Weibull Shape Factor Research Articles

Mathematical Differential Analysis of Atlantic Ocean Wind to Electrical Energy Generation in Lekki Peninsular Lagos Nigeria

This article is a pragmatic approach on the evaluation of wind energy production and it’s estimation in the coastal area of Lagos Nigeria. The work focuses on the accessibility of wind energy production in Lagos Nigeria through analyzing wind data in the look up tables using proficient probability function. Here, three approaches are itemized; Analysis of sets of actual time series data, theoretical Weibull probability function using seven numerical methods and the comparison of theory and the analysis. Two important parameters are used in this analysis are the Weibull shape factor “k” and Weibull scale factor “c”. Theory involves the calculation using seven popular methods of moments (MM), standard deviation method (STDM) or empirical method (EM), maximum likelihood method (MLM), modified maximum likelihood method (MMLM), second modified maximum likelihood method (SMMLM), graphical method (GM) or least mean square method (LSM), energy pattern factor method (EPFM). The performance of the numerical methods has been tested by five methods; RMSE, X2, IA, MAPE and RRMSE. The results expatiate on Actual and theoretical technique being used to find out wind energy conversion per 1 km2. In this paper, a differential performance method for accuracy check has been proposed as an error indicator between the wind energy calculated by theoretical Weibull function and the one by actual time-series data. The wind speed data was measured from January 2018 to December 2021 in the Lekki peninsular area of Lagos State. The suitability values for these parametric; shape and scale parameters of Weibull distribution are determined in selecting the best location for the installation the wind turbine generators. The measured annual mean wind speed and mean wind power are 10.11 ms-1 and 10.4 KWm-2, respectively.

Assessment of wind energy potential in Zambia

An assessment of potential for wind energy in Zambia was carried out to help address the shortage of energy due to increasing energy needs arising from energy requirements for newly opened mining industries and unreliable hydropower generation due to climate change. The assessment was carried out by collecting wind speed data of 25 sites owned by Zambia Meteorological Department. The objective of the study was to analyse wind patterns and determine areas in Zambia where production of electricity from wind can be invested. The analysis was based on the use of Weibull shape factor and yielded 3.32 m/s wind speed and 13.2 shape factor from a site with the most suitable wind speeds (Kasama Meteorological Station). A correlation study was carried out using these results and Goldwin 1.5 MW wind turbine of model GW82/1500. The study results showed that 44.46 kW power output could be obtained at 3.83 m/s wind speed by a correlation equation of this turbine power output with wind speeds. A series of similar power output results were obtained for wind speeds recorded in the years from 2013 to 2021 and compared with those obtained in the same period by using model equation due to Al Buhariri, and found that the power outputs compared very closely at low wind speeds ranging 3 to 3.2 m/s but rather widely at higher wind speeds.This study is significant in that it provides information on decision making and helps determine policy direction for wind utilization in Zambia and it can also help influence investment decision by Zambian mining companies who have financial ability to undertake large scale investments.

Accuracy of wind speed forecasting based on joint probability prediction of the parameters of the Weibull probability density function

This work aims to evaluate different error estimations of the shape and scale parameters of the Weibull probability density function of wind speed measured at the Fujairah site over a 1-year period. This study estimates trends in the variation of Weibull parameters using moving averages and Markov series methods. The focus is on the scale and shape factors, which are evaluated by mapping monthly mean wind speeds into a Weibull probability distribution function. Due to the imprecise nature of these factors, multiple data simulations are used to predict Weibull factors based on data measuring interpolations. A procedural algorithm is proposed to select the overall best forecast based on several estimation methods that evaluate raised prediction errors. A probabilistic analysis is followed to predict future wind speed and wind energy based on variations in the scale and shape factors. This study focuses on the scale factor variation as it is found to be more dominant than the Weibull shape factor. The forecasted wind speed is checked with the measured value in future months and found to be within trend values. The results suggest that the proposed algorithm provides an accurate and reliable method for predicting future wind speed and energy output.

