NGHIÊN cứu cải THIỆN mật độ mô MEN của máy điện từ TRỞ

ĐẠI HỌC ĐÀ NẴNG TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT BÁO CÁO TỔNG KẾT ĐỀ TÀI KHOA HỌC VÀ CÔNG NGHỆ CẤP TRƯỜNG NGHIÊN CỨU CẢI THIỆN MẬT ĐỘ MÔ-MEN CỦA MÁY ĐIỆN TỪ TRỞ Mã số: T2021-06-02 Chủ nhiệm đề tài: TS Ngô Đức Kiên Đà Nẵng, 7/2022 DANH SÁCH THÀNH VIÊN VÀ ĐƠN VỊ PHỐI HỢP CHÍNH DANH SÁCH THÀNH VIÊN THAM GIA ĐỀ TÀI TT Họ tên Đơn vị công tác lĩnh vực chuyên môn Ngô Đức Kiên Khoa Điện - Điện tử, lĩnh vực Kỹ thuật điện Trương Thị Hoa Khoa Điện - Điện tử, lĩnh vực Kỹ thuật điện Hồ Quang Việt Khoa Điện - Điện tử, lĩnh vực Kỹ thuật điện ĐƠN VỊ PHỐI HỢP CHÍNH Tên đơn vị nước Họ tên người đại diện đơn vị National Cheng Kung University, Taiwan Hsieh Min-Fu MỤC LỤC DANH MỤC HÌNH ẢNH iii DANH MỤC BẢNG BIỂU vi DANH MỤC CHỮ VIẾT TẮT vii THÔNG TIN KẾT QUẢ NGHIÊN CỨU ix INFORMATION ON RESEARCH RESULTS xiii PHẦN MỞ ĐẦU i TỔNG QUAN TÌNH HÌNH NGHIÊN CỨU THUỘC LĨNH VỰC CỦA ĐỀ TÀI Ở TRONG VÀ NGOÀI NƯỚC ii TÍNH CẤP THIẾT CỦA ĐỀ TÀI iii MỤC TIÊU CỦA ĐỀ TÀI iv ĐỐI TƯỢNG VÀ PHẠM VI NGHIÊN CỨU v CÁCH TIẾP CẬN VÀ PHƯƠNG PHÁP NGHIÊN CỨU CHƯƠNG TỔNG QUAN VỀ CÁC LOẠI MÁY ĐIỆN TỪ TRỞ 1.1 PHÂN LOẠI MÁY ĐIỆN TỪ TRỞ 1.2 CÁC PHƯƠNG PHÁP NÂNG CAO MẬT ĐỘ MÔ-MEN CỦA MÁY ĐIỆN TỬ TRỞ 1.3 MƠ HÌNH TOÁN HỌC 1.3.1 Mơ hình tốn học máy điện đồng nam châm vĩnh cửu 1.3.2 Mơ hình tốn học máy điện từ trở đồng 11 1.3.3 Mơ hình toán học máy điện từ trở đồng nam châm vĩnh cửu hỗ trợ 13 1.3.4 Mơ hình tồn học máy điện từ trở đồng nam châm vĩnh cửa hỗ trợ từ thông tăng cường 15 1.4 TÓM LƯỢC 16 CHƯƠNG THIẾT KẾ ĐỐI TƯỢNG NGHIÊN CỨU 17 2.1 THIẾT KẾ MƠ HÌNH BAN ĐẦU 17 2.1.1 Rào chắn từ thông xẻ (CFB) 18 2.1.2 Rào chắn từ thông (IFB) 20 2.2 TỐI ƯU ĐẶC TÍNH MƠ-MEN 22 2.2.1 Dịch chuyển rào chắn từ thông xẻ (CFB) 23 Góc dịch chuyển CFB (độ cơ) 23 2.2.2 2.2.3 Dịch chuyển rào chắn từ thông nam châm (MFB) 24 Mở rộng rào chắn từ thông nam châm (CFB) 24 i 2.2.4 Mở rộng MFB với dịch chuyển nam châm vĩnh cửu 25 2.2.5 Tổng hợp kết lựa chọn phương án tối ưu đặc tính mơ-men 26 2.3 TĨM LƯỢC 27 CHƯƠNG ẢNH HƯỞNG CỦA CÁC YẾU TỐ THIẾT KẾ ĐẾN HIỆU NĂNG CỦA MÁY ĐIỆN TỪ TRỞ SỬ DỤNG CƠ CHẾ TỪ THÔNG TĂNG CƯỜNG 28 3.1 CÁC MƠ HÌNH ĐƯỢC KHẢO SÁT 28 3.2 ẢNH HƯỞNG CỦA NAM CHÂM VĨNH CỬU RÀO CHẮN TỪ THÔNG ĐẾN HIỆU NĂNG 32 3.2.1 Phân bố từ trường máy điện 32 3.2.2 Sự biến đổi điện cảm 37 3.2.3 Sự biến đổi mô-men 38 3.3 TÓM LƯỢC 39 CHƯƠNG CẢI THIỆN MẬT ĐỘ MÔ-MEN CỦA MÁY ĐIỆN TỪ TRỞ SỬ DỤNG CƠ CHẾ TỪ THÔNG TĂNG CƯỜNG 41 4.1 SỰ KHỬ TỪ CỤC BỘ 41 4.2 KHẢ NĂNG CẢI THIỆN MẬT ĐỘ MÔ-MEN 42 4.3 TÓM LƯỢC 45 CHƯƠNG CÁC KẾT QUẢ THỰC NGHIỆM 46 KẾT LUẬN VÀ KIẾN NGHỊ 50 TÀI LIỆU THAM KHẢO 52 ii DANH MỤC HÌNH ẢNH Hình 1.1 Cấu hình máy điện từ trở đồng nguyên thủy Hình 1.2 Một số cấu hình động từ trở đồng nam châm vĩnh cửu hỗ trợ Hình 1.3 Phương pháp làm tăng “saliency” Hình 1.4 Đặc tính nam châm N35H Hình 1.5 Cấu trúc rotor đơn giản kiểu máy điện nam châm vĩnh cửu Hình 1.6 Mạch điện tương đường kiểu máy điện đồng nam châm vĩnh cửu 10 Hình 1.7 Biểu đồ pha kiểu máy điện đồng nam châm vĩnh cửu hệ tọa độ d-q 10 Hình 1.8 Cấu trúc rotor đơn giản máy điện từ trở đồng 11 Hình 1.9 Mạch điện tương đường kiểu máy điện từ trở đồng 12 Hình 1.10 Biểu đồ pha kiểu máy điện từ trở đồng hệ tọa độ d-q 12 Hình 1.11 Cấu trúc rotor đơn giản máy điện từ trở đồng nam châm vĩnh cửu hỗ trợ 13 Hình 1.12 