Variable flux memory machines (VFMM) using low coercive force (LCF) permanent magnets (PM) have been extensively investigated [1]-[5]. Normally, the series hybrid
magnet topology equipped with both PM with high coercive force (HCF) and LCF PMs to achieve high torque density and extended constant power speed range simultaneously, and two
kinds of PMs are magnetically connected in series to avoid unintentional demagnetization in LCF magnets. Nevertheless, the role LCF PM acts in the series magnetic circuit and its
potential effect on the air-gap flux density remain unclear. In this paper, the flux barrier effect of LCF PM on series VFMM is revealed and investigated, and an approach to preventing the
air-gap flux density drop is presented.
The conventional series hybrid magnet VFMM and interior permanent magnet (IPM) machine sharing identical usage of HCF PMs are shown in Fig.1. In Fig.1(e), the back-EMF amplitude
of the series VFMM is lower than that of the IPM machine. This is mainly due to the fact that the air-gap flux enhancement by the magnetomotive force of the LCF PM cannot compete
with the weakening effect by the magnetic reluctance of LCF PM. As a result, the flux barrier effect of the LCF PMs is identified, which further leads to a reduction of the torque density.
The topology of VFMM with dual-layer PMs is shown in Fig.1(c). The separation of the PMs weakens the barrier effect on the HCF PM and the bypass flux path reduces the equivalent
reluctance in the magnetic circuit. It can be observed in Fig.1 (d) that the air-gap flux density and flux variable range are improved. That is to say, the magnetic flux barrier effect of LCF
PM is reduced with the proposed dual-layer PM design.
The test results of the open-circuit back-EMF of the dual-layer series hybrid magnet VFMM prototype are shown in Fig.2. The experiments agree well with the FE-predicted results. The
detailed analysis, suppression methods of the flux barrier effect, and the detailed test results, will be given in the full paper. 

**References:** 

[1] V. Ostovic, "Memory motors," IEEE Ind. Appl. Mag., vol. 9, no. 1, pp. 52-61, Jan./Feb. 2003. 
[2] K. Sakai, K. Yuki, Y. Hashiba, N. Takahashi and K. Yasui, "Principle of the variable-magnetic-force memory motor," in Proc. Inter. Conf. Elec. Mach. System. (ICEMS), 2009, pp. 1-6. 
[3] N. Limsuwan, T. Kato, K. Akatsu and R. D. Lorenz, "Design and evaluation of a variable-flux flux-intensifying interior permanent-magnet machine," IEEE Trans. Ind. Appl., vol. 50,
no. 2, pp. 1015-1024, Mar./Apr. 2014. 
[4] H. Hua, Z. Q. Zhu, A. Pride, R. Deodhar and T. Sasaki, "A novel variable flux memory machine with series hybrid magnets," in Proc. 2016 IEEE Energy Conversion Congress and
Exposition (ECCE), 2016, pp. 1-8. 
[5] H. Yang, H. Zheng, H. Lin, Z. Q. Zhu and S. Lyu, "A novel variable flux dual-layer hybrid magnet memory machine with bypass airspace barriers," in Proc. 2019 IEEE International
Electric Machines & Drives Conference (IEMDC), 2019, pp. 2259-2264. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/7a5c9dbea872186ef88d40ecd7615782.png)

Analysis of flux barrier effect of LCF PM in series hybrid magnet variable flux memory machine

