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To design and study an electrical machine, Finite Element Model (FEM) is nowadays the most accurate approach as it takes into account different phenomenon. However, it is also time-consuming which does not always make it suitable for an optimization process. Analytical model can then be used but it has to be as accurate as possible in order to obtain valid and relevant results. In case of squirrel cage induction machines, several analytical models have been proposed under different simplifying hypothesis [1]–[3] The well adapted one is the approach involving winding function to determine the armature Magneto Motive Forces (MMF) along with the air gap permeance. These two quantities can be expressed in a relatively accurate way [4]. The problem then remains in taking into account the rotor part in order to determine the currents which circulate in the bars of the squirrel cage. Indeed, in addition to the well estimate of the magnetic flux through the rotor surfaces, the determining of the elements of the equivalent electrical circuit which makes it possible to precisely calculate the currents of the bars in the most accurate way is required. In the present paper, an analytical model of the squirrel cage based on an equivalent electrical circuit along with the approach to accurately identify its parameters is proposed. This model that enables to determine the rotor bar currents can be generalized to any structure and thus be used either for design or optimization purposes. Results obtained in the case of an induction machine prototype are compared to the ones given by FEM.

Magneto Motive Force is an important quantity to analyze electrical machine performances. Indeed, the latter is directly linked to that of the air gap magnetic flux density and thus to the torque ripples, vibration and then noise. This paper proposes to reduce the MMF harmonic content by means of optimization process using mono-objective or multi-objective algorithms with discrete and continuous variables. For this aim, optimization algorithm is coupled with an analytical tool which enables calculating quickly the MMF harmonic content from winding parameters. A winding optimization of three different windings with the same number of pole pairs is proposed to show the suitability of this process.

Study of the impact of stator MMF from different winding distributions using FEM can be tedious when taking into account the stator slots as it introduces mesh constraint and reluctance variation of the air gap. To avoid this fact, a current sheet spread all around the inner stator surface is used. In the proposed approach, the MMF is modelled by the equivalent current sheet of the real stator MMF in the air gap. This current sheet is coupled with an analytical tool that allows obtaining the spatio-temporal stator MMF of any winding considered. Compared to an analytical model, the proposed approach enables taking into account the non linear behaviour of magnetic material in the yoke and thus testing different combinations of stator windings in more realistic conditions.

Magneto motive force is a key quantity of the energy conversion in the electrical machines. Its harmonic content is important as it leads to the one of the magnetic flux density in the air gap. To analyze it, a first step consists to study the winding function. Many tools already exist to tackle this point but generally they use some methods like Star of slots or matrix representation and the harmonic content is obtained by a Fast Fourier Transform of the total winding function. In the present paper, we propose to build up the winding function using elementary patterns whose harmonic contents are used to reach the one of the whole function using a geometrical construction. This approach is quite fast and allows easy analyzing in order to reduce or cancel a magnetic harmonic.

The magneto motive force is an important physical quantity for electrical machines. Indeed its harmonic content leads to that of the air gap flux density. This paper presents an optimisation of the winding distribution for three phase fractional slot concentrated winding (FSCW) and distributed winding (DW) in order to reduce the magneto motive force harmonic content. This have an important effect on torque ripples, vibration and then noise. The optimization will be done on continue and discrete variables linked to the winding distribution.