Influence of stator segmentation on iron losses in PMSMs for traction applications

Purpose – This paper presents a comparative study of different stator-segmentation topologies of a permanent magnet synchronous machine (PMSM) used in traction drives and their effect on iron losses. Using stator segmentation allows one to achieve more significant copper fill factors, resulting in increased power densities and efficiencies. The segmentation of the stators creates additional air gaps and changes the soft magnetic material’s material properties due to the cut edge effect. The aim of this paper is to present an indepth analysis of the influence of stator segmentation on iron losses. The main goal was to compare various segmentation methods under equal excitation conditions in terms of their influence on iron loss. Design/methodology/approach – A transient finite element method analysis combined with an extended iron-loss model was used to evaluate discussed effects on the stator’s iron losses. The workflow to obtain a homogenized airgap length accounting for cut edge effects was established. Findings – The paper concludes that the segmentation in most cases slightly decreases the iron losses in the stator because of the overall reduced magnetic flux density B due to the additional air gaps in the magnetic circuit. An increase of the individual components, as well as total power loss, was observed in the Pole Chain segmentation design. In general, segmentation did not change the total iron losses significantly. However, different segmentation methods resulted in the different distortion of the magnetic field and, consequently, in different iron loss compositions. The analysed segmentation methods exhibited different iron loss behaviour with respect to the operation points of the machine. The final finding is that analysed stator segmentations had a negligible influence on the total iron loss. Therefore, applying segmentation is an adequate measure to improve PMSMs as it enables, e. g. increase of thewindingfill factor or simplifying the assembly processes, etc. Originality/value – The influence of stator segmentation on iron losses was analysed. An in-depth evaluation was performed to determine how the discussed changes influence the individual iron loss components. A workflowwas developed to achieve a computationally cheap homogenizedmodel.


Introduction
Traction electric drives in light electric vehicles, such as discussed in Kamiev et al. (2013) require on one side high power-density and energy efficiency and on the other side adequately low production costs. These requirements can be met with permanent magnet synchronous machines (PMSMs). The urge for every better and more powerful PMSMs as well as reasonable production processes means that innovations are needed to improve performance. In the production process, the winding technology (e.g. needle winding) is mainly automatized, where the change of such technology would often require excessive changes in the production line. To avoid such changes and increase performance, alternative methods must be considered. With the introduction of the stator segmentation, many advantages can be achieved, such as better cooling, which is achieved with axial segmentation, reduced weight of the machine by removing some sections of the stator, simplified winding process by allowing better automatization techniques, ability to use different materials (e.g. oriented steel) and increased slot copper fill factor (Aggarwal et al., 2020;Kolb and Hameyer, 2020;Rens et al., 2016;Yuan et al., 2014;Balluff et al., 2018;Shen et al., 2016;Camilleri and Mcculloch, 2021). By increasing the slot copper fill factor, the power density and efficiency can be increased due to the higher magneto-motive force (MMF). However, by applying stator segmentation, the magnetic circuit is changed (i.e. introduction of additional air gaps), and the cut-edge effect is increased (Rens et al., 2016;Balluff et al., 2018;Steentjes et al., 2014;Vandenbossche et al., 2010). These changes also have an impact on iron losses (Rens et al., 2016;Vandenbossche et al., 2010;Vandenbossche et al., 2013;Petrun et al., 2016;Caunes et al., 2020;Soda et al., 2021;Baker et al., 2018). The aim of this paper is to present an in-depth analysis of the influence of stator segmentation on iron losses under comparable excitation conditions. The objective was to analyse how different stator segmentations affect the iron loss components and whether the potential negative changes of the total iron loss do not nullify or outweigh the benefits that would be achieved by discussed improvements enabled by stator segmentation (e.g. increased slot copper fill factor, simplification of the assembly, use of tailored electrical steels, etc.).
