Research Papers

Stability of Wind Turbine Switching Control in an Integrated Wind Turbine and Rechargeable Battery System: A Common Quadratic Lyapunov Function Approach

[+] Author and Article Information
Christine Mecklenborg

Graduate Student

Dongmei Chen

Assistant Professor
e-mail: dmchen@me.utexas.edu
Department of Mechanical Engineering,
University of Texas,
Austin, TX 78712

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received January 29, 2011; final manuscript received August 2, 2012; published online February 21, 2013. Assoc. Editor: Nader Jalili.

J. Dyn. Sys., Meas., Control 135(2), 021018 (Feb 21, 2013) (9 pages) Paper No: DS-11-1021; doi: 10.1115/1.4023059 History: Received January 29, 2011; Revised August 02, 2012

The power generated by wind turbines varies due to variations in the wind speed. A pack of rechargeable batteries could be used as a reserve power source to alleviate the intermittency in the wind turbine power. An integrated wind turbine and battery storage system is constructed where the wind turbine is electrically connected to a rechargeable battery system. Such a system can operate in two modes depending on the wind speed, power demand, and battery limit. The switching conditions for the wind turbine to operate in multi-input, single-output and single-input, single-output control mode are discussed. Linearized approximations of the closed loop wind turbine system are derived in order to analyze the switching stability between control modes. Common quadratic Lyapunov function (CQLF) is established for both control modes to prove the system stability. Simulation results demonstrating system stability are also presented.

