Gauss-Newton Method Applied to Impedance Estimation in Grid-Connected Inverters

Jefferson R. P. de Assis; Darlan A. Fernandes; Maurício B. de R. Corrêa; Alfeu J. Sguarezi Filho; Fabiano F. Costa; Edison R. C. da Silva

doi:10.18618/REP.e202619

Authors

Jefferson R. P. de Assis Federal University of Campina Grande https://orcid.org/0000-0002-0462-0368
Darlan A. Fernandes Federal University of Paraíba https://orcid.org/0000-0002-9617-2856
Maurício B. de R. Corrêa Federal University of Alagoas
Alfeu J. Sguarezi Filho Federal University of ABC https://orcid.org/0000-0001-9981-436X
Fabiano F. Costa Federal University of Bahia
Edison R. C. da Silva Federal University of Paraíba https://orcid.org/0000-0002-8678-228X

DOI:

https://doi.org/10.18618/REP.e202619

Keywords:

Gauss-Newton method, grid impedance estimation, nonlinear least squares

Abstract

This work presents a methodology that employs the Gauss–Newton algorithm to perform online impedance estimation for grid-connected inverters. Conventional formulations for this class of problem typically lead to high-order nonlinear systems of equations, often of dimension 8×8. In contrast, the formulation proposed herein recasts the estimation task as a 3×3 least-squares problem, which is then solved via the Gauss–Newton method. To validate the proposed approach, a three-phase grid-connected inverter was adopted as the case study. The control system enforces three distinct active power injection levels into the grid, and the voltage, current, and phase-angle magnitudes at the point of common coupling are measured and used as inputs to the impedance estimation algorithm. Real-time validation was carried out to assess the performance of the method. The results confirm the feasibility of the proposed formulation and indicate that the approach substantially reduces the computational burden of embedded DSP-based algorithms for online grid impedance estimation.

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Author Biographies

Jefferson R. P. de Assis, Federal University of Campina Grande

received the B.S. and M.S. degrees in electrical engineering from the Federal University of Paraíba (UFPB), João Pessoa, Brazil, in 2019 and 2021, respectively. He is currently pursuing the Ph.D. degree in electrical engineering at the Federal University of Campina Grande (UFCG), Brazil. Since November 2025, he has been a Temporary Lecturer with the Federal Institute of Education, Science and Technology of Paraíba (IFPB). He is a member of the Brazilian Power Electronics Society (SOBRAEP) and IEEE Societies, including PELS, IAS, IES, PES, and the Education Society. His research interests include power electronics applications in distribution systems, impedance estimation techniques, power quality, and the modeling and stability analysis of power electronic systems, with a focus on renewable energy integration and real-time simulation.

Darlan A. Fernandes , Federal University of Paraíba

received the B.S. degree in electrical engineering from the Federal University of Paraíba (UFPB), Brazil, in 2002, and the M.S. and Ph.D. degrees from the Federal University of Campina Grande (UFCG), Brazil, in 2004 and 2008, respectively. From 2007 to 2011, he was a Professor with the Federal Center of Technological Education of Rio Grande do Norte (IFRN). From 2018 to 2019, he was a Visiting Scholar with the Center for Power Electronics Systems (CPES) at Virginia Tech, Blacksburg, VA, USA. He is currently a Associate Professor with the Department of Electrical Engineering at the Federal University of Paraíba (UFPB). His research interests include power electronics applications in distribution systems, power quality, photovoltaic systems, and impedance-based control design techniques for power converters.

Maurício B. de R. Corrêa, Federal University of Alagoas

received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Federal University of Paraíba, Campina Grande, Brazil, in 1996, 1997, and 2002, respectively. From 1997 to 2004, he was with the Federal Center for Technological Education of Alagoas (CEFET-AL), Brazil. From 2001 to 2002, he was a Visiting Scholar with the Wisconsin Electric Machines and Power Electronics Consortium (WEMPEC), University of Wisconsin-Madison, WI, USA. After serving as a Professor at the Federal University of Campina Grande (UFCG) for several years, he is currently a Full Professor of Electrical Engineering at the Federal University of Alagoas (UFAL). His research interests include electrical drives, power electronics, and renewable energy systems. Dr. Corrêa has held prominent leadership roles in the IEEE community, having served as the General Co-Chairman of the 2005 IEEE Power Electronics Specialists Conference (PESC) and as the Chair for Topic (B) of the 2011 IEEE International Future Energy Challenge (IFEC).

