sector. To date, in these applications permanent magnet syn chronous machines (PMSM), due to their high power density, or switched reluctance machines (SRM), due to their simple rotor structure capable of reaching higher speeds, are evermore applied. In this respect, the FSPM embodies the combined advantages of both machine types.
The aim of this paper is to illustrate a new way to investigate the FSPM. To date, these machines are primarily designed using finite elements (FE) and only a very limited analytical approaches are available [2]. Therefore, this paper proposes a novel analytical hybrid modeling technique, which combines the advantages of both the magnetic equivalent circuit (MEC) and Fourier analysis. The obtained results are verified with 2D FE. Although the FSPM allows for unconventional stator rotor pole combinations, for a convenient comparison to published articles, a 12 10 pole structure (Fig. 1(a)) has been considered to verify the analytical hybrid model.
2) HYBRID MODEL
The coupling of energy sources, magnetic and electrical, that use an identical magnetic circuit results in a highly saturated FSPM, hence requires an iterative non-linear magnetic analysis method. One way to overcome this is to model the FSPM using a MEC at the cost of a coarse dis cretization compared to the FE analysis [2]. An alternative or supplementary technique, the Fouri er analysis, obtains a fine discretization, however it can only deal with linear magnetic modeling [3]. The proposed analytical hybrid model combines the advantages of both methods in order to predict the output torque.
In this new analytical hybrid model the presence of non-linear soft-magnetic material is included by virtually changing a global machine parameter, i.e. the airgap length. This parameter variation continues until an error-criteria is satisfied, which compares the reference nonlinear MEC flux den sity values in the airgap center with the linear Fourier model. Once an acceptable flux density dis tribution is achieved, the result of the Fourier analysis with adapted airgap length is used in the Maxwell Stress Tensor method to obtain the output torque.
Various error criteria have been researched, where the first two, i.e. A and B, consider a point-wise comparison of the flux density distribution. These initial criteria make use of a mean error function, which compares the solutions in the airgap center from the two analytical methods, the nonlinear MEC and linear Fourier analysis. As such, criterion A differs from B in that it only compares the points where a flux density above 2T is reached, because these locations show the largest deviation from the real machine behavior in the presence of saturation. Criterion B considers all points in the airgap using the same error equation as A. The last criterion C differs from the previous two in the sense that instead of a point-wise, a mean comparison is considered, where each step in the model makes a numerical integration over the airgap area for the two methods, which are compared later in the decision step.
3) RESULTS AND CONCLUSIONS
Depending on the choice of error criterion, a different level of accuracy has been achieved in flux density and mean torque calculation, (Fig. 1(b)). Criterion A has a very short simulation time (e.g.
307 s) with an error in the rated torque output of 330o. The second criterion B has the highest accu racy with the lowest error of 6°o but a larger simulation time (e.g. 487 s). The last criterion C gives a balanced result regarding both aspects with an error of 1 8% and a simulation time between the other criteria.
The hybrid analytical model combines the advantages of the nonlinear analysis capability of the MEC model with the fine discretization of the linear Fourier analysis in order to predict the rated torque output of a FSPM machine with a highly saturated nature. The various error criteria give the designer the freedom to select between calculation time (e.g. for optimization) and model accura cy.
[1] C. Pollock, H. Pollock, R.Barron, R.Sutton, J. Coles, D. Moule, and A. Court, “Flux switching moto automotive applications,” in Industry Applications Conference, 38th lAS Annual Meeting. Conferen of the, vol. I, pp. 242 249 vol.1, Oct. 2003.
[2] Z. Zhu, Y. Pang, D. Howe, S. Iwasaki, R. Deodhar, and A. Pride, “Analysis of electromagnetic performance of flux-switching permanent magnet machines by nonlinear adaptive lumped parameter magnetic Circuit model’ Magnetics,IEEETransactions on, vol. 41, no. II, pp.4277—4287,Nov.2005.
[3]N.Boules, “Two-dimensional field analysis of cylindrical machines with permanent magnet excitation,” Industry Applications,IEEETransactions on, vol. IA-20, no. 5, pp. 1267 1277, Sept. 1984.
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Fig.1 (a) Schematic of the FSPM machine, b) Torque calculations of the hybrid model for vari ous error criteria.
