{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T02:34:28Z","timestamp":1771468468456,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T00:00:00Z","timestamp":1667260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Sichuan Provincial Department of Science and Technology Agency","award":["2021YFG0348"],"award-info":[{"award-number":["2021YFG0348"]}]},{"name":"Sichuan Provincial Department of Science and Technology Agency","award":["61540063"],"award-info":[{"award-number":["61540063"]}]},{"name":"Sichuan Provincial Department of Science and Technology Agency","award":["2016FD058"],"award-info":[{"award-number":["2016FD058"]}]},{"name":"Sichuan Provincial Department of Science and Technology Agency","award":["2018FD055"],"award-info":[{"award-number":["2018FD055"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["2021YFG0348"],"award-info":[{"award-number":["2021YFG0348"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["61540063"],"award-info":[{"award-number":["61540063"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["2016FD058"],"award-info":[{"award-number":["2016FD058"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["2018FD055"],"award-info":[{"award-number":["2018FD055"]}]},{"name":"Yunnan Natural Science Foundation of China","award":["2021YFG0348"],"award-info":[{"award-number":["2021YFG0348"]}]},{"name":"Yunnan Natural Science Foundation of China","award":["61540063"],"award-info":[{"award-number":["61540063"]}]},{"name":"Yunnan Natural Science Foundation of China","award":["2016FD058"],"award-info":[{"award-number":["2016FD058"]}]},{"name":"Yunnan Natural Science Foundation of China","award":["2018FD055"],"award-info":[{"award-number":["2018FD055"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Sag is an important indicator of the operational health of a transmission line, and its timely measurement is of great significance to maintain the stability and reliability of power systems. However, traditional contact measurements may be affected by the electromagnetic interference of conductors. In contrast, measurement methods without direct electrical contact with the subject provide greater portability and flexibility. This paper presents a study of a transmission line sag measurement and simulation based on non-contact electric field sensing. The finite element method was used to analyze the conductor distribution, establish the coupling relationships among the electric field, transmission line, and measurement point, propose a sag inverse calculation model, and assess the impact of the transmission line parameter on the curved drooping measurement. Simultaneously, sag measurement schemes for single-round and dual-circuit lines were designed for multi-conductive lines, and measurement array studies were conducted. The vertical component of the electric field in space measured by the array was obtained, which could be used to perform conductor sag measurement simply and efficiently. The proposed method will facilitate the monitoring of the overhead transmission line status, which is conducive to the effective operation of the entire system.<\/jats:p>","DOI":"10.3390\/s22218379","type":"journal-article","created":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T08:15:12Z","timestamp":1667376912000},"page":"8379","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Transmission Line Sag Measurement and Simulation Research Based on Non-Contact Electric Field Sensing"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7529-1645","authenticated-orcid":false,"given":"Jinhua","family":"Zuo","sequence":"first","affiliation":[{"name":"School of Electrical and Information Technology, Yunnan Minzu University, Kunming 650500, China"},{"name":"University Key Laboratory of Information and Communication on Security Backup and Recovery in Yunnan Province, Kunming 650500, China"}]},{"given":"Jing","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Technology, Yunnan Minzu University, Kunming 650500, China"},{"name":"University Key Laboratory of Information and Communication on Security Backup and Recovery in Yunnan Province, Kunming 650500, China"}]},{"given":"Yong","family":"Ouyang","sequence":"additional","affiliation":[{"name":"Tsinghua Sichuan Energy Internet Research Institute, Chengdu 610213, China"}]},{"given":"Hua","family":"Liu","sequence":"additional","affiliation":[{"name":"Tsinghua Sichuan Energy Internet Research Institute, Chengdu 610213, China"}]},{"given":"Chao","family":"Yang","sequence":"additional","affiliation":[{"name":"Tsinghua Sichuan Energy Internet Research Institute, Chengdu 610213, China"}]},{"given":"Changjin","family":"Hao","sequence":"additional","affiliation":[{"name":"Tsinghua Sichuan Energy Internet Research Institute, Chengdu 610213, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1109\/TPWRD.2019.2891119","article-title":"Overhead