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Developments in numerical simulation of flows and high-performance computing influence one another. More detailed simulation methods create a permanent need for more computational power, while new hardware developments often require changes to the software to exploit new hardware features. This dependency is very pronounced in the case of vector-units which are featured by all modern processors to increase their numerical throughput but require vectorization of the software to be used efficiently. We study the vectorization of a simulation method that exhibits an inherent level of vector-parallelism. This is of particular interest as SIMD operations will hopefully be available with std::simd in a future C++ standard. The simulation method considered here results in the simultaneous solution of multiple sparse linear systems of equations which only differ by their main diagonal and right-hand sides. Such structure arises in the simulation of unsteady flow in turbomachinery by means of a frequency domain approach called harmonic balance. [ABSTRACT FROM AUTHOR]

We analyze the relaxation of non-pharmaceutical interventions (NPIs) under an increasing number of vaccinations in Germany. For the spread of SARS-CoV-2 we employ a SIR-type model that accounts for age-dependence and includes realistic contact patterns between age groups. The implementation of NPIs occurs on changed contact patterns, improved isolation, or reduced infectiousness when, e.g., wearing masks. We account for spatial heterogeneity and commuting activities in between regions in Germany, and the testing of commuters is considered as a further NPI. We include the ongoing vaccination process and analyze the effect of the B.1.617.2 (Delta) variant, which is considered to be 40%–60% more infectious then the currently dominant B.1.1.7 (Alpha) variant. We explore different opening scenarios under the ongoing vaccination process by assuming that local restrictions are either lifted in early July or August with or without continued wearing of masks and testing. Our results indicate that we can counteract the resurgence of SARS-CoV-2 despite the Delta variant with appropriate timing for the relaxation of NPIs. In all cases, however, school children are hit the hardest. Author summary: One of the greatest challenges within the Covid-19 pandemic is to identify the timing and amount of non-pharmaceutical interventions (face masks, travel bans, school closures, etc). In the year 2021 more and more people are getting vaccinated. When can we finally lift all restrictions and stop wearing masks? In order to provide more insights to this question, we use a mathematical model which is capable of simulating the effects of non-pharmaceutical interventions in Germany while accounting for age-dependent factors as well as commuting activities between regions. We include the vaccination process and analyze the much more infectious Delta coronavirus variant. We simulate scenarios that consider the timing of the return to pre-pandemic contacts as well as when to suspend wearing masks and testing. Our results show that a later opening by 1 August in combination with masks and testing reduces the chance of a further infection wave considerably. From the retrospective view of the revision, we see that the rise in infections at the end of summer could have been well predicted by our scenarios that considered lifting of NPIs in July as it happened in many places. In all of our scenarios, the infection manifests in the younger age groups. [ABSTRACT FROM AUTHOR]

Background: Despite the vaccination process in Germany, a large share of the population is still susceptible to SARS-CoV-2. In addition, we face the spread of novel variants. Until we overcome the pandemic, reasonable mitigation and opening strategies are crucial to balance public health and economic interests.Methods: We model the spread of SARS-CoV-2 over the German counties by a graph-SIR-type, metapopulation model with particular focus on commuter testing. We account for political interventions by varying contact reduction values in private and public locations such as homes, schools, workplaces, and other. We consider different levels of lockdown strictness, commuter testing strategies, or the delay of intervention implementation. We conduct numerical simulations to assess the effectiveness of the different intervention strategies after one month. The virus dynamics in the regions (German counties) are initialized randomly with incidences between 75 and 150 weekly new cases per 100,000 inhabitants (red zones) or below (green zones) and consider 25 different initial scenarios of randomly distributed red zones (between 2 and 20% of all counties). To account for uncertainty, we consider an ensemble set of 500 Monte Carlo runs for each scenario.Results: We find that the strength of the lockdown in regions with out of control virus dynamics is most important to avoid the spread into neighboring regions. With very strict lockdowns in red zones, commuter testing rates of twice a week can substantially contribute to the safety of adjacent regions. In contrast, the negative effect of less strict interventions can be overcome by high commuter testing rates. A further key contributor is the potential delay of the intervention implementation. In order to keep the spread of the virus under control, strict regional lockdowns with minimum delay and commuter testing of at least twice a week are advisable. If less strict interventions are in favor, substantially increased testing rates are needed to avoid overall higher infection dynamics.Conclusions: Our results indicate that local containment of outbreaks and maintenance of low overall incidence is possible even in densely populated and highly connected regions such as Germany or Western Europe. While we demonstrate this on data from Germany, similar patterns of mobility likely exist in many countries and our results are, hence, generalizable to a certain extent. [ABSTRACT FROM AUTHOR]

