Bayesian uncertainty quantification framework for wake model calibration and validation with historical wind farm power data

The expected growth in wind energy capacity requires efficient and accurate models for wind farm layout optimization, control, and annual energy predictions. Although analytical wake models are widely used for these applications, several model components must be better understood to improve their accuracy. To this end, we propose a Bayesian uncertainty quantification framework for physics-guided data-driven model enhancement. The framework incorporates turbulence-related aleatoric uncertainty in historical wind farm data, epistemic uncertainty in the empirical parameters, and systematic uncertainty due to unmodeled physics. We apply the framework to the wake expansion parametrization in the Gaussian wake model and employ historical power data of the Westermost Rough Offshore Wind Farm. We find that the framework successfully distinguishes the three sources of uncertainty in the joint posterior distribution of the parameters. On the one hand, the framework allows for wake model calibration by selecting the maximum a posteriori estimators for the empirical parameters. On the other hand, it facilitates model validation by separating the measurement error and the model error distribution. In addition, the model adequacy and the effect of unmodeled physics are assessable via the posterior parameter uncertainty and correlations. Consequently, we believe that the Bayesian uncertainty quantification framework can be used to calibrate and validate existing and upcoming physics-guided models.     

Validation and uncertainty quantification of metocean models for assessing hurricane risk

A reliable metocean model, with its uncertainty quantified and its accuracy validated for conditions appropriate to assessing risk, is essential to understand the risk posed by hurricanes to offshore infrastructure such as offshore wind turbines. In this paper, three metocean models are considered, with the seastate predicted using the commercial software Mike 21, and the meteorological forcing defined by three conditions. The three conditions include (1) reanalysis data within and surrounding the hurricane, (2) predictions from the empirical Holland model within the hurricane and reanalysis data surrounding the hurricane, and (3) predictions from the empirical Holland model within the hurricane and wind‐free conditions surrounding the hurricane. The accuracy of the first metocean model is validated with (1) measurements of wind speed, wave height, wave period, and storm surge during 23 historical hurricanes from 1999 to 2012 and (2) a comparison to hindcast data from WaveWatch III, another numerical metocean model. The prediction performance of the second and third metocean models is then compared with that of the first to evaluate the impact of meteorological conditions on model predictions, as the third metocean model is necessary for risk analysis, where reanalysis data of meteorological conditions is not available. This study shows that the inconsistency between the modeling of meteorological conditions for risk assessment and for validation is influential for hurricanes with low maximum wind speeds, when model predictions are significantly better if the meteorological conditions surrounding the hurricane wind field are included. This study also shows that this inconsistency is effectively diminished when considering only events with high maximum wind speeds. Since high wind speeds are what is relevant to risk assessments, the third metocean model can be reasonably used to assess hurricane risk. Finally, the uncertainties, biases, and correlations of uncertainties in the model predictions for wind speed, wave height, wave period, and storm surge are quantified for the third metocean model, and a numerical example is constructed to illustrate the impact of including uncertainty on the assessment of risk to offshore infrastructure during hurricanes. The example demonstrates how uncertainty and correlation of uncertainty influence the size and shape of a 50‐year environmental contour of wind speed and wave height.     

Simulating the aerodynamic performance and wake dynamics of a vertical‐axis wind turbine

The accurate prediction of the aerodynamics and performance of vertical‐axis wind turbines is essential if their design is to be improved but poses a significant challenge to numerical simulation tools. The cyclic motion of the blades induces large variations in the angle of attack of the blades that can manifest as dynamic stall. In addition, predicting the interaction between the blades and the wake developed by the rotor requires a high‐fidelity representation of the vortical structures within the flow field in which the turbine operates. The aerodynamic performance and wake dynamics of a Darrieus‐type vertical‐axis wind turbine consisting of two straight blades is simulated using Brown's Vorticity Transport Model. The predicted variation with azimuth of the normal and tangential force on the turbine blades compares well with experimental measurements. The interaction between the blades and the vortices that are shed and trailed in previous revolutions of the turbine is shown to have a significant effect on the distribution of aerodynamic loading on the blades. Furthermore, it is suggested that the disagreement between experimental and numerical data that has been presented in previous studies arises because the blade–vortex interactions on the rotor were not modelled with sufficient fidelity. Copyright © 2010 John Wiley & Sons, Ltd.     

