Comparison of Methods for Permanent Magnet Eddy-Current Loss Computations With and Without Reaction Field Considerations in Axial Flux PMSM

Abstract

This paper presents an analytical solution of the eddy currents in the permanent magnets (PMs) in the Axial Flux Permanent Magnet Synchronous Machine (AFPMSM) using a coupled solution of Maxwell's equations and electric circuit network. This is based on calculating the axial field in an accurate way on the surface of the PM. This method is able to take into account the effect of armature field and slots. The eddy currents are obtained by imposing this solution on the PM which is modeled by a simple electric network. This network is composed of simple resistances and inductances. The inductances are used to model the reaction field effect of the eddy currents flowing through the PM and also the skin effect. To show this effect, the machine is excited with different sources at different speeds. Also, a variant of the model is made that neglects the inductances, in order to show in which conditions this "low-frequency approximation" is acceptable. It is concluded from this paper that inclusion of the reaction field is necessary when the machine is excited by a pulse width modulated (PWM) current, while for a sinusoidal excitation, the reaction field effect has minor contributions to the total eddy losses. In addition, the reaction field has major influence at higher speeds rather than lower speeds for PWM injection. In conclusions, for a preliminary design, the resistance model without the reaction field computation would be enough for the calculation of the PM losses. The circuit model is also capable of obtaining the solution with PM segmentation. In this paper different PM segments were studied from the circuit model and FE model point of view. Compared to the Finite Element (FE) Model, the circuit model has the advantage of flexibility in geometrical machine parameters, less CPU time, and accurate results for the PM losses up to 10%.

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

“…In [19,20], the eddy-currents are obtained by additional capacitors in the MEC. Coupling an EEC with a MEC or a 2-D solution of Maxwell's equations is also used in [21]. The authors conclude that the armature reaction does not contribute significantly to the increase of the PM eddy-current losses.…”

“…It can be remarked that NRMSD decreases by increasing the discretization number, ∀h mp . With the discretization used in (21), NRMSD is equal to 4.5% for 6 mm and 3% for 10 mm. Figure 18 shows the normalized root-mean-square deviation (NRMSD) according to the discretization number in both axes (i.e., x-and y-axis).…”

“…It can be remarked that NRMSD decreases by increasing the discretization number, ∀ mp h . With the discretization used in (21), NRMSD is equal to 4.5% for 6 mm and 3% for 10 mm. The eddy-current losses were calculated on different layers in the y-axis of massive conductive parts.…”

3D analytical model for estimation of eddy currentlosses in the magnets of IPM machine considering the reaction field of the induced eddy currents

“…In [14] the eddy current losses in IPM machines during flux weakening is evaluated using a loss coefficient. Eddy current losses in an axial flux PMSM has been dealt in [15] and [16]. In [8], a 2D analytical model developed by the authors which was extended to 3D using an end-effect factor.…”

The ECL Optimization and Experiment of HSPMSM with Improved Method

“…INTRODUCTION As for the HSPMSM, the ECL of rotor of which has higher speed occupies higher percentage of total loss especially in similar power level [1][2][3][4]. The component of ECL consists of spatial harmonic loss and time harmonic loss which occupies the mainly part when the HSPMSM reach more fast speed [5][6][7].…”