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Research Papers

Probabilistic Models for Wind Turbine and Wind Farm Performance

[+] Author and Article Information
Sanjay R. Arwade1

Department of Civil and Environmental Engineering,  University of Massachusetts Amherst, Amherst, MA 01003arwade@ecs.umass.edu

Matthew A. Lackner

Department of Mechanical and Industrial Engineering,  University of Massachusetts Amherst, Amherst, MA 01003lackner@ecs.umass.edu

Mircea D. Grigoriu

School of Civil and Environmental Engineering,  Cornell University, Ithaca, NY 14853mdg12@cornell.edu

1

Corresponding author.

J. Sol. Energy Eng 133(4), 041006 (Oct 11, 2011) (9 pages) doi:10.1115/1.4004273 History: Received May 06, 2010; Revised April 12, 2011; Published October 11, 2011; Online October 11, 2011

A Markov model for the performance of wind turbines is developed that accounts for component reliability and the effect of wind speed and turbine capacity on component reliability. The model is calibrated to the observed performance of offshore turbines in the north of Europe, and uses wind records obtained from the coast of the state of Maine in the northeast United States in simulation. Simulation results indicate availability of 0.91, with mean residence time in the operating state that is nearly exponential and has a mean of 42 days. Using a power curve typical for a 2.5 MW turbine, the capacity factor is found to be beta distributed and highly non-Gaussian. Noticeable seasonal variation in turbine and farm performance metrics are observed and result from seasonal fluctuations in the characteristics of the wind record. The input parameters to the Markov model, as defined in this paper, are limited to those for which field data are available for calibration. Nevertheless, the framework of the model is readily adaptable to include, for example: site specific conditions; turbine details; wake induced loading effects; component redundancies; and dependencies. An on-off model is introduced as an approximation to the stochastic process describing the operating state of a wind turbine, and from this on-off process an Ornstein–Uhlenbeck (O–U) process is developed as a model for the availability of a wind farm. The O–U model agrees well with Monte Carlo (MC) simulation of the Markov model and is accepted as a valid approximation. Using the O–U model in design and management of large wind farms will be advantageous because it can provide statistics of wind farm performance without resort to intensive large scale MC simulation.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Wind speed time history for one typical year. (b) Histogram of wind speeds with statistics.

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Figure 2

GE 2.5 MW turbine power curve and histogram of wind speeds

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Figure 3

Typical year of simulated power generation for a single turbine. The turbine state is shown on the horizontal line below the power with the heavier weighted line indicating an off period resulting from component failure.

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Figure 4

Interarrival times for turbine failures. Each interarrival time consists of a residence period in the on state followed by a repair time. The line is the best fit exponential pdf.

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Figure 5

Seasonal variation of availability and power generation based on estimation for the 19 yrs included in the reference time period

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Figure 6

Histogram and best fit beta pdf for daily capacity factor for 19 yrs of simulation

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Figure 7

Seasonal variation of the number of available turbines and the power generated by a 100 turbine wind farm averaged over a 19 yr period

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Figure 8

Histograms and best fit Gaussian pdfs for the wind farm state F(t) for 100 and 500 turbine wind farms

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Figure 9

Covariance function of F(t) for a farm with 500 turbines based on MC simulation and the Ornstein–Uhlenbeck model. The MC simulation results show a very nearly exponential covariance. The covariance is scaled by the process variance to be unit at τ = 0.

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