{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:12:30Z","timestamp":1766067150632,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,4,29]],"date-time":"2020-04-29T00:00:00Z","timestamp":1588118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020","award":["691714"],"award-info":[{"award-number":["691714"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper describes a simplified model and a generic model of high-frequency current transformer (HFCT) sensors. By analyzing the models, a universal charge estimation method based on the double time integral of the measured voltage is inferred. The method is demonstrated to be valid irrespective of HFCT sensor, assuming that its transfer function can be modelled as a combination of real zeros and poles. This paper describes the mathematical foundation of the method and its particularities when applied to measure nanosecond current pulses. In practice, the applicability of the method is subjected to the characteristics and frequency response of the sensor and the current pulse duration. Therefore, a proposal to use the double time integral or the simple time integral of the measured voltage is described depending upon the sensor response. The procedures used to obtain the respective calibration constants based on the frequency response of the HFCT sensors are explained. Two examples, one using a HFCT sensor with a broadband flat frequency response and another using a HFCT sensor with a non-flat frequency response, are presented.<\/jats:p>","DOI":"10.3390\/s20092520","type":"journal-article","created":{"date-parts":[[2020,4,29]],"date-time":"2020-04-29T13:23:45Z","timestamp":1588166625000},"page":"2520","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Principles of Charge Estimation Methods Using High-Frequency Current Transformer Sensors in Partial Discharge Measurements"],"prefix":"10.3390","volume":"20","author":[{"given":"Armando","family":"Rodrigo-Mor","sequence":"first","affiliation":[{"name":"Electrical Sustainable Energy Department, Delft University of Technology, 2628 CD Delft, The Netherlands"}]},{"given":"Fabio A.","family":"Mu\u00f1oz","sequence":"additional","affiliation":[{"name":"Electrical Sustainable Energy Department, Delft University of Technology, 2628 CD Delft, The Netherlands"}]},{"given":"Luis Carlos","family":"Castro-Heredia","sequence":"additional","affiliation":[{"name":"Electrical Sustainable Energy Department, Delft University of Technology, 2628 CD Delft, The Netherlands"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,29]]},"reference":[{"key":"ref_1","unstructured":"IEC 60270, I (2001). Partial Discharge Measurements, International Electrotechnical Commission. [3rd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1109\/TDEI.2015.7076760","article-title":"Comparison of charge estimation methods in partial discharge cable measurements","volume":"22","author":"Mor","year":"2015","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"ref_3","unstructured":"Lim, Kw., Lwin, Ky., Shin, Do., Park, No., Park, Da., Hwang, Do., and Lim, Jo. (2008, January 21\u201324). A study on the measurement of partial discharges in XLPE power cables using planer loop sensors. Proceedings of the 2008 International Conference on Condition Monitoring and Diagnosis, Beijing, China."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7360","DOI":"10.3390\/s150407360","article-title":"Application of HFCT and UHF Sensors in On-Line Partial Discharge Measurements for Insulation Diagnosis of High Voltage Equipment","volume":"15","author":"Garnacho","year":"2015","journal-title":"Sensors"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Robles, G., Martinez, J.M., Sanz, J., Tellini, B., Zappacosta, C., and Rojas, M. (2008, January 12\u201315). Designing and tuning an air-cored current transformer for partial discharges pulses measurements. Proceedings of the 2008 IEEE Instrumentation and Measurement Technology Conference, Victoria, BC, Canada.","DOI":"10.1109\/IMTC.2008.4547380"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Robles, G., Argueso, M., Sanz, J., Giannetti, R., and Tellini, B. (2007, January 1\u20133). Identification of parameters in a Rogowski coil used for the measurement of partial discharges. Proceedings of the 2007 IEEE Instrumentation & Measurement Technology Conference IMTC 2007, Warsaw, Poland.","DOI":"10.1109\/IMTC.2007.379175"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1109\/TPWRD.2019.2910076","article-title":"Modeling of High-Frequency Current Transformer Based Partial Discharge Detection in High-Voltage Cables","volume":"34","author":"Hu","year":"2019","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/MEI.2016.7656806","article-title":"Special requirements of high frequency current transformers in the on-line detection of partial discharges in power cables","volume":"32","author":"Xu","year":"2016","journal-title":"IEEE Electr. Insul. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ardila-Rey, J., Barrueto, A., Zerene, A., Castro, B., Ulson, J., Mas\u2019ud, A., and Valdivia, P. (2018). Behavior of an Inductive Loop Sensor in the Measurement of Partial Discharge Pulses with Variations in Its Separation from the Primary Conductor. Sensors, 18.","DOI":"10.3390\/s18072324"},{"key":"ref_10","unstructured":"Mor, A.R., Castro-Heredia, L.C., and Mu\u00f1oz, F.A. (2018). A Novel Approach for Partial Discharge Measurements on GIS using HFCT Sensors. Sensors."},{"key":"ref_11","unstructured":"Smith, J.O., and Smith, H.F. (2016). Closed Form Fractional Integration and Differentiation via Real Exponentially Spaced Pole-Zero Pairs. arXiv."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1109\/JSEN.2012.2227712","article-title":"Parameters Identification and Modeling of High-Frequency Current Transducer for Partial Discharge Measurements","volume":"13","author":"Shafiq","year":"2013","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Rodrigo-Mor, A., Mu\u00f1oz, F., and Castro-Heredia, L. (2019). A Novel Antenna for Partial Discharge Measurements in GIS Based on Magnetic Field Detection. Sensors, 19.","DOI":"10.3390\/s19040858"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"105514","DOI":"10.1016\/j.ijepes.2019.105514","article-title":"A magnetic loop antenna for partial discharge measurements on GIS","volume":"115","year":"2020","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1109\/TDEI.2017.006381","article-title":"Estimation of charge, energy and polarity of noisy partial discharge pulses","volume":"24","year":"2017","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1109\/TDEI.2017.006115","article-title":"Transfer function characterization for HFCTs used in partial discharge detection","volume":"24","author":"Hu","year":"2017","journal-title":"IEEE Trans. Dielectr. Electr. Insul."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/20\/9\/2520\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:32:16Z","timestamp":1760362336000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/20\/9\/2520"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,29]]},"references-count":16,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,5]]}},"alternative-id":["s20092520"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/s20092520","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,4,29]]}}}