{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T08:49:29Z","timestamp":1773737369042,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T00:00:00Z","timestamp":1689811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT, Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UIDB\/50021\/2020"],"award-info":[{"award-number":["UIDB\/50021\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>This work introduces modified backstepping methods to design controllers for neutral point clamped (NPC) converters interfacing a DC\/AC microgrid. The modified backstepping controllers are derived from a proper converter model, represented in dq coordinates, and are designed to regulate the DC voltage and to balance the two NPC converter DC capacitor voltages through a DC offset in the sinusoidal pulse width modulation (SPWM) carriers. The averaged and separated dynamics backstepping controllers also enforce nearly sinusoidal AC currents at a given power factor. The two proposed NPC converter controllers are evaluated through MATLAB\/Simulink simulations and experimental implementation using a laboratory prototype. Simulations and experimental results show that the two modified backstepping controllers regulate the microgrid DC voltage in steady state and in transient operation, even with load disturbances or DC voltage reference changes, while enforcing nearly AC sinusoidal currents at a given power factor or injected reactive power. The modified backstepping-controlled NPC converter is bidirectional, converting energy from DC renewable energy sources or storage systems to AC or charging storage systems from AC. The results also highlight the effective balancing of the NPC DC capacitor voltages.<\/jats:p>","DOI":"10.3390\/en16145515","type":"journal-article","created":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T01:58:38Z","timestamp":1689904718000},"page":"5515","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Backstepping Control of NPC Multilevel Converter Interfacing AC and DC Microgrids"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2955-5045","authenticated-orcid":false,"given":"J. Dion\u00edsio","family":"Barros","sequence":"first","affiliation":[{"name":"Departamento de Engenharia Eletrot\u00e9cnica, Faculdade de Ci\u00eancias Exatas e da Engenharia, Universidade da Madeira, Campus Universit\u00e1rio da Penteada, 9020-105 Funchal, Portugal"},{"name":"Instituto de Engenharia de Sistemas e Computadores: Investiga\u00e7\u00e3o e Desenvolvimento em Lisboa, INESC-ID, Rua Alves Redol, 1000-029 Lisboa, Portugal"},{"name":"Grupo de Investiga\u00e7\u00e3o em Engenharia Eletrot\u00e9cnica e de Computadores, GIEEC, Campus Universit\u00e1rio da Penteada, 9020-105 Funchal, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5556-0326","authenticated-orcid":false,"given":"Luis","family":"Rocha","sequence":"additional","affiliation":[{"name":"Instituto de Engenharia de Sistemas e Computadores: Investiga\u00e7\u00e3o e Desenvolvimento em Lisboa, INESC-ID, Rua Alves Redol, 1000-029 Lisboa, Portugal"},{"name":"Instituto Superior de Engenharia de Lisboa, Polytechnic Institute of Lisbon, Rua Conselheiro Em\u00eddio Navarro, 1959-007 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2164-0739","authenticated-orcid":false,"given":"J. Fernando","family":"Silva","sequence":"additional","affiliation":[{"name":"Instituto de Engenharia de Sistemas e Computadores: Investiga\u00e7\u00e3o e Desenvolvimento em Lisboa, INESC-ID, Rua Alves Redol, 1000-029 Lisboa, Portugal"},{"name":"Departamento de Engenharia Eletrot\u00e9cnica e de Computadores, Instituto Superior T\u00e9cnico, University of Lisbon, INESC-ID, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1109\/ACCESS.2015.2443119","article-title":"State of the Art in Research on Microgrids: A Review","volume":"3","author":"Parhizi","year":"2015","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/TIE.2012.2194969","article-title":"Advanced Control Architectures for Intelligent Microgrids\u2014Part I: Decentralized and Hierarchical Control","volume":"60","author":"Guerrero","year":"2012","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Al Sumarmad, K.A., Sulaiman, N., Wahab, N.I.A., and Hizam, H. (2022). Energy Management and Voltage Control in Microgrids Using Artificial Neural Networks, PID, and Fuzzy Logic Controllers. 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