My research focuses on the high-frequency AC copper loss of high-speed flat wire motors that are specifically designed for modern electric cars. Electric cars demand compact, high power-density, and highly efficient traction motors. Flat wire windings have become a preferred solution for electric car traction motors because of their high slot fill factor, improved heat dissipation, and superior torque density. However, when such motors operate at high rotational speeds, the operating frequency rises significantly and the rectangular conductors experience severe skin effect, proximity effect, and circulating-current effects. These phenomena lead to a dramatic increase in AC copper loss, which raises the winding temperature and may degrade the insulation system. Consequently, the main objective of my work is to design a flat wire motor for a category-A electric car, thoroughly investigate the origin and distribution of AC copper loss, propose effective suppression techniques, and validate the resulting temperature distribution using three-dimensional finite element analysis. Throughout this thesis, I always keep the electric car application in mind, because the final motor must satisfy typical driving cycles, overload requirements, and the high-speed field-weakening region of an electric car.
1 Introduction and Background
The clean-energy transition has accelerated the development of electric cars. Compared with conventional vehicles, electric cars are driven by a battery-fed electric motor and therefore have zero tailpipe emissions. Governments and automotive companies around the world have made enormous research investments in key electric car components, especially the drive motor. A permanent-magnet synchronous motor is widely used in electric cars because of its high efficiency, high torque density, and reliable structure. With the rapid development of electric car platforms, the drive system must be increasingly compact, lightweight, and able to operate over a wide constant-power speed range. Many modern electric cars adopt flat wire motors to obtain an outstanding slot fill factor of more than 70%. This is in contrast to conventional round-wire motors, where crossing round wires inevitably leave air gaps in the stator slots. The compact rectangular conductors in flat wire motors provide lower DC resistance and better heat conductivity. Nevertheless, at elevated frequencies the large cross-section of a flat wire conductor creates non-negligible eddy-current losses.
The trend toward higher maximum speeds in electric cars has made AC loss suppression even more critical. For example, many high-performance electric cars have announced maximum motor speeds of 20,000 to 30,000 r/min. If the motor has eight poles, the fundamental frequency can exceed 1,300 Hz at 20,000 r/min. Under such a frequency, a 1.6 mm thick copper conductor experiences a skin depth of approximately 1.81 mm. The AC resistance may become several times larger than the DC resistance, and this increased resistance contributes to extra heat. Because electric cars often operate under highly transient urban conditions, the motor must also maintain high efficiency over a wide torque-speed map. Therefore, neither the designer nor the manufacturer can ignore the importance of accurate AC copper-loss estimation and suppression.
In this study, I first determine a specific performance specification that could satisfy an entry-level compact electric car. Then I design an 8-pole 48-slot interior permanent-magnet motor with hairpin-type flat wire windings. I evaluate its electromagnetic performance and identify the main source of copper loss in each conductor layer. I also investigate the mechanical strength of the rotor under centrifugal load to guarantee safe operation at peak speed. Based on the electromagnetic analysis, I propose three winding-level approaches to suppress AC copper loss without changing the outer envelope of the motor: a non-uniform conductor winding configuration, a stranded-conductor winding configuration, and a litz-wire winding configuration. In addition, I compare their effectiveness through finite-element simulations and discuss the practical constraints, such as manufacturing complexity, slot-fill-factor reduction, and DC-loss penalties. Finally, I construct a three-dimensional thermal model of the motor and study the impact of each suppression method on the winding temperature rise. The methods presented here provide a clear route for low-loss and thermally safe flat wire motors in electric cars.
2 Design Requirements and Initial Motor Parameters
For the target electric car application, the motor must be able to drive a compact sedan with a top speed of about 150 km/h. I thus set the peak rotational speed to 20,000 r/min. In order to provide acceptable acceleration, the rated power was selected as 50 kW and the peak power as 100 kW. The continuous torque is 45 N·m while the peak torque is 90 N·m. The rated speed is derived from the required vehicle speed and the gear ratio; in my calculation, the rated speed is about 10,610 r/min. Since an electric car motor is usually required to have a wide constant-power region, the peak speed is approximately twice the rated speed. The major performance requirements are summarized in Table 1.
| Parameter | Value |
| Rated torque (N·m) | 45 |
| Peak torque (N·m) | 90 |
| Rated power (kW) | 50 |
| Peak power (kW) | 100 |
| Rated speed (r/min) | 10,610 |
| Peak speed (r/min) | 20,000 |
| Maximum efficiency (%) | ≥ 96 |
Table 1: Performance specification of the electric-car flat wire motor.