Section 1 gives a brief introduction. In Section 2, an overview of the finite element method (FEM) model and the implementation of the different segmentation topologies are presented. The transient 2D co-simulation presented by Quintal-Palomo et al.(2019) used a similar modelling approach to the presented approach in this analysis. Furthermore, the extended iron loss model is introduced, which is a slightly modified version of the IEM (Institute of Electrical Machines)formula presented by (Steentjes et al., 2012). The obtained results are presented in Section 3. Firstly, the total iron losses (divided into components) of the drives with different segmentation topologies are introduced. Furthermore, the various components are analysed and explained in great detail. In Section 4, the conclusions are presented.
2. Theoretical background 2.1 Reference design finite element method model realization A 2D transient FEM model of the PMSM was realized in the Ansys Maxwell software environment, where the model was current driven. The FEM model's main input parameters were the phase currents i a , i b , i c and speed n, where the central output value was the electromagnetic torque T em , respectively. The geometry of the PMSM is shown in Figure 1.
The selected slot per pole and phase ratio was q = 0.5, which represented the basis for realizing a fractional slot non-overlapping (tooth-coil, concentrated) winding and further allowing stator segmentation . The parameters of the analysed PMSM are shown in Table 1.
Two distinct operation points (OPs) from the performed analysis are presented to show the influence of the stator segmentation on the iron losses under different operation conditions. In the analysis various OPs were obtained with the help of a reduced-order dynamic model of the machine with a field-oriented control (Weidenholzer et al., 2013) and the presented FEM models. The two OPs are presented in Table 2, where the first point COMPEL (OP 1) was selected at base speed and at the current limit. The second OP (OP 2) was selected in the field weakening region.
A mesh independent study was performed to get an adequate mesh for the presented analysis. OP 1 was chosen to perform the study. Different mesh sizes were chosen, and the electromagnetic torque T em was compared. Selected results are presented in Table 3. Based on these results, the mesh with 5,918 elements was selected for the presented analysis.
2.2 Implementation of stator segmentation in finite element method In the next step, different segmentations were implemented in the FEM model. The reference design (i.e. without stator segmentation) was evaluated versus the application of three   (Jordan, 2015). For every design, a mesh independent study was performed, as presented previously for the example of the reference design. All the analysed designs are presented in Figure 2. In all designs equal material properties and geometries were used. The T segmentation was achieved by separating the stator in the yoke into segments to get single packages that have the form of the letter T [ Figure 2(c)]. The simplest way to divide the segments was a straight cut that completely divides the segments. From the mechanical point of view, this is in general not adequate but also not a major concern because there exist several other different means that support the segmented stator mechanically (Rens et al., 2016;Jordan, 2015;Yuan et al., 2014). For the purposes of this analysis all segmentation air gaps were represented by using straight segmentation air gaps. The PC segmentation, presented in Figure 2(a), strongly resembled the T segmentation, where the main difference was a small connection bridge between the T segments. The advantage of the PC segmentation compared with the T segmentation was that the segments were combined (i.e. easier to handle, mechanically more stable, etc.) and COMPEL easier to assemble into a stator. The YR segmentation applied in this analysis was the YR þ single poles' segmentation, where the stator teeth were separated from the yoke, as presented in Figure 2(d). To adequately increase the mechanical stability of this type of segmentation, in practice, a few laminations in the stator lamination package are connected through slot bridges, which connect the stators teeth. This type of segmentation is called YR þ pole star segmentation (Jordan, 2015). As only a few laminations have the slot bridges in the YR þ pole star segmentation, the influence of these was neglected. Therefore, the subtype YR þ single poles' segmentation was analysed under the general name YR segmentation.

