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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">alternative</journal-id><journal-title-group><journal-title xml:lang="ru">Альтернативная энергетика и экология (ISJAEE)</journal-title><trans-title-group xml:lang="en"><trans-title>Alternative Energy and Ecology (ISJAEE)</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1608-8298</issn><publisher><publisher-name>Международный издательский дом научной периодики "Спейс</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.15518/isjaee.2024.02.043-054</article-id><article-id custom-type="elpub" pub-id-type="custom">alternative-2354</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>I. ВОЗОБНОВЛЯЕМАЯ ЭНЕРГЕТИКА. 2. Ветроэнергетика</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>I. RENEWABLE ENERGY. 2. Wind energy</subject></subj-group></article-categories><title-group><article-title>Экспериментальные и теоретические исследования по минимизации зубчатого момента синхронной машины с постоянными магнитами</article-title><trans-title-group xml:lang="en"><trans-title>Experimental and Theoretical Research on Cogging Torque Minimization for PM Synchronous Machine</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Топорков</surname><given-names>Д. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Toporkov</surname><given-names>D. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Топорков Дмитрий Михайлович, к.т.н., доцент, заведующий кафедрой Электромеханики факультета Мехатроники и автоматизации</p><p>630073, Новосибирск, пр. К. Маркса, 20</p><p>Тел +7-913-752-41-69</p></bio><bio xml:lang="en"><p>Dmitriy M. Toporkov, PhD, Associate Professor, Head of the Electromechanics Department, Faculty of Mechatronics and Automation</p><p>+7-913-752-41-69</p></bio><email xlink:type="simple">toporkov@corp.nstu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Арестова</surname><given-names>А. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Arestova</surname><given-names>A. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Арестова Анна Юрьевна, старший преподаватель кафедры Автоматизированных электроэнергетических систем факультета Энергетики</p><p>630073, Новосибирск, пр. К. Маркса, 20</p><p>Тел. +7-923-246-71-98</p></bio><bio xml:lang="en"><p>Anna Yu. Arestova, Senior lecturer of Automated power systems Department</p><p>+7-923-246-71-98</p></bio><email xlink:type="simple">arestova@corp.nstu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Новосибирский государственный технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Novosibirsk State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>15</day><month>05</month><year>2024</year></pub-date><volume>0</volume><issue>2</issue><fpage>43</fpage><lpage>54</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Международный издательский дом научной периодики "Спейс, 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Международный издательский дом научной периодики "Спейс</copyright-holder><copyright-holder xml:lang="en">Международный издательский дом научной периодики "Спейс</copyright-holder><license xlink:href="https://www.isjaee.com/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://www.isjaee.com/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://www.isjaee.com/jour/article/view/2354">https://www.isjaee.com/jour/article/view/2354</self-uri><abstract><p>.