Probability Density Function Of Wind Speed Research Articles

The added value of high‐resolution EURO‐CORDEX simulations to describe daily wind speed over Europe

AbstractIn the context of the CORDEX project, an ensemble of regional climate simulations (RCMs) of high resolution on a 0.11° grid has been generated for Europe with the objective of improving the representation of regional to local‐scale atmospheric phenomena. However, such simulations are computationally expensive and do not always reveal added value. Here, a recently proposed metric (the distribution added value [DAV]) is used to determine the added value of all available EURO‐CORDEX high‐resolution simulations at 0.11° for daily mean wind speed compared to their respective coarser‐gridded 0.44° counterparts and their driving fields, hindcast and historical experiments. The analysis consists in comparing the degree of similarity between normalized wind probability density function (PDF) of simulations and observations. In addition, the use of a normalized PDF allows for a direct spatial comparison among the different regions and time periods. Results show that RCMs add value to their reanalysis or forcing global model, but the nature and magnitude of the improvement on the representation of wind speed may vary depending on the model, region and season. We found most RCMS at 0.11° to outperform models at the 0.44° resolution in terms of their quality in capturing the measured wind speed PDF. When looking at the upper tail of the wind speed PDF, the benefits of downscaling are generally larger. At the regional scale, added value is obtained for 0.11° with respect to 0.44° resolution for all subdomains studied, particularly over the Mediterranean, the Iberian Peninsula and the Alps. When analysing the added value dependence on altitude, runs at 0.11° models represent better the locations below 50 m and above 350 m of altitude, and the 0.44° increasingly under‐perform for higher altitudes. Overall, DAV are larger at 0.11° than at 0.44° resolution, due to a better performance of local‐scale feedbacks at high resolution.

An Improved Mixture Density Network Via Wasserstein Distance Based Adversarial Learning for Probabilistic Wind Speed Predictions

This paper develops a novel improved mixture density network via Wasserstein distance-based adversarial learning (WA-IMDN) for achieving more accurate probabilistic wind speed predictions (PWSP). The proposed method utilizes the historical supervisory control and data acquisition (SCADA) system data collected from multiple wind turbines (WTs) in different wind farms to predict the wind speed probability density function (PDF) of a targeted WT at the next timestamp. To better capture the fluctuation pattern of historical wind speed sequences and estimate parameters of the probability mixture model for approximating the wind speed PDF, an improved mixture density network (IMDN) is proposed. To address drawbacks of the traditional maximum likelihood estimation (MLE) on training the mixture density network, a Wasserstein distance (WD)-based adversarial learning is developed and the reparameterization trick is employed for the gradient delivery. The effectiveness of the proposed WA-IMDN is validated based on SCADA data (One dataset is publicly accessible) by benchmarking against a set of the commonly considered and recently reported PWSP methods, such as the mixture density network (MDN), maximum likelihood estimation (MLE) based mixture density attention network (MLE-IMDN), recent DMDNN and Improved Deep Mixture Density Network (IDMDN). Results demonstrate the superior performance of the proposed WA-IMDN on the PWSP. To demonstrate the repeatability of the presented research, we release our code at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/IkeYang/WA-IMDN-</uri> .

A novel hybrid forecasting system based on data augmentation and deep learning neural network for short-term wind speed forecasting

As a clean, economical, and renewable energy source, wind energy plays a very important role in easing the shortage of fossil energy, environmental population, and climate change. However, due to the strong intermittency, volatility, and randomness of wind speed, the large-scale connection of wind energy into the power grid is restricted. Therefore, constructing a reliable prediction model to achieve high-accuracy wind speed prediction is necessary. For this purpose, a novel hybrid model for short-term wind speed prediction is proposed in this paper. First, empirical mode decomposition is employed to decompose the raw wind speed time series into a set of subseries. Then, a data augmentation technique is first used to generate more training data to avoid overfitting of the prediction model. Furthermore, a new predictor based on a convolutional neural network (CNN), a long short-term memory (LSTM) network, and an extreme learning machine (ELM) is proposed for deterministic wind speed prediction, where a fuzzy entropy-based partition strategy is implemented to assign subseries to the CNN-LSTM and ELM. To improve the prediction performance, a synchronous optimization method based on an improved hybrid particle swarm optimization/gray wolf optimizer is proposed for feature selection and parameter optimization. Afterward, kernel density estimation is used to estimate the wind speed probability density function for probabilistic prediction. Finally, the performance of the proposed model is compared with seven other models by using three wind speed datasets from four aspects: point prediction, interval prediction, probability prediction comprehensive performance, and prediction reliability. The experimental results show that the proposed method achieves excellent performance on wind speed time series prediction.

