{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T05:34:33Z","timestamp":1777268073026,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2022,12,16]],"date-time":"2022-12-16T00:00:00Z","timestamp":1671148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We develop a probabilistic model for determining the location of dc-link faults in MT-HVdc networks using discrete wavelet transforms (DWTs), Bayesian optimization, and multilayer artificial neural networks (ANNs) based on local information. Likewise, feedforward neural networks (FFNNs) are trained using the Levenberg\u2013Marquardt backpropagation (LMBP) method, which multi-stage BO optimizes for efficiency. During training, the feature vectors at the sending terminal of the dc link are selected based on the norm values of the observed waveforms at various frequency bands. The multilayer ANN is trained using a comprehensive set of offline data that takes the denoising scheme into account. This choice not only helps to reduce the computational load but also provides better accuracy. An overall percentage error of 0.5144% is observed for the proposed algorithm when tested against fault resistances ranging from 10 to 485 \u2126. The simulation results show that the proposed method can accurately estimate the fault site to a precision of 485 \u2126 and is more robust.<\/jats:p>","DOI":"10.3390\/s22249936","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T09:31:01Z","timestamp":1671442261000},"page":"9936","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":55,"title":["Intelligent Sensors for dc Fault Location Scheme Based on Optimized Intelligent Architecture for HVdc Systems"],"prefix":"10.3390","volume":"22","author":[{"given":"Muhammad Zain","family":"Yousaf","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9138-3323","authenticated-orcid":false,"given":"Muhammad Faizan","family":"Tahir","sequence":"additional","affiliation":[{"name":"School of Electric Power, South China University of Technology, Guangzhou 510630, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0947-3616","authenticated-orcid":false,"given":"Ali","family":"Raza","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, University of Engineering and Technology, Lahore 39161, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Ahmad","family":"Khan","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fazal","family":"Badshah","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,16]]},"reference":[{"key":"ref_1","first-page":"35","article-title":"China\u2019s ambitious plan to build the world\u2019s biggest supergrid","volume":"1","author":"Fairley","year":"2019","journal-title":"IEEE Spectr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1109\/TPWRD.2013.2269769","article-title":"Natural frequency-based line fault location in HVDC lines","volume":"29","author":"He","year":"2014","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1109\/TPWRD.2009.2033078","article-title":"A novel fault-location method for HVDC transmission lines","volume":"25","author":"Suonan","year":"2009","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"29711","DOI":"10.1109\/ACCESS.2021.3057659","article-title":"Deep learning for short-term voltage stability assessment of power systems","volume":"9","author":"Zhang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.35833\/MPCE.2021.000218","article-title":"Statistical Measure for Risk-Seeking Stochastic Wind Power Offering Strategies in Electricity Markets","volume":"10","author":"Xiao","year":"2021","journal-title":"J. Mod. Power Syst. Clean Energy"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Nsaif, Y.M., Hossain Lipu, M.S., Hussain, A., Ayob, A., Yusof, Y., and Zainuri, M.A.A. (2022). A Novel Fault Detection and Classification Strategy for Photovoltaic Distribution Network Using Improved Hilbert\u2013Huang Transform and Ensemble Learning Technique. Sustainability, 14.","DOI":"10.3390\/su141811749"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2028","DOI":"10.1109\/TPWRD.2019.2922654","article-title":"Single-ended traveling wave fault location method in DC transmission line based on wave front information","volume":"34","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1109\/TPWRD.2016.2589265","article-title":"Traveling-wave-based fault-location algorithm for hybrid multiterminal circuits","volume":"32","author":"Hamidi","year":"2016","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1109\/TPWRD.2013.2248068","article-title":"Transient-based fault-location method for multiterminal lines employing S-transform","volume":"28","author":"Ahmadimanesh","year":"2013","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Perveen, R., Mohanty, S.R., and Kishor, N. (2016, January 18\u201320). Fault location in VSC-HVDC section for grid integrated offshore wind