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Accurate and reliable energy forecasting is essential for power grid operators who strive to minimize extreme forecasting errors that pose significant operational challenges and incur high intra-day trading costs. Incorporating planning information -- such as anticipated user behavior, scheduled events or timetables -- provides substantial contextual information to enhance forecast accuracy and reduce the occurrence of large forecasting errors. Existing approaches, however, lack the flexibility to effectively integrate both dynamic, forward-looking contextual inputs and historical data. In this work, we conceptualize forecasting as a combined forecasting-regression task, formulated as a sequence-to-sequence prediction problem, and introduce contextually-enhanced transformer models designed to leverage all contextual information effectively. We demonstrate the effectiveness of our approach through a primary case study on nationwide railway energy consumption forecasting, where integrating contextual information into transformer models, particularly timetable data, resulted in a significant average mean absolute error reduction of 26.6%. An auxiliary case study on building energy forecasting, leveraging planned office occupancy data, further illustrates the generalizability of our method, showing an average reduction of 56.3% in mean absolute error. Compared to other state-of-the-art methods, our approach consistently outperforms existing models, underscoring the value of context-aware deep learning techniques in energy forecasting applications., Comment: 39 pages, 8 figures and tables, journal paper

To achieve decarbonization targets, wind turbines are growing in hub height, rotor diameter, and are being deployed in new locations with diverse atmospheric conditions not previously seen, such as offshore. Physics-based analytical wake models commonly used for design and control of wind farms simplify atmospheric boundary layer (ABL) and wake physics to achieve computational efficiency. This is done primarily through a simplified model form that neglects certain flow processes and through parameterization of ABL and wake turbulence through a wake spreading rate. In this study, we analyze the physical mechanisms that govern momentum and turbulence within a wind turbine wake in the stratified ABL. We use large eddy simulation and analysis of the streamwise momentum deficit and wake-added turbulence kinetic energy (TKE) budgets to study wind turbine wakes under neutral and stable conditions. To parse the wake from the turbulent, incident ABL flow, we decompose the flow into the base ABL flow and the deficit flow produced by the presence of a turbine. We analyze the decomposed flow field budgets to study the effects of changing stability on the streamwise momentum deficit and wake-added TKE. The results demonstrate that stability changes the importance of physical mechanisms for both quantities primarily through the nonlinear interactions of the base and deficit flows, with the stable case most affected by higher shear in the base flow and the neutral case by higher base flow TKE. Buoyancy forcing terms in the momentum deficit and wake-added TKE budgets are relatively less important compared to the aforementioned effects. While total TKE is higher in wakes in neutral ABL flows, the wake-added TKE is higher downwind of turbines in stable ABL conditions. The dependence of wake-added TKE on ABL stability is not represented in existing empirical models widely used for mean wake flow modeling., Comment: 42 pages, 22 figures, 1 table

Wind turbines operate in the atmospheric boundary layer (ABL), where Coriolis effects are present. As wind turbines with larger rotor diameters are deployed, the wake structures that they create in the ABL also increase in length. Contemporary utility-scale wind turbines operate at rotor diameter-based Rossby numbers, the nondimensional ratio between inertial and Coriolis forces, of O(100) where Coriolis effects become increasingly relevant. Coriolis forces provide a direct forcing on the wake, but also affect the ABL base flow, which indirectly influences wake evolution. These effects may constructively or destructively interfere because both the magnitude and sign of the direct and indirect Coriolis effects depend on the Rossby number, turbulence, and buoyancy effects in the ABL. Using large eddy simulations, we investigate wake evolution over a wide range of Rossby numbers relevant to offshore wind turbines. Through an analysis of the streamwise and lateral momentum budgets, we show that Coriolis effects have a small impact on the wake recovery rate, but Coriolis effects induce significant wake deflections which can be parsed into two regimes. For high Rossby numbers (weak Coriolis forcing), wakes deflect clockwise in the northern hemisphere. By contrast, for low Rossby numbers (strong Coriolis forcing), wakes deflect anti-clockwise. Decreasing the Rossby number results in increasingly anti-clockwise wake deflections. The transition point between clockwise and anti-clockwise deflection depends on the direct Coriolis forcing, pressure gradients, and turbulent fluxes in the wake. At a Rossby number of 125, Coriolis deflections are comparable to wake deflections induced by 17{\deg} of yaw-misalignment., Comment: 40 pages, 20 figures, 1 table

