# Analysis of Permanent Magnet Motors in High Frequency--A Review
## 3 Analysis Tools
### Analytic Methods
#### 3.2.1 Analysis of the Magnetic Core  
On the one hand, Eddy current losses rise in the iron core when the frequency increases. In [40], it is assumed that Eddy currents are limited to the skin depth, assuming a uniform current density on it. Then, with the length of the stator, the resistivity and the perimeter of the slot, the resistance of the iron loss due to Eddy currents is obtained to consider it in the circuit.  
On the other hand, in [37] the resistance accounting for the core loss at low frequency is considered proportional to the power of the induction machine, and an experimentally estimated damping resistance is added in parallel to the winding inductance to consider the high-frequency iron loss combined with the winding skin and proximity effects. This resistance is added due to the fact that it affects the DM impedance in the first resonance frequency.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Experimental** & \multirow{2}{*}{**Geometry**} & **Rotor** & **End** & **Winding** & **Winding** & **Bearing** & **Stator** & **Turn** \\  & **Validation** & & **Model** & **Winding** & **Stator** & **Rotor** & **Capacitor** & **Rotor** & **Turn** \\ \hline
[73] & Bearing Current & 3-D.1 slot. & x & x & x & x & x & & \\
[85] & CM & 2-D/3-D.1/4 Model. & x & x & x & x & x & & \\
[54] & CM \& DM & 2-D.1/8 Model. & x & & x & x & & x & x \\
[62] & CM & 2-D.1/4 Model. & x & & x & & & & (bulk) \\
[52,86] & Over-voltage & 2-D.1/2 Model & x & & 1 & & & & x \\
[58] & CM \& DM & 2-D slot & x & 2 & x & x & & & x \\
[61] & Over-voltage & 2/3-D & x & x & 1 & & & & x \\
[39] & Over-voltage & 2-D.1 slot & x & & 1 & & & & x \\
[51] & CM & 2-D.1 slot & & 2 & 1 & & & & & x \\
[55] & CM \& DM & 3-D.3 slot & & x & x & & & & x \\
[67] & CM & 2-D.1 slot & & & x & & & & & x \\
[68] & RL & 2-D.1 slot & & x & 1 & & & & & x \\
[57] & Capacitance & 2-D 1-slot & & & x & & & & & x \\
[65] & & 2-D 1-slot & & & x & & & & & x \\
[10] & Bearing Currents & 3-D Full & x & x & & x & x & x & x \\
[70] & CM \& DM & 2-D 1 slot & & x & & & & & & x \\ \hline \hline \end{tabular}  
* \({}^{1}\) Winding to ground. \({}^{2}\) Analytical equations are used.  
\end{table}
Table 2: FEM Electrostatic comparison.  
No reference to Hysteresis or Excess loss is found, except for the model shown in [47] that uses [PERSON]'s iron losses estimation. However, the resulting CM and DM currents are not experimentally validated.  
Moreover, in [11; 48] the common-mode impedance of the stator is calculated. The authors state that when the CM current flows through the stator, a circumferential flux is created in the stator yoke. These currents and flux flow along the iron surface along the skin depth. In the mentioned publications, the magnetic flux in each lamination is the sum of the flux generated by the current flowing through this lamination and the current flowing in the adjacent lamination. Thus, assuming that equal currents flow into each of the N laminations, the core impedance can be calculated in (5) where \(r_{1}\) and \(r_{2}\) are the inner and outer diameter of the stator yoke, respectively.  
\[Z_{c}=(1+j)\frac{N}{3\pi\sigma\delta}\ln\frac{r_{2}}{r_{1}} \tag{5}\]