This paper overviews recent developments and novel topologies of a new class of asymmetric rotor pole interior permanent magnet (AIPM) machines for torque enhancement. The principle for torque enhancement by utilizing magnetic-field-shifting is introduced firstly. AIPM machine topologies are then categorized in terms of asymmetries of PM configurations and rotor core geometries. Subsequently, various AIPMs in each category are described and analyzed with respect to merits and demerits. Finally, electromagnetic performances of selected AIPM machines are compared. INDEX TERMS: Asymmetric interior permanent magnet (AIPM), Magnetic-field-shifting (MFS), PM torque, Reluctance torque I. Introduction Interior permanent magnet (IPM) machines having PMs buried inside the rotor cores are of growing interests due to superior torque density, high efficiency, wide constant power operating speed range, and high rotor robustness [1]. In IPMs, the reluctance torque resulted from the rotor saliency can be utilized to enhance the torque density without increasing the PM usage. However, in conventional IPM machines with symmetrical rotor structures, the maximum PM and reluctance torque components are achieved at different current angles whose difference is theoretically 45 electrical degrees. Consequently, only a portion of both torque components can be utilized at the current angle of maximum synthetic torque. To deal with this issue, a novel design concept for torque enhancement of IPMs by making the maximum PM and reluctance torque components to be reached with a smaller difference of current angles has been firstly proposed by setting the optimal displacement angle between the surface-mounted PM rotor and the reluctance rotor in a two-part rotor PM machine [2] and by employing asymmetric rotor flux barriers in a V-shape IPM [3], respectively. To utilize the concept designated as magnetic-field-shifting (MFS) effect in this paper, the PM field and reluctance axes of IPM machines need to be shifted, resulting in a new class of novel asymmetric rotor IPM machines. The torque enhancement principle of AIPM is illustrated in Fig. 1. This paper overviews various novel AIPM topologies which are categorized in terms of asymmetries of PM configurations and rotor core geometries, analyses various AIPMs in each category with respect to merits and demerits, and compares electromagnetic performances of selected AIPM machines. II. AIPM Machine Topologies In this section, novel AIPM machine topologies in literature are categorized according to whether their PM configurations and rotor core geometries are symmetrical or asymmetric, respectively. The proposed categorization method and some examples reported in references for each category are shown in Fig. 2 (a). An AIPM topology with the asymmetric hybrid-layer PM configuration and asymmetric rotor cavity has been proposed in [4], which achieves torque enhancement with simple structure due to utilizing MFS effect and also shows reduced torque ripples. A hybrid-pole AIPM machine is proposed in [5] that employs V-shape and inset PMs in adjacent poles alternatively, which has asymmetric PMs due to shifted positions of inset PMs but symmetrical rotor core geometry. This hybrid-pole AIPM has higher torque density compared with a V-shape IPM with the same PM usage. An AIPM machine with asymmetric PMs and symmetrical rotor structure is also reported in [6] that can achieve fully aligned maximum PM and reluctance torque components, although the increase of synthetic torque is not notable compared with a PM-assisted reluctance machine because of significant reduction of maximum reluctance torque. The asymmetric flux barrier in one side of symmetrical V-shape PMs in each pole is used in [3] to utilize the MFS effect by shifting the angle of reluctance axis and to clearly increase the synthetic torque. Similar to [2], a two-part rotor design with a SPM rotor and a multi-layer reluctance rotor is proposed in [7] that exhibit symmetrical PM configuration and rotor cavity design, respectively. The MFS effect is utilized by adjusting the displacement angle between both rotor parts, which can also achieve fully aligned maximum PM and reluctance torque components and shows a clear torque enhancement. Four selected AIPM machines with rotor topologies proposed in references [3]-[5] and [7] are redesigned by using the same stator, rotor diameter and PM usage to the conventional Toyota Prius 2010, and their torque performances at 750 r/min and 236A are compared in Fig. 2 (b). Comprehensive overview of more AIPM topologies will be given in the full paper.

**References:**

[1] Z. Zhu and D. Howe, Proc. IEEE, vol. 95, p.746-765 (2007). [2] P. Winzer and M. Doppelbauer, 2014 Int. Conf. Electr. Mach. (ICEM), Berlin, 2014, p. 641-647. [3] W. Zhao, F. Zhao, T. A. Lipo, and B.-I. Kwon, IEEE Trans. on Magn., vol. 50, no. 11, p. 1-4 (2014). [4] Y. Xiao, Z. Q. Zhu, J. T. Chen, D. Wu, and L. M. Gong, 2020 Int. Conf. Electr. Mach. (ICEM), Gothenburg, 2020, p. 26-32. [5] G. Xu, G. Liu, W. Zhao, Q. Chen, and X. Du, IEEE Trans. Ind. Electron., vol. 66, no. 4, p. 2580-2591 (2018). [6] F. Xing, W. Zhao, and B.-I. Kwon, IET Electr. Power Appl., vol. 13, no. 5, p. 573-580 (2018）. [7] H. Yang, Y. Li, H. Y. Lin, Z. Q. Zhu, et al., 2017 IEEE Energy Convers. Congr. Exposition (ECCE), Cincinnati, 2017, pp. 2362-2367.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/339b97d20cc7f72fd8fd7d97e5455425.jpg)
Fig.1.Principle of torque enhancement of AIPM. (a) Conventional IPM. (b) AIPM with reduced △β. Tsyn, Tpm and Trel denote maximum synthetic, PM, and reluctance torques, respectively, and △β denote the current angle difference between maximum PM and reluctance torque components.