The main dimensions of the machine were determined using classical motor sizing equations. Starting from the output coefficient equation and considering a balance between torque density and manufacturing feasibility, I fixed the stator outer diameter at 190 mm and the axial length at 80 mm. A compact outer diameter and short axial length are essential for installing the motor in the limited under-floor space of an electric car. The 8-pole and 48-slot combination was chosen. This combination is popular in electric cars because it provides a small winding pitch and low torque ripple. The stator inner diameter is 136 mm, leaving a 1.5 mm air gap to the rotor outer diameter of 133 mm. The rotor inner diameter is 60 mm, and the active axial length is 80 mm. The stator core and rotor core are both made from 0.25 mm non-oriented electrical steel B25AHV1300. The permanent magnets are sintered NdFeB N48UH, which has a high coercivity and is appropriate for the high-temperature environment inside an electric car drive unit.
I selected a parallel-slot stator geometry capable of hosting six rectangular conductor layers. A double-layer hairpin winding is used. The slot dimensions are given in Table 2. A parallel slot is convenient for inserting hairpin conductors, and the slot opening is relatively small to reduce leakage flux. The slot opening height is only 0.5 mm and the slot opening width is 1.0 mm. The stator tooth width is 5 mm and the slot depth is 15 mm. Since the slot fill factor of a flat-wire motor is an important metric, I calculated it carefully. With six conductor layers per slot and each conductor measuring 4.0 mm by 1.6 mm, the effective copper area occupies about 66.4% of the slot space. This value is much higher than the typical 40%–50% fill factor of a random round-wire winding in an electric car.
| Parameter | Value (mm) |
| Slot opening width | 1.0 |
| Slot opening height | 0.5 |
| Slot depth | 15 |
| Tooth width | 5 |
| Slot corner radius | 0.3 |
Table 2: Main stator slot dimensions.
The rotor topology was selected according to the high-speed requirement of the electric car. A surface-mounted rotor would suffer from excessive centrifugal force on the permanent magnets when the rotor rotates at 20,000 r/min. Therefore, I adopted an interior permanent-magnet rotor. I considered several interior structures and finally chose a double-V arrangement because it creates a strong reluctance torque, reduces the flux leakage, and achieves a sinusoidal air-gap field. The double-V arrangement also helps weaken the air-gap harmonics and reduces the torque ripple, which is beneficial for the NVH behavior of the electric car drivetrain. The motor model was established in three dimensions, and the electromagnetic simulation was performed on one-eighth of the complete model to reduce computational effort. The overall structural parameters after the initial design are listed in Table 3. This model is then used as the baseline for all subsequent loss studies and suppression evaluations.
| Parameter | Value |
| Number of poles / slots | 8 / 48 |
| Stator outer diameter (mm) | 190 |
| Stator inner diameter (mm) | 136 |
| Rotor outer diameter (mm) | 133 |
| Rotor inner diameter (mm) | 60 |
| Active axial length (mm) | 80 |
| Air-gap length (mm) | 1.5 |
| Parallel branches | 2 |
| Conductor size (mm) | 4.0 × 1.6 |
| Slots per pole per phase | 2 |
Table 3: Initial geometric parameters of the motor.
After creating the finite-element model, I carried out no-load and load analyses. At no load, the air-gap flux density waveform was approximately trapezoidal and the fundamental component was about 0.85 T. The harmonic analysis of the back electromotive force showed a total harmonic distortion of about 3.1%, which is below the common 5% limit for electric car motors. At the rated load, the motor produced 46.7 N·m, which is slightly above the required 45 N·m. The rated efficiency reached 96.53%. The efficiency map was calculated over a wide torque-speed plane. More than 94% of the operating points in the considered region had an efficiency above 85%, while 61% of the points had an efficiency above 95%. The high-efficiency island is broad enough for typical electric car driving cycles. Therefore, the baseline motor successfully satisfies the initial specification.
3 AC Copper Loss in the Initial Motor
In the flat wire winding of the baseline motor, the conductor is substantially larger than the round wires used in conventional electric car motors. Consequently, the frequency-dependent effects are more pronounced. The skin effect occurs because a time-varying current creates a changing magnetic field inside the conductor. According to Lenz’s law, eddy currents oppose the main current flow in the centre of the conductor and reinforce the current near the surface. The result is a non-uniform current density distribution. The severity of the skin effect is usually expressed by the skin depth \(\delta\):
$$
\delta = \frac{1}{\sqrt{\pi f \mu \sigma}}
$$
where \(f\) is the electric frequency, \(\mu\) is the conductor permeability, and \(\sigma\) is the electrical conductivity. For copper at about 100°C, when the frequency increases above 1 kHz, the skin depth becomes smaller than the conductor thickness, leading to an apparent resistance increase. The proximity effect is caused by the magnetic fields produced by adjacent conductors. Since the conductors carry alternating currents and are closely packed in a slot, each conductor experiences the alternating external field of the conductors below it. This external field induces eddy currents that distribute the current to one side of the conductor. In a multi-layer hairpin winding, the lower conductors near the slot bottom experience only their own field and the lower-layer field, whereas the conductors near the slot opening experience the combined magnetic field of all other conductors in the same slot. Therefore, the proximity-effect loss is particularly high at the slot-opening side.
