Designing High-Power-Density Electric Motors for Electric Vehicles with Advanced Magnetic Materials

: As we face issues of fossil fuel depletion and environmental pollution, it is becoming increasingly important to transition towards clean renewable energies and electric vehicles (EVs). However, designing electric motors with high power density for EVs can be challenging due to space and weight constraints, as well as issues related to power loss and temperature rise. In order to overcome these challenges, a signiﬁcant amount of research has been conducted on designing high-power-density electric motors with advanced materials, improved physical and mathematical modeling of materials and the motor system, and system-level multidisciplinary optimization of the entire drive system. These technologies aim to achieve high reliability and optimal performance at the system level. This paper provides an overview of the key technologies for designing high-power-density electric motors for EVs with high reliability and system-level optimal performance, with the focus on advanced magnetic materials and the proper modeling of core losses under two-dimensional or three-dimensional vectorial magnetizations. This paper will also discuss the major challenges associated with designing these motors and the possible future research directions in the ﬁeld.

In an electric vehicle (EV), space and weight limitations often restrict the size of the electric motor drives.Thus, designing motors with high power density is highly desirable [47][48][49][50][51][52][53][54][55][56].One approach is to increase the operational speed since the motor power is proportional to the speed.However, increasing the operational speed can significantly increase the motor power loss, leading to high temperature rise and compromising the motor performance and reliability.Therefore, it is crucial to carefully design the motor with low power loss, which implies operational cost savings, environmental friendliness, and appropriate thermal dissipation.Other issues related to high-speed operation, such as mechanical strength and vibration, should also be considered.
Design optimization of high-speed electric motors for electric vehicles is therefore a multi-objective and multi-disciplinary task that has received significant attention in the past few decades.For instance, Eberleh and Hartkopf [47] reported a high-speed induction motor coupled with a two-speed transmission for electric vehicles in 2006.The use of a liquid cooling system increased the continuous output power while reducing the motor size, weight, and costs.In 2007, Huang et al. [48] designed a high-speed claw pole motor using soft magnetic composite material as the stator for low core loss and low manufacturing cost.They considered the rotational core loss and further analyzed the temperature distribution by using thermal networks and three-dimensional finite element analysis with the distributed core loss in 2009 [49].In 2010, Hosseini et al. [50] analyzed linear synchronous motors for high-speed maglev vehicles, accurately calculating major parameters such as magnetic field distribution and thrust force by solving the Maxwell equations in motor layers using analytical methods.
More recently, Damiano et al. [51] presented the design of a high-speed brushless DC motor with ferrite magnets for electric vehicles in 2017.The developed electromagnetic and mechanical models can consider mutual influence when determining the electric motor geometry.Dang et al. [52] reported the design optimization of a high-speed permanent magnet synchronous motor with flux weakening for electric vehicle applications in the same year.They found a solution to determine the motor size from a given driving cycle.Credo et al. [53] presented the design of high-speed synchronous reluctance motors (Syn-RMs) adopting topology optimization for electric vehicles in 2020.Prakht et al. [54] presented the optimization design of a novel three-phase flux reversal motor composed of three single-phase motors sharing a common shaft in 2021.The torque ripple was reduced, and the motor performance was improved.In 2022, Cui et al. [55] proposed a hybrid rotor structure with additional ferrite magnets in the dand q-axis magnetic flux paths, along with rotor surface slotting and GA optimization.The innovative design effectively addresses the issue of excessive eddy current loss in FSCW-PMSMs at high speeds, while also providing a cost-effective solution for EV IPMSMs by reducing the usage of expensive Nd-Fe-B magnets.Mashrouteh et al. [56] designed a multi-actuation model predictive controller that integrates optimal corner torque allocation and active aerodynamics control to enhance the stability of performance vehicles during high-speed maneuvers, considering nonlinear tire behavior and actuator dynamics.In 2023, Credo et al. [57] demonstrated how the Syn-RM is effectively evaluated and optimized for EV applications, considering acceleration time, maximum speed, and flux weakening capabilities.The results show that, despite the motor's limitations, it is possible to meet the requirements through advanced design procedures, as confirmed by experimental tests on a scaled prototype for a city car.

