Lumped model for the calculation of harmonic eddy current losses in permanent magnets for homogeneous flux distributions considering eddy current reaction flux

This is the first of a series of papers on novel methods for the calculation of eddy current losses in permanent magnets (PMs) and the shortcomings of previously conducted analyses. Eddy current losses in PMs and their mitigation are significant factors when designing inverter-fed electric drives. Especially with the need for drives with high power density, a trend toward increased rotational speeds and, therefore, higher fundamental frequencies and inverter switching frequencies are observable. Higher harmonic frequency components of concentrated windings and fractional slot windings are widely taken into account when designing rare sintered earth magnets for permanent magnet synchronous machines (PMSMs). However, inverter-related losses are rarely simulated in Finite Element Method (FEM) co-simulations and can contribute as a major factor to the power losses in PMSMs. In the worst case, this neglection can lead to the thermal demagnetization of the permanent magnets. Segmentation provides an effective measure to limit eddy current losses. However, not every kind of segmentation proves effective in a drive application. Depending on the frequency behavior of the magnetic flux in a permanent magnet, segmentation can increase eddy current losses within the magnet compared to a non-segmented magnet. This behavior is due to the reaction to the flux caused by the eddy currents within the magnet. The reaction of the eddy currents is often neglected [1, 2], and, in other cases, the vicinity of ferromagnetic material is neglected in analytical calculations [3] but proves crucial for the exact calculation of higher frequency losses [4, 5]. In this paper, an analytical solution to calculate harmonic eddy current losses in permanent magnets, including the reaction flux with homogeneous excitation, is given.