A novel double stator hybrid-excited Halbach permanent magnet flux-switching machine for EV/HEV traction applications | Scientific Reports

Scientific Reports volume 14, Article number: 18636 (2024) Cite this article

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This research paper introduces the Double Stator (DS) Hybrid Excitation (HE) Halbach Permanent Magnet (HPM) Flux Switching (FS) machine. The machine construction and its optimization specifically designed for electric vehicle (EV)/hybrid electric vehicle (HEV) traction applications are investigated. The optimization using a multi-objective Genetic Algorithm is conducted following a sensitivity analysis-based identification of key optimization parameters and constraints. The finite element results are compared with the performance of a state-of-the-art benchmark FSPM machine having identical PM volume and winding current densities. The proposed design is shown to outperform the benchmark with 16.2% increase in back-electromotive force and 14.7% reduction in cogging torque. Furthermore, the average torque is improved at flux-enhancing operation by 20.8%, and the torque ripple is reduced by 9.9%. Notably, the proposed machine also is capable of flux regulation thereby having the ability to operate in a wide speed range. A detailed explanation of the reasons for the significant improvements in the proposed machine structure is provided to offer a comprehensive understanding of its rationale. These research findings indicate that this innovative DS-HE-HPM-FS machine can enhance the performance of EVs and HEVs.

Permanent magnet (PM) machines have gained significant popularity in electrified transportation due to advantages in efficiency, torque and power density in addition to multiple other desirable features1,2,3,4,5. In comparison to traditional surface PM or interior PM machines, flux-switching permanent magnet (FSPM) machines exhibit potential for application as electric propulsion motors in electric vehicles (EVs), hybrid electric vehicles (HEVs) in addition to electric ships, and electric aircraft due to the robust rotor structure, near-sinusoidal back-electromotive force (back-EMF), superior high-speed flux-weakening capability, and excellent heat dissipation ability6,7,8,9,10. However, traditional FSPM machines suffer from drawbacks such as relatively high usage of PM material, limited speed range, high cogging torque, large torque ripple, and weak flux regulation capability11,12,13. Several previous studies have attempted to address these limitations mainly by modifying structural configurations, winding arrangements, magnet arrangements, as well as employing advanced design technologies such as partial stator, double-stator (DS), hybrid-excitation (HE), and Halbach PM arrays14,15,16,17.

PM machines with DS configuration have garnered significant attention for their potential high torque density, high power factor and efficiency. The concept of the DS machine is to divide the stator core into inner and outer stators in the radial direction of the machine, with the rotor core sandwiched between them. Utilization of DS technique to improve the performance of FSPM machines can be found in several literature. In 2016, a study on DS-FSPM machines for HEVs demonstrated significant improvement in efficiency, electromagnetic torque, and power density, with reduced magnetic saturation18.

Another noteworthy development is the use of biased PM excitation in dual-stator machines, showcasing high torque and power density, and superior electromagnetic performance19. A novel DS-FSPM machine has been presented in20, showing that this machine topology minimizes flux leakage and even-order harmonics in the back-EMF. Based on this, a topology for a 30 kW traction application is designed using the finite element method and demonstrates constant power operation and high efficiency, especially in the high-speed range. A novel DS-FSPM machine for EV applications is proposed in21 and compared with a conventional double stator permanent magnet synchronous machine (DS-PMSM). Theoretical analysis and simulation-based validation demonstrates that the DS-FSPM machine exhibits higher air-gap flux density and output torque, as well as larger cogging torque.