Motivation
Design optimization of high-power-density electric motors for EVs is a complex and multifaceted challenge that requires careful consideration of multiple factors such as power loss reduction, proper thermal dissipation such as forced cooling design, mechanical component improvements such as bearing, advanced manufacturing technologies, and appropriate types of electric motors such as PMSMs, Syn-RMs, SRMs and axial-flux motors.To tackle these challenges, numerous research efforts have been made in the past few decades .This paper aims to provide an overview of the latest advanced technologies used in electric motor design and optimization for high-speed and high-power-density motors used in EVs.Specifically, the focus will be on advanced magnetic materials and their characterization, such as modeling core losses under 2D and 3D vectorial magnetizations.

Paper Organization
The paper is structured as follows.Section 2 provides an overview of advanced electromagnetic materials and their applications in EV motors.Section 3 discusses the development of modern analysis methods for magnetic properties of electromagnetic materials and their application in motor design and analysis.In Section 4, we briefly summarize the advanced design and optimization techniques, with a focus on the multilevel, multi-objective, multi-disciplinary (MMM), and robust optimization approach to achieve optimal performance of electric motor drive systems.Lastly, Section 5 explores current research trends and major challenges in the field.

Application of Advanced Electromagnetic Materials in EV Motors
Achieving higher power density in electric motors typically involves increasing operational speed within the constraints of application and mechanical strength, increasing air gap magnetic flux density within the constraints of core materials, and increasing current density in windings within the constraints of thermal dissipation.As a result, researchers have been focused on developing advanced novel materials that possess improved mechanical, electromagnetic, and thermal properties.By incorporating these materials into the electric motor design, it is possible to further increase power density and improve overall performance .

Soft Magnetic Materials
Soft ferromagnetic materials are extensively used as the core components of electrical machines, and their magnetic properties have a direct impact on the machine's overall performance.These properties, including the relationship between magnetic field strength and magnetic flux density, as well as the associated core loss, play a crucial role in determining the efficiency and effectiveness of the machine.In order to enhance the magnetic properties of soft ferromagnetic materials, considerable efforts have been invested in improving various aspects, such as increasing their magnetic permeability, saturation flux density, and reducing specific power loss.These improvements are essential for enhancing the overall efficiency and performance of electrical machines.To achieve these goals, researchers and engineers have developed various techniques, such as optimizing material composition and microstructure, applying advanced processing techniques, and using innovative magnetic materials.By continuously improving the magnetic properties of soft ferromagnetic materials, we can expect to see further enhancements in the efficiency and performance of electrical machines in the future .

Thin Electrical Steel Sheets
The core loss in electrical machines is caused by the varying magnetic flux in the core materials, consisting of hysteresis loss, eddy current loss, and anomalous loss.The eddy current loss is proportional to the square of the current frequency, which is in linear relation with the motor speed.Thus, the eddy current loss in a high-speed motor may be significant.Using thin electrical steel sheets is an effective way to reduce eddy current loss, as it is inversely proportional to the square of the sheet thickness.Enokizono et al. designed a high-efficiency, high-power-density, and high-speed motor using an ultra-thin electrical steel with 80 µm thickness.However, the magnetic flux density in an electrical machine is rotational and not aligned with the field strength.Therefore, the vector magnetic properties of ultra-thin steel sheets need to be measured and modeled for accurate motor design [58].
Pei et al. also investigated the use of thin-gauge non-grain-oriented silicon steels with various thicknesses in EV electric motors and their impact on electromagnetic and mechanical properties and core loss numerical models [59].Huynh and Hsieh [60] studied the effect of thin electrical steel sheets on the performance of interior PMSMs for EV traction.While thinner sheets may reduce power loss, they may also decrease output torque due to the lower saturation flux density.Additionally, using thin sheet laminations may increase manufacturing difficulty and cost.

High Silicon Electrical Steel Sheets
To reduce eddy current loss, high resistivity electrical steel sheets have been developed by increasing the silicon content.Hasegawa et al. [61] used a high silicon steel, Super E-Core, in 2002 to improve the efficiency of an SRM.A comparison was made with a test machine that used conventional low core loss silicon steel 35A300 as its core to demonstrate the lower power loss of the high silicon steel.Ou et al. [62] designed a high-speed interior PMSM in 2019 using a high silicon steel 10JNEX900 (6.5% Si) as the rotor core.The electromagnetic and mechanical properties of the 10JNEX900 electrical steel were tested.Ma et al. [63] studied the power loss of the motor stator core with the high silicon steel 10JNEX900 in 2002, taking into account the effects of temperature and compressive stress.
High silicon electrical steel sheets feature high resistivity, near-zero magnetostriction, and high magnetic permeability, making them attractive for electromagnetic device applications.However, due to the high silicon content, these materials can become very brittle and difficult to manufacture.

