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.
Fast Processing Intelligent Wind Farm Controller for Production Maximisation