Data-driven wake model parameter estimation to analyze effects of wake superposition

Low-fidelity wake models are used for wind farm design and control optimization. To generalize to a wind farm model, individually modeled wakes are commonly superimposed using approximate superposition models. Wake models parameterize atmospheric and wake turbulence, introducing unknown model parameters that historically are tuned with idealized simulation or experimental data and neglect uncertainty. We calibrate and estimate the uncertainty of the parameters in a Gaussian wake model using Markov chain Monte Carlo (MCMC) for various wake superposition methods. Posterior distributions of the uncertain parameters are generated using power production data from large eddy simulations and a utility-scale wake steering field experiment. The posteriors for the wake expansion coefficient are sensitive to the choice of superposition method, with relative differences in the means and standard deviations on the order of 100%. This sensitivity illustrates the role of superposition methods in wake modeling error. We compare these data-driven parameter estimates to estimates derived from a standard turbulence-intensity based model as a baseline. To assess predictive accuracy, we calibrate the data-driven parameter estimates with a training dataset for yaw-aligned operation. Using a Monte Carlo approach, we then generate predicted distributions of turbine power production and evaluate against a hold-out test dataset for yaw-misaligned operation. For the cases tested, the MCMC-calibrated parameters reduce the total error of the power predictions by roughly 50% compared to the deterministic empirical model predictions. An additional benefit of the data-driven parameter estimation is the quantification of uncertainty, which enables physically quantified confidence intervals of wake model predictions.