{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T00:31:22Z","timestamp":1773707482604,"version":"3.50.1"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,6,30]]},"abstract":"<jats:p> In this study, a chaos-theoretic method is proposed to model the case of ferroresonance that can occur under nominal conditions in power systems, and the factors that determine the types of ferroresonance to occur are examined. In the ferroresonance chaotic system modeled in Matlab environment, the length of the transmission line and the breaker capacities in the circuit are fixed and its relationship with the transformer efficiency is investigated. In the proposed chaotic modeling, considering the situations that may occur in practical applications, the ferroresonance situations that occur when the single-phase remains open in the three-phase system are examined. In the study, ferroresonance, which occurs when one phase is open in a three-phase system, is analyzed by considering the situations that may happen during practical implementations. The similarity between the mathematical expressions obtained from the systems that create ferroresonance and Duffing oscillator is evaluated. In the chaotic system, fundamental ferroresonance, subharmonic ferroresonance, and chaotic ferroresonance situations are created depending on the transformer loss. Additionally, ferroresonance that occurs when the chaotic system is of fractional-order is analyzed, and it is observed that results of ferroresonance with different fractional-order values are not different. The results show that transformer loss is a significant element to determine the type of ferroresonance in power transformers. Also, when the chaotic system is operated in the fractional-order setting, the ferroresonance cases that occur are re-examined, and it is observed that the system can exit from the chaotic situation and prevent the formation of ferroresonance when fractional-order control is applied. According to the results, the fractional-order method can be used to control ferroresonance. <\/jats:p>","DOI":"10.1142\/s0218127421501182","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T08:18:33Z","timestamp":1624868313000},"page":"2150118","source":"Crossref","is-referenced-by-count":4,"title":["Chaotic Modeling of Ferroresonance with Single-Phase Open in a Three-Phase System and Its Fractional-Order Control"],"prefix":"10.1142","volume":"31","author":[{"given":"Ali\u0307","family":"Durdu","sequence":"first","affiliation":[{"name":"Department of Management Information Systems, Faculty of Political Sciences, Social Sciences University of Ankara, Ankara, Turkey"}]},{"given":"Yilmaz","family":"Uyaro\u011flu","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Engineering Faculty, Sakarya University, Sakarya, Turkey"}]}],"member":"219","published-online":{"date-parts":[[2021,6,26]]},"reference":[{"key":"S0218127421501182BIB001","volume-title":"Ferroresonance Phenomenon in Electrical Power Transformers","author":"Al-Bouthigy R. T.","year":"2012"},{"key":"S0218127421501182BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0217984919503573"},{"key":"S0218127421501182BIB003","doi-asserted-by":"publisher","DOI":"10.3390\/en12040639"},{"key":"S0218127421501182BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2018.10.011"},{"key":"S0218127421501182BIB005","doi-asserted-by":"publisher","DOI":"10.1049\/iet-rpg.2018.5242"},{"key":"S0218127421501182BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/ECCTD.2015.7300089"},{"key":"S0218127421501182BIB008","volume-title":"Circuit Analysis of A-C Power Systems Volume: Vol. I","author":"Clarke E.","year":"2016"},{"key":"S0218127421501182BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00202-017-0594-3"},{"key":"S0218127421501182BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2018.10.008"},{"key":"S0218127421501182BIB011","unstructured":"Dorcak, L.   [1994]  Numerical Models for the Simulation of the Fractional-Order Control Systems  (The Academy of Sciences Institute of Experimental Physics),  pp. 62\u201368."},{"key":"S0218127421501182BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.08.008"},{"key":"S0218127421501182BIB013","doi-asserted-by":"publisher","DOI":"10.1049\/iet-pel.2018.5390"},{"key":"S0218127421501182BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s00202-009-0117-y"},{"key":"S0218127421501182BIB015","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller K. S.","year":"1993"},{"key":"S0218127421501182BIB016","first-page":"55","volume":"14","author":"Negara I. M. Y.","year":"2009","journal-title":"Int. Rev. Electr. Eng."},{"key":"S0218127421501182BIB017","volume-title":"The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order","author":"Oldham K. B.","year":"2006"},{"key":"S0218127421501182BIB018","volume-title":"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation","author":"Petras I.","year":"2010"},{"key":"S0218127421501182BIB019","volume-title":"Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications","author":"Podlubny I.","year":"1999"},{"key":"S0218127421501182BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2019.07.013"},{"key":"S0218127421501182BIB021","first-page":"208","volume-title":"Proc. First IFAC Workshop on Fractional Differentiation and Applications","author":"Val\u00e9rio D.","year":"2004"},{"key":"S0218127421501182BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2003.08.001"},{"key":"S0218127421501182BIB023","first-page":"11368","volume-title":"36th Chinese Control Conf. (CCC)","author":"Wu C.","year":"2017"},{"key":"S0218127421501182BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2018.11.016"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127421501182","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T08:20:03Z","timestamp":1624868403000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127421501182"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,26]]},"references-count":23,"journal-issue":{"issue":"08","published-print":{"date-parts":[[2021,6,30]]}},"alternative-id":["10.1142\/S0218127421501182"],"URL":"https:\/\/doi.org\/10.1142\/s0218127421501182","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,26]]}}}