Transmission line parameter reconstruction for UAV Inspection based on Tunneling magnetoresistive sensors and Inverse models","volume":"34","author":"Wu","year":"2019","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/s11220-017-0172-9","article-title":"Monitoring of Overhead Transmission Lines: A Review from the Perspective of Contactless Technologies","volume":"18","author":"Khawaja","year":"2017","journal-title":"Sens. Imaging"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"12008","DOI":"10.1088\/1742-6596\/2158\/1\/012008","article-title":"Forecast Model of Transmission Line Sag Based on GA","volume":"2158","author":"Zhang","year":"2022","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2363","DOI":"10.1109\/TPWRD.2021.3066157","article-title":"Resilience-Oriented Transmission Line Fragility Modeling and Real-Time Risk Assessment of Thunderstorms","volume":"36","author":"Bao","year":"2021","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_5","first-page":"229","article-title":"Sag and Tension Evaluation of a 330 kV Overhead Transmission Line Network for Upland and Level land Topographies","volume":"11","author":"Omeje","year":"2020","journal-title":"Int. J. Sci. Eng. Res"},{"key":"ref_6","unstructured":"Malhara, S. (2009). Mechanical State Estimation of Transmission Line Sag Using Tilt Sensors. [Ph.D. Thesis, Arizona State University]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1109\/61.400930","article-title":"Accurate Ampacity Determination: Temperature-Sag Model for Operational Real Time Ratings","volume":"10","author":"Seppa","year":"1995","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"42021","DOI":"10.1088\/1757-899X\/1098\/4\/042021","article-title":"Analysis of Knee Point Temperature (KPT) determination on High Capacity Low Sag (HCLS) conductors for optimizing the ampacity load and sag on the overhead transmission lines system","volume":"1098","author":"Prasetyo","year":"2021","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/978-981-15-0214-9_22","article-title":"Designing and Implementation of Overhead Conductor Altitude Measurement System Using GPS for Sag Monitoring","volume":"Volume 607","author":"Kamboj","year":"2020","journal-title":"Intelligent Computing Techniques for Smart Energy Systems"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1109\/TPWRD.2011.2181963","article-title":"A Real-time conductor sag measurement system using a Differential GPS","volume":"27","author":"Mahajan","year":"2012","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Shivani, P.G., Harshit, S., Varma, C.V., and Mahalakshmi, R. (2020, January 22). Detection of Icing and Calculation of Sag of Transmission Line through Computer Vision. Proceedings of the 2020 Third International Conference on Smart Systems and Inventive Technology (ICSSIT), Tirunelveli, India.","DOI":"10.1109\/ICSSIT48917.2020.9214249"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wydra, M., Kisa\u0142a, P., Harasim, D., and Kacejko, P. (2018). Overhead Transmission Line Sag Estimation Using a Simple Optomechanical System with Chirped Fiber Bragg Gratings. Part 1: Preliminary Measurements. Sensors, 18.","DOI":"10.3390\/s18010309"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Skorupski, K., Harasim, D., Panas, P., Ci\u0119szczyk, S., Kisa\u0142a, P., Kacejko, P., Mroczka, J., and Wydra, M. (2020). Overhead Transmission Line Sag Estimation Using the Simple Opto-Mechanical System with Fiber Bragg Gratings\u2014Part 2: Interrogation System. Sensors, 20.","DOI":"10.3390\/s20092652"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"99198","DOI":"10.1109\/ACCESS.2020.2998154","article-title":"Measurement of Power line sagging using sensor data of a Power line inspection robot","volume":"8","author":"Zengin","year":"2020","journal-title":"IEEE Access"},{"key":"ref_15","first-page":"524","article-title":"A Contractless Overvoltage Measurement Method Based on the Principle of Multi Conductor Electrostatic Coupling","volume":"29","author":"Yuan","year":"2014","journal-title":"Trans. China Electrotech. Societa."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"900107","DOI":"10.1109\/TMAG.2013.2294471","article-title":"Magnetics in Smart Grid","volume":"50","author":"Huang","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4013","DOI":"10.1109\/JSEN.2018.2816931","article-title":"Velocity Measurement Technique for Permanent Magnet Synchronous Motors through External Stray Magnetic Field Sensing","volume":"18","author":"Liu","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1109\/TIM.2017.2676140","article-title":"Estimating Sag and Wind-Induced Motion of Overhead Power Lines with Current and Magnetic-Flux Density Measurements","volume":"66","author":"Khawaja","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6100210","DOI":"10.1109\/TMAG.2017.2657490","article-title":"Estimation