Amorphous Ferromagnetic Metal
The high efficiency and low core loss of amorphous metal (AM), particularly amorphous ferromagnetic metal, make it an attractive material for high-speed electric motors [64].Various types of motors have been developed using AM as the core material.In 1992, Jensen et al. [65] reported a low loss axial-flux permanent magnet brushless DC motor with tape wound amorphous iron as the stator core.To simplify manufacturing and reduce costs, the stator core is constructed by winding the AM tapes in a toroidal form to minimize eddy current loss.In 2010, Z. Wang et al. [66] designed an axial-flux PMSM with tape wound amorphous core, investigating different core structures for low core loss.In 2011, L. Wang et al. [67] discussed high-efficiency and high-power-density AM-based motors for EVs.
Recent studies have focused on improving AM motor performance.In 2014, Fan et al. [68] developed a high-power-density electric motor with AM core, which demonstrated higher efficiency than a baseline motor with non-oriented silicon steel.However, optimization design is necessary to ensure optimal performance under all conditions.In 2016, Tong et al. [69] analyzed core loss in a permanent magnet synchronous motor with AM core by numerical computation and experiment.In 2019, Tomioka and Akatsu [70] designed a high-speed SRM with AM core for EV application, using a divided rotor structure to reduce eddy current and windage loss.In 2020, Li et al. [71] studied an in-wheel axial-field electric motor with AM stator core for a solar-powered EV, employing a multi-physics design approach for improved multi-objective performance.In 2021, Fan et al. [72] designed and analyzed a high-speed induction motor with AM cores, focusing on low-loss magnetic materials and reliable rotor structures.
Despite these achievements, the widespread use of AM materials in electric motors is still limited.AM is typically in the form of thin continuous ribbon, which is hard and brittle, making it difficult and expensive to manufacture magnetic cores using conventional methods.Additionally, the low-loss property may deteriorate during the production process.
Despite the unique benefits of SMC materials, there are also some drawbacks.For instance, the magnetic permeability of SMC is quite low, and its mechanical strength is not as high as conventional silicon steel.While molding techniques have been expected to make the fabrication of SMC cores easier, there are still challenging issues, such as the core size and shape against manufacturing productivity and cost, as well as the mass density and uniformity of the molded parts.

Magnetic Properties of SMC
Because the SMC powder particles are coated with surface insulation and bonding adhesive, the eddy current loss is almost ignorable, implying that the material can operate with higher frequency.This property agrees well with the development of high-powerdensity electric motors, in which the output power is basically in a linear relation with the operational speed or frequency.
SMC materials have several advantages over conventional electrical machine core materials, including low eddy current loss, isotropy, and the ability to be manufactured into complex structures, making them an ideal choice for high-speed electrical machine design.As shown in Figure 1, the iron loss of different types of motor stator core materials varies with the working frequency [93].Compared to silicon steel sheets, stators based on amorphous alloy can achieve a much lower iron loss.However, the batch manufacturing technology for amorphous alloy stamping is limited to simple non-slot structures.SMC materials can be a suitable alternative for the stator cores in high-speed permanent magnet machines.When the motor's working frequency is higher than 2000 Hz, SMC can outperform electrical steels in reducing core loss, which in turn helps reduce winding heating.