In order to quantify these effects, I calculated the winding loss for each of the six conductor layers separately. Table 4 presents the layer-loss distribution at the rated operating point of 10,610 r/min and rated torque. The first layer means the layer nearest to the slot opening, while the sixth layer means the layer nearest to the slot bottom. It is clear that the AC loss is not evenly distributed.
| Conductor layer | AC copper loss (W) | Percentage of total AC loss |
| Layer 1 (nearest slot opening) | 285.4 | 32.1% |
| Layer 2 | 223.0 | 25.0% |
| Layer 3 | 166.8 | 18.7% |
| Layer 4 | 116.2 | 13.0% |
| Layer 5 | 70.7 | 7.9% |
| Layer 6 (near slot bottom) | 29.8 | 3.3% |
Table 4: AC copper loss distribution in the six conductor layers at rated speed.
The layer nearest the slot opening consumes about one-third of the entire copper loss, and together the first and second layers account for more than half of the total AC copper loss. This result is consistent with the current density distribution in the slot. At a high frequency, the slot leakage magnetic field is strong near the slot opening, causing the current density to concentrate at the top layer. The current-density distribution of a complete slot shows that the maximum current density occurs at the conductor edge adjacent to the slot opening and gradually decays toward the slot bottom. Such a highly non-uniform distribution always increases the effective resistance. I analysed the loss distribution for several speeds from 2,000 to 14,000 r/min. At low speed, the frequency is low and the difference between layers is small. As speed increases, the proportion of the first-layer loss increases rapidly. At 14,000 r/min, the first layer accounts for nearly 45% of the total AC loss, while the sixth layer contributes only a few percent. The ratio between the first- and sixth-layer AC losses can be as high as twenty. Therefore, any successful suppression method must focus on reducing the severe eddy-current loss in the near-opening conductors. This insight was used for all later optimizations.
Another important feature of the AC loss is that the total copper loss increases significantly with speed. At a constant current, the total loss in the winding at 14,000 r/min is much higher than the DC loss predicted from the nominal resistance. The increase is caused by the combination of skin and proximity effects. The proximity effect is usually the dominating term because the rectangular conductors are all located below the slot opening and are exposed to a strong transverse leakage field. For an electric car, the global efficiency map shows that high-speed operation usually occurs during highway cruising, and the increased AC loss may degrade motor efficiency exactly in that region. Hence, reducing AC copper loss is directly beneficial to the real-world driving range of an electric car.
4 Rotor Mechanical Optimization for High-Speed Safety
During high-speed rotation, the rotor of a permanent-magnet motor suffers a large centrifugal load. Because the magnets are placed in interior cavities, the thin bridges, also called magnetic bridges, that separate adjacent cavities are the most stressed parts. If the local stress exceeds the yield strength of the lamination steel, the rotor may be plastically deformed or even fractured. This is a serious concern for an electric car that must accelerate to high speed repeatedly. I therefore carried out a static structural finite-element simulation at the maximum speed of 20,000 r/min. The simulation model included the laminated rotor core and the magnets. I used a friction-contact formulation between the magnets and the rotor iron. A refined mesh with an element size of 0.3 mm was applied in the high-stress regions. The initial analysis showed a maximum Von Mises stress of 576.31 MPa, located in the central magnetic bridge of the magnet cavity. This value is close to the ultimate yield strength of many lamination steels and is too dangerous for practical use.
To reduce the stress without worsening the electromagnetic performance, I first increased the width of the middle magnetic bridge. A wider bridge can better share the centrifugal force. However, a wider bridge inevitably increases the leakage flux and reduces the torque. I therefore scanned the bridge width from 1.2 mm to 2.4 mm and monitored both the peak torque and the maximum stress. The torque decreased almost linearly as the bridge width increased. A width of 1.8 mm reduced the peak torque to 91.2 N·m, which is still above the required 90 N·m. In this case, the maximum stress was reduced to 476.31 MPa. This improvement was still not sufficient because the stress remained higher than the typical allowable fatigue stress of a high-speed rotor.
To further release the stress concentration, I designed a lightweight groove in the rotor core. The groove was positioned in a region where the main flux does not pass, in order to avoid severe electromagnetic deterioration. The groove can reduce the rotating mass and provide a more flexible path for the deformation caused by the centrifugal force. I examined the influence of the groove width and the inclination angle. Three widths, 4 mm, 8 mm and 12 mm, and two angles, 18° and 36°, were simulated. The results show that increasing the groove width considerably reduces the maximum stress. A groove width of 8 mm and an inclination angle of 36° yielded a maximum stress of 373.56 MPa. The angle is important because a suitable inclined groove improves the stress redistribution. I also added circular holes inside the groove to further reduce the mass. The diameter of the relief holes was varied from 4 mm to 10 mm. The best result was obtained with an 8 mm hole diameter, giving a maximum stress of 323.48 MPa. This value is within the safe range of common silicon steels.
| Before optimization | After optimization | |
| Maximum rotor flux density (T) | 2.176 | 2.014 |
| Peak torque (N·m) | 92.7 | 90.9 |
| Torque ripple (%) | 2.38 | 1.17 |
| Iron loss (kW) | 0.851 | 0.901 |
| Maximum Von Mises stress (MPa) | 576.31 | 323.48 |
Table 5: Rotor performance and stress comparison before and after mechanical optimization.
