Optimal closed-loop wake steering – Part 1: Conventionally neutral atmospheric boundary layer conditions

Abstract

Abstract. Strategies for wake loss mitigation through the use of dynamic closed-loop wake steering are investigated using large eddy simulations of conventionally neutral atmospheric boundary layer conditions in which the neutral boundary layer is capped by an inversion and a stable free atmosphere. The closed-loop controller synthesized in this study consists of a physics-based lifting line wake model combined with a data-driven ensemble Kalman filter (EnKF) state estimation technique to calibrate the wake model as a function of time in a generalized transient atmospheric flow environment. Computationally efficient gradient ascent yaw misalignment selection along with efficient state estimation enables the dynamic yaw calculation for real-time wind farm control. The wake steering controller is tested in a six-turbine array embedded in a statistically quasi-stationary, conventionally neutral flow with geostrophic forcing and Coriolis effects included. The controller statistically significantly increases power production compared to the baseline, greedy, yaw-aligned control provided that the EnKF estimation is constrained and informed with a physics-based prior belief of the wake model parameters. The influence of the model for the coefficient of power Cp as a function of the yaw misalignment is characterized. Errors in estimation of the power reduction as a function of yaw misalignment are shown to result in yaw steering configurations that underperform the baseline yaw-aligned configuration. Overestimating the power reduction due to yaw misalignment leads to increased power over the greedy operation, while underestimating the power reduction leads to decreased power; therefore, in an application where the influence of yaw misalignment on Cp is unknown, a conservative estimate should be taken. The EnKF-augmented wake model predicts the power production in yaw misalignment with a mean absolute error over the turbines in the farm of 0.02P1, with P1 as the power of the leading turbine at the farm. A standard wake model with wake spreading based on an empirical turbulence intensity relationship leads to a mean absolute error of 0.11P1, demonstrating that state estimation improves the predictive capabilities of simplified wake models.

Design and analysis of a wake model for spatially heterogeneous flow

“…This also includes added turbulence caused by nearby turbine operation to more accurately calculate the rate of wake expansion. Many other linear-flow models use a constant parameter that defines the rate of wake expansion and has no dependency on the operating conditions of the turbine (Jensen, 1983). From the concepts of Niayifar and Porté-Agel (2015), the Gaussian model relates the rate of wake expansion in the lateral and vertical directions directly to the ambient turbulence intensity present at a turbine and two tuned parameters, k a = 0.38371 and k b = 0.003678:…”

Wind farm yaw control set-point optimization under model parameter uncertainty

“…For wake model-based closed-loop control (e.g. the method proposed by Howland et al (2020) 21 ), the goal is to calculate the optimal yaw set-points for the wind farm over the finite control update time horizon. In both approaches, the set-point optimization can be considered over wind condition probabilities.…”

“…Wake model parameters have been tuned using LiDAR field data 17 and neutral ABL LES flow fields 18 . Recent work has optimized the wake model parameters using only wind farm power data and analytic gradients 5 , a novel calibration procedure 19 , genetic algorithms 20 , and Kalman filtering 21 and demonstrated that assimilating operational wind farm data into the wake model improves its predictive capability. Zhang & Zhao (2020) 22 used sampling to approximate the Bayesian posterior distributions of wake model parameters given LES data as the ground truth.…”

“…Wake model error correction terms have also been proposed 23 and learned using operational data, which improved wake model predictions. Yaw set-point optimization which is robust to model parameter uncertainty becomes more critical when applying closed-loop control due to limited statistical averaging and additional wind condition uncertainty 21 .…”

Dynamic robust active wake control

“…It should also be pointed out that, as an alternative to the robust design of yaw offset set-points that are valid for a range of conditions, one could consider adaptive solutions in which the yaw set-points are updated in real-life based on (estimates of) the actual operating conditions. Such an approach is pursued in Howland et al (2020), where a gradient ascent algorithm updates the yaw offsets at each iteration based on analytically derived gradients for the lifting line wake model, the parameters of which are estimated online.…”