The HE technology typically combines direct current (DC) excitation with armature excitation, enabling wider operating torque/speed range, increased torque density, and enhanced flux regulation capability of PM machines. Several studies have used HE techniques to improve those characteristics of PM machines. In22, an E-core HE-FSPM machine was proposed, where a DC excitation winding is wound around the middle teeth of the E-core, creating independent paths for excitation flux and the main PM flux thereby improving flux regulation capability. In contrast, Ullah et al. introduced a HE linear machine with enhanced excitation magnetic field, providing improved flux regulation capability achieving a machine capable of a broader speed rang23. In24, Hua et al. compared three different configurations of DC windings and PMs, explaining the principles of flux modulation in detail. The results indicated that machines with PMs placed at the top or bottom exhibited stronger flux regulation capabilities compared to those with magnets in the middle of the spacing in between the E-core modules in HE-FSMs. In 2019, Yu et al. proposed a novel dual-stator hybrid excitation FSPM machine, optimizing the machine structure using the archive-based multi-objective genetic algorithm. The results demonstrated high efficiency, low cost, and effective suppression of radial force and torque ripple25. Similar studies demonstrate the performance improvements that can be achieved by HE-PM-FSMs compared with PM-FSMs with no HE22,23,24.

Transforming the conventional PM configuration into Halbach PM arrays is an effective method to achieve further improvement of magnet utilization and a reduction of PM flux leakage in PM machines. These arrays consist of PMs with different polarities arranged in specific configurations. Literature indicate that this technique is primarily utilized to enhance the performance of the surface-mounted PM machines, as it involves placing the magnets at the tip of the teeth. While it holds significant potential for improving the performance of PM machines in general, its application in FSPM machines remains limited. In 2013, a Halbach array was installed in an FSPM machine, achieving 20% higher electromagnetic torque compared to a C-core machine, while maintaining the same volume of PMs26. In27, Sanabria-Walter et al. demonstrated that implementing the Halbach PM arrays in a FSPM machine could cause a significant reduction of the leakage flux within this machine. In 2016, an implementation of Halbach PM arrays at stator outer diameter of FSPM machine indicated a performance enhancement of this machine through an improved magnetic field shielding28.

An implementation of DS, HE, and Halbach PM arrays techniques have not only been used solely to improve the performance of FSPM machines, rather the combination of these techniques have also been considered in a few studies to improve performance of other types of machines. In11, a combination of DS and HE techniques was used to improve the torque capability and the flux weakening capability over a wide operating range of the FSPM machine. In 2020, Yu et al. transformed the single stator FSPM machine into the DS configuration25. With this configuration with HE applied, the machine was shown to achieve an enhanced torque capability, improved efficiency as well as reduced PM volume. In particular, a literature survey indicates a limited number of studies such as29 have successfully integrated all three techniques of DS, HE, and Halbach PM arrays to improve the performance of PM machines. The authors of24 prove and demonstrate the effectiveness of combining these techniques in improving the torque capability of flux-reversal permanent magnet (FRPM) machines. However, the use of the combined DS, HE, and Halbach PM array technique in FSPM machines has not been documented or proven. Notably, we noticed that implementing this combined technique could effectively address the several weak points of FSPM machines, including high cogging torque, significant torque ripple, and limited flux regulation capability.

Therefore, this paper proposes the novel double stator hybrid-excited Halbach permanent magnet (DS-HE-HPM) flux-switching (FS) machine for EV/HEV traction applications. It is important to note that this paper is the first to present the combined techniques of DS, HE, and HPM for FSPM machine design. Through a multi-objective optimization algorithm to optimize key parameters of the proposed DS-HE-HPM-FS machine, the goal to enhance torque capability has been achieved.

The rest of manuscript is arranged as follows: Section II describes configuration of a novel DS-HE-HPM-FS machine as well as explaining the machine working principle and the flux regulation process. In Section III, the design parameters and multi-objective optimization process are explained. Section IV evaluates the comprehensive performance of the proposed machine using finite element (FE) method and compares it with the benchmark machine. Finally, a summary of the research is provided in Section V.

The FSPM machine used for benchmarking is an E-core dual-PM flux-switching machine adopted from7, as shown in Fig. 1a. This machine is a very recent innovative design and is selected due to its superior torque density and high overload capacity compared to several other FSPM structures. The structure of the benchmark FSPM machine features 12 E-shaped core modules with additional PMs for excitation inserted into the slot opening. The magnetic field generated by this supplementary PM source is parallel to the field produced by the spoke-type magnets between the E-core modules, resulting in a significant enhancement in magnetic flux utilization in stator core. The rotor of this machine contains 19 rotor poles.

Topology of (a) the benchmark HE-FSPM machine and (b) the proposed DS-HE-HPM-FS machine.

