Revista Eletrônica de Potência (Brazilian Journal of Power Electronics)

Palavras Chaves: Filtro LCL

Resumo
Neste artigo é apresentada uma nova estrutura de controle robusta adaptativa, resultante da união de um Controlador Robusto Adaptativo por Modelo de Referência e um Controlador Adaptativo Super-Twisting Sliding Mode, totalmente desenvolvida em tempo discreto. A estrutura resultante é aplicada em um inversor alimentado em tensão trifásico, conectado à rede elétrica através de um filtro LCL em um ambiente de rede fraca, ou seja, que apresenta significativo teor de indutância. A principal contribuição dessa nova proposta de controle é sua alta capacidade de adaptabilidade, mantendo as características de robustez dos controladores que o compõe. Assim, sua implementação é simplificada, pois pode ser projetado considerando um modelo de referência de primeira ordem e aplicado ao controle das correntes injetadas na rede. Para tal, negligencia-se a dinâmica dos capacitores do filtro LCL durante a modelagem da planta, considerando-a como uma dinâmica do tipo aditiva. Ainda, é apresentada uma análise de estabilidade e robustez do controlador proposto, em tempo discreto, considerando a planta como um todo, isto é, em presença de dinâmicas não modeladas. Além disso, para validar a viabilidade da estrutura de controle proposta, resultados experimentais são apresentados, onde se pode observar que a estrutura de controle proposta é capaz de regular a planta adequadamente mesmo em um ambiente de rede fraca, apresentando bom desempenho, com taxa de distorção harmônica de 2,81%.

Title: Reference Model-based Robust Adaptive Super-Twisting Sliding Mode Controller for Weak Grid-Currents Regulation of Three-Phase Inverters with LCL Filter

Keywords: LCL filter

Abstract
This article presents a new robust adaptive control structure, resulting from the union of a Robust Model Reference Adaptive Controller and an adaptive Super-Twisting Sliding Mode Controller, totally developed in discrete time. The resulting structure is applied to a voltage-fed three-phase inverter, connected to the grid by LCL filter in a weak grid environment, that is, which has a significant inductance content. The main contribution of this new control proposal is its high adaptability, maintaining the robustness characteristics of the controllers that compose it. Thereby, its implementation is simplified, as it can be designed considering a first-order reference model and applied to the grid-injected current control. For this, the dynamics of the capacitors of the LCL filter are neglected during the modeling of the plant, considering it as an additive type dynamics. Moreover, a stability and robustness analysis of proposed controller is presented, in discrete time, considering the overall plant, that is, in presence of unmodeled dynamics. In addition, to validate the viability of the proposed control structure, experimental results are presented.

[1] V. C. Gungor, D. Sahin, T. Kocak, S. Ergut,C. Buccella, C. Cecati, G. P. Hancke, “Smartgrid technologies:Communication technologiesand standards”,IEEE Transactions on IndustrialInformatics, vol. 7, no. 4, pp. 529–539, set. 2011.
Doi: 10.1109/TII.2011.2166794

[2] M. Liserre, F. Blaabjerg, S. Hansen, “Design andcontrol of an LCL-filter-based three-phase activerectifier”, IEEE Transactions on Industry Applications,vol. 41, no. 5, pp. 1281–1291, set. 2005.
Doi: 10.1109/TIA.2005.853373

[3] P. J. D. O. Evald, R. V. Tambara, H. A. Gründling,“A Discrete-Time Robust MRAC Applied on Grid-Side Current Control of a Grid-Connected Three-PhaseConverter”,ELECTRIMACS 2019: Selected Papers-Volume 1, vol. 604, pp. 45-50, abr. 2020
Doi: 10.1007/978-3-030-37161-6_4

[4] M. Lindgren, J. Svensson, “Control of a voltage-sourceconverter connected to the grid through an LCL-filter-application to active filtering”,in 29th Power Elect. Spec. Conf., vol. 1, pp. 229–235, maio 1998.
Doi: 10.1109/PESC.1998.701904

[5] J. R. Massing, M. Stefanello, H. A. Grundling, H. Pinheiro, “Adaptive current control for grid-connected converters with LCL filter”, IEEE Transactions on Industrial Electronics, vol. 59, no. 12, pp. 4681–4693, nov. 2011.
Doi: 10.1109/TIE.2011.2177610

[6] H. Alenius, Modeling and electrical emulation of grid impedance for stability studies of grid-connected converters, Master’s Thesis, TU, fev. 2018.

