# Analysis of Permanent Magnet Motors in High Frequency--A Review
## 6 Conclusions
### Analysis Tools  
Regarding the FEM analysis, the detailed geometry of an electric machine can be accurately modeled obtaining precise resistance and inductance values, taking into account the skin and proximity effects, as well as eddy current losses in the stator and the capacitive couplings. The mesh of the geometry is essential to obtain accurate results in FEM. When working in high frequency, the skin depth of the materials must be finely meshed, both in the conductors to consider skin and proximity effects, and in the core, as the Eddy currents flow along the skin depth of the iron sheets. Thus, the mesh size must be thinner than theskin depth. However, this meshing requirement leads to a higher time consumption and computational load. Thus, an equilibrium must be found between the model complexity and the accuracy. For the active length of the machine, 2-D simulations are usually used, even if the resistivity of the sheets must be calibrated to take into account the lamination effects, usually using 3-D models. It must be remarked that not all iron sheets comprising the magnetic core can be modeled in 3-D with a mesh size thinner than the skin depth, otherwise, the model will take ages to solve. Commonly, 2 or 3 sheets are simulated and the results are extrapolated to the whole length. Even if the 3-D FEM is the most complete simulation tool, it is the most computationally demanding too, so it is usually only used for the end-winding calculation, as it is the only way to calculate it accurately. Once a 3-D FEM simulation is done, some authors propose different coefficients to take into account this end winding, by using just 2-D FEM for successive simulations. With respect to the capacitance calculation in electrostatic FEM, the same applied to magnetic calculation is applied, needing 3-D models for the end winding, at least for the winding-to-rotor capacitance calculation, where it has a big impact. In this case, a 2 mesh layer must be defined between the conductors for turn-to-turn capacitance accuracy. Gauss Law method is recommended for the calculation of the capacitance matrix, as it requires fewer simulations. In the case of analytical tools, commonly they require less computation time, as some assumptions and simplifications are considered for each specific case. The skin effect can be easily calculated analytically reducing the effective cross-section area of the conductors. Nonetheless, the computation of the proximity effect is not so simple due to the non-uniform distribution of the magnetic field in the slot. Bessel functions have been used to calculate the AC resistance of the winding, leading to 12% errors at 50 MHz. An analytical method is found to calculate the Joule losses taking into account the proximity losses, but an uniform conductor distribution is assumed in a rectangular slot, so it may not be applicable to all cases, and it is only tested until 1.5 kHz so it may need further development for using it in EMC analysis of electric machines. With respect to the capacitance values, geometric simplifications are done to simplify the calculations to plate capacitors in the case of the winding-to-rotor capacitance or cylindrical ones for the stator-to-rotor capacitance, and even if they converge to the same order of magnitude, they are not accurate enough. A novel approach is proposed for the determination of the winding-to-rotor capacitance using the method of image charges, validating the results with FEM. In the turn-to-turn capacitance, some methods can reach acceptable results. For the turn-to-turn capacitance calculations, the method must be chosen depending on the specific disposition of the winding, otherwise, large errors can appear. Concerning measurement-based tools, rather good accuracy can be reached by adjusting the model behavior in the whole frequency range.