Validation of a CFD model with a synchronized triple‐lidar system in the wind turbine induction zone

A novel validation methodology allows verifying a CFD model over the entire wind turbine induction zone using measurements from three synchronized lidars. The validation procedure relies on spatially discretizing the probability density function of the measured free‐stream wind speed. The resulting distributions are reproduced numerically by weighting steady‐state Reynolds averaged Navier‐Stokes simulations accordingly. The only input varying between these computations is the velocity at the inlet boundary. The rotor is modelled using an actuator disc. So as to compare lidar and simulations, the spatial and temporal uncertainty of the measurements is quantified and propagated through the data processing. For all velocity components the maximal difference between measurements and model are below 4.5% relative to the average wind speed for most of the validation space. This applies to both mean and standard deviation. One rotor radius upstream the difference reaches maximally 1.3% for the axial component. © 2017 The Authors. Wind Energy Published by John Wiley & Sons, Ltd.     

Combining simulations and data with deep learning and uncertainty quantification for advanced energy modeling

A novel and modern framework for energy modeling is developed in this paper with a focus on nuclear energy modeling and simulation. The framework combines multiphysics simulations and real data, with validation by uncertainty quantification tasks and facilitation by machine and deep learning methods. The hybrid framework is built on the basis of a wide range of physical models, real data, mathematical and statistical methods, and artificial intelligence techniques. The framework is demonstrated in different applications, including quantifying uncertainties in computer simulations, multiphysics coupling, analysis of variance using machine learning surrogate models, deep learning of time series phenomena, and propagating parametric uncertainties of nuclear data. The applications demonstrated are oriented to nuclear engineering simulations, even though majority of the methods are applicable to other energy sources (eg, renewable). Efficient utilization of this framework is expected to yield a much better understanding of the physical phenomena analyzed as well as an improvement in the performance of the energy design/model under construction.     

Skeletal reaction model generation,uncertainty quantification and minimization: Combustion of butane

Skeletal reaction models for n-butane and iso-butane combustion are derived from a detailed chemistry model through directed relation graph (DRG) and DRG-aided sensitivity analysis (DRGASA) methods. It is shown that the accuracy of the reduced models can be improved by optimization through the method of uncertainty minimization by polynomial chaos expansion (MUM-PCE). The dependence of model uncertainty on the model size is also investigated by exploring skeletal models containing different number of species. It is shown that the dependence of model uncertainty is subject to the completeness of the model. In principle, for a specific simulation the uncertainty of a complete model, which includes all reactions important to its prediction, is convergent with respect to the model size, while the uncertainty calculated with an incomplete model may display unpredictable correlation with the model size.     

Effect of rotor–tower interaction,tilt angle,and yaw misalignment on the aeroelasticity of a large horizontal axis wind turbine with composite blades

This paper presents a detailed analysis of the rotor–tower interaction and the effects of the rotor's tilt angle and yaw misalignment on a large horizontal axis wind turbine. A high‐fidelity aeroelastic model is employed, coupling computational fluid dynamics (CFD) and structural mechanics (CSM). The wind velocity stratification induced by the atmospheric boundary layer (ABL) is modeled. On the CSM side, the complex composite structure of each blade is accurately modeled using shell elements. The rotor–tower interaction is analyzed by comparing results of a rotor‐only simulation and a full‐machine simulation, observing a sudden drop in loads, deformations, and power production of each blade, when passing in front of the tower. Subsequently, a tilt angle is introduced on the rotor, and its effect on blade displacements, loads, and performance is studied, representing a novelty with respect to the available literature. The tilt angle leads to a different contribution of gravity to the blade deformations, sensibly affecting the stresses in the composite material. Lastly, a yaw misalignment is introduced with respect to the incoming wind, and the resulting changes in the blade solicitations are analyzed. In particular, a reduction of the blade axial displacement amplitude during each revolution is observed.     