The proposed topology of the machine consists of dual stators as depicted in Fig. 1b. The main specifications of this design are provided in Table 1. The hollow rotor occupies the space between the inner and outer stators. The outer stator consists of modular E-shaped cores similar to that of the benchmark. PMs are situated on both outer and inner stators, including spoke-type PMs and slot PMs. The inner stator comprises six teeth, positioned such that the teeth with PM align with that of the outer stator. The spoke-type PMs are magnetized tangentially and are sandwiched between the modular E-shaped cores.

In this study, the slot PMs are implemented as Halbach arrays to enhance magnetic flux concentration at the air gap and to reduce flux leakage. Halbach PM arrays consist of three segments with different magnetization directions. As depicted in the inset figure, the central PM is magnetized radially, while the PMs on both sides are magnetized at a 45-degree angle to the central magnet. Due to the significant differences in configuration, the magnetic fields produced on the respective air-gaps by the inner and outer stators vary. Therefore, the rotor is designed with unequal teeth height of the outer and inner rotor and has also been proven suitable for this stator configuration25. The presence of the rotor yoke enhances the rotor's mechanical strength and significantly impacts the magnetic density of the inner and outer air gaps and the coupling between the dual stators, details of which will be elaborated on in the subsequent optimization section.

A 3-phase single-layer concentrated winding is adopted for this design and is symmetrically distributed on the teeth of both the inner and outer stators. DC field excitation windings are inserted on both the inner and outer stators. For the outer stator, they are wound around the middle teeth to produce a field alongside the armature field to regulate the magnetic flux. The DC field excitation winding of the inner stator is positioned at the inner stator yoke to enhance the flux-enhancing and flux-weakening capabilities of the machine.

The proposed design is a DS-HE-HPM-FS machine. In this configuration, the outer stator typically acts as the primary contributor to electromagnetic performance, while the inner stator serves to enhance the performance and torque density. The total electromagnetic torque, T, produced by the machine is25:

where, To and Ti are the torques generated by the outer stator-inner rotor and inner stator-outer rotor, respectively.

The operational principles of the machine proposed in this paper can be explained by considering the flux paths at different rotor positions. The no-load PM excitation condition is depicted in Fig. 2. The flux excited by spoke PMs, represented by black dotted lines, flows through the outer stator side teeth, middle teeth, rotor, and inner stator teeth. Conversely, the flux excited by slot PM, depicted by blue dotted lines, flows through the edge teeth, outer stator yoke, middle teeth, and rotor. These two excited fluxes flow in parallel through the outer stator teeth.

No-load PM excited flux at different rotor positions indicating the operating principle of the proposed machine. (a) 0 electrical degree. (b) 90 electrical degrees. (c)180 electrical degrees. (d) 270 electrical degrees.

Fig. 3. illustrates the waveform of no-load flux-linkage produced by outer-stator, inner-stator, and their combination. The flux-linkage under all three excitation modes exhibits identical phases, where the flux from the dual-stator equals the combined fluxes from the two single stators. The outer stator significantly contributes more to the total flux-linkage than the inner stator. The peak of flux-linkages occurs at rotor electrical positions of 0° and 180°, indicating alignment between rotor teeth and the side teeth of the inner and outer stators. At these positions, both spoke-PMs and slot-PMs produce magnetic fluxes that flow in the same direction through the armature coils wound on the two side teeth, resulting in the superposition of maximum positive or negative values of both fluxes. The spoke-PMs located in the inner rotor enhances the main flux circulation. Conversely, at rotor electrical positions of 90° and 270°, the magnetic flux linkage becomes zero as the rotor slots and teeth align with the spoke-PMs. Consequently, the fluxes excited in two opposite directions through stator side teeth, middle teeth, and rotor combine to form zero flux through the armature coils. Thus, the effective integration of spoke-PM and slot-PM greatly enhances the utilization of stator core. Furthermore, the opposite directions of magnetic fluxes excited by the two types of PMs in the stator yoke, middle teeth, and rotor effectively mitigate magnetic saturation of stator and rotor cores.