Feasibility Analysis of the Wind Energy Potential in Libya using the RETScreen Expert

This study focuses on the evaluation of the economic viability of various scale wind farms and the assessment for the first time of the wind power potential of 22 locations distributed over Libya. The study utilizes monthly mean wind data collected from the NASA power dataset. The analysis includes determining and analyzing the mean wind speed, frequency distribution, and Weibull distribution scale and shape factors. The results showed that Darnah is the most promising location for insulation wind farms due to the high value of wind speed. Moreover, RETScreen software is used to estimate the energy output and conduct an economic feasibility analysis of the wind farm. Additionally, this paper establishes a relationship between the wake effect, airfoil losses, and the potential for greenhouse gas (GHG) mitigation and the performance of wind farms. The results indicate that wind projects are economically viable when the EWT-DW 52 with a capacity of 500 kW is used. The study findings show that the wake effect is a crucial consideration in wind farm design, and it can be minimized through strategic spacing and turbine design. Furthermore, the accumulation of dirt and debris on wind turbine blades can significantly reduce a wind farm's energy output, causing turbine inefficiency and decreasing the overall energy production. Additionally, the energy production cost from a wind farm is less than that of the electricity tariff and can result in a profitable wind energy project.

Impact of Weibull Wind Speed Distribution on the Costs of Producing Power‐to‐X Products

AbstractA calculation method based on Weibull parameters and cost functions is presented to optimize the levelized cost of electricity and the costs for subsequent power‐to‐X (PTX) production from wind power. PTX products considered are methanol, ammonia, synthetic gasoline, and synthetic diesel as well as the hydrogenation of liquid organic hydrogen carrier. The onshore production sites Haru‐Oni in Chile, Tarfaya in Morocco, and Dornum in Germany were used for illustrative purposes. The model calculations show that the rated power of the installed wind turbines for power generation is generally optimal between 1 and 3 MWel in contrast to the current trend towards ever higher rated power. Also, it has been found that the recoverable wind energy increases with rising Weibull shape factor k if the wind speed at which the rated power is reached is smaller than the Weibull scaling factor A.

Influence of Weibull parameters on the estimation of wind energy potential

Wind potential estimation is generally evaluated using two-parameter (k, c) Weibull distribution. Root Mean Square Error (RMSE), Coefficient of Determination (R2) and Relative Error (RE) are computed in order to comparatively analyse fourteen methods of determining Weibull parameters. They are the Graphical Method, the Standard Deviation Method, the Empirical Method of Justus, the Empirical Method of Lysen, the Energy Pattern Factor Method, the Maximum Likelihood Method, the Modified Maximum Likelihood Method, the Alternative Maximum Likelihood Method, the Least Square Method, the Weighted Least squares Method, the Curve Fitting Method, the Wind Variability Method, the Moroccan Method and the Median and Quartile Method. These methods have been applied on three different windy sites (slightly, moderately and very windy sites) with hourly wind data over a period of 10 years (2005–2014), measured at 10 m height. As a result, compared to the other methods, Energy Pattern Factor method is the more suitable method applicable to assess the Weibull parameters for all wind speeds. However, the values obtained from RMSE, R2 and RE tests revealed that the WVM and MoroM methods are not suitable while all other methods are acceptable for the estimation of k and c. parameters. The determination of the wind power density and the gap between the predicted standard deviation by each method and the measured standard deviation for all the sites highlighted the relevance of EPFM method and the others methods. Moreover, this work reveals that the Weibull shape factor k decrease with height above ground level, while that of the scale factor c increase with height.

On the "intrinsic" breakdown of thick gate oxide.

The thick gate oxide breakdown mechanism has become an important topic again due to the rising demand for power electronics. The failure of the percolation model in explaining the observed Weibull shape factor, β, seriously hampers the establishment of thick gate oxide breakdown models and the ability to project reliability from measurement data. In this work, lifetime shortening by oxide defects are simulated to produce degraded breakdown distributions that match experimentally observed βs. The result shows that even a low density of defects with the right energy is enough to greatly degrade β for thick oxides. Strong area scaling for thin oxides counters this sensitivity to defects effectively and explains why the percolation model is successful in thin oxides but not in thick oxides. Only defects with the appropriate energy can degrade the breakdown distribution. The required energy is consistent with oxygen vacancy defect after capturing a hole and the concentration required is consistent with very high-quality oxide. This explains the consistent low β values for thick oxides universally reported in the literature.