Mạch điện tương đương máy điện từ trở đồng nam châm vĩnh cửu hỗ trợ 14 Hình 1.13 Biểu đồ pha máy điện từ trở đồng nam châm vĩnh cửu hỗ trợ 14 Hình 1.14 Mạch điện tương đương máy điện từ trở đồng nam châm vĩnh cửu hỗ trợ từ thông tăng cường 15 Hình 1.15 Biểu đồ pha máy điện từ trở đồng nam châm vĩnh cửu hỗ trợ từ thông tăng cường 16 Hình 2.1 Mơ hình FI-PMa-SynRM nguyên thủy 17 Hình 2.2 Điều chỉnh độ dày CFB 19 Hình 2.3 Sự thay đổi mô-men độ nhấp nhô mô-men theo độ dày CFB 19 Hình 2.4 Điều chỉnh độ dày IFB 20 Hình 2.5 Sự thay đổi mơ-men độ nhấp nhô mô-men theo độ dày IFB 21 Hình 2.6 Điều chỉnh vị trí IFB 21 iii Hình 2.7 Sự thay đổi mô-men độ nhấp nhô mô-men theo vị trí IFB 22 Hình 2.8 Dịch chuyển CFB theo góc θC (góc cơ) 23 Hình 2.9 Sự thay đổi mô-men độ nhấp nhô mơ-men theo góc dịch chuyển CFB 23 Hình 2.10 Dịch chuyển MFB theo góc θ1m (góc cơ) 24 Hình 2.11 Sự thay đổi mơ-men độ nhấp nhơ mơ-men theo góc dịch chuyển MFB 24 Hình 2.12 Mở rộng MFB theo góc θ2m (góc cơ) 25 Hình 2.13 Sự thay đổi mơ-men độ nhấp nhơ mơ-men theo góc mở rộng MFB 25 Hình 2.14 Mở rộng MFB theo góc θ3m (góc cơ) 26 Hình 2.15 Sự thay đổi mơ-men độ nhấp nhơ mơ-men theo góc mở rộng MFB kèm dịch chuyển nam châm vĩnh cửu 26 Hình 2.16 So sánh phương án 27 Hình 3.1 Cấu trúc rotor mơ hình kháo sát 29 Hình 3.2 Chia lưới mơ hình: (a) FI-PMa-SynRM; (b) Inset SPMSM model; (c) SynRM model; (d) Modified SynRM 31 Hình 3.3 Mật độ từ thơng không tải 33 Hình 3.4 Từ thơng móc vịng nam châm 34 Hình 3.5 Mật độ từ thông điều kiện mô-men cực đại theo dịng điện Phía bên trái: FI-PMa-SynRM, phía bên phải: Inset SPMSM model, phía dưới: SynRM model 35 Hình 3.6 Mật độ từ thơng nam châm vĩnh cửu “Inset SPMSM model” góc dịng điện 19 độ 36 Hình 3.7 Mật độ từ thông nam châm vĩnh cửu góc dịng điện –25 độ 36 Hình 3.8 Sự biến đổi điện cảm saliency theo giá trị dòng điện FIPMa-SynRM (1), Inset SPMSM model (2) SynRM model (3) 37 Hình 3.9 Sự biến thiên mơ-men trung bình theo góc dịng điện 38 Hình 3.10 Mơ-men tức thời theo vị trí rotor 39 Hình 4.1 Các điểm quan sát lựa chọn nam châm vĩnh cửu 41 Hình 4.2 Sự thay đổi giá trị mật độ từ thông điểm quan sát 42 Hình 4.3 So sánh mật độ mơ-men FI-PMa-SynRM Modified SynRM 43 Hình 5.1 Cài đặt thực nghiệm cho mẫu thử FI-PMa-SynRM 46 iv Hình 5.2 Dạng sóng dịng điện FI-PMa-SynRM với giá trí hiệu dụng 32,5 A góc dòng điện –55 độ: (a) Pha A, (b) Pha B, (c) Pha C 47 Hình 5.3 Các thành phần hài dòng điện 48 Hình 5.4 So sánh mô-men đo đạc mô 49 v DANH MỤC BẢNG BIỂU Bảng 2.1 Thông số 18 Bảng 2.2 Thông số mơ hình ban đầu 22 Bảng 3.1 Thông số kết cấu mơ hình 30 Bảng 3.2 Thông tin chia lưới 30 Bảng 4.1 Thông tin mật độ mô-men 45 vi DANH MỤC CHỮ VIẾT TẮT d Dọc trục Id Dòng điện trục d (dọc trục) Iq Dòng điện trục q (ngang trục) Ld Điện cảm dọc trục Lq Điện cảm ngang trục p Số đôi cực q Ngang trục Rs Điện trở pha T Mơ-men λd Từ thơng móc vịng dọc trục λq Từ thơng móc vịng ngang trục λm Từ thơng móc vịng nam châm ω Tốc độ điện CFB Cutoff Flux Barrier FFT Fast Fourier Transform FI Flux Intensifying FI-PMa-SynRM Flux Intensifying IFB Interior Flux Barrier vii Electronics 2022, 11, 397 of 16 3.4 Brief Summary From the above analysis, it can be revealed that: - - The appearance of FBs in the developed FI-PMa-SynRM helps PM be better secured and leads to the reversal of inductance properties (FI-PMa-SynRM vs Inset SPMSM model) The appearance of PM in the developed FI-PMa-SynRM leads to an enhancement of the flux density in the cores and the significant change of d-axis inductance (FI-PMaSynRM vs SynRM model) The coordination of PM and FBs in the FI-PMa-SynRM helps it enhance the torque production compared to those of its counterparts with a small added PM amount Further Analysis of Developed Motor In the above analysis, the Inset SPMSM is made intentionally without interior FBs and likewise, the SynRM is without PM and thus the individual impact of FBs and PMs on the developed motor can be evaluated In this section, the advantages of the FI feature on the developed model will be further analyzed through the evaluation of the demagnetization issue and torque density capability 4.1 Partial Demagnetization Five observed points are selected along the PM span as described in Figure 10a, while the variation of flux density of these points is shown in Figure 10b As can be seen, the flux density at points A and B is lower compared to those of others, which indicates that the PM region between points A and B would be more easily demagnetized Besides, this region is near a FB and this conforms to the prediction of partial demagnetization problem in Section However, it should be noted that these flux densities are not too low so that the irreversible demagnetization is unlikely to occur for a small PM dimension (only 1.5 mm thick) On the other hand, the advantage of this simple structure is such that alternative Electronics 2022, 10, x FOR PEER REVIEW 10 of 17 designs can be easily applied with minor modifications, e.g., using a thicker PM to fully avoid irreversible demagnetization for a similar design (a) (b) Figure10 10.Demagnetization Demagnetizationanalysis: analysis:(a) (a)Observed Observedpoints; points;(b) (b)Flux Fluxdensity densityvariation variationofofobserved observed Figure points at 105 °C ◦ points at 105 C 4.2 4.2.Torque TorqueDensity DensityCapability Capability As Aspreviously previouslydiscussed, discussed,the themodels modelscompared comparedininSection Section22(i.e., (i.e.,the theInset InsetSPMSM SPMSM and andSynRM SynRMmodels) models)are areused usedtotoevaluate evaluatethe therole roleofofFBs FBsand andPM PMin inthe thedeveloped developedFI-PMaFI-PMaSynRM different motors may have dissimilar design considerations, e.g., the SynRM.Nevertheless, Nevertheless, different motors may have dissimilar design considerations, e.g., air-gap length of a SynRM could be smaller To demonstrate the capability of achieving the air-gap length of a SynRM could be smaller To demonstrate the capability of achievhigh density with only smallaamount of PM, of thePM, developed FI-PMa-SynRM will be ing torque high torque density withaonly small amount the developed FI-PMa-SynRM compared to anothertorealistic by model extending the boundary the rotorof surface as well will be compared anothermodel realistic by extending the of boundary the rotor surasface theas end of FB so that the air gap and rotor ribs are the same as those of the developed well as the end of FB so that the air gap and rotor ribs are the same as those of the developed model This model is called the Modified SynRM as also illustrated in Figure (i.e., the right part), where