# Analysis of Permanent Magnet Motors in High Frequency--A Review
## 4 Modeling of Electrical Machines in High-Frequency
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Frequency** & **Model** & **Parameter** & **Inter-Turn** & **Bearing** & **Rotor** & **Integration** & **Simulation** & **Iron** \\  & **Range** & **Type** & **Extraction** & **Effects** & **Model** & **Model** & **in Drive** & **Domain** & **Loss** \\ \hline
[32] & 1 k–13 M & & Measured & x & x & & x & Freq \& Time & Implicit \\
[17] & 10 k–10 M & & Measured & x & x & & x & Freq \& Time & Implicit \\
[20] & 10 k–10 M & & Measured & & & & x & Freq \& Time & R Parallel \\
[23] & 10 k–10 M & & Measured & x & & & & Frequency & Implicit \\
[31] & 100 k–500 M & & Measured & & & & & Frequency & Implicit \\
[12] & 10 k–10 M & & Measured & x & & x & x & Freq \& Time & Implicit \\
[13] & 100-100 M & & Measured & x & & & & Freq \& Time & R \\
[21] & 150 k–10 M & LPM & Measured & x & & x 1 & x & Freq \& Time & R \\
[33] & 100–30 M & Fixed & Measured & x & & x & x & Freq \& Time & R \\
[24] & 100–10 M & Segments & Measured 2  & x & & & & Frequency & R \(\mid\) L \(\mid\) RC \\
[15] & 100 k–10 M & & Measured & & & & & Freq \& Time & Implicit \\
[35] & 100 k–10 M & & Measured & x & & & & Freq \& Time & Implicit \\
[36] & 100–10 M & & Measured & x & & & & Freq \& Time & R Parallel \\
[37] & 10–10 M & & Analytic & x & x & x & x & Freq \& Time & R Parallel \\
[73] & 30–5M & & FEM 3 & x & x & & Time & Time & RL \\
[54] & 100–100 M & & FEM & x & x & x & & Freq \& Time & Implicit \\ \hline
[27] & 1 k–10 M & f(F) & Measured & & & & & x & Freq \& Time & Implicit \\
[22] & 10 k–3 M & Segments & Measured 2  & & & & & & & Freq \& Time & Implicit \\ \hline
[62] & 20–4 M & & FEM 3 & x & & & & Frequency & Implicit \\
[86] & 10 k & & FEM & x & x & x & Time & Implicit \\
[58] & 100–1 M & & FEM 3 & x & x & x & Frequency & R Parallel \\
[61] & 0–100 k & DPM & FEM & x & x & & Time & Implicit \\
[39] & 10–10 M & & FEM & x & & & Freq \& Time & Implicit \\
[51] & 1 k–10 M & & FEM & x & & & Freq \& Time & Implicit \\
[55] & 10 k–20 M & & FEM & x & & & Frequency & Implicit \\
[70] & 10 k–1 M & & FEM & x & & & Frequency & Implicit \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Model Comparison. dependent formula and the decrease of the inductance with the frequency is represented by two empirical factors obtained from [95]. The resultant impedance is shown in Figure 9.  
Something similar is used in [22; 26; 28] for taking into account the resistance and inductance variation with frequency. They use Foster's network, adjusting their values with data fitting procedures. The models are validated obtaining accurate results. Even if all models are based on LCR circuits, they refer to different parts of the machine and include different high-frequency phenomena:  
* **Inter-turn effects:** To make an accurate model in high frequency, the influence between conductors must be modeled. Most FEM-based models consider these effects in the analysis, and in measurement-based methods, this is implicitly included. * **Bearing:** Just a few models include the bearing in the model, as their capacitance is important when simulating bearing currents, but in the rest of the models they are neglected or calculated analytically [41] or empirically [53; 54]. Bearing capacitance can be neglected when using plastic bearings or when the machine is in stand-still as mentioned by [43; 58]. In [37] the rotor, the shaft and the bearing models are included, so it is very useful to analyze the motor's behavior over a wide range of frequencies and it can be also suitable for the study of bearing currents and CM shaft voltage both in time and frequency domain. * **Rotor:** As \(C_{var}\) & \(C_{sr}\) are \(10^{3}\) times smaller than \(C_{sys}\), the rotor does not affect DM impedance in high frequency, but when analyzing CM current paths, stator-to-rotor capacitance is essential, so modeling the rotor is needed [37; 58].