Abstract
Careful management of wake interference is essential to further improve Annual Energy Production (AEP) of wind farms. Wake effects can be minimized through optimization of turbine layout, wind farm control, and turbine design. Realistic wind farm optimization is challenging because it has numerous design degrees of freedom and must account for the stochastic nature of wind. In this paper we provide a framework for calculating AEP for any relevant uncertain (stochastic) variable of interest. We use Polynomial Chaos (PC) to efficiently quantify the effect of the stochastic variables—wind direction and wind speed—on the statistical outputs of interest (AEP) for wind farm layout optimization. When the stochastic variable includes the wind direction, polynomial chaos is one order of magnitude more accurate in computing the AEP when compared to commonly used simplistic integration techniques (rectangle rule), especially for non grid-like wind farm layouts. Furthermore, PC requires less simulations for the same accuracy. This allows for more efficient optimization and uncertainty quantification of wind farm energy production.
Highlights
Wind farm optimization is multidisciplinary, the nature of wind is inherently stochastic, and the design of wind farms contains numerous potential design degrees of freedom
For the uncertainty quantification—calculating the Annual Energy Production (AEP)—we focus on 4 different layouts: grid, Amalia, optimized, and random
This paper has focused on improving uncertainty quantification with application in wind farm design
Summary
Wind farm optimization is multidisciplinary, the nature of wind is inherently stochastic, and the design of wind farms contains numerous potential design degrees of freedom. Our past research has focused on enabling large-scale coupled layout-yaw optimization [5, 6] by reformulating wake models to provide continuously differentiable output, using automatic differentiation to provide numerically exact gradients, and taking advantage of scalable, gradient-based optimization methods [7] Another approach to enable large-scale optimizations is to reduce the number of stochastic wind directions needed to accurately compute the statistical quantities of interest, which is the approach explored in this paper. Past studies have computed statistical outputs, like the annual energy production, using simple integration methods like the rectangle rule and trapezoid rule These quadrature methods are inefficient and generally require a large number of function evaluations to quantify wind farm performance for the stochastic wind conditions.
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