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This study aims to show the application of stochastic optimization for efficient and robust parameter calibration of engineering wake models. Standard values of the wake effect parameters are generally used to predict power using engineering wake models, but some recent studies have shown that these values do not result in accurate prediction. The proposed approach estimates the wake effect parameters using operational data available from actual wind farms to minimize the prediction error of the wake model by using trust-region optimization. To further improve computational efficiency, we implement stratified adaptive sampling. We employ decision trees to stratify the data and propose two ways of adapting the sampling budget to the constructed strata: budget allocation with dynamic weights and fixed weights. We extend our analysis to determine the functional relationship between the turbulence intensity and wake decay coefficient. Our experiments suggest that wake parameters or a functional relationship between turbulence intensity and wake decay coefficient may need adjustments (from assumed standard values) for a particular wind farm using its operational data to characterize the wake effect better. • Engineering wake models have parameters that crucially affect their performance. • Wake parameters can be calibrated as constants or functions of other wind variables. • Stochastic optimization (SO) provides accurate and reliable wake calibrations. • Both point and functional calibration of wake parameters can be done well with SO. • A derivative-free trust-region SO method provides robust wake calibration. • Efficiently implemented trust-region SO uses adaptive sampling and variance reduction. • Stratifying data based on wind characteristics effectively reduces variance during SO. • Choosing strata of wind data and dynamically sampling from each expedites calibration. • Robust wake calibration helps understanding power deficit patterns in wind farms. • Good prediction of power deficit due to wake enables optimal design of new wind farms. [ABSTRACT FROM AUTHOR]

• A new wake model is proposed to predict the turbine wake in yawed conditions. • The wake model can be applied for both wind turbines and hydrokinetic turbines. • The skew distribution is employed to express the spanwise velocity asymmetry. • The wake model is validated by the wind tunnel and open channel flow. • measurements. Predicting the spatial evolution of horizontal-axis turbine wakes is a key factor to enhance the performance of wind and hydrokinetic power plants. The yaw angle misalignment is not only important to account for the uncertainty of the wind direction, but also a control strategy to improve the energy production averaged over the turbine array. In this paper, a new wake model, based on the skew-normal distribution and conservation of mass and momentum, is proposed to predict the turbine wake velocity distribution for given yaw angles. The new model is experimentally validated through wake measurements of yawed miniature wind and hydrokinetic turbines, in wind tunnel and open channel flows, respectively. Predictive capabilities extend from the spatial distribution of the maximum velocity deficit at hub height, to the spanwise asymmetry of the velocity distribution about the wake center. [ABSTRACT FROM AUTHOR]

• A parallel framework for wind farm optimization is developed using six wake models. • Framework accounts for terrain elevation and wake-terrain interaction. • Four turbine specific cost models are developed. • Wind farm area model is developed as the area of convex hull. • Optimization of a realistic wind farm is performed for maximum power generation. A new framework for Wind Farm Layout Optimization (WindFLO) is developed to accelerate the design of wind farms. The framework provides a large set of analytical wake models and wake superposition schemes. It is able to take into account terrain elevation and the ambient wind velocity profile. The schemes in the WindFLO model were validated against experimental data from a wind tunnel to within 1% relative error. A turbine rotor diameter and height dependent cost model was also developed using data from 250 different wind turbines. A land usage model was also developed using the convex hull approach. The framework was used to optimize a wind farm layout for maximum annual energy production using real wind farm terrain and conditions. The nonlinear optimization problem was solved using a robust Single-Objective Hybrid Optimizer. The wind farm layout and wind turbine (rotor diameter and tower height) were optimized and resulted in increased annual energy production, reduced cost and reduced land usage. The WindFLO framework is made publicly available to accelerate and advance the techniques for wind farm optimization. 1 1 WindFLO can be downloaded from https://github.com/sohailrreddy/WindFLO. [ABSTRACT FROM AUTHOR]

• A new engineering wake model for wind farm in complex terrain is proposed. • The new model yields accurate results comparable to CFD simulation and is fast to run. • Systematic comparison of eight algorithms is done for wind farm layout optimization. • Random search, local search and pattern search are found to be the best algorithms. Layout optimization of wind farms constitutes an important and challenging task in complex terrain. This is especially due to the complex interactions of the boundary layer flows in complex terrain and wind turbine wakes, which renders wake modelling in complex terrain difficult. This study tackles this challenge with a new engineering wake model, which is developed by superposing a Gaussian shape wake model on top of the background flow field, assuming that the centerlines of wind turbine wakes follow the streamlines of the background flow field. The model is found to predict wind turbine wakes in complex terrain with good accuracy and at the same time it is computationally cheap to run for optimization applications. Comparisons with high fidelity simulations and field measurements for a real wind farm with 25 turbines in complex terrain demonstrate its effectiveness. A systematic comparison of eight optimization algorithms, which includes two gradient-based and six gradient-free algorithms, is also carried out for the layout optimization problem in complex terrain. To accelerate the optimization process, a double-stage approach is proposed, which optimizes the objective function first neglecting wake effects and then, in the second stage, including them. While all the tested optimization algorithms can improve the original wind farm layout, random search, local search, and pattern search are found to be the top three algorithms in terms of optimization results and computational cost. [ABSTRACT FROM AUTHOR]

• The machine learning framework achieves favorable accuracy and efficiency in the wake prediction. • ADM-R/RANS coupling model can efficiently produce big wake datasets for machine learning model. • For an aligned turbine row, power drops at the second turbine and gradually stabilizes afterwards. • Turbulence model plays an important role in accurate power prediction of wind farm. In the paper, a novel framework that employs the machine learning and CFD (computational fluid dynamics) simulation to develop new wake velocity and turbulence models with high accuracy and good efficiency is proposed to improve the turbine wake predictions. An ANN (artificial neural network) model based on the back-propagation (BP) algorithm is designed to build the underlying spatial relationship between the inflow conditions and the three-dimensional wake flows. To save the computational cost, a reduced-order turbine model ADM-R (actuator disk model with rotation), is incorporated into RANS (Reynolds-averaged Navier-Stokes equations) simulations coupled with a modified k - ε turbulence model to provide big datasets of wake flow for training, testing, and validation of the ANN model. The numerical framework of RANS/ADM-R simulations is validated by a standalone Vestas V80 2 MW wind turbine and NTNU wind tunnel test of double aligned turbines. In the ANN-based wake model, the inflow wind speed and turbulence intensity at hub height are selected as input variables, while the spatial velocity deficit and added turbulence kinetic energy (TKE) in wake field are taken as output variables. The ANN-based wake model is first deployed to a standalone turbine, and then the spatial wake characteristics and power generation of an aligned 8-turbine row as representation of Horns Rev wind farm are also validated against Large Eddy Simulations (LES) and field measurement. The results of ANN-based wake model show good agreement with the numerical simulations and measurement data, indicating that the ANN is capable of establishing the complex spatial relationship between inflow conditions and the wake flows. The machine learning techniques can remarkably improve the accuracy and efficiency of wake predictions. [ABSTRACT FROM AUTHOR]