Abstract
With the development of new energy industries, the demand for the driving range and power quality of electric vehicle (EV) drive systems is growing rapidly. The drive motor is faced with the challenge of continuously improving power density and performance. This paper proposes a multiobjective optimization method for an interior permanent magnet synchronous motor for a traction drive (IPMSMTD). Based on the flat wire winding technology, the multiobjective optimization design of the IPMSMTD is carried out to improve the motor power density and high-efficiency range, reduce the torque ripple, and suppress the electromagnetic vibration and noise. The structure and size equation of the IPMSMTD are described. The mathematical model considering iron losses is established, and the optimization objectives are determined. Based on the genetic algorithm, a multiobjective optimization mechanism of the magnetic pole structure is established. The operation performance of the motor is analyzed by the finite element simulation and efficiency map. In order to ensure the comprehensive operation index of the IPMSMTD, the vibration noise and modal analysis are carried out, which verifies the rationality of the designed motor and the optimization method.
1. Introduction
With the increase of energy crisis and environmental pollution, the study of green new energy vehicles to save energies and reduce pollution has become a global hot spot. In recent years, with the increase of market demand, people put forward higher requirements for driving range and power quality of electric vehicle (EV) drive systems. The motor in the drive system is faced with the challenge of continuously improving the power density and operation performance [1, 2]. The flat wire winding is the stator winding using flat copper wires, and made into a hairpin shape, embedded in the rectangular slot of the stator. Compared with traditional winding, the flat wire winding technology has higher slot filling rate and thermal conductivity, which can greatly improve the motor power density [3–5]. At the same time, the interior permanent magnet synchronous motor (IPMSM) can meet the requirements of high speed and high efficiency, and it is widely used in EVs. An interior permanent magnet synchronous motor for a traction drive (IPMSMTD) is proposed based on the flat wire winding technology in this paper. A multiobjective optimization mechanism of the magnetic pole structure is established, which can improve the operation performance of EV motors by analyzing the motor size equation and the mathematical model considering iron losses.
The permanent magnet synchronous motor (PMSM) has high application value in the field of EVs due to its wide-speed range, high efficiency, and energy saving [6, 7]. In order to improve the power density of EV drive motors, scholars have successively researched hybrid excitation synchronous motors [8], dual-stator axial-field flux-switching permanent magnet motors [9], and modular in-wheel motors [10]. The IPMSM is considered as a popular application to meet the requirements of wide-speed range and high-efficiency operating range [11]. Many optimal designs by optimizing the winding and geometrical parameters were reported to obtain a better comprehensive performance [12–15]. Abdel-Khalik et al. [12] proposed a structure combining multilayer winding and dual three-phase winding, which improved the power density and reduced the harmonic loss at the same time. However, this structure was complex and suitable for 12-slot/10-pole small motors. Hayashi and Igarashi [13] presented a hybrid optimization method to optimize the PM shape, configuration, and flux barrier topology. The rotor structure with double-U shaped PMs with small flux barriers near the air-gap was obtained. Zhao et al. [14] designed a reverse-salient PMSM based on operating conditions of EVs, so that it had a wide constant-power speed range and high-power factor at high speeds. Chen and Lee [15] optimized the design of the V-shaped IPMSM based on the individual sensitivity analysis of six geometric parameters of the motor, which improved its synthetic objective function by 36%. Some scholars established an electromechanical analytic model to improve the speed response of electric motor, which could estimate the electrical performance and the mechanical response [16]. While IPMSM increasing the power density, the setting of high air-gap flux density and the difference in d-&q-inductance introduce complication of the air-gap flux distribution [17], which could increase large torque ripple and vibration noise [18]. Therefore, while improving motor power density, reducing harmonic content of magnetic field and mitigation of the torque ripple and vibration noise in the design stage have become an indispensable specification in EV application [19].
In summary, a multiobjective optimization method for an IPMSMTD is proposed. Based on the flat wire winding technology, the motor is designed and optimized to improve its power density and high-efficiency range, reduce its torque ripple, and reduce vibration noise. The size equation and mathematical model considering iron losses of the IPMSMTD are analyzed to determine optimization objectives. Based on the genetic algorithm, a multiobjective optimization mechanism of the magnetic pole structure is established. The reliability and rationality of the designed motor and optimization method are verified by analyzing the operation performance, vibration noise, and modal frequency of the IPMSMTD.
