{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T09:54:02Z","timestamp":1768557242262,"version":"3.49.0"},"reference-count":57,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,20]],"date-time":"2020-09-20T00:00:00Z","timestamp":1600560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["765585"],"award-info":[{"award-number":["765585"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>As the integration of High Voltage Direct Current (HVDC) systems on modern power networks continues to expand, challenges have appeared in different fields of the network architecture. In the Supervisory, Control and Data Acquisition (SCADA) field, software and toolboxes are expected to be modified to meet the new network characteristics. Therefore, this paper presents a unified Weighted Least Squares (WLS) state estimation algorithm suitable for hybrid HVDC\/AC transmission systems, based on Voltage Source Converter (VSC). The mathematical formulas of the unified approach are derived for modelling the AC, DC and converter coupling components. The method couples the AC and DC sides of the converter through power and voltage constraints and measurement functions. Two hybrid power system test cases have been studied to validate this work, a 4-AC\/4-DC\/4-AC network and Cigre B4 DC test case network. Furthermore, comparison between the fully decentralized state estimation and the unified method is provided, which indicated an accuracy improvement and error reduction.<\/jats:p>","DOI":"10.3390\/en13184932","type":"journal-article","created":{"date-parts":[[2020,9,20]],"date-time":"2020-09-20T21:20:28Z","timestamp":1600636828000},"page":"4932","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["State Estimation for Hybrid VSC Based HVDC\/AC Transmission Networks"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3498-2113","authenticated-orcid":false,"given":"Motaz","family":"Ayiad","sequence":"first","affiliation":[{"name":"Efacec Automation, Grid Management Division, 4471-907 Porto, Portugal"},{"name":"Faculty of Engineering (FEUP), University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1958-964X","authenticated-orcid":false,"given":"Helder","family":"Leite","sequence":"additional","affiliation":[{"name":"Faculty of Engineering (FEUP), University of Porto, 4200-465 Porto, Portugal"}]},{"given":"Hugo","family":"Martins","sequence":"additional","affiliation":[{"name":"Efacec Automation, Grid Management Division, 4471-907 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/MPE.2019.2897407","article-title":"Improving Grid Resilience Using High-Voltage dc: Strengthening the Security of Power System Stability","volume":"17","author":"Roberson","year":"2019","journal-title":"IEEE Power Energy Mag."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lambrechts, J.W., and Sinha, S. 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