Alfeu J. Sguarezi Filho, Federal University of ABC

received the M.S. and Ph.D. degrees in electrical engineering from the School of Electrical and Computer Engineering, University of Campinas (UNICAMP), Brazil, in 2007 and 2010, respectively. He is currently an Associate Professor with the Federal University of ABC (UFABC), Santo André, Brazil. Dr. Sguarezi Filho has authored numerous articles in peer-reviewed journals and several book chapters. His research interests include electrical machines, machine drives, electric vehicles, power electronics, and renewable energy systems, with an emphasis on wind and photovoltaic power generation.

Fabiano F. Costa, Federal University of Bahia

received the B.S. degree in electrical engineering from the University of São Paulo (USP), Brazil, in 1997, and the M.S. and Ph.D. degrees in electrical engineering from the Federal University of Campina Grande (UFCG), Brazil, in 2001 and 2005, respectively. He also completed postdoctoral research at the Center for Power Electronics Systems (CPES), Virginia Tech, Blacksburg, VA, USA. He is currently an Associate Professor with the Department of Electrical Engineering, Federal University of Bahia (UFBA), Brazil. His research interests include the modeling of switched-mode converters using impedance-based techniques, frequency-domain stability analysis of interconnected systems (with an emphasis on grid-connected LCL inverters), phase-locked loop (PLL) synchronization methods, and grid impedance estimation techniques.

Edison R. C. da Silva, Federal University of Paraíba

received the B.S. degree from the Polytechnic School of Pernambuco in 1965, the M.S. degree from COPPE/UFRJ in 1968, and the Ph.D. degree in Industrial Electronics from the University of Toulouse III (Paul Sabatier), France, in 1972. He also completed a post-doctoral fellowship at the University of Wisconsin–Madison in 1991. He is currently a Professor Emeritus at the Federal University of Campina Grande (UFCG) and a Permanent Professor at the Federal University of Paraíba(UFPB). Over his career, he has served as the Head of the Industrial Electronics and Machine Drives Laboratory (LEIAM) and chaired several prestigious conferences, including the 36th IEEE Power Electronics Specialists Conference (PESC 2005). He was also the President of the Brazilian Society of Automatics (SBA) from 2002 to 2004. His research interests include power converter topologies, machine drives, power factor control, and fault diagnosis in power electronics. He has authored numerous highly-cited publications and is an IEEE Life Fellow (class of 2003). Dr. Silva has served as a Distinguished Lecturer for both PELS and IAS and is a recipient of the CAPES/COFECUB Gold Medal for his contributions to international scientific cooperation

References

International Energy Agency - IEA, “The Evolution of Energy Efficiency Policy to Support Clean Energy Transitions”, Digital Format, December 2023, URL: https://www.iea.org/reports/the-evolution-of-energy-efficiency-policy-to-support-clean-energy-transitions.

T. B. Hadj, A. Ghodbane, E. B. Mohamed, A. A. Alfalih, “The transition to renewable energy through financial development and under natural resources threshold in emerging countries”, Environment, Development and Sustainability, Jan 2024, doi:10.1007/s10668-023-04389-1.

F. Blaabjerg, Z. Chen, S. Kjaer, “Power electronics as efficient interface in dispersed power generation systems”, IEEE Transactions on Power Electronics, vol. 19, no. 5, pp. 1184–1194, 2004, doi:10.1109/TPEL.2004.833453.

J. Sun, “Impedance-based stability criterion for grid-connected inverters”, IEEE Trans Power Electron, vol. 26, no. 11, pp. 3075–3078, Nov.2011, doi:10.1109/TPEL.2011.2136439.

M. K. De Meerendre, E. Prieto-Araujo, K. H. Ahmed, O. Gomis-Bellmunt, L. Xu, A. Egea- `Alvarez, “Review of Local Network Impedance Estimation Techniques”, IEEE Access, vol. 8, pp. 213647–213661, 2020, doi:10.1109/ACCESS.2020.3040099.

A. V. Timbus, P. Rodriguez, R. Teodorescu, M. Ciobotaru, “Line Impedance Estimation Using Active and Reactive Power Variations”, in 2007 IEEE Power Electronics Specialists Conference, pp. 1273–1279, 2007, doi:10.1109/PESC.2007.4342176.

M. Cespedes, J. Sun, “Adaptive Control of Grid-Connected Inverters Based on Online Grid Impedance Measurements”, IEEE Transactions on Sustainable Energy, vol. 5, no. 2, pp. 516–523, 2014, doi:10.1109/TSTE.2013.2295201.