2. IPMSMTD Structure
The size and weight of EVs determine the power performance and driving experience, so the difficulty of EV design is to improve its power weight density and power volume density. The main characteristics of high-power density motor are as follows: it has a high air-gap flux density and salient pole ratio to increase torque density but also bring the torque ripple and vibration noise. The high frequency range and large electromagnetic load lead to the increase of harmonic losses per unit volume, which requires optimization of the magnetic circuit structure and enhancement of the heat dissipation capacity. These characteristics determine that the requirements of the high-power density motor design are different from those of ordinary motors. Therefore, this paper designs an IPMSMTD for EVs and optimizes its operation performance.
The structure of the IPMSMTD is shown in Figure 1, which is composed of two parts: a stator and a rotor. The stator adopts the rectangular slot and flat wire winding. The rotor adopts the type of “V−” interior magnetic pole.
3. Design and Optimization of the IPMSMTD
3.1. Size Equation
The required performance parameters of the IPMSMTD are checked against the overall parameters of EVs, especially the dimensional constraints, rating and peak indicators, and operating conditions. In order to complete the main size parameter design of the motor, the size equation of the IPMSMTD is written aswhere is the core length; is the stator inner diameter; is the motor output power; is the rotor angular speed; is the amplitude of the air-gap flux density; is the electromagnetic load; is the winding coefficient; and A is the electrical load as follows:where Z is the number of stator slots; is the number of conductors per slot; a is the number of parallel branches; and I is the effective value of the phase current.
According to equation (1), the power density contribution of the IPMSMTD is determined by its speed and electromagnetic load. The high-power density motor will tend to develop in high-speed and wide-speed range. Therefore, IPMSMTD adopts the type of “V−” magnetic pole structure to expand the weak magnetic depth.
The thermal load directly affects the heating and temperature rise of the motor, which is expressed aswhere Q is the thermal load; and J is the current density.
The thermal load cannot exceed a certain limit to avoid the large temperature rise. When increasing the electrical load improves power density, the current density should be selected smaller, that is, to increase the cross-sectional area of wire. So IPMSMTD uses a flat wire winding technology.
3.2. Mathematical Model considering Iron Losses
Due to the high speed of the high-power density motor with large internal iron losses, the IPMSMTD mathematical model considering iron losses established in the d-q coordinate system to analyze its internal operation mechanism. Also, the iron loss in the motor is equivalent to the iron loss resistance and the induction electromotive force (EMF) of the d-q axis in parallel [20], as shown in Figure 2. The d-axis and q-axis stator current , are divided into iron loss current , , and torque current and .
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Voltage equation can be expressed as follows [21]:where and are the stator d-axis and q-axis voltage; is the winding resistance; and are differential inductances of d- and q-axis; and are full inductances of d- and q-axis; and is the permanent magnet flux linkage.
Flux linkage equation can be expressed as follows:where and is the stator d-axis and q-axis flux linkage.
Electromagnetic torque is defined as and contains full inductances:where is the electromagnetic torque; is the number of pole pairs.
The input power of the IPMSMTD is obtained from above mathematical model and contains full inductances:where is the input power; and is the motor iron loss resistance. The first part on the left is the iron loss . The second part is the copper loss of the winding . The third part is the motor electromagnetic power , which includes mechanical loss , stray loss , and output power .
The IPMSMTD efficiency is as follows:
The salient pole ratio is introduced for optimal analysis:
According to equations (6) and (7), the electromagnetic torque generated by the salient pole PMSM is composed of the reluctance torque and permanent magnet torque. Because the d-axis inductance in the motor is smaller than the q-axis inductance, the magnetic flux is biased in the path selection, and the reluctance torque is generated. When the current is constant, increasing the salient pole ratio of the motor can improve the electromagnetic torque and efficiency, but also increasing the harmonic content of the magnetic field. Although increasing the rotor permanent magnet flux can significantly improve the output torque and power, its iron losses will increase more, so it is necessary to conduct multiobjective optimization of the IPMSMTD rotor structure.
3.3. Multiobjective Optimization of Magnetic Pole Structure
The IPMSMTD rotor adopts the type of “V−” magnetic pole, the structural parameters are shown in Figure 3. In which, the angle of the type of “V” permanent magnet and its thickness , the width and thickness of the type of “−” permanent magnet determine the magnetic field distribution, and then affect the salient pole ratio, torque, efficiency, harmonic content, and other technical indicators. Therefore, the power density of the motor can be improved by multiobjective optimization design to reduce the harmonic loss and improve efficiency.