Homogenized cut-edge finite element method models
To adequately model the effects of the introduced additional cut edges in combination with mechanical segmentation air gaps of length d M , a detailed FEM model of the PMSM with T segmentation was developed. This FEM model was used to determine the equivalent segmentation air gap d EM for the homogenized FEM model without the detailed description of all the cut edges. The main focus was to account for the cut-edge effect on the weakening of the magnetic circuit (i.e. an increase of the effective segmentation air gap d EM ). Additional effects of the cut edges were neglected; therefore, this effect was taken into account by the increased segmentation air gap d EM . The detailed FEM model contained the real-world mechanical segmentation air gap d M = 0.01 mm, which was derived from the minimal mechanical tolerance (Baker et al., 2018). The air gap d M was directly included in the geometry of the PMSM, as presented in Figure 3. In addition to this, the iron core lamination was divided into four zones along all the cut-edges, as presented in Figure 3. The individual zones were used to model the deterioration of lamination magnetic properties in the proximity of the cut-edges. Special attention was paid to provide an adequate meshing in the proximity of all cutedges to accurately model the transition of the magnetic flux density B in the very narrow d M . The cut-edge effect was modelled by separating the stator lamination along the edge into four zones, as shown in Figure 3. Every zone was adequately described by a different B-H characteristic to replicate the cut-edge effect. Those three characteristics were obtained by adequately shearing the original B-H curve of the used soft magnetic material Iron losses in PMSMs (Rens et al., 2016). The characteristic in the outer zone was sheared the most, as the effect of the cutting affected the material the strongest, whereas the inner zone was not affected (i.e. the original B-H characteristic was used).
In the next step, d EM was determined based on the analysis of the detailed FEM model. To determine d EM , a steady-state simulation with the detailed FEM model was performed at the OP 1 with a fixed speed n and input phase currents i a , i b , i c . The electromagnetic torque T em was obtained. Then the homogenized FEM model was simulated at the same OP with the fixed input parameters. The size of d EM was adjusted to such length that the steady-state simulation provided equal output values as the simulation with the detailed FEM model. The resulting d EM had a length of 0.05 mm. This equivalent segmentation air gap d EM was used in homogenized FEM models for the final analysis of the influence of stator segmentation that is presented below. All segmentation designs were equipped with the equivalent segmentation air gap d EM . Table 4. presents T em for the homogenized FEM model with d EM of 0.05 mm and a detailed FEM cut-edge model with the real-word segmentation air gap d M of 0.01 mm. The workflow can be further used to achieve a computationally cheap homogenized model when performing FEM analyses of segmented stators. The relative differences between calculated T em in both cases are also presented in Table 4.

Analysis based on finite element method models
The next step was to analyse all four designs in steady-state OPs, that represented comparable operation conditions. The homogenized model was used for all three segmentation designs, where d EM , was implemented in the geometry of individual FEM models. The input conditions (i a , i b , i c and n) were the same for all four designs. Two OPs were analysed, as presented in Table 2. When equivalent OPs were determined and calculated, the detailed iron loss calculation followed in the post-processing stage.

Extended iron loss model
The calculated magnetic field within the iron core was distorted (i.e. contained higher harmonics) due to saturation of iron, skin effect and slotting effect. To calculate the total iron losses P Fe and consider all the abovementioned effects, the slightly modified IEM-formula (Steentjes et al., 2012;Nell et al., 2022) was used.
