{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T03:42:16Z","timestamp":1775619736199,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,5,14]],"date-time":"2023-05-14T00:00:00Z","timestamp":1684022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chongqing Natural Science Foundation of China","award":["cstc2021jcyj-msxmX1037"],"award-info":[{"award-number":["cstc2021jcyj-msxmX1037"]}]},{"name":"Chongqing Natural Science Foundation of China","award":["cstc2020jcyj-msxmX0881"],"award-info":[{"award-number":["cstc2020jcyj-msxmX0881"]}]},{"name":"Chongqing Natural Science Foundation of China","award":["cstc2019jsyj-yzysbAX0021"],"award-info":[{"award-number":["cstc2019jsyj-yzysbAX0021"]}]},{"name":"Chongqing Natural Science Foundation of China","award":["H20220678"],"award-info":[{"award-number":["H20220678"]}]},{"name":"Chongqing Science and Technology Project","award":["cstc2021jcyj-msxmX1037"],"award-info":[{"award-number":["cstc2021jcyj-msxmX1037"]}]},{"name":"Chongqing Science and Technology Project","award":["cstc2020jcyj-msxmX0881"],"award-info":[{"award-number":["cstc2020jcyj-msxmX0881"]}]},{"name":"Chongqing Science and Technology Project","award":["cstc2019jsyj-yzysbAX0021"],"award-info":[{"award-number":["cstc2019jsyj-yzysbAX0021"]}]},{"name":"Chongqing Science and Technology Project","award":["H20220678"],"award-info":[{"award-number":["H20220678"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Tunnel magnetoresistance (TMR) can measure weak magnetic fields and has significant advantages for use in alternating current\/direct current (AC\/DC ) leakage current sensors for power equipment; however, TMR current sensors are easily perturbed by external magnetic fields, and their measurement accuracy and measurement stability are limited in complex engineering application environments. To enhance the TMR sensor measurement performance, this paper proposes a new multi-stage TMR weak AC\/DC sensor structure with high measurement sensitivity and anti-magnetic interference capability. The front-end magnetic measurement characteristics and interference immunity of the multi-stage TMR sensor are found to be closely related to the multi-stage ring size design via finite element simulation. The optimal size of the multipole magnetic ring is determined using an improved non-dominated ranking genetic algorithm (ACGWO-BP-NSGA-II) to derive the optimal sensor structure. Experimental results demonstrate that the newly designed multi-stage TMR current sensor has a measurement range of 60 mA, a fitting nonlinearity error of less than 1%, a measurement bandwidth of 0\u201380 kHz, a minimum AC measurement value of 85 \u03bcA and a minimum DC measurement value of 50 \u03bcA, as well as a strong external electromagnetic interference. The TMR sensor can effectively enhance measurement precision and stability in the presence of intense external electromagnetic interference.<\/jats:p>","DOI":"10.3390\/s23104749","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T08:28:56Z","timestamp":1684139336000},"page":"4749","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Design and Optimization of Multi-Stage TMR Sensors for Power Equipment AC\/DC Leakage Current Detection"],"prefix":"10.3390","volume":"23","author":[{"given":"Xiaoxu","family":"Hu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security, Chongqing University, Chongqing 400044, China"}]},{"given":"Xuetao","family":"Duan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security, Chongqing University, Chongqing 400044, China"}]},{"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security, Chongqing University, Chongqing 400044, China"}]},{"given":"Yameng","family":"Fu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security, Chongqing University, Chongqing 400044, China"}]},{"given":"Yongfu","family":"Li","sequence":"additional","affiliation":[{"name":"State Grid Chongqing Electric Power Research Institute, Chongqing 401123, China"}]},{"given":"Pengcheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security, Chongqing University, Chongqing 400044, China"}]},{"given":"Xudong","family":"Deng","sequence":"additional","affiliation":[{"name":"State Grid Chongqing Electric Power Company Ultra High Voltage Branch, Chongqing 400039, China"}]},{"given":"Chuanxiang","family":"Yu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security, Chongqing University, Chongqing 400044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4771-9456","authenticated-orcid":false,"given":"Jingang","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security, Chongqing University, Chongqing 400044, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"78818","DOI":"10.1109\/ACCESS.2022.3191349","article-title":"A New Current Transducer for On-Line Monitoring of Leakage Current