farm by EMD. Proceedings of the 18th Mediterranean Electrotechnical Conference (MELECON), Lemesos, Cyprus.","DOI":"10.1109\/MELCON.2016.7495356"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2360","DOI":"10.1109\/TPWRD.2012.2211898","article-title":"Accurate single-phase fault-location method for transmission lines based on k-nearest neighbor algorithm using one-end voltage","volume":"27","author":"Farshad","year":"2012","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"928","DOI":"10.1016\/j.asoc.2012.09.010","article-title":"A systematic fuzzy rule based approach for fault classification in transmission lines","volume":"13","author":"Samantaray","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.1049\/iet-gtd.2019.1414","article-title":"Wigner distribution function and alienation coefficient-based transmission line protection scheme","volume":"14","author":"Ola","year":"2020","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ram Ola, S., Saraswat, A., Goyal, S.K., Jhajharia, S., Khan, B., Mahela, O.P., Haes Alhelou, H., and Siano, P. (2020). A protection scheme for a power system with solar energy penetration. Appl. Sci., 10.","DOI":"10.3390\/app10041516"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1016\/j.epsr.2005.11.003","article-title":"Fault classification and location using HS-transform and radial basis function neural network","volume":"76","author":"Samantaray","year":"2006","journal-title":"Electr. Power Syst. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1109\/TPWRS.2004.825883","article-title":"Accurate fault location in the power transmission line using support vector machine approach","volume":"19","author":"Salat","year":"2004","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_17","first-page":"2414","article-title":"Transient signal identification of HVDC transmission lines based on wavelet entropy and SVM","volume":"2019","author":"Luo","year":"2019","journal-title":"J. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2160","DOI":"10.1016\/j.neucom.2010.02.001","article-title":"Intelligent approaches using support vector machine and extreme learning machine for transmission line protection","volume":"73","author":"Malathi","year":"2010","journal-title":"Neurocomputing"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/j.ijepes.2018.07.044","article-title":"Detection and classification of internal faults in bipolar HVDC transmission lines based on K-means data description method","volume":"104","author":"Farshad","year":"2019","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2937","DOI":"10.1016\/j.eswa.2007.05.011","article-title":"Energy and entropy-based feature extraction for locating fault on transmission lines by using neural network and wavelet packet decomposition","volume":"34","author":"Ekici","year":"2008","journal-title":"Expert Syst. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"145371","DOI":"10.1109\/ACCESS.2019.2945397","article-title":"Wavelet-multi resolution analysis based ANN architecture for fault detection and localization in DC microgrids","volume":"7","author":"Jayamaha","year":"2019","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1049\/iet-rpg.2018.5097","article-title":"Efficient and robust ANN-based method for an improved protection of VSC-HVDC systems","volume":"12","author":"Merlin","year":"2018","journal-title":"IET Renew. Power Gener."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1109\/TPWRD.2017.2721903","article-title":"Fault location in ungrounded photovoltaic system using wavelets and ANN","volume":"33","author":"Karmacharya","year":"2017","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1109\/TVLSI.2017.2784783","article-title":"A global Bayesian optimization algorithm and its application to integrated system design","volume":"26","author":"Torun","year":"2018","journal-title":"IEEE Trans. Very Large Scale Integr. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4263","DOI":"10.1109\/TMTT.2015.2495360","article-title":"Bayesian optimization for broadband high-efficiency power amplifier designs","volume":"63","author":"Chen","year":"2015","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1856","DOI":"10.1109\/TVLSI.2017.2656843","article-title":"Application of machine learning for optimization of 3-D integrated circuits and systems","volume":"25","author":"Park","year":"2017","journal-title":"IEEE Trans. Very Large Scale Integr. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3436","DOI":"10.1109\/TII.2017.2777460","article-title":"Levenberg\u2013Marquardt backpropagation training of multilayer neural networks for state estimation of a safety-critical cyber-physical system","volume":"14","author":"Lv","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/TII.2017.2701823","article-title":"Heath monitoring of capacitors and supercapacitors using the neo-fuzzy neural approach","volume":"14","author":"Soualhi","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1109\/72.329697","article-title":"Training feedforward networks with the Marquardt algorithm","volume":"5","author":"Hagan","year":"1994","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1109\/TAI.2021.3097307","article-title":"Toward the development of versatile brain\u2013computer interfaces","volume":"2","author":"Sadiq","year":"2021","journal-title":"IEEE Trans. Artif. Intell."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.rser.2019.03.040","article-title":"Machine-learning methods for integrated renewable power generation: A comparative study of artificial neural networks, support vector regression, and Gaussian Process Regression","volume":"108","author":"Sharifzadeh","year":"2019","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_32","first-page":"2879","article-title":"Convergence rates of efficient global optimization algorithms","volume":"12","author":"Bull","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Leterme, W., Ahmed, N., Beerten, J., \u00c4ngquist, L., Van Hertem, D., and Norrga, S. (2015, January 10\u201312). A New HVDC Grid Test System for HVDC Grid Dynamics and Protection Studies in EMT-Type Software. Proceedings of the 11th IET International Conference on AC and DC Power Transmission, Birmingham, AL, USA.","DOI":"10.1049\/cp.2015.0068"},{"key":"ref_34","first-page":"2285","article-title":"Fault diagnosis for power cables based on convolutional neural network with chaotic system and discrete wavelet transform","volume":"21","author":"Wang","year":"2021","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ukil, A., Yeap, Y.M., and Satpathi, K. (2020). Fault Analysis and Protection System Design for DC Grids, Springer.","DOI":"10.1007\/978-981-15-2977-1"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2286","DOI":"10.1109\/TPWRD.2012.2202405","article-title":"Traveling-wave-based line fault location in star-connected multiterminal HVDC systems","volume":"27","author":"Nanayakkara","year":"2012","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1109\/TPWRD.2011.2174067","article-title":"Location of DC line faults in conventional HVDC systems with segments of cables and overhead lines using terminal measurements","volume":"27","author":"Nanayakkara","year":"2011","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2552","DOI":"10.1109\/TPWRD.2014.2323356","article-title":"A traveling-wave-based methodology for wide-area fault location in multiterminal DC systems","volume":"29","author":"Azizi","year":"2014","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"203398","DOI":"10.1109\/ACCESS.2020.3035905","article-title":"Voltage and current measuring technologies for high voltage direct current supergrids: A technology review identifying the options for protection, fault location and automation applications","volume":"8","author":"Tzelepis","year":"2020","journal-title":"IEEE Access"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1109\/TPWRD.2019.2942016","article-title":"On the application of modal transient analysis for online fault localization in HVDC cable bundles","volume":"35","author":"Ashouri","year":"2019","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.compeleceng.2019.07.022","article-title":"Multi extreme learning machine approach for fault location in multi-terminal high-voltage direct current systems","volume":"78","author":"Hadaeghi","year":"2019","journal-title":"Comput. Electr. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.epsr.2013.10.006","article-title":"A single-ended fault location method for segmented HVDC transmission line","volume":"107","author":"Livani","year":"2014","journal-title":"Electr. Power Syst. Res."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.ijepes.2017.10.040","article-title":"Advanced fault location in MTDC networks utilising optically-multiplexed current measurements and machine learning approach","volume":"97","author":"Tzelepis","year":"2018","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"10124","DOI":"10.1109\/ACCESS.2022.3142534","article-title":"Time-domain protection of superconducting cables based on artificial intelligence classifiers","volume":"10","author":"Tsotsopoulou","year":"2022","journal-title":"IEEE Access"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/24\/9936\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:42:49Z","timestamp":1760146969000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/24\/9936"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,16]]},"references-count":44,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["s22249936"],"URL":"https:\/\/doi.org\/10.3390\/s22249936","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,16]]}}}