*2.1. Fundamental Wave Model*

Modeling of a squirrel cage IM in the FWM is performed using the single-phase Equivalent Circuit Diagram (ECD) presented in Figure 2. In this paper, the T-ECD is used, which allows the consideration of saturation in terms of a current-dependent main inductance. The use of a stator flux or rotor flux based ECD is also possible but is not applied here. The ECD is composed of the stator resistance *R*S, the rotor resistance *R* <sup>R</sup> divided by the slip *s*, the leakage reactances *Xσ*,S and *X <sup>σ</sup>*,R, and the main reactance *X*h. The rotor-side quantities related to the stator by the transmission factor are thereby characterized by a . For the calculation of these elements of the ECD, which can be derived exclusively from the machine geometry and constant parameters, reference is made to the literature [7]. Important physical quantities and effects which affect the range of values or the level of detail of the machine modeling are briefly explained.

**Figure 2.** Representation of the single-phase ECD of the IM with a squirrel cage rotor.

#### 2.1.1. Rotor Resistance

To consider the short circuit ring of the squirrel cage, the bar resistance *R*bar and the ring resistance component Δ*R*∗ ring are used to calculate the two dimensional rotor resistance *R*R. The latter results from the transformation of the resistance of a ring section Δ*R*ring into a series equivalent resistance. The rotor resistance is thus given by:

$$R\_{\rm R} = R\_{\rm bar} + 2\Delta R\_{\rm ring}^\*.\tag{1}$$

This procedure is also used for the calculation of the rotor resistance in the other machine models. A more detailed derivation of the rotor resistance for 2D modeling is given in [8].