In the considered mathematical model, the electromagnetic process of peak torque, peak speed, and rated operating points are guaranteed, and the input variables are angular speed, current, and permanent magnet flux linkage. While meeting the required speed, torque, and voltage limits of the corresponding operating points, the magnetic circuit structure of the rotor is optimized [22, 23]. The peak speed of the motor is 16000 r/min and its centrifugal force is large, so the thickness of permanent magnet bridge needs to be limited. The genetic algorithm draws lessons from natural selection and natural heredity mechanisms in the biological world. It can search for the optimal solution in simulating the output torque of different rotor structures under certain excitation in finite element software. The genetic algorithm and finite element simulation are used to optimize above four structural parameters for increasing salient pole ratio , efficiency and average output torque , reducing torque ripple and back-EMF harmonic content , so as to improve the IPMSMTD performance. The optimal model of the angle and thickness of the type of “V” permanent magnet in the “V−” structure is as follows:
At the rated and no-load operating point, the solution results are shown in Figure 4. With the increase of the angle and thickness of the type of “V” permanent magnet, the salient pole ratio, efficiency, average output torque, and back-EMF harmonic content increase, but the torque ripple decreases. In order to reduce the harmonic content and improve the motor performance, the optimal solution is obtained as: = 100°, = 4.5 mm.
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Based on the genetic algorithm, the optimal model of the width and thickness of the type of “−” permanent magnet in the “V−” structure is established as follows:
The solution results are shown in Figure 5. With the increase of the width and thickness of the type of “−” permanent magnet, the salient pole ratio, efficiency, average output torque, and back-EMF harmonic content increase, but the torque ripple decreases. The thickness of permanent magnet has little influence on each objective. However, if the thickness of the permanent magnet is too small, it is easy to produce the irreversible demagnetization. By comprehensive comparison, the optimal solution is obtained as: = 18 mm, = 3.2 mm.
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After multiobjective optimization, the efficiency and output torque of the motor are obviously improved, but the torque ripple and back-EMF harmonic content of 6.65% and 6.6% are still large. In order to further reduce the torque ripple and harmonic content, the multiobjective optimization method is still used to optimize the rotor staggered pole structure. It is determined that the rotor adopts a 3-segment-staggered poles structure. The no-load back-EMF of the motor before and after optimization is shown in Figure 6. The cogging torque is shown in Figure 7. The back-EMF harmonic content decreases from 6.6% to 1.77%, and the cogging torque ripple decreases from 0.9% to 0.1%.
The rated torque of the motor under load operation is shown in Figure 8. The rated torque of the motor after staggered pole decreases from 139.6 N·m to 134.3 N·m, and the torque ripple decreases from 6.65% to 2.06%. It can be seen that the output torque is reduced after staggered pole, but the harmonic content and torque ripple are significantly reduced, so the rotor adopts a 3-segment staggered poles structure.
4. Operation Characteristic
4.1. No-Load Operation Characteristics
A 90 kW IPMSMTD is designed according to the multiobjective optimization method. The main parameters are shown in Table 1. Its operation characteristics are analyzed by the finite element software. The no-load magnetic force line distribution and the no-load magnetic density cloud diagram are drawn in Figure 9. No-load air-gap magnetic density of the motor is drawn in Figure 10. The magnetic field distribution is symmetrical. The air-gap magnetic density is 0.459 T and its waveform is sinusoidal, which accords with the operation mechanism of PMSMs.
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4.2. Load Operation Characteristics
When the input current varies from 0 to 1.8 times the rated current, the average torque of the motor is shown in Figure 11. The output torque increases almost linearly with the increase of input current. Due to the wide-speed range of the motor, the no-load magnetic field strength is designed to be low to meet the weak magnetic depth. Therefore, the saturation degree of armature magnetic field is not obvious when the current increases.
The torque-angle characteristic of the motor at rated current is drawn in Figure 12. It can be seen that IPMSMTD adopts a “V−” magnetic pole structure, the salient pole is relatively high, and the reluctance torque is larger. Therefore, the motor can increase the output torque and overload capacity by increasing the reluctance torque. The IPMSMTD output the maximum torque when the phase current angle is 120°, which meets the requirements of rated operating point and overload capacity during climbing.
4.3. Efficiency Map
After optimal design, the external characteristic curve of the IPMSMTD is shown in Figure 13. Its peak power can reach 240 kW. The peak torque can reach 222 N·m. It still has a certain torque output capability at 16000 r/min, which can meet the requirements for the output torque capacity of the motor.
The efficiency map of the IPMSMTD in the whole operating range is shown in Figure 14. It can be seen that near the rated operating point of 6500 r/min and 134 N·m torque, the efficiency of the motor can reach 96.2%, which can meet the design requirements of the motor for rated efficiency. In addition, the dark areas in the figure are high efficiency intervals. The area where the motor efficiency is greater than 90% accounts for 88.23%, which indicates that the motor has high efficiency over a wide-speed range and can meet performance requirements.
