Short-term wind forecasting via surface pressure measurements: stochastic modeling and sensor placement

TL;DR

This work develops a short-term wind-forecasting framework that couples a 2D hub-height stochastic wake model with ground-level pressure and nacelle measurements via Kalman filtering. It introduces white- and colored-in-time stochastic forcing to align the prior with LES statistics and employs a data-driven pressure projection from hub height to ground to enable real-time updates with multiple Kalman-filter variants (LKF, EKF, EnKF, UKF). The study compares filtering performance in non-yawed and yawed configurations, adds nacelle-based sign correction to improve upwind tracking, and proposes a convex optimization-based sensor placement strategy to reduce ground sensors while maintaining accuracy. The results indicate that EKF with colored forcing offers a practical balance of accuracy and computational demand, delivering meaningful preview times, while sensor-selection strategies can substantially reduce sensor counts by concentrating measurements in wake regions. The framework provides a feasible, low-cost pathway for real-time wind-field estimation with clear directions for 3D extensions and robustness to atmospheric stability variations.

Abstract

We propose a short-term wind forecasting framework for predicting real-time variations in atmospheric turbulence based on nacelle-mounted anemometer and ground-level air-pressure measurements. Our approach combines linear stochastic estimation and Kalman filtering algorithms to assimilate and process real-time field measurements with the predictions of a stochastic reduced-order model that is confined to a two-dimensional plane at the hub height of turbines. We bridge the vertical gap between the computational plane of the model at hub height and the measurement plane on the ground using a projection technique that allows us to infer the pressure in one plane from the other. Depending on the quality of this inference, we show that customized variants of the extended and ensemble Kalman filters can be tuned to balance estimation quality and computational speed 1-1.5 diameters ahead and behind leading turbines. In particular, we show how synchronizing the sign of estimates with that of velocity fluctuations recorded at the nacelle can significantly improve the ability to follow temporal variations upwind of the leading turbine. We also propose a convex optimization-based framework for selecting a subset of pressure sensors that achieve a desired level of accuracy relative to the optimal Kalman filter that uses all sensing capabilities.

Figures (24)

• Figure 1: Computational (top) and sensing (bottom) planes in our estimation framework. Blue and red dots mark the locations of training points for stochastic modeling and sensing, respectively, and the red star marks an estimation point in the wake of the leading turbine.
• Figure 2: Streamwise mean velocity provided by Eq. \ref{['eq.base_flow']} at the hub height of a wind farm with $\gamma=15^\degree$. The velocity is non-dimensionalized by the free-stream mean velocity. Thick red lines mark turbine rotors and the wind direction is from left to right.
• Figure 3: A schematic of the potential wake core within the shaded triangular region for a yawed wind turbine.
• Figure 4: Eigenvalues of the matrix $-(A{\bf V}_{LES}+{\bf V}_{LES}\, A^T)$, corresponding to a cascade of 2 non-yawed turbines that are separated by 4 diameters. The negative eigenvalues indicate that the turbulent velocity covariance cannot be reproduced by the linearized NS equations \ref{['eq.lnse1']} with white-in-time stochastic input ${\bf d}$.
• Figure 5: Cascade connection of the linearized flow dynamics and a linear coloring filter that is used to match partially available second-order statistics of the output velocity ${\bf v}$.