Wind Speed Probability Distribution Research Articles

Robust damping improvement against the vortex-induced vibration in flexible bridges using multiple tuned mass damper inerters

The tuned mass damper inerter (TMDI) is considered as one of countermeasures to mitigate the very-low-frequency vertical bending vortex-induced vibration (VIV) in flexible bridges. However, the control robustness of the TMDI against the system uncertainty is a serious concern due to the limited inerter span capacity. In this paper, the multiple tuned mass damper inerter (MTMDI) is used instead of identical TMDIs to provide a robust equivalent damping ratio against the uncertain VIV within the entire lock-in wind speed range. A design framework of the MTMDI considering the inerter span length is proposed based on a universal VIV model suitable for the fully closed, centrally slotted, and semi-closed box decks. In the framework, the fluctuation of VIV characteristics with the wind speed, the probability of occurrence of the VIV, and the uncertainties in VIV characteristics and deck dynamics are considered, simultaneously. Two objection functions are defined to focus on the maximizing the equivalent damper ratio and reducing the VIV mitigation failure, respectively. Finally, numerical analysis of a flexible bridge-MTMDI system subjected to the VIV is performed. The results show that the wind speed probability distribution plays a role of weighting coefficient in the MTMDI optimization. The choice of the objective function depends on the mass ratio of the MTMDI and the level of the system uncertainty. The well-optimized MTMDI achieved a more robust control result than the TMDI within the entire lock-in wind speed range.

A novel method for studying the wind speed probability distribution and estimating the average wind energy density

Traditional distribution models generally have large fitting errors at low wind speeds and poor fitting effects at multi-peak wind speed distributions. In this paper, a novel approach is proposed to fit different wind speed distributions, introducing a Gumbel distribution into common hybrid distribution models. The model parameters are solved by a combination of snake optimizer and nonlinear least squares (SO-NLS), using the optimal values obtained by the nonlinear least squares method as a set of initial input vectors for the snake optimizer. Simulation experiments were conducted using multi-peak wind speed distribution datasets with varying characteristics, comparing the fitting performance of the improved hybrid models against the conventional Weibull, Normal, and Rayleigh hybrid models. The results show that the proposed approach improved the model fit effects, particularly at low wind speeds, in all five experimental datasets. In most cases, the overall fitting effects were also improved. Furthermore, the validity and superiority of the improved hybrid models were further verified by comparing the estimated average wind energy density. Meanwhile, the experimental results also verified that SO-NLS not only yielded better optimization results but also accelerated the convergence speed than the snake optimizer. The improvements presented in this study effectively address the problem of large fitting errors at the low wind speed sections of the distribution, providing a theoretical basis for wind farm planning and design.

THE COMPARISON SOME EXTENDED WEIBULL DISTRIBUTION (WEIBULL (W), EXPONENTIATED WEIBULL (EW), EXPONENTIATED EXPONENTIAL WEIBULL (EEW) AND ADDITIVE WEIBULL (AW)) FOR THE WIND SPEED PROBABILITY MODELLING

Accurate wind speed modeling is critical in estimating wind energy potential for harnessing wind power effectively. One of the bases for assessment of wind energy potential for a specified region is the probability distribution of wind speed, therefore wind speed data is needed to produce statistical modeling, especially in determining the best probability distribution. For this purpose, several modified weibull distributions will be used and tested to determine the best model to describe wind speed in Pekanbaru. The main goal of this study is to find the best fitting distribution to the daily wind speed measured over Pekanbaru region for the years 1999-2020 by using the four modified weibull distributions, namely Weibull (W), Exponentiated Weibull (EW), Additive Weibull (AW) and Exponentiated Exponential Weibull (EEW). The maximum likelihood method will be used to get the estimated parameter value from the distribution used in this study. Furthermore, the graphical inspection (density-density plot and cumulative plot) and numerical criteria (Akaike’s information criterion (AIC), Bayesian Information Criteria (BIC), - log likelihood (- l) ) were used to determine the best fit model. In most cases, the results produced by the graphical inspection were similar, and differed from the numerical criteria . The best fit result was chosen as the distribution with the lowest values of AIC, BIC and - l. In general, the Exponentiated Exponential Weibull (EEW) distribution has been selected as the best model.

