A Probabilistic Approach to Estimating Wind Farm Annual Energy Production with Bayesian Quadrature
Ryan King, Andrew Glaws, Gianluca Geraci, Michael Eldred
Abstract
Wind farm optimization studies often seek a turbine layout or control strategy that maximizes the annual energy production (AEP). This quantity of interest represents an expectation of the plant's power output with respect to the site-specific joint distribution of wind speed and inflow direction. Traditionally, this quantity has been estimated using a midpoint quadrature rule where the joint pdf is divided into regularly spaced speed and direction bins. This approach generally requires O(103) function evaluations which is intractable for the emerging suite of medium- and high-fidelity computational fluid dynamics codes developed for wind energy applications. To remedy this, we propose a sample-efficient probabilistic approach to estimating AEP using Bayesian quadrature (BQ). In BQ, sample function evaluations are drawn to train a Gaussian process (GP) surrogate model of the wind farm power output, which is integrated to estimate AEP. Because the trained GP variance can be estimated a priori, the sampling strategy can be constructed to optimally reduce the variance on the estimate of expected AEP. We apply BQ to the AEP estimation for the Princess Amalia wind farm, and show the BQ estimate reaches a less than 1% error level with 22x fewer function evaluations than the finest midpoint rule estimate while also substantially decreasing the estimator variance.