Analysis and Optimization of the Winding Loss of Flat-Wire Motors

Abstract

The flat-wire motor has the characteristics of small size, low noise, high slot fill factor and good thermal conductivity in the slot. It can significantly improve the power density of the motor and is widely used in electric vehicles. The skin effect and proximity effect of the flat wire under high-speed conditions lead to high loss. Based on the established finite element model of a two-dimensional flat-wire motor, this paper first studies the high-frequency loss of different winding layers and the conductor sizes of each layer. Secondly, the influence of the magnetic field on AC loss is reduced by optimizing the tooth-tip height and tooth-tip width. Finally, it is verified that the high-frequency loss is reduced by 16% with the optimized layers, conductor sizes and tooth-tip sizes under the drive condition of the CLTC-P (China Light-duty Test Cycle—Passenger).

1. Introduction

As the propulsion source for new energy vehicles (NEVs), the caliber of the drive motor is paramount, directly influencing the performance benchmarks of the NEV. NEV stands for “new energy vehicle” and is a term used to describe all types of electric vehicles, from battery-powered fully electric vehicles to plug-in hybrid cars. The ongoing enhancement in the dynamic and economic attributes of NEVs has steered the development of drive motors towards the characteristics of high-speed operation, elevated power density and superior efficiency. Motors with flat-wire windings, acclaimed for their high power and torque densities, have consequently attracted considerable interest and are now widely integrated into the NEV sector. The hairpin windings and assorted motor configurations are illustrated in Figure 1. The comparison of different winding motors is shown in Figure 2. Researchers, including Takashi Ishigami, have engineered a stator structure for hybrid electric motors featuring a rectangular wire distribution winding [1]. This design not only boasts high productivity but also offers robust design adaptability. The team elucidated the fabrication process of the flat-wire windings and conducted calculations for AC losses predicated on the geometric configuration and interconnection modalities of the conductors. The outcomes of these calculations are commensurate with the precision demands of the engineering industry.

The power density of electric motors is frequently bounded by thermal limitations. There are two predominant methodologies to augment the power density of electric motors: firstly, by mitigating internal losses to reduce the heat-generating sources; secondly, by enhancing the thermal dissipation capabilities of the motor, thus enabling it to withstand increased levels of losses. The internal losses within an electric motor are predominantly categorized into copper losses, iron losses, eddy losses within the permanent magnets and mechanical losses. The copper losses, which arise from the conduction of current through the motor’s windings, constitute the most substantial portion of these losses. The stator winding, serving as the pivotal region for the conversion of electromagnetic energy, is the primary source of thermal losses and, to a significant degree, dictates the efficiency of the motor. Hence, the mitigation of copper losses represents a principal research focus for the elevation of motor power density. Motors employing flat-wire windings possess a larger cross-sectional area of copper conductors, which, under conditions of high-frequency operation, are subject to pronounced skin and proximity effects. These effects lead to an escalation in high-frequency AC copper losses, which can negatively influence the motor’s efficiency and thermal integrity. However, with the continual advancement of research, the impediments to the application of flat-wire motors are progressively being surmounted. Mircea Popescu et al. [2] based research on the field-circuit-coupled finite element method to calculate and compare the current density distribution and AC losses of hairpin windings with different reset topologies. The current density distribution and AC losses of hairpin windings with different winding topologies were calculated and compared, and the effects of different topologies and winding connections on AC losses at different speeds and loads were investigated [3]. Jiang Hua et al. [4] from Shanghai University, to improve the accuracy of the 2D model simulation calculation of AC losses, studied the use of external circuit co-simulation to achieve the simulation accuracy of the 3D calculation model. Yue Wu, Jianying Chen et al. [5,6] proposed a maximum efficiency algorithm to minimize the copper loss to calculate the copper loss of the motor, to take into account the calculation accuracy and the computation time, the analytical calculation method and the hybrid machine algorithm, and a fast semi-analytical calculation method based on flat-wire winding AC copper loss by reducing the computational cycle and simplifying the number of computational grids, which improves the computational efficiency in both time and space dimensions. Qiang Li [7] binduced a hybrid analytical–finite element analysis (FEA) method for the fast calculation of eddy current losses in rectangular cross-section wires based on tangential and axial leakage flux distributions in the slots to optimize the efficiency by choosing the cross-section specification of the flat wires to achieve a compromise between AC and DC winding losses, based on the characteristics of PMSM with many turns and few strands [8]. Christian Du-Bar et al. [9] compared flat-wire motors and round-wire motors in electric vehicle applications while the conductors between the conventional winding and the hairpin winding were compared. A comparison of eddy current losses in the conductor between hairpin windings was made by Christian Du-Bar et al. and it was concluded that the AC losses in flat copper wire windings at high speeds are much higher than those in conventional windings [10]. Zhang Bingyi et al. used the 2D finite element method to study the AC copper loss of flat copper wire winding at high frequency and summarized the optimum width-to-thickness ratio of flat copper wire winding at different frequencies but did not study the effect of conductor cross-section dimensions on AC loss with different numbers of layers. Raldo Preci et al. [11] used simulation analysis to investigate whether reducing the height of the flat-wire winding legs to reduce the slot filling factor can affect the AC loss of the flat copper wire winding at different stator parameters. AC losses were studied by analyzing the relationship between different stator parameters (tooth width, slot opening, etc.) and stator winding copper losses as a means of developing an optimal design of individual stator slots, which does not take into account the effect of slot opening parameters on high-frequency AC losses [12,13,14].