Fitting wind speed and wind direction probability distribution using mixture B-spline function

Fitting wind speed and wind direction probability distribution is a crucial and fundamental task for the investigation of wind resource. This paper proposes a mixture basis(B)-spline function to fit wind speed and wind direction probability distribution. Such mixture B-spline function requires no prior assumption and eliminates the influence of subjective experience. A procedure has been developed that combines a binary genetic algorithm, maximum likelihood estimation, and a chi-squared test. This procedure can enable mixture B-spline function to adapt to various probabilistic behaviors. The wind speed and wind direction probability distributions of four North Dakota, U.S. sites are fitted by the mixture B-spline function and other five methods. Their goodness-of-fits are examined by chi-squared tests. The results indicate that the mixture B-spline function passes all the chi-squared tests and presents the highest goodness-of-fit. Additionally, the mixture B-spline function is used to calculate the mean wind power density, which can help identify sites with richer wind resources.

Smart Urban Wind Power Forecasting: Integrating Weibull Distribution, Recurrent Neural Networks, and Numerical Weather Prediction

The design, operational planning, and integration of wind power plants with other renewables and the grid face challenges attributed to the intermittent nature of wind power generation. Addressing this issue necessitates the development of a smart wind power (and in particular wind speed) forecasting approach. This is a complex task due to substantial fluctuations in wind speed. To overcome the inherent stochastic nature of wind speed and mitigate related challenges, traditionally, numerical weather prediction (NWP) models are employed for wind speed forecasting. However, the applicability of NWP models is limited to short-term forecasting due to their computational constraints. In this study, a hybrid AI-based approach is proposed to improve forecast accuracy over a 48 h horizon for the city of Montreal. The results demonstrate that by integrating the probability distribution of wind speed with a deep learning model, the forecasted values align closely with the observed values in terms of seasonality and trend, exhibiting enhanced accuracy. Evaluation metrics reveal a substantial reduction in the root mean squared error (13–31%) across three prediction horizons (summer, fall, and winter) compared to a single long, short-term memory model. Furthermore, integrating the improved model with the numerical weather prediction model yields increased accuracy and decreased error compared to the LSTM–Weibull model.

A Review on Wind Speed Extreme Values Modeling and Bayes Estimation for Wind Power Plant Design and Construction

Rapid growth of the use of wind energy calls for a more careful representation of wind speed probability distribution, both for identification and estimation purposes. In particular, a key point of the above identification and estimation aspects is representing the extreme values of wind speed probability distributions, which are of great interest both for wind energy applications and structural tower reliability analysis. The paper reviews the most adopted probability distribution models and estimation methods. In particular, for reasons which are properly discussed, attention is focused on the evaluation of an opportune “safety index” related to extreme values of wind speeds or gusts. This topic has gained increasing attention in recent years in both wind energy generation assessment and also in risk and structural reliability and safety analysis. With regard to wind energy generation, there is great sensitivity in the relationship between wind speed extreme upper quantiles and the corresponding wind energy quantiles. Concerning the risk and reliability analysis of structures, extreme wind speed value characterization is useful for a proper understanding of the destructive wind forces that may affect structural tower reliability analysis and, consequently, the proper choice of the cut off wind speed value; therefore, the above two kinds of analyses are somewhat related to each other. The focus is on the applications of the Bayesian inference technique for estimating the above safety index due to its effectiveness and usefulness.

An extensive mathematical approach for wind speed evaluation using inverse Weibull distribution

Wind velocity and potential are frequently estimated using probability density functions (PDFs) such as the Inverse Weibull and Rayleigh. Determining whether they are suitable for modelling observed distributions is crucial. Many wind energy systems require a thorough understanding of wind speed probability distributions. This research presents an extensive mathematical approach for wind speed evaluation using the inverse Weibull distribution (IWD) and a modified maximum likelihood function. IWD is a valuable tool for modelling wind speed characteristics, providing insights into the PDF and cumulative distribution function (CDF) of wind speeds. The suggested modified maximum likelihood (MML) function includes tweaks and improvements to increase parameter estimate accuracy in the IWD. The IWD is computed using the MML function, which considers data features, outliers, and unique research demands. Model calibration techniques, including goodness-of-fit assessment, sensitivity analysis, and error analysis, are employed to refine and assess the model’s accuracy. The developed mathematical model based on the inverse Weibull distribution and modified maximum likelihood function offers a robust approach for wind speed evaluation and analysis, contributing to renewable energy resource assessment, wind farm design, and structural engineering applications.

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.

