{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T05:24:30Z","timestamp":1765344270388,"version":"3.46.0"},"reference-count":28,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T00:00:00Z","timestamp":1765152000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"publisher","award":["142000\/2019-01"],"award-info":[{"award-number":["142000\/2019-01"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Brazilian Coordination for the Improvement of Higher Education Personnel","award":["001"],"award-info":[{"award-number":["001"]}]},{"name":"INESC P&amp;D Brasil","award":["-"],"award-info":[{"award-number":["-"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>Reliability evaluation of power distribution systems is computationally intensive, as standard Monte Carlo simulations require extensive sampling to accurately estimate rare event-based indices like SAIDI and SAIFI. This paper introduces a multi-objective cross-entropy approach for reliability evaluation of power distribution systems, aiming to accelerate reliability evaluation by optimizing importance sampling reference parameters. The multi-objective approach aims to optimize a set of objective functions related to systemic and load point reliability indices. A deduction of an analytical solution for the optimization of reference parameters of the cross-entropy method is developed, taking into account the standard hypotheses used in reliability assessments. The proposed method has been validated on a real 181-node Brazilian distribution feeder. Results show that the proposed approach can accelerate the convergence of estimates for reliability indices in comparison with the crude Monte Carlo approach and the single-objective CE method.<\/jats:p>","DOI":"10.3390\/en18246421","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T15:30:07Z","timestamp":1765207807000},"page":"6421","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Objective Cross-Entropy Approach for Distribution System Reliability Evaluation"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4933-3562","authenticated-orcid":false,"given":"Lucas Fritzen","family":"Venturini","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, SC, Brazil"},{"name":"Institute for Systems and Computer Engineering, Research & Development of Brazil\u2014INESC P&D Brasil, Santos 11055-300, SP, Brazil"},{"name":"CELESC Distribui\u00e7\u00e3o S.A., Florian\u00f3polis 88034-900, SC, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6939-7935","authenticated-orcid":false,"given":"Beatriz Silveira","family":"Buss","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, SC, Brazil"},{"name":"Institute for Systems and Computer Engineering, Research & Development of Brazil\u2014INESC P&D Brasil, Santos 11055-300, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5211-8885","authenticated-orcid":false,"given":"Erika","family":"Pequeno dos Santos","sequence":"additional","affiliation":[{"name":"National Service for Industrial Training\u2014SENAI\/SC, Florian\u00f3polis 88034-001, SC, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9097-3679","authenticated-orcid":false,"given":"Leonel Magalh\u00e3es","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Centro Universit\u00e1rio do Porto, Universidade Lus\u00f3fona, 4000-098 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7937-8115","authenticated-orcid":false,"given":"Diego","family":"Issicaba","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, SC, Brazil"},{"name":"Institute for Systems and Computer Engineering, Research & Development of Brazil\u2014INESC P&D Brasil, Santos 11055-300, SP, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rubinstein, R.Y., and Kroese, D.P. 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