Robust power stabilizing control of a grid-connected inverter using linear matrix inequality

Year 2024, Volume: 42 Issue: 5, 1367 - 1377, 04.10.2024

Panha Soth , Sokleng Noun Heng Tang Chanmoly Or Sarot Srang Yahya Danayiyen , Chivon Choeung

Abstract

A linear matrix inequality (LMI)-based robust stabilizing control is proposed in this paper for a three-phase grid-connected inverter (GCI) with L-filtered output. Previous research, such as MPC, required high computational power and precise modeling in order to obtain offset-free performance. Achieving optimal performance in the case of PI control poses a persistent chal-lenge in terms of gain tuning. This proposed control strategy effectively addresses the afore-mentioned issues by the utilization of systematic control design, incorporating integral action to mitigate the presence of offset error. The set of state feedback and integral gain is obtained by solving the LMI-based optimization problem to maximize the convergence rate to a steady state in the presence of uncertainty in the L-filter. The mentioned uncertainties are represent-ed by potential ranges of the inductor values. Output power delivery can be simply regulated by a computed reference state using a given power reference and measured grid current and voltage. The effectiveness of the proposed method is verified through simulations. The pro-posed robust control method demonstrates a significant decrease in ripple, with a reduction of 86.66% when compared to the conventional PI control approach.

