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

Abstract

Wake steering, the intentional yaw misalignment of certain turbines in an array, has demonstrated potential as a wind farm control approach to increase collective power. Existing algorithms optimize the yaw misalignment angle set-points using steady-state wake models and either deterministic frameworks, or optimizers which account for wind direction and yaw misalignment variability and uncertainty. Wake models rely on parameterizations of physical phenomena in the mean flow field, such as the wake spreading rate. The wake model parameters are uncertain and vary in time at a wind farm depending on the atmospheric conditions, including turbulence intensity, stability, shear, veer, and other atmospheric features. In this study, we develop a yaw set-point optimization approach which includes model parameter uncertainty, in addition to wind condition variability and uncertainty. The optimization is tested in open-loop control numerical experiments using utility-scale wind farm operational data for which the set-point optimization framework with parameter uncertainty has a statistically significant impact on the wind farm power production for certain wind turbine layouts at low turbulence intensity, but the results are not significant for all layouts considered nor at higher turbulence intensity. The set-point optimizer is also tested for closed-loop wake steering control of a model wind farm in large eddy simulations of a convective atmospheric boundary layer. The yaw set-point optimization with model parameter uncertainty improved the robustness of the closed-loop wake steering control to increases in the yaw controller update frequency. Increases in wind farm power production were not statistically significant due to the high ambient power variability in the turbulent, convective ABL.

Figures (17)

• Figure 1: Set-point optimization under model parameter uncertainty. The wake model parameters $\psi$ are estimated by the ensemble Kalman filter (EnKF) for a set of wind conditions $\bm{c}$ and averaged power data $P_{\mathrm{data}}$. The probability distribution of the parameters $f(\psi)$ is derived from the power data and used in tandem with the condition probability distributions $f(\bm{c})$ to compute $\gamma_s^*$ with set-point optimization (Eq. \ref{['eq:opti_param']}).
• Figure 2: (a) Utility-scale wind farm layout for Cluster A. The turbines are oriented for flow from the north ($\alpha=0^\circ$) and the coordinates are normalized by the wind turbine diameter $D$. (b) Cluster B layout oriented for flow from the west ($\alpha=270^\circ$). The wind turbine which is used as a wind condition reference is shown in red. The $x$ and $y$ axes correspond to easting and northing directions.
• Figure 3: (a) Wind direction probability distribution within a $268.75^\circ<\alpha<271.25^\circ$ wind direction bin. (b) Wind speed empirical probability density function. A best-fit Weibull distribution with $k=3.8$ and $\lambda=7$ is shown with a solid black line.
• Figure 4: (a) Yaw misalignment empirical probability density function with a best-fit Gaussian distribution shown with a solid black line. The mean and standard deviation of the Gaussian distribution are $\mu_\gamma=0.4^\circ$ and $\sigma_\gamma=5.6^\circ$. (b) Wind turbine power ratio probability distributions for wind direction bins centered at $\alpha=2.5^\circ \pm 2.5^\circ$ and $\alpha=270^\circ \pm 2.5^\circ$ for $u=7\pm 1$ m/s and $TI=5\%\pm2.5\%$. The vertical lines correspond the means of the respective power ratio distributions.
• Figure 5: Normalized power production for waked turbine $B2$ in Cluster B as a function of the incident wind direction for $u=7\pm1$ m/s and (a) $TI=5\pm2.5\%$ and (b) $TI=10\pm2.5\%$. Errorbars represent one standard deviation about the mean from the one-minute averaged SCADA data. The stochastic wake model predictions are represented by $\sigma_p \neq 0$. The shaded region corresponds to one standard deviation about the mean wake model power estimate.