Wind speed and direction variations across the rotor affect power production. As utility-scale turbines extend higher into the atmospheric boundary layer (ABL) with larger rotor diameters and hub heights, they increasingly encounter more complex wind speed and direction variations. We assess three models for power production that account for wind speed and direction shear. Two are based on actuator disc representations and the third is a blade element representation. We also evaluate the predictions from a standard power curve model that has no knowledge of wind shear. The predictions from each model, driven by wind profile measurements from a profiling LiDAR, are compared to concurrent power measurements from an adjacent utility-scale wind turbine. In the field measurements of the utility-scale turbine, discrete combinations of speed and direction shear induce changes in power production of -19% to +34% relative to the turbine power curve for a given hub height wind speed. Positive speed shear generally corresponds to over-performance and positive direction shear to under-performance, relative to the power curve. Overall, the blade element model produces both higher correlation and lower error relative to the other models, but its quantitative accuracy depends on induction and controller sub-models. To further assess the influence of complex, non-monotonic wind profiles, we also drive the models with best-fit power law wind speed profiles and linear wind direction profiles. These idealized inputs produce qualitative and quantitative differences in power predictions from each model, demonstrating that time-varying, non-monotonic wind shear affects wind power production., Comment: 28 pages, 14 figures in main body, 1 figure in Appendix A, to be published in Wiley Wind Energy

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 (LES) 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. Compared to the deterministic predictions of the baseline parameter estimates, we find that the MCMC-calibrated parameters reduce the total error of the power predictions by roughly 50%. An additional benefit of the data-driven parameter estimation is the quantification of uncertainty, which enables physically-quantified confidence intervals of wake model predictions., Comment: 35 pages, 10 figures, 1 table

Accurate measurements of atmospheric flows at meter-scale resolution are essential for a broad range of sustainability applications, including optimal design of wind and solar farms, safe and efficient urban air mobility, monitoring of environmental phenomena such as wildfires and air pollution dispersal, and data assimilation into weather and climate models. Measurement of the relevant microscale wind flows is inherently challenged by the optical transparency of the wind. This review explores new ways in which physics can be leveraged to "see" environmental flows non-intrusively, that is, without the need to place measurement instruments directly in the flows of interest. Specifically, while the wind itself is transparent, its effect can be visually observed in the motion of objects embedded in the environment and subjected to wind -- swaying trees and flapping flags are commonly encountered examples. We describe emerging efforts to accomplish visual anemometry, the task of quantitatively inferring local wind conditions based on the physics of observed flow-structure interactions. Approaches based on first-principles physics as well as data-driven, machine learning methods will be described, and remaining obstacles to fully generalizable visual anemometry will be discussed., Comment: Revised with expanded bibliography

Collective wind farm flow control, where wind turbines are operated in an individually suboptimal strategy to benefit the aggregate farm, has demonstrated potential to reduce wake interactions and increase farm energy production. However, existing wake models used for flow control often estimate the thrust and power of yaw misaligned turbines using simplified empirical expressions which require expensive calibration data and do not accurately extrapolate between turbine models. The thrust, wake velocity deficit, wake deflection, and power of a yawed wind turbine depend on its induced velocity. Here, we extend classical one-dimensional momentum theory to model the induction of a yaw misaligned actuator disk. Analytical expressions for the induction, thrust, initial wake velocities, and power are developed as a function of the yaw angle and thrust coefficient. The analytical model is validated against large eddy simulations of a yawed actuator disk. Because the induction depends on the yaw and thrust coefficient, the power generated by a yawed actuator disk will always be greater than a $\cos^3(\gamma)$ model suggests, where $\gamma$ is yaw. The power lost by yaw depends on the thrust coefficient. An analytical expression for the thrust coefficient that maximizes power, depending on the yaw, is developed and validated. Finally, using the developed induction model as an initial condition for a turbulent far-wake model, we demonstrate how combining wake steering and thrust (induction) control can increase array power, compared to either independent steering or induction control, due to the joint dependence of the induction on the thrust coefficient and yaw angle., Comment: 22 pages, 9 figures