Conducting Materials
The copper loss, caused by the current flowing in the winding, is typically the largest power loss in an electrical machine.It can be calculated by multiplying the winding resistance with the square of the current.To reduce copper losses, researchers have explored conducting materials with low or zero resistivity, such as superconductors.High-temperature superconductors (HTSs) have been particularly promising for electric motors as they can operate at higher temperatures than low-temperature superconductors, such as those cooled with liquid nitrogen.This makes them more practical and cost-effective for real-world applications.As a result, several HTS electric motors have been developed [99][100][101][102][103][104].
In  In 2014, Maloberti et al. [94] presented magnetic modeling for an axial field PM motor utilizing SMC core in EVs.The following year, in 2015, Kobler et al. [95] developed an axial motor with SMC core and ferrite magnets, which showed promising potential for a lowcost, high-power-density design without the use of rare-earth PM.More recently, in 2021, Du et al. [96] presented a claw pole motor that utilized SMC cores.Their research on the SMC preparation process demonstrated that the best magnetic and mechanical properties were achieved with a pressing pressure of 700 MPa and an annealing temperature of 500 °C.In 2022, Chu et al. [97] conducted an analysis on a PM claw pole motor with SMC core, taking into consideration the material characteristics over a wide range of temperatures.Further, in 2022, Li et al. [98] conducted a study on a flux reversal claw pole SMC motor to minimize cogging torque.

Conducting Materials
The copper loss, caused by the current flowing in the winding, is typically the largest power loss in an electrical machine.It can be calculated by multiplying the winding resistance with the square of the current.To reduce copper losses, researchers have explored conducting materials with low or zero resistivity, such as superconductors.High-temperature superconductors (HTSs) have been particularly promising for electric motors as they can operate at higher temperatures than low-temperature superconductors, such as those cooled with liquid nitrogen.This makes them more practical and cost-effective for real-world applications.As a result, several HTS electric motors have been developed [99][100][101][102][103][104].
In 2005, Snitchler et al. [99] presented a 5 MW HTS ship propulsion motor featuring high power density, efficiency, and low noise operation.In 2012, Gonzalez-Parada et al. [100] demonstrated increased power capability by applying HTS BSCOO tapes to the rotor of an axial field induction motor.Moreover, also in 2012, Jin et al. [101] designed a double-sided HTS linear synchronous motor integrated with HTS magnetic suspension, combining the advantages of HTS linear drive and HTS maglev technologies.In 2016, Moon et al. [102] developed a 5 MW 2G HTS motor for ship propulsion, focusing on the rotor with HTS coil, damper, torque disk, and hollow shaft.In 2018, Liu et al. [103] designed a high-speed HTS induction motor with a saddle-shaped HTS armature winding and analyzed its electromagnetic characteristics.In 2021, Zanegin et al. [104] investigated the 2G AC losses in HTS coils of electrical machines under various conditions.
Despite the significant progress made in HTS electric motors, they still face challenges in terms of commercial viability.The design of HTS windings and cooling systems remains complex, and the cost of HTS motor drives is still high, both in terms of initial production and operational expenses.As a result, researchers are continuing their efforts to develop more cost-effective HTS materials and motors.