Self-adjoint differential operators often arise from variational calculus on energy functionals. In this case, a direct discretization of the energy functional induces a discretization of the differential operator. Following this approach, the discrete equations are naturally symmetric if the energy functional is self-adjoint, a property that may be lost when using standard difference formulas on nonuniform meshes or when the differential operator has varying coefficients. Low order finite difference or finite element systems can be derived by this approach in a systematic way and on logically structured meshes they become compact difference formulas. Extrapolation formulas used on the discrete energy can then lead to higher oder approximations of the differential operator. A rigorous analysis is presented for extrapolation used in combination with nonstandard integration rules for finite elements. Extrapolation can likewise be applied on matrix-free finite difference stencils. In our applications, both schemes show up to quartic order of convergence. [ABSTRACT FROM AUTHOR]

Lifetime evaluation with fatigue loads is commonly used in the design phase of wind turbines, but rarely during operation due to the cost of extra measurements. Fatigue load prediction with neural networks, using existing SCADA signals, is a potential cost-effective alternative to continuously monitor lifetime consumption. However, although assessments for turbines in wind farm flow have been pointed out as deficient, the evaluations were limited to single cases and the implication for the design of a monitoring system was not discussed. Hence, we proposed metrics to evaluate prediction quality and, using one year of measurements at two wind turbines, we evaluated predictions in six different flow conditions. The quality of fatigue load predictions were evaluated for bending moments of two blades, in edgewise and flapwise directions. Results, based on 48 analyses, demonstrated that prediction quality varies marginally with varying flow conditions. Predictions were accurate in all cases and had an average error below 1.5%, but their precision slightly deteriorated in wake flow conditions. In general, results demonstrated that a reasonable monitoring system can be based on a neural network model without the need to distinguish between inflow conditions. [ABSTRACT FROM AUTHOR]

Doppler LiDARs have become flexible and versatile remote sensing devices for wind energy applications. The possibility to measure radial wind speed components contemporaneously at multiple distances is an advantage with respect to meteorological masts. However, these measurements must be filtered due to the measurement geometry, hard targets and atmospheric conditions. To ensure a maximum data availability while producing low measurement errors, we introduce a dynamic data filter approach that conditionally decouples the dependency of data availability with increasing range. The new filter approach is based on the assumption of self-similarity, that has not been used so far for LiDAR data filtering. We tested the accuracy of the dynamic data filter approach together with other commonly used filter approaches, from research and industry applications. This has been done with data from a long-range pulsed LiDAR installed at the offshore wind farm 'alpha ventus'. There, an ultrasonic anemometer located approximately 2.8 km from the LiDAR was used as reference. The analysis of around 1.5 weeks of data shows, that the error of mean radial velocity can be minimised for wake and free stream conditions. [ABSTRACT FROM AUTHOR]

An adaptive coarse space approach including a condition number bound for dual primal finite element tearing and interconnecting (FETI-DP) methods applied to three dimensional problems with coefficient jumps inside subdomains and across subdomain boundaries is presented. The approach is based on a known adaptive coarse space approach enriched by a small number of additional local edge eigenvalue problems. These edge eigenvalue problems serve to make the method robust and permit a condition number bound which depends only on the tolerance of the local eigenvalue problems and some properties of the domain decomposition. The introduction of the edge eigenvalue problems thus turns a well-known condition number indicator for FETI-DP and balancing domain decomposition by constraints (BDDC) methods into a condition number estimate. Numerical results are presented for linear elasticity and heterogeneous materials supporting our theoretical findings. The problems considered include those with random coefficients and almost incompressible material components. [ABSTRACT FROM AUTHOR]

