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Comparisons include closed loop outer voltage controllers based on predictive, sliding mode and decoupled proportional-integral controllers in dqo synchronous space, fitted with an inner hysteretic current loop vector controller in     \u03b1 \u03b2 \u03b3     space. The 3-phase four-leg VSI output voltages waveform quality is analysed under unbalanced and non-linear loads.<\/jats:p>","DOI":"10.3390\/en10040504","type":"journal-article","created":{"date-parts":[[2017,4,13]],"date-time":"2017-04-13T02:39:17Z","timestamp":1492051157000},"page":"504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Output Voltage Quality Evaluation of Stand-alone Four-Leg Inverters Using Linear and Non-Linear Controllers"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7975-5726","authenticated-orcid":false,"given":"Ricardo","family":"Lu\u00eds","sequence":"first","affiliation":[{"name":"INESC-ID, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"},{"name":"Instituto Superior de Engenharia de Lisboa, Polytechnic Institute of Lisbon, 1959-007 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2164-0739","authenticated-orcid":false,"given":"Jos\u00e9","family":"Silva","sequence":"additional","affiliation":[{"name":"INESC-ID, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"given":"Jos\u00e9","family":"Quadrado","sequence":"additional","affiliation":[{"name":"Instituto Superior de Engenharia de Lisboa, Polytechnic Institute of Lisbon, 1959-007 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hu, Y., McKenzie, H., and Chen, Z. (2008, January 6\u20139). Voltage source converters in distributed generation systems. Proceedings of the 3rd International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, Nanjing, China.","DOI":"10.1109\/DRPT.2008.4523882"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.epsr.2011.12.014","article-title":"Neutral current compensation in three-phase four-wire systems: A review","volume":"86","author":"Sreenivasarao","year":"2012","journal-title":"Electr. Power Syst. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1109\/TPEL.2007.911816","article-title":"A Three-phase four-wire inverter control technique for a single distributed generation unit in island mode","volume":"23","author":"Dai","year":"2008","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1109\/TPEL.2007.911783","article-title":"Control of three-phase four-wire PWM rectifier","volume":"23","author":"Ghosh","year":"2008","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yang, X., Wu, W.Y., and Shen, H. (2006, January 14\u201316). Adaptive three dimensional space vector modulation in abc coordinates for three phase four wire split capacitor converter. Proceedings of the 5th International Power Electronics and Motion Control Conference, Shanghai, China.","DOI":"10.1109\/IPEMC.2006.297348"},{"key":"ref_6","unstructured":"Bellini, A., and Bifaretti, S. (2006, January 22\u201324). Modulation techniques for three-phase four-leg inverters. Proceedings of the 6th WSEAS Internationa Conference on Power Systems, Lisbon, Portugal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1016\/j.epsr.2011.01.001","article-title":"A four-leg unified series\u2013parallel active filter system for periodic and non-periodic disturbance compensation","volume":"5","author":"Ucar","year":"2011","journal-title":"Electr. Power Syst. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2733","DOI":"10.1016\/j.renene.2011.03.007","article-title":"Adaptive decoupled control of 4-leg voltage-source inverters for standalone photovoltaic systems: Adjusting transient state response","volume":"10","author":"Nasiri","year":"2011","journal-title":"Renew. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1594","DOI":"10.1109\/TIE.2006.882014","article-title":"H\u221e Control of the neutral point in four-wire three-phase DC-AC converter","volume":"53","author":"Zhong","year":"2006","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_10","unstructured":"Zhang, R. (1998). High Performance Power Converter Systems for Nonlinear and Unbalanced Load\/Source. [Ph.D. Thesis, Virginia Polytechnic Institute]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1109\/TEC.2013.2288774","article-title":"A three-phase inverter for a standalone distributed generation system: Adaptive voltage control design and stability analysis","volume":"29","author":"Jung","year":"2014","journal-title":"IEEE Trans. Energy Conv."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1109\/TEC.2014.2360071","article-title":"A short-term energy storage system for voltage quality improvement in distributed wind power","volume":"29","author":"Ammar","year":"2014","journal-title":"IEEE Trans. Energy Conv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1109\/TEC.2014.2303203","article-title":"Control scheme for a stand-alone wind energy conversion system","volume":"29","author":"Satpathy","year":"2014","journal-title":"IEEE Trans. Energy Conv."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1109\/TEC.2013.2260752","article-title":"Control of a supercapacitor energy storage system for microgrid applications","volume":"28","author":"Inthamoussou","year":"2013","journal-title":"IEEE Trans. Energy Conv."},{"key":"ref_15","unstructured":"Lu\u00eds, R. (2015). Gerador de Velocidade Vari\u00e1vel para Aumento da Efici\u00eancia Energ\u00e9tica em Grupos Eletrog\u00e9neos Aut\u00f3nomo. [Ph.D. Thesis, Electrical and Computer Engineering Department of Instituto Superior T\u00e9cnico]."},{"key":"ref_16","unstructured":"Retter, G.J. (1987). Matrix and Space-Phasor Theory of Electrical Machines, Akad\u00e9miai Kiad\u00f3."},{"key":"ref_17","unstructured":"Rashid, M. (2011). Advanced Control of Switching Power Converters. Power Electronics Handbook, Butterworth-Heinemann."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2747","DOI":"10.1109\/TIE.2009.2034172","article-title":"Multilevel optimal predictive dynamic voltage restorer","volume":"57","author":"Barros","year":"2010","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0378-4754(03)00076-4","article-title":"Advanced control methods for power electronics systems","volume":"63","author":"Silva","year":"2003","journal-title":"Math. Comput. Simul."},{"key":"ref_20","unstructured":"Silva, J. (1997, January 7\u201311). Sliding mode control of voltage sourced boost-type reversible rectifiers. Proceedings of the IEEE ISIE\u201997 International Symposium on Industrial Electronics, Guimar\u00e3es, Portugal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/41.720337","article-title":"A novel and simple current controller for three-phase PWM power inverters","volume":"45","author":"Martins","year":"1998","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_22","unstructured":"Silva, J. (1998, January 7\u201310). PWM audio power amplifiers: Sigma delta versus sliding mode control. Proceedings of the IEEE International Conference on Electronics Circuits and Systems, Lisbon, Portugal."},{"key":"ref_23","unstructured":"Courriou, J. (2004). Process Control: Theory and Applications, Springer."},{"key":"ref_24","unstructured":"(2009). Recommended Practice for Monitoring Electric Power Quality, IEEE Standard 1159, IEEE."},{"key":"ref_25","unstructured":"Fuchs, E., and Masoum, M. (2008). Power Quality in Power Systems and Electrical Machines, Academic Press."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Chattopadhyay, S., Mitra, M., and Sengupta, S. (2011). Electric Power Quality, Springer.","DOI":"10.1007\/978-94-007-0635-4"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1016\/j.epsr.2010.11.024","article-title":"Three-phase inverter-connected DG-units and voltage unbalance","volume":"81","author":"Meersman","year":"2011","journal-title":"Electr. Power Syst. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1109\/TPWRD.2016.2535258","article-title":"Damping-based droop control strategy allowing an increased penetration of renewable energy resources in low-voltage grids","volume":"31","author":"Bozalakov","year":"2016","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Demirkutlu, E. (2006). Output Voltage Control of a Four-Leg Inverter Based Three-Phase UPS by Means of Stationary Frame Resonant Filter Banks. 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