Characteristics of Wind Resources and Post-Project Evaluation of Wind Farms in Coastal Areas of Zhejiang

As the onshore wind farm technology matures, offshore wind energy has attracted increasing attention. Zhejiang has coastal areas with massive potential for wind resources because of its geographical location. Therefore, understanding the wind resources in these areas can lay a foundation for future development and utilization. On this basis, this study used the measured wind field data of a wind farm along the coast of Zhejiang from March 2014 to February 2015 and from March 2016 to February 2018 to investigate and compare the characteristics of wind energy resources, including average wind speed, Weibull shape and scale factors, wind direction variation, and wind energy density. Then, the capacity coefficient of a wind turbine predicted using the wind farm data was compared with the actual capacity coefficients of two wind turbines in the wind farm in 2019. Results revealed the following observations: The overall variations in the evaluation indicators followed clear patterns over the 3 years. For example, the main wind direction in the same season was the same, and the variations in the monthly average wind speed, the monthly wind power density, and the theoretical capacity factors were highly similar. The time-series data indicated that the difference in the indicators between summer and autumn was significantly larger than that between other seasons, with the maximum difference in monthly average wind speed of 1.46 times and the maximum difference in monthly wind power density of 1.5 times. The comparison results of the capacity coefficient showed that the theoretical and actual capacity coefficients were extremely close when the monthly average wind speed was less than 6 m/s, with the average difference being less than 9%. When the monthly average wind speed was greater than 6 m/s, the proximity between the theoretical and actual capacity coefficients was reduced, with an average difference of more than 9% and a maximum value of 28%. In general, the overall characteristics of wind resources in coastal areas of Zhejiang exhibited similar trends but fluctuated considerably in some months. Wind energy forecasts had significant discrepancies from the actual operation indicators of the wind farm when the wind speed was high.

Thermal and digital imaging information acquisition regarding the development of Aspergillus flavus in pistachios against Aspergillus carbonarius in table grapes

The phenotypic diagnostics in food mycology exhibit hysteresis in fungal detection during the early stages since hyphal and fruiting structures become visible only in advanced growth stage. Aspergillus flavus is a saprotrophic and pathogenic fungus colonizing cereal grains, legumes, and tree nuts. This fungus produces significant quantities of aflatoxins which have nephrotoxic, hepatotoxic, teratogenic and immunosuppressive effects on humans. The spatial temperature heterogeneity of A. flavus in infected pistachios was assessed by means of thermal imaging along with the digital RGB imaging analysis. The image analysis in terms of hue angle, exhibited not significant variation of non-infected pistachios compared to the infected ones at the early stages of fungal invasion but it became significantly different 72 h since infection. The fungal growth rate was assessed by comparing the Weibull shape factor of pistachios inoculated with A. flavus against grapes inoculated with A. carbonarius. The latter showed that the first 6 h since inoculation showed similar growth rate (∂β¯/∂t=6.7) while between 6 and 20 h showed lesser but almost double growth rate of the infected grapes (∂β¯grapes/∂t=5.4) against the infected pistachios (∂β¯pistachios/∂t=2.2). Infected pistachios and grapes were both stored at 28 °C and 60% RH, hence, the noted variation in growth rate should be fungus and substrate dependent. The peak of the temporal variation of the Weibull shape factor in pistachios and grapes extends between 15 and 20 h since inoculation, while for the infected grapes it is 71% higher than the one of the infected pistachios, revealing a distinctive fungal growth rate.