Open-circuit phase flux-linkage waveforms of proposed machine.

Since the application of HE is another major contribution of the proposed DS-HE-HPM FS machine, the no-load flux-linkage under different polarities of rated DC current density Jdc (10 A/mm2) is analyzed, as presented in Fig. 4. Variation of flux linkage under different DC field excitation conditions are observed, confirming the influence of the HE in this structure. Fig. 5. displays the distribution of open-circuit flux lines of the proposed machine under various DC field excitation conditions. It is apparent that when applying flux enhancing DC excitation currents, as shown in Fig. 5c, the flux in the stator poles is larger, while the flux passing through the middle teeth of the outer stator iron and the back iron of the dual stators is significantly lower compared to the case of applying flux weakening DC excitation current, as shown in Fig. 5a. The magnetic flux generated by DC excitation can be superimposed on the main flux, thereby altering the flux linkage.

Open-circuit phase flux-linkage waveforms of proposed machine under different excitation conditions (Jdc = 10 A/mm2).

Open-circuit flux line distribution under different field excitation conditions. (a) Jdc =− 10 A/mm2. (b) Jdc = 0 A/mm2. (c) Jdc = 10 A/mm2.

This section presents a mathematical derivation to illustrate the working principle of the proposed machine and to quantify the mechanism of electromagnetic torque generation. The calculations are simplified by neglecting iron saturation and reluctance torque of the stator and rotor. The analysis process is carried out separately for the inner and outer air gaps according to the DS configuration of the proposed machine. The total torque is obtained by summation of the contributing torques. The air-gap permeance function is given by30;

where Λ, θ, g and μ0 represent the permeance, the circumferential angle, the air-gap length and air permeability, respectively. Functions Λs (θ) and Λr (θ, t) denote the air-gap permeance function for slotted stator and slotted rotor, respectively. However, the distribution of rotor permeance, Λr, is non-uniform due to the slotting effect. It can be expressed as a Fourier series, as31;

where Λj, Nr and Ω represent the amplitude of the jth-order harmonic contribution of the rotor permeance, the rotor poles number and the rotor mechanical angular speed, respectively. Since the higher order rotor air-gap magnetization amplitude is negligible, j is taken as 17. Then, (3) is equivalent to:

where Λr0 is the average rotor permeability of the Fourier series. In quantitative analysis, the equivalent stator MMF model function Fs(θ) can be obtained by summing the equivalent MMF amplitudes corresponding to the ith-order harmonics. The air-gap permeability mainly contributes to the odd harmonics and can be expressed as:

where Ps is the pole-pair number of equivalent stator MMF. FPM(θ) represents the MMF generated by PM excitation. The (2), (4), and (5) can be combined and expressed as follows:

where Nr is rotor teeth number. Pole pairs of air-gap flux density harmonics n=| iPs±Nr|. The winding function Nc(θ) is defined as32

where Tp, kch, and Pa represent the number of winding turns per phase, winding factor corresponding to the hth harmonic of the armature winding, and pole-pair number of armature winding. Harmonics of different orders of air-gap flux density contribute differently to the generated back-EMF and electromagnetic torque. Fig. 6 illustrates the flux densities of the inner and outer air gaps and their harmonic distributions under no-load conditions for different numbers of pole pairs. The amplitudes of the outer stator pole pairs in the proposed machine are larger than those of the inner stator, except for the 10th and 28th pole pairs. This confirms the previous analysis indicating that the outer stator contributes to the majority of the torque. To analyze the contribution of different harmonics, combining (6) and (7) yields an expression for the back-EMF more precisely as7

where Din and L represent the inner diameter and stack length of the stator, respectively. Bgn and kcn denote the amplitude and winding factor, respectively, for the air-gap magnetic density harmonics corresponding to the pole-pair number n. By incorporating (8) into the torque equation, the resulting expression for the total electromagnetic torque (Te) is given in (9).

Inner and outer air-gap flux densities and harmonics of the proposed machine. (a) waveforms. (b) Harmonics.

