Optimal Adaptive Robust Pitch Control with Load Mitigation for Uncertain Variable Speed Wind Turbines

Document Type : Research Article


Department of Electrical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran


In this paper, an optimal adaptive robust pitch controller is proposed for variable speed wind turbines (VSWTs). The proposed pitch controller has stability analysis, while it simultaneously keeps the generated power of the wind turbine at the rated power and mitigates the mechanical loads on the gearbox. The proposed pitch controller in this paper has two terms. The first term is a radial basis function neural network (RBFNN), to approximate unknown nonlinear functions of the wind turbine. Another term is a chattering-free continuous robust structure, which can cope with the approximation error. The weights of RBFNN and the gain of the robust structure are derived via the Lyapunov synthesis approach. It is proved that the closed-loop signals are semi-globally uniformed and ultimately bounded. The optimal parameters of the proposed controller are derived by solving a proposed multi-objective optimization problem using non-dominated sorting genetic algorithm-II (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm. The effectiveness of the proposed controller is compared to the baseline PI controller designed by NREL. First, both the proposed and the baseline PI controllers are applied to the general model (2-mass model) of the wind turbine, and then they are validated via a highly reliable simulator called FAST. The results demonstrate the effectiveness and applicability of the proposed pitch controller.


Main Subjects

[1] Z. Wang, Z. Shen, C. Cai, K. Jia, Adaptive control of wind turbine generator system based on RBF-PID neural network, in:  2014 International Joint Conference on Neural Networks (IJCNN), IEEE, 2014, pp. 538-543.
[2] F. Jaramillo-Lopez, G. Kenne, F. Lamnabhi-Lagarrigue, A novel online training neural network-based algorithm for wind speed estimation and adaptive control of PMSG wind turbine system for maximum power extraction, Renewable Energy, 86 (2016) 38-48.
[3] H. Jafarnejadsani, L1-optimal control of variable-speed variable-pitch wind turbines, University of Calgary,  (2013).
[4] Q. Luo, Q. Yang, C. Han, P. Cheng, Pitch angle controller of variable-speed wind turbine based on L 1 adaptive control theory, in:  2014 International Conference on Mechatronics and Control (ICMC), IEEE, 2014, pp. 955-960.
[5] A. Mazinan, R. Ghasemzadeh, Application of Adaptive Nonsingular Sliding Mode Control Approach to Wind Turbine Grid Fault-Tolerance, in:  2017 International Conference on Computer and Applications (ICCA), IEEE, 2017, pp. 74-78.
[6] X.D. Zhang, G.Q. Wu, J.F. Mao, K. Yang, Self Adaptive Integral-Type Sliding Mode Control for Supporting Structure of a Magnetic Vertical Axis Wind Turbine, in:  Applied Mechanics and Materials, Trans Tech Publ, 2012, pp. 90-94.
[7] X. Yao, Yingming Liu, and Changchun Guo, Adaptive fuzzy sliding-mode control in variable speed adjustable pitch wind turbine, IEEE International Conference on Automation and Logistics,  (2007).
[8] E.K. El Mjabber, A. El Hajjaji, A. Khamlichi, A hybrid adaptive controller based on sliding mode control and RBF neural network for variable speed wind turbine, International Review of Applied Sciences and Engineering, 7(2) (2016) 61-70.
[9] S.M. Arbatsofla, A. Toloei, F. Soudagary, A. Naseri, DFIG wind turbine control despite the uncertainties in the model using high-order adaptive sliding, in:  2017 Smart Grid Conference (SGC), IEEE, 2017, pp. 1-7.
[10] H. Dastres, A. Mohammadi, M. Shamekhi, A Neural Network Based Adaptive Sliding Mode Controller for Pitch Angle Control of a Wind Turbine, in:  2020 11th Power Electronics, Drive Systems, and Technologies Conference (PEDSTC), IEEE, 2020, pp. 1-6.
[11] X. Yin, W. Zhang, Z. Jiang, L. Pan, Adaptive robust integral sliding mode pitch angle control of an electro-hydraulic servo pitch system for wind turbine, Mechanical Systems and Signal Processing, 133 (2019) 105704.
[12] M. Kamarzarrin, M.H. Refan, Intelligent Sliding Mode Adaptive Controller Design for Wind Turbine Pitch Control System Using PSO-SVM in Presence of Disturbance, Journal of Control, Automation and Electrical Systems,  (2020) 1-14.