Identification of optimum wind turbine parameters for varying wind climates using a novel month-based turbine performance index

The capacity factor (CF) and power coefficient (Cp) are two important wind turbine characteristics. CF describes the power generation capacity during a given period, and Cp describes the efficiency of the wind turbine. Both quantities depend on the rated wind speed. Determining the optimal rated wind speed that maximizes a function of CF and Cp that is directly related to a wind turbine’s output wind power density thus is of utmost importance as it leads to a maximum energy output. This paper proposes a novel Month-based Turbine Performance Index (MTPI) that considers the hourly mean wind speed data month-wise and enables the evaluation of this desired optimum rated turbine speed (Vr,opt) for a given site. Here, the 2-parameter Weibull distribution is employed as a single tool to parameterize the wind speed data and determine the wind speed probability density function, wind power density, vertical wind shear, CF, and Cp of the wind turbine. The examined stations taken for the analysis are from Trivandrum, Ahmedabad, and Calcutta in India. Our index is especially important in regions with intra annular variability, since it is the first to consider monthly instead of annual data.

LES study of topographical effects of simplified 3D hills with different slopes on ABL flows considering terrain exposure conditions

The oncoming turbulence is of particular importance with respect to the investigation of the turbulent flow fields over hilly terrain, which plays an essential role regarding the optimization of micro-siting of the wind farm and reasonable structural design of wind turbines. In this study, large-eddy simulations (LES) are performed to elucidate the effects of wind shear coefficients (WSCs) and upstream turbulence intensities (TIs) on the complex wind flow fields over the simplified 3-D hills. Systematical analysis of the wind turbulence properties related to the micro-siting and fatigue loads of wind turbines, including fractional speed-up ratio (SUR), terrain-induced TI, velocity spectrum and wind speed probability density function, is performed in a quantitative manner. Stronger non-Gaussianity is identified in the wake of gentle-sloped and moderate-sloped hills, which is weakened by increased WSC and enhanced TI. In addition, remarkable SURs are observed mostly at the summit of a steep-sloped hill near the hill surface, and the fractional speed-up factor is found to increase significantly under higher WSC and larger TI. Furthermore, the influence of topography on the wind direction field is also examined, which shows little dependence on the WSCs and TIs.

A correction to the unimodal and bimodal truncated normal distributions for a more accurate representation of extreme and calm wind speeds

The use of wind speed probability density functions is a standard practice to represent different wind regimes. Generally, these regimes are distinguished by the following three characteristics: the shape of the distribution in the central wind speeds, amount of the calm wind speeds (CWS), and extreme wind speeds (EWS). An in-depth review has highlighted that none of the parametric distributions available is suitable to represent the three main characteristics at the same time. To overcome this gap, the use of the corrected mixture of two truncated normal distributions (CMTTND) and corrected single truncated normal distribution (CTND) are proposed to represent, respectively, bimodal and unimodal wind speed distribution shapes. The CMTTND and CTND are obtained by introducing a correction, respectively, to the mixture of two truncated normal distributions (MTTND) and to the single truncated normal distribution (TND). The MTTND and TND permit an accurate representation of distributions with high levels of CWS. The CMTTND and CTND employ a new parameter, to accurately quantifying also the relative frequencies associated with EWS. The performance of the CMTTND and CTND was assessed using a goodness-of-fit (GOF) test and statistical measures of error in the evaluation of the characteristic mean wind speeds. The analytical expressions of these mean wind speeds are obtained and validated by a numerical integration method for the first time in this work. The accuracy of these distributions is compared with that of other conventional probability distribution models, of which three are unimodal and six bimodal, in four Italian locations and three American locations. The analysis of the results showed that the CTND and CMTTND allow obtaining high GOF of the experimental distributions with R2 and RMSE higher and lower than, respectively, 0.977 and 0.054. Moreover, the CTND results in the most accurate distribution in the estimation of the characteristic mean wind speeds in the case of localities with unimodal experimental distributions and the CMTTND in the case of localities with bimodal experimental distributions. Contrary to other distribution, CTND and CMTTND accuracies grow by increasing the grade of the characteristic mean wind speed by reaching also estimation values lower than 2% of the real ones. This is a great advantage in the wind energy source determination in a location since the available energy depends on the mean cubic wind speed.