A comprehensive performance evaluation methodology for sea-crossing cable-stayed bridges under wind and wave loads

This study proposes a probabilistic performance evaluation framework for sea-crossing cable-stayed bridges (SCBs) subjected to wind and wave excitations with the incorporation of wind speed and direction, bridge orientation, wind-wave correlation and parameter uncertainties. Both the bridge serviceability and safety are taken into account in the performance assessment. The fragility analysis of the SCB under wind and wave loads is conducted using the wind-wave correlation model constructed based on field data. The actual damage probability of a local SCB is computed by combining the fragilities of bridge under different wind incidence angles with the copula-based joint probability distribution (JPD) of wind speed and direction, which is developed using the wind field data recorded in Lianyungang city of China from 1971 to 2020. The results show that under the defined wind incidence angle of 0°, the exemplar SCB suffers the highest fragility. Moreover, with the data-based occurrence probability model of wind and wave hazards, the damage probabilities under all possible wind speeds and directions are computed; then the optimal and most unfavorable orientations of the SCB are obtained. This investigation provides a comprehensive and practical method for the performance evaluation and design optimization of SCBs under wind and wave loads with long-term recorded hazard data at the local site.

Impact of components number selection in truncated Gaussian mixture model and interval partition on wind speed probability distribution estimation

Owing to global environmental concerns in recent years, wind power has garnered significant attention as a clean and renewable energy source. The probability distribution of the wind speed plays a pivotal role in assessing the wind energy potential and power system operation. As a single Gaussian may be powerless in capturing features of real wind speed distributions owing to the randomness of wind speed, this study aimed to use a truncated Gaussian mixture (TGM) distribution with determined optimal Gaussian components number and suitable interval partitions as a possible alternative model to estimate the wind speed probability distribution (WSPD). In particular, two expectation-maximization algorithms were employed to determine the parameters of the TGM models. Subsequently, the continuous ranked probability score loss theory related to TGM models with two arbitrary truncated points was developed and employed to detect the optimal number of Gaussian components in the TGM models, in addition to casually or empirically setting the number of Gaussian components. Subsequently, the WSPD is estimated using the detected optimal Gaussian component number and the corresponding parameter determination results. Considering that different interval partitions may result in diverse accuracy results, to enhance the flexibility of the above TGM models, another technique is designed using the False-Discovery-Rate-inspired algorithm. This algorithm performs well in the case of large-scale hypothesis tests and can determine the suitable interval partition number. The feasibility and effectiveness of the proposed model were validated using real wind speed data collected from two stations: Haikou and Wulumuqi stations. Comparison of the different goodness-of-fit evaluations demonstrates that the estimation accuracy of WSPD of the proposed approach is comparable to those of the truncated Gaussian mixture distribution with arbitrary Gaussian component numbers and some other comparison models.

Comparison of Wind Speed Probability Distribution Models for Accurate Evaluation of Wind Energy Potential: A Case Study from Kerala, India

Comparison of Wind Speed Probability Distribution Models for Accurate Evaluation of Wind Energy Potential: A Case Study from Kerala, India

EFFICIENCY OF A WIND PLANT IN REAL CONDITIONS WITH ADDITIONAL COSTS AND THE MARKET PRICE OF ELECTRICITY

In its development, the global energy sector is constantly demonstrating the growth of electricity consumption. Traditional power plants in this process ensure an increase in greenhouse emissions and aggravation of climate problems, which are becoming more relevant every year. Against this background, modern alternative energy sources, namely wind power plants, contribute to reducing the impact of traditional power plants and encourage solving environmental problems. The development of global wind energy is accompanied by the growth of unit capacities of generators of wind power plants. The paper analyzes the efficiency of a wind power plant based on modern wind generators for predetermined location conditions, taking into account operating costs based on operational experience and based on the assessment of the power plant's participation in the balancing market of electricity with a waiver of the "green tariff". Calculations of the technical and economic indicators of an imaginary designed 4-unit wind power plant with various wind generators under the wind conditions of a predetermined industrial site located in the Carpathian region of Ukraine were carried out. The calculations take into account the modern typical characteristics of wind generators, additional operating costs and the estimated cost of electricity purchase of the station under the "green tariff" and in the conditions of a balancing electricity market to compare economic efficiency. In order to make an optimal design technical decision with a comparative assessment, three types of wind generators were determined for installation at an imaginary wind farm - Enercon E-175 EP5, Vestas V136-4.5 MW and Vestas V172-7.2 MW. In the conditions of the predetermined construction site of the projected wind farm on the Carpathian ridges of Ukraine, the measured and calculated annual probability distribution of wind speed according to the analytical Weibull distribution is applied, and the characteristics of the annual productivity of the 4-unit wind farm for the adopted three types of wind generators are given. The technical and economic characteristics were obtained in the work: capital investment, operating costs, characteristics of electricity production, the gross profit during the annual operation of the wind power plant with three options for installing wind generators was calculated, making it possible to estimate the payback time of the investment in the construction of the wind plant. So, for a 4-unit station with generators of the Enercon E-175 EP5, the payback period is 3.3 years, and with wind generators of the Vestas V136-4.5 MW - 3.4 years, as well as for the Vestas V172-7.2 MW in operating conditions of the "green tariff" and, respectively, 2.9 years, 2.9 years and 3.0 years under conditions of sale of electricity at balancing market prices. Additional operating costs for the disposal of worn wind turbine blades do not have a significant impact on the overall cost indicators and amount to 5-7% of the total costs.