In the realm of infectious disease control, accurate modeling of the transmission dynamics is pivotal. As human mobility and commuting patterns are key components of communicable disease spread, we introduce a novel travel time aware metapopulation model. Our model aims to enhance estimations of disease transmission. By providing more reliable assessments on the efficacy of interventions, curtailing personal rights or human mobility behavior through interventions can be minimized. The proposed model is an advancement over traditional compartmental models, integrating explicit transmission on travel and commute, a factor available in agent-based models but often neglected with metapopulation models. Our approach employs a multi-edge graph ODE-based (Graph-ODE) model, which represents the intricate interplay between mobility and disease spread. This granular modeling is particularly important when assessing the dynamics in densely connected urban areas or when heterogeneous structures across entire countries have to be assessed. The given approach can be coupled with any kind of ODE-based model. In addition, we propose a novel multi-layer waning immunity model that integrates waning of different paces for protection against mild and severe courses of the disease. As this is of particular interest for late-phase epidemic or endemic scenarios, we consider the late-phase of SARS-CoV-2 in Germany. The results of this work show that accounting for resolved mobility significantly influences the pattern of outbreaks. The improved model provides a refined tool for predicting outbreak trajectories and evaluating intervention strategies in relation to mobility by allowing us to assess the transmission that result on traveling. The insights derived from this model can serve as a basis for decisions on the implementation or suspension of interventions, such as mandatory masks on public transportation. Eventually, our model contributes to maintaining mobility as a social good while reducing exuberant disease dynamics potentially driven by travel activities. Author summary: As human contacts and contact networks are key to the development and prediction of infectious disease spread, travel and commuting activities are important components to be considered in mathematical-epidemiological modeling. Two, often contrasting modeling approaches, based on subpopulations and based on individuals can provide insights of different granularity but also come at different levels of complexity. With this article, we extend a recently introduced Graph-ODE-based model by the explicit introduction of mobility-based infection models in which we allow focused nonpharmaceutical interventions, like face mask mandates in public transport, and in which we can explicitly keep track of secondary cases induced by travel activities, a component mostly not available with equation-based models. In addition, we introduce a novel multi-layer waning immunity model particularly suitable for late-phase epidemic or endemic scenarios. On a daily level and geographically small scale, the newly proposed model often develops similarly, although our results show that complex mobility networks can lead to substantially different disease dynamics in the entirety of a federal state or country. The proposed model thus enables a better understanding of infectious disease dynamics through mobility. It allows for targeted numerical investigations and thus leads to more appropriate real-world interventions. [ABSTRACT FROM AUTHOR]

Power diagrams are a generalization of Voronoi diagrams for arbitrary dimensions. We present a modeling and optimization scheme for power diagrams in three spacial dimensions based on the statistics of experimental data obtained from cross-sectional images of polycrystalline materials. Our optimization scheme based on the grains’ area and perimeter distributions can be used to obtain realistic three-dimensional polycrystalline structures which can subsequently be used for numerical simulations. As a proof of the concept we apply our scheme to high-performance ceramics and present the results of initial shock-impact simulations of the obtained polycrystalline structures. [ABSTRACT FROM AUTHOR]

This paper presents a method for reconstructing the wake wind field of a wind turbine based on planar light detection and ranging (LiDAR) scans crossing the wake transversally in the vertical and horizontal directions. Volumetric measurements enable the study of wake characteristics in these two directions. Due to a lack of highly resolved wind speed measurements as reference data, we evaluate the reconstruction in a synthetic environment and determine the reconstruction errors. The wake flow of a multi-megawatt wind turbine is calculated within a 10-min large-eddy simulation (LES) for high-thrust loading conditions. We apply a numerical LiDAR simulator to this wake wind field to achieve realistic one-dimensional velocity data. We perform a nacelle-based set-up with combined plan position indicator and range height indicator scans with eight scanning velocities each. We temporally up-sample the synthetic LiDAR data with a weighted combination of forward- and backward-oriented space–time conversion to retrospectively extract high-resolution wake characteristic dynamics. These dynamics are used to create a dynamic volumetric wake deficit. Finally, we reconstruct the dynamic wake wind field in three spatial dimensions by superposing an ambient wind field with the dynamic volumetric wake deficit. These results demonstrate the feasibility of wake field reconstruction using long-range LiDAR measurements. [ABSTRACT FROM AUTHOR]