the blue arrows indicate the boundary extension Figure 11 shows the comparison of torque density versus current amplitude and angle (from −90 to degrees) between the FI-PMa-SynRM and the Modified SynRM As can Electronics 2022, 11, 397 10 of 16 model This model is called the Modified SynRM as also illustrated in Figure (i.e., the right part), where the blue arrows indicate the boundary extension Figure 11 shows the comparison of torque density versus current amplitude and angle (from −90 to degrees) between the FI-PMa-SynRM and the Modified SynRM As can be seen, the FI-PMa-SynRM offers a better torque density Moreover, the FI-PMa-SynRM has a much broader high torque density zone (above 20 Nm/L) for the given current magnitude and angle ranges This can be explained by the fact that the FI-PMa-SynRM is capable of effectively combining reluctance torque and PM torque in comparison with other types of motors, with multiple FBs to gain high reluctance torque and a small amount of surface-inset PM for an extra portion of torque Most importantly, since the PM in the FI-PMa-SynRM is not easily demagnetized, a higher current can be applied to gain even higher torque output However, this will be limited by the magnetic saturation, heat dissipation, and possible partial PM demagnetization as mentioned above As a result, this Electronics 2022, 10, x FOR PEER REVIEW 11 of 17 motor can achieve high torque density, i.e., 13.45 Nm/L and 24.79 Nm/L at the rated and peak conditions, respectively density between between FI-PMa-SynRM FI-PMa-SynRM and and Modified Modified SynRM SynRM Figure 11 Comparison of torque density 5 Experiment Experiment Results Results The experimental measured current current waveforms waveforms of of the the develdevelThe experimental setup setup for for evaluation, evaluation, measured oped FI-PMa-SynRM prototype, current harmonics, and torque comparison are shown oped FI-PMa-SynRM prototype, current harmonics, and torque comparison are shown in in Figures Figures 12–15, 12–15, respectively respectively In In Figure Figure 14, 14, the the fundamental fundamental frequency frequency is is 42 42 Hz Hz Because Because of of the limitation of the power source and measurement devices in our laboratories, the develthe limitation of the power source and measurement devices in our laboratories, the deoped FI-PMa-SynRM is only measured up to 32.5 A, where the total harmonic distortion veloped FI-PMa-SynRM is only measured up to 32.5 A, where the total harmonic distor(THD) of the motor current is around 13.04% The torque production of the developed FItion (THD) of the motor current is around 13.04% The torque production of the developed PMa-SynRM for the measurement and simulation are compared and presented in Figure 15 FI-PMa-SynRM for the measurement and simulation are compared and presented in As can be seen, the two cases agree well On the other hand, the simulation results of the Figure 15 As can be seen, the two cases agree well On the other hand, the simulation modified SynRM are added to compare with the developed FI-PMa-SynRM As depicted results of the modified SynRM are added to compare with the developed FI-PMa-SynRM in Figure 15, with a small current angle (about −55 degrees), the torque production of the As depicted in Figure 15, with