Segmented Hairpin Topology for Reduced Losses at High-Frequency Operations

Nowadays, one of the key challenges in transport electrification is the reduction of components’ size and weight. The electrical machine plays a relevant role in this regard. Designing machines with higher rotational speeds and excitation frequencies is one of the most effective solutions to increase power densities, but this comes at the cost of increased losses in cores and windings. This challenge is even more pronounced in preformed windings, such as hairpins, which enable higher slot fill factors and shorten manufacturing cycle times. In this work, an improved hairpin winding concept is proposed, aiming to minimize high-frequency losses while maintaining the benefits deriving from the implementation of hairpin windings onto electrical machines. Analytical and finite element models are first used to assess the high-frequency losses in the proposed winding concept, namely the segmented hairpin, proving the benefits compared to conventional layouts. Experimental tests are also performed on a number of motorettes comprising both conventional and proposed segmented hairpin configurations. Finally, these experimental results are compared against those collected from motorettes equipped with random windings, demonstrating the competitiveness of the segmented hairpin layout even at high-frequency operations.

objectives of primary importance to achieve when designing a more electric vehicle. In this regard, the components of the vehicle's powertrain play a key role. Of these, the electrical machine is experiencing an ever-increasing interest and research focusing on the maximization of their power density [5], efficiency [6], and reliability [7] is now underway at an unprecedented rate.
Nevertheless, achieving all these requirements concurrently is a difficult task. In fact, while the operating speed represents the main lever to increase the machine power for a given volume [8], it results in higher operating frequencies. These, in turn, reflect on increased losses in cores and windings as well as higher stresses on coil insulations, thus efficiency and reliability are compromised [9], [10]. An evident example in this regard is represented by hairpin windings, whose full penetration in the transportation market is curbed by their inherently high ohmic losses at high-frequency operations, where skin and proximity effects occur.
On the other hand, this technology offers higher slot fill factors, reduced end-winding lengths, and lower low-frequency copper losses than their random-wound counterpart. In addition, their manufacturing allows for automatized, repeatable, and reliable procedures, making hairpin windings ideal when high production volumes are required, such as in automotive transportation. In this case, cost minimization is another key driver. Studies carried out in [11] have proven that, for a production target of 1 million units per year, manufacturing hairpin stators is cheaper than manufacturing stators employing random windings. It becomes then clear why hairpin windings are considered by many scholars and industries as the way forward for next-generation electrical machines [12].
However, the bottle-neck remains the ohmic loss produced at high-frequency operation (ac losses). Therefore, to fully meet the green revolution requirements, hairpin designs should be aimed to mitigate this challenge. In the last few years, the focus of several researches has been on ways to model, estimate, and reduce ac losses in hairpins. In [13], guidelines on how to make suitable connections for reduced losses have been provided, along with a 1-D model for the evaluation of copper losses. In [14], a 2-D analytical model has been proposed and validated via finite element analysis (FEA). Methods such as removing the closest conductor to the slot opening or reducing the conductors' height while increasing the number of conductors have been proposed to reduce ac losses [15]. However, the first solution reduces the fill factor since part of the slot is left empty [11], whereas the second option increases the manufacturing complexity [13]. Asymmetric windings consisting of series-connected conductors featuring different cross-sections have been studied via FEA in [16]. Here, promising results have been achieved, but experimental validation is missing. In addition, the method increases the dc resistance of the asymmetric conductors and may represent a limit to the maximum obtainable current density.
Another interesting technique to reduce ac losses in hairpin windings comes from the "strand" concept typical of random windings, where the conductor is divided into several parallelconnected sub-conductors (strands). In hairpins, this method cannot be applied as flexibly as in random windings. The number of parallel-connected elements should be kept low to avoid unfeasible solutions or excessive complications of the bending and welding processes [17]. Although the concept of parallel conductors has been widely implemented in large power machines equipped with pre-formed winding [18], to the authors' knowledge, the parallel-connected concept in hairpin windings has been proposed in [19] for the first time, but the analysis only focused on the 2-D aspects (i.e., endwindings effects are neglected) and no experimental validation was provided.
This work fills these gaps by including the 3-D effects in both analytical and FE models and, most importantly, by experimentally validating the segmented hairpin concept. In particular, concerning the modeling aspects, a simplified 2-D FE model is proposed for the analysis of the end regions, yet taking into account the phenomena potentially occurring at high frequencies. Regarding the experimental validation, a segmented hairpin winding is implemented onto purposelybuilt motorettes. Four motorettes are prototyped and tested, each of them equipped with different winding arrangements for comparative analyses. Besides proving the benefits of the proposed technique in terms of loss reduction, the experimental results are used to demonstrate that the segmented hairpin winding can compete against random windings even at highfrequency operations. This is done by comparing these results to those obtained in [20] on motorettes equipped with round wire random windings.