Advanced Modeling and Analysis
Numerous studies have explored the use of advanced electromagnetic materials in electric motors by replacing conventional electrical steel cores.However, simply swapping out the core material is not enough to enhance motor performance.To fully benefit from the new materials, meticulous design optimization that takes into account the unique properties of these materials is crucial.Unfortunately, the property mechanism and mathematical modeling of these new materials have not been fully investigated, particularly in situations where the electric motor experiences two-dimensional (2D) or three-dimensional (3D) vectorial magnetic fluxes.As a result, there is a need to thoroughly study the properties of these materials under 2D and 3D vectorial magnetizations to fully exploit their potential benefits .
For example, in 1984, Brix et al. [105] presented a method for investigating the rotational magnetization process in electrical steel sheets based on a 2D magnetic measurement apparatus.In 1990, Sievert [106] summarized the advances in 1D alternating and 2D rotational magnetic measurement techniques for electrical steel sheet.Various methods are used for determining the rotational power loss and it was found that the field sensing methods are more convenient and versatile than the thermometric methods, yielding more information.In 1993, Zhu and Ramsden [107] improved the measurement accuracy of 2D magnetic field in a single-sheet square sample core loss measuring system, in which a novel sandwich structure of sensing coils was proposed.In 1997, Enokizono and Tanabe [108] studied a simplified rotational loss tester, which can be used for any sized sample sheet.In 2014, Appino et al. [109] measured the rotational core loss in non-oriented Fe-Si and Fe-Co sheets up to kilohertz range.In 2016, Li et al. [110] measured the core loss of silicon steel laminations by using a 3D magnetic tester.In 2019, Boubaker et al. [111] reported the design and measurements of a rotational core loss tester, ensuring the rotating flux density vector and uniform distribution in the sample.
As described in Section 2.1.4,SMC materials are very suitable for designing electric motors with 3D magnetic fluxes, and a lot of research has been done on the 2D and 3D magnetic property measurements of SMC [112][113][114][115][116]. Figure 2 shows the experimental results of the magnetization curves obtained with the SMC samples under various magnetization patterns, by using the developed 3D magnetic testing system shown in Figures 3 and 4 [117,118].
In 2021, Sarker et al. [119,120] measured the rotational core loss of a Fe-based amorphous magnetic material by using a square specimen tester (SST) as shown in Figure 5.The 2D rotational magnetic fluxes are generated by the currents flowing in the two sets of excitation coils wound on Xand Y-axis magnetic poles.Some rotational magnetic property measurements have also been carried out on HTS materials.Soomro et al. [121,122] reported their experimental setup and measurement results of AC loss in HTS YBCO bulks by modifying the 2D magnetic testing system as shown in Figure 6.For experiment purposes, the HTS sample was cooled down to the superconducting mode in a liquid nitrogen box.
The large amount of data of magnetic properties measured under 2D and 3D vectorial magnetizations are necessary for in-depth understanding of the core loss mechanism and proper mathematic modeling for designing various electric motors.
particularly in situations where the electric motor experiences two-dimensional (2D) or three-dimensional (3D) vectorial magnetic fluxes.As a result, there is a need to thoroughly study the properties of these materials under 2D and 3D vectorial magnetizations to fully exploit their potential benefits .
For example, in 1984, Brix et al. [105] presented a method for investigating the rotational magnetization process in electrical steel sheets based on a 2D magnetic measurement apparatus.In 1990, Sievert [106] summarized the advances in 1D alternating and 2D rotational magnetic measurement techniques for electrical steel sheet.Various methods are used for determining the rotational power loss and it was found that the field sensing methods are more convenient and versatile than the thermometric methods, yielding more information.In 1993, Zhu and Ramsden [107] improved the measurement accuracy of 2D magnetic field in a single-sheet square sample core loss measuring system, in which a novel sandwich structure of sensing coils was proposed.In 1997, Enokizono and Tanabe [108] studied a simplified rotational loss tester, which can be used for any sized sample sheet.In 2014, Appino et al. [109] measured the rotational core loss in nonoriented Fe-Si and Fe-Co sheets up to kilohertz range.In 2016, Li et al. [110] measured the core loss of silicon steel laminations by using a 3D magnetic tester.In 2019, Boubaker et al. [111] reported the design and measurements of a rotational core loss tester, ensuring the rotating flux density vector and uniform distribution in the sample.
As described in Section 2.1.4,SMC materials are very suitable for designing electric motors with 3D magnetic fluxes, and a lot of research has been done on the 2D and 3D magnetic property measurements of SMC [112][113][114][115][116]. Figure 2 shows the experimental results of the magnetization curves obtained with the SMC samples under various magnetization patterns, by using the developed 3D magnetic testing system shown in Figures 3 and 4 [117,118].
-9000 -6000 -3000 0 3000 6000 9000 -1.8In 2021, Sarker et al. [119,120] measured the rotational core loss of a Fe-based amorphous magnetic material by using a square specimen tester (SST) as shown in Figure 5.The 2D rotational magnetic fluxes are generated by the currents flowing in the two sets of excitation coils wound on Xand Y-axis magnetic poles.Some rotational magnetic property measurements have also been carried out on HTS materials.Soomro et al. [121,122] reported their experimental setup and measurement results of AC loss in HTS YBCO bulks by modifying the 2D magnetic testing system as shown in Figure 6.For experiment purposes, the HTS sample was cooled down to the superconducting mode in a liquid nitrogen box.
The large amount of data of magnetic properties measured under 2D and 3D vectorial magnetizations are necessary for in-depth understanding of the core loss mechanism and proper mathematic modeling for designing various electric motors.In 2021, Sarker et al. [119,120] measured the rotational core loss of a Fe-based amorphous magnetic material by using a square specimen tester (SST) as shown in Figure 5.The 2D rotational magnetic fluxes are generated by the currents flowing in the two sets of excitation coils wound on Xand Y-axis magnetic poles.Some rotational magnetic property measurements have also been carried out on HTS materials.Soomro et al. [121,122] reported their experimental setup and measurement results of AC loss in HTS YBCO bulks by modifying the 2D magnetic testing system as shown in Figure 6.For experiment purposes, the HTS sample was cooled down to the superconducting mode in a liquid nitrogen box.
The large amount of data of magnetic properties measured under 2D and 3D vectorial magnetizations are necessary for in-depth understanding of the core loss mechanism and proper mathematic modeling for designing various electric motors.Sensor Outputs Liquid Nitrogen Box

