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Research Papers

Optimizing Energy Capture of Cascaded Wind Turbine Array With Nested-Loop Extremum Seeking Control

[+] Author and Article Information
Zhongzhou Yang

EXA Corporation,
38777 Six Mile Road, Suite 210,
Livonia, MI 48152
e-mail: zzyang21@gmail.com

Yaoyu Li

Mem. ASME
Department of Mechanical Engineering,
University of Texas at Dallas,
800 W. Campbell Road, EC-38,
Richardson, TX 75080
e-mail: yaoyu.li@utdallas.edu

John E. Seem

Johnson Controls, Inc.,
507 E. Michigan Street,
Milwaukee, WI 53201
e-mail: john.seem@gmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 4, 2014; final manuscript received September 9, 2015; published online October 5, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 137(12), 121010 (Oct 05, 2015) (9 pages) Paper No: DS-14-1398; doi: 10.1115/1.4031593 History: Received October 04, 2014; Revised September 09, 2015

This paper proposes a nested-loop extremum seeking control (NLESC) scheme for optimizing the energy capture of wind farm that is formed by a wind turbine array along the prevailing wind direction. It has been shown in earlier work that the axial induction factors of individual wind turbines can be optimized from downstream to upstream units in a sequential manner, which is a spatial domain analogy to the principle of optimality in dynamic programing. Therefore, it is proposed to optimize the turbine operation by a nested-loop optimization framework from the downstream to upstream turbines, based on feedback of the power of the immediate turbine and its downstream units. The extremum seeking control (ESC) based on dither–demodulation scheme is selected as a model-free real-time optimization solution for the individual loops. First, the principle of optimality for optimizing wind farm energy capture is proved for the cascaded wind turbine array based on the disk model. Analysis shows that the optimal torque gain of each turbine in a cascade of turbines is invariant with wind speed if the wind direction does not change. Then, the NLESC scheme is proposed, with the array power coefficient selected as the performance index to be optimized in real-time. As changes of upstream turbine operation affect downstream turbines with significant delays due to wind propagation, a cross-covariance based delay estimate is used to improve the determination of the array power coefficient. The proposed scheme is evaluated with simulation study using a three-turbine wind farm with the simwindfarm simulation platform. Simulation study is performed under both smooth and turbulent winds, and the results indicate the convergence to the actual optimum. Also, simulation under different wind speeds supports the earlier analysis results that the optimal torque gains of the cascaded turbines are invariant to wind speed.

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Figures

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Fig. 1

Illustration of a cascaded wind turbine array

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Fig. 2

Schematic of NLESC for cascaded wind turbine array

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Fig. 3

Block diagram of dither ESC algorithms

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Fig. 4

Static map of power capture for turbines 2 and 3 at 6 m/s

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Fig. 5

Torque gain profiles for ESC simulation under 6 m/s

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Fig. 6

Effective wind speeds of NLESC simulation under 6 m/s

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Fig. 7

Generator speeds of NLESC simulation under 6 m/s

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Fig. 8

Total power profile for NLESC simulation under 6 m/s

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Fig. 9

Total power capture of NLESC simulation under 10 m/s

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Fig. 10

Wind profile for NLESC simulation under 8 m/s turbulent wind

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Fig. 11

Torque gains trajectories of NLESC under 8 m/s turbulent wind

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Fig. 12

Total power of wind turbine array under 8 m/s turbulent wind

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