Document Type: Research paper

**Authors**

Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran

**Abstract**

Model predictive control (MPC) based methods are gaining more and more attention in power converters and electrical drives. Nevertheless, high computational burden of MPC is an obstacle for its application, especially when the prediction horizon increases extends. At the same time, increasing the prediction horizon leads to a superior response. In this paper, a long horizon MPC is proposed to control the power converter employed in the rotor side of DFIG. The main contribution of this paper is to propose a new comparative algorithm to speed up the optimization of the objective function. The proposed algorithm prevents examining all inputs in each prediction step to saving the computational time. Additionally, the proposed method along with the use of an incremental algorithm applies a sequence of weighting factors in the cost function over the prediction horizon to maximize the impact of primary samples on the optimal vector selection. Therefore, the proposed MPC strategy can predict a longer horizon with relatively low computational burden. Finally, results show that the proposed controller has the fastest dynamic response with lower overshoots compared to direct torque control and vector control method. In addition, the proposed strategy with more accurate response reduces the calculation time by up to 48% compared to classical MPC, for the prediction horizon of three.

**Keywords**

- Model predictive control
- Computational effort
- Doubly fed induction generator, Wind energy conversion system.

**Main Subjects**

[1] L. L. Rodrigues, O. A. C. Vilcanqui, A. L. L. F. Murari, and A. J. S. Filho, "Predictive power control for DFIG: A FARE-based weighting matrices approach," *IEEE J. Emerging Sel. Top. Power Electron., *vol. 7, pp. 967-975, 2019.

[2] S. Wang and L. Shang, "Fault ride through strategy of virtual-synchronous-controlled DFIG-based wind turbines under symmetrical grid faults," *IEEE Trans. Energy Convers. *pp. 1-1, 2020.

[3] A. Nafar, G. R. Arab Markadeh, A. Elahi, and R. pouraghababa, "Low voltage ride through enhancement based on improved direct power control of DFIG under unbalanced and harmonically distorted grid voltage," *J. Oper. Autom. Power Eng., *vol. 4, pp. 16-28, 06/01 2016.

[4] R. Pena, J. C. Clare, and G. M. Asher, "Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation," *IEE Proc.: Electr. Power Appl., *vol. 143, pp. 231-241, 1996.

[5] A. Tapia, G. Tapia, J. X. Ostolaza, and J. R. Saenz, "Modeling and control of a wind turbine driven doubly fed induction generator," *IEEE Trans. Energy Convers., *vol. 18, pp. 194-204, 2003.

[6] K. K. Jaladi and K. S. Sandhu, "A new hybrid control scheme for minimizing torque and flux ripple for DFIG-based WES under random change in wind speed," *Int. Trans. Electr. Energy Syst., *vol. 0, p. e2818.

[7] G. Abad, M. Á. Rodriguez, and J. Poza, "Two-level VSC based predictive direct torque control of the doubly fed induction machine with reduced torque and flux ripples at low constant switching frequency," *IEEE Trans. Power Electron., *vol. 23, pp. 1050-1061, 2008.

[8] X. Wang and D. Sun, "Three-vector-based low-complexity model predictive direct power control strategy for doubly fed induction generators," *IEEE Trans. Power Electron., *vol. 32, pp. 773-782, 2017.

[9] I. Takahashi and T. Noguchi, "A new quick-response and high-efficiency control strategy of an induction motor," *IEEE Trans. Ind. Appl., *vol. IA-22, pp. 820-827, 1986.

[10] S. Arnalte, J. C. Burgos, and J. L. Rodríguez-Amenedo, "direct torque control of a doubly-fed induction generator for variable speed wind turbines," *Electr. Power Compon. Syst. , *vol. 30, pp. 199-216, 2002/02/01 2002.

[11] A. Izanlo, Gholamian, S.A. & Kazemi, M.V., "Using of four-switch three-phase converter in the structure DPC of DFIG under unbalanced grid voltage condition," *Electr. Eng., *vol. 100, pp. 1925-1938, 2018.

[12] S. A. Davari, D. A. Khaburi, and R. Kennel, "An improved MPC algorithm for an induction motor with an imposed optimized weighting factor," *IEEE Trans. Power Electr-on., *vol. 27, pp. 1540-1551, 2012.

[13] S. A. Davari, D. A. Khaburi, F. Wang, and R. M. Kennel, "Using full order and reduced order observers for robust sensorless predictive torque control of induction motors," *IEEE Trans. Power Electron., *vol. 27, pp. 3424-3433, 2012.