</p></abstract><trans-abstract xml:lang="en"><p>The paper presents the cogging torque minimization method based on numerical calculation. The considered method assumes that the amplitude of the permeance harmonic is a periodic function of the slot opening, and it will be equal to zero if the opening value is a multiple of or equal to the period of the permeance harmonic. The numerical methods are applied for accuracy enchantment under magnetic field calculation. The air gap permeance function is calculated considering the actual pattern of field distribution in the area of the gap and slot opening, the edge effects, and steel saturation. The two-dimensional finite element model corresponding to the cross-section of a cylindrical machine and the Maxwell stress tensor method is used for cogging torque calculation. The paper provides a quantitative comparison of the relative slot opening values under analytical and finite element method calculation. The developed permanent magnet machine prototype is presented. The harmonic composition of cogging torque is obtained for machine prototype, and the fundamental harmonic is determined. Thus, the fundamental harmonic of the cogging torque can be eliminated by means of optimal slot opening width. The experimental and analytical results confirmed the cogging torque could be reduced by 2-8 times.</p></trans-abstract><kwd-group xml:lang="en"><kwd>Auxiliary slots</kwd><kwd>claw-pole</kwd><kwd>cogging torque</kwd><kwd>magnetic flux density</kwd><kwd>numerical analysis</kwd><kwd>permanent magnet synchronous  machines</kwd><kwd>torque ripple</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">. E. Agamloh, A. Von Jouanne and A. Yokochi. «An overview of electric machine trends in modern electric vehicles» Machines, vol. 8(2), pp. 1-20, April 2020.</mixed-citation><mixed-citation xml:lang="en">. E. Agamloh, A. Von Jouanne and A. Yokochi. «An overview of electric machine trends in modern electric vehicles» Machines, vol. 8(2), pp. 1-20, April 2020.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">. T. He, Z. Zhu, F. Eastham, Y. Wang, H. Bin, D. Wu, and J. Chen, «Permanent magnet machines for high-speed applications» World Electric Vehicle Journal, vol. 13(1), pp. 1-18, Jan. 2022.</mixed-citation><mixed-citation xml:lang="en">. T. He, Z. Zhu, F. Eastham, Y. Wang, H. Bin, D. Wu, and J. Chen, «Permanent magnet machines for high-speed applications» World Electric Vehicle Journal, vol. 13(1), pp. 1-18, Jan. 2022.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">. X. C. Le, M. Q. Duong, and K. H. Le. «Review of the modern maximum power tracking algorithms for permanent magnet synchronous generator of wind power conversion systems». Energies, vol. 16(1), pp.1-25, Dec. 2022.</mixed-citation><mixed-citation xml:lang="en">. X. C. Le, M. Q. Duong, and K. H. Le. «Review of the modern maximum power tracking algorithms for permanent magnet synchronous generator of wind power conversion systems». Energies, vol. 16(1), pp.1-25, Dec. 2022.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">. T. Y. Heng, T. J. Ding, C. C. W. Chang, T. J. Ping, H. C. Yian, and M. Dahari, «Permanent Magnet Synchronous Generator design optimization for wind energy conversion system: A review». Energy Reports, vol. 8, pp. 277-282, Dec. 2022.</mixed-citation><mixed-citation xml:lang="en">. T. Y. Heng, T. J. Ding, C. C. W. Chang, T. J. Ping, H. C. Yian, and M. Dahari, «Permanent Magnet Synchronous Generator design optimization for wind energy conversion system: A review». Energy Reports, vol. 8, pp. 277-282, Dec. 2022.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">. J. Zhao, X. Liu, S. Wang, and L. Zheng, «Review of Design and Control Optimization of Axial Flux PMSM in Renewable-energy Applications». Chinese Journal of Mechanical Engineering, vol. 36(1), pp. 1-21, 2023.</mixed-citation><mixed-citation xml:lang="en">. J. Zhao, X. Liu, S. Wang, and L. Zheng, «Review of Design and Control Optimization of Axial Flux PMSM in Renewable-energy Applications». Chinese Journal of Mechanical Engineering, vol. 36(1), pp. 1-21, 2023.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">. S. Singh, S. N. Singh, and A. N. Tiwari, «PMSM drives and its application: An overview». Recent Advances in Electrical &amp; Electronic Engineering, vol. 16(1), pp. 4-16, 2023.</mixed-citation><mixed-citation xml:lang="en">. S. Singh, S. N. Singh, and A. N. Tiwari, «PMSM drives and its application: An overview». Recent Advances in Electrical &amp; Electronic Engineering, vol. 16(1), pp. 4-16, 2023.