{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:31:14Z","timestamp":1760236274664,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,11,6]],"date-time":"2021-11-06T00:00:00Z","timestamp":1636156800000},"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>In this paper, a new method for characterizing the dielectric breakdown voltage of dielectric oils is presented, based on the IEC 60156 international standard. In this standard, the effective value of the dielectric breakdown voltage is obtained, but information is not provided on the distribution of Kelvin forces an instant before the dynamic behavior of the arc begins or the state of the gases that are produced an instant after the moment of appearance of the electric arc in the oil. In this paper, the behavior of the oil before and after the appearance of the electric arc is characterized by combining a low-cost CMOS imaging sensor and a new matrix of electrical permittivity associated with the dielectric oil, using the 3D cell method. In this way, we also predict the electric field before and after the electric rupture. The error compared to the finite element method is less than 0.36%. In addition, a new method is proposed to measure the kinematic viscosity of dielectric oils. Using a low-cost imaging sensor, the distribution of bubbles is measured, together with their diameters and their rates of ascent after the electric arc occurs. This method is verified using ASTM standards and data provided by the oil manufacturer. The results of these tests can be used to prevent incipient failures and evaluate preventive maintenance processes such as transformer oil replacement or recovery.<\/jats:p>","DOI":"10.3390\/s21217380","type":"journal-article","created":{"date-parts":[[2021,11,7]],"date-time":"2021-11-07T20:42:54Z","timestamp":1636317774000},"page":"7380","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Characterization of Dielectric Oil with a Low-Cost CMOS Imaging Sensor and a New Electric Permittivity Matrix Using the 3D Cell Method"],"prefix":"10.3390","volume":"21","author":[{"given":"Jos\u00e9 Miguel","family":"Monz\u00f3n-Verona","sequence":"first","affiliation":[{"name":"Electrical Engineering Department (DIE), University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"},{"name":"Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pablo Ignacio","family":"Gonz\u00e1lez-Dom\u00ednguez","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department (DIE), University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"},{"name":"Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4389-0632","authenticated-orcid":false,"given":"Santiago","family":"Garc\u00eda-Alonso","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering and Automatics (DIEA), University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8699-1583","authenticated-orcid":false,"given":"Jenifer","family":"Vaswani Reboso","sequence":"additional","affiliation":[{"name":"Process Engineering Department (DIP), University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s00202-017-0532-4","article-title":"A review of condition monitoring techniques and diagnostic tests for lifetime estimation of power transformers","volume":"100","author":"Islam","year":"2017","journal-title":"Electr. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1730001","DOI":"10.1142\/S2010135X17300018","article-title":"Electrical insulating liquid: A review","volume":"7","author":"Mahanta","year":"2017","journal-title":"J. Adv. Dielectr."},{"key":"ref_3","unstructured":"IEEE (2015). Guide for Acceptance and Maintenance of Insulating Mineral Oil in Electrical Equipment, IEEE."},{"key":"ref_4","unstructured":"CIGRE (2003). Life Management Techniques for Power Transformers, CIGRE."},{"key":"ref_5","unstructured":"Kuffel, E., Zaengl, W., and Kuffel, J. (2000). High Voltage Engineering Fundamentals, Elsevier."},{"key":"ref_6","first-page":"105","article-title":"The breakdown mechanisms in electrical discharges: The role of the field emission effect in direct current discharges in microgaps","volume":"63","author":"Radjenovic","year":"2014","journal-title":"Acta Phys. Slovaca"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"12601290","DOI":"10.1016\/j.jcp.2013.08.016","article-title":"Why starting from diferential equations for computational physics?","volume":"257","author":"Tonti","year":"2014","journal-title":"J. Comput. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tonti, E. (2013). The Mathematical Structure of Classical and Relativistic Physics, Birkh\u00e4user.","DOI":"10.1007\/978-1-4614-7422-7"},{"key":"ref_9","first-page":"237","article-title":"A Direct Discrete Formulation of Field Laws: The Cell Method","volume":"2","author":"Tonti","year":"2001","journal-title":"CMES Comput. Model. Eng. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"317","DOI":"10.2528\/PIER00080113","article-title":"Computational Aspects of the Cell Method in Electrodynamics","volume":"32","author":"Marrone","year":"2001","journal-title":"Prog. Electromagn. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1894","DOI":"10.1016\/j.jcp.2007.02.032","article-title":"Constitutive equations for discrete electromagnetic problems over polyhedral grids","volume":"225","author":"Codecasa","year":"2007","journal-title":"J. Comput. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1109\/TMAG.2004.825418","article-title":"Isotropic and Anisotropic Electrostatic Field Computation by Means of the Cell Method","volume":"40","author":"Bullo","year":"2004","journal-title":"IEEE Trans. Magn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1109\/TMAG.2003.810194","article-title":"Electrostatic analysis for plane problems with finite formulation","volume":"39","author":"Bettini","year":"2003","journal-title":"IEEE Trans. Magn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1109\/TMAG.2009.2012538","article-title":"Electroquasistatic Analysis of the Gas Insulated Line for the ITER Neutral Beam Injector","volume":"45","author":"Bettini","year":"2009","journal-title":"IEEE Trans. Magn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"9102","DOI":"10.3390\/s101009102","article-title":"Electro-quasistatic analysis of an electro-static induction micromotor using the cell method","volume":"10","year":"2010","journal-title":"Sensors"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1109\/TMAG.2005.844841","article-title":"Discrete constitutive equations in A-\u03c7 geometric eddy-current formulation","volume":"41","author":"Specogna","year":"2005","journal-title":"IEEE Trans. Magn."},{"key":"ref_17","unstructured":"(2021, September 23). IEC 60156 Insulating Liquids Determination of the Breakdown Voltage at Power Frequency. Test Method. Available online: https:\/\/webstore.iec.ch\/publication\/28297IEC."},{"key":"ref_18","unstructured":"Haus, H.A., and Melcher, J.R. (1989). Electromagnetic Fields and Energy, Prentice-Hall. Available online: https:\/\/ocw.mit.edu\/resources\/res-6-001-electromagnetic-fields-and-energy-spring-2008\/chapter-3\/03.pdf."},{"key":"ref_19","first-page":"269","article-title":"Rising velocity for single bubbles in Pure Liquids","volume":"11","author":"Soria","year":"2012","journal-title":"Rev. Mex. Ing. Qu\u00edm."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"013014","DOI":"10.1117\/1.JEI.26.1.013014","article-title":"Laying the foundation to use Raspberry Pi 3 V2 camera module imagery for scientific and engineering purposes","volume":"26","author":"Pagnutti","year":"2017","journal-title":"J. Electron. Imaging"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Riba, J.-R., G\u00f3mez-Pau, \u00c1., and Moreno-Eguilaz, M. (2020). Experimental Study of Visual Corona under Aeronautic Pressure Conditions Using Low-Cost Imaging Sensors. Sensors, 20.","DOI":"10.3390\/s20020411"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e12348","DOI":"10.1111\/str.12348","article-title":"Low-cost digital image correlation and strain measurement for geotechnical applications","volume":"56","author":"Eichhorn","year":"2020","journal-title":"Strain"},{"key":"ref_23","unstructured":"(2021, September 23). Book: Electromagnetics and Applications (Staelin). Available online: https:\/\/phys.libretexts.org\/Bookshelves\/Electricity_and_Magnetism\/Book%3A_Electromagnetics_and_Applications_(Staelin)."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"54510","DOI":"10.1063\/1.3309027","article-title":"Modeling the Kelvin polarization force actuation of micro- and nanomechanical systems","volume":"107","author":"Schmid","year":"2010","journal-title":"J. Appl. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1109\/TDEI.2014.6832249","article-title":"A study on electric conduction of transformer oil","volume":"21","author":"Sha","year":"2014","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1109\/TDEI.2014.004332","article-title":"The resistivity of oil and oil-impregnated pressboard varies with temperature and electric field strength","volume":"21","author":"Li","year":"2014","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s00202-016-0501-3","article-title":"Analyses of the insulating characteristics of mineral oil at operating conditions","volume":"100","author":"Taslak","year":"2017","journal-title":"Electr. Eng."