{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:35Z","timestamp":1760242355773,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,5,23]],"date-time":"2017-05-23T00:00:00Z","timestamp":1495497600000},"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>This paper presents a backward Euler stabilized-based control strategy applied to a neutral point clamped (NPC) back-to-back connected five level converters. A generalized method is used to obtain the back-to-back NPC converter system model. The backward Euler stabilized-based control strategy uses one set of calculations to compute the optimum voltage vector needed to reach the references and to balance the voltage of the DC-bus capacitors. The output voltage vector is selected using a modified cost functional that includes variable tracking errors in the functional weights, whereas in classic approaches, the weights are considered constant. The proposed modified cost functional enables AC current tracking and DC-bus voltage balancing in a wide range of operating conditions. The paper main contributions are: (i) a backward Euler stabilized-based control strategy applied to a double, back-to-back connected, five level NPC converter; (ii) the use of cost functional weight varying as a function of the controlled variable tracking errors to enforce the controlled variables and to balance the DC capacitor voltages; and (iii) the demonstration of system feasibility for this type of converter topology and control strategy, ensuring a high enough computational efficiency and extending the modulation index from 0.6 to 0.93. Experimental results are presented using a prototype of a five level NPC back-to-back converter.<\/jats:p>","DOI":"10.3390\/en10060735","type":"journal-article","created":{"date-parts":[[2017,5,23]],"date-time":"2017-05-23T11:14:33Z","timestamp":1495538073000},"page":"735","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New Backward Euler Stabilized Optimum Controller for NPC Back-to-Back Five Level Converters"],"prefix":"10.3390","volume":"10","author":[{"given":"Miguel","family":"Chaves","sequence":"first","affiliation":[{"name":"Instituto Superior de Engenharia de Lisboa (ISEL), Instituto Polit\u00e9cnico de Lisboa, Rua Conselheiro Em\u00eddio Navarro 1, Lisboa 1959-007, Portugal"},{"name":"Instituto de Engenharia de Sistemas e Computadores, Investiga\u00e7\u00e3o e Desenvolvimento em Lisboa (INESC-ID), R. Alves Redol 9, Lisboa 1000-029, Portugal"},{"name":"Centro de Eletrotecnia e Eletr\u00f3nica Industrial (CEEI), Rua Conselheiro Em\u00eddio Navarro 1, Lisboa 1959-007, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2164-0739","authenticated-orcid":false,"given":"Jos\u00e9","family":"Silva","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Eletrot\u00e9cnica e de Computadores, Instituto Superior T\u00e9cnico, TU Lisbon, Av. Rovisco Pais 1, Lisboa 1049-001, Portugal"},{"name":"Instituto de Engenharia de Sistemas e Computadores, Investiga\u00e7\u00e3o e Desenvolvimento em Lisboa (INESC-ID), R. Alves Redol 9, Lisboa 1000-029, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3266-7881","authenticated-orcid":false,"given":"S\u00f3nia","family":"Pinto","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Eletrot\u00e9cnica e de Computadores, Instituto Superior T\u00e9cnico, TU Lisbon, Av. Rovisco Pais 1, Lisboa 1049-001, Portugal"},{"name":"Instituto de Engenharia de Sistemas e Computadores, Investiga\u00e7\u00e3o e Desenvolvimento em Lisboa (INESC-ID), R. Alves Redol 9, Lisboa 1000-029, Portugal"}]},{"given":"Elmano","family":"Margato","sequence":"additional","affiliation":[{"name":"Instituto Superior de Engenharia de Lisboa (ISEL), Instituto Polit\u00e9cnico de Lisboa, Rua Conselheiro Em\u00eddio Navarro 1, Lisboa 1959-007, Portugal"},{"name":"Instituto de Engenharia de Sistemas e Computadores, Investiga\u00e7\u00e3o e Desenvolvimento em Lisboa (INESC-ID), R. Alves Redol 9, Lisboa 1000-029, Portugal"},{"name":"Centro de Eletrotecnia e Eletr\u00f3nica Industrial (CEEI), Rua Conselheiro Em\u00eddio Navarro 1, Lisboa 1959-007, Portugal"}]},{"given":"Jo\u00e3o","family":"Santana","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Eletrot\u00e9cnica e de Computadores, Instituto Superior T\u00e9cnico, TU Lisbon, Av. 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