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">. I. Boldea, L. N. Tutelea, N. Muntean, A. Popa, and F. Blaabjerg. «Robotics Electric Actuators: Recent Progress in High Torque Density Designs and Their Advanced Motion Control–A Review». Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, vol. 21(4), pp. 337-355, 2020.</mixed-citation><mixed-citation xml:lang="en">. I. Boldea, L. N. Tutelea, N. Muntean, A. Popa, and F. Blaabjerg. «Robotics Electric Actuators: Recent Progress in High Torque Density Designs and Their Advanced Motion Control–A Review». Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, vol. 21(4), pp. 337-355, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">. K. Ullah, J. Guzinski, and A. F. Mirza, «Critical review on robust speed control techniques for permanent magnet synchronous motor (PMSM) speed regulation». Energies, vol. 15(3), pp. 1-13, Feb. 2022.</mixed-citation><mixed-citation xml:lang="en">. K. Ullah, J. Guzinski, and A. F. Mirza, «Critical review on robust speed control techniques for permanent magnet synchronous motor (PMSM) speed regulation». Energies, vol. 15(3), pp. 1-13, Feb. 2022.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">. Q. Hou, S. Ding, and X. Yu, «Composite super-twisting sliding mode control design for PMSM speed regulation problem based on a novel disturbance observer» IEEE Transactions on Energy Conversion, vol. 36(4), pp. 2591-2599, 2020.</mixed-citation><mixed-citation xml:lang="en">. Q. Hou, S. Ding, and X. Yu, «Composite super-twisting sliding mode control design for PMSM speed regulation problem based on a novel disturbance observer» IEEE Transactions on Energy Conversion, vol. 36(4), pp. 2591-2599, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">. Z. Li, J. An, Q. Zhang, H. Liu and H. Sun, «Design of PMSLM position controller based on model predictive control algorithm». IEEE Access, vol. 9, pp. 78835-78846, 2021.</mixed-citation><mixed-citation xml:lang="en">. Z. Li, J. An, Q. Zhang, H. Liu and H. Sun, «Design of PMSLM position controller based on model predictive control algorithm». IEEE Access, vol. 9, pp. 78835-78846, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">. Y. Lu, Z. Jiang, C. Chen, and Y. Zhuang. «Energy efficiency optimization of field-oriented control for PMSM in all electric system» Sustainable Energy Technologies and Assessments, vol. 48, pp. 1-8, 2021.</mixed-citation><mixed-citation xml:lang="en">. Y. Lu, Z. Jiang, C. Chen, and Y. Zhuang. «Energy efficiency optimization of field-oriented control for PMSM in all electric system» Sustainable Energy Technologies and Assessments, vol. 48, pp. 1-8, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">. K. Dambrauskas, J. Vanagas, T. Zimnickas, A. Kalvaitis, and M. Ažubalis. «A method for efficiency determination of permanent magnet synchronous motor» Energies, vol. 13(4), pp. 1-15, 2020.</mixed-citation><mixed-citation xml:lang="en">. K. Dambrauskas, J. Vanagas, T. Zimnickas, A. Kalvaitis, and M. Ažubalis. «A method for efficiency determination of permanent magnet synchronous motor» Energies, vol. 13(4), pp. 1-15, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">. C. Candelo-Zuluaga, J. R. Riba, and A. Garcia. «PMSM torque-speed-efficiency map evaluation from parameter estimation based on the stand still test» Energies, vol. 14(20), pp. 1-15, 2021.</mixed-citation><mixed-citation xml:lang="en">. C. Candelo-Zuluaga, J. R. Riba, and A. Garcia. «PMSM torque-speed-efficiency map evaluation from parameter estimation based on the stand still test» Energies, vol. 14(20), pp. 1-15, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">. Y. Yang, Q. He, C. Fu, S. Liao, and P. Tan. «Efficiency improvement of permanent magnet synchronous motor for electric vehicles». Energy, vol. 213, pp. 1-11, 2020.