After the optimization, the rotor magnetic saturation is slightly lower and the torque ripple is actually reduced. The iron loss increases slightly, but the mechanical safety is significantly improved. The maximum stress is reduced by about 254 MPa. This optimization step is necessary for a high-speed flat wire motor intended for a production electric car, where the field-weakening operating range and the frequent speed changes impose strict safety margins.
5 Influence of Stator Parameters on AC Copper Loss
Before introducing new winding configurations, I evaluated whether conventional stator-side adjustments can sufficiently suppress the AC copper loss. In an electric car traction motor, the slot geometry and the winding geometry must be selected carefully. Thus, I started with the conductor aspect ratio. The baseline conductor is 4 mm wide and 1.6 mm thick, with an area of 6.4 mm². I compared it with a wider and thinner conductor having the same area, namely 3.2 mm wide and 2 mm thick, while keeping the same slot fill factor. At the rated condition, the baseline conductor produced 892 W total copper loss, whereas the alternative conductor produced 912 W. The thicker alternative conductor has a larger cross-section along the slot-depth direction, which intensifies the skin effect. Consequently, the layer close to the slot opening carries even more current and produces a higher loss. This result confirms that a higher aspect ratio is beneficial for reducing the AC loss, as long as the slot geometry allows a sufficiently thin conductor. However, an extremely thin conductor increases manufacturing complexity and makes the conductor closer to the stator yoke, possibly increasing yoke saturation and reducing torque.
I also analysed the effect of the phase arrangement of the six conductors in adjacent slots. In a real winding, two different phase belts occupy adjacent slots. I compared three possible sinusoidal distributions: all conductors of phase A in one slot and all conductors of phase B in the adjacent slot; two-phase alternation with AAB and BBA; and the most mixed arrangement of ABB and BAA. The mixed arrangement can partially cancel the phase fields between adjacent slots, thus reducing the slot leakage field amplitude and the induced eddy currents. Nevertheless, the simulation showed only about 3% gain at the maximum speed. Therefore, conductor interleaving is not a very powerful approach if one already has to respect the phase-belt rules and the end-winding layout.
Next, I investigated the stator slot geometry. I compared an open slot, a semi-closed slot, and a fully closed slot. The semi-closed and closed slots reduce the leakage flux because the slot opening is smaller. At the rated speed, the open slot increased the AC loss by 3%. At 20,000 r/min, the increase was 14%. On the other hand, the fully closed slot only reduced the loss by a small amount compared with the semi-closed slot. A closed slot also creates an additional magnetic bridge that can easily saturate and produce extra harmonic effects. For a practical hairpin winding and simple manufacturing, a semi-closed slot is the most reasonable choice.
The slot-opening height was varied from 0.3 mm to 1.5 mm. A greater slot-opening height moves the slot bottom closer to the air gap, but reduces the yoke thickness. I observed that increasing the opening height can reduce the leakage field seen by the top conductors, and the AC loss is reduced by about 7% at high speed. However, this parameter is not recommended as a main loss-reduction design variable because the yoke thickness decrease leads to higher iron loss and a higher risk of magnetic saturation. The slot-opening width was also scanned from 0.4 mm to 4 mm. A smaller opening width reduces the leakage flux and the AC loss. The maximum effect was 8% at high speed, but below 2 mm the improvement saturates. Moreover, the opening width must be large enough to insert the hairpin conductors during bending operations. In summary, conventional stator iron-shape adjustments can reduce the AC copper loss by only a few percentage points. The main limiting factor remains the cross-sectional distribution of the rectangular conductors themselves. I therefore moved from the electromagnetic design of the iron core to the design of specialised winding conductors.
6 AC Copper Loss Suppression Using Special Conductor Geometries
6.1 Non-Uniform Conductor Winding
The first suppression concept that I investigated is based on the observation that the loss is not uniformly distributed along the slot height. The slot leakage magnetic field is high near the slot opening and decreases toward the bottom. If all conductors have the same thickness, the conductor near the opening experiences the strongest eddy current. I then proposed a non-uniform thickness profile in which the conductor layers near the slot opening are thinner than those near the slot bottom. Reducing the thickness of the top-layer conductors directly reduces the eddy-current loss caused by the skin and proximity effects. To avoid a significant loss of copper area, the removed copper area is added to the lower-layer conductors, whose operating field is weaker. In this way, the total copper area per slot and thus the slot fill factor can remain exactly the same as the baseline design.