Uncertainty quantification of infinite aligned wind farm performance using non‐intrusive polynomial chaos and a distributed roughness model

Uncertainty of wind farm parameters can have a significant effect on wind farm power output. Knowledge of the uncertainty‐produced stochastic distribution of the entire wind farm power output and the corresponding uncertainty propagation mechanisms is very important for evaluating the uncertainty effects on the wind farm performance during wind farm planning stage and providing insights on improving the performance of the existing wind farms. In this work, the propagation of uncertainties from surface roughness and induction factor in infinite aligned wind farms modeled by a modified distributed roughness model is investigated using non‐intrusive polynomial chaos. Stochastic analysis of surface roughness indicates that 30% uncertainty can propagate such that there is up a 8% uncertainty in the power output of the wind farm by affecting the uncertainty in the position of the individual wind turbines in the vertical boundary layer profile and uncertainty in vertical momentum fluxes which replenish energy in the wake in large wind farms. Induction factor uncertainty of the wind turbines can also have a significant effect on power output. Not only does its uncertainty substantially affect the vertical boundary layer profile, but the uncertainty in turbine wake growth which affects how neighboring turbine wakes interact. We found that optimal power output in terms of reduction of uncertainty closely correlates with the Betz limit and is dependent on the mean induction factor. Copyright © 2016 John Wiley & Sons, Ltd.     

Multicamera measurement system to evaluate the dynamic response of utility‐scale wind turbine blades

Wind turbine blade certification requires static and fatigue testing at a large‐scale facility similar to the Wind Technology Testing Center (WTTC) located in Charlestown, Massachusetts. Usually, these tests are conducted by using wire‐based sensors such as strain gages, accelerometers, and string potentiometers. These systems are expensive, require a time‐consuming installation (e.g., up to 3 weeks and $35 k–$50 k for a strain gage system on a 55‐m‐long blade), are difficult to deploy on large‐sized structures, require additional instrumentations (e.g., power amplifiers and data acquisition systems), and produce results only at a handful of a discrete number of measurement points. In this study, a multicamera measurement system is implemented and experimentally evaluated to obtain full‐field displacement and strain over a ~12‐m‐long portion of a ~60‐m utility‐scale wind turbine blade. The proposed system has the potential to streamline the certification process by reducing the blade's preparation and sensor installation cost and time to a few hundreds of dollars (for painting equipment) and a few days for preparing the surface of the blade for the test. Furthermore, operational modal analysis was used in conjunction with the multicamera system to estimate the natural frequencies and mode shapes of the wind turbine blade. The obtained results have shown that the proposed approach can detect in‐plane displacement as low as 0.2 mm, mechanical strain with an error below 3% when compared with measurement performed using strain gages, and the first five natural frequencies with an error below 2% when compared with data recorded using traditional wire‐based accelerometers. This paper presents these results and provides a summary of the strengths and weaknesses of the proposed optical measurement approach in the context of streamlining the blade certification/testing process and performing vision‐based structural dynamic measurements on large‐scale structures.     

A combined aeroelastic‐aeroacoustic model for wind turbine noise: verification and analysis of field measurements

In this paper, semi‐empirical engineering models for the three main wind turbine aerodynamic noise sources, namely, turbulent inflow, trailing edge and stall noise, are introduced. They are implemented into the in‐house aeroelastic code HAWC2 commonly used for wind turbine load calculations and design. The results of the combined aeroelastic and aeroacoustic model are compared with field noise measurements of a 500 kW wind turbine. Model and experimental data are in fairly good agreement in terms of noise levels and directivity. The combined model allows separating the various noise sources and highlights a number of mechanisms that are difficult to differentiate when only the overall noise from a wind turbine is measured. Copyright © 2017 John Wiley & Sons, Ltd.     

Development of a wind turbine model and simulation platform using an acausal approach: Multiphysics modeling,validation, and control

This article presents the development of the Control-oriented, Reconfigurable, and Acausal Floating Turbine Simulator (CRAFTS). CRAFTS has a modular, hierarchical model architecture that enables rapid and accurate simulation of wind turbines. The architecture facilitates the incorporation of model variants, and its system reconfiguration features help simulate multiple design variants. CRAFTS also supports the integration of models developed on a causality-free platform (e.g., Modelica®) with existing causal models. This article focuses on the validation of a land-based wind turbine models against OpenFAST, an industry-standard platform, for several test cases. Closed-loop scenarios are also tested using the standard ROSCO controller and compared against OpenFAST. In addition, a nonlinear controller developed in our prior work is also evaluated. The test cases demonstrate the user-friendly and computationally efficient capabilities of CRAFTS to facilitate control co-design, assist in incorporating multiphysics models, be adaptable to design variants, and allow for rapid simulations to validate models and evaluate controllers.     

