{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:13:55Z","timestamp":1787030035321,"version":"build-2736575974"},"reference-count":60,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T00:00:00Z","timestamp":1758585600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In many countries, most one-phase residential electricity consumers are supplied from three-phase, four-wire local networks operated in radial tree-like configurations. Uneven consumer placement on the wires of the three-phase circuit leads to unbalanced phase loads that break the voltage symmetry and increase the energy losses. One way to mitigate these problems is to balance the phase loads on the feeders by choosing the optimal phase of connection of the consumers. The authors proposed earlier a phase balancing algorithm based on metaheuristic optimization. For networks with a high number of supply nodes, this algorithm requires finding a solution for all the consumers simultaneously. Two alternative approaches are proposed in this paper that use the tree-like structure of the network to divide the optimization between a main distribution feeder and several branches, creating a multistage process, with the aim of minimizing energy losses. A case study is performed using a real low-voltage distribution network and a comparison is made between the three algorithms. The resulting losses have marginal variations between the proposed approaches, with a maximum of 1.3% difference.<\/jats:p>","DOI":"10.3390\/sym17101589","type":"journal-article","created":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T13:48:37Z","timestamp":1758635317000},"page":"1589","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Multistage Algorithm for Phase Load Balancing in Low-Voltage Electricity Distribution Networks Operated in Asymmetrical Conditions"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8336-1300","authenticated-orcid":false,"given":"Ovidiu","family":"Ivanov","sequence":"first","affiliation":[{"name":"Power Engineering Department, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1015-417X","authenticated-orcid":false,"given":"Florin-Constantin","family":"B\u0103iceanu","sequence":"additional","affiliation":[{"name":"Power Engineering Department, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ciprian-Mircea","family":"Neme\u0219","sequence":"additional","affiliation":[{"name":"Power Engineering Department, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3811-6298","authenticated-orcid":false,"given":"Gheorghe","family":"Grigora\u0219","sequence":"additional","affiliation":[{"name":"Power Engineering Department, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bianca-Elena","family":"\u021auchendria","sequence":"additional","affiliation":[{"name":"Power Engineering Department, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mihai","family":"Gavrila\u0219","sequence":"additional","affiliation":[{"name":"Power Engineering Department, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Das, S.R., Ray, P.K., Sahoo, A.K., Ramasubbareddy, S., Babu, T.S., Kumar, N.M., Elavarasan, R.M., and Mihet-Popa, L. 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