Since the six layers are symmetric with respect to the phase, I divided the six layers into three groups: group one includes layers 1 and 2, group two includes layers 3 and 4, and group three includes layers 5 and 6. The conductor thickness of group one \(h_1\), group two \(h_2\), and group three \(h_3\) is calculated from the thickness ratio \(\delta_1 : \delta_2 : \delta_3\). Under the constraint that the total conductor thickness is 9.6 mm, we can write:
$$
\begin{aligned}
h_1 &= \frac{\delta_1}{\delta_1+\delta_2+\delta_3} \times 9.6,\\
h_2 &= \frac{\delta_2}{\delta_1+\delta_2+\delta_3} \times 9.6,\\
h_3 &= \frac{\delta_3}{\delta_1+\delta_2+\delta_3} \times 9.6.
\end{aligned}
$$
Three non-uniform thickness ratios were selected: 3:4:5, 5:8:11, and 1:2:3. The DC resistance of the whole slot winding is proportional to the sum of the reciprocal thickness of each conductor because the conductor width is the same. With a large thickness ratio, the extremely thin top conductors have higher resistance. The calculated DC loss of the eight-slot winding at 150 A is presented in Table 6. The DC loss increases by 4.5%, 10.9%, and 22.3% for the three ratios, respectively, compared with the uniform baseline. This is the price we pay for suppressing the high-frequency loss.
| Thickness ratio | DC loss (kW) | AC loss at 10,610 r/min (kW) | Total copper loss (kW) | Total loss reduction (%) |
| Uniform 1:1:1 | 0.825 | 2.269 | 3.094 | — |
| 3:4:5 | 0.862 | 1.899 | 2.761 | 10.8% |
| 5:8:11 | 0.915 | 1.645 | 2.560 | 17.3% |
| 1:2:3 | 1.009 | 1.200 | 2.209 | 28.6% |
Table 6: Comparison of non-uniform conductor windings at the peak-torque condition.
For all speeds from 2,000 to 16,000 r/min, the non-uniform winding with the largest ratio 1:2:3 gives the greatest AC loss reduction. At 16,000 r/min, the AC loss reductions are 11.6%, 23.5%, and 46.4% for the ratios 3:4:5, 5:8:11, and 1:2:3, respectively. The current-density cloud chart shows that the maximum current density is reduced by 45.1% and the high-current-density area is reduced by 48.9% for the 1:2:3 configuration. Because the top conductors are thinner, the eddy-current loop in these conductors is limited, so the current distribution in each individual conductor becomes more uniform. The loss distribution is also more balanced along the layers. For the uniform winding, the first-layer loss at 14,000 r/min is about 45% of the total AC loss. For the non-uniform 1:2:3 winding this proportion drops to 34.5%, which is a significant improvement. The non-uniform conductor concept is attractive because it keeps the outer slot profile unchanged, uses the same number of terminal connections, and does not reduce the slot fill factor. One practical concern is that a very thin conductor, for example the top conductor of the 1:2:3 scheme, may be difficult to handle and bend without damage. Nevertheless, the concept demonstrates that a tailored thickness distribution is an effective way to reduce AC loss in a high-frequency flat-wire motor for an electric car.
6.2 Stranded-Conductor Winding
The second approach that I considered is to strand the original rectangular conductor into several smaller rectangular sub-conductors separated by thin insulation. Splitting a conductor in the direction of the slot depth is a natural way to reduce the thickness of each conducting path, and therefore to suppress the skin effect. At the same time, the side-by-side sub-conductors can reduce the eddy-current loss caused by the transverse leakage field. I defined five configurations: the original single conductor; two conductors side by side in the width direction (one row and two columns); two conductors stacked in the thickness direction (two rows and one column); four conductors arranged in two rows and two columns; and six conductors arranged in three rows and two columns. The total conductor area is not exactly preserved because each sub-conductor must be coated with an insulating layer. The slot fill factor decreases slightly from 66.4% for the original conductor to 58.6% for the three-row-two-column configuration. The dimensions of the sub-conductors are listed in Table 7.
| Stranding scheme | Single-wire width (mm) | Single-wire thickness (mm) | Slot fill factor (%) |
| Single (original) | 4.00 | 1.60 | 66.4 |
| One row / two columns | 1.96 | 1.60 | 65.1 |
| Two rows / one column | 4.00 | 0.76 | 63.1 |
| Two rows / two columns | 1.96 | 0.76 | 61.9 |
| Three rows / two columns | 1.96 | 0.48 | 58.6 |
Table 7: Dimensions of the stranded-conductor configurations.
