## 4 Topology of the Permanent Magnet Synchronous Motor  
The first step in implementing the design process described in the previous section required selecting number of poles \(2p\) and number of slots \(Q_{s}\). The number of slots then determined the relationship between the number of conductors per slot \(\mathrm{n_{s}}\) and number of turns per phase \(\mathrm{Ns}\) according to Equation (17). Having chosen the nominal speed to be equal to 500 rpm for the case of the permanent magnet synchronous motor, the supply frequency was related to the number of poles as follows: \(f=500(2p)/120\). The variation of frequency as a function of the number of poles is given in Figure 7.  
The required speed could therefore be achieved using various combinations of frequency and number of poles. The small number of poles did not seem consistent with the case under study due to the high power of the motor and the increased requirements for the output torque. Therefore, cases with a number of poles less than 14 were rejected. Although a relatively small number of poles, and consequently, a low frequency would lead to lower core losses for the stator and rotor, in this case height of the magnets \(h_{m}\) had to be increased to achieve the desired value for the magnetic flux density in gap \(B_{g}\). Despite the fact that the large height of the magnets contributed to preventing their possible demagnetization, it significantly increased the manufacturing difficulty. Additionally, the small number of magnets and poles would have led to a greater concentration of magnetic flux (saturation) in the stator teeth. Choosing too large a number of poles would have excessively increased core losses due to the increased frequency. Therefore, a compromise was made in choosing the appropriate combination, taking into account what was mentioned above. In addition, the value of fundamental winding factor \(k_{w}\) had to be considered when selecting the \(2p\)-\(Q_{s}\) combination. A high value for this factor was desirable, as that would contribute to achieving an induced voltage close to that of the phase voltage, thus reducing the operating current of the motor and contributing to an increase in power density. Taking into account the above, the selection process of the appropriate \(2p\)-\(Q_{s}\) combination had to be done with the following criteria:  
* A combination that allows the realization of the concentrated double-layer winding had a fundamental winding factor \(k_{w}>0.93\). * We rejected cases where the number of \(2p\) poles was less than 14 and \(Q_{s}\) was less than 42. * Cases where \(Q_{s}\) was an odd number were discarded, because in the case where the number of grooves was even, a more uniform magnetic loading was achieved on the motor. * We rejected combinations where \(2p>>Q_{s}\) or the difference between these quantities was large. Applying the above criteria to the sensitivity analysis resulted in few available combinations. Table 4 shows the extreme values of these combinations and the final optimal  
Figure 7: Supply frequency (Hz) vs. number of poles (2p). choice in bold. The supply frequency ranged from 158.33 Hz up to 375 Hz. It was understood that cases leading to a particularly high frequency should be rejected. At the same time, it was deemed necessary that the number of grooves be large enough so that the given number of coils per phase was divided into more grooves, thus reducing the electrical load on the motor. Therefore, it was decided to further study the combination \(2p=60\) and \(Q_{s}=72\), which yielded a fundamental winding factor of 0.933 and a supply frequency of 250 Hz. When the number of poles, the number of slots, and the fundamental factor of the winding had been determined, and assuming that gap length L\({}_{\text{g}}\) was equal to 6 mm, the product \(N_{s}\) (D \(-\) L\({}_{\text{g}}\)) L was calculated using Equation (16). Then, the following four cases were considered in terms of the number of conductors per groove \(n_{\text{s}}\).