This study introduces a new variant of the peak count, termed the crossing-consistent peak count. Crossing consistency implies that the number of cycles with peaks above and valleys below a certain level equals the number of up-crossings of that level. The conventional peak count does not exhibit crossing consistency. In the crossing-consistent peak count, valleys are paired with the nearest peaks, from the largest to the smallest, and each cycle is counted as a full cycle. To include half cycles, the reversals of the time series are considered twice, except for the start and end points, such that each cycle is counted as a half cycle. Based on the fatigue framework developed by the Lund University, in which the cumulative cycle histogram is a key element, this study shows that the crossing-consistent peak count is the most conservative crossing-consistent counting method. This holds true for all time series, not only Gaussian signals. The crossing-consistent peak count was applied to wind turbine loads and compared with the rainflow count and conventional peak count. Moreover, it was applied to broad-band Gaussian signals, and it was concluded that the mean damage follows the narrow-band approximation.

When wind passes through the rotor of a wind turbine, the velocity is decreased while turbulence is increased. The region of decreased wind speed behind the rotor is known as the wind turbine wake and is bounded by a complex structure of helical vortices. This structure occurs to be more stable in low ambient turbulence and low tip speed ratio conditions, leading to a delayed recovery of the wake. The diminished wind speed in the wake leads to a decline in power output for downstream wind turbines, with this loss scaling proportionally to the cube of the velocity. This study uses field tests and simulations to evaluate enhanced wake recovery with segmented Gurney flaps on a 3.8-MW research wind turbine. Four Gurney flaps were attached at regions near the tip of each blade. This configuration is hypothesized to induce turbulence that destabilizes the vortex system, resulting in faster wake recovery. Field tests using a scanning LiDAR were conducted to quantify the wind turbine wake recovery between the baseline and the retrofitted configuration in various atmospheric conditions. The results show a consistent increase in wake recovery for the Gurney flap configuration, generally at all downstream distances. This was illustrated by a reduction of axial velocity deficits of roughly 10% at hub height, at five diameters downstream distance. The influence of retrofitting on turbine power and loads was limited. Summarizing, a very successful field test campaign was executed, which demonstrated the use of segmented Gurney flaps as a promising add-on to promote enhanced wind turbine wake recovery for improved overall wind farm performance.

Ramp events, i.e., significant changes in wind speed in a short time period, have become critically important to end-users. However, only a few studies address their impact on wind turbine loads. To the best of the authors' knowledge, these results have not yet been validated with measurements. Therefore, this paper aims to investigate the impact of extreme wind speed ramps on ultimate wind turbine loads using eight months of offshore measurements. We also compare the measured loads with simulations following the International Electrotechnical Commission (IEC) extreme turbulence model, in order to improve the modelling of ultimate loads. This is because events with a 10-min horizontal wind speed standard deviation higher than the prescribed IEC turbulence class, in line with other research, are primarily associated with ramp events. They are found to be design driving for the blade root flap-wise moments below and beyond rated wind speed, but not in the transition region. The high-frequency analysis of these moments showed a sudden pitch transition from the inactive to the active region. In general, the loads associated with ramp events did not exceed the simulations. In addition, non-ramp related extreme loads around rated wind speed, which exceeded the simulations, were associated with standard deviations slightly above the normal turbulence model (NTM) of IEC for a waked turbine, indicating the impact of wake added turbulence. In conclusion, for the ultimate load analysis, the wind speed time series should include a sudden pitch transition from the inactive to the active region in addition to wake added turbulence.

