{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T23:42:30Z","timestamp":1771026150299,"version":"3.50.1"},"reference-count":22,"publisher":"Institution of Engineering and Technology (IET)","issue":"4","license":[{"start":{"date-parts":[[2022,1,4]],"date-time":"2022-01-04T00:00:00Z","timestamp":1641254400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52007133"],"award-info":[{"award-number":["52007133"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["ietresearch.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["IET Circuits, Devices &amp; Syst"],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Severe harmonics propagation in power systems may result in increased power losses and equipment damages. In this paper, an elliptic formula is derived to analyse the harmonic spatial distribution not only at the substations but also along the power lines or cables and to give a system\u2010wide overview of harmonic levels. It is observed that harmonic distortion along power lines can be higher than that at the busbars and the maximum amplitude of harmonic voltage and current denoted as weak positions along power lines depends on the steady\u2010state harmonic angle difference of voltage and current at busbars, the length of power lines, and the harmonic order. All cases are modelled in detail by analytical geometry and analysed in MATLAB. In this regard, a method to identify the weak positions in terms of maximum harmonic levels in a power system is presented, and its corresponding harmonic orders are determined. The accuracy of the model is tested using time\u2010domain simulations in PSCAD\/EMTDC.<\/jats:p>","DOI":"10.1049\/cds2.12107","type":"journal-article","created":{"date-parts":[[2022,1,5]],"date-time":"2022-01-05T02:47:42Z","timestamp":1641350862000},"page":"337-349","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A study of harmonic spatial propagation along AC power lines of meshed power systems"],"prefix":"10.1049","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0262-5314","authenticated-orcid":false,"given":"Chengxi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Automation Wuhan University  Wuhan China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6037-2995","authenticated-orcid":false,"given":"Zhen","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation Wuhan University  Wuhan China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2640-0964","authenticated-orcid":false,"given":"Filipe","family":"Faria da Silva","sequence":"additional","affiliation":[{"name":"Department of Energy Technology Aalborg University  Aalborg Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1500-8684","authenticated-orcid":false,"given":"Qiupin","family":"Lai","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation Wuhan University  Wuhan China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1952-0666","authenticated-orcid":false,"given":"Pan","family":"Hu","sequence":"additional","affiliation":[{"name":"Hubei Electric Power Research Institute  Wuhan China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"265","published-online":{"date-parts":[[2022,1,4]]},"reference":[{"key":"e_1_2_9_2_1","first-page":"60","volume-title":"Energinet analysis assumption","author":"Energinet","year":"2017"},{"key":"e_1_2_9_3_1","first-page":"29","volume-title":"IEEE recommended practice and requirements for harmonic control in electric power systems","author":"IEEE","year":"2014"},{"key":"e_1_2_9_4_1","volume-title":"Analysis and simulation of electromagnetic transients in HVAC cable transmission grids, PhD thesis","author":"Da Silva F.F.","year":"2011"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsr.2018.03.009"},{"key":"e_1_2_9_6_1","first-page":"132","volume-title":"Technical issues related to new transmission lines in Denmark \u2010 west coast line from German border to Edrup and Endrup\u2010Idomlund","author":"Energinet dk","year":"2018"},{"key":"e_1_2_9_7_1","volume-title":"Network Modelling for Harmonic Studies, Technical Brochures","author":"Escudero M.V.","year":"2019"},{"key":"e_1_2_9_8_1","first-page":"1","volume-title":"Proceedings of the International Conference on Power System Transients","author":"Fillion Y.","year":"2015"},{"key":"e_1_2_9_9_1","first-page":"1","volume-title":"Proceedings of International Conference on Power System Transients","author":"Velitsikakis K.","year":"2019"},{"key":"e_1_2_9_10_1","volume-title":"Proceedings of CIGRE Paris Session, Paper c4\u2010305","author":"Kwon J.B.","year":"2020"},{"key":"e_1_2_9_11_1","volume-title":"Proceedings of CIGRE Paris Session, paper C4\u2010208","author":"Cunniffe N.","year":"2016"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRD.2019.2928565"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TEC.2014.2332497"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRD.2016.2603440"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIM.2017.2660019"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1049\/cp:20010773"},{"key":"e_1_2_9_17_1","volume-title":"Telegrapher\u2019s Equation","author":"Wikipedia [Internet]","year":"2001"},{"key":"e_1_2_9_18_1","volume-title":"McCammon, R.: SPICE Simulation of Transmission Lines by the Tele\u2010grapher\u2019s Equations into a Circuit","author":"Wikipedia [internet]","year":"2001"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1109\/ECCTD.2017.8093252"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.egyr.2018.09.005"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2016.09.104"},{"key":"e_1_2_9_22_1","volume-title":"Power System Model for Resonance Studies [internet]","author":"Lennerhag O.","year":"2018"},{"key":"e_1_2_9_23_1","volume-title":"IEEE 39 Bus System [Internet]","author":"PSCAD","year":"2018"}],"container-title":["IET Circuits, Devices &amp; 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