The eddy current copper loss of the motor is affected by many factors, such as the shape of the slot, the size of the slot, the size and position of the flat wire, and the number of winding roots. Therefore, it is not completely accurate to study the influence of a single factor on the loss. It is imperative to account for the synergistic effects of these factors on the alternating current (AC) copper losses within the windings under high-frequency operation. Consequently, there is a need to expand upon the current body of research, with a focus on the motor’s high-speed operation and the driving conditions specific to new energy vehicles, to conduct a more comprehensive analysis of the factors that affect the losses in flat-wire windings. This research should culminate in the design of a more rational motor model. The research is centered around a high-speed flat-wire permanent magnet synchronous motor utilized in the new energy vehicle sector. A two-dimensional finite element model is constructed to scrutinize the effects of the flat conductor’s dimensions, the stratification of the windings and the tooth-tip geometry parameters on the winding losses. The optimal flat-wire winding scheme is identified through this analysis. Subsequently, the performance of the motor model is optimized and analyzed under the CLPC-P (China Light-duty Plug-in Hybrid Electric Vehicle Test Procedure) driving conditions, aiming to design a motor model with superior performance characteristics.

2. Flat-Wire Permanent Magnet Synchronous Motor Loss Model

2.1. AC Loss Theory

The loss in the winding of the motor is generally composed of two kinds of loss, namely, alternating current loss (AC loss) and direct current loss (DC loss).

$$P_{cu}=P_{AC}+P_{DC}$$

(1)

where $P_{cu}$ is the total winding loss; $P_{AC}$ is the AC loss; and $P_{DC}$ is the DC loss. $P_{DC}$ is as long as the influence of the winding DC resistance, i.e., $P_{DC}\propto R_{DC}$.

The mechanism of DC loss is relatively simple and can be calculated by some empirical formulas, while AC loss is a complex conductor loss phenomenon, which is mainly affected by the proximity effect and skin effect.

The skin effect refers to the phenomenon where alternating current (AC) flows through a conductor and, as the frequency of the electrons increases, the current tends to concentrate on the surface of the conductor. This leads to a decrease in the current density from the surface towards the center, rather than an even distribution across the entire cross-section of the conductor. The higher the frequency, the more significant the skin effect. Skin depth is defined as follows:

$$\delta =\sqrt{{\displaystyle \frac{1}{\pi f{\mu }_0\sigma }}}$$

(2)

where $\delta$ is the skinning depth, f is the motor operating current frequency, and ${\mu }_0$ and $\sigma$ are the conductor’s magnetic permeability and electrical conductivity.

