Wind Speed Probability Distribution Function Research Articles

Probabilistic method for wind speed prediction and statistics distribution inference based on SHM data-driven

For wind-sensitive structures, such as long-span bridges, high-rise buildings, transmission towers, etc., the prediction of wind speed and its statistical distribution are vital steps in the design and operation stages. Specifically, wind speed prediction is directly related to the value of wind load in the next occurrence; the statistical distribution of wind speed has regular characteristics, which can represent the random characteristics of wind field. In this paper, a probabilistic prediction model of wind speed based on Bayes’ theorem is proposed and verified based on structural health monitoring (SHM) data. Firstly, the Gaussian process is derived and used as an a priori function in Bayes’ theorem. In addition, the influence of six covariance functions on the prediction performance are discussed, that is, squared exponential (SE), Matern-3/2 (MA-3/2), Matern-5/2 (MA-5/2), automatic relevance determination SE (ARDSE), ARDMA-3/2, and ARDMA-5/2. Secondly, the correlation between the next wind speed and the previous wind speed is discussed by using the moving window method. Finally, the parameters in the three wind speed probability distribution functions (PDF), that is, Gumbel distribution, Weibull distribution, Rayleigh distribution, are updated in real time by increasing the SHM data based on Bayes’ theorem.

Interval Deep Generative Neural Network for Wind Speed Forecasting

In recent years, wind speed forecasting is a challenging task required for the prediction of wind energy resources. As a highly varying data source, wind speed time series requires highly nonlinear temporal features for the prediction tasks. However, most forecasting approaches apply shallow supervised features extracted using architectures with few nonlinear hidden layers. Moreover, the exact features captured in such methodologies cannot decrease the wind data uncertainties. In this paper, an interval probability distribution learning (IPDL) model is proposed based on restricted Boltzmann machines and rough set theory to capture unsupervised temporal features from wind speed data. The proposed model contains a set of interval latent variables tuned to capture the probability distribution of wind speed time series data using contrastive divergence with Gibbs sampling. A real-valued interval deep belief network (IDBN) is further designed employing a stack of IPDLs with a fuzzy type II inference system (FT2IS) for the supervised regression of future wind speed values. In order to automatically learn meaningful unsupervised features from the underlying wind speed data, real-valued input units are designed inside IDBN to better approximate the wind speed probability distribution function compared to classic deep belief networks. The high generalization capability of our unsupervised feature learning model incorporated with the robustness of IPDLs and FT2IS leads to accurate predictions. Simulation results on the Western Wind Dataset reveal significant performance improvement in 1-h up to 24-h ahead predictions compared to single-model approaches including both shallow and deep architectures, as well as recently proposed hybrid methodologies.

Uncertainty cost functions for solar photovoltaic generation, wind energy generation, and plug-in electric vehicles: mathematical expected value and verification by Monte Carlo simulation

Electrical power systems which incorporate solar or wind energy sources, or electric vehicles, must deal with the uncertainty about the availability of injected or demanded power. This creates uncertainty costs to be considered in stochastic economic dispatch models. The estimation of these costs is important for proper management of energy resources and accurate allocation of the amount of energy available for the system. In this paper, analytical formulas of uncertainty penalty costs are calculated, for solar and wind energy and for electric vehicles, through a mathematical expected value formulation. In order to get the proposed uncertainty cost functions, probability distribution functions (PDF) of the energy primary sources are considered, that is to say: log-normal distribution for solar irradiance PDF, Rayleigh distribution for wind speed PDF and normal distribution for loading and unloading behaviour PDF of electric vehicles. The analytical formulation is verified through Monte Carlo simulations.

Estimation of wind speed probability distribution and wind energy potential using adaptive neuro-fuzzy methodology

The probabilistic wind speed distribution and evaluation of wind energy potential are very important factors while selecting a suitable site for wind turbine installation and estimating wind farm design parameters. Wind farm designers use Weibull wind speed probability distribution function (PDF) to analyze the wind speed characteristics and variations at a specific site. In this study, a hybrid intelligent learning based adaptive neuro-fuzzy inference system (ANFIS) is proposed to accurately estimate the Weibull wind speed PDF and the results are compared with five well-known numerical methods. The results indicate that ANFIS provides the best fit of measured Weibull distribution curve. The Weibull parameters are further utilized to calculate some important parameters which are helpful to estimate the wind energy potential of a site. Then the problem of selecting the most efficient and economically viable wind turbine is addressed. For this purpose, four small scale wind turbines are taken into consideration for available wind resources. The average electrical power, the annual energy produced and the capacity factor are calculated to check the economic viability each wind turbine model. According to the results, wind turbines with rated power 50 kW and 100 kW are most economically viable for available wind resources.

Evaluation of Energy in Wind Turbine System Using Probability Distribution

In this work, annual energy output of a variable speed wind turbine is analyzed using annual Weibull wind speed probability distribution function. The power coefficient variety with tip speed proportion in torque control district and pitch point variety for most extreme power yield from wind turbine are examined for distinguishing control framework parameters. The wind turbine power output and variation of power coefficient with tip speed ratio as well as pitch angle are examined / reported using annual Wei bull distribution function. Finally the variation of the estimated annual energy output of the given wind turbine with the mean wind speed is presented.

