Two-Dimensional Exact Subdomain Technique of Switched Reluctance Machines with Sinusoidal Current Excitation

Abstract

This paper presents a two-dimensional (2D) exact subdomain technique in polar coordinates considering the iron relative permeability in 6/4 switched reluctance machines (SRM) supplied by sinusoidal waveform of current (aka, variable flux reluctance machines). In non-periodic regions (e.g., rotor and/or stator slots/teeth), magnetostatic Maxwell’s equations are solved considering non-homogeneous Neumann boundary conditions (BCs). The general solutions of magnetic vector potential in all subdomains are obtained by applying the interface conditions (ICs) in both directions (i.e., r- and θ-edges ICs). The global saturation effect is taken into account, with a constant magnetic permeability corresponding to the linear zone of the nonlinear B(H) curve. In this investigation, the magnetic flux density distribution inside the electrical machine, the static/dynamic electromagnetic torques, the magnetic flux linkage, the self-/mutual inductances, the magnetic pressures, and the unbalanced magnetic forces (UMFs) have been calculated for 6/4 SRM with two various non-overlapping (or concentrated) windings. One of the case studies is a M1 with a non-overlapping all teeth wound winding (double-layer winding with left and right layer) and the other is a M2 with a non-overlapping alternate teeth wound winding (single-layer winding). It is important to note that the developed semi-analytical model based on the 2D exact subdomain technique is also valid for any number of slot/pole combinations and for non-overlapping teeth wound windings with a single/double layer. Finally, the semi-analytical results have been performed for different values of iron core relative permeability (viz., 100 and 800), and compared with those obtained by the 2D finite-element method (FEM). The comparisons with FEM show good results for the proposed approach.

2-D Analytical Model of Conventional Switched Reluctance Machines

“…The analytical expression of electromagnetic torque and the method for calculating the flux are given in [9,10,[13][14][15][16][17][18][19][20][21]. We have used the parameters of SRM given in [24] for our comparison study.…”

“…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].…”

Exact Two-Dimensional Analytical Calculations for Magnetic Field, Electromagnetic Torque, UMF, Back-EMF, and Inductance of Outer Rotor Surface Inset Permanent Magnet Machines

“…Two-dimensional analytical models are presented for the slotted [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]19,20,[29][30][31][32][33][34][35][36][37][38]41,42,44,45] and slotless [21][22][23][24][25][26][27][28] machines, equipped with surface mounted [3][4][5][6][10][11][12][14][15][16][17][18][19]…”

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.…”