Wind turbines located in wind farms are operated to maximize only their own power production. Individual operation results in wake losses that reduce farm energy. In this study, we operate a wind turbine array collectively to maximize total array production through wake steering. The selection of the farm control strategy relies on the optimization of computationally efficient flow models. We develop a physics-based, data-assisted flow control model to predict the optimal control strategy. In contrast to previous studies, we first design and implement a multi-month field experiment at a utility-scale wind farm to validate the model over a range of control strategies, most of which are suboptimal. The flow control model is able to predict the optimal yaw misalignment angles for the array within +/- 5 degrees for most wind directions (11-32% power gains). Using the validated model, we design a control protocol which increases the energy production of the farm in a second multi-month experiment by 2.7% and 1.0%, for the wind directions of interest and for wind speeds between 6 and 8 m/s and all wind speeds, respectively. The developed and validated predictive model can enable a wider adoption of collective wind farm operation., Comment: 14 pages, 5 figures, 1 table

Data required to calibrate uncertain GCM parameterizations are often only available in limited regions or time periods, for example, observational data from field campaigns, or data generated in local high-resolution simulations. This raises the question of where and when to acquire additional data to be maximally informative about parameterizations in a GCM. Here we construct a new ensemble-based parallel algorithm to automatically target data acquisition to regions and times that maximize the uncertainty reduction, or information gain, about GCM parameters. The algorithm uses a Bayesian framework that exploits a quantified distribution of GCM parameters as a measure of uncertainty. This distribution is informed by time-averaged climate statistics restricted to local regions and times. The algorithm is embedded in the recently developed calibrate-emulate-sample (CES) framework, which performs efficient model calibration and uncertainty quantification with only $\mathcal{O}(10^2)$ model evaluations, compared with $\mathcal{O}(10^5)$ evaluations typically needed for traditional approaches to Bayesian calibration. We demonstrate the algorithm with an idealized GCM, with which we generate surrogates of local data. In this perfect-model setting, we calibrate parameters and quantify uncertainties in a quasi-equilibrium convection scheme in the GCM. We consider targeted data that are (i) localized in space for statistically stationary simulations, and (ii) localized in space and time for seasonally varying simulations. In these proof-of-concept applications, the calculated information gain reflects the reduction in parametric uncertainty obtained from Bayesian inference when harnessing a targeted sample of data. The largest information gain typically, but not always, results from regions near the intertropical convergence zone (ITCZ).

Climate models are generally calibrated manually by comparing selected climate statistics, such as the global top-of-atmosphere energy balance, to observations. The manual tuning only targets a limited subset of observational data and parameters. Bayesian calibration can estimate climate model parameters and their uncertainty using a larger fraction of the available data and automatically exploring the parameter space more broadly. In Bayesian learning, it is natural to exploit the seasonal cycle, which has large amplitude, compared with anthropogenic climate change, in many climate statistics. In this study, we develop methods for the calibration and uncertainty quantification (UQ) of model parameters exploiting the seasonal cycle, and we demonstrate a proof-of-concept with an idealized general circulation model (GCM). Uncertainty quantification is performed using the calibrate-emulate-sample approach, which combines stochastic optimization and machine learning emulation to speed up Bayesian learning. The methods are demonstrated in a perfect-model setting through the calibration and UQ of a convective parameterization in an idealized GCM with a seasonal cycle. Calibration and UQ based on seasonally averaged climate statistics, compared to annually averaged, reduces the calibration error by up to an order of magnitude and narrows the spread of posterior distributions by factors between two and five, depending on the variables used for UQ. The reduction in the size of the parameter posterior distributions leads to a reduction in the uncertainty of climate model predictions., Comment: 21 pages, 11 figures, 2 tables

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., Comment: 36 pages, 16 figures, 3 tables

The intentional yaw misalignment of leading, upwind turbines in a wind farm, termed wake steering, has demonstrated potential as a collective control approach for wind farm power maximization. The optimal control strategy, and resulting effect of wake steering on wind farm power production, are in part dictated by the power degradation of the upwind yaw misaligned wind turbines. In the atmospheric boundary layer, the wind speed and direction may vary significantly over the wind turbine rotor area, depending on atmospheric conditions and stability, resulting in freestream turbine power production which is asymmetric as a function of the direction of yaw misalignment and which varies during the diurnal cycle. In this study, we propose a model for the power production of a wind turbine in yaw misalignment based on aerodynamic blade elements which incorporates the effects of wind speed and direction changes over the turbine rotor area in yaw misalignment. A field experiment is performed using multiple utility-scale wind turbines to characterize the power production of yawed freestream operating turbines depending on the wind conditions, and the model is validated using the experimental data. The resulting power production of a yaw misaligned variable speed wind turbine depends on a nonlinear interaction between the yaw misalignment, the atmospheric conditions, and the wind turbine control system., Comment: 37 pages, 15 figures

