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

Abstract

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 5 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. 10PC 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 15 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.

Best Practices for Wake Model and Optimization Algorithm Selection in Wind Farm Layout Optimization

“…The first approach aims at improving the quality of individual models. The second approach is to improve the formulation of the optimization problem, as well as the algorithms used to perform the optimization [3].…”

Optimizing wind farms layouts for maximum energy production using probabilistic inference: Benchmarking reveals superior computational efficiency and scalability

“…This confidence levels on the energy production can be complemented by quantifying uncertainty of both input parameters [78,79,80] and wake models [81,82], which are likely to have a more significant impact in the resulting optimal layout. A comprehensive robust optimization approach that considers and quantifies all these uncertainties, although beyond of the scope of the present study, would be a worthy goal for future work in this area.…”

Using Graph Coloring To Compute Total Derivatives More Efficiently in OpenMDAO

“…Any form of bin-packing problem or spatial arrangement problem [25] is an obvious use case. Additionally any problem that requires maintaining separation of a set of bodies is also directly applicable, such as maintaining a minimum separation distance between all aircraft within an airspace, all spacecraft in a set of intersecting orbits, or all wind turbines within a wind farm [26,27].…”