where P hyst is hysteresis losses, P eddy is eddy (i.e. eddy current) losses, P excess is excess losses, and P sat is saturation losses. In high performing machines, the iron losses can be modelled more accurate by using the IEM-formula compared with the Bertotti formulas, as shown by Steentjes et al. (2012). Eddy losses P eddy and excess losses P excess are defined by the Bertotti formula (Bertotti, 1998) and were extended with a summation over all harmonics by the following: where a 2 and a 5 are material-specific parameters, f is the fundamental frequency, n is the number of the harmonic component andB n ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f B 2 n;x þB 2 n;y q is the peak value of the nth harmonic of the magnetic flux density, whereB n;x andB n;y represent the amplitude value of the magnetic flux density of the nth harmonic in both x-and y-directions. The hysteresis losses P hyst were also extended from the Bertotti formula and included the influence of rotational and flux distortion effects by the following: where a 1 is a material-specific parameter, a 1 and b 2 are the exponential material-specific coefficients, B min and B max are the minima and maximum value of the magnetic flux density B over one electrical period, and r hyst (J, J 0 ) is the rotational loss factor determined by the value of the magnetic polarization J and the magnetic polarization saturation J 0 . The rotational loss factor r hyst (J, J 0 ) is added to model the rotational distortion on P hyst . It was modelled as a decreasing function of the magnetic polarization J and the calculated value of the magnetic polarization saturation J 0 (Appino et al., 2016). Saturation losses P sat were added to account for the nonlinear magnetization behaviour at high magnetic flux density by the following: where a 3 and a 4 are material-specific parameters. The parameters a 1 to a 5 were determined by mathematical fitting performed on the measured data sets for the non-oriented electrical steel with the thickness of 0.35 mm that was used in the analysed machine. The measurements were performed by a single-sheet tester. The IEM-formula was validated for the material used in this study. The calculation of the iron losses was performed in post-processing, where the results from FEM simulation were used. One magnetic period in steady-state was simulated, and the magnetic flux density B, magnetic flux density in x-direction B n , x , y-direction B n , y and magnetic polarization J were obtained for every mesh element. The iron losses were calculated for the stator by using the software package Matlab. In the detailed analysis also, the peak values of the magnetic flux density B p in one magnetic period were determined, and the total harmonic distortion (THD) was calculated for the magnetic flux density B in every mesh element by the following:

Iron losses in PMSMs
Furthermore, P hyst and P eddy were determined for all the different higher harmonic components.

Results
To perform an adequate comparison between the segmentation topologies and the reference machine design, the equivalent segmentation air gap d EM was applied for all segmentation types. Furthermore, the analysis was performed under the same speed n and same input phase currents i a , i b , i c to accomplish the same current excitation (i.e. equal MMF) in all analysed cases. Two different OPs are presented, one in the constant torque region and one in the field weakening region. The obtained results reflect the effect of the change of the magnetic flux density B in the stator on all the presented iron loss components. In Figure 4, the total stator iron losses P Fe with the corresponding components for the reference design and all three segmentation types for the two OPs are shown. When comparing the loss components of the two OPs it was observed that in OP 1, most of P Fe were contributed by the P hyst , whereas in OP 2, the loss components are more evenly split between P eddy , P excess and P hyst . In both OPs the lowest component was represented by P sat .
When analysing P Fe of the different segmentation types and their components, it was observed that almost in all cases, P Fe of the segmented stators is lower than the reference design. Only in OP 2 P Fe in the case of PC segmentation exceed the losses of the reference design. The performed analysis showed that this was due to the higher harmonic components of the magnetic flux density B and the higher ratio between B min Bmax in this case compared with other designs, as presented in the following subsections. In OP 1, P Fe is the highest in the case of the T segmentation for the segmentation designs, whereas, in OP 2, this is true for the PC segmentation. Table 5 presents the total and relative decrease of P Fe and their corresponding components for the reference design and all three segmentation types for both OPs.
3.1 Influence of higher harmonics Firstly, P eddy and P excess are discussed, as they were calculated through a summation over all the harmonic components of B. In OP 1, it was observed that these two loss components were higher for the YR and PC segmentation compared with the T segmentation. For OP 2,  Iron losses in PMSMs these two loss components were higher for the PC segmentation compared with the T and YR segmentation. Because both components were dependent on higher harmonics, further analysis in respect to higher harmonics was performed. The results are presented in Figure 5.
In the harmonic components of the P eddy for OP 1, an increase of the third harmonic component of the reference design and YR segmentation compared with the PC and T segmentations was observed. Due to the higher harmonic components of the PC segmentation, P eddy was higher than the T segmentation in OP 1.