To design and optimize arrays of vertical-axis wind turbines (VAWTs) for maximal power density and minimal wake losses, a careful consideration of the inherently three-dimensional structure of the wakes of these turbines in real operating conditions is needed. Accordingly, a new volumetric particle-tracking velocimetry method was developed to measure three-dimensional flow fields around full-scale VAWTs in field conditions. Experiments were conducted at the Field Laboratory for Optimized Wind Energy (FLOWE) in Lancaster, CA, using six cameras and artificial snow as tracer particles. Velocity and vorticity measurements were obtained for a 2-kW turbine with five straight blades and a 1-kW turbine with three helical blades, each at two distinct tip-speed ratios and at Reynolds numbers based on the rotor diameter $D$ between $1.26 \times 10^6$ and $1.81 \times 10^6$. A tilted wake was observed to be induced by the helical-bladed turbine. By considering the dynamics of vortex lines shed from the rotating blades, the tilted wake was connected to the geometry of the helical blades. Furthermore, the effects of the tilted wake on a streamwise horseshoe vortex induced by the rotation of the turbine were quantified. Lastly, the implications of these dynamics for the recovery of the wake were examined. This study thus establishes a fluid-mechanical connection between the geometric features of a VAWT and the salient three-dimensional flow characteristics of its near-wake region, which can potentially inform both the design of turbines and the arrangement of turbines into highly efficient arrays., Comment: Version 2, currently under review

Wind energy resource quantification, air pollution monitoring, and weather forecasting all rely on rapid, accurate measurement of local wind conditions. Visual observations of the effects of wind---the swaying of trees and flapping of flags, for example---encode information regarding local wind conditions that can potentially be leveraged for visual anemometry that is inexpensive and ubiquitous. Here, we demonstrate a coupled convolutional neural network and recurrent neural network architecture that extracts the wind speed encoded in visually recorded flow-structure interactions of a flag and tree in naturally occurring wind. Predictions for wind speeds ranging from 0.75-11 m/s showed agreement with measurements from a cup anemometer on site, with a root-mean-squared error approaching the natural wind speed variability due to atmospheric turbulence. Generalizability of the network was demonstrated by successful prediction of wind speed based on recordings of other flags in the field and in a controlled wind tunnel test. Furthermore, physics-based scaling of the flapping dynamics accurately predicts the dependence of the network performance on the video frame rate and duration., Comment: NeurIPS 2019 (to appear). The dataset has been expanded to include videos of a tree canopy in addition to flags. The models were retrained, and results were updated accordingly. The introduction and related work sections were also expand upon. Clarifying details were added to explain author choices such as time averaging windows and to further discuss test set results

The benefits of legged locomotion shown in nature overcome challenges such as obstacles or terrain smoothness typically encountered with wheeled vehicles. This paper evaluates the benefits of using optimal control on a single leg hopper during the entire hopping motion. Basic control without considering physical constraints is implemented through hand-tuned PD controllers following the Raibert control framework. The differential flatness of the first-order equations of motion and the Liouvillian property for the second-order equations for the hopper system are proved, enabling flat outputs for control. A two-point boundary value problem (BVP) is then used to minimize jerk in the flat system to gain implicit smoothness in the output controls. This smoothness ensures that the planned trajectories are feasible, allowing for given waypoints to be reached., Comment: 6 pages, 8 figures

Reducing wake losses in wind farms by deflecting the wakes through turbine yawing has been shown to be a feasible wind farm controls approach. Nonetheless, the effectiveness of yawing depends not only on the degree of wake deflection but also on the resulting shape of the wake. In this work, the deflection and morphology of wakes behind a wind turbine operating in yawed conditions are studied using wind tunnel experiments of a wind turbine modeled as a porous disk in a uniform inflow. First, by measuring velocity distributions at various downstream positions and comparing with prior studies, we confirm that the non-rotating wind turbine model in yaw generates realistic wake deflections. Second, we characterize the wake shape and make first observations of what is termed a curled wake, displaying significant spanwise asymmetry. The wake curling observed in the experiments is also reproduced qualitatively in large eddy simulations using both actuator disk and actuator line models. When a wind turbine is yawed for the benefit of downstream turbines, the asymmetric shape of the wake must be taken into account since it affects how much of it intersects the downstream turbines., Comment: 17 pages, 13 figures, presented at APS-DFD 2015