**2. Mathematical Model**

#### *2.1. Analysed Machine*

The subject of research presented in the present work is a high-speed machine with a homogeneous solid rotor, already analysed in the previous works by the authors [30,31]. The basic data of the converter and the materials' magnetization characteristics of the stator and rotor area adopted for the calculations are shown in Table 1 and Figures 1 and 2.

**Table 1.** Basic specifications of tested induction motor [31].


**Figure 1.** Solid rotor induction machine taking into consideration: (**a**) dimensions of the stator package (cross-section area), (**b**) dimensions of the rotor [31].

**Figure 2.** DC magnetization curves used in computations.

For the sake of simplicity, the influence of the rotor end-effects and losses in the stator package, and those due to the hysteresis in the rotor area, have been neglected. The influence of the rotor end-effects can be taken into account by applying the so-called rotor endeffect coefficient, that can be calculated analytically or numerically as shown in [21]. Taking into account the above losses, however, will require separate research, which is the authors' aim for the future. It should be noticed that the above assumptions are necessary from the point of view of the possibility to validate the proposed approach by the comprehensive time-domain model. It is also worth noticing that due to these assumptions the obtained results will be very hard or even impossible to verify on the experimental test-stand.
