An analytical model of the induction machine for the development of diagnostic techniques

In the technical literature many models capable of representing the behavior of the induction machine have been presented. The traditional Park model is very easy to be implemented but it does not take into account the flux density space harmonics. It is well known that it can be modified in order to consider stator and rotor asymmetries. However for some applications such as the study and the development of diagnostic techniques the results are not accurate enough. More detailed models have been presented; many of them are based on the winding function approach. They are suitable to represent the behavior of the machine under faulty conditions, since they take into account the effect of the eccentricity, the bar skewing, the magnetic saturation and the electrical asymmetries. All of them are very complex and their employment implies a huge computational burden. In this paper the authors propose a new accurate model based on the winding functions which is capable of representing any kind of stator and rotor asymmetry; air gap eccentricity and magnetic saturation have been neglected. Under these hypotheses it will be shown how all of the inductances can be calculated analytically: this dramatically reduces the requirements in terms of computational power. Some numerical results obtained with the presented model will be shown.