When two conductors close to each other are fed with alternating current, it causes each conductor to be simultaneously in the magnetic field generated by itself and the electromagnetic field generated by the current of the other conductor, thus inducing an eddy current, which becomes the proximity effect. Losses are defined as follows:

$$P_e={\displaystyle \frac{\pi d^4{\omega }^2{B}_n^2}{128{\rho }_c}}$$

(3)

where $P_e$ is the loss per unit length, d is the diameter of the conductor, $\omega$ is the angular frequency, and ${\rho }_c$ and $B_n$ are the resistivity and flux density, respectively.

For AC losses, their increase relative to DC losses is usually expressed using the AC loss coefficient $K_{A}C$:

$$P_{AC}=K_{AC}{P}_{DC}(K_{AC}>1)$$

(4)

Assuming that the windings are insulated in the slot and ignoring the eddy current magnetic field generated inside the slot, the AC loss coefficients can be calculated for the round and flat-wire conductors in the first layer:

$$K_{AC}=1+{\displaystyle \frac{1}{4}}{\left({\displaystyle \frac{{\sum }_{l-1}NI}{N_1{I}_0}}\right)}^2{\left(\sqrt{{\epsilon }_1}{\displaystyle \frac{h_c}{\delta }}\right)}^4$$

(5)

$$K_{AC}=C_1\left(\eta \right)+{\left(1+2{\displaystyle \frac{{\sum }_{l-1}NI}{N_1{I}_0}}\right)}^2{C}_{11}\left(\eta \right)$$

(6)

where ${\sum }_{l-1}NI$ is the sum of the currents in all conductors below the the layer l; $h_c$ is the diameter of the circular conductor. $N_1{I}_0$ is the sum of the currents at layer l. $\delta$ and ${\epsilon }_1$ is the skinning depth and the copper occupancy slot ratio for each layer l, which is calculated by the following formula:

$${\epsilon }_1={\displaystyle \frac{N_1\left(\pi \frac{h_c^2}{4}\right)}{w_1{h}_c}}$$

(7)

where: $w_1$ is the slot width at the l layer conductor.

The remaining $C_1\left(\eta \right)$ and $C_{11}\left(\eta \right)$ can be calculated from the following two equations:

$$C_1\left(\eta \right)={\displaystyle \frac{\eta }{2}}{\displaystyle \frac{sinh\left(\eta \right)+sin\left(\eta \right)}{cosh\left(\eta \right)-cos\left(\eta \right)}}$$

(8)

$$C_{11}\left(\eta \right)={\displaystyle \frac{\eta }{2}}{\displaystyle \frac{sinh\left(\eta \right)-sin\left(\eta \right)}{cosh\left(\eta \right)+cos\left(\eta \right)}}$$

(9)

$$\eta =\sqrt{{\epsilon }_1}{\displaystyle \frac{h_c}{\delta }}$$

(10)

where $h_c$ is the height of the flat conductor.

2.2. Main Parameters

The performance indexes and basic parameters of the motor are shown in

Table 1. Motor performance indicators.

Parameter	Value	Parameter	Value
Rated torque (N·m)	180	Rated power (kW)	115
Rated speed (r/min)	6000	Peak power (kW)	225
Maximum speed (r/min)	12,000	Efficiency (%)	96

and

Table 2. Main structural parameters.

Parameter	Value	Parameter	Value
Stator outer diameter (mm)	250	Rotor inner diameter (mm)	135
Stator inner diameter (mm)	175	Tooth-tip height (mm)	0.2
Slot width (mm)	5.5	Tooth-tip width (mm)	3
Slot depth (mm)	25.5	Slot shoulder angle (°)	20

, and the motor is a double-deck interior permanent magnet synchronous motor.

The two-dimensional finite element model of the motor is shown in Figure 3. The motor adopts 8 poles and 48 slots; the stator slots are designed as rectangular slots, the flat-wire winding is adopted to improve the efficiency and power density of the motor, and the rotor is a built-in “one” type double-layer permanent magnet structure, which can effectively increase the speed range of the motor and the percentage of the high-efficiency zone.

The main design parameters are shown in Figure 4, where h is the slot opening height and w is the slot opening width.

