In this paper we propose a new method to calculate the relative harmonic spectrum of the magnetomotive force per phase, based on the generalization of calculating the winding distribution factors and including the Fourier matrix F and matrix C of the winding spatial representation in the calculations. In the proposed methodology, the winding distribution factors are calculated taking into account all poles of the machine and not only a couple of poles, as illustrated in some textbooks. In addition, in this article we analyzed the unbalanced regime windings through the calculation of the components of the electromotive force sequence in empty slot, and these components were related to the harmonic spectrum of the magnetomotive force per pase in symmetric regime. The calculation methods were implemented and validated in a Java application. From the results we proposed a method for calculating the magnetomotive force harmonic spectrum by pase which may be applied to windings of any spatial distribution, as well as a methodology to represent an asymmetrical system of m phases, through sequence components of electromotive force of slot in vacuum.
Harmonics, sequence components, distribution factor, FourierArmónicos, componentes de secuencia, factor de distribución, Fourier
BIANCHI, N.; BOLOGNANI, S.;PRE, M. D., et al. Design considerations for fractional-slot winding configurations of synchronous machines. IEEE Transactions on Industry Applications. 2006, vol. 42, núm.4, pp. 997-1006.
CHEN, J. T.; ZHU, Z. Q. Winding Configurations and Optimal Stator and Rotor Pole Combination of Flux-Switching PM Brushless AC Machines. IEEE Transactions on Energy Conversion. 2010, vol. 25, núm 2, pp. 293-302.
EPRI Report EL-4059, Temporary Operation of Motor with Cut-Out Coils. 1985.
GROP, H.; SOULARD, J.; PERSSON, H.. Theoretical investigation of fractional conductor windings for AC-machines - definition, air-gap m.m.f. and winding factors. IEEE 18th International Conference on Electrical Machines, Vilamoura, 2008, pp. 1-6.
IVANOV-SMOLENSKI, A. V. Máquinas Eléctricas. Moscú: Mir, 1988. 288 p.
KOSTENKO, M. P.; PIOTROVSKI, L. M. Máquinas Eléctricas Tomo II. Moscú: Mir, 1976. 718 p.
LARA, T. Matrices Circulantes. Divulgaciones Matemáticas. 2001, vol. 9, núm. 1, pp. 85-102.
LIANG, X.; LUY, Y. Harmonic Analysis for Induction Motors. IEEE Canadian Conference on Electrical and Computer Engineering. Ottawa, 2006, pp. 172-177.
STONE, G. C.; BOULTER, E. A.; CULBERT, I. et al. Electrical Insulation for Rotating Machines. Hoboken, NJ, USA: John Wiley & Sons, 2003. 392 p.
WACH, P. Algorithmic method of design and analysis of fractional-slot windings of AC machines. Electrical Engineering. 1998, vol. 81, núm. 3, pp. 163-170.