{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:47:55Z","timestamp":1754156875340,"version":"3.41.2"},"reference-count":35,"publisher":"Emerald","issue":"6","license":[{"start":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T00:00:00Z","timestamp":1674604800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["COMPEL"],"published-print":{"date-parts":[[2023,11,23]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>This paper aims to overcome the lack of methodologies for optimizing the volume of bulky low-frequency inductors that the authors came across with when working on the design of hybrid active power filters. Sound work was published concerning this well-known technology, but it became evident that the mentioned optimization topic was left unaddressed.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>Using the Lagrange multipliers optimization method combined with the electromagnetic laws of inductor design, it was possible to establish a new design method to determine the optimal solutions that fulfil any given scenario of specifications. In other words, it is now possible to obtain the inductor\u2019s geometric and electric parameters that not only satisfy the system\u2019s electromagnetic requirements but also lead to smaller, lighter or economical solutions.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>A generalized set of equations was obtained to facilitate the calculations of all the inductor-building parameters. As expected, these equations take as inputs the inductor\u2019s required inductance, its maximum current and the desired resistance, but also a customizable cost function. The later cost function will optimize the inductor\u2019s volumes of copper and iron and can be settled, among other purposes, for minimizing the total weight, volume or cost.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>All the mathematical expressions to obtain the general optimal solutions are given as well as practical graphics for the three above-mentioned optimization criteria. Using these charts, the reader will be able to obtain by simple inspection the optimal solutions for a large, generalized universe of intended specifications.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/compel-09-2022-0304","type":"journal-article","created":{"date-parts":[[2023,1,24]],"date-time":"2023-01-24T07:08:19Z","timestamp":1674544099000},"page":"1382-1395","source":"Crossref","is-referenced-by-count":0,"title":["Lagrange multiplier optimization method for high current\u2013low frequency inductor design"],"prefix":"10.1108","volume":"42","author":[{"given":"Hugo dos Santos","family":"Marques","sequence":"first","affiliation":[]},{"given":"Maria Beatriz","family":"Borges","sequence":"additional","affiliation":[]}],"member":"140","published-online":{"date-parts":[[2023,1,25]]},"reference":[{"key":"key2023112206500298900_ref001","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/PEDS.2003.1282661","article-title":"Trends in power electronics and motor drives","year":"2003"},{"issue":"1","key":"key2023112206500298900_ref002","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1109\/TIE.2011.2141099","article-title":"Optimal C-type passive filter based on minimization of the voltage harmonic distortion for nonlinear loads","volume":"59","year":"2011","journal-title":"IEEE Transactions on Industrial Electronics"},{"issue":"1","key":"key2023112206500298900_ref003","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1108\/03321640810836609","article-title":"Comparison between torque calculation methods in a non\u2010conforming movement interface","volume":"27","year":"2008","journal-title":"COMPEL \u2013 The International Journal for Computation and Mathematics in Electrical and Electronic Engineering"},{"issue":"11","key":"key2023112206500298900_ref004","doi-asserted-by":"publisher","first-page":"4007","DOI":"10.1109\/TIE.2011.2173893","article-title":"Parallel-connected shunt hybrid active power filters operating at different switching frequencies for improved performance","volume":"59","year":"2011","journal-title":"IEEE Transactions on Industrial Electronics"},{"issue":"4","key":"key2023112206500298900_ref005","doi-asserted-by":"publisher","first-page":"606","DOI":"10.1016\/j.epsr.2008.08.014","article-title":"An efficient procedure to design passive LCL-filters for active power filters","volume":"79","year":"2009","journal-title":"Electric Power Systems Research"},{"issue":"4","key":"key2023112206500298900_ref006","doi-asserted-by":"publisher","first-page":"1677","DOI":"10.1108\/EC-04-2020-0183","article-title":"A