Measurement campaigns in wind energy research are becoming increasingly complex, which has exacerbated the difficulty of taking optimal measurements using light detection and ranging (LiDAR) systems. Compromises between spatial and temporal resolutions are always necessary in the study of heterogeneous flows, like wind turbine wakes. Below, we develop a method for space-time conversion that acts as a temporal fluid-dynamic interpolation without incurring the immense computing costs of a 4D flow solver. We tested this space-time conversion with synthetic LiDAR data extracted from a large-eddy-simulation (LES) of a neutrally stable single-turbine wake field. The data was synthesised with a numerical LiDAR simulator. Then, we performed a parametric study of 11 different scanning velocities. We found that temporal error dominates the mapping error at low scanning speeds and that spatial error becomes dominant at fast scanning speeds. Our space-time conversion method increases the temporal resolution of the LiDAR data by a factor 2.4 to 40 to correct the scan-containing temporal shift and to synchronise the scan with the time code of the LES data. The mean-value error of the test case is reduced to a minimum relative error of 0.13% and the standard-deviation error is reduced to a minimum of 0.6% when the optimal scanning velocity is used. When working with the original unprocessed LiDAR measurements, the space-time-conversion yielded a maximal error reduction of 69% in the mean value and 58% in the standard deviation with the parameters identified with our analysis. [ABSTRACT FROM AUTHOR]

For second-order elliptic partial differential equations large discontinuities in the coefficients yield ill-conditioned stiffness matrices. The convergence of domain decomposition methods (DDM) can be improved by incorporating (numerically computed) local eigenvectors into the coarse space. Different adaptive coarse spaces for DDM have been constructed and used successfully. For two-level Schwarz, FETI-1 and BDD methods, adaptive coarse spaces with a rigorous theoretical basis are known for 2D and 3D. Although successfully in use for almost a decade, a theory for adaptive coarse spaces for FETI-DP and BDDC was lacking. While the problem was recently settled for 2D, the estimate for the 3D adaptive algorithm required improved coarse spaces. We give an brief overview of the literature, i. e., the different known approaches, and show numerical results for a specific adaptive FETI-DP method in 3D, where the condition number bound could only recently be proven. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The accurate characterization of offshore wind resources is crucial for the efficient design and operation of wind energy projects. However, the scarcity of in situ observation in marine environments requires exploration of alternative approaches. For this reason, this study presents a comprehensive comparison between wind profiles derived from the Advanced Scatterometer ASCAT) satellite observations and the ERA5 reanalysis dataset against ship-based lidar measurements in the Northern Baltic Sea. In order to extrapolate ASCAT observations to wind turbine relevant heights, a long-term correction approach has been implemented. Due to the sensitivity of this method to the accurate characterization of the atmospheric stability, two different approaches were assessed to characterize the stability conditions, showing a great robustness of the methodology employed and leading to noticeable differences only in specific coastal locations. The comparison reveals a close agreement between ASCAT and ERA5 beyond 40 km distance from the coast. Specifically, ASCAT tends to overestimate the mean wind speed derived from lidar measurements, while ERA5 exhibits a consistent underestimation. In terms of vertical accuracy, ERA5 displays a consistent bias of approximately 0.5 m s-1 along the profile, whereas ASCAT exhibits a smaller bias within the lower 200 m of the profile. These findings underline the potential and limitations of ASCAT-derived wind profiles and ERA5 for offshore wind characterization. [ABSTRACT FROM AUTHOR]

Dual-Doppler lidar is a powerful remote sensing technique that can accurately measure horizontal wind speeds and enable the reconstruction of two-dimensional wind fields based on measurements from two separate lidars. Previous research has provided a framework of dual-Doppler algorithms for processing both radar and lidar measurements, but their application to wake measurements has not been addressed in detail yet. The objective of this paper is to reconstruct two-dimensional wind fields of wind turbine wakes and assess the performance of dual-Doppler lidar scanning strategies, using the newly developed Multiple-Lidar Wind Field Evaluation Algorithm (MuLiWEA). This processes non-synchronous dual-Doppler lidar measurements and solves the horizontal wind field with a set of linear equations, also considering the mass continuity equation. MuLiWEA was applied on simulated measurements of a simulated wind turbine wake, with two typical dual-Doppler lidar measurement scenarios. The results showed inaccuracies caused by the inhomogeneous spatial distribution of the measurements in all directions, related to the ground-based scanning of a wind field at wind turbine hub height. Additionally, MuLiWEA was applied on a real dual-Doppler lidar measurement scenario in the German offshore wind farm “alpha ventus”. It was concluded that the performance of both simulated and real lidar measurement scenarios in combination with MuLiWEA is promising. Although the accuracy of the reconstructed wind fields is compromised by the practical limitations of an offshore dual-Doppler lidar measurement setup, the performance shows sufficient accuracy to serve as a basis for 10 min average steady wake model validation. [ABSTRACT FROM AUTHOR]