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US Department of Energy, 2010, “Funding Opportunity Announcement DE-FOA-0000290-GRIDS.”
Annual Energy Review, 2008, “United States Department of Energy,” Energy Information Administration,” Report No. DOE/EIA-0384.
World Wind Energy Association, 2009, “ World Wind Energy Report 2008,” February.
Global Energy Concepts, LLC, 2003, “New Mexico Resources Assessment: Lee Ranch Data,” Online Abstracts and Reports, Sandia National Laboratories.
Young, M., and Vilhauer, R., 2003, “Sri Lanka Wind Farm Analysis and Site Selection Assistance,” National Renewable Energy Laboratory, Report No. NREL/SR-710-34646.
Hansen, L. H., Helle, L., Blaabjerg, F., Ritchie, E., Munk-Nielsen, S., Bindner, H., Sorensen, P., and Bak-Jensen, B., 2001, “Conceptual Survey of Generators and Power Electronics for Wind Turbines,” Report of Riso National Laboratory, Roskilde, Denmark.
Bose, B. K., 2000, “Energy, Environment, and Advances in Power Electronics,” IEEE Trans. Power Electron., 15(4), pp. 688–701. [CrossRef]
Bueno, C., and Carta, J. A., 2006, “Wind Powered Pumped Hydro Storage Systems, a Means of Increasing the Penetration of Renewable Energy in the Canary Islands,” Renewable Sustainable Energy Rev., 10(4), pp. 312–340. [CrossRef]
Finley, B., 2005, “Compressed Air Wind Energy Storage,” Energy Bulletin, Nov. 27, http://www.energybulletin.net/stories/2005-11-27/compressed-air-wind-energy-storage
Bullough, C., Gatzen, C., Jakiel, C., Koller, M., Nowi, A., and Zunft, S., 2004, “Advanced Adiabatic Compressed Air Energy Storage for the Integration of Wind Energy,” Proceedings of the European Wind Energy Conference (EWEC 2004), London, UK, Nov. 22–25.
Chu, S., 2009, “Investing in Our Energy Future,” Presentation of Grid Week, Washington, DC, Sep. 21.
Ibrahim, H., Ilinca, A., and Perron, J., 2008, “Energy Storage Systems—Characteristics and Comparisons,” Renewable Sustainable Energy Rev., 12(5), pp. 1221–1250. [CrossRef]
Battaglini, A., Lilliestam, J., Haas, A., and Patt, A., 2009, “Development of SuperSmart Grids for a More Efficient Utilisation of Electricity From Renewable Sources,” J. Cleaner Prod., 17(10), pp. 911–918. [CrossRef]
Johnson, K. E., Pao, L. Y., Balas, M. J., and Fingersh, L. J., 2006, “Control of Variable-Speed Wind Turbines: Standard and Adaptive Techniques for Maximizing Energy Capture,” IEEE Control Syst. Mag., 26(3), pp. 70–81. [CrossRef]
Muljadi, E., and Butterfield, C. P., 1999, “Pitch-Controlled Variable-Speed Wind Turbine Generation,” 1999 IEEE Industry Applications Society Annual Meeting, Phoenix, AZ, Oct. 3–7. [CrossRef]
Creaby, J., Li, Y., and Seem, J. E., 2009, “Maximizing Wind Turbine Energy Capture Using Multivariable Extremum Seeking Control,” Wind Eng., 33(4), pp. 361–387. [CrossRef]
Shorten, R., Wirth, F., Mason, O., Wulff, K., and King, C., 2007, “Stability Criteria for Switched and Hybrid Systems,” SIAM Rev., 49(4), pp. 545–592. [CrossRef]
Siam, M. Z., and Krunz, M., 2009, “Channel Access Scheme for MIMO-Enabled Ad Hoc Networks With Adaptive Diversity/Multiplexing Gains,” Mobile Netw. Appl., 14(4), pp. 433–450 [CrossRef].
Coppel, W. A., 1978, “Dichotomies in Stability Theory,” Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin.
Dayawansa, W. P., and Martin, C. F., 1999, “A Converse Lyapunov Theorem for a Class of Dynamical Systems Which Undergo Switching,” IEEE Trans. Autom. Control, 44, pp. 751–760. [CrossRef]
Liberzon, D., and Morse, A. S., 1999, “Basic Problems in Stability and Design of Switched Systems,” IEEE Control Syst. Mag, 19, pp. 59–70. [CrossRef]
Molchanov, P., and Pyatnitskii, E. S., 1989, “Criteria of Asymptotic Stability of Differential and Difference Inclusions Encountered in Control Theory,” Syst. Control Lett., 13, pp. 59–64. [CrossRef]
Morse, S., 1996, “Supervisory Control of Families of Linear Set-Point Controllers, Part 1: Exact Matching,” IEEE Trans. Autom. Control, 41, pp. 1413–1431. [CrossRef]
Chesi, G., Colaneri, P., Geromel, J. C., Middleton, R., and Shorten, R., 2010, “Computing Upper-Bounds of the Minimum Dwell Time of Linear Switched Systems via Homogeneous Polynomial Lyapunov Functions,” Proceedings of 2010 American Control Conference.
Wicks, M. A., Peleties, P., and DeCarlo, R., 1994, “Construction of Piecewise Lyapunov Functions for Stabilising Switched Systems,” Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, pp. 3492–3497.
Zhai, G., Hu, B., Yasuda, K., and Michel, A. N., 2001, “Stability Analysis of Switched Systems With Stable and Unstable Subsystems: An Average Dwell Time Approach,” Int. J. Syst. Sci., 32(8), pp. 1055–1061. [CrossRef]
Chase, C., Serrano, J., and Ramadge, P., 1993, “Periodicity and Chaos From Switched Flow Systems: Contrasting Examples of Discretely Controlled Continuous Systems,” IEEE Trans. Autom. Control, 38, pp. 70–83. [CrossRef]
Blondel, V. D., and Tsitsiklis, J. N., 2000, “A Survey of Computational Complexity Results in Systems and Control,” Automatica, 36, pp. 1249–1274. [CrossRef]
Daubechies, I., and Lagarias, J. C., 1992, “Sets of Matrices All Finite Products of Which Converge,” Numer. Linear Algebra Appl., 161, pp. 227–263. [CrossRef]
Gurvits, L., 1995, “Stability of Discrete Linear Inclusion,” Linear Algebra Appl., 231, pp. 47–85. [CrossRef]
Lagarias, J., and Wang, Y., 1995, “The Finiteness Conjecture for the Generalized Spectral Radius of a Set of Matrices,” Linear Algebra Appl., 214, pp. 17–42. [CrossRef]
Wulff, K., Foy, J., and Shorten, R., 2003, “Comments on Periodic and Absolute Stability for Switched Linear Systems,” Proceedings of the American Control Conference (ACC), Denver, CO. [CrossRef]
Patel, M., 2006, Wind and Solar Power Systems Design, Analysis, and Operation, Taylor & Francis, Boca Raton, FL.
Hau, E., 2006, Wind Turbines: Fundamentals, Technologies, Application, Economics, Springer, Berlin.
Heier, S., 1998, Grid Integration of Wind Energy Conversion Systems, Wiley, New York.
Liberzon, D., and Morse, A. S., 1999, “Basic Problems in Stability and Design of Switched Systems,” IEEE Control Syst. Mag., 19(5), pp. 59–70. [CrossRef]
Pao, L. Y., and Johnson, K. E., 2009, “A Tutorial on Wind Turbine Dynamics and Control,” Proceedings of the American Control Conference, pp. 545–592.
Manwell, J., 2009, Wind Energy Explained: Theory, Design and Application, Wiley, Chichester, UK.
Electropaedia, 2005, “Electricity Demand,” Woodbank Communications Ltd., http://www.mpoweruk.com/electricity_demand.htm


Grahic Jump Location
Fig. 1

Integrated wind turbine and battery system

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Fig. 3

Wind turbine power coefficient

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Fig. 2

Control block diagram of integrated wind turbine and battery system

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Fig. 7

Varying demand, varying wind speed simulation

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Fig. 4

Positive and negative regions of Eq. (24) for different Kpvw3 values

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Fig. 5

Constant demand, constant wind speed simulation

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Fig. 6

Constant demand, varying wind speed simulation

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Fig. 8

Switching in positive region




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