Analytical Calculations of Induced Eddy Currents Losses in the Magnets of Surface Mounted PM Machines With Consideration of Circumferential and Axial Segmentation Effects

Eddy currents in a passive magnetic axial thrust bearing for a flywheel energy storage system

“…There are different ways of estimating eddy current losses, of which a few are listed here in rising order of computational complexity: Analytical solutions [5,15]; stationary Finite Element Method (FEM) solutions coupled with analytical equations [4,19]; quasi-stationary FEM-simulations [20]; and time-dependent FEM-simulations. Analytical equations have been developed to model electric machines with good accuracy compared to quasi-stationary 3D-FEM simulations [9]. Other recent interesting applications of the quasi-stationary 3D FEM-simulations for eddy currents include models of magnetic brakes [16] and in electromagnetical dampers [6].…”

Influence of 2D and 3D meshes in FE computation of eddy-current losses in surface PMSMs

“…However, rare-earth materials have a relative high conductivity [3] and eddy currents can develop in the permanent magnets (PMs). As the fundamental component of the magnetic flux is stationary with respect to the rotor, eddy-current losses are generally negligible compared to the other loss components [1]: only spatial flux harmonics (related to slotting and winding distribution) and temporal ones (due to switching) generate losses [1], [4], [5]. Despite this aspect, the temperature rise may be important due to the relative thermal insulation of the magnets [1] and deteriorate their properties (coercive field and remanent flux), possibly leading to their demagnetization [2], [5].…”

“…for interior PMs) [6]. Furthermore, often they do not take the reaction field from the eddy currents into account, leading to inaccurate results at high frequencies [2], [4]. This aspect is, however, considered in the method developed in [2], which computes the induced currents generated by all relevant spatial and temporal harmonics.…”

“…3D effects are also modelled in [2] by the multiplication of the losses obtained with a 2D model with a correction factor depending on the axial length based on analytical approach. In [4], a "quasi-3D" analytical solution is also developed by imposing a flux density normal to the PM surface and a zero normal component of current density in the magnets.…”

“…More advanced methods subtract this average value from the results, but their accuracy is limited because they neglect skin effect [2]. 3D FE computations are more accurate, but also much more computationally expensive [2], [4]. A combined 2D axial and radial method is proposed in [6] to avoid 3D FE computations.…”