Application of the convolution theorem for the modeling of saturated induction motors

Abstract

This paper proposes a new method for inductance calculation of induction motors (IM) based on the convolution theorem. The integral form leading to the inductance expressions is derived from the 2D modified winding function approach (2D-MWFA). As first application, a model allowing teeth saturation to be taken into account by the corresponding air-gap permeance variation is proposed. The work points out that appropriate arrangements make it possible to use convolution theorem in favor of integral calculation leading to IM inductances. It is shown that the implication of the convolution concept in such a task reduces strongly the calculation process. Moreover, this method proves to be faster than integrations based on conventional methods. Simulation and experimental results confirm the performance and utility of the proposed technique.

Transient and steady‐state modelling of healthy and eccentric induction motors considering the main and third harmonic saturation factors

“…No full design parameters are needed any more as it is the tradition with the numerical ways. Furthermore, the method provides sometimes amazing decrease of the simulation time [19,20]. From [18][19][20][21][22], several attempts to improve the technique can be noted.…”

A new model of rotor eccentricity in induction motors considering the local air-gap over-flux concentration

“…As reported in [21], thanks to a recent idea based on adapting the conventional numerical convolution algorithms to the inductance calculation, there is generally no need for Fourier series expansion, neither for the inverse of the air-gap function nor for the turns functions, in the inductance evaluation stage whatever their level of complexity. However, this technique is not yet generalized.…”

“…However, this technique is not yet generalized. For the particular case of static eccentricity, it is important to notice that, even with the suggested additions to the initial saturation model explained in [10,21], the inverse of the air-gap function described by Eq. (8) remains independent from x r .…”

“…(8) remains independent from x r . Furthermore, it is shown in [21] that the integral bounds down the axial direction (z 1j and z 2j ) may be viewed as a function of the difference (x r − x) instead of the double variable (x, x r ). It means that the convolution theorem can be once more called up in order to calculate the inductances.…”

“…As recommended in [21], it is also possible here to separate the field position terms and the rotor position terms in the developed inductance expression. Such an arrangement will make easer the calculation of the partial derivatives of the inductances as well as calling simple one dimensional look-up tables in the dynamic resolution of the circuital equations by the general method of interpolation [23].…”