I simulated all configurations under a constant phase current of 150 A at rated speed. Table 8 summarizes the DC loss, AC loss, total loss and the overall loss reduction compared with the original conductor. The configuration with one row and two columns, which is only split along the width direction, gives almost no loss reduction. This result is logical because the magnetic field that dominates the eddy current in a hairpin winding is parallel to the width direction and is weak along the width. Splitting along the width does not shorten the eddy-current path significantly. In contrast, splitting along the thickness direction is very effective. The two-row one-column configuration gives an 11.2% total loss reduction. The four-conductor and six-conductor configurations give further improvements of 14.8% and 20.3%, respectively. The current-density distribution shows that the top edge of the conductor still carries the highest current density, but the maximum value is reduced when the number of layers in the thickness direction is increased. Compared with the non-uniform conductor, the stranded conductor has a lower AC loss only if the number of strands is very high. The drawback is the decrease in the slot fill factor and the corresponding increase in the DC resistance. Moreover, more strands imply more parallel paths and the possibility of circulating currents among them if the end connections are not perfectly symmetrical. In this work the parallel strands are all connected at both ends, but the different positions inside the slot create slightly different induced voltages. These circulating currents can be harmful. In my simulation, I did not include the circulating current between strands because each strand was modelled as an independent conductor connected in parallel through ideal end connections? In practice, the end connections of a hairpin have a finite length and the spread of the strands can help equalize the inductances. Nevertheless, the results confirm that thickness-direction stranding is a valid method, and it can be combined with non-uniform thickness to realize a more uniform current distribution.
| Scheme | DC loss (kW) | AC loss (kW) | Total loss (kW) | Reduction (%) |
| Single conductor | 0.825 | 2.269 | 3.094 | — |
| One row / two columns | 1.048 | 2.198 | 3.246 | −4.9% |
| Two rows / one column | 1.063 | 1.684 | 2.747 | +11.2% |
| Two rows / two columns | 1.081 | 1.584 | 2.665 | +14.8% |
| Three rows / two columns | 1.109 | 1.358 | 2.467 | +20.3% |
Table 8: Loss comparison for different stranding schemes.
6.3 Litz-Wire Winding and Experimental Verification
The third method is the use of litz wire. A litz wire is composed of many thin enameled wires that are twisted or braided in a predetermined pattern. Because each individual wire is very thin, its thickness is much smaller than the skin depth up to the rated inverter frequency. The continuous transposition balances the position of each strand in the magnetic field, so that the induced voltages among strands are equalized and the circulating current is substantially reduced. In the electric-car motor context, the original rectangular conductor can be replaced by a formed litz-wire conductor, which has a rectangular outer cross-section and therefore can still achieve a relatively high slot fill factor. I selected two commercially available formed litz-wire types: type 1 has a strand diameter of 0.1 mm and 250 strands; type 2 has a strand diameter of 0.2 mm and 150 strands. Both are designed to have an outer width of 4 mm and an outer thickness of 1.6 mm. However, due to the unavoidable gaps between the round strands, the effective copper area is lower. The actual slot fill factors for type 1 and type 2 were 50.4% and 47.8%, respectively. The corresponding DC loss values are 1.124 kW and 1.185 kW under 150 A, which are substantially higher than the 0.825 kW of the solid conductor. In spite of this, the AC loss is reduced so significantly that the total loss is still much lower. At 10,610 r/min, the total copper loss with litz-wire type 1 is 1.908 kW, a 38.3% reduction relative to the solid copper flat wire, while type 2 gives 1.838 kW, a 40.6% reduction. At high speed, the advantage of the litz wire is even more obvious. For this reason, I recommend choosing a sufficiently small strand diameter so that at the maximum operating frequency the strand radius is less than the skin depth. In the present motor, the maximum fundamental frequency is 1,333 Hz and the copper skin depth is about 1.81 mm. Both 0.1 mm and 0.2 mm strand diameters are much smaller than this value, so they are both in the inductive-loss regime. The higher strand diameter gives a lower total loss because it has fewer inter-strand gaps and thus a larger effective copper area, while the strand diameter is still small enough to prevent skin effect inside a strand.
To verify the frequency dependence and to compare different litz geometries, I built several E-core inductors using four litz-wire types with strand diameters of 0.1 mm and 0.2 mm and strand numbers of 150 and 250. I measured the AC resistance from 50 Hz to 2,500 Hz with a precision impedance analyzer. The resistance of each litz wire increases slowly from 50 Hz to about 1,000 Hz, and then increases faster above 1,000 Hz. At 2,500 Hz the resistance can be more than two times the resistance at 50 Hz. For the same strand diameter, a larger number of strands reduces the resistance because the total copper area is larger. For the same number of strands, the wire with a larger strand diameter has lower resistance at low frequency but is more sensitive to frequency. In the frequency range important for an electric car (500 Hz to 2,000 Hz), the formed litz wire with a 0.2 mm strand diameter and 150 strands appears to offer the best compromise between DC resistance and AC loss. The experimental results also show that the skin-effect model alone cannot fully describe the resistance increase; the proximity effect among strands is a significant contributor. Therefore, when selecting litz wire for a high-speed flat wire motor, one must consider both the fundamental frequency and the harmonic content of the pulse-width-modulated inverter. The litz wire is generally more expensive and less robust in mass production than a solid copper hairpin, so its use should be justified by the high-speed efficiency gain and the thermal benefits.
