Realimentação Parcial de Estados Baseada em LMIs para Controle Robusto de Conversores Conectados à Rede
DOI:
https://doi.org/10.18618/REP.2021.4.0011Keywords:
Controle Robusto, Conversor Conectado à Rede, Desigualdades Matriciais Lineares, Mata-heurística, Realimentação parcial de estadosAbstract
Este trabalho propõe um procedimento para obter ganhos robustos de realimentação parcial de estados para controle das correntes de conversores conectados à rede com incertezas paramétricas. Controladores por realimentação parcial de estados permitem diminuir o número de sensores, produzindo respostas de boa qualidade com menor custo de implementação. Neste cenário, condições de projeto baseadas em LMIs podem fornecer resultados conservadores devido a restrições de estrutura (e.g., diagonal) que devem ser impostas nas variáveis de otimização. Em contrapartida, LMIs de análise são menos conservadoras e podem prover um certificado de estabilidade robusta do sistema em malha fechada de forma eficiente para um dado controlador. Como contribuição, é proposto aqui um procedimento de projeto para encontrar ganhos de realimentação parcial de estados otimizados, combinando uma meta-heurística com uma LMI de análise, para prover uma garantia teórica de estabilidade. Um estudo de caso mostra a vantagem da proposta em relação a LMIs de síntese para obter ganhos de realimentação parcial de estados. Resultados em tempo real mostram a superioridade do controlador proposto quando comparado a um controlador proporcional-integral da literatura. Resultados experimentais em protótipo de padrão industrial confirmam a viabilidade prática da proposta, com respostas em conformidade com a norma IEEE 1547.
Downloads
References
[ 1]F. Blaabjerg, R. Teodorescu, M. Liserre, A. Timbus,"Overview of Control and Grid Synchronizationfor Distributed Power Generation Systems",IEEETransactions on Industrial Electronics, vol. 53, no. 5,pp. 1398 -1409, oct. 2006. https://doi.org/10.1109/TIE.2006.881997 DOI: https://doi.org/10.1109/TIE.2006.881997
[ 2]"IEEE:1547 Standard for interconnecting distributedresources with electric power systems", , feb. 2018.
[ 3]J. Dannehl, F. Fuchs, P. Thøgersen, "PI StateSpace Current Control of Grid-Connected PWMConverters With LCL Filters",Power Electronics,IEEE Transactions on, vol. 25, no. 9, pp. 2320 -2330,sept. 2010. https://doi.org/10.1109/TPEL.2010.2047408 DOI: https://doi.org/10.1109/TPEL.2010.2047408
[ 4]C. Bao, X. Ruan, X. Wang, W. Li, D. Pan,K. Weng, "Step-by-step controller design for LCL-type grid-connected inverter with capacitor-current-feedback active-damping",IEEE Transactions onPower Electronics, vol. 29, no. 3, pp. 1239-1253, jun.2013. https://doi.org/10.1109/TPEL.2013.2262378 DOI: https://doi.org/10.1109/TPEL.2013.2262378
[ 5]R. Teodorescu, F. Blaabjerg, M. Liserre, P. Loh,"Proportional-resonant controllers and filters for grid-connected voltage-source converters",IEEProceedings Electric Power Applications, vol. 153,no. 5, pp. 750-762, sept. 2006 https://doi.org/10.1049/ip-epa:20060008 DOI: https://doi.org/10.1049/ip-epa:20060008
[ 6]A. Al-Durra, R. Errouissi, "Robust feedback-linearization technique for grid-tied LCL filter systemsusing disturbance estimation",IEEE Transactions onIndustry Applications, vol. 55, no. 3, pp. 3185-3197,jan. 2019. https://doi.org/10.1109/TIA.2019.2894991 DOI: https://doi.org/10.1109/TIA.2019.2894991
[ 7]C. A. Busada, S. G. Jorge, J. A. Solsona, "Full-statefeedback equivalent controller for active damping inLCL-filtered grid-connected inverters using a reducednumber of sensors",IEEE Transactions on IndustrialElectronics, vol. 62, no. 10, pp. 5993-6002, apr. 2015. https://doi.org/10.1109/TIE.2015.2424391 DOI: https://doi.org/10.1109/TIE.2015.2424391
[ 8]R. Pérez-Ibacache, C. A. Silva, A. Yazdani, "Linearstate-feedback primary control for enhanced dynamicresponse of AC microgrids",IEEE Transactions onSmart Grid, vol. 10, no. 3, pp. 3149-3161, mar. 2018. https://doi.org/10.1109/TSG.2018.2818624 DOI: https://doi.org/10.1109/TSG.2018.2818624
[ 9]R. C. Dorf, R. H. Bishop,Modern control systems,Pearson, jan. 2011.
