3-D Sub-Domain Analytical Model to Calculate Magnetic Flux Density in Induction Machines With Semiclosed Slots Under No-Load Condition

In this paper, a novel 3-D sub-domain analytical model is developed to determine magnetic flux distribution in single-cage induction machines (IMs) with skewed rotor bars under no-load condition in an effort to more detailed analysis of spatial harmonics. The proposed model, along with an optimization algorithm, is as an alternative solution to finite-element analysis (FEA) in optimizing the geometry of IMs. The analytical method is based on the resolution of 3-D Laplace and Poisson’s equations in cylindrical coordinates using the separation of variables method to calculate the magnetic vector potential for corresponding sub-domain. The proposed model includes the effect of slotting and tooth tips for the stator and rotor slots, which is usually neglected in a 2-D analysis due to the complexity of differential equations. Also, the proposed 3-D model can be used for any slot-pole combination in addition to considering the asymmetrical effect in the axial direction, which is a source of noise, vibration, and excessive losses in IMs. To evaluate the performance of the proposed 3-D analytical model, calculated magnetic-field distribution is compared with the results obtained from the 3-D FEA.