The CMOD7 Geophysical Model Function for ASCAT and ERS Wind Retrievals

A new geophysical model function (GMF), called CMOD7, has been developed for intercalibrated ERS (ESCAT) and ASCAT C-band scatterometers. It is valid for their combined incidence angle range and being used to generate wind climate data records. CMOD7 has been developed in several steps as a successor of CMOD5.n. First, CMOD5.n has been adapted to the ASCAT transponder calibration, which is considered more accurate than any ESCAT gain calibration. This results in a linear scaling of the backscatter values. Second, for low winds, there is a clear mismatch between CMOD5.n and the measurements. An independently developed ASCAT C-band GMF, C2013, which performs particularly well for low winds was adopted to improve low winds for the ASCAT incidence angle range. Third, retrievals with CMOD5.n show wind speed probability distribution functions (pdf) that undesirably depend on wind vector cell (WVC) position across the swath. To overcome this effect, a higher order calibration is applied, which matches the wind speed pdfs for all WVCs of ASCAT and ESCAT. The resulting CMOD7 GMF indeed shows overall improved performance on all relevant quality parameters compared to CMOD5.n. It is found that the standard deviations of error for wind speed and wind direction of ASCAT are improved. The same holds for the maximum-likelihood estimates, showing an 8% improved consistency with the local triplet of backscatter measurements. As a consequence, triple collocation with moored buoy and numerical weather prediction winds results in smaller wind vector components and wind direction retrieval errorsim.

Reliability over time of wind turbines steel towers subjected to fatigue

A probabilistic approach that combines structural demand hazard analysis with cumulative damage assessment is presented and applied to a steel tower of a wind turbine. The study presents the step by step procedure to compare the reliability over time of the structure subjected to fatigue, assuming: a) a binomial Weibull annual wind speed, and b) a traditional Weibull probability distribution function (PDF). The probabilistic analysis involves the calculation of force time simulated histories, fatigue analysis at the steel tower base, wind hazard curves and structural fragility curves. Differences in the structural reliability over time depending on the wind speed PDF assumed are found, and recommendations about selecting a real PDF are given.

Wind Velocity Vertical Extrapolation by Extended Power Law

Wind energy gains more attention day by day as one of the clean renewable energy resources. We predicted wind speed vertical extrapolation by using extended power law. In this study, an extended vertical wind velocity extrapolation formulation is derived on the basis of perturbation theory by considering power law and Weibull wind speed probability distribution function. In the proposed methodology not only the mean values of the wind speeds at different elevations but also their standard deviations and the cross-correlation coefficient between different elevations are taken into consideration. The application of the presented methodology is performed for wind speed measurements at Karaburun/Istanbul, Turkey. At this location, hourly wind speed measurements are available for three different heights above the earth surface.

Theoretical derivation of wind power probability distribution function and applications

The instantaneous wind power contained in the air current is directly proportional with the cube of the wind speed. In practice, there is a record of wind speeds in the form of a time series. It is, therefore, necessary to develop a formulation that takes into consideration the statistical parameters of such a time series. The purpose of this paper is to derive the general wind power formulation in terms of the statistical parameters by using the perturbation theory, which leads to a general formulation of the wind power expectation and other statistical parameter expressions such as the standard deviation and the coefficient of variation. The formulation is very general and can be applied specifically for any wind speed probability distribution function. Its application to two-parameter Weibull probability distribution of wind speeds is presented in full detail. It is concluded that provided wind speed is distributed according to a Weibull distribution, the wind power could be derived based on wind speed data. It is possible to determine wind power at any desired risk level, however, in practical studies most often 5% or 10% risk levels are preferred and the necessary simple procedure is presented for this purpose in this paper.

A new probabilistic method to estimate the long-term wind speed characteristics at a potential wind energy conversion site

This paper proposes the use of a new Measure–Correlate–Predict (MCP) method to estimate the long-term wind speed characteristics at a potential wind energy conversion site. The proposed method uses the probability density function of the wind speed at a candidate site conditioned to the wind speed at a reference site. Contingency-type bivariate distributions with specified marginal distributions are used for this purpose. The proposed model was applied in this paper to wind speeds recorded at six weather stations located in the Canary Islands (Spain). The conclusion reached is that the method presented in this paper, in the majority of cases, provides better results than those obtained with other MCP methods used for purposes of comparison. The metrics employed in the analysis were the coefficient of determination ( R 2) and the root relative squared error (RRSE). The characteristics that were analysed were the capacity of the model to estimate the long-term wind speed probability distribution function, the long-term wind power density probability distribution function and the long-term wind turbine power output probability distribution function at the candidate site.

Simulation of wind energy output at Guajira, Colombia

A methodology is developed to estimate the chord distribution airfoil and blade twist along the radius of the blade by using axial and angular moment conservation equations, blade element theory and optimization processes. This methodology takes into account the concept related with getting wind power for different chord blade values and selecting one that facilitates to get the maximum value for wind power. Simulation of power generation output was carried out by using a wind-speed probability distribution function (PDF) obtained from data collected at the Guajira region of Colombia.

Height variation of wind speed and wind distributions statistics

For use in various wind engineering applications (e.g. wind energy conversion, wind loads on structures, air pollution transport) it is desirable to have a consistent relationship by which to project height variations of both "instantaneous" (e.g. few minute average) winds and parameters of the wind speed probability distribution. The power law V2/V1 = (Z2/Z1)n is often used for height projection of wind profiles, with the exponent n sometimes taken as depending on surface conditions or on atmospheric stability. The power law profile for wind speed is shown here to be consistent with observed height variation of Weibull wind speed probability distribution functions which have been found to fit observed wind speed distributions (at least above relevant threshold wind speeds). For consistency between the wind speed profiles and the height variation of the Weibull wind speed probability distributions, it is necessary only that the exponent n vary as n = a + b ℓn V1, where a and b are constants whose values depend on the reference height at which wind speed V1 is measured. For a reference height of 10 m, it is found that a = 0.37 and b = −0.0881 (with V1 in m/s) adequately describes both the observed height variation of wind speed and wind speed probability distributions.