4.4. Performance Comparison of Different Rotor Structures
At present, the representative EV motor rotor structures include Tesla “V” type and BYD “double V” type, as shown in Figure 15. Only by changing rotor structures, efficiency maps of “V” type and “double V” type are obtained, as shown in Figure 16. In the type of “V”, the area where the motor efficiency is greater than 90% accounts for 87.78%. In the type of “double V”, the area where the motor efficiency is greater than 90% accounts for 88.02%. Compared with Figure 14, it can be seen that the designed “V−” structure has better efficiency and external characteristics.
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5. Electromagnetic Vibration Noise
5.1. Radial Electromagnetic Force Analysis
When the IPMSMTD input current is running, it will generate a radial electromagnetic force. As the input current increases, its radial electromagnetic force will also increase. Further, greater electromagnetic vibration and noise will be generated, which will affect the comprehensive performance of EV. Therefore, it is necessary to conduct harmonic response analysis of its rated operating point. Through the finite element simulation, the radial electromagnetic force wave on the inner surface of stator teeth is obtained when IPMSMTD inputs rated current, as shown in Figure 17. The generated radial electromagnetic force is symmetrically distributed, and the electromagnetic force density is = 582 kN/m2.
5.2. Vibration Response
The radial electromagnetic force of each tooth changing with time is converted to the frequency through Fourier decomposition and added to the corresponding tooth as the excitation source for vibration analysis. Through finite element calculation, its stator vibration deformation and displacement distribution under rated operation of the IPMSMTD are obtained, as shown in Figures 18 and 19.
The results indicate that the primary stator deformation occurs in the teeth. At a frequency of 866.6 Hz, it reaches a maximum deformation displacement of 3.84 × 10−4 mm. Therefore, during operation of the IPMSMTD, the stator will be deformed due to the radial electromagnetic force, but the deformation displacement is minimal and inconsequential to the operation of the motor.
5.3. Noise Response
The results of electromagnetic vibration are used as the excitation of sound field for noise simulation. The sound pressure level distribution of electromagnetic noise at different frequencies under rated operation of the IPMSMTD is shown in Figure 20. At a frequency of 3466 Hz, it reaches a maximum sound pressure level of 75.5 dB. At this time, its noise pressure distribution is shown in Figure 21. The noise pressure distribution is uniform, and its sound pressure is relatively small. Through analysis of the noise spectrum, it can be found that the maximum sound pressure level is 75.5 dB at the frequency point 3466 Hz, serving as the primary source of electromagnetic noise during operation. However, this noise level complies with the standards for sound pressure levels of EV motors.
6. Modal Analysis
When the electromagnetic vibration frequency is close to the natural frequency of the motor, it may trigger resonance, potentially leading to the rapid destruction of the entire motor. Therefore, the numerical calculation of the motor structure modal is very necessary. The first five order radial vibration modal frequencies of the stator core are extracted through simulation, as shown in Figure 22.
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The radial vibration modal frequency of the stator has steered clear of the low-order frequency of the radial electromagnetic force, thus preventing the occurrence of resonance. This demonstrates that the motor is capable of running in a stable and reliable manner. The validity of the designed IPMSMTD and the optimization method has been confirmed.
7. Conclusion
This paper presents an IPMSMTD. The basic structure and mathematical model of the motor are described. The multiobjective optimization method is established. The following conclusions are drawn after analysis:(1)The IPMSMTD mathematical model considering iron losses is established and the optimization objectives are determined. A multiobjective optimization method for the magnetic pole structure of the IPMSMTD is established based on the genetic algorithm. It improves the power density and efficiency of the motor and realizes the high-performance development of EV drive motors.(2)The operation characteristics and efficiency map of the IPMSMTD are simulated and analyzed. The simulation results show that the designed motor can meet the performance requirements of output torque capacity, high-power density, and high efficiency in a wide-speed range.(3)The electromagnetic vibration noise analysis is carried out. The vibration and noise distribution of the motor under rated operation are obtained. The natural frequency of the motor is compared to provide a basis for avoiding the resonance point.(4)Above simulation results prove the correctness and rationality of the designed motor and its optimization method. The improvement of the IPMSMTD efficiency and power density realizes the lightweight of drive systems, saves the installation space of EVs, and facilitates the integrated installation. In practical application, it can improve the system reliability and economy, and realize the high efficiency and energy saving of EVs.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Authors’ Contributions
Y.C. and Z.F. proposed the original conceptualization and developed methodology. M.X. and H.L. were in charge of data investigation and validation. Y.X. was in charge of writing and simulation analysis. L.C. was in charge of formal analysis and visualization. All authors have read and agreed to the published version of the manuscript.
Acknowledgments
This research was funded by the Science and Technology Bureau of Dalian, Liaoning Province, China, Grant number: 2023RQ061.