Bayesian uncertainty quantification framework for wake model calibration and validation with historical wind farm power data

Abstract

The expected growth in wind energy capacity requires efficient and accurate models for wind farm layout optimization, control, and annual energy predictions. Although analytical wake models are widely used for these applications, several model components must be better understood to improve their accuracy. To this end, we propose a Bayesian uncertainty quantification framework for physics-guided data-driven model enhancement. The framework incorporates turbulence-related aleatoric uncertainty in historical wind farm data, epistemic uncertainty in the empirical parameters, and systematic uncertainty due to unmodeled physics. We apply the framework to the wake expansion parametrization in the Gaussian wake model and employ historical power data of the Westermost Rough Offshore Wind Farm. We find that the framework successfully distinguishes the three sources of uncertainty in the joint posterior distribution of the parameters. On the one hand, the framework allows for wake model calibration by selecting the maximum a posteriori estimators for the empirical parameters. On the other hand, it facilitates model validation by separating the measurement error and the model error distribution. In addition, the model adequacy and the effect of unmodeled physics are assessable via the posterior parameter uncertainty and correlations. Consequently, we believe that the Bayesian uncertainty quantification framework can be used to calibrate and validate existing and upcoming physics-guided models.