on HV Insulator Strings","volume":"10","author":"Villalobos","year":"2022","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ketjoy, N., Mensin, P., and Chamsa-Ard, W. (2022). Impacts on Insulation Resistance of Thin Film Modules: A Case Study of a Flooding of a Photovoltaic Power Plant in Thailand. PLoS ONE, 17.","DOI":"10.1371\/journal.pone.0274839"},{"key":"ref_3","first-page":"92514","article-title":"The Leakage Current Components as a Diagnostic Tool to Estimate Contamination Level on High Voltage Insulators","volume":"8","author":"Salem","year":"2020","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1109\/TEC.2018.2874101","article-title":"Mitigation of DC Current Injection in Transformer-Less Grid-Connected Inverters Using a Voltage Filtering DC Extraction Approach","volume":"34","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1109\/TIE.2016.2542126","article-title":"High-Precision Active Suppression of DC Bias in AC Grids by Grid-Connected Power Converters","volume":"64","author":"Vukosavic","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TPWRD.2014.2386257","article-title":"High-Precision Sensing of DC Bias in AC Grids","volume":"30","author":"Vukosavic","year":"2015","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1109\/JSEN.2009.2013914","article-title":"Current Sensing Techniques: A Review","volume":"9","author":"Ziegler","year":"2009","journal-title":"IEEE Sens. J."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yatchev, I., Sen, M., Balabozov, I., and Kostov, I. (2018). Modelling of a Hall Effect-Based Current Sensor with an Open Core Magnetic Concentrator. Sensors, 18.","DOI":"10.3390\/s18041260"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"45015","DOI":"10.1063\/5.0048167","article-title":"AC\/DC Dual-Mode Magnetoelectric Sensor with High Magnetic Field Resolution and Broad Operating Bandwidth","volume":"11","author":"Li","year":"2021","journal-title":"AIP Adv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10930","DOI":"10.1109\/TPEL.2020.2980680","article-title":"Tunnel Magnetoresistance-Based Short-Circuit and Over-Current Protection for IGBT Module","volume":"35","author":"Shao","year":"2020","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"64009","DOI":"10.1103\/PhysRevApplied.13.064009","article-title":"Anomalous Hall Sensors with High Sensitivity and Stability Based on Interlayer Exchange-Coupled Magnetic Thin Films","volume":"13","author":"Wang","year":"2020","journal-title":"Phys. Rev. Appl"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2271","DOI":"10.1109\/JSEN.2013.2251971","article-title":"A Fully Integrated Hall Sensor Microsystem for Contactless Current Measurement","volume":"13","author":"Ajbl","year":"2013","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1470","DOI":"10.1109\/TIM.2018.2795248","article-title":"A Broadband, On-Chip Sensor Based on Hall Effect for Current Measurements in Smart Power Circuits","volume":"67","author":"Crescentini","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"125702","DOI":"10.1088\/1361-6501\/aba011","article-title":"Development and Validation of a Device for in Vitro Uniaxial Cell Substrate Deformation with Real-Time Strain Control","volume":"31","author":"Apa","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1109\/TIM.2016.2644918","article-title":"Flexible Microwire Residence Times Difference Fluxgate Magnetometer","volume":"66","author":"Trigona","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Watanabe, Y., Otsubo, M., Yanai, T., Nakano, M., and Fukunaga, H. (2015). Temperature Characteristics of a Fluxgate Current Sensor with Fe-Ni-Co Ring Core, IEEE.","DOI":"10.1109\/INTMAG.2015.7156764"},{"key":"ref_17","first-page":"2104","article-title":"Wide range bidirectional saturation fluxgate current sensor","volume":"38","author":"Yang","year":"2018","journal-title":"Chin. J. Electr. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"18418","DOI":"10.1109\/JSEN.2022.3200359","article-title":"Analysis on the Zero Offset of a Microampere DC Current Sensor Using the Open-Loop Magnetic Modulator and the Suppression","volume":"22","author":"Li","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"82001","DOI":"10.1088\/0957-0233\/24\/8\/082001","article-title":"Advanced Giant Magnetoresistance Technology for Measurement Applications","volume":"24","author":"Weiss","year":"2013","journal-title":"Meas. Sci. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1016\/j.sna.2007.10.016","article-title":"AMR Current Measurement Device","volume":"141","author":"Mlejnek","year":"2008","journal-title":"Sens. Actuator A-Phys."