II. BACKGROUND AND PROPOSED CONCEPT
This work considers an electrical machine designed for automotive traction with power and maximum speed equal to 115 kW and 12000 r/min, respectively. As detailed in [19], the design and optimization process of such traction motor has led to select a permanent-magnet-assisted synchronous reluctance machine with four poles and three rotor barriers per pole, as shown in Fig. 1, and the geometrical parameters are provided in Table I. Regarding the stator, two different numbers of slots-per-pole-per-phase q are envisioned (i.e., q = 2 and q = 4), while fixing stator inner and outer diameters. Also in [19], both random and hairpin windings have been considered for the designed motor. In this work, the focus is on the hairpin option and the following layouts  are considered: 1) q = 2 and number of layers per slot k = 4; 2) q = 4 and k = 8; 3) q = 4 and k = 4; and 4) q = 4 and k = 6. For the sake of completeness, the main stator dimensions are provided in Table II, whereas the conductors' dimensions are given in Table III. In reality, layouts 3) and 4) are electrically identical, i.e., the number of equivalent conductors in series per slot is four for both layouts. However, layout 4) implements the proposed segmented hairpin concept, consisting of splitting some of the conductors into two or more layers. This concept can be extended to any hairpin winding configuration (i.e., different number of layers or different parallel paths), and does not impact the equivalent number of turns per phase but only splits one or more conductors in two or more smaller parallel-connected conductors, with the aim of reducing the ac copper losses. To better envisage this concept, in Fig. 2(a) the conventional solution corresponding to option 3 is modified by segmenting the two closest conductors to the slot opening in two sub-layers having identical cross-sections. This modified layout is named "proposed solution" in Fig. 2(a) and corresponds to the aforementioned option 4), where the number of conductors is series per slot is four, but the number of layers per slot is six. For this reason, this layout can be labeled with "k = 4 segmented," as seen in Table III. Thanks to Table III, we can note that both solutions have the same fill factor, the segmented layers result placed nearer to the slot opening zone because of the physical gap needed between the layers. The electrical connections of the segmented hairpin winding are shown in Fig. 2(b), where each of the last two conductors (namely 3 and 4) are subdivided into two sub-layers (3.1 and 3.2, and 4.1 and 4.2), whereas in Fig. 2(c) the connections typical of a standard hairpin layout are illustrated to highlight the major differences.

A. Manufacturing Considerations
In theory, each segmented conductor can be composed of more than two parallel-connected layers. However, using more than two sub-layers may complicate the manufacturing process, taking into account that: 1) a transposition is needed to make the segmented technique effective; 2) the number of welding points increases; and 3) the total number of layers per slot increases too. Therefore, in this work, it is deemed sufficient to segment only two conductors. These are obviously the closest to the stator slot openings, being the most critical ones from a loss perspective. Additionally, the number of sub-layers is chosen equal to two, thus minimizing the impact on the manufacturing.
Assuming a high-volume production context, hairpin manufacturing would be a fully automated process. Thanks to the technological progress in hairpin manufacturing lines, the segmented hairpin winding will not have a significant impact on the manufacturing process and cost. In fact, even if the number of elementary pins to use increases, nowadays several configurable tooling can be used to bend and twist them, and this allows using the same manufacturing line for all the types of pins. Attention must be paid to the constraints related to the hairpins' width-to-height ratio during the bending process. Additionally, the number of conductors must be kept below the current manufacturing limitation. In other words, as long as the width-to-height ratio and the number of layers per slot are kept below the current limits, then no complications are seen when implementing the segmented technology. Regarding the welding points, if a standard hairpin winding was to be considered for the application at hand, then the number of welding points would have been 15, whereas the proposed segmented layout presents 22 welding points. This does not represent a significant complication. Moreover, the technology progress in manufacturing lines is leading to manage the welding process in a very reliable way, thus avoiding the risk of short circuits in actual applications.
An example of these technology progresses is represented by AUTOmated Manufacturing of wound components for next generation Electrical mAchines (AUTO-MEA) [21], a Clean Sky 2 project which aims to develop novel methodologies for winding design and to deliver an innovative and flexible coil fabrication system, which can provide programmable 3-D formed coil shapes suitable for high-frequency operation, effective coil insertion, and automated welding strategies to form a complete winding system for aerospace and automotive wound components.
Although a detailed cost-benefit analysis is impossible to carry out if the volume production is not specified, it is anyway clear that the segmentation concept will not bring a significant cost increment to the overall process, while the benefits in terms of loss reduction and energy savings can be impressive. This would lead to a series of additional benefits such as higher efficiencies, lower temperatures, increased insulation lifetimes, and so on.

