applied sciences  
A Method to Determine the Torque Ripple Harmonic Reduction in Skewed Synchronous Reluctance Machines  
[PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON], [PERSON] A Method to Determine the Torque Ripple Harmonic Reduction in Skewed Synchronous Reluctance Machines. [PERSON], [PERSON]; [PERSON]; [PERSON], [PERSON], [PERSON] A Method to Determine the Torque Ripple Harmonic Reduction in Skewed Synchronous Reluctance Machines. of its geometry, or the positioning and dimension of the iron ribs [11; 12; 13; 14; 15]. Among these techniques, skewing the stator or rotor structure is one of the most predominant [16; 17; 18] since it provides a reliable and straightforward solution for mitigating the torque ripple. Moreover, skewing is the most used method for suppressing torque ripple in SynRM [18]. Skewing techniques can be classified into two main categories: continuous skewing and discrete skewing (also called step skewing). The first one involves rotating each lamination of the stator or rotor core in regular angular distribution, between the first and the last slice equal to the skew angle [15], as depicted in Figure 2b. This can drastically reduce torque ripple, but complicates and makes the manufacturing process more expensive since each lamination of the rotor has a different position with respect to a symmetry axis, thus requiring specific tooling. In turn, the second category, considers the division of the rotor stack into a few discrete segments, as shown in Figure 2c. A considerable number of studies have addressed the rotor skewing technique using the conventional one-slot-pitch skew angle. These studies can be found in references [19; 20; 21; 22; 23; 24; 25]. In [19], the performance of a SynRM is compared when it is operated without skewing to when the rotor is skewed by one stator tooth pitch. Reference [20] investigates the effect  
Figure 1: Three-dimensional sketch of a one-barrier four-pole synchronous reluctance motor. Figure 2: Three-dimensional sketches of different types of skew: (**a**) reference skewless rotor, (**b**) continuous skew, (**c**) discrete skew, also called step skew. of rotor skewing on reducing slot harmonic torques, using a conventional skew angle of one stator slot pitch, but this reduces the average torque as well. This was confirmed in [21; 22]. In [23], the equation to calculate the skew angle to suppress the stator slot harmonic component (one-slot-pitch) was presented, considering the number of slices in the calculation. The novel forced feasibility concept was introduced in [24] to improve optimization convergence and reduce overall optimization time in a SynRM design. A rotor skew was chosen as the best suited torque-ripple mitigation option by skewing the rotor at an angle of one stator slot. Recently in [25], a SynRM with salient pole rotor was continuously skewed by one stator slot pitch to improve energy conversion and reduce torque ripple. The impact of rotor skewing on torque ripple in SynRMs was analyzed in recent research [16], comparing both continuous and segmented rotor skewing. Post-optimization simulations were performed for both methods and yielded similar results, with a slight advantage to segmented rotor skewing due to the increased cost of continuous skewing. In both cases, the total skew angle was equal to one stator slot. As it may be noted from the dates of these works, the one-slot-pitch skewing trend is dominant as a post-optimization process, applicable to several up-to-date machine topologies. In turn, several papers have discussed the skewing technique for reducing torque ripple [26; 27; 28; 29; 30; 31; 32], but they lack information on the selection of the skew angle or the skewing parameters used. In [26], a rotor design with an asymmetric flux barrier was created to reduce torque ripple by splitting the rotor into two step-skewed parts. However, the paper does not mention the method used to determine the skew angle, which is assumed to be equal to the slot pitch.