{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T16:39:33Z","timestamp":1780591173731,"version":"3.54.1"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,26]],"date-time":"2019-01-26T00:00:00Z","timestamp":1548460800000},"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 power engineering, the     Y  b u s      is a symmetric     N \u00d7 N     square matrix describing a power system network with N buses. By partitioning, manipulating and using its symmetry properties, it is possible to derive the     K  G L      and     Y  G G M      matrices, which are useful to define a loss minimisation dispatch for generators. This article focuses on the case of constant-current loads and studies the theoretical framework of a second order optimization method for analytic loss minimization by taking into account the symmetry properties of     Y  b u s     . We define an appropriate matrix functional of several variables with complex elements and aim to obtain the minimum values of generator voltages.<\/jats:p>","DOI":"10.3390\/sym11020136","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T03:40:55Z","timestamp":1548733255000},"page":"136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Analytic Loss Minimization: Theoretical Framework of a Second Order Optimization Method"],"prefix":"10.3390","volume":"11","author":[{"given":"Ioannis K.","family":"Dassios","sequence":"first","affiliation":[{"name":"AMPSAS, University College Dublin, Dublin 4, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,26]]},"reference":[{"key":"ref_1","unstructured":"(2019, January 26). MD1: Structural and Dynamic Modelling of Integrated Energy Systems. 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