{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T13:40:35Z","timestamp":1766065235447,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T00:00:00Z","timestamp":1641945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010880","name":"State Grid Corporation of China","doi-asserted-by":"publisher","award":["5500-202124103A-0-0-00"],"award-info":[{"award-number":["5500-202124103A-0-0-00"]}],"id":[{"id":"10.13039\/501100010880","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>According to the vibration characteristics of converter transformers, considering the Maxwell equation, magnetostrictive effect, Lorentz force and structural mechanics, the similarity criterion suitable for converter transformers is deduced in this paper. Using the finite element simulation platform, the multi physical field coupling model of converter transformers is constructed, and the scale coefficient is 0.1. The magnetic flux density distribution, stress distribution, shape variable and vibration characteristics of the model before and after the similarity are analyzed. The results show that the variation law of the model before and after the similarity conforms to the similarity criterion, and the correctness of the similarity criterion is verified. The converter transformer vibration similarity model and its verification method can effectively reduce the unnecessary waste of resources before the preparation of converter transformers and have important reference value for the analysis and improvement of converter transformer vibration characteristics.<\/jats:p>","DOI":"10.3390\/sym14010143","type":"journal-article","created":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T09:10:36Z","timestamp":1641978636000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Vibration Similarity Model of Converter Transformers and Its Verification Method"],"prefix":"10.3390","volume":"14","author":[{"given":"Hao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youliang","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9523-3020","authenticated-orcid":false,"given":"Liang","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/MPER.2000.819913","article-title":"Role of HVDC transmission in future energy development","volume":"20","author":"Hammons","year":"2000","journal-title":"IEEE Power Eng. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105426","DOI":"10.1016\/j.ijepes.2019.105426","article-title":"Impact of DC bias on differential protection of converter transformers","volume":"115","author":"Zhao","year":"2020","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16420","DOI":"10.1007\/s10854-020-04194-w","article-title":"Electromagneto-mechanical numerical analysis and experiment of transformer influenced by DC bias considering core magnetostriction","volume":"31","author":"Liu","year":"2020","journal-title":"J. Mater. Sci. Mater. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3759","DOI":"10.1109\/20.908346","article-title":"Relevance of magnetostriction and forces for the generation of audible noise of transformer cores","volume":"36","author":"Weiser","year":"2000","journal-title":"IEEE Trans. Magn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0304-8853(96)00171-0","article-title":"Mechanisms of noise generation of model transformer cores","volume":"160","author":"Weiser","year":"1996","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1002\/eej.20947","article-title":"Analysis of structural deformation and vibration of a transformer core by using magnetic property of magnetostriction","volume":"172","author":"Kitagawa","year":"2010","journal-title":"Electr. Eng. Jpn."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1049\/iet-epa.2012.0144","article-title":"Modelling methodology for transformer core vibrations based on the magnetostrictive properties","volume":"6","author":"Li","year":"2012","journal-title":"IET Electr. Power Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2014.2331697","article-title":"Analysis of Voltage Distribution Characteristics in UHVDC Converter Transformer Winding Based on the Reduced-Scale Model","volume":"50","author":"Pu","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_9","first-page":"1","article-title":"Study on Vibration of Iron Core of Transformer and Reactor Based on Maxwell Stress and Anisotropic Magnetostriction","volume":"55","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Magn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2016.2584004","article-title":"Localized Surface Vibration and Acoustic Noise Emitted from Laboratory-Scale Transformer Cores Assembled from Grain-Oriented Electrical Steel","volume":"52","author":"Moses","year":"2016","journal-title":"IEEE Trans. Magn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"107634","DOI":"10.1016\/j.epsr.2021.107634","article-title":"Novel accurate modeling of dust loaded wire-duct precipitators using FDM-FMG method on one fine computational domains","volume":"203","author":"Sayed","year":"2022","journal-title":"Electr. Power Syst. Res."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zalhaf, A.S., Mansour, D.-E.A., Han, Y., Yang, P., Yang, P., and Darwish, M.M.F. (2021). Numerical and Experimental Analysis of the Transient Behavior of Wind Turbines when Two Blades are Simultaneously Struck by Lightning. IEEE Trans. Instrum. Meas.","DOI":"10.1109\/TIM.2021.3132076"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"107370","DOI":"10.1016\/j.epsr.2021.107370","article-title":"Measurement and assessment of corona current density for HVDC bundle conductors by FDM integrated with full multigrid technique","volume":"199","author":"Abouelatta","year":"2021","journal-title":"Electr. Power Syst. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"225872","DOI":"10.1109\/ACCESS.2020.3045073","article-title":"Fast Corona Discharge Assessment Using FDM integrated With Full Multigrid Method in HVDC Transmission Lines Considering Wind Impact","volume":"8","author":"Abouelatta","year":"2020","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/TPWRD.2005.852280","article-title":"Transformer Tank Vibration Modeling as a Method of Detecting Winding Deformations-Part I: Theoretical Foundation","volume":"21","author":"Garcia","year":"2006","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1109\/TPWRD.2005.852275","article-title":"Transformer Tank Vibration Modeling as a Method of Detecting Winding Deformations-Part II: Experimental Verification","volume":"21","author":"Garcia","year":"2006","journal-title":"IEEE Trans. Power Deliv."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/1\/143\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:14:57Z","timestamp":1760364897000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/1\/143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,12]]},"references-count":16,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["sym14010143"],"URL":"https:\/\/doi.org\/10.3390\/sym14010143","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,1,12]]}}}