Research Papers

Dynamic Optimization of Drivetrain Gear Ratio to Maximize Wind Turbine Power Generation—Part 2: Control Design

[+] Author and Article Information
Dongmei Chen

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

Performed on a MS Windows-based 64-bit system with an Intel Core i7-950 processor and 12.0 GB of RAM.

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 17, 2011; final manuscript received April 5, 2012; published online October 30, 2012. Assoc. Editor: Alexander Leonessa.

J. Dyn. Sys., Meas., Control 135(1), 011017 (Oct 30, 2012) (10 pages) Paper No: DS-11-1213; doi: 10.1115/1.4006886 History: Received July 17, 2011; Revised April 05, 2012; Accepted April 24, 2012

The cost of electrical power produced by small wind turbines impedes the use of this technology, which can otherwise provide power to millions of homes in rural regions worldwide. To encourage their use, small wind turbines must capture wind energy more effectively while avoiding increased equipment costs. A variable ratio gearbox (VRG) can provide this capability to the simple fixed-speed wind turbine through discrete operating speeds. This is the second of a two-part publication that focuses on the control of a VRG-enabled wind turbine. The first part presented a 100 kW fixed speed, wind turbine model, and a method for manipulating the VRG and mechanical brake to achieve full load operation. In this study, an optimal control algorithm is developed to maximize the power production in light of the limited brake pad life. Recorded wind data are used to develop a customized control design that is specific to a given site. Three decision-making modules interact with the wind turbine model developed in Part 1 to create possible VRG gear ratio (GR) combinations. Dynamic programming is applied to select the optimal combination and establish the operating protocol. The technique is performed on 20 different wind profiles. The results suggest an increase in wind energy production of nearly 10%.