[ 10]P. Dorato, C. T. Abdallah, V. Cerone,Linear quadraticcontrol: an introduction, Krieger Pub. Co., Malabar,USA, jan. 2000.
[ 11]R. Bimarta, K.-H. Kim, "A robust frequency-adaptivecurrent control of a grid-connected inverter basedon LMI-LQR under polytopic uncertainties",IEEEAccess, vol. 8, pp. 28756-28773, feb. 2020. https://doi.org/10.1109/ACCESS.2020.2972028 DOI: https://doi.org/10.1109/ACCESS.2020.2972028
[ 12]G. G. Koch, C. R. D. Osório, H. Pinheiro,R. C. L. F. Oliveira, V. F. Montagner, "DesignProcedure Combining Linear Matrix Inequalitiesand Genetic Algorithm for Robust Control ofGrid-Connected Converters",IEEE Transactions onIndustry Applications, vol. 56, no. 2, pp. 1896-1906,dec. 2019. https://doi.org/10.1109/TIA.2019.2959604 DOI: https://doi.org/10.1109/TIA.2019.2959604
[ 13]C. R. D. Osório, G. G. Koch, R. C. L. F. Oliveira, V. F.Montagner, "A practical design procedure for robustH2 controllers applied to grid-connected inverters",Control Engineering Practice, vol. 92, p. 104157, nov.2019. https://doi.org/10.1016/j.conengprac.2019.104157 DOI: https://doi.org/10.1016/j.conengprac.2019.104157
[ 14]S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan,Linear Matrix Inequalities in System and ControlTheory, SIAM Studies in Applied Mathematics,Philadelphia, PA, jan. 1994. https://doi.org/10.1137/1.9781611970777 DOI: https://doi.org/10.1137/1.9781611970777
[ 15]I. J. Gabe, V. F. Montagner, H. Pinheiro, "Design andimplementation of a robust current controller for VSIconnected to the grid through an LCL filter",IEEETransactions on Power Electronics, vol. 24, no. 6, pp.1444-1452, may 2009. https://doi.org/10.1109/TPEL.2009.2016097 DOI: https://doi.org/10.1109/TPEL.2009.2016097
[ 16]V. F. Montagner, L. A. Maccari, G. G. Koch,J. R. Massing, H. Pinheiro, A. A. Ferreira, R. C.L. F. Oliveira, "Partial state feedback controllersapplied to grid-connected converters",in 2015 IEEE13th Brazilian Power Electronics Conference and1st Southern Power Electronics Conference, pp. 1-4,IEEE, dec. 2015. https://doi.org/10.1109/COBEP.2015.7420030 DOI: https://doi.org/10.1109/COBEP.2015.7420030
[ 17]R. C. L. F. Oliveira, P. L. D. Peres, "Parameter-dependent LMIs in robust analysis: characterizationof homogeneous polynomially parameter-dependentsolutions via LMI relaxations",IEEE Transactions onAutomatic Control, vol. 52, no. 7, pp. 1334--1340, jul.2007. https://doi.org/10.1109/TAC.2007.900848 DOI: https://doi.org/10.1109/TAC.2007.900848
[ 18]D. C. Ramos, P. L. Peres, "A less conservativeLMI condition for the robust stability of discrete-timeuncertain systems",Systems&Control Letters, vol. 43,no. 5, pp. 371-378, aug. 2001. https://doi.org/10.1016/S0167-6911(01)00120-7 DOI: https://doi.org/10.1016/S0167-6911(01)00120-7
[ 19]L. C. Borin, I. Cleveston, G. G. Koch, C. R. D.Osório, E. Mattos, V. F. Montagner, "RobustControl of Grid-Tied Inverters using Particle SwarmOptimization and Linear Matrix Inequalities",in 2020IEEE 14th International Conference on Compatibility,Power Electronics and Power Engineering (CPE-POWERENG), vol. 1, pp. 285-290, IEEE, jul. 2020. https://doi.org/10.1109/CPE-POWERENG48600.2020.9161470 DOI: https://doi.org/10.1109/CPE-POWERENG48600.2020.9161470
[ 20]C. R. D. Osório, G. G. Koch, I. Cleveston, L. C.Borin, F. H. Dupont, R. C. L. F. Oliveira, V. F.Montagner, "Otimização multiobjetivo para controlerobusto aplicado a inversores conectados à rede",Eletrônica de potência, Brazilian journal of powerelectronics, jan. 2019. https://doi.org/10.18618/REP.2019.1.0041 DOI: https://doi.org/10.18618/REP.2019.1.0041
[ 21]R. Teodorescu, M. Liserre, P. Rodríguez,GridConverters for Photovoltaic and Wind Power Systems,Wiley - IEEE, John Wiley & Sons, jan. 2011. https://doi.org/10.1002/9780470667057 DOI: https://doi.org/10.1002/9780470667057
[ 22]Q. Liu, T. Caldognetto, S. Buso, "Stability analysisand auto-tuning of interlinking converters connected toweak grids",IEEE Transactions on Power Electronics,vol. 34, no. 10, pp. 9435-9446, feb. 2019. https://doi.org/10.1109/TPEL.2019.2899191 DOI: https://doi.org/10.1109/TPEL.2019.2899191
[ 23]K. Aström, B. Wittenmark,Computer-controlledsystems: theory and design, Prentice Hall, jan. 1997.