![](https://assets.underline.io/uploads/markdown_image/1/image/4d44aa957f2775e6ab24c779072c37ef.jpg)
Fig.2. Categorization of some typical AIPM machine topologies. In (a), PMs in red and blue denote N- and S-poles.

 Novel Asymmetric Rotor Pole Interior Permanent Magnet Machines with Enhanced Torque Density: An Overview

This paper proposes an efficient surrogate-assisted design optimization method based on multicriteria optimal Latin hypercube design (LHD) for multi-objective optimization of a permanent-magnet vernier machine (PMVM). By combining simulated annealing algorithm, the uniformity and orthogonality of spatial distribution of the LHD are optimized to efficiently capture data features over the optimization parameter ranges. Consequently, an accurate surrogate model with high generalization capability can be built with a small training set by using the optimal LHD. The optimal design of the PMVM is obtained by multi-objective design optimization based on the surrogate model. A prototype is made and tested to validate the proposed method. I. Introduction Due to high torque capability at low speeds, permanent-magnet vernier machines (PMVMs) are suitable for direct-drive applications such as wind power generation and electric drilling [1]. To deal with the issue of massive finite-element analysis (FEA) for multi-objective design optimization, this paper proposes a novel surrogate-assisted multi-objective design optimization method for PMVMs. A multicriteria optimal Latin hypercube design (LHD) employing simulated annealing (SA) algorithm is proposed for efficient date feature capturing that enables to use a small training dataset for obtaining an accurate surrogate model. The sparrow search algorithm (SSA)-optimized multi-output least squares support vector machine (MLS-SVM) [2] and the non-dominant sorted genetic algorithm-III (NSGA-III) [3] are combined to build the multi-output surrogate model and to perform the multi-objective design optimization. A prototype is made based on the obtained optimal design and tested for validation. II. PMVM and Sensitivity Analysis A surface-mounted PMVM with 18 slots and 15 pole pairs is studied as an example, whose topology is illustrated in Fig. 1 (a). The four optimization objectives are average torque, power factor, THD of back-EMF, and cogging torque. To improve the optimization efficiency, a global sensitivity analysis (GSA) of four optimization targets is performed using the Sobol’s method [4], the stack bars of total sensitivity coefficient (TSC) for optimization parameters are given in Fig. 1 (b), which shows the geometrical parameters that have the greatest influence on design objectives. Thus, five geometrical parameters including PM thickness (tPM) and width (wPM), yoke thickness (ty), slot width (ws), and stator split ratio (k=Rsi/Rso) are selected for optimization while stator outside diameter, axial length, air-gap length, and current density are fixed. III. Surrogate-Assisted Optimization with LHD The optimal LHD employs SA to minimize a composite indicator ψp that consists of the Morris-Mitchell index Φp and the correlation coefficient of the test factors ρ2 to guarantee the spatial distribution uniformity and orthogonality as given in (1), where ω1 and ω2 are the weight factors. Subsequently, a 270*5 LHD is built to capture the data feature over the optimization parameter ranges more efficiently as shown in Fig.2 (a), in which 20 sets of data are used for testing the regression results. minψp = ω1Φp + ω2ρ2(1) Finite element analysis (FEA) simulations are only performed within the optimal LHD to acquire the training data. The surrogate model based on MLS-SVM are trained using the data of the optimal LHD. The radial basis function (RBF) kernel is adopted for MLS-SVM and SSA is combined with MLS-SVM to find an optimal hyper-parameter set that produces a surrogate model with the highest average determination coefficient R2. The four-objectives optimization is performed by NSGA-III and an optimal design is selected from the Pareto front shown in Fig. 2 (b). A prototype is made based on the optimal design and tested, Figs. 2 (c) and (d), to validate the proposed method and the optimization. The proposed method needs only 270 FEA simulation cases during the whole design optimization procedure. For the conventional FEA-based parametric optimization method, even when only 5 levels are selected for each of the five geometrical parameters, 3125 FEA cases are required. Meanwhile, since the parameter space is discretized, the results of the conventional optimization method are likely to be locally optimal. For the method employing randomly generated LHDs [5], it requires nearly 500 FEA cases to achieve consistent R2s, which consumes 2 times the time of the proposed method. Thus, the proposed method can secure both efficient and accurate global design optimization of PMVMs. IV. Conclusions This paper proposes a novel optimal LHD-based surrogate assisted design optimization method for multi-objective optimization of PMVMs, which can perform high efficiency and high validity simultaneously. The proposed method and optimal design are validated by experiments on a prototype. Details of the design optimization and test results will be given in the full paper.