Multi-hazard joint probability distribution model for wind speed, wind direction and rain intensity

Multiple disasters such as strong wind and torrential rain pose great threats to civil infrastructures. However, most existing studies ignored the dependence structure between them, as well as the effect of wind direction. From the dimension of the engineering sector, this paper introduces the vine copula to model the joint probability distribution (JPD) of wind speed, wind direction and rain intensity based on the field data in Yangjiang, China during 1971–2020. First, the profiles of wind and rain in the studied area are statistically analyzed, and the original rainfall amounts are converted into short-term rain intensity. Then, the marginal distributions of individual variables and their pairwise dependence structures are built, followed by the development of the trivariate joint distribution model. The results show that the constructed vine copula-based model can well characterize the dependence structure between wind speed, wind direction and rain intensity. Meanwhile, the JPD characteristics of wind speed and rain intensity show significant variations depending on wind direction, thus the effect of wind direction cannot be neglected. The proposed JPD model will be conducive for reasonable and precise performance assessment of structures subjected to multiple hazards of wind and rain actions.

Research on the Derated Power Data Identification Method of a Wind Turbine Based on a Multi-Gaussian-Discrete Joint Probability Model.

This paper focuses on how to identify normal, derated power and abnormal data in operation data, which is key to intelligent operation and maintenance applications such as wind turbine condition diagnosis and performance evaluation. Existing identification methods can distinguish normal data from the original data, but usually remove power curtailment data as outliers. A multi-Gaussian-discrete probability distribution model was used to characterize the joint probability distribution of wind speed and power from wind turbine SCADA data, taking the derated power of the wind turbine as a hidden random variable. The maximum expectation algorithm (EM), an iterative algorithm derived from model parameters estimation, was applied to achieve the maximum likelihood estimation of the proposed probability model. According to the posterior probability of the wind-power scatter points, the normal, derated power and abnormal data in the wind turbine SCADA data were identified. The validity of the proposed method was verified by three wind turbine operational data sets with different distribution characteristics. The results are that the proposed method has a degree of universality with regard to derated power operational data with different distribution characteristics, and in particular, it is able to identify the operating data with clustered distribution effectively.

Atmospheric Drivers of Wind Turbine Blade Leading Edge Erosion: Review and Recommendations for Future Research

Leading edge erosion (LEE) of wind turbine blades causes decreased aerodynamic performance leading to lower power production and revenue and increased operations and maintenance costs. LEE is caused primarily by materials stresses when hydrometeors (rain and hail) impact on rotating blades. The kinetic energy transferred by these impacts is a function of the precipitation intensity, droplet size distributions (DSD), hydrometeor phase and the wind turbine rotational speed which in turn depends on the wind speed at hub-height. Hence, there is a need to better understand the hydrometeor properties and the joint probability distributions of precipitation and wind speeds at prospective and operating wind farms in order to quantify the potential for LEE and the financial efficacy of LEE mitigation measures. However, there are relatively few observational datasets of hydrometeor DSD available for such locations. Here, we analyze six observational datasets from spatially dispersed locations and compare them with existing literature and assumed DSD used in laboratory experiments of material fatigue. We show that the so-called Best DSD being recommended for use in whirling arm experiments does not represent the observational data. Neither does the Marshall Palmer approximation. We also use these data to derive and compare joint probability distributions of drivers of LEE; precipitation intensity (and phase) and wind speed. We further review and summarize observational metrologies for hydrometeor DSD, provide information regarding measurement uncertainty in the parameters of critical importance to kinetic energy transfer and closure of data sets from different instruments. A series of recommendations are made about research needed to evolve towards the required fidelity for a priori estimates of LEE potential.