of Current and Sag in Overhead power transmission lines with Optimized magnetic field sensor array placement","volume":"53","author":"Khawaja","year":"2017","journal-title":"IEEE Trans. Magn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4003307","DOI":"10.1109\/TMAG.2019.2905567","article-title":"Magnetic-Field-Sensing-Based Approach for Current reconstruction, sag detection, and Inclination detection for Overhead transmission system","volume":"55","author":"Xu","year":"2019","journal-title":"IEEE Trans. Magn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6998","DOI":"10.1109\/JSEN.2020.3041328","article-title":"Contactless Phase comparison method for Overhead transmission lines","volume":"21","author":"Chen","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2891","DOI":"10.1109\/TPWRD.2010.2051340","article-title":"The Effects of the Span configurations and Conductor sag on the Electric-field distribution under overhead transmission lines","volume":"25","author":"Wahab","year":"2010","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"166740","DOI":"10.1109\/ACCESS.2019.2953756","article-title":"Improved Three-Dimension Mathematical Model for Voltage Inversion of AC Overhead Transmission Lines","volume":"7","author":"Xiao","year":"2019","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7494","DOI":"10.1109\/TIM.2020.2983576","article-title":"Non-contact Monitoring of Overhead transmission lines using space potential phaser measurements","volume":"69","author":"Mukherjee","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9002312","DOI":"10.1109\/TIM.2022.3157907","article-title":"Overhead Transmission lines sag and Voltage monitoring method based on Electrostatic inverse calculation","volume":"71","author":"Ji","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3121","DOI":"10.1109\/JSEN.2019.2892498","article-title":"Non-Contact Voltage Monitoring of HVDC Transmission Lines Based on Electromagnetic Fields","volume":"19","author":"Zhu","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_27","first-page":"9001413","article-title":"Contactless Islanding Detection Method Using Electric Field Sensors","volume":"70","author":"Chen","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.sna.2011.02.019","article-title":"Dual capacitive sensors for non-contact AC voltage measurement","volume":"167","author":"Tsang","year":"2011","journal-title":"Sens. Actuators A Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"012034","DOI":"10.1088\/1755-1315\/647\/1\/012034","article-title":"Three-dimensional simulation analysis of electric field distribution at the middle joint of 110 kV cable with typical defects","volume":"647","author":"Xu","year":"2021","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Li, X., Wan, M., Yan, S., and Lin, X. (2021). Temperature and Electric Field Distribution Characteristics of a DC-GIL Basin-Type Spacer with 3D Modelling and Simulation. Energies, 14.","DOI":"10.3390\/en14237889"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2856","DOI":"10.1109\/TPWRD.2018.2854678","article-title":"Fully Coupled finite element analysis for Ion flow field under HVDC Transmission lines employing field enhancement factor","volume":"33","author":"Park","year":"2018","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1109\/61.517518","article-title":"Effects of Conductor Sag on Spatial Distribution of Power Line Magnetic Field","volume":"11","author":"Mamishev","year":"1996","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_33","unstructured":"Fernandez, J.C., and Soibelzon, H.L. (2001). The Surface Electric Field of Catenary High Voltage Overhead Transmission Lines. EMC Powers Syst., 22\u201326."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Amiri, R., Hadi, H., and Marich, M. (2006, January 15\u201318). The influence of sag in the electric field calculation around high voltage overhead transmission lines. Proceedings of the Electrical Insulation and Dielectric Phenomena IEEE Conference on IEEE, Kansas City, MO, USA.","DOI":"10.1109\/CEIDP.2006.312097"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1109\/TPWRD.2008.916748","article-title":"Analytical Calculation of the Electric field produced by Single-circuit power lines","volume":"23","author":"Tzinevrakis","year":"2008","journal-title":"IEEE Trans. Power Deliv."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8379\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:07:15Z","timestamp":1760144835000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8379"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,1]]},"references-count":35,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22218379"],"URL":"https:\/\/doi.org\/10.3390\/s22218379","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,1]]}}}