comparative analysis of Lagrange multiplier and penalty approaches for modelling fluid-structure interaction","volume":"38","year":"2021","journal-title":"Engineering Computations"},{"issue":"1","key":"key2023112206500298900_ref007","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1109\/TIE.2002.807664","article-title":"Passive filter design using genetic algorithms","volume":"50","year":"2003","journal-title":"IEEE Transactions on Industrial Electronics"},{"key":"key2023112206500298900_ref008","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1109\/PESC.2004.1355564","article-title":"The application and optimization of C-type filter in a combined harmonic power filter","year":"2004"},{"issue":"2","key":"key2023112206500298900_ref009","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1109\/TAES.2003.1207259","article-title":"Design and evaluation of a hybrid passive\/active ripple filter with voltage injection","volume":"39","year":"2003","journal-title":"IEEE Transactions on Aerospace and Electronic Systems"},{"issue":"1","key":"key2023112206500298900_ref010","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1109\/TIA.2003.821666","article-title":"Passive filters-potentialities and limitations","volume":"40","year":"2004","journal-title":"IEEE Transactions on Industry Applications"},{"first-page":"416","article-title":"A new downsized large current choke coil with magnet bias method","year":"2003","key":"key2023112206500298900_ref011"},{"key":"key2023112206500298900_ref012","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1109\/PESC.1995.474813","article-title":"A new single-phase active power filter with reduced energy storage capacitor","year":"1995"},{"key":"key2023112206500298900_ref035","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1109\/APEC.2008.4522832","article-title":"A 10KV shunt hybrid active filter for a power distribution system","year":"2008"},{"issue":"7","key":"key2023112206500298900_ref013","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1016\/j.ijepes.2006.02.008","article-title":"A hybrid compensation system comprising hybrid power filter and AC power capacitor","volume":"28","year":"2006","journal-title":"International Journal of Electrical Power and Energy Systems"},{"issue":"12","key":"key2023112206500298900_ref014","doi-asserted-by":"publisher","first-page":"5376","DOI":"10.1109\/TIE.2012.2235394","article-title":"A noniterative optimized algorithm for shunt active power filter under distorted and unbalanced supply voltages","volume":"60","year":"2012","journal-title":"IEEE Transactions on Industrial Electronics"},{"key":"key2023112206500298900_ref015","doi-asserted-by":"publisher","first-page":"1636","DOI":"10.1109\/07IAS.2007.252","article-title":"New control strategy for hybrid power filters using sinusoidal signal integrators for current reference generation","year":"2007"},{"issue":"4","key":"key2023112206500298900_ref016","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1049\/ip-epa:20000438","article-title":"Development of a single-phase half-bridge active power filter with the function of uninterruptible power supplies","volume":"147","year":"2000","journal-title":"IEE Proceedings \u2013 Electric Power Applications"},{"key":"key2023112206500298900_ref017","doi-asserted-by":"publisher","first-page":"1760","DOI":"10.1109\/PESC.2007.4342266","article-title":"Design algorithm for high-current gapped foil-wound inductors in low-to-medium frequency dc-dc converters","year":"2007"},{"key":"key2023112206500298900_ref018","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1109\/APEX.2007.357497","article-title":"Magnetic material comparisons for high-current inductors in low-medium frequency dc-dc converters","year":"2007"},{"issue":"1","key":"key2023112206500298900_ref019","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.ijepes.2009.06.008","article-title":"Power grid current harmonics mitigation drawn on low voltage rated switching devices with effortless control","volume":"32","year":"2010","journal-title":"International Journal of Electrical Power and Energy Systems"},{"issue":"7","key":"key2023112206500298900_ref020","doi-asserted-by":"publisher","first-page":"3114","DOI":"10.1109\/TPEL.2012.2225641","article-title":"Optimal design of LCL harmonic filters for three-phase PFC rectifiers","volume":"28","year":"2012","journal-title":"IEEE Transactions on Power Electronics"},{"article-title":"Optimized size design of integrated magnetic components using area product