Ensemble forecasts are a valuable addition to deterministic wind forecasts since they allow the quantification of forecast uncertainties. To remove common deficiencies of ensemble forecasts such as biases and ensemble spread deficits, various postprocessing methods for the calibration of wind speed (univariate calibration) and wind vector (bivariate calibration) ensemble forecasts have been developed in recent years. The objective of this paper is to compare the performance of state-of-the-art calibration methods at distinct off- and onshore sites in central Europe. The aim is to identify calibration- and site-dependent improvements in forecast skill over uncalibrated 100-m ensemble forecasts from the ECMWF Ensemble Prediction System. The ensemble forecasts were evaluated at four onshore and three offshore measurement towers in central Europe at 100-m height for lead times up to 5 days. The results show that the recursive and adaptive wind vector calibration (AUV) outperforms calibration methods such as univariate ensemble model output statistics (EMOS), bivariate EMOS, variance deficit calibration, and ensemble copula coupling in terms of the root-mean-square error and continuous ranked probability score at almost all sites. It was found that exponential downweighting of past measurements in AUV contributes to higher forecast skill since similar downweighting approaches in the other calibration methods improved forecast skill. Proposing a bidimensional bias correction in bivariate EMOS similar to the approach taken in AUV yields bivariate EMOS skill at onshore sites that is similar to AUV skill. Deterministic and probabilistic improvements are usually much lower at offshore sites and increase with increasing complexity of the site characteristics since systematic forecast errors and ensemble underdispersion are larger at high-roughness sites. [ABSTRACT FROM AUTHOR]

The design of rotor blades is based on information about aerodynamic phenomena. An important one is fluid-structure interaction (FSI) which describes the interaction between a flexible object (rotor blade) and the surrounding fluid (wind). However, the acquisition of FSI is complex, and only a few practical concepts are known. This paper presents a measurement setup to acquire real information about the FSI of rotating wind turbines in wind tunnel experiments. The setup consists of two optical measurement systems to simultaneously record fluid (PIV system) and deformation (photogrammetry system) information in one global coordinate system. Techniques to combine both systems temporally and spatially are discussed in this paper. Furthermore, the successful application is shown by several experiments. Here, different wind conditions are applied. The experiments show that the new setup can acquire high-quality area-based information about fluid and deformation. [ABSTRACT FROM AUTHOR]

Preview measurements of the inflow by turbine-mounted lidar systems can be used to optimise wind turbine performance or alleviate structural loads. However, nacelle-mounted lidars suffer data losses due to unfavourable environmental conditions and laser beam obstruction by the rotating blades. Here, we apply proper orthogonal decomposition (POD) to the simulated line-of-sight wind speed measurements of a turbine-mounted scanning lidar obtained from two large eddy simulations. This work aimed at identifying the dominant POD modes that can be used to subsequently derive a reduced-order representation of the turbine inflow. Secondly, we reconstructed the data points lost due to blade passage by using Gappy-POD. We found that only a few modes are required to capture the dynamics of the wind field parameters commonly used for lidar-assisted wind turbine control, such as the effective wind speed, vertical shear and directional misalignment. By evaluating turbine-relevant metrics in the time and frequency domain, we found that a ten-mode reconstruction could accurately describe most spatio-temporal variations in the inflow. Furthermore, a modal interpretation is presented by direct comparison with these wind field parameters. We found that the Gappy-POD method performs substantially better than spatial interpolation techniques, accurately reconstructing up to even 50% of missing data. A POD-based wind field reconstruction offers a trade-off between wind field reconstruction techniques requiring flow assumptions and more complex physics-based representations, offers dimensional reduction and can overcome the blade passage limitation of nacelle-mounted lidar systems. [ABSTRACT FROM AUTHOR]

