## 8 Discussion and Conclusions  
The method described in this paper allows a very fast induction motor analysis using magneto-static finite element analyses. The rotor current is computed linking the analytical laws in the rotor field-oriented reference frame with the precise estimation of the parameters from the finite element model. The result is a rapid procedure which avoids the time-domain formulation to get a precise estimation of the performance.  
The time-domain analysis, run with any commercial software, requires many minutes or even hours to get the steady state solution, especially because of the electrical transient. Furthermore, in the presence of rotor skewing, the finite element problem becomes more  
Figure 19: Comparison between measurements and simulations about on-load additional losses. The motor under test is the IEC 132, stack length 200 mm and \(P_{\text{n}}=\)11 kW.  
Figure 18: Comparison between simulations and measurements about the no-load losses in different IMs.  
complicated and the computational effort much greater. The solution proposed in this paper adopts a hybrid analytical finite-element approach which allows the immediate computation of the rotor current and the easy implementation of the skewing effect. Thus, the computation time to achieve steady state performance requires less than a minute with the proper mesh and when applying the correct periodicity. The classic analytical model results in being the faster alternative, but the saturation model is too simplified and does not consider the contribution of the on-load current. Furthermore, only simple iron losses models can be coupled with the analytical equivalent circuit analysis.  
The method is useful also for skewed machines, representing a computational efficient approach. The final comparison between experimental and simulation results proves the effectiveness of the new procedure.  
The applicability of this analysis method is actually rather broad. Such a simple and rapid analysis method is very useful in the machine design stage. In fact, to the aim of achieving the optimal motor geometry, a huge number of solutions could be analysed in a relatively low time.  
The first example application reported in this work concerns the computation of the torque and current vs. slip characteristics, obtaining good results compared to experiments.  
The second application method shows the possibility of computing the iron losses whilst accounting for the contribution of the stator and rotor space harmonics. The procedure is based on the storing of the flux density behavior in each element, considering a central rotation. The losses are computed in post-processing, analyzing the flux-density variation.  
The proposed method can find application as the fast analysis procedure in a design optimization tool. The proposed approach can be useful, especially in the automotive sector, where special induction motors have to be designed, not following the \"industrial design rules\".  
In conclusion, the induction motor analysis procedure proposed in this paper represents a valid alternative to the common time-domain analysis. The method is actually based on the equivalent circuit theory, but the computation of the flux linkages carefully considers the iron saturation in every working condition.  
[PERSON] and [PERSON] equally contributed to the research: in the conceiving of the work, in the preparation of the scientific material concerning the analytical formulation, computer coding and simulation. Both of them took care of the manuscript preparation. All authors have read and agreed to the published version of the manuscript.  
This research did not receive any external funding.  
Not applicable.  
The research activity and the prototypes used in this work have been supported by Pentax Pump S.p.a., Veronella, Verona, Italy.  
The authors declare no conflict of interest.