When analysing the harmonic components of P eddy in OP 2, it was observed that the PC segmentation's harmonic components were the highest for all harmonics. By comparing the harmonic components of P eddy between OP 1 and OP 2, it was detected that in OP 2, the value of harmonic components was larger than for OP 1, in the fifth and all higher odd components.
This effect is also shown in Figure 6 for OP 1, where the THD values of B in every mesh element in the stator for all four different designs are presented. The black circles in Figure 6 represent the areas where the distortion of B (i.e. high THD values) was specific for the segmentation type and was connected to a property that was specific for that design.
The THD values in the PC and YR segmentation increased in the areas around the segmentation air gap d EM because of the distorted B. For the T segmentation, no significant increase was observed. In the PC segmentation [ Figure 6(b)], an increase of the THD occurred in the connecting bridges because of the saturation of these bridges. When comparing the PC segmentation THD to the T segmentation, it was shown that no increase of THD in the T segmentation was observed, as there no connecting bridge was included. The THD for the YR segmentation was higher in the YR above the segmentation, as indicated by the black circle [ Figure 6(c)]. In the reference design, the THD values of B were in general higher than the other three segmentation designs. This was connected to the higher values of B, whereas the iron core was more saturated. The higher values compared with the other three designs were detected in the yoke area, as shown by the black circle in Figure 6.
3.2 Influence of weaker magnetic circuit Further, P hyst and P sat were analysed. They were for all three segmentation types and both OPs lower than the reference design, with the exception of P sat in OP2 for the PC segmentation. In OP 1, these two loss components were the highest for the T segmentation when comparing only the three segmentation designs. In contrast to this, in OP 2, P hyst and Figure 5. Distribution of eddy losses by harmonic components for operations points 1 and 2 COMPEL P sat , where the highest in the PC segmentation out of the three segmentation designs. Because both discussed loss components relate to the amplitude values of B, the distribution of relative occurrence was calculated for all the designs. Figure 7 presents the relative occurrence of B p in the stator for OP 1 and OP 2, where B p is the maximum value of the magnetic flux density B of one magnetic period in an individual mesh element.
The two distinct peaks in the occurrence distribution of B p in all analysed designs for OP 1 in Figure 7 correspond to B in the teeth (the occurrence peaks are located at higher values of B p ) and yoke (the occurrence peaks are located at lower values of B p ). The results of this analysis showed that in the case of reference design, both the yoke as well as the teeth regions were subjected to higher B than the segmentation designs (both occurrence peaks in Figure 7 occurred at higher B p ). This was attributed to the weaker magnetic circuits when segmentation is applied and was observed also in the case of OP 2. In OP 1, PC and T segmentations designs gave comparable locations of both occurrence peaks but lower than the reference design. The relative occurrence of B p in the peaks was higher for T segmentations. The location of peaks for the YR segmentation was the lowest. When observing OP 2, the peak locations are lower as in OP 1 because the machine operates in a flux weakening region. In the reference design, T segmentation and YR segmentation also two peaks were observed, but in this case, the higher values correspond to the B in the yoke, whereas the lower values correspond to the B in the teeth. In the case of PC segmentation, the two peaks were very close together and were almost combined into one peak, which reflected that the distribution of B was the more homogeneous.
The similarity of distribution of B p between the T and PC segmentation in OP 1 was connected to almost identical geometry. In general, the reduction of B p for all three designs compared with the reference was related to the weakening of the machine's magnetic circuit. This influenced the P hyst and P sat for T and PC segmentation, as the lower peak magnetic flux density B p had a direct effect on lowering those two-loss components. The weakening effect in both OPs was the strongest for the YR segmentation, which also explained the lowest P hyst (in OP1 equal to PC segmentation) and P sat in the analysed case. It is important to note that despite peak magnetic flux density B p of the PC segmentation in OP 2 being lower when compared with the T segmentation, the corresponding P hyst was higher for the PC segmentation. This was related to the rotational loss factor r hyst (J,J 0 ) in combination with the ratio between B min B max according to equation (4), which was higher in the case of PC segmentation. In OP 2, P sat were in all cases lower than 5% compared with the total losses P Fe due to significantly lower saturation of the cores.