approach","year":"2005","key":"key2023112206500298900_ref021","doi-asserted-by":"publisher","DOI":"10.1109\/EPE.2005.219605"},{"key":"key2023112206500298900_ref022","doi-asserted-by":"publisher","first-page":"1151","DOI":"10.1109\/PESC.1988.18256","article-title":"A novel harmonic power filter","year":"1988"},{"issue":"6","key":"key2023112206500298900_ref023","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1002\/eej.4391100509","article-title":"A new approach to harmonic compensation in power system \u2013 a combined system of series active and shunt passive filters","volume":"26","year":"1990","journal-title":"IEEE Transactions on Industry Applications"},{"key":"key2023112206500298900_ref024","doi-asserted-by":"publisher","first-page":"3955","DOI":"10.1109\/ECCE.2010.5617796","article-title":"Four-branch star neutral current hybrid power filter and var compensator","year":"2010"},{"key":"key2023112206500298900_ref025","doi-asserted-by":"publisher","first-page":"1249","DOI":"10.1109\/EPEPEMC.2008.4635440","article-title":"Magnetic material comparisons for high-current gapped and gapless foil wound inductors in high frequency dc-dc converters","year":"2008"},{"issue":"4","key":"key2023112206500298900_ref026","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1016\/j.ijepes.2006.07.010","article-title":"An improved hybrid filter for compensation of current and voltage harmonics for varying rectifier loads","volume":"29","year":"2007","journal-title":"International Journal of Electrical Power and Energy Systems"},{"issue":"5","key":"key2023112206500298900_ref027","doi-asserted-by":"publisher","first-page":"960","DOI":"10.1109\/41.793345","article-title":"A review of active filters for power quality improvement","volume":"46","year":"1999","journal-title":"IEEE Transactions on Industrial Electronics"},{"issue":"3","key":"key2023112206500298900_ref028","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1049\/ip-gtd:20045027","article-title":"Hybrid filters for power quality improvement","volume":"152","year":"2005","journal-title":"IEE Proceedings \u2013 Generation, Transmission and Distribution"},{"issue":"5","key":"key2023112206500298900_ref029","doi-asserted-by":"publisher","first-page":"1919","DOI":"10.1109\/TIE.2012.2209611","article-title":"The new high-efficiency hybrid neutral-point-clamped converter","volume":"60","year":"2012","journal-title":"IEEE Transactions on Industrial Electronics"},{"key":"key2023112206500298900_ref030","doi-asserted-by":"publisher","first-page":"1816","DOI":"10.1109\/07IAS.2007.277","article-title":"Optimization of the main inductor in a LCL filter for three phase active rectifier","year":"2007"},{"issue":"3","key":"key2023112206500298900_ref031","doi-asserted-by":"publisher","first-page":"1033","DOI":"10.1109\/TIE.2012.2189543","article-title":"Analytical optimization of solid\u2013round-wire windings","volume":"60","year":"2012","journal-title":"IEEE Transactions on Industrial Electronics"},{"key":"key2023112206500298900_ref032","doi-asserted-by":"publisher","first-page":"3171","DOI":"10.1109\/PESC.2008.4592441","article-title":"Design of a high-temperature pre-biased line choke for power electronics applications","year":"2008"},{"key":"key2023112206500298900_ref033","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1002\/net.3230150112","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","year":"1985"},{"issue":"3","key":"key2023112206500298900_ref034","doi-asserted-by":"publisher","first-page":"1228","DOI":"10.1109\/TPEL.2011.2162748","article-title":"An integrated AC choke design for common-mode current suppression in neutral-connected power converter systems","volume":"27","year":"2011","journal-title":"IEEE Transactions on Power Electronics"}],"container-title":["COMPEL - The international journal for computation and mathematics in electrical and electronic engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/COMPEL-09-2022-0304\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/COMPEL-09-2022-0304\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T23:15:32Z","timestamp":1753398932000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/compel\/article\/42\/6\/1382-1395\/113724"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,25]]},"references-count":35,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,1,25]]},"published-print":{"date-parts":[[2023,11,23]]}},"alternative-id":["10.1108\/COMPEL-09-2022-0304"],"URL":"https:\/\/doi.org\/10.1108\/compel-09-2022-0304","relation":{},"ISSN":["0332-1649","0332-1649"],"issn-type":[{"type":"print","value":"0332-1649"},{"type":"electronic","value":"0332-1649"}],"subject":[],"published":{"date-parts":[[2023,1,25]]}}}