Analytical design of Spoke Internal Permanent Magnet machines using polar-consistent approximation of cubic subdomains

Finite element modeling is the main tool in the design of internal permanent magnet electric machines for which accurate analytical designs are hard to be developed. Despite the high accuracy, the main drawback of this type of numerical modeling is the immense burden of calculation and time especially for implementation of complex structures. On the other hand, most of the fast analytical methods have been ineffective in accurate modeling of Internal Permanent Magnet (IPM) machines. This inefficiency is due to the complexity of the IPM segments and their inconsistency with other polar subdomains in rotary machines. In this research, one successful approach which divides the inconsistent domains into several polar-consistent subdomains is applied for fast and accurate analytical calculation of the quantities and objective functions. On the basis of this efficient analytical model and by evolutionary optimization tools, the loss and volume of a spoke PM machine are minimized, then the optimal machine is verified satisfactorily by the Finite Element Method (FEM).