[14] F. Niu, K. Li, and Y. Wang, "Direct torque control for permanent-magnet synchronous machines based on duty ratio modulation," *IEEE Trans. Ind. Electron., *vol. 62, pp. 6160-6170, 2015.

[15] K. C. Wong, S. L. Ho, and K. W. E. Cheng, "Direct torque control of a doubly-fed induction generator with space vector modulation," *Electr. Power Compon. Syst., *vol. 36, pp. 1337-1350, 2008.

[16] M. R. A. Kashkooli, S. M. Madani, and R. Sadeghi, "Improved direct torque control of DFIG with reduced torque and flux ripples at constant switching frequency," Proc. *7*^{th} Power Electron. Drive Syst. Tech. Conf. (PEDSTC), 2016, pp. 58-63.

[17] D. Zhi and L. Xu, "direct power control of DFIG with constant switching frequency and improved transient performance," *IEEE Trans. Energy Convers., *vol. 22, pp. 110-118, 2007.

[18] A. Younesi, H. Shayeghi, M. Moradzadeh, “Application of reinforcement learning for generating optimal control signal to the IPFC for damping of low‐frequency oscilla-tions”, *Int Trans Electr. Energy Syst.*, vol. 28, no. 2, 2018.

[19] J. Liang, W. Qiao, and R. G. Harley, "Feed-forward transient current control for low-voltage ride-through enh-ancement of DFIG wind turbines," *IEEE Trans. Energy Convers., *vol. 25, pp. 836-843, 2010.

[20] H. M. Jabr, D. Lu, and N. C. Kar, "Design and implementation of neuro-fuzzy vector control for wind-driven doubly-fed induction generator," *IEEE Trans. Sustainable Energy, *vol. 2, pp. 404-413, 2011.

[21] S. A. E. M. Ardjoun, M. Denai, and M. Abid, "A robust power control strategy to enhance LVRT capability of grid-connected DFIG-based wind energy systems," *Wind Energy, *vol. 22, no. 6, 2019.

[22] X. Liu, Y. Han, and C. Wang, "Second-order sliding mode control for power optimisation of DFIG-based variable speed wind turbine," *IET Renewable Power Gener., *vol. 11, pp. 408-418, 2017.

[23] D. Sun, X. Wang, H. Nian, and Z. Q. Zhu, "A sliding-mode direct power control strategy for DFIG under both balanced and unbalanced grid conditions using extended active power," *IEEE Trans. Power Electron., *vol. 33, pp. 1313-1322, 2018.

[24] H. Chaoui and P. Sicard, "Adaptive fuzzy logic control of permanent magnet synchronous machines with nonlinear friction," *IEEE Trans. Ind. Electron., *vol. 59, pp. 1123-1133, 2012.

[25] J. Yang, W. H. Chen, S. Li, L. Guo, and Y. Yan, "Disturbance/Uncertainty Estimation and Attenuation Techniques in PMSM drives; a survey," *IEEE Trans. Ind. Electron., *vol. PP, pp. 1-1, 2016.

[26] R. Ajabi-Farshbaf, M. R. Azizian, and V. Yousefizad, "A novel algorithm for rotor speed estimation of DFIGs using machine active power based MRAS observer," *J. Oper. Autom. Power Eng., *vol. 6, pp. 61-68, 2018.

[27] M. Preindl and S. Bolognani, "Model predictive direct speed control with finite control set of PMSM drive systems," *IEEE Trans. Power Electron., *vol. 28, pp. 1007-1015, 2013.

[28] Y. Venkata and W. Bin, "Overview of digital control techniques," Proc. *Model Predict. Control Wind Energy Convers. Syst.*, ed: Wiley-IEEE Press, 2017, p. 512.

[29] M. Khosravi, M. Amirbande, D. A. Khaburi, M. Rivera, J. Riveros, J. Rodriguez*, et al.*, "Review of model predictive control strategies for matrix converters," *IET Power Electron., *vol. 12, pp. 3021-3032, 2019.

[30] M. J. Khodaei, N. Candelino, A. Mehrvarz, and N. Jalili, "Physiological closed-loop control (PCLC) systems: review of a modern frontier in automation," *IEEE Access, *vol. 8, pp. 23965-24005, 2020.