Estimation of the electric fields and dielectric breakdown in non‐conductive wind turbine blades subjected to a lightning stepped leader

In this paper, the electric fields in the wind turbine blades due to the lightning stepped leader are studied, and the dielectric breakdown is assessed. The developed finite element analysis (FEA) includes the full length of the leader and enables one to incorporate various uniform and non‐uniform charge density models. The lightning striking distance is calculated using the rolling sphere method. The electric field in a horizontal axis wind turbine with three blades representing Sandia 100 m All‐glass Baseline Wind Turbine Blades (SNL 100‐00) at three different lightning protection levels (LPL) is computed and compared to the dielectric breakdown strength of the blades. The dielectric breakdown strength of the blades is evaluated based on the experimental data. The results show that the tip region of the blade is the most vulnerable to the dielectric breakdown with the safety factor as low as 1.32 at LPL I. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved BEM model for the power curve prediction of stall‐regulated wind turbines

Blade element momentum (BEM) theory is the standard computational technique for the prediction of power curves of wind turbines; it is based on the two‐dimensional aerodynamic properties of aerofoil blade elements and some corrections accounting for three‐dimensional wing aerodynamics. Although most BEM models yield acceptable results for low‐wind and pitch‐controlled regimes where the local angles of attack are small, no generally accepted model exists up to date that consistently predicts the power curve in the stall regime for a variety of blade properties and operating conditions. In this article we present a modified BEM model which satisfactorily reproduces the power curves of four experimental wind turbines reported in the literature, using no free fit parameters. Since these four experimental cases comprehend a great variety of conditions (wind tunnel vs field experiments, different air densities) and blade parameters (no twist and no taper, no taper but twist, both twist and taper, different aerofoil families), it is believed that our model represents a useful working tool for the aerodynamic design of stall‐regulated wind turbines. Copyright © 2004 John Wiley & Sons, Ltd.     

Qualitative performance assessment of semiconductor switching device,converter and generator candidates for 10 MW offshore wind turbine generators

This paper investigates the possibilities of viable power electronics converters, semiconductor switching devices and electric machines for 10 MW variable‐speed wind turbine generators. The maximum rated power of existing wind turbine configurations is in the range of 6 MW. The proposed alternatives are compared against several technical and economical factors, and their advantages over the present wind turbines are highlighted. A comprehensive performance comparison of modern power semiconductor devices, their electrical characteristics and the key differentiators among them are presented. The power electronics converters considered include all commercially available multilevel voltage source and current source converters as well as the opportunities offered by power electronics building block‐based design. The factors used for the comparison include the converter power range, capacitor voltage balancing, common mode voltage and current, electromagnetic interference emissions, fault ride‐through capability, reliability, footprint, harmonic performance, efficiency and losses, component count, risk of torsional vibration by the harmonics and inter‐harmonics, complexity, ease of back‐to‐back operation and filtering requirements. For the electric machines, this study concentrates on high‐temperature superconducting machines, multi‐phase induction machines and permanent magnet synchronous machines. These machines are compared against existing wind generator technologies in terms of their power range, torque density, efficiency, fault ride‐through capability, reliability, footprint, harmonic performance, ease of fault detection, excitation control, noise and vibration signature, oscillation damping, gearbox requirement, cost and the size of the associated converter. Copyright © 2010 John Wiley & Sons, Ltd.     

Rapid optimization of stall‐regulated wind turbine blades using a frequency‐domain method: Part 2, cost function selection and results

A fast and effective frequency‐domain optimization method was developed for stall‐regulated blades. It was found that when using linearized dynamics, typical cost functions employing damage‐equivalent root bending moments are not suitable for stall‐regulated wind turbines: when the cost function is minimized, the edgewise damping can be low, and the flapwise damping can approach zero during an extreme operating gust. A new cost function is proposed that leads to nicely balanced stall behavior and damping over the entire operating windspeed range. The method was used to design the blades of two multi‐MW, stall‐regulated, offshore wind turbines, comparable with the NREL 5 MW and NTNU 10 MW pitch‐regulated turbines. It is shown that the optimal stall‐regulated blade has a unique aerodynamic profile that gives high flapwise and edgewise damping and a uniform mean power output above the rated windspeed. The blades are described in sufficient detail that they can be used in further aeroelastic analyses, to compare large stall‐regulated and pitch‐regulated turbines. Copyright © 2014 John Wiley & Sons, Ltd.     

