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https://doi.org/10.5194/wes-2017-56
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Research articles 12 Jan 2018

Research articles | 12 Jan 2018

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This discussion paper is a preprint. A revision of the manuscript is under review for the journal Wind Energy Science (WES).

Polynomial chaos to efficiently compute the annual energy production in wind farm layout optimization

Andrés Santiago Padrón1, Jared Thomas2, Andrew P. J. Stanley2, Juan J. Alonso1, and Andrew Ning2 Andrés Santiago Padrón et al.
  • 1Department of Aeronautics & Astronautics, Stanford University, Stanford, CA, 94305, USA
  • 2Department of Mechanical Engineering, Brigham Young University, Provo, UT, 84602, USA

Abstract. In this paper, we develop computationally-efficient techniques to calculate statistics used in wind farm optimization with the goal of enabling the use of higher-fidelity models and larger wind farm optimization problems. We apply these techniques to maximize the Annual Energy Production (AEP) of a wind farm by optimizing the position of the individual wind turbines. The AEP (a statistic itself) is the expected power produced by the wind farm over a period of one year subject to uncertainties in the wind conditions (wind direction and wind speed) that are described with empirically-determined probability distributions. To compute the AEP of the wind farm, we use a wake model to simulate the power at different input conditions composed of wind direction and wind speed pairs. We use polynomial chaos (PC), an uncertainty quantification method, to construct a polynomial approximation of the power over the entire stochastic space and to efficiently (using as few simulations as possible) compute the expected power (AEP). We explore both regression and quadrature approaches to compute the PC coefficients. PC based on regression is significantly more efficient than the rectangle rule (the method most commonly used to compute the expected power). With PC based on regression, we have reduced by as much as an order of magnitude the number of simulations required to accurately compute the AEP, thus enabling the use of more expensive, higher-fidelity models or larger wind farm optimizations. We perform a large suite of gradient-based optimizations with different initial turbine locations and with different numbers of samples to compute the AEP. The optimizations with PC based on regression result in optimized layouts that produce the same AEP as the optimized layouts found with the rectangle rule but using only one-third of the samples. Furthermore, for the same number of samples, the AEP of the optimal layouts found with PC is 1% higher than the AEP of the layouts found with the rectangle rule.

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Andrés Santiago Padrón et al.
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Andrés Santiago Padrón et al.
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Short summary
We explore computational methods to efficiently compute the Annual Energy Production (AEP) of a wind farm by properly handling the uncertainties in the wind direction and wind speed. We apply the new ideas to the layout optimization of a large wind farm. We show up to an order of magnitude reduction in the number of simulations required for the optimization.
We explore computational methods to efficiently compute the Annual Energy Production (AEP) of a...
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