In this study, advanced electromagnetic simulation technology is used to conduct a comprehensive simulation analysis of the designed motor model, and an accurate magnetic field distribution and electromagnetic force calculation are carried out to evaluate the performance of the motor. The mesh generation of the 2D model is shown in Figure 5. In the key areas such as air gap, winding and boundary layer, finer meshes are used to capture subtle changes and accurate calculation results in areas where changes are more intense. In the non-critical region, the mesh gradually becomes wider, reducing unnecessary calculations, and each mesh element is close to the ideal shape. Through multiple simulations, the results under different grid densities are compared to ensure that the results converge with the refinement of the grid. The electromagnetic cloud diagram of the electromagnetic simulation is shown in Figure 6. As shown in Figure 7, by analyzing the electromagnetic torque waveforms at different rotor positions, it is verified that the motor can produce smooth and continuous torque output, which is in line with the expected operating characteristics. As shown in Figure 8, the efficiency MAP analysis shows that the efficiency of the motor exceeds 95% over a wide operating range, which proves the superiority of the design and the high-efficiency energy conversion capability.

3. Influence of Stator Windings on AC Losses in Flat-Wire Motors

3.1. The Effect of the Number of Conductor Layers on AC Copper Loss

Flat-wire motors oriented to electric vehicles have relatively fewer conductors but the same number of turns in the slots, and the conductors are solid compared to traditional round-wire motors. As a result, the skin and proximity effects are also more significant. The AC loss of the winding is much higher than the DC loss under high-speed operation, in which the number of layers of the winding conductor is a key factor to reduce the AC loss of the winding.

In this paper, to explore the influence of conductor layer numbers on AC copper loss, three flat-wire motor models of 6 layers, 8 layers and 10 layers were set up for the modeling calculation, as shown in

Table 3. Main parameters of the model.

Parameter	Model A	Model B	Model C
Conductor area (mm2)	88.9	88.9	88.9
Conductor layers	6	8	10
Slot fill factor	0.8176	0.8169	0.8173
Length/width (mm)	4.3/3.45	3.7/2.98	3.33/2.67
Aspect ratio of conductor	1.25	1.25	1.25

, keeping the total conductor cross-sectional area and aspect ratio in a single slot unchanged, the conductor length and width narrowed proportionally with the increase in the number of layers, and the same number of parallel branching circuits and the same connection method as shown in Figure 9.

The AC losses of different layers of flat copper wire windings under a rated speed of 6000 r/min are shown in Figure 10. It can be seen that the AC copper loss mainly exists in a conductor near the tooth tip and slot opening. This is because the main component of AC copper loss is the slot flux leakage. The closer to the top position of the slot or at the slot opening, the smaller the influence of leakage flux and the larger the influence of the skin effect and proximity effect. As the number of layers increases, the total cross-sectional area of the conductor remains unchanged and the cross-sectional area of individual conductors becomes smaller, reducing the AC copper loss caused by flux leakage.

The AC losses generated at different numbers of conductor layers as the speed increases are shown in Figure 11. As the number of conductor layers increases, the cross-sectional area of a single flat wire decreases and the skin effect is weakened, which corresponds to a decrease in the AC copper losses generated.

Table 4. Losses under CLTC-P driving cycle.

Number of Conductor Layers	6	8	10
AC copper loss (W)	48.88	37.37	40.27
Total loss (W)	125.94	101.86	108.41
Efficiency (%)	96.04	96.78	96.58

shows the copper loss and total loss of the motor under the CLTC-P drive cycle. It can be seen that, when the number of winding layers is increased from 6 to 8, both the copper losses and the total efficiency decrease. However, when the number of winding layers is further increased from 8 to 10, the losses slightly increase. At the same time, the efficiency is reduced. This is because the increase in the number of layers will increase the ratio of the area of insulating material, due to the additional insulation layer between the winding layer caused by the reduction of the fill factor, which usually leads to an increase in DC copper losses, giving the flat-wire motor of high-power density an advantage in reduction. As the number of layers increases, the self-inductance and mutual inductance between the windings will increase, increasing the overall inductance value. As the slot fill factor increases, the leakage reactance will also increase. The change in reactance value will directly affect the performance, efficiency and control characteristics of the motor. Combined with the table considering the complexity of the actual production of motors, the number of layers of flat wires should not be too large, and the selected flat-wire winding prototype is the eight-layer flat-wire winding.