Modeling of 2D/3D Vectorial Magnetic Properties
Based on the measured magnetic properties including the relations between B (magnetic flux density) and H (magnetic field strength) vectors, and associated core loss, some mathematical models of the 2D/3D vectorial magnetic properties have been established, which are essential for magnetic field analysis of electric motors.
Because of the vectorial rotational magnetization, there is generally a phase difference between the B and H vectors, and their relationship should be described in a matrix form as below [123][124][125][126][127][128]: Figure 6.Photo of the 2D magnetic property measurement system for HTS samples.

Modeling of 2D/3D Vectorial Magnetic Properties
Based on the measured magnetic properties including the relations between B (magnetic flux density) and H (magnetic field strength) vectors, and associated core loss, some mathematical models of the 2D/3D vectorial magnetic properties have been established, which are essential for magnetic field analysis of electric motors.
Because of the vectorial rotational magnetization, there is generally a phase difference between the B and H vectors, and their relationship should be described in a matrix form as below [123][124][125][126][127][128]: where ν ij is the reluctivity matrix (i,j = x,y,z in rectangular coordinate or i,j = r,θ,z in cylindrical coordinate).According to the Maxwell's equations, in magnetic static field analysis, the relation between magnetic vector potential A and the applied current density vector J 0 can be derived as ∇ × (v∇ In rectangular coordinates, the equation for the x-component of J 0 can be written as (3).The equations for J y and J z can be derived in a similar way.
Different measurements of magnetic materials have indicated that the behavior of core loss under vectorial rotational magnetization is distinct from that observed under alternating magnetic flux.An example of this is demonstrated in Figure 7, where the core loss of an SMC sample was measured under varying peak values and frequencies of flux densities, for both alternating and purely rotational magnetizations [114].
It is evident that rotational core loss behaves differently than its alternating counterpart, and thus requires novel and appropriate models to be proposed.When an electrical machine rotates, the magnetic flux density B vector at any given location on the core typically forms a 3D irregular locus [129].The B components projected onto the three coordinate axes are periodic functions of time, which can be decomposed into fundamental and harmonic terms using Fourier series.For each harmonic order, including the fundamental, the three components form an elliptical locus on a plane that may not align with any major coordinate plane, such as the XoY, YoZ, or ZoX plane.Previous research has shown that the total core loss can be obtained by summing up the losses contributed by all harmonics [120,129].
Several new models have been proposed to account for the rotational core loss in electrical machines, as discussed in references [130][131][132].These models have been developed based on measured data obtained from material samples exposed to both alternating and circularly rotating magnetizations.
In rectangular coordinates, the equation for the x-component of J0 can be written as (3).The equations for Jy and Jz can be derived in a similar way.
Different measurements of magnetic materials have indicated that the behavior of core loss under vectorial rotational magnetization is distinct from that observed under alternating magnetic flux.An example of this is demonstrated in Figure 7, where the core loss of an SMC sample was measured under varying peak values and frequencies of flux densities, for both alternating and purely rotational magnetizations [114].It is evident that rotational core loss behaves differently than its alternating counterpart, and thus requires novel and appropriate models to be proposed.When an electrical machine rotates, the magnetic flux density B vector at any given location on the core typically forms a 3D irregular locus [129].The B components projected onto the three coordinate axes are periodic functions of time, which can be decomposed into fundamental and harmonic terms using Fourier series.For each harmonic order, including the fundamental, the three components form an elliptical locus on a plane that may not align with any major coordinate plane, such as the XoY, YoZ, or ZoX plane.Previous

