Analytical Prediction of 3-D Magnet Eddy Current Losses in Surface Mounted PM Machines Accounting Slotting Effect

Abstract

Abstract-This paper presents a novel analytical technique for predicting 3-dimensional (3D) magnet eddy current losses accounting the slotting effect of any pole-slot combinations for a surface mounted permanent magnet machine under any conditions of load. The slotting effect is incorporated from a subdomain model and the 3D boundary conditions are imposed with the current vector potential to represent the 3D eddy currents circulating in the magnets. The proposed model in polar coordinate system is demonstrated on a fractional slot rare-earth permanent magnet machine by analyzing its magnet losses as functions of axial and circumferential segmentations. The results have shown an excellent match with 3D numerical calculations. The analytical prediction has also been validated by experimental tests. The interaction of the armature reaction field with the slotting harmonics is analyzed and their effect on eddy current loss in rotor magnets is established. The proposed technique is employed to evaluate the effect of slotting on magnet loss with increase in field weakening angle.Index Terms-Current vector potential, eddy currents, finite element, subdomain model, permanent magnet, 3D analytical. I. INTRODUCTIONhe rotor magnets of permanent magnet (PM) machines used in high speed and power density applications are exposed in increased rate of alternating magnetic field and incur eddy current loss. Eddy currents are more pronounced in magnets especially at higher speeds for such machines with modular or concentrated winding configurations [1,2], as their stator magneto-motive force (mmf) contains a large number of space harmonics which rotate at different speeds along the rotor. Accurate prediction of magnet losses at the design stage, not only gives better efficiency evaluation, but also may prevent its excessive temperature rise and hence reduce the risk of partial demagnetization.In order to evaluate the eddy current losses in permanent magnets, variety of methods have been reported in a large number in literatures. In general, evaluation of rotor eddy current losses requires simultaneous solutions for the governing equations of the magnetic and eddy current fields.The computationally efficient 2D numerical methods such as transient finite element analysis (FEA) to calculate the eddy current losses [3], [4] can yield good results but lacks any physical insight on the mechanism of eddy current loss. Hence a few 2D analytical methods are developed to predict the magnet eddy current loss with varying degree of accuracy [5][6][7][8][9]. These methods often neglect the slotting effect and approximate winding currents by an equivalent current sheet distributed over the stator bore radius.Unless the slotting harmonics are considered in the loss evaluation, the no load magnetic loss and also its interaction with the armature filed harmonics at diverse load conditions cannot be quantified. As the eddy current density inside the magnets is dependent on the time derivative of the magnetic vector potential within it, a sufficie...

Interior Permanent Magnet Synchronous Motor Design for Eddy Current Loss Reduction in Permanent Magnets to Prevent Irreversible Demagnetization

“…The PM is inserted into the rotor core in a solid form, so the return path and the axial direction of the eddy current cannot be ignored. For this reason, the eddy current loss of the PM should be calculated by three-dimensional (3-D) finite element analysis (FEA) or 3-D analytical analysis so that accurate values can be obtained [9][10][11][12]. However, 3-D FEA has many limitations in terms of time, cost, and effort.…”

Permanent-Magnet Eddy-Current Losses: A Global Revision of Calculation and Analysis

“…The calculation in the conducting regions of a rotor of PMSMs was presented in [12]. The determination of the PM eddy-current losses due to the slotting effect was investigated in [13][14][15][16] and in fractional-slot surface-mounted PMSMs in [17][18][19].…”

“…A 3D subdomain model was used to englobe the slotting effect [95,96], where the method of variable separation was used to get the 3D eddy-currents in PMs. The work in [18] used an analytical method in polar coordinates for any pole-slot combinations of a surface-mounted PMSM under any conditions of load.…”

Fast calculation of eddy current losses caused by pulse‐width modulation in magnets of surface‐mounted PM machines based on small‐signal time‐harmonic finite element analysis

“…Permanent magnet synchronous machines (PMSMs) with surface‐mounted permanent magnets (PMs) or interior PMs are widely applied in industry applications due to their merits of high torque density and high efficiency [1–22]. Besides, they are usually supplied by pulse‐width modulation (PWM) voltage source inverters (VSIs) for dynamically adjusting their torque and speed.…”