J. Sun, “Frequency-Domain Stability Criteria for Converter-Based Power Systems”, IEEE Open Journal of Power Electronics, vol. 3, pp. 222–254, 2022, doi:10.1109/OJPEL.2022.3155568.

K. Pedersen, A. Nielsen, N. Poulsen, “Short-circuit impedance measurement”, IEE Proceedings - Generation, Transmission and Distribution, vol. 150, pp. 169–174, 2003, doi:10.1049/ip-gtd:20030193.

S. Cobreces, E. J. Bueno, D. Pizarro, F. J. Rodriguez, F. Huerta, “Grid Impedance Monitoring System for Distributed Power Generation Electronic Interfaces”, IEEE Transactions on Instrumentation and Measurement, vol. 58, no. 9, pp. 3112–3121, 2009, doi:10.1109/TIM.2009.2016883.

N. Mohammed, T. Kerekes, M. Ciobotaru, “An Online Event-Based Grid Impedance Estimation Technique Using Grid-Connected Inverters”, IEEE Transactions on Power Electronics, vol. 36, no. 5, pp. 6106–6117, 2021, doi:10.1109/TPEL.2020.3029872.

D. O. Cardoso, H. M. T. C. Gomes, F. A. d. C. Bahia, A. P. N. Tahim, J. R. Pinheiro, F. F. Costa, “Impacto do PLL para Estimação de Impedância de Rede e Avaliação de Estabilidade no Domínio DQ em Sistemas com Inversores Conectados”, Eletrônica de Potência, vol. 28, no. 2, p. 107–118, Mar. 2023, doi:10.18618/REP.2023.2.0050.

Y. Cheng, W. Wu, Y. Yang, E. Koutroulis, H. S.-H. Chung, M. Liserre, F. Blaabjerg, “Zero-Sequence Voltage Injection-Based Grid Impedance Estimation Method for Three-Phase Four-Wire DC/AC Grid-Connected Inverter”, IEEE Transactions on Industrial Electronics, vol. 71, no. 7, pp. 7273–7279, 2024, doi:10.1109/TIE.2023.3306395.

J. Mace, A. Cervone, D. Dujic, “Self-Synchronized Grid Impedance Estimation Unit Using Interpolated DFT Technique”, IEEE Transactions on Power Electronics, vol. 39, no. 4, pp. 4624–4635, 2024, doi:10.1109/TPEL.2023.3342317.

J. Fang, H. Deng, S. M. Goetz, “Grid Impedance Estimation Through Grid-Forming Power Converters”, IEEE Transactions on Power Electronics, vol. 36, no. 2, pp. 2094–2104, 2021, doi:10.1109/TPEL.2020.3010874.

H. M. T. C. Gomes, L. L. O. Carralero, J. H. Su´arez, A. P. N. Tahim, J. R. Pinheiro, F. F. Costa, “Estimativa de Impedância para Suporte de Estabilidade e Qualidade de Energia em Inversores Conectados à Rede”, Eletrônica de Potência, vol. 27, no. 2, p. 165–176, Jun. 2022, doi:10.18618/REP.2022.2.0004.

H. M. T. C. Gomes, L. L. O. Carralero, J. H. Suárez, A. N. Tahim, J. R. Pinheiro, F. F. Costa, “A Grid Impedance Estimation Method Robust Against Grid Voltages Unbalance and Harmonic Distortions”, Journal of Control, Automation and Electrical Systems, vol. 34, no. 2, pp. 289–301, apr 2023, doi:10.1007/s40313-022-00963-6.

J. R. P. de Assis, A. d. S. Gomes, H. M. T. C. Gomes, F. F. Costa, W. F. Felipe, M. B. d. R. Corrˆea, D. A. Fernandes, “Iterative Methods for Nonlinear Systems Applied to Grid Impedance Estimation: A Comparative Study”, Eletrônica de Potência, vol. 29, p. e202446, Nov. 2024, doi:10.18618/REP.e202446.

D. A. Fernandes, S. R. Naidu, C. Coura, “Instantaneous Sequence-Component Resolution of 3-Phase Variables and Its Application to Dynamic Voltage Restoration”, IEEE Transactions on Instrumentation and Measurement, vol. 58, no. 8, pp. 2580–2587, 2009, doi:10.1109/TIM.2009.2015634.

I. Argyros, Computational Theory of Iterative Methods, vol. 15, Elsevier Science, 2007.