Applications of 2D/3D Rotational Core Loss Models
According to references [130][131][132], it may be sufficient for material suppliers to provide data for 1D alternating and 2D purely circular flux densities of various peak values and frequencies.In 1991, Bertotti et al. [130] employed the common three-term model [133] to calculate the core loss of an induction motor.The hysteresis loss with an ellipsoidal rotating flux density was estimated using linear interpolation between alternating and rotational core losses.However, this interpolation method is a rough approximation.In 1994, Zhu et al. [134] improved the accuracy of the prediction by deriving an elliptically rotational core loss formula, given by Equation (4).In this formula, P t represents the core loss caused by an ellipsoidal rotating B, P r is the corresponding loss due to a circularly rotating B with the same peak value and frequency, and P a is due to an alternating B. Additionally, R B denotes the axis ratio of the ellipsoidal B.
In 1998, Zhu and Ramsden [131] proposed enhanced models for computing the rotational core losses of electrical machines, where the rotational hysteresis loss P hr is computed using Equations ( 5) and ( 6), where f, B P , and B s are, respectively, the frequency, peak value, and saturated value of flux density, and a 1 , a 2 , and a 3 are coefficients.These models were employed to estimate the core loss of a PM motor and achieved better accuracy.In 2005, Guo et al. [132] applied this improved model to calculate the core loss of a PM claw pole motor with an SMC stator core, resulting in a high level of accuracy when compared with experimental data obtained from a motor prototype.
where f is the field excitation frequency, B P the magnitude of the circular B vector, B s the saturation flux density.A 1 , a 2 , and a 3 are all coefficients that can be obtained by curve-fitting the data.

Advanced Design and Optimization
As new materials have both advantages and disadvantages, a system-level design approach is necessary to maximize the benefits while minimizing the drawbacks.However, electric motor drives are complex systems that consist not only of the motor but also of the power electronic converter and controller.Even within the motor itself, there are numerous components with multi-physics considerations such as electromagnetic, thermal, and mechanical aspects.Furthermore, many factors, such as material properties, are nonlinear, and motor parameter and performance calculations are highly time-consuming, especially when accurate determination requires 3D finite element analysis.Additionally, design optimization necessitates numerous iterations.
To address these challenges, researchers have developed and applied the so-called multi-level, multi-objective, and multi-physics optimization technique in the design and analysis of electric motor drive systems .This approach enables designers to consider multiple levels of the motor drive system, including the motor, converter, and controller, as well as the numerous interdependent physics involved.The MMM optimization technique also allows for the consideration of multiple objectives, such as efficiency, power density, cost, and reliability, to achieve an optimal design.
Many researchers have applied the MMM optimization technique in their studies.For instance, Knorr et al. [135] introduced a multi-level modeling methodology for analyzing a claw pole alternator, considering the trade-off between simulation efficiency and accuracy.Guo et al. [136] applied the multi-level multi-domain modeling for designing a transverse flux motor, in which a two-level hierarchical design architecture is constructed.This ap-proach appears to be effective, with fast calculation and good accuracy.Wang et al. [137] conducted multi-level optimization of a permanent magnet motor by using a multi-level genetic algorithm.Lei et al. [138] carried out the system-level design of a transverse flux motor drive system with the six sigma robust optimization technique included.Lei et al. presented their studies on the system-level design optimization of electric motor drive systems using the traditional deterministic approach [139], and the robust approach considering parameter uncertainty [140].They also summarized the key techniques of multi-level design optimization for permanent magnet motors [141].Asef et al. reported a rotor shape multi-level design optimization for a permanent magnet synchronous motor, aiming to reduce the mechanical stress in the rotor core [142].Meng et al. [143] conducted the multilevel optimization of a flux-modulated machine based on machine learning techniques.
In conclusion, the MMM optimization technique is an effective tool for designing and analyzing electric motor drive systems.Researchers have successfully applied the technique to optimize various types of motors, and the approach has evolved to include multi-objective and multi-physics optimization.Additionally, recent research work has focused on the mutual effects of multi-disciplinary factors, contributing to the development of digital twin models of electric motor drives.

Discussions and Conclusions
This paper provides an overview of advanced design and analysis techniques used to develop high-power-density electric motors for electric vehicles.The techniques include the application of novel electromagnetic materials, advanced characterization of material properties under motor operational conditions, and accurate mathematical modeling.The paper also discusses the use of system-level multi-physics optimization for achieving optimal system performance.