Table 2 presents the contributions of the main harmonics and pole pairs to the back-EMF and Te. The back-EMF and Te were calculated using equations (8) and (9) for different pole-pair contributions and compared with the FEA results. The table shows that the maximum contribution to back-EMF and Te occurs when the pole-pair harmonics are 2, 4, and 8. On the other hand, the 14th, 16th, and 22nd pole-pair harmonics have negative winding factors and weaken the output. Comparative calculations and FEA results indicate that the total back-EMF and Te errors are within 10%, which is acceptable.

In order to improve the torque capability of the DS-HE-HPM-FS machine, the multi-objective genetic algorithm optimization (MOGA) is performed to refine the design parameters. The optimization process is performed under flux enhancing conditions at which the machine produces highest flux linkage and electromagnetic torque. The optimization process consists of five steps illustrated in Fig. 7.

Flowchart of the optimization process.

In Step 1, the objective functions are defined followed by Step 2 at which the design variables are categorized into two groups based on a sensitivity analysis. The sensitivity analysis identifies strong-sensitive and weak-sensitive parameters respectively. In Step 3, the MOGA algorithm, detailed in Fig. 7, is used to optimize the strong-sensitive parameters and obtain the optimal Pareto solution. In Step 4, the parameters obtained in step 3 are kept constant, and weak-sensitive parameters are optimized based on this foundation to attain the Pareto optimal solution. Finally Step 5 compares the machine performance before and after optimization.

Number Since the DS-HE-HPM-FS machine is specifically designed for EV or HEV traction applications, the design goal prioritizes high torque density, high overload capacity, and low noise and vibration6. Considering these requirements, this paper focuses on maximizing the electromagnetic torque and minimizing torque ripple. The design constraints are detailed as follows:

(1) The optimization process is conducted using identical parameters to the benchmark structure, including a rated current of 6.4 A, a package factor of 0.5, and a speed of 1000 r/min.

(2) The proposed machine mirrors the benchmark structure in terms of outer stator diameter, permanent magnet (PM) volume, spoke PM size, and stack length.

(3) All parts of the proposed machine are constructed from the same materials as those used in the benchmark machine.

(4) Minimum values for the rotor yoke thickness, stator outer yoke thickness, middle tooth width, and stator tooth width are established to ensure the structural robustness of the proposed machine.

In order to determine the influence of each design variable on the optimization objectives, the sensitivities of all design parameters are evaluated. The selected design variables are depicted in Fig. 8, where their definition and respective range are indicated in Table 3. To ensure the robustness of the machine structure, the values for the outer stator tooth width, outer stator middle tooth width, outer stator yoke thickness, and inner stator yoke thickness must be greater than 4 mm, while the minimum value for the rotor yoke width is 1.5 mm.

Dimensional parameters of the DS-HE-HPM FS machine.

In order to evaluate the precise impact of design variables on the optimization objective effectively, a quantitative analysis of the sensitivity of each parameter is conducted. A comprehensive sensitivity function Sc(xi) is defined as follows:

where the sensitivity index for each parameter variable, S(xi), is defined as33.

Variable y represents the optimization objective. V (y/xi) represents the variance of y associated with a certain parameter xi. Variable \(\overline{y }\) denotes the average value of y corresponding to the variation of parameter xi.

Table 4 indicates the sensitivity analysis of each design parameter on the output torque and torque ripple. It shows that both Roy and Tow_1 exert the highest influence on both output torque and torque ripple. Parameters Tisw and Tosw primarily affect the output torque. Meanwhile Tow_2, Tiw_1 and Dosy also have a relatively large impact on torque ripple. The sensitivity indices for each parameter and the comprehensive sensitivity indices are listed in Table 3. Given the large number of design variables, the threshold value, the threshold value of Sc(xi) is set to 0.05 based on the number of design parameters and their variation range. This threshold categorizes sensitivity as either “strong” or “weak”.