A novel approach is proposed to reduce, compared with the conventional binning approach, the large number of aeroelastic code evaluations that are necessary to obtain equivalent loads acting on wind turbines. These loads describe the effect of long-term environmental variability on the fatigue loads of a horizontal-axis wind turbine. In particular, Design Load Case 1.2, as standardized by IEC, is considered. The approach is based on numerical integration techniques and, more specifically, quadrature rules. The quadrature rule used in this work is a recently proposed “implicit” quadrature rule, which has the main advantage that it can be constructed directly using measurements of the environment. It is demonstrated that the proposed approach yields accurate estimations of the equivalent loads using a significantly reduced number of aeroelastic model evaluations (compared with binning). Moreover, the error introduced by the seeds (introduced by averaging over random wind fields and sea states) is incorporated in the quadrature framework, yielding an even further reduction in the number of aeroelastic code evaluations. The reduction in computational time is demonstrated by assessing the fatigue loads on the NREL 5 MW reference offshore wind turbine in conjunction with measurement data obtained at the North Sea, for both a simplified and a full load case.

An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics: using a prior distribution and a likelihood, the posterior distribution is obtained through application of Bayes' law. Our novel algorithm to accurately determine this posterior requires significantly fewer discrete model evaluations than traditional Monte Carlo methods. The key idea is to replace the expensive model by an interpolating surrogate model and to construct the interpolating nodal set maximizing the accuracy of the posterior. To determine such a nodal set an extension to weighted Leja nodes is introduced, based on a new weighting function. We prove that the convergence of the posterior has the same rate as the convergence of the model. If the convergence of the posterior is measured in the Kullback-Leibler divergence, the rate doubles. The algorithm and its theoretical properties are verified in three different test cases: analytical cases that confirm the correctness of the theoretical findings, Burgers' equation to show its applicability in implicit problems, and finally the calibration of the closure parameters of a turbulence model to show the effectiveness for computationally expensive problems.

A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian prediction. The novel idea is to construct a sequence of nested quadrature rules with positive weights that converge to a quadrature rule that is weighted with respect to the posterior. The quadrature rules are constructed using a proposal distribution that is determined by means of nearest neighbor interpolation of all available evaluations of the posterior. It is demonstrated both theoretically and numerically that this approach yields accurate estimates of the integrals involved in Bayesian prediction. The applicability of the approach for a fluid dynamics test case is demonstrated by inferring accurate predictions of the transonic flow over the RAE2822 airfoil with a small number of model evaluations. Here, the closure coefficients of the Spalart–Allmaras turbulence model are considered to be uncertain and are calibrated using wind tunnel measurements.

For the purpose of uncertainty propagation a new quadrature rule technique is proposed that has positive weights, has high degree, and is constructed using only samples that describe the probability distribution of the uncertain parameters. Moreover, nodes can be added to the quadrature rule, resulting in a sequence of nested rules. The rule is constructed by iterating over the samples of the distribution and exploiting the null space of the Vandermonde system that describes the nodes and weights, in order to select which samples will be used as nodes in the quadrature rule. The main novelty of the quadrature rule is that it can be constructed using any number of dimensions, using any basis, in any space, and using any distribution. It is demonstrated both theoretically and numerically that the rule always has positive weights and therefore has high convergence rates for sufficiently smooth functions. The convergence properties are demonstrated by approximating the integral of the Genz test functions. The applicability of the quadrature rule to complex uncertainty propagation cases is demonstrated by determining the statistics of the flow over an airfoil governed by the Euler equations, including the case of dependent uncertain input parameters. The new quadrature rule significantly outperforms classical sparse grid methods.

The use of the rotor equivalent wind speed for determination of power curves and annual energy production for wind turbines is advocated in the second edition of the IEC 61400-12-1 standard. This requires the measurements of wind speeds at different heights, for which remote sensing equipment is recommended in addition to meteorological masts. In this paper, we present a theoretical analysis that shows that the relevance of the rotor equivalent wind speed method depends on turbine dimensions and wind shear regime. For situations where the ratio of rotor diameter and hub height is smaller than 1.8, the rotor equivalent wind speed method is not needed if the wind shear coefficient at the location of the wind turbine has a constant value between −0.05 and 0.4: in these cases, the rotor equivalent wind speed and the wind speed at hub height are within 1%. For complex terrains with high wind shear deviations are larger. The effect of non-constant wind shear exponent, ie, different wind shear coefficients for lower and upper half of the rotor swept area especially at offshore conditions is limited to also about 1%.

