Semi-Analytical Magnetic Field Predicting in Many Structures of Permanent-Magnet Synchronous Machines Considering the Iron Permeability

2-D Analytical Model of Conventional Switched Reluctance Machines

“…Solving of PDEs given by (1) allows to obtain the general solution of z A in each domain [8][9][10]. The integration constants are determined by using a Fourier series expansion of z A in each region and the boundary conditions (BCs) [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. The linear systeme can be written as…”

“…In the literature, we find different methods of electromagnetic modeling of electric machines; semi-analytical modeling based on the magnetic equivalent circuit (or permeance network) [6,7], subdomain method in linear conditions (i.e., infinite permeability of the iron parts) [8][9][10], and the exact subdomain method taken into account the iron permeability [11][12][13][14][15]. In addition, we find analytical methods based on multi-layers [16][17][18][19] or elementary subdomains for the local saturation effect [20][21]. The analytical methods cited previously give an accurate electromagnetic result compared with numerical calculations, with reduced computation time.…”

Magnetic Field Analytical Solution for Non-homogeneous Permeability in Retaining Sleeve of a High-Speed Permanent-Magnet Machine

“…The analytical solution is confronted with finite-element method, which confirms validity of the proposed methodology.The available literature on (semi-)analytical technique for PM machine evaluation is extensive, with published papers ranging over twenty-five years, to the best of the authors' knowledge [10][11][12]. Moreover, there is still great effort towards methods with better accuracy and less restricting assumptions [4,[13][14][15][16][17][18][19][20][21][22] to list a few recently published works. Dubas et al [23] realized an overview on the existing (semi-)analytical models in Maxwell-Fourier methods (vis., multi-layer models, eigenvalues model, subdomain technique and hybrid models) with the effect of local/global saturation.…”

“…According to Pfister et al [35], the first work on the semi-analytical subdomain technique was published by [36] with the state-of-the-art in the introduction. Moreover, the method based on the Cauchy's product theorem has been improved to account for saturation in stator tooth [19] and a configurable model, adaptable to many machine geometries [20].However, among the presented references, a small number of authors give a proper realistic evaluation for RS [3,6,9,14,18,28]. Furthermore, only a few of these works evaluate all electromagnetic properties of the retaining sleeve, where relative permeability is different from the air [14,18] and eddy-currents are considered [3,6,9,18,28].In this paper, a novel formulation is presented to extend a two-dimensional analytical solution from Laplace's and Poisson's equation in polar coordinates.…”

“…According to Pfister et al [35], the first work on the semi-analytical subdomain technique was published by [36] with the state-of-the-art in the introduction. Moreover, the method based on the Cauchy's product theorem has been improved to account for saturation in stator tooth [19] and a configurable model, adaptable to many machine geometries [20].…”