</mixed-citation><mixed-citation xml:lang="en">. Y. Yang, Q. He, C. Fu, S. Liao, and P. Tan. «Efficiency improvement of permanent magnet synchronous motor for electric vehicles». Energy, vol. 213, pp. 1-11, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">. P. J. Megia, A. J. Vizcaíno, J. A. Calles, and A. Carrero. «Hydrogen production technologies: from fossil fuels toward renewable sources. A mini review». Energy &amp; Fuels, vol. 35(20), pp. 16403-16415, 2021.</mixed-citation><mixed-citation xml:lang="en">. P. J. Megia, A. J. Vizcaíno, J. A. Calles, and A. Carrero. «Hydrogen production technologies: from fossil fuels toward renewable sources. A mini review». Energy &amp; Fuels, vol. 35(20), pp. 16403-16415, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">. A. T. Hoang, and X. P. Nguyen. «Integrating renewable sources into energy system for smart city as a sagacious strategy towards clean and sustainable process». Journal of Cleaner Production, vol. 305, pp. 1-33, 2021.</mixed-citation><mixed-citation xml:lang="en">. A. T. Hoang, and X. P. Nguyen. «Integrating renewable sources into energy system for smart city as a sagacious strategy towards clean and sustainable process». Journal of Cleaner Production, vol. 305, pp. 1-33, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">. F. Chien, H. W. Kamran, G. Albashar, and W. Iqbal. «Dynamic planning, conversion, and management strategy of different renewable energy sources: a sustainable solution for severe energy crises in emerging economies». International Journal of Hydrogen Energy, vol. 46(11), pp. 7745-7758, 2021.</mixed-citation><mixed-citation xml:lang="en">. F. Chien, H. W. Kamran, G. Albashar, and W. Iqbal. «Dynamic planning, conversion, and management strategy of different renewable energy sources: a sustainable solution for severe energy crises in emerging economies». International Journal of Hydrogen Energy, vol. 46(11), pp. 7745-7758, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">. S. Kumar, R. K. Saket, D. K. Dheer, J. B. Holm-Nielsen, and P. Sanjeevikumar. «Reliability enhancement of electrical power system including impacts of renewable energy sources: a comprehensive review» IET Generation, Transmission &amp; Distribution, vol. 14(10), pp. 1799-1815, 2020.</mixed-citation><mixed-citation xml:lang="en">. S. Kumar, R. K. Saket, D. K. Dheer, J. B. Holm-Nielsen, and P. Sanjeevikumar. «Reliability enhancement of electrical power system including impacts of renewable energy sources: a comprehensive review» IET Generation, Transmission &amp; Distribution, vol. 14(10), pp. 1799-1815, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">. D. Cevasco, S. Koukoura, and A. J. Kolios. «Reliability, availability, maintainability data review for the identification of trends in offshore wind energy applications». Renewable and Sustainable Energy Reviews, vol. 136, pp. 1-21, 2021.</mixed-citation><mixed-citation xml:lang="en">. D. Cevasco, S. Koukoura, and A. J. Kolios. «Reliability, availability, maintainability data review for the identification of trends in offshore wind energy applications». Renewable and Sustainable Energy Reviews, vol. 136, pp. 1-21, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">. S. Peyghami, F. Blaabjerg, and P. Palensky. «Incorporating power electronic converters reliability into modern power system reliability analysis» IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9(2), pp. 1668-1681, 2020.</mixed-citation><mixed-citation xml:lang="en">. S. Peyghami, F. Blaabjerg, and P. Palensky. «Incorporating power electronic converters reliability into modern power system reliability analysis» IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9(2), pp. 1668-1681, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">. P. M. Tlali, R. J. Wang, S. Gerber, C. D. Botha, and M. J. Kamper. «Design and performance comparison of vernier and conventional PM synchronous wind generators». IEEE Transactions on Industry Applications, vol. 56(3), pp. 2570-2579, 2020.