Keywords

Grid-Connected Inverter, Linear Matrix Inequality (LMI), Robust Power Control

References

• REFERENCES
• [1] Al-Dori O, Şakar B, Dönük A. Comprehensive analysis of losses and leakage reactance of distribution transformers. Arab J Sci Eng 2022;47:1416314171. [CrossRef]
• [2] Dönük A, Al-Dori̇ O. Performance and harmonic analysis of a three-phase induction motor with various coil pitch configurations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 2023;28:3847. [CrossRef]
• [3] Al-Dori O, Şakar B, Dönük A. Optimal design and performance analysis of three-phase distribution transformer with variable loading. Electric Power Compon Syst 2022;50:458468. [CrossRef]
• [4] Huang L, Wu C, Zhou D, Blaabjerg F. Impact of grid strength and impedance characteristics on the maximum power transfer capability of grid-connected inverters. Appl Sci 2021;11:4288. [CrossRef]
• [5] Etxegarai A, Eguia P, Torres E, Iturregi A, Valverde V. Review of grid connection requirements for generation assets in weak power grids. Renew Sustain Energy Rev 2015;41:15011514. [CrossRef]
• [6] Collins L, Ward JK. Real and reactive power control of distributed PV inverters for overvoltage prevention and increased renewable generation hosting capacity. Renew Energy. 2015;81:464471. [CrossRef]
• [7] Chen J, Yang F, Han QL. Model-free predictive H∞ control for grid-connected solar power generation systems. IEEE Trans Contr Syst Technol 2014;22:20392047. [CrossRef]
• [8] Liao H, Zhang X, Ma Z. Robust dichotomy solution-based model predictive control for the grid-connected inverters with disturbance observer. Trans Electr Mach Syst 2021;5:8189. [CrossRef]
• [9] Song Z, Chen W, Xia C. Predictive direct power control for three-phase grid-connected converters without sector information and voltage vector selection. IEEE Trans Power Electron 2014;29:55185531. [CrossRef]
• [10] Judewicz MG, Gonzalez SA, Fischer JR, Martinez JF, Carrica DO. Inverter-side current control of grid-connected voltage source inverters with LCL filter based on generalized predictive control. IEEE J Emerg Sel Topics Power Electron 2018;6:17321743. [CrossRef]
• [11] Kim Y, Tran TV, Kim KH. LMI-based model predictive current control for an LCL-filtered grid-connected inverter under unexpected grid and system uncertainties. Electronics 2022;11:731. [CrossRef]
• [12] Qin G, Chen Q, Zhang L. Finite control set model predictive control based on three-phase four-leg grid-connected inverters. 2020 35th Youth Academic Annual Conference of Chinese Association of Automation (YAC), Zhanjiang, China: IEEE; 2020. p. 680684. [CrossRef]
• [13] Moreno JC, Espi Huerta JM, Gil RG, Gonzalez SA. A robust predictive current control for three-phase grid-connected inverters. IEEE Trans Ind Electron 2009;56:19932004. [CrossRef]
• [14] Espi Huerta JM, Castello-Moreno J, Fischer JR, Garcia-Gil R. A synchronous reference frame robust predictive current control for three-phase grid-connected inverters. IEEE Trans Ind Electron 2010;57:954962. [CrossRef]
• [15] Ma L, Zheng TQ. Synchronous PI control for three-phase grid-connected photovoltaic inverter. 2010 Chinese Control and Decision Conference, Xuzhou, China: IEEE; 2010. p. 23022307. [CrossRef]
• [16] Alqatamin M, Latham J, Smith ZT, Grainger BM, McIntyre ML. Current control of a three-phase, grid-connected inverter in the presence of unknown grid parameters without a phase-locked loop. IEEE J Emerg Sel Topics Power Electron 2021;9:31273136. [CrossRef]
• [17] Mirhosseini M, Pou J, Agelidis VG. Current improvement of a grid-connected photovoltaic system under unbalanced voltage conditions. 2013 IEEE ECCE Asia Downunder, Melbourne, Australia: IEEE; 2013. p. 6672. [CrossRef]
• [18] Liu J, Wu W, Chung HS-H, Blaabjerg F. Disturbance observer-based adaptive current control with self-learning ability to improve the grid-injected current for LCL-filtered grid-connected inverter. IEEE Access 2019;7:105376105390. [CrossRef]
• [19] Yoon SJ, Lai NB, Kim KH. A systematic controller design for a grid-connected inverter with LCL filter using a discrete-time integral state feedback control and state observer. Energies 2018;11:437. [CrossRef]
• [20] Pena JCU, Sampaio LP, Canesin CA. A LMI-based control of a three-phase voltage source inverter capable to operate in islanded and grid connected modes. 2015 IEEE 13th Brazilian Power Electronics Conference and 1st Southern Power Electronics Conference (COBEP/SPEC), Fortaleza: IEEE; 2015. p. 16. [CrossRef]
• [21] Lim JS, Park C, Han J, Lee YI. Robust tracking control of a three-phase DC–AC inverter for UPS applications. IEEE Trans Ind Electron 2014;61:4142151. [CrossRef]
• [22] Barden AT, Alves Pereira LF. Robust control design of multiple resonant controllers applied to three-phase UPS inverter under unbalanced and nonlinear loads. IECON 2015 - 41st Annual Conference of the IEEE Industrial Electronics Society, Yokohama: IEEE; 2015. p. 001483001488. [CrossRef]
• [23] Danayiyen Y, Lee K, Choi M, Lee YI. Model predictive control of uninterruptible power supply with robust disturbance observer. Energies 2019;12:2871. [CrossRef]
• [24] Kim SK, Park CR, Yoon TW, Lee YI. Disturbance-observer-based model predictive control for output voltage regulation of three-phase inverter for uninterruptible-power-supply applications. Eur J Control 2015;23:7183. [CrossRef]
• [25] Huy V, Tang H, Soth P, Yay S, Sovan K, Choeung C. Three-phase inverter using robust tracking control based interpolation. 2023 Third International Symposium on Instrumentation, Control, Artificial Intelligence, and Robotics (ICA-SYMP), Bangkok, Thailand: IEEE; 2023. p. 9195. [CrossRef]
• [26] Saggin F, Coutinho D, Heldwein ML. Parallel operation of single-phase voltage source inverters: Modeling and control based on LMI constraints. IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society, Florence, Italy: IEEE; 2016. p. 270275. [CrossRef]
• [27] Choeung C, Kry ML, Lee YI. Robust tracking control of a three-phase bidirectional charger for electric vehicle. J Adv Transp 2022;2022:112. [CrossRef]
• [28] Fitri I, Kim JS, Song H. A robust suboptimal current control of an interlink converter for a hybrid AC/DC microgrid. Energies 2018;11:1382. [CrossRef]
• [29] Choeung C, Tang H, Soth P, Keo S, Leang P, Cheng H, et al. Linear matrix inequality-based optimal state feedback control of a three-phase L-filtered grid-connected inverter. 2023 Third International Symposium on Instrumentation, Control, Artificial Intelligence, and Robotics (ICA-SYMP), Bangkok, Thailand: IEEE; 2023. p. 135139. [CrossRef]
• [30] Soth P, Tang H, So B, San S, Cheng H, Choeung C, et al. Robust dual-current control of a three-phase grid-tied inverter under unbalanced grid voltage using LMI approach. 2023 International Electrical Engineering Congress (iEECON), Krabi, Thailand: IEEE; 2023. p. 611. [CrossRef]
• [31] Choeung C, Kry ML, Lee YI. Robust tracking control of a three-phase charger under unbalanced grid conditions. Energies 2018;11:3389. [CrossRef]
• [32] Açıkmeşe AB, Corless M. Robust output tracking for uncertain/nonlinear systems subject to almost constant disturbances. Automatica 2002;38:19191926. [CrossRef]
• [33] Boyd SP, editor. Linear matrix inequalities in system and control theory. Philadelphia: Society for Industrial and Applied Mathematics; 1994. [CrossRef]
• [34] Lofberg J. YALMIP: a toolbox for modeling and optimization in MATLAB. 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), Taipei, Taiwan: IEEE; 2004. p. 284289.
• [35] Tang H, In S, Soth P, Soeng S, Cheng H, Huy V, et al. Design of a robust control for a single-phase AC-DC converter using LMI technique. 2023 International Electrical Engineering Congress (iEECON), Krabi, Thailand: IEEE; 2023. p. 15. [CrossRef]