{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:25:28Z","timestamp":1761294328478,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T00:00:00Z","timestamp":1623888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>Voltage source converters (VSCs) are self-commutated converters able to generate AC voltages with or without the support of an AC connecting grid. VSCs allow fast control of active and reactive powers in an independent way. VSCs also have black start capability. Their use in high-voltage direct current (HVDC) systems, comparative to the more mature current source converter (CSC)-based HVDC, offers faster active power flow control. In addition, VSCs provide flexible reactive power control, independent at each converter terminal. It is also useful when connecting DC sources to weak AC grids. Steady-state RMS analysis techniques are commonly used for early-stage analysis, for design purposes and for relaying. Sources interfaced through DC\/AC or AC\/DC\/AC converters, opposite to conventional generators, are not well represented by electromotive forces (E) behind impedance models. A methodology to include voltage source converters (VSCs) in conventional RMS short-circuit analysis techniques is advanced in this work. It represents an iterative procedure inside general calculation techniques and can even be used by those with only basic power electronics knowledge. Results are compared to those of the commercial software package PSS\u00aeCAPE to demonstrate the validity of the proposed rmsVSC algorithm.<\/jats:p>","DOI":"10.3390\/en14123610","type":"journal-article","created":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T11:20:26Z","timestamp":1623928826000},"page":"3610","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Integration of Voltage Source Converters in Steady-State RMS Short-Circuit Analysis"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3668-5710","authenticated-orcid":false,"given":"Carlos Coelho","family":"Teixeira","sequence":"first","affiliation":[{"name":"Coimbra Institute of Engineering, Polytechnic of Coimbra, 3030-199 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1958-964X","authenticated-orcid":false,"given":"Helder","family":"Leite","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,17]]},"reference":[{"key":"ref_1","unstructured":"ENTSO-E (2021, January 04). Voltage Source Converters (Vsc). Available online: https:\/\/www.entsoe.eu\/Technopedia\/techsheets\/voltage-source-converters-vsc."},{"key":"ref_2","unstructured":"Sandeberg, P., and Stendius, L. (April, January 31). Large scale offshore wind power energy evacuation by hvdc light\u00ae. Proceedings of the European Wind Energy Conference & Exhibition, Brussels, Belgium."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Chaudhary, S.K., Teodorescu, R., and Rodriguez, P. (2008, January 17\u201318). Wind farm grid integration using vsc based hvdc transmission\u2014An overview. Proceedings of the Energy 2030 Conference, ENERGY 2008, Atlanta, GA, USA.","DOI":"10.1109\/ENERGY.2008.4781061"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/TEC.2006.889624","article-title":"Hvdc connection of offshore wind farms to the transmission system","volume":"22","author":"Bresesti","year":"2007","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_5","unstructured":"Du, C. (2007). Vsc-Hvdc for Industrial Power Systems, Chalmers University of Technology."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Fischer, M., and Mendonca, A. (2011, January 24\u201329). Representation of variable speed full conversion wind energy converters for steady state short-circuit calculations. Proceedings of the IEEE Power and Energy Society General Meeting, Detroit, MI, USA.","DOI":"10.1109\/PES.2011.6039644"},{"key":"ref_7","unstructured":"Yan, L., and Zhe, C. (2011, January 7\u201310). Short circuit ratio analysis of multi-infeed hvdc system with a vsc-hvdc link. Proceedings of the IECON 2011\u201437th Annual Conference on IEEE Industrial Electronics Society, Melbourne, VIC, Australia."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Goksu, O., Teodorescu, R., Bak-Jensen, B., Iov, F., and Kjaer, P.C. (2012, January 22\u201326). An iterative approach for symmetrical and asymmetrical short-circuit calculations with converter-based connected renewable energy sources. Application to wind power. Proceedings of the Power and Energy Society General Meeting, San Diego, CA, USA.","DOI":"10.1109\/PESGM.2012.6344906"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gautam, P.V.P., and Joseph, F.C. (2018, January 14\u201316). Evaluation of short circuit currents in networks with low voltage ride through (lvrt) enabled voltage source converters (vsc) based wind turbines. Proceedings of the 2018 20th National Power Systems Conference (NPSC), Tiruchirappalli, India.","DOI":"10.1109\/NPSC.2018.8771815"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Arrilaga, J., Liu, Y.H., and Watson, N.R. (2007). Flexible Power Transmission\u2014The Hvdc Options, John Wiley & Sons, Ltd.","DOI":"10.1002\/9780470511862"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.ijepes.2012.03.008","article-title":"A three phase pll with a dynamic feed forward frequency estimator for synchronization of grid connected converters under wide frequency variations","volume":"41","author":"Aravind","year":"2012","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1109\/TPEL.2008.2005580","article-title":"A generic open-loop algorithm for three-phase grid voltage\/current synchronization with particular reference to phase, frequency, and amplitude estimation","volume":"24","author":"Freijedo","year":"2009","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_13","unstructured":"Kundur, P. (1994). Power System Stability AND Control, McGraw-Hill, Inc."},{"key":"ref_14","first-page":"2471","article-title":"Fault characteristics of full power inverted sources and its short-circuit current calculation model","volume":"2017","author":"Zhang","year":"2017","journal-title":"J. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1109\/TPWRS.2009.2023264","article-title":"Enhanced fault ride-through method for wind farms connected to the grid through vsc-based hvdc transmission","volume":"24","author":"Feltes","year":"2009","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_16","unstructured":"IEC (2016). IEC 60909-0\u2014Short-Circuit Currents in Three-Phase A.C. Systems, IEC (International Electrotechnical Commission)."},{"key":"ref_17","unstructured":"Grainger, J.J., and Stevenson, W.D. (1994). Power Systems Analysis, McGraw-Hill."},{"key":"ref_18","unstructured":"Elgerd, O.I. (1982). Electric Energy Systems Theory, McGraw-Hill."},{"key":"ref_19","unstructured":"Brown, H.E. (1975). Solution of Large Networks by Matrix Methods, John Wiley & Sons, Inc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1109\/PROC.1980.11787","article-title":"A new method using the bus-impedance matrix model for short-circuit calculations","volume":"68","author":"Reitan","year":"1980","journal-title":"Proc. IEEE"},{"key":"ref_21","unstructured":"Siemens (2019). Inverter-based generator models with controlled power and current. 2019 PSS\u00aeCAPE User Group Meeting, Siemens Industry, Inc."},{"key":"ref_22","unstructured":"Siemens (2021, March 20). Pss\u00aecape 14. Available online: https:\/\/new.siemens.com\/global\/en\/products\/energy\/energy-automation-and-smart-grid\/grid-resiliency-software\/psscape.html."}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/14\/12\/3610\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:17:37Z","timestamp":1760163457000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/14\/12\/3610"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,17]]},"references-count":22,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["en14123610"],"URL":"https:\/\/doi.org\/10.3390\/en14123610","relation":{},"ISSN":["1996-1073"],"issn-type":[{"type":"electronic","value":"1996-1073"}],"subject":[],"published":{"date-parts":[[2021,6,17]]}}}