This paper describes the development of a theoretical model for the turbulence spectrum measured by a short-range, continuous-wave lidar (light detection and ranging). The lidar performance was assessed by measurements conducted with two WindScanners in an open-jet wind tunnel equipped with an active grid, for a range of different turbulent wind conditions. A hot-wire anemometer is used as reference to assess the lidar's measured statistics, time series and spectra. In addition to evaluating the statistics, the correlation between the time series and the root-mean-square error (RMSE) on the wind speed, the turbulence spectrum measured by the lidar is compared with a modelled spectrum. The theoretical spectral model is applied in the frequency domain, using a Lorentzian filter in combination with Taylor's frozen turbulence hypothesis for the probe length averaging effect and an added white noise term, evaluated by qualitatively matching the lidar measurement spectrum. High goodness-of-fit coefficients and low RMSE values between the hot wire and WindScanner were observed for the measured time series. The correlation showed an inverse relationship with the prevalent turbulence intensity in the flow for cases with a comparable power spectrum shape. Larger flow structures can be captured more accurately by the lidar, whereas small-scale turbulent flow structures are partly filtered out as a result of the lidar's probe volume averaging effect. It is demonstrated that an accurate way to define the cut-off frequency at which the lidar's power spectrum starts to deviate from the hot-wire reference spectrum is the frequency at which the coherence drops below 0.5. This coherence-based cut-off frequency increases linearly with the mean wind speed and is generally an order of magnitude lower than the probe length equivalent cut-off frequency, estimated according to a simple model based on the full width at half maximum (FWHM) of the laser beam intensity along the line of sight and assuming Taylor's frozen turbulence hypothesis. A convincing match between the modelled and the measured WindScanner power spectrum was found for various different cases, which confirmed that the deviation of the lidar's measured power spectrum in the higher frequency range can be analytically explained and modelled as a combination of a Lorentzian-shaped intensity function and white noise in the lidar measurement. Although the models were developed on the basis of wind tunnel measurements, they should be applicable to atmospheric boundary layer field measurements as well. [ABSTRACT FROM AUTHOR]

This paper describes the development of a model for the turbulence spectrum measured by a short-range, continuous-wave lidar. The lidar performance was assessed by measurements conducted with two WindScanners in an open jet wind tunnel equipped with an active grid, for a range of different turbulent wind conditions. A one-dimensional hot wire anemometer was used as a reference for characterising the lidar turbulence measurement. In addition to addressing the statistics, the correlation between the time series and the mean error on the wind speed, the lidar measurement turbulence spectrum is compared with a theoretical spectrum using Taylor's frozen turbulence hypothesis. A theoretical model for the probe length averaging effect is applied in the frequency domain, using a Lorentzian filter in combination with generated white noise, and evaluated by qualitatively matching the lidar measurement spectrum. High goodness of fit coefficients and low mean absolute errors between hot wire and WindScanner were observed for the measured time series. The correlation showed an inverse relationship with the prevalent turbulence intensity in the flow for cases with a comparable power spectrum shape. Larger flow structures can be captured more accurately by the lidar, whereas small-scale turbulent flow structures are partly filtered out as a result of the lidars' probe volume averaging. It is demonstrated that an accurate way to define the frequency at which the lidar power spectrum starts to deviate from the hot wire reference spectrum is the point at which the coherence drops below 0.5. This coherence-based cut-off frequency increases linearly with the mean wind speed and is generally an order of magnitude lower than the probe length cut-off frequency, estimated according to a simple model based on Taylor's frozen turbulence hypothesis. A convincing match between the modelled and the actual WindScanner power spectrum was found for various different cases, which confirmed that the deviation of the lidar measurement power spectrum in the higher frequency range can be analytically explained and modelled as a combination of a Lorentzian probe length averaging effect and white noise in the lidar measurement. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a model predictive control (MPC) is proposed for wind farms to minimize wake-induced power losses. A constrained optimization problem is formulated to maximize the total power production of a wind farm. The developed controller employs a two-dimensional dynamic wind farm model to predict wake interactions in advance. An adjoint approach as an efficient tool is utilized to compute the gradient of the performance index for such a large-scale system. The wind turbine axial induction factors are considered as the control inputs to influence the overall performance by taking the wake interactions into account. A layout of a 2 × 3 wind farm is considered in this study. The parameterization of the controller is discussed in detail for a practical optimal energy extraction. The performance of the adjoint-based model predictive control (AMPC) is investigated with time-varying changes in wind direction. The simulation results show the effectiveness of the proposed approach. The computational complexity of the developed AMPC is also outlined with respect to the real time control implementation. [ABSTRACT FROM AUTHOR]