The parameters of MOGA algorithm are initialized with a population size of 200, mutation probability of 0.1, and crossover probability set to 0.9. The optimization process is conducted over 800 generations, and convergence to the optimal solution is observed when nearing approximately 600 generations of optimization. To determine the best compromise from the set of Pareto solutions, the evaluation function is defined as shown in equation (12). The solution that minimizes fgoal (xi) is considered optimal.

where xi (i = 1, 2, 3 . . . 10) are the design variables listed in Table 3. T 'avg and T 'rip are the initial values of the average torque and torque ripple, and Tavg(xi) and Trip(xi) are the optimized values, respectively. Weights μ1 and μ2 are chosen at 0.7 and 0.3, respectively, to meet the design requirements.

The optimization results for the strong-sensitive indices are depicted in Fig. 9. Based on the Pareto curve, the optimal solution is determined based on objective function, showing that the optimized machine produces an output torque of 16.49 N.m and a torque ripple of 3.8%.

Strong-sensitive optimization results.

The results of optimizing the weak-sensitive parameters are shown in Fig. 10. The high-sensitive parameters are kept at the optimized values as explained earlier. Based on the Pareto curve and the corresponding optimization objective weights, the optimal design point is determined. The optimization results are summarized in Table 5. The optimal machine produces an output torque of 16.67 N.m with a torque ripple of 3.5%. demostrating7.4% higher torque and 28.5% lower ripple compared to the initial design.

Weak-sensitive optimization results.

This section analyses the performance of the optimized DS-HE-HPM FS machine and compares it with the benchmark machine. The comparison is conducted under the same current density and at rated speed of 1000 rpm.

The flux regulation capability is a significant parameter of hybrid excitation PM machines and influences starting torque during field enhanced operation and the speed range the machine can operate with a limited voltage supply in field weakening operation. Flux regulation, γ, is defined as22:

where ψenh and ψwea represent the fundamental amplitude of flux-linkage under flux-enhancing and flux-weakening conditions, respectively. Parameter ψpm is the fundamental amplitude of flux-linkage without DC excitation. Fig. 11 demonstrates the flux regulation capability of the DS-HE-HPM FS machine under different DC current densities in the field windings. It shows that the curve is linear with a higher gradient at negative DC currents and a lower gradient with positive DC currents. This effect is primarily due to the reduced saturation of the core during flux weakening and higher saturation of the core during flux enhanced operation. It was found that the flux regulation of the DS-HE-HPM FS machine is 15% under flux-weakening operation and 6.3% under flux-enhancing condition, while overall flux regulation range is 21.3%. These values are found to be acceptable in comparison with the other hybrid PM machines. The phase back-EMF waveforms of the DS-HE-HPM FS machine under different excitation conditions are also shown in Fig. 12 and also mirror the observations of flux linkage and the impact of saturation.

No-load flux-linkage under different excitation currents.

Phase back-EMF waveforms under different excitation conditions.

The no-load back-EMF waveforms and their harmonics generated by the proposed and benchmark structures of the DS-HE-HPM-FS machine under PM excitation and flux-enhancing operations has been characterized and are illustrated in Fig. 13. Without DC excitation, the proposed machine exhibits a higher back-EMF with a 140V peak compared to that of the benchmark with a 129V peak, which is an 8.5% increase. This enhancement is primarily due to the utilization of the DS structure, which allows the machine to generate back-EMF from both the inner and outer stators. Under flux-enhancing operation, the back-EMF reaches 149.9V, representing a 16.2% improvement over the benchmark value. Additionally, the DS-HE-HPM FS machine structure is designed to have a larger slot area, enabling more winding turns to be installed under the same package factor. The spectral analysis depicted in Fig. 13b reveals that each machine manifests a very low level of THD, with values well below the acceptable threshold for EV traction applications.

Open-circuit phase back-EMF waveforms excited by PMs and its spectra. (a) Waveforms. (b) Harmonics.

Fig. 14 displays the cogging torque waveforms for both the DS-HE-HPM-FS and benchmark machines. The peak-to-peak cogging torque magnitude of the proposed machine with only PM excitation is 14.7% lower than that of the benchmark machine. This reduction is attributed to a more distributed air-gap flux from the stator teeth caused by the improved compatibility of the stators and rotor after optimization. However, the magnitude of the cogging torque increases by 32% in comparison to the benchmark value when the machine operates in flux-enhancing conditions. This increase is mainly due to the enhancement of the total air-gap flux caused by the DC magnetic field.