},{"key":"ref_28","unstructured":"Woodson, H.H., and Melcher, J.R. (1968). Electromechanical Dynamics, John Wiley and Sons, Inc.. Reprint Krieger Publishing Company: Malabar, FL, USA, 1990, 1985, ISBN 9780894644597 (v.1), 9780898748475 (v. 2), 9780898748482 (v. 3).18."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4869","DOI":"10.1080\/01431161.2018.1466085","article-title":"Radiometric and spectral comparison of inexpensive camera systems used for remote sensing","volume":"39","author":"Craig","year":"2018","journal-title":"Int. J. Remote Sens."},{"key":"ref_30","unstructured":"(2021, September 23). Home\u2014OpenCV. Available online: https:\/\/opencv.org."},{"key":"ref_31","unstructured":"(2021, September 23). NumPy. Available online: https:\/\/numpy.org\/."},{"key":"ref_32","unstructured":"(2021, September 23). Picamara. Available online: https:\/\/picamera.readthedocs.io\/en\/release-1.13\/."},{"key":"ref_33","unstructured":"(2021, September 23). Portable, Extensible Toolkit for Scientic Computation, Available online: http:\/\/www.mcs.anl.gov\/petsc."},{"key":"ref_34","unstructured":"Dular, P., and Geuzaine, C. (2021, September 23). GetDP Reference Manual: The Documentation for GetDP, a General Environment for the Treatment of Discrete Problems. Available online: http:\/\/getdp.info."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"13091331","DOI":"10.1002\/nme.2579","article-title":"Gmsh: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities","volume":"79","author":"Geuzaine","year":"2009","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_36","first-page":"317","article-title":"Errores frecuentes en la interpretaci\u00f3n del coeficiente de determinaci\u00f3n lineal","volume":"38","year":"2005","journal-title":"Anu. Jurid. Econ. Escur."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.ijforecast.2006.03.001","article-title":"Another look at measures of forecast accuracy","volume":"22","author":"Hyndman","year":"2006","journal-title":"Int. J. Forecast."},{"key":"ref_38","unstructured":"Sanabria, J., Garc\u00eda, J., and Lhomme, J.P. (2006). Calibraci\u00f3n y Validaci\u00f3n de Modelos de Pron\u00f3stico de Heladas en el Valle del Mantaro. [Master\u2019s Thesis, Universidad Nacional Agraria La Molina]."},{"key":"ref_39","unstructured":"ASTM D445 (2019). Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and Calculation of Dynamic Viscosity), ASTM. ASTM Volume 05.01 Petroleum Products, Liquid Fuels, and Lubricants (II): C1234\u2014D4176."},{"key":"ref_40","unstructured":"ASTM (2018). ASTM D4052. Standard Test Method for Density, Relative Density, and API Gravity of Liquids by Digital Density Meter, ASTM. ASTM Volume 05.01 Petroleum Products, Liquid Fuels, and Lubricants (II): C1234\u2014D4176."},{"key":"ref_41","unstructured":"ASTM (2018). ASTM D92. Standard Test Method for Flash and Fire Points by Cleveland Open Cup Tester, ASTM. ASTM Volume 05.01 Petroleum Products, Liquid Fuels, and Lubricants (II): C1234\u2014D4176."},{"key":"ref_42","unstructured":"ASTM (2020). ASTM D1533: Standard Test Method for Water in Insulating Liquids by Coulometric Karl Fischer Titration, ASTM. ASTM Volume 10.03 Electrical Insulating Liquids and Gases; Electrical Protective Equipment."},{"key":"ref_43","unstructured":"ASTM (2017). ASTM D1500\u201412 Standard Test Method for ASTM Color of Petroleum Products (ASTM Color Scale), ASTM. ASTM Volume 05.01 Petroleum Products, Liquid Fuels, and Lubricants (II): C1234\u2014D4176."},{"key":"ref_44","unstructured":"Norma UNE 60296:2012 (2012). Fluidos para Aplicaciones Electrot\u00e9cnicas. Aceites Minerales Aislantes Nuevos para Transformadores y Aparamenta de Conexi\u00f3n, AENOR."},{"key":"ref_45","unstructured":"(2021, September 23). ImajeJ. Available online: https:\/\/imagej.net\/Welcome."},{"key":"ref_46","unstructured":"(2021, September 23). Aceites Diel\u00e9ctricos. Available online: https:\/\/www.repsol.com\/imagenes\/global\/es\/af-catalogo-aceites-dielectricos_tcm13-48939.pdf."},{"key":"ref_47","first-page":"27","article-title":"A new viscosity-temperature relationship for mineral oil SAE 10W","volume":"23","author":"Stanciu","year":"2012","journal-title":"Analele Univ. Ovidius Constanta Ser. Chim."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/21\/7380\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:26:46Z","timestamp":1760167606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/21\/7380"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,6]]},"references-count":47,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21217380"],"URL":"https:\/\/doi.org\/10.3390\/s21217380","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,11,6]]}}}