다양한 유사성 척도를 이용한 바람권역의 군집분석

To assess wind resources in a given area, it is necessary to select a representative measurement point by identifying a wind zone where the wind resource characteristics are homogeneous. In this study, to identify the spatial homogeneity of wind resources, it was necessary to test several similarity measures for clustering analysis, such as time-series wind vector similarity, Pearson's correlation coefficient of time-series wind speed, the cosine distance of time-series wind direction, the index of agreement of time-series wind speed, the 24-hour autocorrelation function, and the principal components of wind resource factors. It was found that the primary components of wind resources were the Weibull scale and shape factors of wind speed distribution, while terrain elevation and the 24-hour autocorrelation function were chosen as the secondary components. The similarity measures were applied to Jeju Island, which has a simple topography, and the Pohang region, which has a complex mountainous topography, to classify the wind zones; while poly-serial correlation coefficients, together with box plots, were used to evaluate whether there was a significant statistical difference in the wind resource factors within a given cluster. In conclusion, it was confirmed that the time-series wind vector similarity and the primary components of wind resource factors are the most effective similarity measures of clustering analysis.

To pool or not to pool: That is the question in microbial kinetics

Variation observed in heat inactivation of Salmonella strains (data from Combase) was characterized using multilevel modeling with two case studies. One study concerned repetitions at one temperature, the other concerned isothermal experiments at various temperatures. Multilevel models characterize variation at various levels and handle dependencies in the data. The Weibull model was applied using Bayesian regression. The research question was how parameters varied with experimental conditions and how data can best be analyzed: no pooling (each experiment analyzed separately), complete pooling (all data analyzed together) or partial pooling (connecting the experiments while allowing for variation between experiments).In the first case study, level 1 consisted of the measurements, level 2 of the group of repetitions. While variation in the initial number parameter was low (set by the researchers), the Weibull shape factor varied for each repetition from 0.58–1.44, and the rate parameter from 0.006–0.074 h. With partial pooling variation was much less, with complete pooling variation was strongly underestimated.In the second case study, level 1 consisted of the measurements, level 2 of the group of repetitions per temperature experiment, level 3 of the cluster of various temperature experiments. The research question was how temperature affected the Weibull parameters. Variation in initial numbers was low (set by the researchers), the rate parameter was obviously affected by temperature, the estimate of the shape parameter depended on how the data were analyzed. With partial pooling, and one-step global modeling with a Bigelow-type model for the rate parameter, shape parameter variation was minimal. Model comparison based on prediction capacity of the various models was explored.The probability distribution of calculated decimal reduction times was much narrower using multilevel global modeling compared to the usual single level two-step approach. Multilevel modeling of microbial heat inactivation appears to be a suitable and powerful method to characterize and quantify variation at various levels. It handles possible dependencies in the data, and yields unbiased parameter estimates. The answer on the question “to pool or not to pool” depends on the goal of modeling, but if the goal is prediction, then partial pooling using multilevel modeling is the answer, provided that the experimental data allow that.

Offshore Wind Energy Resource Assessment across the Territory of Oman: A Spatial-Temporal Data Analysis

Despite the long shoreline of Oman, the wind energy industry is still confined to onshore due to the lack of knowledge about offshore wind potential. A spatial-temporal wind data analysis is performed in this research to find the locations in Oman’s territorial seas with the highest potential for offshore wind energy. Thus, wind data are statistically analyzed for assessing wind characteristics. Statistical analysis of wind data include the wind power density, and Weibull scale and shape factors. In addition, there is an estimation of the possible energy production and capacity factor by three commercial offshore wind turbines suitable for 80 up to a 110 m hub height. The findings show that offshore wind turbines can produce at least 1.34 times more energy than land-based and nearshore wind turbines. Additionally, offshore wind turbines generate more power in the Omani peak electricity demand during the summer. Thus, offshore wind turbines have great advantages over land-based wind turbines in Oman. Overall, this work provides guidance on the deployment and production of offshore wind energy in Oman. A thorough study using bankable wind data along with various logistical considerations would still be required to turn offshore wind potential into real wind farms in Oman.