</mixed-citation><mixed-citation xml:lang="en">. P. M. Tlali, R. J. Wang, S. Gerber, C. D. Botha, and M. J. Kamper. «Design and performance comparison of vernier and conventional PM synchronous wind generators». IEEE Transactions on Industry Applications, vol. 56(3), pp. 2570-2579, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">. R. M. Pindoriya, R. K. Thakur, B. S. Rajpurohit, and R. Kumar. «Numerical and experimental analysis of torsional vibration and acoustic noise of PMSM coupled with DC generator». IEEE Transactions on Industrial Electronics, vol. 69(4), pp. 3345-3356, 2021.</mixed-citation><mixed-citation xml:lang="en">. R. M. Pindoriya, R. K. Thakur, B. S. Rajpurohit, and R. Kumar. «Numerical and experimental analysis of torsional vibration and acoustic noise of PMSM coupled with DC generator». IEEE Transactions on Industrial Electronics, vol. 69(4), pp. 3345-3356, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">. S. German-Galkin, and M. Staude. «Energy properties of a hybrid DC generator with PMSM». In 2020 19th International Conference on Mechatronics-Mechatronika, pp. 1-7, Dec. 2020.</mixed-citation><mixed-citation xml:lang="en">. S. German-Galkin, and M. Staude. «Energy properties of a hybrid DC generator with PMSM». In 2020 19th International Conference on Mechatronics-Mechatronika, pp. 1-7, Dec. 2020.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">. Y. Xu, M. Ai, and Z. Xu. «Influence of partial winding fault on electromagnetic performance of permanent magnet wind generator with double three-phase winding». Energy Reports, vol. 7, pp. 6462-6472, Nov. 2021.</mixed-citation><mixed-citation xml:lang="en">. Y. Xu, M. Ai, and Z. Xu. «Influence of partial winding fault on electromagnetic performance of permanent magnet wind generator with double three-phase winding». Energy Reports, vol. 7, pp. 6462-6472, Nov. 2021.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">. H. Fang, Y. Wei, and Y. Feng. «Design of dual-rotor PMSG for wave energy conversion». Energy Reports, vol. 6, pp. 397-401, Dec. 2020.</mixed-citation><mixed-citation xml:lang="en">. H. Fang, Y. Wei, and Y. Feng. «Design of dual-rotor PMSG for wave energy conversion». Energy Reports, vol. 6, pp. 397-401, Dec. 2020.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">. V. Prakht, V. Dmitrievskii, V. Kazakbaev, and M. N. Ibrahim. «Comparison between rare-earth and ferrite permanent magnet flux-switching generators for gearless wind turbines». Energy Reports, vol. 6, pp. 1365-1369, Dec. 2020.</mixed-citation><mixed-citation xml:lang="en">. V. Prakht, V. Dmitrievskii, V. Kazakbaev, and M. N. Ibrahim. «Comparison between rare-earth and ferrite permanent magnet flux-switching generators for gearless wind turbines». Energy Reports, vol. 6, pp. 1365-1369, Dec. 2020.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">. Y. Merizalde, L. Hernández-Callejo, and O. Duque-Perez. «State of the art and trends in the monitoring, detection and diagnosis of failures in electric induction motors». Energies, vol. 10(7), pp. 1056, July 2017.</mixed-citation><mixed-citation xml:lang="en">. Y. Merizalde, L. Hernández-Callejo, and O. Duque-Perez. «State of the art and trends in the monitoring, detection and diagnosis of failures in electric induction motors». Energies, vol. 10(7), pp. 1056, July 2017.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">. F. Bu, Z. Yang, Y. Gao, Z. Pan, T. Pu, M. Degano, and C. Gerada. «Speed ripple reduction of direct-drive PMSM servo system at low-speed operation using virtual cogging torque control method». IEEE Transactions on Industrial Electronics, vol. 68(1), pp. 160-174, 2020.