Optimization method for multi-access capacity of wind power based on copula

With the increasing penetration of distributed wind power, the problem of wind power curtailment is becoming more and more serious due to the unreasonable installed capacity. A method is proposed to optimize the wind power capacity allocation for regional power grids. The main factors that affect wind power accommodation are analyzed according to the wind speed probability density function and the wind power output model. The correlation model of different wind farms is established by the Frank-Copula function. Aiming at reducing the total wind power curtailment, a distributed wind power installed capacity optimization method is proposed with the correlation model. The optimal capacity allocation of the system is calculated by genetic algorithm and the effectiveness of the proposed method is verified by the case of IEEE RTS-79.

Evaluation of rare velocity at a pedestrian level due to turbulence in a neutrally stable shear flow over simplified urban arrays

The geometric dependency of the wind environment at a pedestrian level is an important issue that influences human comfort and safety in urban outdoor spaces. As such, this paper proposes to investigate the statistical features of wind speeds at the pedestrian level by calculating wind speed probability density functions based on flow field data from large-eddy simulations of simplified urban arrays, aiming to clarify the effects of urban geometry on rare velocity events such as strong gusts or extremely weak air flow. Though strong wind events occur infrequently, a positive correlation was demonstrated between percentile and mean wind speeds, indicating that the risk of gusty events increases with the increase of mean wind speeds. Conversely, the frequency of weak wind events shows an inverse correlation with mean wind speeds, showing that better ventilated urban arrays will retain higher wind speeds. Furthermore, these percentiles and occurrence frequencies are clearly expressed by the frontal area indices of urban block arrays. These results imply a trade-off between the following two objectives for urban area wind environments characterized by the urban geometry: enhancing air ventilation in urban areas and preventing strong wind gust events at a pedestrian level.

Estimation of wind speed probability density function using a mixture of two truncated normal distributions

Probability density functions (PDFs) are normally used to describe wind speed distribution for the proper selection of wind turbines in a given location. The identification of a suitable PDF is fundamental for accurately assessing the wind energy potential and designing the wind farms.To achieve this objective, the use of a mixture of two truncated normal distributions (MTTND), defined for v ≥ 0 and obtained by linearly combining two normal distributions with different means and variances, is proposed in this work for the representation of the wind speed PDF. The distribution is a function of five parameters, does not require a high computational burden and allows the representation of wind calm hours (v = 0). The use of the MTTND allows an accurate estimation to be obtained of the experimental discrete distribution of the probability density and cumulative probability, and the characteristic statistical quantities used to estimate the available energy and the performance indicators in the selection of both the site and wind turbine.The validity of the use of the MTTND was verified by comparison with the most widespread PDFs in the scientific literature: Weibull, Rayleigh, lognormal, gamma, inverse Gaussian and Burr. This comparison was developed using experimental wind speed data relating to five Italian locations and a location in Colorado (USA) belonging to the National Renewable Energy Laboratory. For each location, the parameters of each PDF were obtained with the least squares non-linear regression method. The results of the comparisons, in terms of the coefficient of determination R2 and root mean square error (RMSE) for goodness of fit and in terms of relative error in the calculation of the statistical quantities, show that the use of the MTTND gives rise to greater accuracy than a conventional wind speed PDF.