Potential and economic feasibility of wind energy in south West region of Algeria

The present research is focused on windfarm economic viability and wind power potential assessment by RETScreen and WAsP tools, respectively, for the South-West region of Algeria. This study considers the atlas development of wind characteristics analysis. Hourly mean wind data recorded during the years 2003 to 2008 by ONM “Office National de la Météorologie” (the Algerian Meteorological Office), is used for the study. The mean wind speed, energy flux, the dominant wind direction, the frequency distribution, and the Weibull distribution scale and shape factors are determined and analyzed. Finally, RETScreen software is used to estimate the energy output and to conduct the economic feasibility of the wind farm in terms of Simple Payback Period (SPP), Internal Rate of Return, Annual Life Cycle Saving, Net Present Value, Year to Positive Cash Flow, Benefit-Cost ratio and cost of electricity production (COE). The economic analysis indicates that the project at Adrar region was economically viable with good energy production of 3146 MWh/yr and a Capacity Factor (CF) of 36%.The SPP was found to be around 3.9 years, and the COE of 3.25 US Cents/kWh was found lower than the wholesale price of electricity during the feed-in tariff period.

A statistical exploration of interval-deficient wind speed data for application to wind power assessments

Gathering quality wind speed data can be time-consuming and expensive. The present study established whether interval-deficient wind speed data could be rendered useful for wind power assessments. The effect of interval deficiency on the quality of the wind speed data was investigated by studying the behaviour of the Weibull scale and shape factors as the interval size between wind speed measurements increased. Five wind speed data sets obtained from the Southern African Universities Radiometric Network (Sauran) were analysed, based on a proposed procedure to find the true Weibull parameters from an interval-deficient wind speed data set. It was found that the relative errors in the Weibull parameters were, on average, less than 1%, compared with the Weibull parameters computed from a wind speed data set that complies with the IEC 61400-12-1:2005(E) standard. This finding may contribute to time and cost reduction in wind power assessments. It may also promote the application of statistical methods in the renewable energy sector.

Wind Resource Assessment using Weibull Function for Different Periods of the Day in the Yucatan Peninsula

One of the most important variables in wind assessment as resource is Wind Power Density (WPD) which is finally the parameter that gives information about the site analyzed. To calculated WPD is strongly recommended to determine the two parameters of Weibull function, shape factor (k) and scale factor (c) to have a preliminary idea of how the wind resource is on the evaluated site. In this study has been analyzed wind speed as resource with Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) data, these are re-analysis hourly data from 1980-2016 at 50m height, over the Yucatan Peninsula. An algorithm was designed to separate data in four periods of time for an average day (00:00-05:00; 06:00-11:00; 12:00-17:00; 18:00-23:00) in order to obtain a more accurate wind description according to the Weibull function, its parameters k and c, as well as the prevailing direction on every site. The aim of this study is comparing WPD to energy demand curve in the Yucatan Peninsula, according to the different periods of the day.

Weibull Probability Distribution of Wind Speed for Gaza Strip for 10 Years

The need of clean and renewable energy, as well as the power shortage in Gaza strip with few wind energy studies conducted in Palestine, provide the importance of this paper. Probability density function is commonly used to represent wind speed frequency distributions for the evaluation of wind energy potential in a specific area. This study shows the analysis of the climatology of the wind profile over the State of Palestine; the selections of the suitable probability density function decrease the wind power estimation error percentage. A selection of probability density function is used to model average daily wind speed data recorded at for 10 years in Gaza strip. Weibull probability distribution function has been estimated for Gaza based on average wind speed for 10 years. This assessment is done by analyzing wind data using Weibull probability function to find out the characteristics of wind energy conversion. The wind speed data measured from January 1996 to December 2005 in Gaza is used as a sample of actual data to this study. The main aim is to use the Weibull representative wind data for Gaza strip to show how statistical model for Gaza Strip over ten years. Weibull parameters determine by author depend on the pervious study using seven numerical methods, Weibull shape factor parameter is 1.7848, scale factor parameter is 4.3642 ms-1, average wind speed for Gaza strip based on 10 years actual data is 2.95 ms-1 per a day so the behavior of wind velocity based on probability density function show that we can produce energy in Gaza strip.