[7] M. Liserre, R. Teodorescu, F. Blaabjerg, “Stability of photovoltaic and wind turbine grid-connected inverters for a large set of grid impedance values”, IEEE Trans. on Power Elect., vol. 21, no. 1, pp. 263–272, jan. 2006.
Doi: 10.1109/TPEL.2005.861185

[8] R. A. Guisso, T. Vargas, M. L. Martins, H. L.Hey, “Sistema de Controle Multi-malhas para Inversor Multiníveis Quasi-Z-Source com uma Única Fonte de Entrada”, Revista Eletrônica de Potência, vol. 24, no. 2, pp. 165–176, jun. 2019.
Doi: http://dx.doi.org/10.18618/REP.2019.2.0049

[9] I. Gabe, H. Pinheiro, “Design and implementation of a robust current controller for VSI connected to the grid through an LCL filter”, IEEE Transactions on Power Electronics, vol. 24, no. 6, pp. 1444–1452, maio 2009.
Doi: 10.1109/TPEL.2009.2016097

[10] R. V. Tambara, , H. Pinheiro, H. A. Gründling, “A digital RMRAC controller based on a modified RLS algorithm applied to the control of the output currents of an LCL-filter connected to the grid”, in 15th European Conference on Power Electronics and Applications (EPE), pp. 1–8, IEEE, set. 2013.
Doi: 10.1109/EPE.2013.6634360

[11] L. T. Martins, M. Stefanello, H. Pinheiro, R. P. Vieira, “Current control of grid-tied LCL-VSI with a sliding mode controller in a multiloop approach”, IEEE Transactions on Power Electronics, vol. 34,no. 12, pp. 12356–12367, mar. 2019.
Doi: 10.1109/TPEL.2019.2905717

[12] R. Tambara, H. Gründling, “A discrete-time MRAC-SM applied to grid connected converters with LCL-filter”, in IEEE 19th Workshop on Control and Modeling for Power Electronics, pp. 1–6, jun. 2018.
Doi: 10.1109/COMPEL.2018.8460061

[13] A. Levant, “Higher-order sliding modes, differentiation and output-feedback control”, International Journal of Control, vol. 76, no. 9-10, pp. 924–941, nov. 2003.
Doi: https://doi.org/10.1080/0020717031000099029

[14] A. Msaddek, A. Gaaloul, F. M’sahli, “Comparative study of higher order sliding mode controllers”, in 2014 15th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), pp. 915–922, IEEE, dez. 2014.
Doi: 10.1109/STA.2014.7086681

[15] B. Guo, , H. Dan, Z. Tang, B. Cheng, “A robust second-order sliding mode control for single-phase photovoltaic grid-connected voltage source inverter”, IEEE Access, vol. 7, pp. 53202–53212, abr. 2019.
Doi: 10.1109/ACCESS.2019.2912033

[16] S. Bouyahia, S. Semcheddine, B. Talbi, O. Boutalbi, Y. Terchi, “An adaptive super-twisting sliding mode algorithm for robust control of a biotechnological process”, International Journal of Dynamics and Control, pp. 1–11, maio 2019.
Doi: https://doi.org/10.1007/s40435-019-00551-8

[17] P. J. D. O. Evald, R. V. Tambara, H. A. Gründling, “A Direct Discrete-Time Reduced Order Robust Model Reference Adaptive Control for Grid-tied Power Converters with LCL Filter”, Revista Eletrônica de Potência, vol. 25, no. 3, pp. 361–372, set. 2020.
Doi: http://dx.doi.org/10.18618/REP.2020.3.0039

[18] R. W. Erickson, D. Maksimovic, Fundamentals of power electronics, Springer Science, jul. 2007.

[19] I. G. Macdonald, Symmetric functions and Hallpolynomials, Oxford university press, out. 1998

[20] P. Ioannou, K. Tsakalis, “A robust discrete-time adaptive controller”, in 1986 25th IEEE Conference on Decision and Control, pp. 838–843, IEEE, dez. 1986.

[21] R. Cardoso, R. F. de Camargo, H. Pinheiro, H. A. Gründling, “Kalman filter based synchronisation methods”, IET Generation, Transmission & Distribution, vol. 2, no. 4, pp. 542–555, jun. 2008.
Doi: 10.1109/pesc.2006.1712058