**References:**

[1] Y. Oner, Z. Q. Zhu and L. J. Wu, IEEE Trans. Ind. Electron., Vol. 63, No. 7, pp. 4105–4117 (2016). [2] S. Xu, X. An and X. Qiao, Pattern Recognit. Lett., Vol. 34, No. 9, pp. 1078–1084 (2013). [3] A. M. Usman, U. K. Yusof and S. Naim, IEEE Access, Vol. 8, pp. 76333-76356 (2020). [4] J. Yin, X. Zhu, L. Quan and C. Zhang, IET Electr. Power Appl., Vol. 11, pp. 72–79 (2017). [5] J. B. Kim, K. Y. Hwang and B. I. Kwon, IEEE Trans. Magn., Vol. 47, No. 5, pp. 1078-1081 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a02e0d4508835ed9b436b082204c4f95.jpg)
Fig. 1 Topology of PMVM and GSA results. (a) PMVM. (b) GSA results characterized by TSCs.

![](https://assets.underline.io/uploads/markdown_image/1/image/0710c9f0c14fbc22cb16e33d2590d647.jpg)
Fig. 2 Surrogate-assisted optimization. (a) Optimal LHD. (b) Pareto front of multi-objective optimization. (c) Rotor and stator of the prototype. (d) Test platform.

 Multicriteria Optimal Latin Hypercube Design-Based Surrogate-Assisted Design Optimization for a Permanent-Magnet Vernier Machine