During the design phase of an offshore wind turbine, it is required to assess the impact of loads on the turbine life time. Due to the varying environmental conditions, the effect of various uncertain parameters has to be studied to provide meaningful conclusions. Incorporating such uncertain parameters in this regard is often done by applying binning, where the probability density function under consideration is binned and in each bin random simulations are run to estimate the loads. A different methodology for quantifying uncertainties proposed in this work is polynomial interpolation, a more efficient technique that allows to more accurately predict the loads on the turbine for specific load cases. This efficiency is demonstrated by applying the technique to a power production test problem and to IEC Design Load Case 1.1, where the ultimate loads are determined using BLADED. The results show that the interpolating polynomial is capable of representing the load model. Our proposed surrogate modeling approach therefore has the potential to significantly speed up the design and analysis of offshore wind turbines by reducing the time required for load case assessment.

Wake effects in wind farms are a major source of power production losses and fatigue loads on the rotors. It has been demonstrated that in large wind farms the only source of kinetic energy to balance the energy extracted by the turbines is the vertical transport of the free-stream flow kinetic energy from above the wind turbine canopy. This chapter explores the possibility to enhance this transport process by introducing kites in steady flight within a small wind turbine array. In a first step, an array of four wind turbines, aligned with the streamwise velocity component, is simulated within a large eddy simulation framework. The turbines are placed in a pre-generated turbulent atmospheric boundary layer and modeled as actuator disks with both axial and tangential inductions, to account for the wake rotation. In a second step an identical turbine configuration with interspersed kites is investigated. The kites are modeled as body forces on the flow, equal in magnitude and opposite in direction to the vector sum of the lift and drag forces acting on the kite surfaces. A qualitative comparison of the mean flow statistics, before and after the introduction of the kites is presented.

In this research the diabatic surface layer wind shear model is extended for offshore wind energy purposes to higher altitudes based on Gryning's wind profile and the resistance functions proposed by Byun. The wind profile is in theory applicable up to the boundary layer height, which is parametrized with the Rossby-Montgommery equation. The coefficient c of the Rossby-Montgommery equation is found to be stability dependent with decreasing values up to 0.04 for stable conditions and increasing values up to 0.17 for unstable conditions. The proposed shear profile has been validated with 1 year of offshore observation data, and a significant improvement in accuracy is found compared to traditional surface layer shear profiles or power laws. The influence of adopting this extended shear profile for wind energy is analysed in terms of the kinetic energy flux and blade root fatigue loads experienced by a wind turbine. It is found that, especially for stable conditions, results deviate significantly compared to using the traditional surface layer shear profile. The kinetic energy flux decreases by up to 15%.

In recent years, there has been a growing interest by the wind energy community to assess the impact of atmospheric stability on wind turbine performance; however, up to now, typically, stability is considered in several distinct arbitrary stability classes. As a consequence, each stability class considered still covers a wide range of conditions. In this paper, wind turbine fatigue loads are studied as a function of atmospheric stability without a classification system, and instead, atmospheric conditions are described by a continuous joint probability distribution of wind speed and stability. Simulated fatigue loads based upon this joint probability distribution have been compared with two distinct different cases, one in which seven stability classes are adopted and one neglecting atmospheric stability by following International Electrotechnical Commission (IEC) standards. It is found that for the offshore site considered in this study, fatigue loads of the blade root, rotor and tower loads significantly increase if one follows the IEC standards (by up to 28% for the tower loads) and decrease if one considers several stability classes (by up to 13% for the tower loads). The substantial decrease found for the specific stability classes can be limited by considering one stability class that coincides with the mean stability of a given hub height wind speed. The difference in simulated fatigue loads by adopting distinct stability classes is primarily caused by neglecting strong unstable conditions for which relatively high fatigue loads occur. Combined, it is found that one has to carefully consider all stability conditions in wind turbine fatigue load simulations.