Nonlinear Adaptive Magnetic Equivalent Circuit of a Radial-Flux Interior Permanent-Magnet Machine Using Air-Gap Sliding-Line Technic

Abstract

This paper describes a two-dimensional (2-D) nonlinear adaptive magnetic equivalent circuit (MEC) of radial-flux interior permanent-magnet (PM) synchronous machines (PMSMs) for automotive application, mainly for electric/hybrid/fuel cell vehicles (EVs/HEVs/FCVs). It includes the automatic mesh of static/moving zones, the saturation effect, and the connection of the zones for the rotor motion which is ensured by a new approach called "Air-gap sliding-line technic". The local/integral quantities at no-load/load (viz., the magnetic flux density, the magnetic flux linkage and the voltage) have been validated with the 2-D finiteelement analysis (FEA) in the case of radial-flux interior PMSM with 18-slots/16-poles having a double-layer concentrated winding (all teeth wound type). The semi-analytical results are in good agreement, considering both amplitude and waveform. The computation time is divided by 3/2 with an error less than 7 %.

Combining the Magnetic Equivalent Circuit and Maxwell–Fourier Method for Eddy-Current Loss Calculation

“…For a saturated system, it is interesting to note that (3) can be solved iteratively with a constant relative magnetic permeability µ ri according to the nonlinear B(H) curve at each iteration by using the fixed-point iteration method. The flowchart of the nonlinear system solving is detailed in [37].…”

“…Non-homogeneous BCs at the edges of the massive conductive part related to magnetic leakages (see Figure 10) affect to the distribution of the magnetic field σ y H inside the massive conductive part, and therefore the eddy-current losses. However, in [37], a 3-D generic MEC considering the skin effect would improve the volumic eddy-current loss calculation and observe the magnetic reaction field influence of the massive conductive parts on the magnetic circuit of the U-cored static electromagnetic device. Figure 11), and the results comparison are given in Figure 17.…”

Iron Losses in Electromagnetic Devices: Nonlinear Adaptive MEC & Dynamic Hysteresis Model

“…For the electrical machines, it includes the automatic mesh of static/moving zones, the saturation effect, and the connection of the zones for the rotor motion (which is ensured by a new approach called "Air-gap sliding-line technic"). This generalized semi-analytical model has been applied to an axial-/radial-flux interior PMSM [46][47][48] and a coaxial magnetic gear equipped with surface-mounted PMs [49].…”

“…The rotor bridge must be as thin as possible to avoid flux leakage. Its thickness should be obtained by optimal design to ensure best electromagnetic performances and mechanical robustness [48]. The geometrical and physical parameters of the studied radial-flux interior PMSM are represented in Figure 8b and given in Table 1.…”

2-D Analytical Model of Conventional Switched Reluctance Machines

“…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].…”