It is important to note that in OP 2, P Fe was higher in the case of PC segmentation than the reference design. This increase was connected to P eddy and P excess , which were the highest in the case of PC segmentation due to high values of the harmonic components of B. However, because of the higher ratio between B min B max in the case of PC segmentation, also an increase in P hyst was observed. All these effects resulted in the higher P Fe , despite a significantly weaker magnetic circuit and lower saturation than the reference design.

Conclusions
In the paper, the effects of different stator segmentation topologies on iron losses in the stator of a PMSM were analysed and discussed. The presented analysis was performed by using an extended iron-loss model in combination with a 2D transient FEM model of an electrical drive. Three segmentation topologies (PC, T and YR segmentation) were compared with the non-segmented reference machine design at the same phase currents and speed for two OPs.

COMPEL
The total iron losses P Fe were in the case of all three-segmented designs lower than the reference design when the PMSM operated at nominal B. In the field weakening region OP, however, P Fe were the highest for the PC segmentation. The eddy losses P eddy and excess losses P excess were the highest for the reference design in OP 1. When observing just the segmentation designs in OP1, P eddy and P excess were higher for the PC and YR segmentations. In OP 2 (field weakening region), those two-loss components were the highest for the PC segmentation. In the PC and YR segmentation, local saturation effects appeared, which caused distortion of B and the appearance of higher harmonics and consequently increased loss components.
The hysteresis losses P hyst and saturation losses P sat were in all three segmentation types in OP 1 lower than the reference design. In OP 2, P hyst was in all three segmentation types lower than the reference design, whereas P sat was higher than the reference design in the case of PC segmentation. No significant effect on the P Fe was observed, as the P sat in OP 2 were in all cases lower than 5% compared with P Fe . Due to the introduction of segmentation (i.e. additional segmentation air gap and cut-edges effect), the magnetic circuit was significantly weakened. Even though the weaker magnetic circuit resulted in generally lower B, this did not necessarily lead to lower losses in the segmented stator of the corresponding PMSM. No segmentation is from the electromagnetic perspective optimal, and the segmentation types can behave differently in different operation conditions. It was observed that also pitfalls are possible when applying segmentation, as in some cases, the iron losses can even increase, despite weaker magnetic circuits. In the presented analysis, P Fe were higher than the corresponding P Fe in the reference design in the case of PC segmentation in OP 2. This related to the harmonic components that were higher than other designs and the higher ratio between B min B max . It is worthwhile to note that, in general, segmentation did not change the total iron losses significantly. However, different segmentation methods resulted in the different distortion of the magnetic field and, consequently, in different iron loss compositions. The analysed segmentation methods exhibited, furthermore, different iron loss behaviour in respect to the OPs of the machine.
The presented findings are helpful in the machine design process and provide insight into how different stator segmentations influence iron losses. It is concluded that in the presented cases, the changes in the total iron loss were negligible in respect to the reference design. Consequently, the discussed segmentation techniques present viable measures to exploit the potential benefits of, e.g. increasing the slot fill factor, simplifying the assembly process, etc.
Future work based on the presented analysis will include the following tasks. The effect of different excitation currents will be analysed (e.g. block commutation, PWM, etc.). Furthermore, the detailed cut-edge FEM model will be used to perform the iron loss analysis, to include all other effects that the cut edge has on the magnetic characteristics of the materials. Furthermore, the process for developing the equivalent segmentation air gap d EM will be used to build a FEM model of the whole drive. An analysis of the drive will be performed, and torque/speed characteristics will be obtained. With the help of the extended iron loss model, efficiency maps will be calculated.