The solution of Poisson-like equations defined on a complex geometry is required for gyrokinetic simulations, which are important for the modelling of plasma turbulence in nuclear fusion devices such as the ITER tokamak. In this paper, we compare three existing solvers finely tuned to solve this problem, in terms of the accuracy of the solution, and their computational efficiency. We also consider practical implementation aspects, including the parallel efficiency of the code, potentially enabling an integration of the solvers in a state-of-the-art first-principle gyrokinetic simulation framework. The first, the Spline FEM solver, uses C 1 polar splines to construct a finite elements method which solves the equation on curvilinear coordinates. The resulting linear system is solved using a conjugate gradient method. The second, the GMGPolar solver, uses a symmetric finite difference method to discretise the differential equation. The resulting linear system is solved using a tailored geometric multigrid scheme, with a combination of zebra circle and radial line smoothers, together with an implicit extrapolation scheme. The third, the Embedded Boundary solver, uses a finite volumes method on Cartesian coordinates with an embedded boundary scheme. The resulting linear system is solved using a multigrid scheme. The Spline FEM solver is shown to be the most accurate. The GMGPolar solver is shown to use the least memory. The Embedded Boundary solver is shown to be the fastest in most cases. All three solvers are shown to be capable of solving the equation on a realistic non-analytical geometry. The Embedded Boundary solver is additionally used to attempt to solve an X-point geometry. • Solver comparison for the gyrokinetic Poisson-like equation on complex geometry. • High-order spline FEM solver based on C1 polar splines and conjugate gradient. • Curvilinear finite difference method using multigrid with low memory footprint. • Embedded boundary scheme with fast multigrid for simple X-point geometry. [ABSTRACT FROM AUTHOR]

To monitor wind turbine vibrations, normal behaviour models are built to predict tower top accelerations and drive-train vibrations. Signal deviations from model prediction are labelled as anomalies and are further investigated. In this paper we assess a stochastic approach to reconstruct the 1 Hz tower top acceleration signal, which was measured in a wind turbine located at the wind farm Alpha Ventus in the German North Sea. We compare the resulting data reconstruction with that of a model based on a neural network, which has been previously reported as a data-mining algorithm suitable for reconstructing this signal. Our results present evidence that the stochastic approach outperforms the neural network in the high frequency domain (1 Hz). Although neural network retrieves accurate step-forward predictions, with low mean square errors, the stochastic approach predictions better preserve the statistics and the frequency components of the original signal, retaining high accuracy levels. The implementation of our stochastic approach is available as open source code and can easily be adapted for other situations involving stochastic data reconstruction. Based on our findings we argue that such an approach could be implemented in signal reconstruction for monitoring purposes or for abnormal behaviour detection. [ABSTRACT FROM AUTHOR]

Wind measurements using classical profiling lidars suffer from systematic measurement errors in complex terrain. Moreover, their ability to measure turbulence quantities is unsatisfactory for wind-energy applications. This paper presents results from a measurement campaign during which multiple WindScanners were focused on one point next to a reference mast in complex terrain. This multi-lidar (ML) technique is also compared to a profiling lidar using the Doppler beam swinging (DBS) method. First- and second-order statistics of the radial wind velocities from the individual instruments and the horizontal wind components of several ML combinations are analysed in comparison to sonic anemometry and DBS measurements. The results for the wind speed show significantly reduced scatter and directional error for the ML method in comparison to the DBS lidar. The analysis of the second-order statistics also reveals a significantly better correlation for the ML technique than for the DBS lidar, when compared to the sonic. However, the probe volume averaging of the lidars leads to an attenuation of the turbulence at high wave numbers. Also the configuration (i.e., angles) of the WindScanners in the ML method seems to be more important for turbulence measurements. In summary, the results clearly show the advantages of the ML technique in complex terrain and indicate that it has the potential to achieve significantly higher accuracy in measuring turbulence quantities for wind-energy applications than classical profiling lidars. [ABSTRACT FROM AUTHOR]

In terms of predicting wind turbine wakes, the stably stratified atmospheric boundary layer (SABL) is taking an exceptional position as wake effects and thus loads on subsequent turbines are stronger. In this study we show the impact of the SABL on power production and wake effects (power deficits) in offshore wind farms by means of measurements as well as large-eddy simulations (LES). Measurements show enhanced wake effects in the SABL compared to the unstable situation. Another influence on the power generation of an offshore wind farm is the distance of the wind farm to the shore. This is accounted for in the LES by a modification of surface characteristics at the coastal discontinuity. In addition to the effect of the coast, the numerical case study also shows the existence of local jets between the turbines of the wind farm. [ABSTRACT FROM AUTHOR]