AC loss at different time points is shown in Figure 12. The maximum loss of 8 layers is significantly lower than that of 6 layers, but the maximum loss of 10 layers is slightly increased. As shown in Figure 13 where the drive cycle envelope is presented, the torque-speed loss cloud diagram is established according to the requirements of CLTP-P. Under the winding loss map of an electric machine, the loss and the need for motor cooling can be better understood.

3.2. Effect of Conductor Size on AC Copper Losses

The flux density in the slot has a significant effect on the AC copper losses. To reduce AC losses, conductor width and height can also be optimized to avoid flux leakage near the stator slot openings. Optimization of conductor dimensions should also be considered when optimizing the motor. To reasonably assess the effect of the conductor aspect ratio on losses, a flat-wire motor with different conductor sizes ranging from 1.0 to 2.2 is modeled with the constraint of a constant conductor cross-sectional area under the premise of ensuring the stator outer diameter remaining unchanged, and the simulation results of AC losses with different numbers of layers are shown in Figure 14.

With the increase in the aspect ratio at different layers, the AC losses are reduced and, at 10 layers, the aspect ratio is too small, which will lead to too large a slot depth; the slot flux leakage increases and the AC losses of 10-layer windings are larger than those of 8-layer windings. Therefore, the 8-layer winding motor is selected to set up three flat-wire motor models with aspect ratios of 1, 1.6 and 2 layers, respectively, for modeling calculations, keeping the total conductor cross-sectional area in a single slot unchanged, as shown in

Table 5. Main parameters of models.

Parameter	Model D	Model E	Model F
Conductor area (mm2)	88.9	88.9	88.9
Conductor layers	8	8	8
Slot fill factor	0.8174	0.8162	0.8176
Length/width (mm)	3.3/3.3	4.22/2.64	4.7/2.36
Aspect ratio of conductor	1.	1.6	1.2

.

Figure 15 shows the loss distribution of three different models under eight layers of windings. The simulated AC losses are 1226 W, 402.6 W and 343.3 W. It can be seen that the smaller the length–width ratio of the 8-layer conductor is, the higher the copper loss of the conductor closest to the tooth-tip layer is and the larger the ratio to the total copper loss is. The size of the difference in the impact of copper loss mainly lies in the conductor across the slot leakage magnitude of different sizes; as the conductor aspect ratio increases, the width decreases and the magnetic field distribution of the amplitude drop along the bottom of the slot decreases; from the results of the model of a conductor, the leakage magnitude across the slot is the largest, corresponding to the generation of AC copper consumption also being the largest.

As shown in

Table 6. Core flux density and losses of different models.

	Model D	Model E	Model F
Core flux density	0.9138 T	1.158 T	1.249 T
Core losses	454.05 W	555.53 W	516.31 W
AC losses	1226 W	402.6 W	343.3 W

, as the aspect ratio of the winding increases, the AC loss gradually decreases but, during the period of 1–1.6, the core loss increases and then gradually decreases, but the total loss still gradually decreases. At the same time, the flux density of the magnetic core gradually increases and the inductance value of the motor will gradually increase, which will affect the dynamic performance of the motor. At the same time, when the aspect ratio is 2, the torque of the motor decreases.

Figure 16 shows the simulation results of AC losses for eight-layer winding motors with different aspect ratios at different speeds. From the figure, it can be seen that increasing the aspect ratio of the conductor can effectively reduce the AC loss of the winding in the slot under the condition that the total conductor cross-sectional area remains unchanged. This is because, under the condition of the same area of the flat-wire winding, with the increase in the aspect ratio, the circumference of the flat-wire winding will increase and the AC loss of the winding will decrease. When the winding aspect ratio increases to a certain extent, it will shorten the width of the stator teeth, resulting in oversaturation of the magnetic density of the teeth, and the slot leakage increases, exacerbating the winding AC losses. At the same time, the AC copper loss of flat-wire motors increases rapidly with the increase in speed, so flat-wire motors are not suitable for long-term operation at high speeds.