a small current angle (about −55 degrees), the torque proModified SynRM is only slightly smaller than that of the FI-PMa-SynRM, while with a duction of the Modified SynRM is only slightly smaller than that of the FI-PMa-SynRM, higher current angle, the torque of the Modified SynRM decreases very quickly The torque while with a higher current angle, the torque of the Modified SynRM decreases very of the Modified SynRM can become negative but that of FI-PMa-SynRM is still positive quickly The torque of the Modified SynRM can become negative but that of FI-PMaThese results also conform to the theory mentioned above SynRM is still positive These results also conform to the theory mentioned above In future research, to further evaluate the overall efficacy of the developed FI-PMaSynRM, the core loss properties and efficiency under the excitation of power electronics inverters will be investigated in detail by simulation and experiment [27,28] duction of the Modified SynRM is only slightly smaller than that of the FI-PMa-SynRM, while with a higher current angle, the torque of the Modified SynRM decreases very quickly The torque of the Modified SynRM can become negative but that of FI-PMaSynRM is still positive These results also conform to the theory mentioned above In future research, to further evaluate the overall efficacy of the developed FI-PMa11 of 16 SynRM, the core loss properties and efficiency under the excitation of power electronics inverters will be investigated in detail by simulation and experiment [27,28] Electronics 2022, 11, 397 Electronics 2022, 10, x FOR PEER REVIEW 12 of 17 Figure 12 Experimental setup for evaluation of developed FI-PMa-SynRM prototype Figure 12 Experimental setup for evaluation of developed FI-PMa-SynRM prototype (a) (b) Figure 13 Cont Electronics 2022, 11, 397 12 of 16 (b) (c) Electronics 2022, 10, x FOR PEER REVIEW Figure 13 ofof1732.5 A 13.13.Measured waveforms developed FI-PMa-SynRM with the of current Figure Measured current current waveforms of of developed FI-PMa-SynRM with the current 32.5 A and andangle angle −55 degrees: Phase U;Phase (b) Phase (c) Phase W of of −55 degrees: (a) (a) Phase U; (b) V; (c) V; Phase W Figure 14 Current Current harmonics of developed FI-PMa-SynRM In future research, to further evaluate the overall efficacy of the developed FI-PMaSynRM, the core loss properties and efficiency under the excitation of power electronics inverters will be investigated in detail by simulation and experiment [27,28] Electronics 2022, 11, 397 13 of 16 Figure 14 Current harmonics of developed FI-PMa-SynRM Figure Figure15 15.Comparison Comparisonof ofmeasured measuredtorque torque and and simulation simulation results results 6.Conclusions Conclusions In this thispaper, paper,aathorough thoroughinvestigation investigation feature PMa-SynRM (denoted In ofof thethe FI FI feature on on PMa-SynRM (denoted FIFI-PMa-SynRM) to achieve a high torque density was shown.Firstly, Firstly,through throughaacomparison comparison PMa-SynRM) to achieve a high torque density was shown of the the developed developed FI-PMa-SynRM FI-PMa-SynRMwith withits itstwo two counterparts counterpartswhich whichwere were obtained obtainedsimply simply of by eliminating interior FB or PM, the role of these elements on the developed