{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:44:43Z","timestamp":1759970683656,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,25]],"date-time":"2025-01-25T00:00:00Z","timestamp":1737763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52077053","52377008"],"award-info":[{"award-number":["52077053","52377008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An efficient numerical calculation method of stray-field loss is investigated for typical magnetic load components (grain-oriented silicon steel sheets (GO), magnetic steel plate, and combined components of both materials) under non-sinusoidal excitations (NSE) containing symmetrical harmonic and DC to avoid the local overheating caused by high stray-field loss density. The paper investigates the stray-field loss with different types of load components and working conditions based on the leakage flux complementary-based measurement method, derives an analytical formulation calculating the energetic hysteresis model parameters under different magnetic flux densities to reduce the dependence on measurement data, establishes a loss calculation method considering the influence of non-sinusoidal magnetization on magnetic loss, and discusses the advantages and limitations of existing numerical approaches of additional loss to establish an effective computational strategy of stray-field loss. Finally, the effectiveness of the proposed method is verified by simulations and experiments.<\/jats:p>","DOI":"10.3390\/sym17020189","type":"journal-article","created":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T04:59:10Z","timestamp":1737953950000},"page":"189","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Calculation of Stray-Field Loss of TEAM P21 Model Under Complex Excitations Based on the Improved Energetic Hysteresis Model"],"prefix":"10.3390","volume":"17","author":[{"given":"Zhigang","family":"Zhao","sequence":"first","affiliation":[{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dehai","family":"Li","sequence":"additional","affiliation":[{"name":"Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/OJPEL.2024.3515798","article-title":"Extending the Steinmetz Equation: Incorporating Mechanical Stress Effects in Ferrite Core Loss Calculations","volume":"6","author":"Rohner","year":"2025","journal-title":"IEEE Open J. Power Electron."},{"key":"ref_2","first-page":"5900205","article-title":"Hysteresis and Coupling Loss in Filamentized REBCO Tapes","volume":"35","author":"Solovyov","year":"2025","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"11561","DOI":"10.1109\/LRA.2024.3495374","article-title":"A Voltage Minimization Control Method for Magnetic Navigation Systems to Enhance the Rotating Magnetic Field","volume":"9","author":"Kwon","year":"2024","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7402807","DOI":"10.1109\/TMAG.2024.3486752","article-title":"Analysis of Magnetic Properties of Soft Magnetic Composite Using Magnetic Circuits Generated by Discrete Element Method","volume":"60","author":"Sato","year":"2024","journal-title":"IEEE Trans. Magn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.1109\/OJPEL.2024.3476166","article-title":"Analytical Loss Model for Magnetic Cores Based on Vector Magnetic Circuit Theory","volume":"5","author":"Li","year":"2024","journal-title":"IEEE Open J. Power Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5501105","DOI":"10.1109\/TASC.2024.3463511","article-title":"Advanced Soft Magnetic Materials for the Development of High-Frequency Magnetic Core Used in Solid-State Transformers","volume":"34","author":"Hossain","year":"2024","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7301405","DOI":"10.1109\/TMAG.2024.3458798","article-title":"A Hysteresis Model for Soft Magnetic Composites Considering Particle Size Distribution","volume":"60","author":"Li","year":"2024","journal-title":"IEEE Trans. Magn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7301107","DOI":"10.1109\/TMAG.2024.3452593","article-title":"A Circuit-Based Formulation for Soft Magnetic Materials Using the Jiles\u2013Atherton Model","volume":"60","author":"Kanakgiri","year":"2024","journal-title":"IEEE Trans. Magn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"144432","DOI":"10.1109\/ACCESS.2020.3014685","article-title":"Experimental and numerical study on stray loss in laminated magnetic shielding under 3-D AC-DC hybrid excitations for HVDC transformers","volume":"8","author":"Zhao","year":"2020","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5697","DOI":"10.1109\/TPEL.2018.2867264","article-title":"A practical approach for core loss estimation of a high-current gapped inductor in PWM converters with a user-friendly loss map","volume":"34","author":"Wang","year":"2019","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1109\/PROC.1984.12842","article-title":"On the law of hysteresis","volume":"72","author":"Steinmetz","year":"1984","journal-title":"Proc. IEEE"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1109\/28.936396","article-title":"Calculation of losses in ferro- and ferrimagnetic materials based on the modified Steinmetz equation","volume":"37","author":"Reinert","year":"2001","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_13","unstructured":"Li, J., Abdallah, T., and Sullivan, C.R. (October, January 30). Improved calculation of core loss with nonsinusoidal waveforms. Proceedings of the Conference Record of the 2001 IEEE Industry Applications Conference. 