Highlights: [•] Vanadium redox flow battery utilized for wind power grid integration was studied. [•] Technical and financial analyses at single wind farm level were performed. [•] 2MW/6MWh VRFB is suitable for mitigating power deviations for a 10MW wind farm. [•] Economic incentives might be required in the short-term until the VRFB prices drop. [ABSTRACT FROM AUTHOR]

Long-range Doppler wind light detection and ranging (lidar) measurements at a wind turbine were carried out for the first time. The turbine was of the type Areva M5000 and is located at a site near the coastline in Bremerhaven, in the northern part of Germany. This wind turbine is the prototype for the German offshore test site 'alpha ventus' and has a rated power of 5 MW. Information about the ambient wind field before and after this multimegawatt wind turbine was obtained. In this paper the measurement technique is discussed and the results of measurements in the diurnal layer and in the stable nocturnal boundary layer are shown. The main focus of this work is to determine the reduction of the wind speed at certain distances downstream from the rotor. [ABSTRACT FROM AUTHOR]

Owing to the aerodynamic conversion process, wind turbines exhibit a nonlinear behavior and encounter turbulent operating conditions that demand well-defined closed-loop dynamics to withstand accumulated loading over the lifetime. Wind excitation is the main disturbance and driving force for the system and determines the necessary operating strategy, but it usually represents an unmeasurable quantity. In this study, we used a linear-matrix-inequalities-based control and observer design to operate a variable-speed, variable-pitch wind turbine in a wind tunnel experiment at different reproducible inflow conditions while relying on a wind speed estimate obtained from a disturbance observer. The computational complexity of the stability framework incorporating the reconstruction of the unknown wind speed is reduced by exploiting characteristics of the modeling approach based on a convex combination of linear submodels. The assumption used in the proposed stability consideration is evaluated based on measurement data. We introduced an extended operating range compared to the commonly considered operating trajectory of wind turbines in the control design. A controller based on Takagi–Sugeno modeling is used to operate the turbine at challenging power tracking requirements demonstrating the capability to support fast stabilization of the electrical grid while discussing the loading and operational constraints observed during the experiments. [Display omitted] • Nonlinear model-based control design using linear matrix inequalities was performed. • The control design was applied to a wind turbine to provide power tracking capability. • Proof of stability of the observer-based strategy considering unmeasurable wind speed was realized. • Experimental wind tunnel validation in a large operational range under reproducible turbulent inflow conditions was attained. [ABSTRACT FROM AUTHOR]

With the ongoing increase in the size of wind turbines, experimental investigations have become more complicated and expensive. Therefore, computational models have proven to be a viable solution for design purposes. This article aims to validate CFD simulations of an experimental model wind turbine (MoWiTO 1.8) using Delayed Detached Eddy Simulation (DDES) and Improved DDES (IDDES) turbulence modelling approaches. For the purpose of validation, integral quantities (such as power, thrust, torque and blade-root bending moment in the flapwise direction) measured in the wind tunnel are compared with numerical results obtained with OpenFOAM. In general, the computational results show a very good agreement with the measurements for most of the monitored quantities. In particular, the blade-root bending moment presents the largest difference, taking into account that the simulation assumes the turbine blades are rigid. Nevertheless, the simulation does achieve in recreating the turbulent behavior as can be evidenced by the Power Spectral Density graphs, and the wake's velocity measurements. In general, the IDDES turbulent model achieves a better agreement to the experimental results, while maintaining a very similar computational time as the DDES model. [ABSTRACT FROM AUTHOR]

Very short-term forecasts of wind power provide electricity market participants with extremely valuable information, especially in power systems with high penetration of wind energy. In very short-term horizons, statistical methods based on historical data are frequently used. This paper explores the use of dual-Doppler radar observations of wind speed and direction to derive five-minute ahead deterministic and probabilistic forecasts of wind power. An advection-based technique is introduced, which estimates the predictive densities of wind speed at the target wind turbine. In a case study, the proposed methodology is used to forecast the power generated by seven turbines in the North Sea with a temporal resolution of one minute. The radar-based forecast outperforms the persistence and climatology benchmarks in terms of overall forecasting skill. Results indicate that when a large spatial coverage of the inflow of the wind turbine is available, the proposed methodology is also able to generate reliable density forecasts. Future perspectives on the application of Doppler radar observations for very short-term wind power forecasting are discussed in this paper. [ABSTRACT FROM AUTHOR]