motor was by eliminating interior FB or PM, the role of these elements on the developed motor was studied Secondly, the partial demagnetization of the developed motor was analyzed, studied Secondly, the partial demagnetization of the developed motor was analyzed, and and its torque density capability was investigated a comparison with realistic another its torque density capability was investigated throughthrough a comparison with another realistic motor It was found that adopting the FI configuration leads to the difference in motor It was found that adopting the FI configuration leads to the difference in the magthe magnetic field patterns and current to achieve the MTPA operation As a result, netic field patterns and current angle toangle achieve the MTPA operation As a result, a higha high torque density was demonstrated to be achievable with only a small amount of PM torque density was demonstrated to be achievable with only a small amount of PM while while the ability to avoid PM irreversible demagnetization was validated by simulation the ability to avoid PM irreversible demagnetization was validated by simulation and exand experimental results These have illustrated the feasibility of applying the FI feature perimental results These have illustrated the feasibility of applying the FI feature to PMato PMa-SynRM Moreover, the simple structure of the developed FI-PMa-SynRM can be SynRM Moreover, the simple structure of the developed FI-PMa-SynRM can be treated treated as an interesting and helpful design reference Author Contributions: Conceptualization and methodology, M.-F.H and D.-K.N.; software and investigation, D.-K.N and N.G.M.T.; result analysis and evaluation, M.-F.H., D.-K.N and N.G.M.T., writing—review and editing, M.-F.H., D.-K.N and N.G.M.T All authors have read and agreed to the published version of the manuscript Funding: This work was supported in part by The University of Danang—University of Technology and Education under Grant Number T2021-06-02, Ministry of Science and Technology of Taiwan under contract MOST 110-2221-E-006-184-MY2, and JSPS KAKENHI Grant Number 21K14182 Acknowledgments: The authors would like to thank JSOL Corporation for supporting JMAG Conflicts of Interest: The authors declare no conflict of interest Nomenclature and Abbreviations The following nomenclature and abbreviations are used in this paper: Electronics 2022, 11, 397 14 of 16 d Id Iq Ld Lq p q T VFI-PMa-SynRM Vinset SPMSM VSynRM λFI-PMa-SynRM λinset SPMSM λm λSynRM ω EV FB FEM FI FI-PMa-SynRM FI-PMSM FW IPMSM MTPA PM PMa-SynRM PMSM SPMSM SynRM THD Direct axis D-axis current Q-axis current D-axis stator inductance Q-axis stator inductance Number of pole pairs Quadrature axis Torque Voltage of FI-PMa-SynRM Voltage of inset SPMSM Voltage of SynRM Flux linkage of FI-PMa-SynRM Flux linkage of inset SPMSM PM flux linkage Flux linkage of SynRM Electric angular speed Electric vehicle Flux barrier Finite element method Flux intensifying Flux intensifying permanent magnet assisted synchronous reluctance motor Flux intensifying permanent magnet synchronous motor Flux weakening/weakened Interior permanent magnet synchronous motor Maximum torque per ampere Permanent magnet Permanent magnet assisted synchronous reluctance motor Permanent magnet