III. ANALYTICAL MODEL
To exploit the benefits of the proposed methodology versus conventional ones, a 1-D analytical model for ac loss estimation is developed and described in this section.
AC losses are those occurring above the frequency level where the current is no longer uniformly distributed within the conductors. These losses are mostly due to skin and proximity effects, assuming that circulating currents are zeroed by a suitable transposition. Usually, the ac losses PAC are quantified through the product of dc losses and a non-dimensional factor KAC, which is defined in (1). The dc loss PDC is found through the simple relationship reported in (2), where l c and A c are, respectively, the conductor length and its cross-section, while σ is the electric conductivity of the material. When skin and proximity effects occur, the cross-section where the current flows is a fraction of ac, thus the equivalent resistance (namely the ac resistance) increases and ac losses are consequently enhanced by the factor KAC These high-frequency phenomena can be significant especially in the slot region, but they may have some influence also in the end-winding regions. Hence, both regions are modeled analytically aiming to accurately estimate the overall ac losses.

A. Slot Region Model
A 1-D model is developed leveraging the discretization of the domain under investigation. This allows achieving an acceptable accuracy while minimizing the calculation effort. The slot domain under analysis is shown in Fig. 3 and consists of a single slot comprising k conductors (hairpin legs). This domain can be analyzed using the discretization layer approach, where each conductor is located in a layer. The magnetic field inside the slot produced by the current flowing in the conductors is considered parallel to their width W ck , meaning that the field component parallel to their height hc is neglected.
Under the assumptions of linear behavior of the ferromagnetic materials, the application of the Ampere's law to any of the red circuits Y k shown in Fig. 4 leads to obtain (3).
Here, H is the magnetic field strength, W sk is the slot width, J k is the current density in the kth layer, y k−1 and y k are the (k − 1)th and kth layers, and I k − 1 is the total current Exploiting (3) leads to the partial differential equations provided in (4) and (5), where the physical quantities can be expressed by phasors thanks to the hypothesis of sinusoidal current feeding the conductors. In (5), ω is the supply electric pulsation, while μ is the magnetic permeability of the conductive material Combining (4) and (5) leads to obtain (6), the general solution of which is provided in (7). Here, the quantity η is the skin depth which is defined as in (8) The constant terms A 1 and A 2 involved in (7) are found through the boundary conditions (9) and (10), where h is the height of the considered layer (see Fig. 3) The current density in the kth layer is finally obtained as in (11), as shown at the bottom of the next page, whereas the associated losses are finally determined as in (12), as shown at the bottom of the next page. In (12), l ck is the length of the kth conductor in the slot region, while vol is its volume.

B. Slot Region Model
In the end-winding region, the model described above cannot be directly used since the ferromagnetic material surrounding the conductors is no longer present and the geometry of the end-windings is rather complex. However, since the end-windings are basically surrounded by air, the magnetic field magnitude is much lower than the slot region. It becomes then reasonable to neglect the proximity effect [22], meaning that the only contribution to ac losses is due to the skin effect.
As a first approximation, the skin effect can be considered invariant along the direction of the conductor length, thus leading to tackle the loss determination problem as a 1-D one also in the end-winding region. Equation (13) is then used for determining the skin effect resistance R skin [23], which depends on the parameter ξ the expression of which is provided in (14) IV. FE MODEL As per the analytical approach, FE models of both slot and end-winding regions are developed to evaluate the ac losses using MagNet® from Simcenter. For both regions, the solution mesh is defined according to a detailed sensitivity analysis aimed at finding the best trade-off between accuracy and computational effort. Time harmonic simulations are used for the sake of resolution speed and consistency with the sinusoidal supply assumption. According to [24], only the stator model is needed to reduce the computational effort without losing accuracy in estimating the ac losses, being the latter mainly dependent on the slot flux leakage [19].