36th IAS Annual Meeting (Cat. No.01CH37248), Chicago, IL, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1109\/TPEL.2011.2162252","article-title":"Improved core loss calculation for magnetic components employed in power electronic systems","volume":"27","author":"Mulethaler","year":"2012","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1109\/TPEL.2007.911881","article-title":"Loss characterization and calculation of nanocrystalline cores for high-frequency applications","volume":"23","author":"Shen","year":"2008","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2146","DOI":"10.1109\/TPEL.2016.2555359","article-title":"An improved empirical formulation for magnetic core losses estimation under nonsinusoidal induction","volume":"32","author":"Barg","year":"2017","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2001507","DOI":"10.1109\/TMAG.2014.2354317","article-title":"Core-loss prediction for non-oriented electrical steels based on the steinmetz equation using fixed coefficients with a wide frequency range of validity","volume":"51","author":"Novak","year":"2015","journal-title":"IEEE Trans. Magn."},{"key":"ref_18","first-page":"1915","article-title":"The prediction of power losses in soft magnetic materials","volume":"49","author":"Bertotti","year":"1988","journal-title":"Le J. Phys. Colloq."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2904","DOI":"10.1109\/20.104905","article-title":"An improved approach to power losses in magnetic laminations under nonsinusoidal induction waveform","volume":"26","author":"Fiorillo","year":"1990","journal-title":"IEEE Trans. Magn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3021","DOI":"10.1109\/TMAG.2012.2208944","article-title":"Advanced iron-loss estimation for nonlinear material behavior","volume":"48","author":"Eggers","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2009","DOI":"10.1109\/TPEL.2020.3009283","article-title":"Analytical prediction model of energy losses in soft magnetic materials over broadband frequency range","volume":"36","author":"Liu","year":"2021","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2655","DOI":"10.1109\/TPEL.2018.2837657","article-title":"Energy losses in soft magnetic materials under symmetric and asymmetric induction waveforms","volume":"34","author":"Zhao","year":"2019","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"085222","DOI":"10.1063\/5.0020789","article-title":"Modified loss separation in FeSi laminations under arbitrary distorted flux","volume":"10","author":"Zhao","year":"2020","journal-title":"AIP Adv."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1109\/TMAG.1978.1059858","article-title":"A simple method of estimating the minor loop hysteresis loss in thin laminations","volume":"14","author":"Lavers","year":"1978","journal-title":"IEEE Trans. Magn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/20.119813","article-title":"Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis","volume":"28","author":"Jiles","year":"1992","journal-title":"IEEE Trans. Magn."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1109\/TMAG.2010.2097274","article-title":"Efficient algorithms for the inclusion of the preisach hysteresis model in nonlinear finite-element methods","volume":"47","author":"Dlala","year":"2011","journal-title":"IEEE Trans. Magn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2753","DOI":"10.1063\/1.1771479","article-title":"Energetic model of ferromagnetic hysteresis: Isotropic magnetization","volume":"96","author":"Hauser","year":"2004","journal-title":"J. Appl. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7511405","DOI":"10.1109\/TMAG.2019.2953887","article-title":"A dynamic magnetostriction model of grain-oriented sheet steels based on Becker\u2013D\u00f6ring crystal magnetization model and Jiles-Atherton theory of magnetic hysteresis","volume":"56","author":"Li","year":"2020","journal-title":"IEEE Trans. Magn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"7510204","DOI":"10.1109\/TMAG.2019.2956475","article-title":"Accurate symmetrical minor loops calculation with a modified energetic hysteresis model","volume":"56","author":"Liu","year":"2020","journal-title":"IEEE Trans. Magn."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3672","DOI":"10.1109\/20.952687","article-title":"Nonlinear analysis of eddy current and hysteresis losses of 3-D stray field loss model (Problem 21)","volume":"37","author":"Takahashi","year":"2001","journal-title":"IEEE Trans. Magn."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1108\/COMPEL-03-2021-0114","article-title":"Modeling and validation of stray-field loss inside magnetic and non-magnetic components under harmonics-DC hybrid excitations based on updated TEAM Problem 21","volume":"40","author":"Cheng","year":"2021","journal-title":"COMPEL"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.jmmm.2015.06.082","article-title":"Dynamic magnetization models for soft ferromagnetic materials with coarse and fine domain structures","volume":"394","author":"Zirka","year":"2015","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_33","unstructured":"Bertotti, G. (1998). Hysteresis in Magnetism for Physicists, Materials Scientists, and Engineers, Academic Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/189\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:36:10Z","timestamp":1759919770000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/189"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,25]]},"references-count":33,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020189"],"URL":"https:\/\/doi.org\/10.3390\/sym17020189","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,1,25]]}}}