[13] V. Azimi, M.B. Menhaj, Output Electrical Power Control of Horizontal Axis Wind Turbine Using Indirect Model Reference Adaptive Neuro Controller, Majlesi Journal of Electrical Engineering, 9(2) (2015) 11-26.
[14] X. Wang, W. Gao, T. Gao, Q. Li, J. Wang, X. Li, Robust Model Reference Adaptive Control Design for Wind Turbine Speed Regulation Simulated by Using FAST, Journal of Energy Engineering, 144(2) (2018) 04018007.
[15] S. Frost, M. Balas, A. Wright, Adaptive control of a utility-scale wind turbine operating in region 3, in:  47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, 2009, pp. 480.
[16] S. Frost, M. Balas, A. Wright, Modified adaptive control for region 3 operation in the presence of wind turbine structural modes, in:  48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010, pp. 249.
[17] R. Sakamoto, T. Senjyu, T. Kinjo, N. Urasaki, T. Funabashi, Output power leveling of wind turbine generator by pitch angle control using adaptive control method, in:  2004 International Conference on Power System Technology, 2004. PowerCon 2004., IEEE, 2004, pp. 834-839.
[18] A. Hatami, B. Moetakef-Imani, Innovative adaptive pitch control for small wind turbine fatigue load reduction, Mechatronics, 40 (2016) 137-145.
[19] J.-S. Kim, J. Jeon, H. Heo, Design of adaptive PID for pitch control of large wind turbine generator, in:  2011 10th International Conference on Environment and Electrical Engineering, IEEE, 2011, pp. 1-4.
[20] J. Maknunah, A. Musyafa’, I. Abadi, Control system design of adaptive wind turbine pitch angle using particle swarm optimization algorithm, in:  AIP Conference Proceedings, AIP Publishing, 2019, pp. 020021.
[21] R. Galeazzi, K.T. Borup, H. Niemann, N.K. Poulsen, F. Caponetti, Adaptive backstepping control of lightweight tower wind turbine, in:  2015 American Control Conference (ACC), IEEE, 2015, pp. 3058-3065.
[22] X.-x. Yin, Y.-g. Lin, W. Li, Y.-j. Gu, P.-f. Lei, H.-w. Liu, Adaptive back-stepping pitch angle control for wind turbine based on a new electro-hydraulic pitch system, International Journal of Control, 88(11) (2015) 2316-2326.
[23] B. Bidikli, A robust adaptive control design for the rotor speed control of variable speed wind turbines, International Journal of Control,  (2019) 1-14.
[24] W. Yin, Xin Wu, and Xiaoming Rui, Adaptive robust backstepping control of the speed regulating differential mechanism for wind turbines, IEEE Transactions on Sustainable Energy (2018).
[25] H. Dong, L. Yang, G. Yin, H. Li, Wind turbine active power control based on multi-model adaptive control, International Journal of Control and Automation, 8(8) (2015) 273-284.
[26] H. Guo, Q. Guo, Research on Synchrodrive Control Technology for Wind Turbine Adjustable-Pitch System Based on Adaptive decoupling Control, in:  2006 CES/IEEE 5th International Power Electronics and Motion Control Conference, IEEE, 2006, pp. 1-5.
[27] M.J. Balas, N. Li, Adaptive Control of Flow Over Rotating Wind Turbine Blades Using the Beddoes-Leishman Dynamic Stall Model, in:  ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference, American Society of Mechanical Engineers, 2012, pp. 25-32.
[28] M. Balas, N. Li, Adaptive Control of Flow over a Wind Turbine Blades, in:  AIAA Atmospheric Flight Mechanics Conference, 2012, pp. 4857.
[29] N. Boumalha, R. Hachelef, D. Kouchih, M. Tadjine, M. Boucherit, Diagnostic and fault tolerant control by adaptive observer of doubly-fed induction generators with inter-turn rotor and stator fault based wind turbine, in:  2017 5th International Conference on Electrical Engineering-Boumerdes (ICEE-B), IEEE, 2017, pp. 1-6.
[30] H. Habibi, Hamed Rahimi Nohooji, and Ian Howard, Adaptive PID control of wind turbines for power regulation with unknown control direction and actuator faults, IEEE Access 6,  (2018).