A. Slot Region Model
Contrarily to the analytical approach, for the slot region the FE models consist of two poles being analyzed for any of the four configurations introduced in Section II. Only one phase and only the stator is modeled, as shown in Fig. 4 for one of the considered layouts, i.e., the case with q = 2 and k = 4.

B. End Winding Region
The estimation of ac losses in hairpin windings including the end-windings is an inherently 3-D problem. Also, the end regions of hairpin windings are rather complex and only a 3-D analysis would be fully accurate. However, a 3-D model would be very consuming in terms of both modeling and simulation times. To enable a 2-D analysis, first of all, the proximity effect is neglected and only the skin effect is taken into account, consistently to the analytical approach discussed in Section III. To simplistically evaluate the influence of the end-winding geometries, two conductors with different shapes are considered, as reported in Fig. 5. The two conductors have identical cross-sections and lengths, but the first one is obtained through axial extrusion [see Fig. 5(a)], whereas the second one is extruded angularly [see Fig. 5(b)]. Apart from the major bends typical of hairpin windings, the conductor shown in Fig. 5  reproduces a shape close approximation to the ones that can really be found in this region. This conductor is modeled through a 3-D FEA, whereas the one shown in Fig. 5(a) is studied as a 2-D problem. The FE evaluations for both conductors' shapes are carried out at 1000 Hz to enhance the high-frequency effects. The comparison is shown in Table IV and highlights a 1.5% mismatch between the results in terms of losses. In Table IV, the number of mesh elements and the solution times are also reported to emphasize and justify the use of the 2-D models for the analysis of the end-winding regions.
Considering the above and passing to the analysis of the study cases at hand, it is worth mentioning that a full 3-D CAD model is usually available for a hairpin winding design ready to be manufactured. Hence, it would be straightforward to determine cross-sections and lengths of all conductors to use in the simplified 2-D FE models. However, since motorettes are manually built to prove the concepts proposed in this article, a full 3-D CAD model is not available. Therefore, to estimate the end-winding length for the FE evaluations, first, the overall dc resistance R dcmeasured is measured with an impedance analyzer, and then, knowing the winding characteristics in the slot region, it becomes possible to extract the 2-D resistance R dc2−D and the end-winding resistance and length R end and L end . To such purposes, (14) and (15) are used, where σ Cu is the copper conductivity and A Cu is the conductor cross-section In Table V, the end-winding lengths calculated in this way are reported for each investigated case study. Finally, using such lengths, the simplified models shown in Fig. 6 are built  to estimate the ac losses in the end-winding region of each considered winding layout.

V. COMPARISON BETWEEN ANALYTICAL AND FE MODEL RESULTS
In this section, the results obtained with the analytical and FE models described above are presented and compared. These results aim to highlight the accuracy of the analytical model and the importance of including the end-winding effects in the evaluation of the overall ac losses.

A. Slot Region Model: Analytical Versus FE Results
The results obtained from the developed slot region analytical and FE models are compared in Fig. 7, which shows the trend of the parameter K ac [defined in (1)] versus frequency. The machine electrical frequency at the maximum speed of 12 000 r/min is equal to 400 Hz. However, the analysis is carried out for a frequency range up to 1200 Hz for a better understanding of the losses behavior of the studied topologies and for potential applications at higher speeds and/or frequencies. For the sake of clarity, the results relative to the four study cases have been split in Fig. 7(a) and (b). The match is very positive for all the conventional winding schemes, with a maximum error lower than 3% over the whole frequency range analyzed. Regarding the segmented layout, the error becomes ≈50% at 1200 Hz [see Fig. 7(b)], since the developed model does not take into account the updated boundary conditions resulting from such an unconventional arrangement [17]. On the other hand, both the analytical and FE results prove the perceived benefits of the segmented layout, with a significant loss reduction achieved compared to the conventional q = 4, k = 4 configuration.