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Mu\u0219uroi, C., Oproiu, M., Volmer, M., and Firastrau, I. (2020). High Sensitivity Differential Giant Magnetoresistance (GMR) Based Sensor for Non-Contacting DC\/AC Current Measurement. Sensors, 20.","DOI":"10.3390\/s20010323"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Garcia Vidal, E., Ramirez Munoz, D., Ravelo Arias, S.I., Sanchez Moreno, J., Cardoso, S., Ferreira, R., and Freitas, P. (2017). Electronic Energy Meter Based on a Tunnel Magnetoresistive Effect (TMR) Current Sensor. Materials, 10.","DOI":"10.3390\/ma10101134"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1109\/LED.2019.2913506","article-title":"Linear Anisotropic Magnetoresistive Sensor Without Barber-Pole Electrodes","volume":"40","author":"Su","year":"2019","journal-title":"IEEE Electron Device Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2472","DOI":"10.1103\/PhysRevLett.61.2472","article-title":"Giant Magnetoresistance of (001)Fe\/(001) Cr Magnetic Superlattices","volume":"61","author":"Baibich","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"L231","DOI":"10.1016\/0304-8853(95)90001-2","article-title":"Giant Magnetic Tunneling Effect in Fe\/Al2o3\/Fe Junction","volume":"139","author":"Miyazaki","year":"1995","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"92502","DOI":"10.1063\/1.1871344","article-title":"230% Room-Temperature Magnetoresistance in CoFeB\u2215MgO\u2215CoFeB Magnetic Tunnel Junctions","volume":"86","author":"Djayaprawira","year":"2005","journal-title":"Appl. Phys. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"800130","DOI":"10.1109\/TMAG.2019.2896036","article-title":"Magnetoresistive Sensor Development Roadmap (Non-Recording Applications)","volume":"55","author":"Zheng","year":"2019","journal-title":"IEEE Trans. Magn."},{"key":"ref_28","first-page":"9500304","article-title":"Optimization Design of a Giant Magneto Resistive Effect Based Current Sensor with a Magnetic Shielding","volume":"24","author":"Yang","year":"2014","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1504109","DOI":"10.1109\/TIM.2021.3089775","article-title":"TMR Busbar Current Sensor with Good Frequency Characteristics","volume":"70","author":"Xu","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","first-page":"28","article-title":"Research on weak current measurement method based on giant magnetoresistive sensors","volume":"53","author":"Li","year":"2016","journal-title":"Electr. Meas. Instrum."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.egyr.2022.08.062","article-title":"Optimal Design and Implementation of Tunnelling Magnetoresistance Based Small Current Sensor with Temperature Compensation","volume":"8","author":"Lei","year":"2022","journal-title":"Energy Rep."},{"key":"ref_32","first-page":"2545","article-title":"Design and noise analysis of broadband tiny range current sensors based on tunneling magnetoresistance effect","volume":"46","author":"Hu","year":"2020","journal-title":"High Volt. Technol."},{"key":"ref_33","unstructured":"Song, J.K., Zhang, G.Q., Nie, Y., Wang, G.Z., Li, H.B., and Hou, Y.W. (2020, January 17\u201319). Design and Simulation of a magnetic balance weak current sensor based on TMR. Proceedings of the 2020 2nd International Conference on Electronic Engineering and Informatics, Lanzhou, China."},{"key":"ref_34","unstructured":"Zhou, L.Y. (2020). Research on Current Sensing Technology Based on Tunneling Magnetoresistance Effect. [Master\u2019s Thesis, Chongqing University]."},{"key":"ref_35","first-page":"108","article-title":"Open-loop fluxgate current sensor polycyclic design","volume":"40","author":"Yang","year":"2021","journal-title":"Sens. Microsyst."},{"key":"ref_36","first-page":"49","article-title":"Analysis of the factors affecting electromagnetic interference in substations and anti-interference measures","volume":"34","author":"Wang","year":"2015","journal-title":"Hebei Electr. Power Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey Wolf Optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.engappai.2017.10.024","article-title":"An Exploration-Enhanced Grey Wolf Optimizer to Solve High-Dimensional Numerical Optimization","volume":"68","author":"Long","year":"2018","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Mu\u0219uroi, C., Oproiu, M., Volmer, M., Neamtu, J., Avram, M., and Helerea, E. (2021). Low Field Optimization of a Non-Contacting High-Sensitivity GMR-Based DC\/AC Current Sensor. Sensors, 21.","DOI":"10.3390\/s21072564"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/10\/4749\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:34:48Z","timestamp":1760124888000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/10\/4749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,14]]},"references-count":40,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["s23104749"],"URL":"https:\/\/doi.org\/10.3390\/s23104749","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,14]]}}}