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.
Highlights
The soft magnetic material permeability is constant corresponding to the linear zone of the B(H) curve
The results of the semi-analytical model are verified by 2D finite-element method (FEM)
The waveforms of r- and θ-components of the magnetic flux density in the various regions are computed with a finite number of harmonic terms, viz., N = 200 and M = K = 30
Summary
Benefiting from the advantages of a simple mechanical structure—the rotor does not carry any windings, commutators, or permanent magnets (PMs)—and a robust, fault-tolerant nature, low-cost maintenance, high-thermal capability, and high-speed potential [1,2,3], SRM is receiving renewed attention as a viable candidate for various adjustable-speed and high-torque applications such as in the automotive and traction fields [4,5,6,7,8]. The Maxwell-Fourier method is one of the most used semi-analytical methods, and combines the very accurate electromagnetic performances calculation with a reduced computation time compared to numerical methods In models from this method (viz., multi-layer models, eigenvalues model, and subdomain technique), the magnetic field solutions are based on the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series. The Dubas superposition technique has been implemented in radial-flux electrical machines with(out) PMs supplied by a direct or alternate current (with any waveforms) [34] This technique has been extended to: (i) the thermal modelling for the steady-state temperature distribution in rotating electrical machines [35], and (ii) elementary subdomains in the rotor and stator regions for full prediction of magnetic field in rotating electrical machines with the local saturation effect solving by the Newton-Raphson iterative algorithm [36].
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