B. Complete Analytical Model Versus Complete FE Model
To evaluate the effects of the end winding regions on ac losses, the FE results shown in Section III (labeled as "slot region FEM") are compared against the complete FE model (labeled as "complete FEM"), which includes both the contributions from the slot and end winding regions. The discrepancies can be very high, thus proving the need for an accurate end winding region model. The last comparison of this sensitivity study is carried out between analytical and FE models when both include the overall effects (slot and end-winding regions) into account. The results are reported in Fig. 8, where the segmented hairpin is not reported as the discrepancy would be excessive due to the reasons given in Section V-A. It can be noticed that the analytical model is not as accurate as in the slot region. For the study cases q = 4 with k = 4, q = 4 with k = 8 and q = 2 with k = 4 the maximum errors are 28%, 15%, and 17%, respectively. Despite these discrepancies, it is worth underlying again the need of including the 3-D effects also in the analytical model. In fact, this is faster than the FE evaluations and this can lead designers and researchers to prefer the analytical approach in some specific cases (e.g., when long optimization processes are used), yet accepting the inherent limitations and inaccuracies.

VI. THERMAL ANALYSIS
The loss reduction achieved by the segmented hairpin winding would lead to a temperature reduction which could lead either to increase the power rating of the electrical machine or to operate it at a lower temperature in order to extend the insulation lifetime. For the sake of completeness, a thermal analysis via Simcenter MAGNET Thermal is performed on the segmented hairpin and its conventional version. The environmental condition boundaries are set in the surfaces in contact with the ambient air, imposing an environmental temperature of 20 • C and a convective heat transfer coefficient of 20 W/(m 2 • C) according to [25]. Coupled simulations are carried out using the electromagnetic field simulation software Simcenter MagNet and the thermal tool MAGNET Thermal. First, 2-D time-harmonic simulations are made to evaluate the losses, and then these are automatically acquired by the thermal software and used as heat sources for the 2-D static thermal simulations. A significant operating point at a frequency equal to 1 kHz is chosen for the comparison, with the current set at 40 A to achieve reasonable temperature levels. Fig. 9 shows the temperature distribution for the standard solution [ Fig. 9(a)] and for the proposed concept [ Fig. 9(b)].
With the proposed solution the peak temperature registered in the conductors is 67.8 • C, whereas with the standard solution the peak temperature is 141.9 • C. These values are justified by the significantly different values of copper losses produced with the conventional and the segmented configurations, being respectively equal to 119 and 52.9 W. The ratio between losses is consistent with what is reported in Fig. 7(b) where, at 1 kHz, for the conventional hairpin winding KAC is about twice that of the segmented layout.

VII. EXPERIMENTAL RESULTS
Aiming at demonstrating the proposed segmented concept as a means to reduce ac losses in hairpin windings, as well as to prove the methodologies presented in the previous section, four motorettes (i.e., stator portions corresponding to one pole pair) are built according to the dimensions provided in Tables II and III. As mentioned in Section IV-B, these motorettes are manually wound for the sake of simplicity, i.e., to minimize costs, resulting in oversized end-windings as observed in the figure. The motorettes are shown in Fig. 10 and are representative of the four study cases investigated in this work. Therefore, one of these implements the segmented hairpin winding concept, i.e., the one labeled as "q = 4, k = 4 Seg" in Fig. 10. For the sake of consistency with the sinusoidal supply assumptions used in both analytical and FE evaluations, the signal feeding the motorettes is first produced by a SiC voltage pulse generator with 60 kHz switching frequency and, then, filtered by a low pass LC filter with a cutoff frequency at 2 kHz to obtain an output signal as close as possible to a pure sinusoidal waveform. The power loss is measured by a precision power analyzer (PPA 5530) and an oscilloscope is used to double-check the losses value and the signal waveforms. All measurements are taken at the same temperature (20 • C) and the winding temperatures are monitored with a thermal camera during testing. The whole test setup is shown in Fig. 11(a), whereas the relevant circuital schematic is illustrated in Fig. 11(b).
The experimental tests are performed ranging from 0 to 1200 Hz and the relevant results are compared in terms of K ac against the complete FE simulation results. This comparative exercise is reported in Fig. 12, where an excellent match between FE and experimental results is achieved in the whole frequency range considered. The maximum error is less than 15% and this could be justified by the additional resistance introduced by the welded connections.
Apart from the match accuracy between FE and experimental results, the main achievement here is the proof of the effectiveness of the segmented hairpin concept. Compared to the conventional q = 4, k = 4 layout, its modified segmented version, i.e., q = 4, k = 4 segmented, achieves an experimental loss reduction by more than 20% starting from 600 Hz, with a peak reduction of 28% registered at 1000 Hz. It is worth mentioning that, as done for the analytical and FE evaluations, the same magneto-motive force is used to feed the hairpin layouts to make the comparison fully fair.
Having proven the effectiveness of the proposed technique, the last step is to demonstrate that the segmented hairpin  windings can compete against random windings envisioned for the same application. This is the focus of the next section.