[31] N. Li, M.J. Balas, Flutter Suppression of Wind Turbine Blade Using Adaptive Control, in:  ASME 2013 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, 2013, pp. V04AT04A007-V004AT004A007.
[32] N. Li, M.J. Balas, H. Yang, W. Jiang, Flow control and stability analysis of rotating wind turbine blade system, Journal of Guidance, Control, and Dynamics,  (2016).
[33] S. Frost, M. Balas, K. Goebel, A. Wright, Adaptive contingency control: Wind turbine operation integrated with blade condition monitoring, in:  50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2012, pp. 1155.
[34] T. Barlas, J.W. van Wingerden, A. Hulskamp, G. van Kuik, Closed-loop control wind tunnel tests on an adaptive wind turbine blade for load reduction, in:  46th AIAA Aerospace Sciences Meeting and Exhibit, 2008, pp. 1318.
[35] F. Asharif, S. Tamaki, T. Nagado, T. Nagtata, M.R. Asharif, Analysis of Non-linear Adaptive Friction and Pitch Angle Control of Small-Scaled Wind Turbine System, in:  Control and Automation, and Energy System Engineering, Springer, 2011, pp. 26-35.
[36] D. Li, Y. Song, W. Cai, P. Li, H.R. Karimi, Wind turbine pitch control and load mitigation using an adaptive approach, Mathematical Problems in Engineering, 2014 (2014).
[37] J. Lan, R.J. Patton, X. Zhu, Fault-tolerant wind turbine pitch control using adaptive sliding mode estimation, Renewable Energy, 116 (2018) 219-231.
[38] K.T. Magar, Mark J. Balas, and Susan A. Frost, Smooth transitioning of wind turbine operation between region II and region III with adaptive disturbance tracking control, Wind Engineering, 38.3 (2014) 337-348.
[39] Y. Yuan, J. Tang, Adaptive pitch control of wind turbine for load mitigation under structural uncertainties, Renewable Energy, 105 (2017) 483-494.
[40] A. Yaakoubi, K. Attari, L. Amhaimar, A. Asselman, Adaptive state feedback pitch angle control of wind turbines for speed regulation and blades loadings alleviation,  (2018).
[41] O. Barambones, J.M.G. DE DURANA, P. ALKORTA, J.A. RAMOS, M. DE LA SEN, Adaptive variable structure control law for a variable speed wind turbine, in:  Proceedings of the 13th WSEAS international conference on Automatic control, modelling & simulation, World Scientific and Engineering Academy and Society (WSEAS), 2011, pp. 21-27.
[42] V. Kumar, Navdeep Singh, and Bhanu Pratap, Adaptive pitch control design for variable speed wind turbine using chebyshev neural network, International Conference on Information, Communication, Instrumentation and Control (ICICIC),  (2017).
[43] X. Yin, Hybrid adaptive control for variable-speed variable-pitch wind energy systems using general regression neural network,  (2007).
[44] D. Deb, and Sukanya Sonowal, Synthetic jet actuator based adaptive neural network control of nonlinear fixed pitch wind turbine blades, IEEE International Conference on Control Applications (CCA),  (2013).
[45] J. Yang, J. Li, J. Wu, J. Yang, Fuzzy adaptive control of novel brushless doubly-fed wind turbine, in:  2006 6th World Congress on Intelligent Control and Automation, IEEE, 2006, pp. 8241-8245.
[46] H.-q. Yu, Y. Gao, H. Zhang, Fuzzy self-adaptive PID control of the variable speed constant frequency variable-pitch wind turbine system, in:  2014 IEEE International Conference on System Science and Engineering (ICSSE), IEEE, 2014, pp. 124-127.
[47] T.L. Van, N.K. Dang, X.N. Doan, T.H. Truong, H.N. Minh, Adaptive Fuzzy Logic Control to Enhance Pitch Angle Controller for Variable-Speed Wind Turbines, in:  2018 10th International Conference on Knowledge and Systems Engineering (KSE), IEEE, 2018, pp. 225-229.
[48] Y. Hocini, A. Allali, H.M. Boulouiha, Power fuzzy adaptive control for wind turbine, International Journal of Electrical and Computer Engineering (IJECE), 10(5) (2020) 5262-5273.
