Article

Data-driven wake model parameter estimation to analyze effects of wake superposition

AIP Publishing
Journal of Renewable and Sustainable Energy
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Abstract

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 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. For the cases tested, the MCMC-calibrated parameters reduce the total error of the power predictions by roughly 50% compared to the deterministic empirical model predictions. An additional benefit of the data-driven parameter estimation is the quantification of uncertainty, which enables physically quantified confidence intervals of wake model predictions.

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... No wake-added turbulence model is necessary since we are modeling a single turbine wake in all cases. 43 This means that wake-added turbulence does not affect wake recovery for a single turbine case. ...
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We present and test a coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a wind-farm. This model couples the traditional, industry-standard wake model approach with a “top-down” model for the overall wind-farm boundary layer structure. The wake model captures the effect of turbine positioning, while the “top-down” portion of the model adds the interactions between the wind-turbine wakes and the atmospheric boundary layer. Each portion of the model requires specification of a parameter that is not known a-priori. For the wake model, the wake expansion coefficient is required, while the “top-down” model requires an effective spanwise turbine spacing within which the model's momentum balance is relevant. The wake expansion coefficient is obtained by matching the predicted mean velocity at the turbine from both approaches, while the effective spanwise turbine spacing depends on turbine positioning and thus can be determined from the wake model. Coupling of the constitutive components of the CWBL model is achieved by iterating these parameters until convergence is reached. We illustrate the performance of the model by applying it to both developing wind-farms including entrance effects and to fully developed (deep-array) conditions. Comparisons of the CWBL model predictions with results from a suite of large eddy simulations show that the model closely represents the results obtained in these high-fidelity numerical simulations. A comparison with measured power degradation at the Horns Rev and Nysted wind-farms shows that the model can also be successfully applied to real wind-farms.
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A momentum-conserving wake superposition method for wind farm power prediction - Volume 889 - Haohua Zong, Fernando Porté-Agel
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The accelerating growth of wind energy in recent years mandates improved understanding of wind turbine, wind farm and atmospheric turbulence interactions. Fluid turbulence plays a vital role in these interactions, motivating the present formulation of several pertinent questions for turbulence research. These questions touch upon the need for better analytical, synthetic and reduced order models of turbulence, better model coupling methods and basic understanding of flow phenomena governing kinetic energy entrainment and limiting power densities. Responding to the formulated questions may lead to improvements in wind energy harvesting.
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Reynolds-Averaged Navier-Stokes models are not very accurate for high-Reynolds-number compressible jet-incrossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-Averaged Navier-Stokes model. In this work, the hypothesis is pursued that Reynolds-Averaged Navier-Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.ABayesian inverse problem is formulated to estimate three Reynolds-Averaged Navier-Stokes parameters (Cμ;Cϵ2;Cϵ1), and a Markov chain Monte Carlo method is used to develop a probability density function for them. The cost of the Markov chain Monte Carlo is addressed by developing statistical surrogates for the Reynolds-Averaged Navier-Stokes model. It is found that only a subset of the (Cμ;Cϵ2;Cϵ1) spaceRsupports realistic flow simulations.Ris used as a prior belief when formulating the inverse problem. It is enforced with a classifier in the current Markov chain Monte Carlo solution. It is found that the calibrated parameters improve predictions of the entire flowfield substantially when compared to the nominal/ literature values of (Cμ;Cϵ2;Cϵ1); furthermore, this improvement is seen to hold for interactions at other Mach numbers and jet strengths for which the experimental data are available to provide a comparison. The residual error is quantifies, which is an approximation of the model-form error; it is most easily measured in terms of turbulent stresses. © Copyright 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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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 porous disk model of a wind turbine operating in yawed conditions are studied using wind tunnel experiments and uniform inflow. First, by measuring velocity distributions at various downstream positions and comparing with prior studies, we confirm that the non-rotating porous disk wind turbine model in yaw generates realistic wake deflections. Second, we characterize the wake shape and make observations of what is termed as 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. Results suggest that when a wind turbine is yawed for the benefit of downstream turbines, the curled shape of the wake and its asymmetry must be taken into account since it affects how much of it intersects the downstream turbines.
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In the present paper a new approach for the analysis of wake effects in wind parks is presented. The wake model used to simulate the energy extraction process is a kinematic one, based on Abramovich's turbulent jets. The most significant features introduced herein are: 1) the use of the power curve of the turbine for the determination of the initial velocity deficit, 2) the use of a weighted formula for the estimation of the onset velocities of the turbines, 3) the use of energy considerations for the approximation of the interactions of the wakes of the turbines and 4) the use of boundary layer velocity profiles in accounting for ground effects. Comparisons between experimental data and numerical results show that these modifications provide more precise predictions of the output of wind parks. (A)
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A modeling framework is proposed and validated to simulate turbine wakes and associated power losses in wind farms. It combines the large-eddy simulation (LES) technique with blade element theory and a turbine-model-specific relationship between shaft torque and rotational speed. In the LES, the turbulent subgrid-scale stresses are parameterized with a tuning-free Lagrangian scale-dependent dynamic model. The turbine-induced forces and turbine-generated power are modeled using a recently developed actuator-disk model with rotation (ADM-R), which adopts blade element theory to calculate the lift and drag forces (that produce thrust, rotor shaft torque and power) based on the local simulated flow and the blade characteristics. In order to predict simultaneously the turbine angular velocity and the turbine-induced forces (and thus the power output), a new iterative dynamic procedure is developed to couple the ADM-R turbine model with a relationship between shaft torque and rotational speed. This relationship, which is unique for a given turbine model and independent of the inflow condition, is derived from simulations of a stand-alone wind turbine in conditions for which the thrust coefficient can be validated. Comparison with observed power data from the Horns Rev wind farm shows that better power predictions are obtained with the dynamic ADM-R than with the standard ADM, which assumes a uniform thrust distribution and ignores the torque effect on the turbine wakes and rotor power. The results are also compared with the power predictions obtained using two commercial wind-farm design tools (WindSim and WAsP). These models are found to underestimate the power output compared with the results from the proposed LES framework.
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The intention of this study is to propose and validate a simple and efficient analytical model for the prediction of the wake velocity downwind of a stand-alone wind-turbine. Extensive efforts have been carried out to model the wake region analytically. One of the most popular models, proposed by Jensen, assumes a top-hat distribution of the velocity deficit at any plane perpendicular to the wake. That model has been extensively used in the literature and commercial softwares, but it has two important limitations that should be pointed out: (a) Even though this model is supposed to satisfy momentum conservation, in reality mass conservation is only used to derive it; (b) the assumption of a top-hat distribution of the velocity deficit is expected to underestimate that deficit in the center of the wake, and overestimate it near the edge of the wake. In order to overcome the above-mentioned limitations, here we propose an alternative analytical model that satisfies both mass and momentum conservation, and assumes a Gaussian distribution of the velocity deficit. For this purpose, we apply momentum and mass conservation to two different control volumes which have been previously used in the context of analytical modeling of wakes. The velocity profiles obtained with our proposed model are in good agreement with large-eddy simulation data and experimental measurements. By contrast, the top hat models, as expected, clearly underestimate the velocity deficit at the center of the wake region and overestimate it near the edge of the wake.