VIII. COMPARISON BETWEEN HAIRPIN AND RANDOM EXPERIMENTAL RESULTS
For the same application (see Section II), motorettes with trapezoidal slots hosting a random winding with round conductors are built and tested in order to identify the trend of the parameter K ac versus frequency. The full analysis and experimental campaign are detailed in [21], where different winding topologies were proposed with the goal of achieving an optimal solution for reduced copper losses. The built motorettes are shown in Fig. 13, with two configurations being realized: q = 2 and q = 4. The winding details are summarized in Table VI. In [21], it was found that the ac losses are significantly dependent on the position of the various strands, especially for high frequency operating points. Hence, in this work, where the results have to be compared against those relative to the hairpin motorettes, the trend of K ac is plotted considering a mean value μ ESM and a standard deviation σ ESM found out leveraging on the experimental statistical method [21]. Fig. 14 shows the experimental comparison between the hairpin and random windings in terms of K ac versus frequency, up to 1 kHz. For the random winding, the minimum and maximum K ac values that give the 66% probability of having a value inside the range μ ESM ∓ σ ESM are considered. It can be noticed that the hairpin solutions perform better than the random ones in the low-frequency range. This is due to the higher slot fill factor and the ensuing lower dc resistance. Most importantly, Fig. 14 highlights that the two hairpin solutions q = 4, k = 8 and q = 4, k = 4 segmented achieve lower losses than the 66% of the possible solutions that can happen with random windings up to ≈900 Hz. These results, besides proving that some hairpin layouts (including the proposed segmented one) can present lower losses than random windings even at high-frequency operations, also demonstrate that the segmented layout presents similar performance to the eightlayer hairpin configuration, albeit with a reduced number of layers per slot, thus potentially leading to a simplification of the manufacturing process.

IX. CONCLUSION
In this work, an improved hairpin winding topology was proposed to reduce ohmic losses at high-frequency operations. This concept, named as segmented hairpin, consists of splitting one or more slot conductors into two or more sub-conductors, similar to the "strand" concept usually implemented in random windings. In this article, it was decided to split two conductors into two sub-conductors, as this was deemed to be the optimal solution in terms of loss reduction and minimization of the manufacturing complexities.
The losses produced at various frequency operations within the proposed segmented hairpin winding were assessed against conventional hairpin and random solutions. Analytical and finite element models were used for such purposes, taking into account both slot and end-winding regions. A simplified 2-D finite element model was implemented to predict losses in the end-windings, thus avoiding the need of building an accurate but very computationally expensive 3-D model. The relevant findings proved that the ac end-winding losses can be significant in some cases, whereas they are regularly overlooked in previous literature.
In terms of loss reduction, promising analytical and finite element results were obtained for the proposed segmented concept. These perceived benefits were then validated by building and testing stator motorettes featuring various winding arrangements. Compared to conventional hairpin layouts, the segmented hairpin solution achieved a loss reduction always higher than 20% starting from ≈600 Hz, reaching a peak reduction of 28% at 1 kHz, thus proving its potential.
Finally, a comparison between random and hairpin windings designed for the same traction application was performed. Both conventional and segmented hairpin layouts provided lower losses than random windings at low frequency, as expected. Additionally and importantly, the proposed segmented hairpin solution achieved loss values similar to random windings up to 900 Hz, thus proving its competitiveness for a broader range of operational frequencies.