</mixed-citation><mixed-citation xml:lang="en">. F. Bu, Z. Yang, Y. Gao, Z. Pan, T. Pu, M. Degano, and C. Gerada. «Speed ripple reduction of direct-drive PMSM servo system at low-speed operation using virtual cogging torque control method». IEEE Transactions on Industrial Electronics, vol. 68(1), pp. 160-174, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">. X. Duan, X. Zhang, Y. Tang, and M. Hao. «Cogging torque reduction in pmsm in wide temperature range by response surface methodology». Symmetry, vol. 13(10), pp. 1-17, 2021.</mixed-citation><mixed-citation xml:lang="en">. X. Duan, X. Zhang, Y. Tang, and M. Hao. «Cogging torque reduction in pmsm in wide temperature range by response surface methodology». Symmetry, vol. 13(10), pp. 1-17, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">. D. M. Toporkov, and G. B. Vialcev. «Impact of equalizing currents on losses and torque ripples in electrical machines with fractional slot concentrated windings». In IOP Conference Series: Earth and Environmental Science, vol. 87(3), pp. 1-7, Oct. 2017</mixed-citation><mixed-citation xml:lang="en">. D. M. Toporkov, and G. B. Vialcev. «Impact of equalizing currents on losses and torque ripples in electrical machines with fractional slot concentrated windings». In IOP Conference Series: Earth and Environmental Science, vol. 87(3), pp. 1-7, Oct. 2017</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">. T. Orlowska-Kowalska, M. Wolkiewicz, P. Pietrzak, M. Skowron, P. Ewert, G. Tarchala, and C. T. Kowalski. «Fault diagnosis and fault-tolerant control of PMSM drives-state of the art and future challenges.». IEEE Access, vol. 10, pp. 59979-60024, 2022.</mixed-citation><mixed-citation xml:lang="en">. T. Orlowska-Kowalska, M. Wolkiewicz, P. Pietrzak, M. Skowron, P. Ewert, G. Tarchala, and C. T. Kowalski. «Fault diagnosis and fault-tolerant control of PMSM drives-state of the art and future challenges.». IEEE Access, vol. 10, pp. 59979-60024, 2022.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">. Z. Ullah, B. A. Lodhi, and J. Hur. «Detection and identification of demagnetization and bearing faults in PMSM using transfer learning-based VGG». Energies, vol. 13(15), pp. 1-17, 2020.</mixed-citation><mixed-citation xml:lang="en">. Z. Ullah, B. A. Lodhi, and J. Hur. «Detection and identification of demagnetization and bearing faults in PMSM using transfer learning-based VGG». Energies, vol. 13(15), pp. 1-17, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">. M. Skowron, T. Orlowska-Kowalska, and C. T. Kowalski. «Detection of permanent magnet damage of PMSM drive based on direct analysis of the stator phase currents using convolutional neural network». IEEE Transactions on Industrial Electronics, vol. 69(12), pp. 13665-13675, 2022.</mixed-citation><mixed-citation xml:lang="en">. M. Skowron, T. Orlowska-Kowalska, and C. T. Kowalski. «Detection of permanent magnet damage of PMSM drive based on direct analysis of the stator phase currents using convolutional neural network». IEEE Transactions on Industrial Electronics, vol. 69(12), pp. 13665-13675, 2022.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">. X. Li, L. Zhang, H. Ying Ying, S. Huang, and Q. Zhang. «Study of suppression of vibration and noise of PMSM for electric vehicles». IET Electric Power Applications, vol. 14(7), pp. 1274-1282, 2020.</mixed-citation><mixed-citation xml:lang="en">. X. Li, L. Zhang, H. Ying Ying, S. Huang, and Q. Zhang. «Study of suppression of vibration and noise of PMSM for electric vehicles». IET Electric Power Applications, vol. 14(7), pp. 1274-1282, 2020.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">. N. Remus, M. S. Toulabi, S. Mukundan, H. Dhulipati, W. Li, C. Novak, and N. C. Kar. «Electromagnetic noise and vibration in pmsm and their sources: An overview». In 2020 IEEE Canadian Conference on Electrical and Computer Engineering, pp. 1-4, Aug. 2020.</mixed-citation><mixed-citation xml:lang="en">. N. Remus, M. S. Toulabi, S. Mukundan, H. Dhulipati, W. Li, C. Novak, and N. C. Kar. «Electromagnetic noise and vibration in pmsm and their sources: An overview». In 2020 IEEE Canadian Conference on Electrical and Computer Engineering, pp. 1-4, Aug. 2020.