© 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Rex, A., and Johnson, K., 2008, Model Development of a Wind Turbine System With a Continuously Variable Transmission for Design of Region 2 Speed Control, Reno, NV.
Johnson, K. E., 2004, “Adaptive Torque Control of Variable Speed Wind Turbines,” National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/TP-500-36265.
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]
Koutroulis, E., and Kalaitzakis, K., 2006, “Design of a Maximum Power Tracking System for Wind-Energy-Conversion Applications,” IEEE Trans. Ind. Electron., 53(2), pp.486–494. [CrossRef]
Nadhir, A., and Hiyama, T., 2010, “Maximum Power Point Tracking Based Optimal Control Wind Energy Conversion System,” 2010 Second International Conference on Advances in Computing, Control and Telecommunication Technologies (ACT), pp.41–44.
Thongam, J. S., Bouchard, P., Ezzaidi, H., and Ouhrouche, M., 2009, “Wind Speed Sensorless Maximum Power Point Tracking Control of Variable Speed Wind Energy Conversion Systems,” IEEE International Electric Machines and Drives Conference, IEMDC′09, pp.1832–1837.
Valenciaga, F., and Puleston, P. F., 2007, “Variable Structure Control of a Wind Energy Conversion System Based on a Brushless Doubly Fed Reluctance Generator,” IEEE Trans. Energy Conversion, 22(2), pp.499–506. [CrossRef]
Song, L., Xing, S., Peng, X., and Wen, W., 2010, “Variable Structure Fuzzy-PI Control for Strategy of Maximal Wind Energy Capture and Conversion of Doubly Fed Induction Generators,” 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), pp.26–29.
Evangelista, C., Puleston, P., and Valenciaga, F., 2010, “A Simple Robust Controller for Power Maximization of a Variable-Speed Wind Turbine,” Int. J. Energy Res., 34(10), pp.924–932. [CrossRef]
Bratcu, A. I., Munteanu, I., and Ceanga, E., 2008, “Optimal Control of Wind Energy Conversion Systems: From Energy Optimization to Multi-Purpose Criteria—A Short Survey,” 2008 16th Mediterranean Conference on Control and Automation, pp.759–766.
Lin, C.-C., Kim, M.-J., Peng, H., and Grizzle, J. W., 2006, “System-Level Model and Stochastic Optimal Control for a PEM Fuel Cell Hybrid Vehicle,” ASME J. Dyn. Syst., Meas., Control, 128(4), pp.878–890. [CrossRef]
Koot, M., Kessels, J. T. B. A., de Jager, B., Heemels, W. P. M. H., van den Bosch, P. P. J., and Steinbuch, M., 2005, “Energy Management Strategies for Vehicular Electric Power Systems,” IEEE Trans. Veh. Technol., 54(3), pp.771–782. [CrossRef]
Lin, C.-C., Peng, H., Grizzle, J. W., and Kang, J.-M., 2003, “Power Management Strategy for a Parallel Hybrid Electric Truck,” IEEE Trans. Control Syst. Technol., 11(6), pp.839–849. [CrossRef]
Brahma, A., Guezennec, Y., and Rizzoni, G., 2000, “Optimal Energy Management in Series Hybrid Electric Vehicles,” Proceedings of the 2000 American Control Conference, Vol.1, pp.60–64.
Chou, L.-S., and Song, S.-M., 1992, “Geometric Work of Manipulators and Path Planning Based on Minimum Energy Consumption,” ASME J. Mech. Des., 114(3), pp.414–421. [CrossRef]
Zameroski, D., Starr, G., Wood, J., and Lumia, R., 2008, “Rapid Swing-Free Transport of Nonlinear Payloads Using Dynamic Programming,” ASME J. Dyn. Syst., Meas., Control, 130(4), p. 041001. [CrossRef]
Vukobratovic, M., and Kircanski, M., 1982, “A Method for Optimal Synthesis of Manipulation Robot Trajectories,” ASME J. Dyn. Syst., Meas., Control, 104(2), pp.188–193. [CrossRef]
Lee, C. W., 2009, “Dynamic Optimization of the Grinding Process in Batch Production,” ASME J. Manufac. Sci. Eng., 131(2), p. 021006. [CrossRef]
Hippalgaonkar, R. R., and Shin, Y. C., 2010, “Robust Optimisation of Machining Conditions With Tool Life and Surface Roughness Uncertainties,” Int. J. Prod. Res., 49(13), pp.3963–3978. [CrossRef]
Dong, S., Danai, K., and Malkin, S., 2004, “Continuous Optimal Infeed Control for Cylindrical Plunge Grinding, Part 2: Controller Design and Implementation,” ASME J. Manuf. Sci. Eng., 126(2), pp.334–340. [CrossRef]
2011, “NREL: Wind Integration Datasets—Obtaining the Western Wind Dataset,” National Renewable Energy Laboratory, accessed May 10, 2011, http://www.nrel.gov/wind/integrationdatasets/western/data.html
2011, “Wind Energy Resource Atlas of the United States,” National Renewable Energy Laboratory, accessed May 10, 2011, http://rredc.nrel.gov/wind/pubs/atlas/tables/1-1T.html
Orthwein, W., 2004, Clutches and Brakes Design and Selection, Marcel Dekker, New York.
Archard, J. F., 1953, “Contact and Rubbing of Flat Surfaces,” J. Appl. Phys., 24(8), pp.981–988. [CrossRef]
Limpert, R., 1999, Brake Design and Safety, Society of Automotive Engineers, Warrendale, PA.
Hall, J. F., Mecklenborg, C. A., Chen, D., and Pratap, S. B., 2011, “Wind Energy Conversion With a Variable-Ratio Gearbox: Design and Analysis,” Renewable Energy, 36(3), pp.1075–1080. [CrossRef]
Manwell, J., 2009, Wind Energy Explained: Theory, Design and Application, Wiley, Chichester, UK, Chap. 2. [CrossRef]
Justus, C., 1978, Winds and Wind System Performance, Franklin Institute Press, Philadelphia.
The U.S. Department of Energy, 2009, Annual Energy Review2008, United States Department of Energy, Energy Information Administration.


Grahic Jump Location
Fig. 1

Power curve for VRG, defining regions 2′ and 3′

Grahic Jump Location
Fig. 2

Modified rules used with program optimization

Grahic Jump Location
Fig. 3

Wind turbine decision-making model

Grahic Jump Location
Fig. 4

Decision-making structure for preliminary programming

Grahic Jump Location
Fig. 5

Example of a valid (top) and an invalid (bottom) VRG combination

Grahic Jump Location
Fig. 6

Dynamic programming algorithm for computing the cost at step k

Grahic Jump Location
Fig. 7

Plot showing total energy produced (top), brake wear (middle), and cost (bottom) for site 16577 (set no. 16) for weight, α = 0.960

Grahic Jump Location
Fig. 8

Technique for finding optimal VRG combination, and weight variable, α, that will be used to operate the wind turbine

Grahic Jump Location
Fig. 9

Surface plot showing total cost (top) and total energy (bottom) as a function of α for each of the 575,413 gear combination for site 16577 (set no. 16)

Grahic Jump Location
Fig. 10

Plot showing wind speed (top), additional energy produced by the VRG (bottom, left axis) and cumulative brake pad used (bottom, right axis) over a three-year period, for site 21291 (set no. 14), programmed with a weight coefficient, α = 0.980

Grahic Jump Location
Fig. 11

Results for site 21291 (set no. 14) with weight, α = 0.980, showing VRG power curve (top), gear data used for control (upper–middle), power dissipated (lower–middle), and turbine speed (bottom)

Grahic Jump Location
Fig. 12

Optimal VRG ratios for each set of wind data



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In