[31] A. Bahrami, M. Narimani, M. Norambuena, and J. Rodriguez, "Current control of a seven-level voltage source inverter," *IEEE Trans. Power Electron., *vol. 35, pp. 2308-2316, 2020.

[32] A. Younesi, S. Tohidi, M. R. Feyzi, and M. Baradarannia, "An improved nonlinear model predictive direct speed control of permanent magnet synchronous motors," *Int. Trans. Electr. Energy Syst., *vol. 28, p. e2535, 2018.

[33] J. Z. Lu, "Closing the gap between planning and control: A multiscale MPC cascade approach," *Annu. Rev. Control, *vol. 40, pp. 3-13, // 2015.

[34] J. Fallah Ardashir, M. Sabahi, S. H. Hosseini, E. Babaei, and G. B. Gharehpetian, "A grid connected transformerles-s inverter and its model predictive control strategy with leakage current elimination capability," *Iran. J. Electr. Electron. Eng., *vol. 13, pp. 161-169, 2017.

[35] C. Cheng and H. Nian, "Low-complexity model predictive stator current control of DFIG under harmonic grid voltages," *IEEE Trans. Energy Convers., *vol. 32, pp. 1072-1080, 2017.

[36] S. Kim, R. Kim, and S. Kim, "Generalized model predictive control method for single-phase N-level flying capacitor multilevel rectifiers for solid state transformer," *IEEE Trans. Ind. Appl., *vol. 55, pp. 7505-7514, 2019.

[37] M. Majstorović, M. E. R. Abarca, and L. Ristic, "Review of MPC techniques for MMCs," Proc. *20*^{th} Int. Symp. Power Electron., 2019, pp. 1-7.

[38] Y. Zhang, J. Jiao, D. Xu, D. Jiang, Z. Wang, and C. Tong, "Model predictive direct power control of doubly fed induction generators under balanced and unbalanced network conditions," *IEEE Trans. Ind. Appl., *vol. 56, pp. 771-786, 2020.

[39] B. Hu, L. Kang, J. Cheng, Z. Zhang, J. Zhang, and X. Luo, "Double-step model predictive direct power control with delay compensation for three-level converter," *IET Power Electron., *vol. 12, pp. 899-906, 2019.

[40] M. Moazen, R. Kazemzadeh, and M. R. Azizian, "A model-based PDPC method for control of BDFRG under unbalanced grid voltage condition using power compensa-tion strategy," *J. Oper. Autom. Power Eng., *pp. 1-13, 2019.

[41] P. Kou, D. Liang, J. Li, L. Gao, and Q. Ze, "Finite-control-set model predictive control for DFIG wind turbines," *IEEE Trans. Autom. Sci. Eng., *vol. 15, pp. 1004-1013, 2018.

[42] L. L. Rodrigues, A. S. Potts, O. A. C. Vilcanqui, and A. J. S. Filho, "Tuning a model predictive controller for doubly fed induction generator employing a constrained genetic algorithm," *IET Electr. Power Appl., *vol. 13, pp. 819-826, 2019.

[43] A. Younesi, S. Tohidi, and M. R. Feyzi, "Improved optimization process for nonlinear model predictive control of PMSM," *Iran. J. of Electr. Electron. Eng., *vol. 14, no. 3, pp. 278-288, 2018.

[44] Y. Venkata and W. Bin, "Control of DFIG wecs with voltage source converters," Proc. *Model Predict. Control Wind Energy Convers. Syst.*, ed: Wiley-IEEE Press, 2017, p. 512.

[45] Y. Venkata and W. Bin, "Chapter appendices," Proc. *Model Predict. Control Wind Energy Convers. Syst.*, ed: IEEE, 2017, p. 1.

[46] M. M. Vayeghan and S. A. Davari, "Torque ripple reduction of DFIG by a new and robust predictive torque control method," *IET Renewable Power Gener., *vol. 11, pp. 1345-1352, 2017.

[47] X. Lie and P. Cartwright, "Direct active and reactive power control of DFIG for wind energy generation," *IEEE Trans. Energy Convers., *vol. 21, pp. 750-758, 2006.

[48] T. Yifan and X. Longya, "A flexible active and reactive power control strategy for a variable speed constant frequency generating system," *IEEE Trans. Power Electron., *vol. 10, pp. 472-478, 1995.

Volume 8, Issue 2

Summer 2020

Pages 172-181

**Receive Date:**01 December 2019**Revise Date:**29 March 2020**Accept Date:**12 April 2020