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">. R. M. Pindoriya, R. K. Thakur, B. S. Rajpurohit, and R. Kumar. «Numerical and experimental analysis of torsional vibration and acoustic noise of PMSM coupled with DC generator». IEEE Transactions on Industrial Electronics, vol. 69(4), pp. 3345-3356, 2021.</mixed-citation><mixed-citation xml:lang="en">. R. M. Pindoriya, R. K. Thakur, B. S. Rajpurohit, and R. Kumar. «Numerical and experimental analysis of torsional vibration and acoustic noise of PMSM coupled with DC generator». IEEE Transactions on Industrial Electronics, vol. 69(4), pp. 3345-3356, 2021.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">. H. K. Lee, T. K. Bang, J. H. Woo, H. S. Shin, and J. Y. Choi. «Electromagnetic characteristic analysis of permanent magnet synchronous machine considering current waveform according to static rotor eccentricity». Applied Sciences, vol. 10(23), pp. 8453, Nov. 2020.</mixed-citation><mixed-citation xml:lang="en">. H. K. Lee, T. K. Bang, J. H. Woo, H. S. Shin, and J. Y. Choi. «Electromagnetic characteristic analysis of permanent magnet synchronous machine considering current waveform according to static rotor eccentricity». Applied Sciences, vol. 10(23), pp. 8453, Nov. 2020.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">. Y. Chen, S. Liang, W. Li, H. Liang, and C. Wang. «Faults and diagnosis methods of permanent magnet synchronous motors: A review». Applied Sciences, vol. 9(10), pp. 2116, May 2019.</mixed-citation><mixed-citation xml:lang="en">. Y. Chen, S. Liang, W. Li, H. Liang, and C. Wang. «Faults and diagnosis methods of permanent magnet synchronous motors: A review». Applied Sciences, vol. 9(10), pp. 2116, May 2019.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">. M. Sahraoui, A. Ghoggal, S. Guedidi, and S. E. Zouzou. «Detection of inter-turn short-circuit in induction motors using Park–Hilbert method». International Journal of System Assurance Engineering and Management, vol. 5(3), pp. 337-351, June 2014.</mixed-citation><mixed-citation xml:lang="en">. M. Sahraoui, A. Ghoggal, S. Guedidi, and S. E. Zouzou. «Detection of inter-turn short-circuit in induction motors using Park–Hilbert method». International Journal of System Assurance Engineering and Management, vol. 5(3), pp. 337-351, June 2014.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">. L. A. García-Escudero, O. Duque-Perez, M. Fernandez-Temprano, and D. Morinigo-Sotelo «Robust detection of incipient faults in VSI-fed induction motors using quality control charts». IEEE Transactions on Industry Applications, vol. 53(3), pp. 3076-3085, Oct. 2016.</mixed-citation><mixed-citation xml:lang="en">. L. A. García-Escudero, O. Duque-Perez, M. Fernandez-Temprano, and D. Morinigo-Sotelo «Robust detection of incipient faults in VSI-fed induction motors using quality control charts». IEEE Transactions on Industry Applications, vol. 53(3), pp. 3076-3085, Oct. 2016.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">. Z. Liu, Q. Xia, L. Chen, H. Zhang, C. Wang, and X. Li. «Demagnetization fault diagnosis of PMSM based on fuzzy extreme learning machine». In 2020 Chinese Automation Congress (CAC), pp. 5690-5695, Nov. 2020.</mixed-citation><mixed-citation xml:lang="en">. Z. Liu, Q. Xia, L. Chen, H. Zhang, C. Wang, and X. Li. «Demagnetization fault diagnosis of PMSM based on fuzzy extreme learning machine». In 2020 Chinese Automation Congress (CAC), pp. 5690-5695, Nov. 2020.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">. G. A. Skarmoutsos, K. N. Gyftakis, and M. Mueller. «Analytical prediction of the MCSA signatures under dynamic eccentricity in pm machines with concentrated non-overlapping windings.». IEEE Transactions on Energy Conversion, vol. 37(2), pp. 1011-1019, Oct. 2021.