Iterative Methods for Nonlinear Systems Applied to Grid Impedance Estimation: A Comparative Study

Jefferson R. P. de Assis; Andréia da S. Gomes; Hugo M. T. C. Gomes; Fabiano F. Costa; Wellington F. Felipe; Maurício B. de R. Corrêa; Darlan A. Fernandes

doi:10.18618/REP.e202446

Authors

Jefferson R. P. de Assis Universidade Federal de Campina Grande https://orcid.org/0000-0002-0462-0368
Andréia da S. Gomes Universidade Federal da Bahia https://orcid.org/0009-0005-4646-2096
Hugo M. T. C. Gomes Universidade Federal da Bahia
Fabiano F. Costa Universidade Federal da Bahia https://orcid.org/0000-0002-0320-6384
Wellington F. Felipe Universidade Federal da Paraíba https://orcid.org/0009-0008-1725-8557
Maurício B. de R. Corrêa Universidade Federal de Alagoas https://orcid.org/0000-0002-4823-6683
Darlan A. Fernandes Universidade Federal da Paraíba https://orcid.org/0000-0002-9617-2856

DOI:

https://doi.org/10.18618/REP.e202446

Keywords:

Chun method, comparative analysis, grid impedance estimation,, iterative methods, Newton-Raphson method, Potra-Pták method, nonlinear systems

Abstract

In this work, a comparative study is presented to evaluate the performance of iterative methods to solve nonlinear systems applied to grid impedance estimation. The iterative methods of Newton-Raphson, Potra-Pták, and Chun were embedded in the control system of a three-phase inverter supported by a photovoltaic plant connected to the grid. The adopted impedance estimation technique consists of successive variation of the power injected into the grid, more precisely, at three different levels. The voltage and current amplitudes at the point of common coupling~(PCC) are monitored and serve as input for the iterative methods, which, after processing them, provide an estimate of the grid impedance. To compare the performance between the methods, the following merit figures were listed: execution time, number of iterations required to deliver the estimates, percentage error, efficiency index, computational efficiency, computational efficiency index, and stability of the iterative method. The results presented were obtained through real-time simulations. From that, it was possible to conclude about the method with the best performance, thus contributing to greater assertiveness on the part of designers when choosing the most efficient iterative method to be embedded in a microcontroller for grid impedance estimation purposes.

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Author Biographies

Jefferson R. P. de Assis, Universidade Federal de Campina Grande

received his bachelor's degree (2019) and master's degree (2021) in Electrical Engineering from the Federal University of Paraíba. He is currently a Ph.D. student in Electrical Engineering at the Federal University of Campina Grande. His research interests include applications of power electronics in distribution systems, power quality, integration of renewable energy, grid impedance estimation techniques, and stability of grid-connected converters. He is a student member of the Brazilian Power Electronics Association (SOBRAEP) and Institute of Electrical Engineering and Electronics (IEEE).

Andréia da S. Gomes, Universidade Federal da Bahia

received a bachelor's degree (2021) in electrical engineering from the Federal University of Campina Grande and a master's degree (2024) in electrical engineering from the Federal University of Paraíba. She is currently a Ph.D. student in electrical engineering at the Federal University of Bahia. Her research interests include distributed generation, integration of renewable energy sources, electrical installations, electrical power systems, energy quality, and electrotechnical projects.

Hugo M. T. C. Gomes, Universidade Federal da Bahia

received his bachelor's degree (2010), master's degree (2016), and Ph.D. (2022) in Electrical Engineering from the Federal Institute of Bahia and the Federal University of Bahia, respectively. His research topics include control in distributed generation systems, PLL, grid impedance estimation techniques, and stability study.

Fabiano F. Costa, Universidade Federal da Bahia

holds a degree in Engineering Electrical from the University of São Paulo (1997), master's degree in Electrical Engineering from the Federal University of Campina Grande (2001) and Ph.D. in Electrical Engineering from Federal University of Campina Grande (2005). Realized postdoctoral research at CPES (Center for Power Electronics Systems) at Virginia Tech (USA). He is currently a professor associate at the Federal University of Bahia in the Department of Electrical Engineering. His research interests include topics related to modeling switched converters through impedance techniques; systems stability interconnected switches in the frequency domain, with emphasis on grid-connected LCL inverters; methods phase capture loop synchronization (PLLs) and electrical grid impedance estimation techniques. He is a member of the Brazilian Power Electronics Association (SOBRAEP) and a Senior Member of the Institute of Electrical Engineering and Electronics (IEEE).

Wellington F. Felipe, Universidade Federal da Paraíba

received a bachelor's degree in Electrical Engineering from the Federal University of Campina Grande (2007) and a master's degree in Electrical Engineering from the Federal University of Paraíba (2023). He is currently a higher level III professional at Eletrobras-Chesf. He has experience in the area of Electrical Engineering with an emphasis on Electrical Energy Generation, working mainly on the following topics: Measurement, Protection, Command, Control and Supervision of Substations (MPCCS), modernization of hydroelectric plants, photovoltaic systems, and power electronics. He is a student member of the Brazilian Power Electronics Association (SOBRAEP).

Maurício B. de R. Corrêa, Universidade Federal de Alagoas

received the titles Electrical Engineer, Master and Doctor in Electrical Engineering at the Federal University of Paraíba, Campina Grande, Brazil, respectively, in 1996, 1997 and 2002. From 1997 to 2004, he was at the Federal Education Center Technology of Alagoas, Brazil. From 2001 to 2002, he did an internship at Wisconsin Electric Machines and Power Electronics Consortium (WEMPEC), at the University of Wisconsin, Madison, WI, USA as part of the PhD program. From 2004 to 2024, he worked in the Electrical Engineering Department of the Federal University of Campina Grande, Campina Grande. He is currently a professor at the Federal University of Alagoas. He was deputy general coordinator of the “The 2005 IEEE Power Electronics Specialists Conference”(PESC 2005) and the IEEE International Future Topic (B) Coordinator Energy Challenge 2011 (IFEC 2011). Your interests research include drive systems, power electronics, and renewable energy.

Darlan A. Fernandes, Universidade Federal da Paraíba

received the B.S. degree in electrical engineering from the Federal University of Paraiba, Brazil, in 2002, and the M.S. and Ph.D. degrees in electrical engineering from the Federal University of Campina Grande, Brazil, in 2004 and 2008, respectively. He was a Visiting Scholar at the Center for Power Electronics Systems (CPES) at the Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, United States, from 2018 to 2019. From 2007 to 2011, he was a Professor with the Industry Department in the Federal Center of Technological Education of Rio Grande do Norte. He is currently an Associate Professor with the Department of Electrical Engineering, Federal University of Paraiba, Brazil. His research interests are in the applications of power electronics in distribution systems, power quality, photovoltaic systems, and impedance-based control design techniques for static converters. He is a member of the Brazilian Power Electronics Association (SOBRAEP) and IEEE.

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