I. Introduction Variable flux memory machines (VFMM) equipped with low coercive force (LCF) aluminum-nickel-cobalt (AlNiCo) magnets [1]-[4] can achieve high efficiency over a wide operation range by applying a current pulse to magnetize the LCF magnets with negeligible copper loss. Thus, VFMM is widely recognized as a competitive candidate for traction applications. For elevating the the electromagnetic performance of VFMMs, hybrid usage of high coercive force (HCF) and LCF magnets are applied in VFMMs. A novel hybrid-magnet-circuit VFMM (HMC-VFMM) is proposed in [5], which combines the design concepts and strengths of VFMMs with parallel and series magnetic circuit of HCF and LCF magnets. Due to the special hybrid magnetic circuit design, it is essential to provide an insightful understanding about the nonlinear hysteresis behavior of the LCF working point considering the resultant effects of parallel and series branches and to analyze the magnetic field variation phenomenon of the developed HMC-VFMM due to the transient current pulse by an effective solution. This paper attempts to reveal and investigate a balanced bidirectional-magnetization effect of the proposed HMC-VFMM, i.e., the required demagnetizing and remagnetizing current levels are basically similar, which will benefit the inverter rating reduction and online flux control. The balanced bidirectional-magnetization effect is analytically revealed by using a simplified Fourier-series based hysteresis model. In addition, the numerical hysteresis model is programmed with FE model so as to accurately investigate the magnetization characteristics of HMC-VFMM. Finally, the experimental results on a prototype are carried out to verify the theoretical analyses. II. Machine configuration and working principle The proposed 21-slot/4-pole HMC-VFMM is investigated, in which the cross-section is illustrated in Figs. 1(a). The proposed HMC design is characterized by a dual-layer PM structure. For the parallel branch, the “U”-shaped hybrid PM arrangement is employed. For the series branch, the HCF PMs form a spoke-type flux concentration type. The proposed HMC-VFMM can combine the advantages of wide flux regulation range in parallel type and excellent on-load demagnetization withstand capability in series type. The variable-flux principle of the proposed HMC-VFMM can be illustrated by the open-circuit field distributions under different magnetization states (MSs) in Fig. 1(b). It can be observed that the air-gap flux can be flexibly adjusted by applying a transient magnetizing or demagnetizing current pulse. Meanwhile, due to the variable flux property, the losses at different speeds and loads can be also manipulated to realize efficiency improvement over a wide operating range. III. Analytical Analysis of Balanced Bidirectional-Magnetization Effect The nonlinear hysteresis characteristics of the LCF PMs used in the proposed HMC-VFMM can be characterized by a simple Fourier-series based hysteresis model as shown in Fig. 2(a). The PM working point can track along different recoil lines by applying a specific remagnetizing or demagnetizing current pulse. The underlying mechanism of the balanced bidirectional-magnetization effect can be physically characterized by hysteresis curves of the LCF PM in Fig. 2(b). The load line of the HMC design is placed between the two load lines of the parallel and series cases, which allows a better balance between the magnetizing and demagnetizing current amplitudes. Meanwhile, the oversized inverter rating issue for either parallel or series VFMMs can be well avoided by appropriately reducing maximum remagnetizing currents. The detailed analysis and investigation of magnetization characteristics of HMC-VFMM will be given in the full paper.

**References:**

[1] V. Ostovic, "Memory Motors," IEEE Ind. Appl. Mag., vol. 9, no. 1, pp. 52-61, Jan./Feb. 2003. [2] H. Liu, H. Lin, Z. Q. Zhu, M. Huang, and P. Jin, "Permanent Magnet Remagnetizing Physics of a Variable Flux Memory Motor," IEEE Trans. Magn., vol. 46, no. 6, pp. 1679-1682, 2010. [3] Yu, C. and K. T. Chau . "Design, Analysis, and Control of DC-Excited Memory Motors," IEEE Trans. Energy Convers., vol. 26, no. 2, pp.479-489, 2011. [4] N. Limsuwan, T. Kato, K. Akatsu, and R. D. Lorenz, "Design and Evaluation of a Variable-Flux Flux-Intensifying Interior Permanent-Magnet Machine," IEEE Trans. Ind. Appl., vol. 50, no. 2, 2014. [5] H. Yang, S. Lyu, H. Lin, Z. Q. Zhu, H. Zheng and T. Wang, "A novel hybrid-magnetic-circuit variable flux memory machine," IEEE Trans. Ind. Electron., vol. 67, no. 7, pp. 5258-5268, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fd15041edf173bd5308f52185a96915d.jpg)
Fig. 1 VFMM topology and open-circuit field distributions under different magnetization states. (a) Topology. (b) Open-circuit field distributions under different magnetization states.

![](https://assets.underline.io/uploads/markdown_image/1/image/c7f4e39097f597c7fe82679fc137ef9c.jpg)
Fig. 2 Illustration of Fourier-series based hysteresis model. (a) Simplified view for illustrating the variable flux principle. (b) Numerical representation.

 Investigation of Balanced Bidirectional-Magnetization Effect of a Novel Hybrid-Magnet-Circuit Variable Flux Memory Machine

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Analysis of flux barrier effect of LCF PM in series hybrid magnet variable flux memory machine

Novel Asymmetric Rotor Pole Interior Permanent Magnet Machines with Enhanced Torque Density: An Overview

Multicriteria Optimal Latin Hypercube Design-Based Surrogate-Assisted Design Optimization for a Permanent-Magnet Vernier Machine

Investigation of Balanced Bidirectional-Magnetization Effect of a Novel Hybrid-Magnet-Circuit Variable Flux Memory Machine

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