Development of a statistical bivariate wind speed-wind shear model (WSWS) to quantify the height-dependent wind resource

The goal of this study was to develop a statistical bivariate wind speed-wind shear model (WSWS). The development of WSWS is based on near surface wind speed data available from 397 measurement stations distributed over Germany, as well as on ERA-Interim reanalysis wind speed data available in 1000m above ground level (a.g.l.). These data were used (1) to calculate empirical distributions of wind speed in 1000ma.g.l., (2) empirical distributions of the wind shear exponent, and (3) to fit theoretical distributions to the empirical wind speed and wind shear exponent distributions. It was found that the four parameter Johnson SB distribution reproduces the shape of the wind speed in 1000ma.g.l. empirical distributions best. The four parameter Dagum distribution provided good fits to the empirical wind shear distributions. The parameterized wind speed and wind shear marginal distributions were then linked by 16 joint copulas. Goodness-of-fit evaluation of the joint copulas demonstrates that the Gaussian-Gaussian copula reproduces the empirical bivariate wind speed-wind shear distribution most accurately. By using WSWS it is possible to continuously calculate the wind speed probability density function in hub heights between 10ma.g.l. and 200ma.g.l. This allows WSWS to be applied to virtually any power curve for computing the wind energy yield and capacity factor in the analyzed hub height range. A one-time site-specific parametrization of WSWS is sufficient for a comprehensive height-dependent exploitation of the available wind resource.

Protection of surface assets on Mars from wind blown jettisoned spacecraft components

Jettisoned Entry, Descent and Landing System (EDLS) hardware from landing spacecraft have been observed by orbiting spacecraft, strewn over the Martian surface. Future Mars missions that land spacecraft close to prelanded assets will have to use a landing architecture that somehow minimises the possibility of impacts from these jettisoned EDLS components. Computer modelling is used here to investigate the influence of wind speed and direction on the distribution of EDLS components on the surface. Typical wind speeds encountered in the Martian Planetary Boundary Layer (PBL) were found to be of sufficient strength to blow items having a low ballistic coefficient, i.e. Hypersonic Inflatable Aerodynamic Decelerators (HIADs) or parachutes, onto prelanded assets even when the lander itself touches down several kilometres away. Employing meteorological measurements and careful characterisation of the Martian PBL, e.g. appropriate wind speed probability density functions, may then benefit future spacecraft landings, increase safety and possibly help reduce the delta v budget for Mars landers that rely on aerodynamic decelerators.

An SST‐dependent Ku‐band geophysical model function for RapidScat

AbstractA new Ku‐band geophysical model function (GMF), which includes sea surface temperature (SST) dependence, named NSCAT‐5, is developed for improved RapidScat wind retrieval. The RapidScat scatterometer instrument mounted on the International Space Station (ISS) provides near‐global wind data over the oceans. Starting from the existing NSCAT‐4 GMF, the variation of is approximated as a second‐order Taylor expansion in sea surface temperature for each given wind speed , and the fitting coefficients are obtained from both observed and simulated radar cross sections, using ASCAT winds, of either vertical or horizontal polarizations. Furthermore, an intercalibration is performed which aligns the distribution of RapidScat wind speeds to that of ASCAT. NSCAT‐5 is obtained by correcting NSCAT‐4 with SST dependencies and intercalibration information. Validation of the new RapidScat wind products retrieved using NSCAT‐5 shows clear improvements over those obtained with NSCAT‐4: Wind inversion residuals no longer depend on SST, and the wind speed Probability Density Functions (PDFs) are closely overlapping with those of ASCAT. Also, RapidScat NSCAT‐5 minus ASCAT wind speed differences show no SST dependence. The work presented here opens a door for further improving the quality of wind products from Ku‐band backscatter measurements, and helps to build a long‐term and consistent essential Climate Data Record (CDR) of scatterometer winds.