In the optimization of aspect ratio for the suppression of AC losses, the motor torque output performance will also be affected, with the conductor width increasing, the corresponding stator yoke part gradually shortening and the magnetically saturated situation of the yoke becoming more serious, so that the motor output torque capacity shows a trend of first increase and then decrease, as shown in Figure 17. Therefore, taking into account the motor’s AC losses and torque output and performance, the conductor aspect ratio of 1.6 near the electromagnetic torque reaches the maximum, combined with the conductor aspect ratio on the loss of the impact of the winding aspect ratio of 1.6, that is, the flat conductor cross-section length of 4.22 mm and width of 2.64 mm.

4. Influence of Flat-Wire Motor Stator Core Slot Parameters on AC Copper Losses

4.1. Effect of Slot Shape on AC Copper Loss

In addition to the conductor parameters of the stator parameters having a certain impact on AC losses, the core parameters also have a certain impact. The tooth tip has a great influence on the magnetic circuit of the stator tooth tip, and the stator tooth tip will affect the size and distribution of the magnetic density in the slot to a certain extent, which in turn affects the winding losses.

As shown in Figure 18, by comparing the magnetic density under the four tooth-tip shapes, it can be found that the tooth-tip parameters have a great influence on the magnetic circuit of the tooth crown. The larger the tooth-tip height, the farther the distance from the permanent magnet, the smaller the magnetic density and the smaller the loss of the winding affected by the permanent magnet.

The losses induced in the conductor under different tooth-tip widths and tooth-tip heights are shown in Figure 19. In the case of a certain tooth-tip width, the conductor loss decreases with the increase in the tooth-tip height; when the tooth-tip height is certain, the losses induced in the conductor inside the slot increase with the increase in the conductor width. Therefore, to assess the loss conditions of different tooth-tip openings, conduct better thermal management and thus select the optimal tooth-tip dimensions, it is necessary to analyze the impact of tooth-tip width and height on AC losses. This will enhance the efficiency of the system.

4.2. Effect of Tooth-Tip Width on AC Copper Loss

In the case of the same tooth-tip height h, the wider the tooth-tip, the greater the conductor loss caused by the permanent magnet, and the winding loss under different tooth-tip widths is shown in Figure 20. It can be seen that, regardless of the rated condition or high-speed condition, when the tooth-tip width is changed between 0.5 mm and 2.5 mm, the AC loss of the winding due to the permanent magnet does not change much and, when the tooth-tip width is 4 mm, the increase in the conductor loss is larger, which shows that changing the width of the tooth-tip opening in a certain range will not significantly reduce or increase the AC loss of the rectangular tooth-tip, but, when the width of the tooth-tip increases to a certain value, the AC loss of the winding caused by the permanent magnet will not be significantly reduced or increased. AC losses in the windings due to permanent magnets increase more substantially. The actual placement of the flat-wire winding should also be taken into account when selecting the slot width, where the tooth-tip opening width needs to be greater than the conductor width.

4.3. Effect of Tooth-Tip Opening Height on AC Copper Loss

The tooth-tip opening height is one of the important factors affecting the AC losses of flat-wire motor windings. When the tooth-tip opening height increases, the conductor in the slot is far away from the permanent magnet, which makes the magnetic resistance at the tooth-tip opening smaller, which also makes it easier for the permanent magnet magnetic field to pass through the tooth-tip closure at the slot opening, thus protecting the conductor in the slot from the influence of the permanent magnet magnetic field. Therefore, precise control of the slot opening height is required to minimize motor losses. The slot opening height is modeled with different dimensions ranging from 0.2 to 2 mm, keeping other motor parameters unchanged, and the length of the stator yoke is shortened correspondingly with the increase in the slot opening height, and the results of the simulation calculation to obtain the AC copper consumption under the rated operating conditions are shown in Figure 21.

From the figure, it can be seen that with the increase in tooth-tip height the armature reaction magnetic field induced by the winding AC loss decreases, but the tooth-tip height increases so that the conductor layer close to the slot across the slot leakage magnitude decreases but not significantly.