An effective two-stage optimization method on aerodynamic measures to mitigate wind loads considering uncertainties in wind direction and velocity

At present, deterministic optimization methods on aerodynamic measures are usually employed to mitigate wind loads at one certain wind direction, ignoring the effects of the uncertainties in wind direction and velocity on wind loads. The uncertain optimization method with the consideration of the joint probability distribution (JPD) of wind speed and direction is hardly to conduct because it is very time-consuming and costly. In order to overcome these shortcomings, this study proposes an effective two-stage uncertain optimization method considering uncertainties in wind direction and velocity to achieve a considerable reduction of wind loads. In the first stage, the exceedance probability distribution of wind loads is determined based on the JPD and the wind load coefficients on the building, and the wind loads in the most unfavorable range of wind directions are chosen as the optimization objective. In the second stage, the optimal values of the design variables are determined by an interval optimization algorithm using the surrogate model and non-dominated sorting genetic algorithm II in the most unfavorable range of wind directions, where the surrogate model is constructed by the radial basis function method to relate the wind load coefficients to the design variables of aerodynamic measures, and can significantly improve the efficiency of the optimization algorithm. To validate the effectiveness of the proposed method, a flat-roof building with four spoilers is investigated and the rotation angles of spoilers are set as the design variables. The results show that the proposed method reduces the uplift wind loads with a 50-years return period up to 15.48% compared to the deterministic optimization method for one certain wind direction.

Wind-induced failure analysis of a transmission tower-line system with long-term measured data and orientation effect

This paper proposes a comprehensive wind-induced performance evaluation framework for transmission tower-line systems (TTLSs) from both structural safety and normal operation dimensions, incorporating the joint effect of wind speed and direction, as well as the line orientation. Based on the field wind data recorded in Weifang, China during 1971–2020, the actual failure probability of a local TTLS is calculated considering the joint probability distribution (JPD) of wind speed and direction, and the optimal layout of the transmission line is provided. The results show that the developed QS copula model can not only account for the continuity and cyclicity of wind direction but also have a fine goodness-of-fit. The wind direction with a relatively lower occurrence probability does not necessarily yield smaller failure probability of the TTLS, thereby the JPD of wind speed and direction should be incorporated to achieve reliable performance assessment. For the failure analysis with respect to structural damage, the most favorable layout of the exemplar TTLS is the orientation of 265°; while the most advantageous layout is the orientation of 38° in terms of flashover risk. The presented framework is conducive to performance assessment and optimization design of TTLSs subjected to wind hazards.

Nonlinear dynamic response of sea-crossing bridges to 3D correlated wind and wave loads

Long span sea-crossing bridges are often slender and sensitive to wind and wave loads. Nonlinear dynamic response analysis of the bridges under three-dimensional (3D) correlated wind and wave loads is performed in this study in consideration of both geometric and aerodynamic nonlinearities. An optimized C-vine copula is first used to construct a 3D joint probability distribution and environmental contour of mean wind speed, significant wave height and peak wave period. Multi-point fluctuating wind loads with Davenport coherence function and random wave loads with pile group effect are then determined using wind and wave spectra respectively. The nonlinear wind-wave-bridge system considering geometric and aerodynamic nonlinearities is solved by the Newmark-β method with the 3D correlated wind and wave parameters as an input. The proposed approach is finally applied to a real sea-crossing cable-stayed bridge with the measured wind and wave data. The results show that the nonlinear response of the bridge is higher than its linear response with the same input. The bridge response is significantly reduced if the 3D correlated wind and wave loads other than conventional uncorrelated wind and wave loads are considered.

Estimation of Wind Speed Probability Distribution Parameters by Using Four Different Metaheuristic Algorithms

The inclusion of energy produced from renewable energy sources (RES) such as solar and wind energy into existing energy systems is important to reduce carbon emissions, air pollution and climate change, and to ensure sustainable development. However, the integration of RES into the energy system is quite difficult due to their highly uncertain and intermittent nature. In this study, considering three different probability density functions in total, the scale and shape parameters of the Weibull probability density function (PDF), the scale parameter of the Rayleigh PDF, and the scale and shape parameters of the Gamma PDF were estimated for the wind speed data obtained from urban stations located in Istanbul by using the four different metaheuristic algorithms, namely Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO) algorithms. Calculating the mean absolute error (MAE), root mean squared error (RMSE), and R2 values for each PDF at each station, the PDF that characterizes the wind speed probability distribution the best was identified.

The Significant of Efficient Wind Turbines Arrangement in Mersing

In this work, the results of wind velocity and its impact on wind energy power are reviewed. It incorporates statistical study of the wind regime, power analysis, and the probability distribution of wind speed. A thorough probability distribution selection yields a clear power analysis. Weibull and Gama probability distribution is the primary distribution used. The wind power equation is created using a transformation approach, and the results of the research to show that Malaysia may effectively collect wind energy especially when the wind turbines are located at the coastal area. The Mersing area's potential for producing wind energy with the exact location and direction for placing the wind turbine is suggested in this paper.