Remaining Challenges
Despite significant progress in research and industrial applications, there are still several challenging tasks that require attention in the future development of high-powerdensity electric motors in EVs.These include: (1) The lack of sufficient fundamental property data for electromagnetic materials, such as the relationship between magnetic field strength and flux density under various conditions such as magnetization patterns, magnitudes, frequency, temperature, mechanical stress, DC bias, and magnetostriction; (2) The need for system-level design optimization of the entire PMSM drive system for optimal performance since assembling individually optimal components such as motor and inverter cannot guarantee optimal system performance.The interaction of multiphysics effects, such as thermal and stress characteristics, should also be considered to improve the accuracy of iron loss prediction for PMSMs, reducing computational cost and providing better accuracy; (3) The importance of using new materials or high-quality manufacturing in EV drive systems design optimization.New materials such as SMC have great potential for designing electrical machines with high performance and/or low-cost and novel topologies.Future robust design optimization should fully consider manufacturing tolerances, material diversities, and assembling errors to present a comprehensive solution for high quality manufacturing and design; (4) The need for effective control circuit design for dynamic and steady-state performances of PMSM drive systems.Traditional control algorithms including field-oriented control (FOC), direct torque control (DTC), and model predictive control (MPC) have been developed and employed successfully, but are challenging to guarantee satisfactory performance in the presence of parameter uncertainties and external disturbances during changing operating conditions.Future development should focus on coordinated control strategies at both system and subregion levels; (5) The challenge of achieving effective modeling with sufficient accuracy and reasonable computation speed using existing mathematical models of material properties.There is a trend towards designing electric motors and drives with digital twin (DT)-based models, optimizing motor performance, as well as manufacturing and operation processes throughout the entire cycle of motor life.

Comparison between Vectorial Magnetic Properties and Conventional Alternating Properties
Vectorial magnetic properties refer to the magnetic behavior of materials under different vectorial rotational magnetic fields.This approach differs from traditional alternating magnetic properties, which only consider the behavior of materials under a sinusoidal magnetic field in one direction.Vectorial magnetic properties are particularly relevant in the context of electrical machines, as they can provide a more accurate representation of the materials' behavior under rotational magnetic conditions.However, one of the challenges of using vectorial magnetic properties is the complexity of the characterization process.Traditional alternating magnetic properties can be measured using simple laboratory equipment, while vectorial magnetic properties require more advanced measurement techniques and analysis tools, which can increase the cost and time required for the characterization process.Despite these challenges, vectorial magnetic properties offer a more comprehensive understanding of the magnetic behavior of materials, and are becoming increasingly important in the design and development of high-performance electrical machines.Nevertheless, traditional alternating magnetic properties are still widely used due to their simplicity and ease of measurement.

Benefits
This paper offers an overview of advanced magnetic materials and their applications in designing high-power-density electric motors for electric vehicles, with a key focus on the benefits of vectorial rotational magnetic properties.By exploring these properties, the paper contributes to the development of more accurate mathematical models for predicting the performance of electric motors.Optimized design based on these models can lead to improved efficiency, power density, and reliability of electric motors.Additionally, this paper highlights the potential advantages of using various advanced electromagnetic materials.The emphasis on vectorial rotational magnetic properties and advanced materials underscores the potential for future progress in the field and the advancement of more efficient and reliable electric vehicles.

Figure 1 .
Figure 1.Iron loss of different core materials with respect to frequency.
2005, Snitchler et al. [99] presented a 5 MW HTS ship propulsion motor featuring high power density, efficiency, and low noise operation.In 2012, Gonzalez-Parada et al.

Figure 1 .
Figure 1.Iron loss of different core materials with respect to frequency.

Figure 5 .
Figure 5. Photo of the 2D vectorial magnetic property measurement system.

Figure 5 .
Figure 5. Photo of the 2D vectorial magnetic property measurement system.

Figure 6 .
Figure 6.Photo of the 2D magnetic property measurement system for HTS samples.

Figure 7 .
Figure 7. Measured core losses of an SMC sample under (a) alternating and (b) circularly rotating magnetizations with different peak values and frequencies of flux density.

Figure 7 .
Figure 7. Measured core losses of an SMC sample under (a) alternating and (b) circularly rotating magnetizations with different peak values and frequencies of flux density.