*2.6. Used Iron Loss Model*

The IEM-5 parameter formula is used to calculate the iron losses in each model. It is based on the Bertotti model and adds an additional term considering the non-linear material behavior [21]. The IEM-formula to calculate the iron loss density *p*Fe is given by:

$$p\_{\rm Fe} = a\_1 \mathcal{B}^a f + a\_2 \mathcal{B}^2 f^2 (1 + a\_3 \mathcal{B}^{a\_4}) + a\_5 \mathcal{B}^{1.5} f^{1.5},\tag{24}$$

where *a*1, *a*2, *a*<sup>5</sup> are the hysteresis, eddy current, and excess loss factors, *a*<sup>3</sup> and *a*<sup>5</sup> are loss parameters describing the non-linear saturation losses, *f* the frequency, and *B*ˆ the amplitude of the magnetic flux density for the given frequency. In the numerical models, the iron loss densities are calculated element by element and weighted by the element area. The summation of the iron loss densities over all elements and multiplication by the iron length then results in the iron losses. In the analytical models, the iron loss densities are calculated for the stator and rotor yokes and teeth respectively with the calculated mean tooth and yoke flux densities. Multiplication by the yoke and teeth mass then also results in the value of the iron losses.

#### **3. Model Selection Approach**

The four-step generic procedure of the approach for model selection is shown in Figure 7. The problem definition is based on four input variables. These describe the searched output quantities, the effects to be investigated are whose influence on the output quantities is to be modeled, and the respective required precision, i.e., the problem-specific level of detail. Since the precision of the models depends on the operating point, a selection of the operating points to be considered is also necessary. The problem-specific output quantities to be considered define the electromagnetic coupling quantities for a coupled model. Analogously, the effects to be studied describe the external coupling variables. By means of this problem definition, suitable models can be derived on the basis of the value ranges and levels of detail of the available models and simulation methods, respectively. From the consideration of the value range the possible models follow, which represent all output quantities and effects and can model an influence of the output quantities by the effects. For the possible models, the required level of detail is examined in the following step and the suitable models that meet all requirements are derived from this. From these, the one with the lowest computational effort is selected.

**Figure 7.** Process of the approach for the model selection.

One possibility to characterize the range of values and the level of detail of the models are tables, which contain entries for possible output quantities and effects, separated by the available models. The value range table contains a reference to the general ability of the models to describe the output quantities and effects, whereas the level of detail table contains the respective precision. The precision can be given in relation to a reference model, if quantifiable. Alternatively, qualitative scales can be used to describe precision. It is important to have a stringent procedure for the definition of these precisions in order to allow a future consideration of further effects and to make them comparable. Another possibility to describe the range of values and the level of detail, e.g. to consider geometry and material effects, is given by sensitivity analyses, where the parameters to be investigated are slightly varied and it is checked whether the models represent an influence of the parameters on the searched output quantities. Precision is again defined by a reference model. The characterization of the solution effort of the models is done via the number of the respective degrees of freedom since the computation time depends on computer-specific parameters such as the clock speed, the number of cores and the main memory and thus cannot be generalized. In this paper, the described approach for the model selection is presented using the example of an IM. An automated implementation allows finding the most suitable problem-specific model based on the four problem-defining input variables. In the following, the sensitivity analysis used in the selection process and the four steps of the model selection process are presented.