Cogging torque waveforms.

The torque performance of the DS-HE-HPM FS machine is analyzed and compared to the benchmark machine, as shown in Fig. 15. The proposed machine exhibits an average electromagnetic torque of 16.35 N.m under the PM excitation condition, marking a significant improvement of 18.5% compared with the benchmark. Meanwhile, torque ripple is reduced by 6.6% under this condition, equating to 3.66%. When DC excitation is applied, the DS-HE-HPM FS machine generates 20.8% higher torque than the benchmark machine and experiences a 9.9% reduction in torque ripple at the rated point of flux-enhancing operation. The improved torque performance is mainly attributed to the DS configuration. The DS structure also increases improved available slot area, leading to an increase in the number of turns in the armature windings. Additionally, the use of a Halbach PM array enhances the local magnetic field, reduces the leakage flux, improves the utilization of PMs, and enhances the air-gap flux. When DC excitation is applied, the torque performance is enhanced because it strengthens the main flux and weakens the flux flowing through the stator back iron and intermediate teeth. Consequently, the DS-HE-HPM FS machine exhibits superior torque characteristics compared to the benchmark.

Comparison of electromagnetic torque waveforms.

The torque capability of the DS-HE-HPM FS machine under different DC excitation currents is shown in Fig. 16. It clearly indicates that the proposed machine exhibits a higher average torque than the benchmark structure under PM excitation, flux-enhancing, and flux-weakening conditions. The variation of average torque during varying DC excitation currents is consistent with the variation of EMF and flux-linkage profiles previously presented in Figs. 10 and 11, respectively. Applying DC excitation results in a lower torque variation during flux-enhancing conditions compared to flux-weakening conditions since the enhancement of DC excitation creates partial short-circuit flux in the outer stator back iron, middle teeth, and rotor yoke, leading to a reduction in the flux increment distributed in the stator teeth. Additionally, the DC excitation flux saturates the iron core, weakening the regulation capability of flux enhancement. The torque ripple during flux-enhancing conditions seems to be slightly higher than that during flux-weakening conditions. Overall, the DS-HE-HPM FS machine outperforms the benchmark machine in terms of torque capability.

Electromagnetic torque waveforms of the proposed DS-HE-HPMFS machine under different excitation conditions.

Table 6 compares the on-load performance of the DS-HE-HPMFS machine under flux-enhancing conditions with that of the benchmark machine at a rated current of 6.4 A and a speed of 1000 r/min. The results show that the copper loss of the proposed machine is higher than that of the benchmark machine due to the greater winding usage in its hybrid-excitation. Additionally, the higher iron loss is attributed to the increased steel usage in its double stator configuration. However, the segmentation of the PMs in the proposed structure results in reduced PM loss. The power factor of both structures is similar, but the efficiency of the proposed structure is improved compared to the benchmark structure.

Figure 17 presents the efficiency maps under the maximum torque per ampere control method for the DS-HE-HPMFS machine under flux-enhancing conditions, compared to the benchmark machine, along with their torque-speed curves. The proposed machine can produce higher torque than the benchmark structure below a speed of 1000 r/min. Above this speed, the benchmark structure achieves slightly higher torque. Both machines reach a maximum efficiency of over 95%; however, the DS-HE-HPMFS machine has broader high-efficiency regions.

Efficiency maps (Irms = 6.4 A, Udc = 500 V). (a) the DS-HE-HPMFS machine. (b) The benchmark machine.

Since the proposed DS-HE-HPMFS machine contains two armature windings and DC excitation windings, it is necessary to analyze the demagnetization capability of the PMs as they might be affected by heat induced by the current. Figure 18 illustrates the flux density distribution of the PMs under a two-times overload operation. The working range of the N35UH PM in the proposed machine is 0 T to 1.6 T, with an operating temperature of 120 °C and a corresponding knee point of − 0.28 T. The flux density of ten PM segments is evaluated to analyze their demagnetization. For each PM segment, five points, including the center and corners, were selected to analyze the flux density variation over one electrical cycle of rotor rotation. The possible values of flux density for each PM segment are summarized in Fig. 19. The results clearly show that the flux density of every PM is within the operational range, indicating that there is no risk of demagnetization in the proposed DS-HE-HPMFS machine.