Mesoscale modeling of offshore wind turbine wakes at the wind farm resolving scale: a composite‐based analysis with the Weather Research and Forecasting model over Horns Rev

The use of mesoscale modeling to reproduce the power deficits associated with wind turbine wakes in an offshore environment is analyzed. The study is based on multiyear (3 years) observational and modeling results at the Horns Rev wind farm. The simulations are performed with the Weather Research and Forecasting mesoscale model configured at a high horizontal resolution of 333 m over Horns Rev. The wind turbines are represented as an elevated momentum sink and a source of turbulent kinetic energy. Composites with different atmospheric conditions are extracted from both the observed and simulated datasets in order to inspect the ability of the model to reproduce the power deficit in a wide range of atmospheric conditions. Results indicate that mesoscale models such as Weather Research and Forecasting are able to qualitatively reproduce the power deficit at the wind farm scale. Some specific differences are identified. Mesoscale modeling is therefore a suitable framework to analyze potential downstream effects associated with offshore wind farms. Copyright © 2014 John Wiley & Sons, Ltd.     

Prediction of mineral scale formation in geothermal and oilfield operations using the Extended UNIQUAC model: Part II. Carbonate-scaling minerals

Two parameters have been added to the Extended UNIQUAC model of Thomsen and Rasmussen [Thomsen, K., Rasmussen, P., 1999. Modeling of vapor–liquid–solid equilibrium in gas-aqueous electrolyte systems. Chem. Eng. Sci. 54, 1787–1802] to account for the pressure dependency of mineral solubility. The improved model has been used for correlating and predicting vapor–liquid–solid equilibrium for different carbonate systems (CaCO₃, MgCO₃, BaCO₃ and SrCO₃) causing mineral scaling problems. The solubility of NaCl and CO₂ in pure water and the solubility of CO₂ in NaCl and Na₂SO₄ solutions have also been correlated. The results show that the Extended UNIQUAC model, with the added pressure parameters, is able to represent binary (NaCl–H₂O, CaCO₃–H₂O, BaCO₃–H₂O, SrCO₃–H₂O, MgCO₃–H₂O, Mg(OH)₂–H₂O and CO₂–H₂O), ternary (CaCO₃–CO₂–H₂O, BaCO₃–CO₂–H₂O, SrCO₃–CO₂–H₂O, MgCO₃–CO₂–H₂O, CO₂–NaCl–H₂O and CO₂–Na₂SO₄–H₂O), and quaternary (CO₂–NaCl–Na₂SO₄–H₂O) solubility data within the experimental accuracy in the range of temperatures and pressures considered in the study, i.e. from 0 to 250 °C, and from 1 to 1000 bar, respectively.The modified Extended UNIQUAC model will be a useful tool for predicting and quantifying the scaling problems that may occur in wells and surface equipment during geothermal operations. This would allow adequate preventive measures to be taken before mineral deposition becomes troublesome.     

The use of accounting information systems in the evaluation of environmental costs: a cost–benefit analysis model proposal

The increasing pressures in the environment and the environmental social awareness have produced the need for studying interactions between the sectors of the economy and the environment. For a more comprehensive evaluation of sustainability and growth, the field of financial accounting needs to be expanded in order to comprise the use of natural resources and losses in the production process. The paper examines and proposes the cost–benefit analysis model as a useful estimation method of environmental revenues and costs incurred in Greece. These revenues and costs will appear in the profit and loss account statement. Environmental tax is an important cost for all industries with sustainable growth. Taxes are imposed on the natural units, which have a determined negative effect on the environment. Moreover, this paper examines the inherent interaction between the environment and the economic performance of enterprises by adopting environmental management and information green accounting systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of the preload in the general static load‐carrying capacity of four‐contact‐point slewing bearings for wind turbine generators: theoretical model and finite element calculations

This paper presents a generalization of previous works developed by the authors in the field of the calculation and selection of slewing bearings, where a theoretical model for the estimation of the static load‐carrying capacity of four‐contact‐point slewing bearings was obtained. Those previous works assumed that there was no preload in the balls; in the present work, the model has been improved in order to consider the effect of the preload, in such a way that it provides more realistic results because this type of bearings are preloaded in several applications to increase the stiffness and therefore the accuracy of the system. In parallel, and for comparison purposes, the finite element model built by the authors in previous works has been also adapted to include the preload in the balls. Both models, theoretical and FE, assess in complete agreement the increase of the stiffness with the preload level; the results show that the static load‐carrying capacity does not vary appreciably with the usual values adopted for the preload. Copyright © 2013 John Wiley & Sons, Ltd.