7 Thermal Analysis and Comparison of Suppression Methods
After showing the loss reduction, I evaluated the temperature distribution of the motor because the winding temperature is the ultimate limit for the reliability of an electric-car motor. A lower AC copper loss directly reduces the heat source inside the slot, while an improved current distribution also equalizes the local heat generation. I built a three-dimensional finite-element thermal model using one-eighth of the complete motor due to symmetry. The model includes the stator core, rotor core, permanent magnets, windings, slot insulation, and the housing. The cooling method is a water jacket outside the stator. The cooling water temperature is set to 40°C and the ambient air temperature is 30°C. In the slot region, the copper conductors, the enamel insulation, the slot liner, and the impregnation materials are replaced by an equivalent homogeneous material with an anisotropic thermal conductivity. For the air-gap heat transfer, I considered a turbulent flow condition because the rotor surface speed is high. The equivalent thermal conductivity of the air gap was calculated from the Nusselt number according to the classic Taylor-Couette flow correlations. The stator and rotor iron cores have different axial and radial thermal conductivities because of the lamination stack. The heat-transfer coefficient of the water cooling duct was obtained from the Dittus-Boelter correlation:
$$
Nu = 0.023 \, Re^{0.8} \, Pr^{0.4}
$$
where \(Nu\) is the Nusselt number, \(Re\) is the Reynolds number and \(Pr\) is the Prandtl number. I then converted the Nusselt number into an equivalent heat-transfer coefficient on the stator housing surface. Since the motor is operated at a long high-speed cruise point, I selected the rated operating condition of 10,610 r/min and 80 A of phase current. The losses in each layer were extracted from the electromagnetic simulations and loaded into the thermal model as volume heat sources. The iron loss, magnet eddy-current loss, and copper loss for the baseline motor are given in Table 9.
| Component | Loss value (W) | Loss density (W/m³) |
| Stator core | 570 | 972,893 |
| Rotor core | 9 | 30,873 |
| Permanent magnet | 16 | 49,535 |
| Layer 1 winding | 422.9 | 721,887 |
| Layer 2 winding | 360.5 | 615,312 |
| Layer 3 winding | 304.3 | 519,388 |
| Layer 4 winding | 253.7 | 433,074 |
| Layer 5 winding | 208.2 | 355,430 |
| Layer 6 winding | 167.3 | 285,536 |
Table 9: Loss input data for the baseline motor thermal model.
The steady-state temperature field shows that the winding is the hottest component. The maximum temperature of 78.1°C occurs in the end-winding region. This is expected because the end winding is exposed to the internal air, whose convective heat-transfer coefficient is much lower than that of the water-cooled stator back iron. Along the stator radial direction, the stator teeth and yoke are cooled by the water jacket, so their temperatures decrease toward the outer housing. The rotor and the permanent magnets have a temperature of about 64°C, which is acceptable for N48UH magnets and does not cause demagnetization. The winding layers near the slot opening are exceptionally hot because they not only have the highest loss but are also farther away from the cooling water than the slot-bottom layers? In fact, the slot-bottom layers are closer to the stator yoke and the water jacket, while the slot-opening layers are close to the air gap and the hot rotor. Therefore, the top layers have the highest temperature. This thermal finding further emphasizes the need to suppress the top-layer losses.
I repeated the thermal analysis for the three most promising suppression configurations: the non-uniform conductor with the ratio 1:2:3, the stranded conductor with three rows and two columns, and the formed litz wire type 2. The loss values in each layer for each configuration were used as heat sources. For the litz wire, because the finite-element simulation cannot easily model each strand, I applied a uniform volume heat source in every layer equal to the average value calculated from the total AC loss. The maximum temperatures of the main components are compared in Table 10. The non-uniform winding reduces the maximum winding temperature from 78.1°C to 74.3°C, a reduction of about 4 K. The three-row/two-column stranded winding reduces the maximum winding temperature to 76.4°C, even though its total loss is similar to that of the non-uniform scheme. The reason is that the insulating layers of each strand reduce the effective thermal conductivity inside the slot, causing the generated heat to be removed less efficiently. Meanwhile, the litz wire gives the greatest temperature reduction, to 70.5°C. This is a drop of about 8 K compared with the baseline. In addition, the litz wire shows a more uniform temperature distribution inside the slot because its AC loss is distributed almost equally among the layers. The stator core temperature is reduced from 76.4°C to 68.5°C, and the rotor and magnet temperature is reduced from 64.3°C to 53.9°C. This global temperature reduction has a positive impact on the life of the insulation and on the magnet stability. It also allows the motor to run for a longer overload period before reaching the thermal limit.
