2.1.3. Main Inductance and Saturation

By calculating the main inductance via the flux linkage, it is possible to consider the material saturation of the stator and rotor laminations of the IM. With a magnetic ECD of the machine geometry, the magnetic flux densities *B* and magnetic voltages *V* in the teeth (T) and yokes (Y) of the stator (S) and rotor (R) and in the air gap (*δ*) are calculated. The saturated main inductance *L*<sup>h</sup> is obtained by dividing the operating point specific main flux linkage Ψ<sup>h</sup> by the magnetizing current *I*0:

$$L\_{\mathbf{h}} = \frac{\Psi\_{\mathbf{h}}}{I\_0},\tag{2}$$

$$\text{with}\quad\Theta\_0 = V\_\delta + V\_{\mathbb{S},Y} + V\_{\mathbb{S},\mathbb{T}} + V\_{\mathbb{R},Y} + V\_{\mathbb{R},\mathbb{T}} \quad\text{and}\quad I\_0 = \frac{\pi p}{6\sqrt{2}\chi\_{\text{tot}}w\_{\mathbb{S}}}\Theta\_0.$$

The factor *χ*tot describes the total winding factor including the distribution and pitch factors, *w*<sup>S</sup> the number of windings per phase, and *p* the number of pole pairs.