Global comparison of the goodness-of-fit of wind speed distributions

The aim of this study was evaluating the goodness-of-fit of 24 one-component probability density functions and 21 mixture probability density functions to empirical wind speed probability density functions on a global scale. Era-Interim reanalysis wind speed data for the period 2011-01-01 to 2015-12-31 with a spatial resolution of 1°×1° were used to compare the goodness-of-fit of 69 combinations of probability density functions and mixture probability density functions fitted with four different parameter estimation methods. The distribution parameters were obtained by applying the moment method, the L-moment method, the maximum likelihood estimation method and the least-squares estimation method. Four goodness-of-fit metrics related to the probability-probability plot, three goodness-of-fit metrics related to the quantile-quantile plot and one goodness-of-fit metric related to the average wind power density were calculated to assess the suitability of distributions. One important result of this study is that mixture probability density functions like the seven-parameter Burr-Generalized Extreme Value, the seven-parameter Dagum-Generalized Extreme Value, the six-parameter Dagum-Weibull and the six-parameter Generalized Extreme Value-Weibull generally provide a superior fit to one-component probability density functions according to goodness-of-fit metrics related to the probability-probability plot. Another important result is that based on the evaluation of goodness-of-fit metrics related to the quantile-quantile plot, the five-parameter Wakeby probability density function is a suitable choice for onshore and the four-parameter Kappa probability density function for offshore wind speed regimes. The four-parameter Johnson system of distributions and Wakeby probability density functions provided the overall best fit for average wind power density. Only for few wind speed regimes, the often used two-parameter Weibull probability density function was identified as the most appropriate distribution. Maps were produced that country-by-country show the most appropriate on- and offshore distributions on a global scale.

The importance of rare, high-wind events for dust uplift in northern Africa.

Dust uplift is a nonlinear thresholded function of wind speed and therefore particularly sensitive to the long tails of observed wind speed probability density functions. This suggests that a few rare high‐wind events can contribute substantially to annual dust emission. Here we quantify the relative roles of different wind speeds to dust‐generating winds using surface synoptic observations of dust emission and wind from northern Africa. The results show that winds between 2 and 5 m s−1 above the threshold cause the most emission. Of the dust‐generating winds, 25% is produced by very rare events occurring only at 0.1 to 1.4% of the time, depending on the region. Dust‐producing winds are underestimated in ERA‐I, since it misses the long tail found in observations. ERA‐I overpredicts (underpredicts) the frequency of emission strength winds in the southern (northern) regions. These problems cannot be solved by simple tunings. Finally, we show that rare events make the largest contribution to interannual variability in dust‐generating winds and that ERA severely underestimates this interannual variability.

An Analytical Solution for Wind Farm Power Output

An ad-hoc probabilistic analytical solution for modeling wind farm power output is proposed in this letter. In accordance with the unit impulse function described in signals and systems engineering, and combined with the output power versus wind speed curve with wake effect consideration and the wind speed probability density function (PDF), the PDF of wind farm power output is deduced analytically. The comparisons with Monte Carlo method are given to demonstrate the validity of the proposed model.

A long-term perspective of wind power output variability

The study of the wind power output variability comprises different time scales. Among these, low-frequency variations can substantially modify the performance of a wind power plant during its lifetime. In recent years, other temporal scales such as the short-term variability or the climatological conditions of wind and the corresponding generated power have been investigated in depth. However, the study of longer decadal and multidecadal variations is still in its early stages. In this work, the wind power output long-term variability is analysed for two locations in Spain, during the period 1871–2009. This is attained by computing the annual wind speed probability density functions derived from an ensemble of atmospheric sea level pressure data set through a statistical downscaling based in evolutionary algorithms. Results reveal significant trends and periodicities in multidecadal bands including 13, 25 and 46 years, as well as significant differences among both sites. The impact of the leading large-scale circulation patterns (NAO, EA, SCAND and AMO) on wind power output and its stationarity is analysed. Results on both locations show non-stationary significant and opposite seasonal couplings with these forcings. Finally, the long-term variability of the reconstructed Weibull parameters of the annual wind speed distributions is used to derive a linear model to estimate the annual wind power.

A height dependent evaluation of wind and temperature over Europe in the CMIP5 Earth System Models