A new strategy for wind turbine selection using optimization based on rated wind speed

It is generally anticipated that larger wind turbines result in better electrical power generation in more efficient and economical manner. However, the question remains is that how large a wind turbine is the optimum size for a selected wind site? To answer this, three important objective functions, the levelized cost of electricity (LCOE), the capacity factor (CF) and a normalized annual energy production (AEP) are optimized versus the rated wind speed. Four empirical power curve models for large wind turbines and Weibull wind distribution are investigated to produce a Pareto front within range of practical wind conditions. It is observed that the optimized values of the objective functions are merely dependant on the Weibull shape factor, k. Also, the optimum rated wind speed is a linear function of the Weibull scale factor, c. Therefore, it is concluded that, there are limits for the optimum rated wind power and the costs. Consequently within the Pareto front, the lower rated power wind turbines may be selected to reduce LCOE albeit the higher rated power wind turbines may be adopted to produce higher AEP and CF.

Assessment of fresh water wind resources on Lake Erie

Wind farms are better been built at locations with higher wind resource potentials. As the appropriate locations become fewer and fewer to build onshore wind farms, significant attention has been drawn to the wind energy industry to build offshore wind farms. The terrain effect has fewer effects offshore than onshore since the sea level is flat and no artificial buildings are built there. The coastal line of the Great Lakes is one of those areas that not only has great wind energy potential but is also near the high population coastal cities which is short of the land surface. This article makes the detailed statistical analysis of 1-year offshore wind data in Lake Erie from a Light Detection and Ranging system placed on a water intake crib 4 miles away from near the coast of Cleveland. For comparison purpose, a nearby onshore wind monitoring station’s data have also been analyzed to study the wind and power characteristics. Specifically, the statistical analysis of the data includes Weibull shape and scale factors, the monthly average of the wind speed, turbulence intensity, and wind power density. In addition, two site-matching commercial wind turbines with 50 (Vestas® 39) and 80 m (Vestas® V90) hub heights have been chosen to estimate the 1-year energy output. The result shows great preponderances of building offshore wind farms than building onshore wind farms. This study gives guidance to the cost-benefit analysis to build the offshore wind farms in Lake Erie.

Onshore and offshore wind energy potential assessment near Lake Erie shoreline: A spatial and temporal analysis

Choosing a proper location is a pivotal initial step in building a wind farm. As appropriate locations for onshore wind farms become more and more scarce, offshore wind farms have drawn significant attention. The coastal line of the Great Lakes is an area that has great wind energy potential. This research conducted detailed statistical analysis of the onshore, nearshore, and offshore wind energy potential of Lake Erie near Cleveland, Ohio. It analyzed the wind data collected in 10-min time intervals from three locations near the Lake Erie shoreline to assess wind characteristics. Statistical analyses of wind data include the Weibull shape and scale factors, turbulence intensity, and wind power density. In addition, the capacity factor and the potential energy output are estimated by using two commercial wind turbines, which are appropriate for the sites at 50 m and 80 m hub heights. The results show that offshore sites will produce at least 1.7 times more energy than the onshore and nearshore sites when using the same commercial wind turbine. Furthermore, offshore wind turbines could produce more power during peak hours in the spring and winter. This indicates that offshore wind turbines offer advantages over onshore wind turbines in Lake Erie.

Evaluation of wind characteristics in Bac Lieu in 2016 using the weibull function

In this paper, the characteristics of wind speed at 20 m height at the Bac Lieu atmospheric physic station (Bac Lieu station) in 2016 were evaluated using the Weibull distribution function. The wind speed data set (every minute) from January 7th to December 31st, 2016 was used to calculate the two parameters of Weibull function including Weibull shape factor “k” and Weibull scale factor “c”. The results showed that at the Bac Lieu station in 2016, the values of k and c were 1.69 and 3.91, respectively. Some characteristics of wind speed were also estimated such as wind energy density (Pa/A=57.3 W/m2), wind speed of maximum energy carrier (Vmec=6.2 m/s), the most probable wind speed (Vmp=2.3 m/s), mean wind speed (Vmean­=3.5 m/s) and standard deviation of wind speeds (s = 2.1 m/s).