</mixed-citation><mixed-citation xml:lang="en">. G. A. Skarmoutsos, K. N. Gyftakis, and M. Mueller. «Analytical prediction of the MCSA signatures under dynamic eccentricity in pm machines with concentrated non-overlapping windings.». IEEE Transactions on Energy Conversion, vol. 37(2), pp. 1011-1019, Oct. 2021.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">. P. Ewert, and M. Jaworski. «Application of selected higher-order methods to detect rotor unbalance of drive system with PMSM». In 2021 IEEE 19th International Power Electronics and Motion Control Conference (PEMC), pp. 874-879, Apr. 2021.</mixed-citation><mixed-citation xml:lang="en">. P. Ewert, and M. Jaworski. «Application of selected higher-order methods to detect rotor unbalance of drive system with PMSM». In 2021 IEEE 19th International Power Electronics and Motion Control Conference (PEMC), pp. 874-879, Apr. 2021.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">. J. De Bisschop, P. Sergeant, A. Hemeida, H. Vansompel, and L. Dupré. «Analytical model for combined study of magnet demagnetization and eccentricity defects in axial flux permanent magnet synchronous machines». IEEE Transactions on Magnetics, vol. 53(9), pp.1-12, May 2017.</mixed-citation><mixed-citation xml:lang="en">. J. De Bisschop, P. Sergeant, A. Hemeida, H. Vansompel, and L. Dupré. «Analytical model for combined study of magnet demagnetization and eccentricity defects in axial flux permanent magnet synchronous machines». IEEE Transactions on Magnetics, vol. 53(9), pp.1-12, May 2017.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">. S. Leitner, H. Gruebler, and A. Muetze. «Cogging torque minimization and performance of the sub-fractional HP BLDC claw-pole motor». IEEE Transactions on Industry Applications, vol. 55(5), pp. 4653-4664, Oct. 2019.</mixed-citation><mixed-citation xml:lang="en">. S. Leitner, H. Gruebler, and A. Muetze. «Cogging torque minimization and performance of the sub-fractional HP BLDC claw-pole motor». IEEE Transactions on Industry Applications, vol. 55(5), pp. 4653-4664, Oct. 2019.</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">. J. Ou, Y. Liu, R. Qu, and M. Doppelbauer. «Experimental and theoretical research on cogging torque of PM synchronous motors considering manufacturing tolerances». IEEE Transactions on Industrial Electronics, vol. 65(5), pp. 3772-3783, Oct. 2017.</mixed-citation><mixed-citation xml:lang="en">. J. Ou, Y. Liu, R. Qu, and M. Doppelbauer. «Experimental and theoretical research on cogging torque of PM synchronous motors considering manufacturing tolerances». IEEE Transactions on Industrial Electronics, vol. 65(5), pp. 3772-3783, Oct. 2017.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">. Z. Xue, H. Li, Y. Zhou, N. Ren, and W. Wen. «Analytical prediction and optimization of cogging torque in surface-mounted permanent magnet machines with modified particle swarm optimization». IEEE Transactions on Industrial Electronics, 64(12), pp. 9795-9805, June 2017.</mixed-citation><mixed-citation xml:lang="en">. Z. Xue, H. Li, Y. Zhou, N. Ren, and W. Wen. «Analytical prediction and optimization of cogging torque in surface-mounted permanent magnet machines with modified particle swarm optimization». IEEE Transactions on Industrial Electronics, 64(12), pp. 9795-9805, June 2017.</mixed-citation></citation-alternatives></ref><ref id="cit48"><label>48</label><citation-alternatives><mixed-citation xml:lang="ru">. A. G. Pristup, D. M. Toporkov, and A. F. Shevchenko. «A study of cogging torque in permanent magnet synchronous machines with fractional slot windings». Russian Electrical Engineering, 85(12), pp. 743-747, Feb. 2014</mixed-citation><mixed-citation xml:lang="en">. A. G. Pristup, D. M. Toporkov, and A. F. Shevchenko. «A study of cogging torque in permanent magnet synchronous machines with fractional slot windings». Russian Electrical Engineering, 85(12), pp. 743-747, Feb. 2014</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