| Component | Baseline (°C) | Non-uniform 1:2:3 (°C) | Stranded 3×2 (°C) | Litz wire type 2 (°C) |
| Stator core | 76.4 | 72.2 | 74.2 | 68.5 |
| Rotor core | 64.3 | 63.7 | 64.1 | 53.9 |
| Winding | 78.1 | 74.3 | 76.4 | 70.5 |
| Permanent magnet | 64.3 | 63.7 | 64.1 | 53.9 |
Table 10: Maximum temperature comparison for different AC-loss suppression schemes.
From the thermal point of view, the litz-wire winding is the most effective because it drastically lowers not only the total loss but also the local heat concentration. The non-uniform conductor is the second-best scheme and has the advantage that the slot fill factor is preserved. The stranded conductor is less advantageous because the multiple thin insulation layers impede the heat transfer. Nevertheless, all three methods can be used in different situations. In an electric car motor, where the space is limited and thermal management is critical, the temperature reduction achieved by the litz-wire winding can be exploited to increase the continuous torque or to reduce the cooling water flow rate, thus improving overall system efficiency. On the other hand, the cost of the formed litz wire is higher and the winding production requires additional handling, so manufacturers should compare the additional cost with the benefit of reduced battery energy consumption over the lifetime of the electric car.
8 Conclusion and Outlook
In this thesis, I have presented a complete study of AC copper loss in a high-speed flat wire motor for electric cars. I began with the design of an 8-pole 48-slot interior permanent-magnet motor rated 50 kW and 45 N·m, with a peak speed of 20,000 r/min. The motor meets the target efficiency of more than 96% and has a sufficiently high slot fill factor. The loss distribution in the slot demonstrates that more than half of the AC loss is concentrated in the first two layers near the slot opening, which is a consequence of the skin effect, the proximity effect, and the rapidly changing leakage field in the slot. I also optimized the rotor mechanical structure by widening the magnetic bridge, adding a lightweight relief groove and an 8 mm relief hole. The maximum stress was reduced from 576 MPa to 323 MPa, ensuring that the rotor is safe at the maximum operating speed of the electric car.
I then investigated the possibilities of reducing the AC loss by adjusting the stator and winding parameters. I found that merely changing the slot opening width, slot opening height, slot shape, or conductor aspect ratio can provide only a few percent of loss reduction. This is not enough for high-frequency operation. Consequently, I proposed and evaluated three winding-level suppression methods: non-uniform conductor thickness, thickness-direction strand splitting, and formed litz wire. In the non-uniform winding, a thickness ratio of 1:2:3 from the opening to the bottom yields a total copper loss reduction of 28.6% at the rated condition compared with the uniform winding. In the stranded winding, splitting in the thickness direction is much more effective than splitting in the width direction. A six-conductor configuration with three rows and two columns reduces the total copper loss by 20.3%. The formed litz-wire winding gives the largest reduction of about 40% at the same operating point, because the thin strands suppress both skin and proximity effects and the transposition equalizes the induced voltages among the strands. I also verified through AC-resistance tests that the litz-wire resistance is strongly frequency dependent and that the selection of the strand diameter and strand number should be made according to the target frequency range. The measured resistance data support the simulation conclusion that a strand diameter of 0.2 mm with 150 strands is a good compromise for this electric-car drive application.
The final thermal analysis compared the three suppression schemes. The litz-wire winding achieves the lowest maximum winding temperature, about 70.5°C under the selected rated condition, which is 7.6 K below the baseline. The non-uniform winding achieves a 3.8 K reduction, while the stranded winding achieves a 1.7 K reduction. The litz-wire winding also leads to a more uniform temperature distribution because the loss is distributed evenly among the layers. Thus, for high-speed flat wire motors in electric cars, the litz-wire winding is the most robust solution from both the loss and thermal points of view, although its commercial viability depends on the cost and the required production rate. The non-uniform conductor is promising because it can be manufactured with conventional hairpin bending if the minimum thickness is not too small. In the future, I plan to manufacture prototype motors with the non-uniform conductor and the formed litz-wire winding to validate the simulation results. I also intend to study the coupling between the AC loss and the temperature field in an iterative way, considering the temperature-dependent resistivity of copper. Furthermore, the influence of the pulse-width-modulated current harmonics on the AC loss needs to be investigated because an electric car inverter introduces a wide spectrum of high-frequency harmonics. I believe that the results of this thesis provide an effective pathway for designing low-loss, high-speed flat wire motors for the next generation of electric cars.