To visualize the effect of tooth-tip parameters on the eddy loss components of the windings, the winding losses under some tooth-tip parameters are given in

Table 7. AC losses for different tooth-tip parameters.

Tooth-Tip Width (mm)	Tooth-Tip Height (mm)	AC Loss (W)
0.5	0.2	451.8
0.5	1	454.2
0.5	1.8	473.1
2	0.2	493.7
2	1	477
2	1.8	473.3
4	0.2	552.7
4	1	482.3
4	1.8	470

.

As can be seen from the table, but in the rated condition, as the tooth-tip height increases, the slot leakage magnitude across the slot of the conductor layer near the slot is reduced but not significantly, corresponding to the additional AC copper loss suppression effect being general; in the high-frequency conditions, the slot leakage magnitude is larger; the difference in magnetic field landing from the bottom of the slot is large; increasing the tooth-tip height causes leakage across the slot to a certain extent in the conductor layer close to the slot, corresponding to the additional copper consumption being reduced. However, at the same time, increasing the tooth-tip height will shorten the yoke length making it easier for the yoke core to saturate, and increasing the tooth-tip height has a general effect on the suppression of high-frequency copper consumption. At the same time, by increasing the tooth-tip height, the stator yoke length will be shortened to makes the yoke core more easily saturated, and the tooth-tip height of the high-frequency copper consumption suppression effect is general and even has a tendency to increase. Therefore, it is not easy to choose a tooth-tip height that is not too large.

5. Machine Performance Improvement

Through the comprehensive optimization of the stator, the specific geometric parameter change is shown in

Table 8. Geometric parameter change between the original and optimized motors.

	Original	Optimization
Conductor layers	6	8
Aspect ratio of conductor	1.24	1.6
Tooth-tip width (mm)	4	3
Tooth-tip height (mm)	1	0.2

. The performance parameters of the original motor and the optimized motor under rated operating conditions are shown in

Table 9. Performance comparison between the original and optimized motors.

	Original	Optimization
Average torque (Nm)	182.82	186.71
Torque fluctuation (%)	14.04	12.766
AC loss (W)	1111	549.5
Power factor	0.95	0.99

. It can be seen that the optimized eight-layer flat-wire motor has better performance and lower losses.

Through comprehensive simulation calculations across the entire speed range, the efficiency map diagrams of the motor before and after optimization were obtained, as shown in Figure 22. The comparison reveals that the optimized motor achieves a peak efficiency of 98.1%, while the original motor’s peak efficiency is 97.41%. The high-efficiency region of the optimized motor is shifted towards higher speeds and it occupies a larger proportion. Additionally, due to the reduced AC losses in the optimized motor, it exhibits a higher average efficiency.

CLTC-P is a passenger car test condition applicable to Chinese roads in Chinese vehicle driving conditions researched and developed by the China Conditions Project Group from 2015 to 2017. As shown in the

Table 10. Comparison of the performance of the original and optimized motors under CLTC-P.

	Original	Optimization
AC loss (W)	153.59	128.67
Efficiency (%)	96.04	96.78

, under the CLTC-P drive cycle, the optimized design of the motor has lower AC copper losses and higher overall efficiency.

6. Conclusions

Flat-copper-wire wound motors have the advantages of low DC copper loss, good thermal conductivity in the slot, high efficiency, etc., but this is accompanied by excessive AC losses, causing limitations to further increasing the power density of the hairpin motor. Therefore, we conducted research and analysis of the flat-copper-wire winding motor to reduce AC copper loss. Starting from the design size parameters of the motor body, we first established a two-dimensional finite element model of the flat-wire permanent magnet synchronous motor and loss, analyzed the influence of the number of conductor layers and conductor size on the AC copper loss in the parameters of the stator winding, and determined that the optimum number of conductor layers is 8, and the optimum size of the conductor is 4.22 mm in length and 2.64 mm in width, and then we analyzed the influence of the slot parameters of the stator core on the AC copper loss to determine the optimum slot parameters to reduce AC copper loss. The optimum slot parameters were determined to reduce AC copper loss. Finally, the optimized motor model was verified under different working conditions to suppress AC copper loss.