[ 24]L. A. Maccari Jr, H. Pinheiro, R. C. L. F. Oliveira, V. F.Montagner, "Robust pole location with experimentalvalidation for three-phase grid-connected converters",Control Engineering Practice, vol. 59, pp. 16-26, feb.2017. https://doi.org/10.1016/j.conengprac.2016.10.013 DOI: https://doi.org/10.1016/j.conengprac.2016.10.013
[ 25]J. Bernussou, P. L. D. Peres, J. C. Geromel, "Alinear programming oriented procedure for quadraticstabilization of uncertain systems",Systems&ControlLetters, vol. 13, no. 1, pp. 65-72, jul. 1989. https://doi.org/10.1016/0167-6911(89)90022-4 DOI: https://doi.org/10.1016/0167-6911(89)90022-4
[ 26]B. Ufnalski, A. Kaszewski, L. M. Grzesiak, "ParticleSwarm Optimization of the Multioscillatory LQR for aThree-Phase Four-Wire Voltage-Source Inverter Withan LC Output Filter",IEEE Transactions on IndustrialElectronics, vol. 62, no. 1, pp. 484-493, jan. 2015. https://doi.org/10.1109/TIE.2014.2334669 DOI: https://doi.org/10.1109/TIE.2014.2334669
[ 27]R. Eberhart, J. Kennedy, "A new optimizer usingparticle swarm theory",in In Proceedings of theSixth International Symposium on Micro Machine andHuman Science., pp. 39-43, IEEE, oct. 1995.
[ 28]D. Majstorovic, I. Celanovic, N. D. Teslic,N. Celanovic, V. A. Katic, "Ultralow-latencyhardware-in-the-loop platform for rapid validation ofpower electronics designs",IEEE Transactions onIndustrial Electronics, vol. 58, no. 10, pp. 4708-4716,may 2011. https://doi.org/10.1109/TIE.2011.2112318 DOI: https://doi.org/10.1109/TIE.2011.2112318
[ 29]H. Gholizade-Narm, S. A. Khajehoddin, M. Karimi-Ghartemani, "Reduced-Order Controllers UsingIntegrated Controller-Plant Dynamics Approach forGrid-Connected Inverters",IEEE Transactions onIndustrial Electronics, vol. 68, no. 8, pp. 7444-7453,jul. 2021. https://doi.org/10.1109/TIE.2020.3007119 DOI: https://doi.org/10.1109/TIE.2020.3007119
[ 30]O. Kukrer, S. Bayhan, H. Komurcugil, "Model-basedcurrent control strategy with virtual time constant or improved dynamic response of three-phase grid-connected VSI",IEEE Transactions on IndustrialElectronics, vol. 66, no. 6, pp. 4156-4165, aug. 2019 https://doi.org/10.1109/TIE.2018.2863195 DOI: https://doi.org/10.1109/TIE.2018.2863195
[ 31]E. Standard, "50160",Voltage characteristics of publicdistribution systems, p. 18, jul. 2010.
[ 32]R. Cardoso, R. F. de Camargo, H. Pinheiro, H. A.Gründling, "Kalman filter based synchronisationmethods",IET generation, transmission&distribution, vol. 2, no. 4, pp. 542-555, jul. 2008 https://doi.org/10.1049/iet-gtd:20070281 DOI: https://doi.org/10.1049/iet-gtd:20070281
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Revista Eletrônica de Potência
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.