Flux density distribution of PMs at two-times overload current.

Range of flux density of different PMs in one electrical cycle of the rotor.

Overall, the electromagnetic performance of the DS-HE-HPM FS machine is superior to that of the benchmark machine. It should be noted that the manufacturing cost of the proposed machine could be higher than that of the benchmark machine, primarily due to increased assembly costs and greater copper usage. Hence, the findings confirm that the proposed DS-HE-HPM FS machine has high torque capability and is an outstanding choice for EVs/HEVs traction applications. In forthcoming efforts, it is recommended to incorporate experimental verification. When manufacturing the DS-HE-HPM FS machine, installing the DC windings in the inner stator may require high-precision machining, as they must be wrapped around the entire inner stator core.

A novel DS-HE-HPM FS machine was proposed and developed for EV/HEV traction applications. The proposed machine was initialized by transforming the single stator of the benchmark DPM-FS machine structure into a DS configuration, and then implementing Halbach PM arrays on the primary stator. DC field excitations were inserted into both the inner and outer stators to enhance the machine’s flux regulation capability. The structural design parameters of the proposed machine were optimized using a multi-objective Genetic algorithm, considering their sensitivity analysis-based constraints. Firstly, the operational principle of the proposed machine was analyzed and described. The behavior of the machine under flux-enhancing and flux-weakening conditions was analyzed. The analysis also confirms that the machine operation with the flux switching concept. When compared to the benchmark machine operating at a rated speed of 100 rpm under identical current density and only PM excitation condition, the proposed machine demonstrates significant improvements, including an 11.7% enhancement in back-EMF, an 18.5% increase in torque, a 6.6% reduction in torque ripple, and a 14.7% decrease in cogging torque. With the presence of DC excitation, flux regulation capability of the proposed machine is enhanced. It is worth noting that the DS-HE-HPM FS machine has a narrower flux adjustment range and stronger flux-weakening capability than flux-enhancing capability. Under flux-enhancing conditions, the proposed machine exhibits a 20.8% higher electromagnetic torque and a 9.9% lower torque ripple than the benchmark machine. These enhancements are attributed to its double stator topology, reduced flux leakage, and improved PM utilization. Hence, the DS-HE-HPM FS machine presents itself as a promising choice for EV/HEV traction applications.

Data is provided within the manuscript or supplementary information files.

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This work was funded by National Research Council of Thailand and Khon Kaen University under Grant no. N42A660360, Major Science and Technology Innovation Projects in Fujian Province under Grant no. 2021G02016, Natural Science Foundation of Fujian Province under Grant no. 2023J01352, 2023J011091 and Collaborative Innovation Center of Ningde Normal University under Grant no. 2022ZX02.

Department of Electrical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen, 40002, Thailand

Shichao Ning, Pattasad Seangwong, Apirat Siritaratiwat & Pirat Khunkitti

Faculty of Mechanical and Electrical Engineering, Ningde Normal University, Ningde, 352100, China

Shichao Ning

School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne, VIC, 3000, Australia

Nuwantha Fernando

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Shichao Ning: Conceptualization, Methodology, Analysed the results, Writing- Original draft preparation. Pattasad Seangwong: Visualization Analysed the results. Nuwantha Fernando: Visualization, Analysed the results. Apirat Siritaratiwat: Visualization, Analysed the results. Pirat Khunkitti: Methodology, Analysed the results, Supervision, Writing- Reviewing and Editing.

Correspondence to Pirat Khunkitti.

The authors declare no competing interests.

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Ning, S., Seangwong, P., Fernando, N. et al. A novel double stator hybrid-excited Halbach permanent magnet flux-switching machine for EV/HEV traction applications. Sci Rep 14, 18636 (2024). https://doi.org/10.1038/s41598-024-69857-8

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Received: 03 May 2024

Accepted: 09 August 2024

Published: 11 August 2024

DOI: https://doi.org/10.1038/s41598-024-69857-8

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