## 7 Method Application 2: Iron Losses Computation
### Measurements Comparison  
At first, the comparison between measurements and simulation results concerns only the motor considered in Section 6. The no-load test on the machine has been performed applying the stator voltages 30%, 40%, 50%, 70%, 85%, 100% and 115% of the rated value. Then, the iron losses are computed, following the procedure reported in the Standard for the AC machines' efficiency evaluation. The first comparison result is reported in Figure 17.  
Figure 16: Variation of specific iron losses, considering several slice angles. Figure 15: IM stator and rotor instantaneous losses, computed using the Bertotti formulation. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Steinmetz Formulation** & **Bertotti Formulation** \\  & **[W]** & **[W]** \\ \hline Stator hysteresis & 52 & 51 \\ Stator eddy current & 86 & 80 \\ Rotor eddy current & 57 & 55 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison Steinmetz and Bertotti iron losses computation. Even if the model takes carefully into account the role of the high frequency harmonics in the losses computation, the simulations do not fill very well the measurements. Possible reasons are related to the implemented losses model: in (23), \(\hat{B}_{\text{el},\
u}\), represents the amplitude of the flux density harmonic, thus the model does not consider the presence of rotational fields [17; 18], that occurs specially in the top of the stator teeth and in the stator and rotor tooth tips [19]. A further improvement can be obtained by summing the losses components, related to \(B_{x,\
u}\) and \(B_{y,\
u}\), in each element. Another possible reason is that the adopted model does not take into consideration the manufacturing defects introduced by the punching and the rotor turning. Generally, the increasing factor is applied to the overall value of the calculated losses, including also the first harmonic component. Actually, as shown in Figure 13, the high frequency losses are placed where the manufacturing defects can have a strong influence: in the stator and rotor teeth tips, where, in addition, an high concentration of rotational field losses take place [19]. On the other hand, the first harmonic flux lines are parallel (in the stator teeth and back iron) to those surfaces that have been punched. For these reasons, it can be defined an increasing factor that concerns only the high frequency components of the losses. Considering the \(11\) kW prototype, for each voltage level, an increasing factor for the iron losses has been defined as:  
\[k_{\text{i}}=\frac{(P_{\text{meas}}-P_{\text{sim},1})}{\sum_{\
u>1}P_{\text{ sim},\
u}} \tag{29}\]  
where \(P_{\text{meas}}\) are the measured iron losses, \(P_{\text{sim},1}\) are the first harmonic losses from the simulation and \(\sum_{\
u>1}P_{\text{sim},\
u}\) are the high frequency losses from the simulation. It has been found out that the value of \(k_{\text{i}}\) is almost constant for each voltage level, except the last one, where it is rather higher. For the highest value of the voltage, the flux density in the iron reaches the saturation level (about 1.75-1.85 T) and it is worth to notice that the approximation in Figure 14a was able to fit neither the datasheet curve at high flux density, using the formulation in (27). Thus, the increasing factor is defined considering the voltage levels lower or equal to the rated value (400 V); making the average value, \(k_{\text{i}}=2.2\). Furthermore, the same increasing factor for the high frequency losses has been used for several motors in order to test the validity for different prototypes. Several motors belonging to the frame size IEC 132 have been measured, with stack length 150 mm, 180 mm and 200 mm, with a mechanical power of 7.5 kW, 9.5 kW and 11 kW, respectively. For all the motors the lamination is the M400-50A.