*3.4. Analysis of the Level of Detail*

The procedure for characterizing the level of detail is analogous to that for characterizing the range of values via tables and sensitivity analysis. The tables contain precision values of the different physical output parameters and physical effects for linear and non-linear operating points of an exemplary machine in the given power range. The quantification of the precision values of the physical output parameters and effects is performed on the basis of individual categories. These are subdivided as follows:


The level of detail is analyzed for all output quantities and effects and matched with the required level of detail. The affiliation of an operating point to the linear and nonlinear operating range of the machine is thereby determined on the basis of the FWM. The influence of geometry and material effects to be considered must achieve the required precision for each individual influenced output variable.

**Figure 8.** Magnetic air gap flux density simulated by two different models.

#### *3.5. Model Selection*

Based on the results of the value range analysis and the level of detail analysis, the model with the lowest degree of freedom is then selected from all suitable models. This promises the lowest computational effort and thus the most efficient calculation for the precision requirements. If a working point matrix is considered in the model selection process, the selection of possible models is done analogously based on the range of values. For the resulting models, the precision of the output quantities and effects to be examined are considered in each working point. The selection of the most suitable machine model can then be made using two procedures. One option is to consider those models that have the required level of detail at all operating points. From these, the one with the lowest computational effort is then derived. An alternative is a operating point specific model selection by means of a Branch and Bound optimization, on the basis of which different models can be assigned to different operating points, so that the required level of detail is achieved at each point, but the overall solution effort is minimized.

#### **4. Approach for Parameter Selection**

Mathematical optimization algorithms are gaining importance for the design, revision, and optimization of electrical machines. The optimization parameters in the context of such machine optimizations represent those geometry and material parameters that are varied during the optimization procedure in order to find a better solution. These parameters should therefore cover a high degree of freedom of the geometry. However, as the number of optimization parameters increases, so does the search space and the associated solution effort. For this reason, it is advisable to select those geometry parameters that have the greatest influence on the searched output quantities but have the lowest degree of redundancy among themselves. The parameter selection approach presented in this paper describes the selection of such parameters as a methodical procedure. The generic threestep procedure of parameter selection is shown in Figure 9. The process of the parameter selection is problem-specific and is also influenced by the selected system model, which follows from the approach for the model selection. In the context of the optimization environment, the output quantities and effects to be considered in the model selection describe those variables that influence the decision parameters of the optimization problem. The input variables for the problem definition of the parameter selection describe on the one hand the resulting model and the output quantities already described for the methodology for the model selection, but also those problem variables which come into question as optimization parameters. In addition, a selection of the number of parameters to be determined is required, which defines the degrees of freedom and thus the accuracy of the optimization environment, but also describes the required solution effort.

**Figure 9.** Process of the approach for the parameter selection.

Based on these input variables, a sensitivity analysis is performed for each possible optimization parameter using the model resulting from the model selection approach. Here, the elasticities of the output quantities relevant to the optimization are examined so that the possible optimization parameters can be sorted based on their elasticity. This identifies those parameters that have the greatest possible influence on the optimization problem, minimizing the global optimum in particular, since this correlates negatively with the elasticity of the optimization parameters. From the sorting of the optimization parameters, starting with the highest elasticity, the given number of parameters can be selected. For each new optimization parameter to be added, the correlation with already selected parameters must be checked, since the individual optimization variables must be independent of each other and must not influence each other. Otherwise, contradictory solutions may result. The optimization parameters resulting from the parameter selection procedure serve as input variables of an optimization environment. Here, a problem-specific, experience-based selection of upper and lower bounds of the parameters is important to reduce the size of the solution space and thus the computational effort. A multi-step optimization environment for the design of an IM using the model and parameter selection procedure presented here is given in [3].