[49] H. Jafarnejadsani, J. Pieper, J. Ehlers, Adaptive control of a variable-speed variable-pitch wind turbine using radial-basis function neural network, IEEE transactions on control systems technology, 21(6) (2013) 2264-2272.
[50] P. Bagheri, Q. Sun, Adaptive robust control of a class of non-affine variable-speed variable-pitch wind turbines with unmodeled dynamics, ISA transactions, 63 (2016) 233-241.
[51] X. Jiao, W. Meng, Q. Yang, L. Fu, Q. Chen, Adaptive Continuous Neural Pitch Angle Control for Variableā€Speed Wind Turbines, Asian Journal of Control,  (2019).
[52] S. Li, D.C. Wunsch, E. O’Hair, M.G. Giesselmann, Comparative analysis of regression and artificial neural network models for wind turbine power curve estimation, J. Sol. Energy Eng., 123(4) (2001) 327-332.
[53] A.S. Yilmaz, Z. Özer, Pitch angle control in wind turbines above the rated wind speed by multi-layer perceptron and radial basis function neural networks, Expert Systems with Applications, 36(6) (2009) 9767-9775.
[54] C.C. Coello, M.S. Lechuga, MOPSO: A proposal for multiple objective particle swarm optimization, in:  Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No. 02TH8600), IEEE, 2002, pp. 1051-1056.
[55] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE transactions on evolutionary computation, 6(2) (2002) 182-197.
[56] J. Jonkman, S. Butterfield, W. Musial, G. Scott, Definition of a 5-MW reference wind turbine for offshore system development, National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/TP-500-38060,  (2009).
[57] T. Esbensen, B. Jensen, M. Niss, C. Sloth, J. Stoustrup, Joint power and speed control of wind turbines, Aalborg University, Aalborg, 120 (2008).
[58] B. Boukhezzar, H. Siguerdidjane, Nonlinear control of a variable-speed wind turbine using a two-mass model, IEEE Transactions on Energy Conversion, 26(1) (2011) 149-162.
[59] J. Park, I.W. Sandberg, Universal approximation using radial-basis-function networks, Neural computation, 3(2) (1991) 246-257.
[60] H. Jafarnejadsani, J.K. Pieper, J. Ehlers, Adaptive Control of a Variable-Speed Variable-Pitch Wind Turbine Using Radial-Basis Function Neural Network, IEEE Trans. Contr. Sys. Techn., 21(6) (2013) 2264-2272.
[61] A. Di Crescenzo, A probabilistic analogue of the mean value theorem and its applications to reliability theory, Journal of Applied Probability, 36(3) (1999) 706-719.
[62] M.M. Polycarpou, P.A. Ioannou, A robust adaptive nonlinear control design, in:  1993 American Control Conference, IEEE, 1993, pp. 1365-1369.
[63] R. Shahnazi, N. Pariz, A.V. Kamyad, Adaptive fuzzy output feedback control for a class of uncertain nonlinear systems with unknown backlash-like hysteresis, Communications in Nonlinear Science and Numerical Simulation, 15(8) (2010) 2206-2221.
[64] H.K. Khalil, Nonlinear systems, Upper Saddle River,  (2002).
[65] C.A.C. Coello, G.B. Lamont, D.A. Van Veldhuizen, Evolutionary algorithms for solving multi-objective problems, Springer, 2007.
[66] C.A.C. Coello, G.T. Pulido, M.S. Lechuga, Handling multiple objectives with particle swarm optimization, IEEE Transactions on evolutionary computation, 8(3) (2004) 256-279.
[67] D. Jung, Y. Choi, J. Kim, Multiobjective automatic parameter calibration of a hydrological model, Water, 9(3) (2017) 187.
[68] M. Reyes-Sierra, C.C. Coello, Multi-objective particle swarm optimizers: A survey of the state-of-the-art, International journal of computational intelligence research, 2(3) (2006) 287-308.
[69] I.E. Commission, IEC 61400-1: Wind turbines part 1: Design requirements, International Electrotechnical Commission,  (2005).
[70] J.R. Schott, Fault tolerant design using single and multicriteria genetic algorithm optimization, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH, 1995.
[71] D. Van der Merwe, A.P. Engelbrecht, Data clustering using particle swarm optimization, in:  The 2003 Congress on Evolutionary Computation, 2003. CEC'03., IEEE, 2003, pp. 215-220.