To date, evaluation studies of global circulation models (GCMs) generally focus on large-scale circulation variables. However, since the resolution of GCMs is increasing and their interaction with the surface is improving, GCM representations of near-surface variables are becoming increasingly realistic. For downscaling practices, this implies that near-surface vari- ables might become suitable as predictors in statistical models, and might increase the added value of dynamical models. This study focuses on the representation of wind and temperature in the lowest 1.5 km of the atmosphere over Europe as simulated by 6 of the earth system models (ESMs) from the Coupled Model Intercomparison Project Phase 5. The evaluation is based on the representation of the variables' probability density functions (PDFs) using ERA-Interim reanalysis data as the reference. The PDF biases are analyzed according to their scale and origin. Above coastal bays and capes, small-scale biases in the ESMs result in unskillful wind speed PDFs up to 400 m. High orography affects wind speeds throughout the lowest 1.5 km of the atmosphere, espe- cially during summer and night. Apart from these small-scale biases, the surface wind speed PDFs north of 45° N are well represented by all the ESMs. Therefore, these PDFs can be considered skillful inputs for statistical downscaling practices. South of 45° N, winds are affected by a large- scale bias originating from errors in the representation of the large-scale circulation, especially during winter. For temperature, near-surface levels as well as upper-atmospheric levels are affected by small-scale and large-scale biases. Large-scale biases are adopted by the downscaling models, underlining the importance of model evaluation before downscaling.

On the wind power potential in the northwest of the Yucatan Peninsula in Mexico

Wind power density, vertical velocity profiles, and other wind characteristics were established using a 51 m meteorological mast located very close to the shoreline on the northwest of the Yucatan peninsula in the Gulf of Mexico. A comparative study of the wind power density was carried out using information obtained between September 2010 and September 2011. The wind speed probability density function was found to be bimodal due to sea-land breezes, a characteristic that becomes less evident as the vertical distance to the ground increases. The distinction between these two wind regimes was used to fit the Weibull-Weibull curve using a linear least-squares criterion in the parameters. In addition, numerical simulations from a mesoscale model are in close agreement with measurements above z=50m (z is the vertical distance to the ground). This result suggests that some mesoscale simulations may serve as a preliminary wind energy assessment tool in coastal zones with extended low-lying areas.

Statistical Downscaling Prediction of Sea Surface Winds over the Global Ocean

Abstract The statistical prediction of local sea surface winds from large-scale, free-tropospheric fields is investigated at a number of locations over the global ocean using a statistical downscaling model based on multiple linear regression. The predictands (the mean and standard deviation of both vector wind components and wind speed) calculated from ocean buoy observations on daily, weekly, and monthly scales are regressed on upper-level predictor fields from reanalysis products. It is found that in general the mean vector wind components are more predictable than mean wind speed in the North Pacific and Atlantic, while in the tropical Pacific and Atlantic the difference in predictive skill between mean vector wind components and wind speed is not substantial. The predictability of wind speed relative to vector wind components is interpreted by an idealized model of the wind speed probability density function, which indicates that in the midlatitudes the mean wind speed is more sensitive to the vector wind standard deviations (which generally are not well predicted) than to the mean vector winds. In the tropics, the mean wind speed is found to be more sensitive to the mean vector winds. While the idealized probability model does a good job of characterizing month-to-month variations in the mean wind speed in terms of the vector wind statistics, month-to-month variations in the standard deviation of speed are not well modeled. A series of Monte Carlo experiments demonstrates that the inconsistency in the characterization of wind speed standard deviation is the result of differences of sampling variability between the vector wind and wind speed statistics.

Tractable Analytic Expressions for the Wind Speed Probability Density Functions Using Expansions of Orthogonal Polynomials

AbstractThe use of the two-parameter Weibull function as an estimator of the wind speed probability density function (PDF) is known to be problematic when a high accuracy of fit is required, such as in the computation of the wind power density function. Various types of nonparametric kernels can provide excellent fits to wind speed histograms but cannot provide tractable analytical expressions. Analytic expressions for the wind speed PDF are needed for many applications, particularly in the downscaling of model or satellite wind speed estimates to the regional or point scale. It is demonstrated that the judicious use of an expansion of orthogonal polynomials can produce more accurate estimates of the wind speed PDF than relatively simply parametric functions, such as the commonly used Weibull function. This study examines four such expansions applied to two different surface wind speed datasets in Oklahoma. The results indicate that the accuracy of fit of a given expansion is strongly related to how close the basis weight function in an expansion resembles the wind speed histogram. It is shown that this basis function, which is the first term in the expansion, acts as a first “best guess” to the true wind speed PDF and that the additional terms act to “adjust” the fit to converge on the true density function. The results indicate that appropriately chosen orthogonal polynomials can provide an excellent fit and are quite tractable.