synchronous motor Surface permanent magnet synchronous motor Synchronous reluctance motor Total harmonic distortion Appendix A Brief Information of Motor Models A survey of the volumetric torque density and PM-to-motor-volume ratio is provided in Table A1 Note that the torque density of the individual motors would depend on the design, current, current density, thermal condition, and so forth; thus, the comparison in Table A1 is only used for reference but not an accurate indication of motor performance Table A1 Brief information of motor models Models Volumetric Torque Density (Nm/L) PM-to-Motor Volume Ratio (%) Peak Current Density (A/mm2 ) Anti-Demagnetization Ability Prototype FI-PMa-SynRM Model in [6] Model in [7] Model in [10] 24.79 63.79 52.82 14.91 0.72 4.22 N/A 4.32 15.35 26.87 25.1 N/A Validated Validated N/A Validated Done Not yet Done Done Appendix B Finite Element Mesh Information The finite element software package utilized in this paper is JMAG from JOSL Corporation The finite element models of the considered motors are constructed through the standard meshing setup of JMAG The detailed mesh information used in this study is described in Table A2, and the meshing for the four models is illustrated in Figure A1 Model in [7] Model in [10] 52.82 14.91 N/A 4.32 25.1 N/A N/A Validated Done Done Appendix B Finite Element Mesh Information Electronics 2022, 11, 397 The finite element software package utilized in this paper is JMAG from JOSL Cor15 of 16 poration The finite element models of the considered motors are constructed through the standard meshing setup of JMAG The detailed mesh information used in this study is described in Table A2, and the meshing for the four models is illustrated in Figure A1 Table A2 Mesh information of considered four models Table A2 Mesh information of considered four models Motor Models Number of Elements Motor Models Number of Elements FI-PMa-SynRM 12,467 FI-PMa-SynRM 12,467 Inset SPMSM 10,147 Inset SPMSM 10,147 SynRM 12,615 Modified SynRM 11,845 SynRM 12,615 Modified SynRM 11,845 Number of Nodes Number of Nodes 6712 6712 5553 5553 6786 6396 6786 6396 Figure A1 Meshing illustration: (a) FI-PMa-SynRM; (b) Inset SPMSM model; 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Zhong, S.; Fujisaki, K.; Iwamoto, F.; Kimura, T.; Yamada, T Assessment of motor core loss, copper loss and magnetic flux density with PAM inverter under dissimilar excitation angles IET Electr Power Appl 2020, 14, 622–637 [CrossRef] Thao, N.G.M.; Denis, N.; Wu, Y.; Odawara, S.; Fujisaki, K Study of the Effect of Load Torque on the Iron Losses of Permanent Magnet Motors by using Finite Element Analysis IEEJ J Ind Appl 2019, 8, 522–531 [CrossRef] Downloaded on 8/7/2022 16:56:27 2021 Journal Performance Data for: Electronics Open Access since 2012 ISSN EISSN N/A 2079-9292 JCR ABBREVIATION ISO ABBREVIATION ELECTRONICS-SWITZ Electronics Journal Information EDITION CATEGORY Science Citation Index Expanded (SCIE) PHYSICS, APPLIED - SCIE COMPUTER SCIENCE, INFORMATION SYSTEMS - SCIE ENGINEERING, ELECTRICAL & ELECTRONIC - SCIE LANGUAGES REGION 1ST ELECTRONIC JCR YEAR English SWITZERLAND 2017 PUBLISHER ADDRESS PUBLICATION FREQUENCY MDPI ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND 12 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