Power Density Error Research Articles

Novel exploration of hub heights on economics and Weibull distribution methods for wind power potential in Indian sites

Wind energy is a clean and practical way to create electricity. It necessitates the assessment of Wind Power Potential (WPP) and its economic analysis at different heights. In this context, this study examines WPP assessment for 62 different locations of 12 states in India from 10 m to 150 m height using six methods. The effectiveness of each method was performed through the computation of Relative Power Density Error (RPDE). The results suggested that the best method to estimate the WPP is the Novel Energy Pattern Factor Method (NEPFM) followed by the Empirical Method of Mabchour (EMM), the Empirical Method of Justus (EMJ), and the Empirical Method of Lysen (EML). A technical assessment is also made using six different wind turbine Models, through the computation of their respective capacity factors, annual power, and energy outputs. Furthermore the economic feasibility of these wind turbines gave Cost of Energy (COE) variation from 0.28 to 15.31 $/kWh at 10 m hub height of wind turbine and 150 m hub height of wind turbine COE varies from 0.10 to 3.53 $/kWh. This study is useful for industry.

Wind Energy Assessment Using Weibull Distribution with Different Numerical Estimation Methods: A Case Study

The demand for electrical energy is increasing every day, which is one of the critical challenges facing the world today. Hence, the necessity of turning to clean renewable energy sources that are not harmful to the environment as an alternative to the traditional generation based on fossil fuels has become more important than ever before. Wind power is one of the renewable sources that provides a clean solution to generate electricity. In this context, the Kingdom of Saudi Arabia announces renewable energy projects to generate 9 GW from wind in 2032. Hence, the aim of this paper is to investigate the most suitable method of Weibull parameter estimation in order to predict wind characteristics and employ it for wind energy assessment in the Qassim region located in the center of the country. In this study, wind data is collected from NASA's forecasts of global energy resources for 2010–2015 based on their availability at altitudes of 10m and 50m and analyzed by using six different methods for Weibull parameter estimation: the graphical method (GM), standard deviation method (SDM), energy pattern factor method (EPF), moment method (MM), alternative maximum likelihood method (AMLM), and novel energy pattern factor method (NEPF). The efficiency of each method is tested by calculating the root mean square error (RMSE) and the relative wind power density error (RPDE). The comparison shows that the most appropriate method for estimating wind power density in the country is the Moment Method (MM), with the lowest RPDE ratio equal to 0.2018%. It has been found that the wind power density in the Qassim region falls into the class 1 category, as it is less than 100 W/m2 at a height of 10m and less than 200 W/m2at an altitude of 50m. The results show the region is only suitable for small off-grid projects. Doi: 10.28991/ESJ-2023-07-06-024 Full Text: PDF

Wind Speed Analysis for Coastal Regions of Pakistan using Extended Generalized Lindley Distribution

The wind energy potential of a specified area can be estimated using wind speed distribution. In this study, the selection of probability density functions is used to model wind speed data recorded at two stations in Pakistan. The suitability of fitted distributions is evaluated using the goodness of fit criterion, power density error, log-likelihood, root mean square error, coefficient of determination, AIC, and BIC. The wind speed data are obtained from two coastal regions of Pakistan at 10m/s average rate for session 2017-2018. Findings indicated that the extended generalized Lindley distribution provide generally the best fit to the wind speed data for both stations. However, it is also observed that power Lindley and extended generalized Lindley distributions have better performance based on power density error criteria in Gwadar and Haripur, respectively.

Wind energy of Cameroon by determining Weibull parameters: potential of a environmentally friendly energy

Cameroon, a country of the Sub-Saharan Africa, faces a challenging problem of access to electricity. Its overall electricity production in 2012 was 305 kWh per inhabitant for gross electricity consumption of 6.2 TWh. Recently, the Cameroonian government launched many wind farm installation projects among which a 42-MW wind farm in Mount Bamboutos hills in 2015 that would expand to 80 MW. Therefore, there is a necessity for a clear assessment of the wind potential of the country. In this study, thirteen numerical methods were used to estimate the Weibull parameters to assess the wind potential. The wind speed data were collected in a period of 38 years (from January 1982 to December 2019) from the NASA website. The effectiveness of each method was performed through the computation of relative power density error, the coefficient of determination (R2), the root mean square error and Chi-square test (χ2). The results suggested that the best method to estimate the wind power density is the energy density method, followed by the novel energy pattern factor method. It was found that the maximum likelihood method was the best in three sites. The graphical method was the effective method to estimate the cumulative data frequency distribution, followed by the empirical method of Lysen. The wind power densities were found to be of class 1 and favorable for small-scale applications like livestock watering, farm irrigation and water pumping.

A new distribution for modeling the wind speed data in Inner Mongolia of China

In this paper, we introduce a Topp-Leone Lindley (TLL) distribution by using Topp-Leone (TL) family. Mathematical properties of the TLL distribution are studied. Estimation of the unknown parameters is derived by the methods of maximum likelihood, least squares and maximum product spacings. The performance of the estimation methods is evaluated by means of Monte-Carlo simulation. In the application part of the research, we have used a long term measured wind speed data from ten stations in Inner Mongolia of China. The suitability of the TLL distribution and other six distributions (inverse Gaussian, Birnbaum-Saunders, power Lindley, weighted Lindley, Weibull, inverse Weibull) used to fit for wind speed data is evaluated based on root mean square error, coefficient of determination, the log-likelihood, Akaike information criterion (AIC), Bayesian information criterion (BIC), Kolmogorov-Smirnov (K–S) statistic and power density error. The results substantiate that TLL distribution is widely applicable at all selected stations. TLL distribution outperforms the others at five stations, ranks the second at three stations and classifies as the third in remaining two stations. Alternatively, Weighted Lindley distribution is the next best distribution for analyzing wind speed data in selected stations. It is stronger than others at three stations while ranking the second at five stations and fourth in two stations. Although this finding questions the accuracy of Weibull distribution in modeling wind speed data, it provides superior estimation of wind power density for the ten stations.

Inverted Kumarswamy distribution for modeling the wind speed data: Lake Van, Turkey

In calculating the wind energy potential of a region, some important points such as determining the distribution used to model wind speeds and estimating the parameters of the distribution accurately should be considered. Many different distributions have been proposed in wind energy literature over the years. In this paper, some of these studies are reviewed. Then, Inverted Kumaraswamy (IKum) distribution is used for the first time to model wind speed data as an alternative to the well-accepted Weibull distribution. Maximum Likelihood, Least Squares, and Maximum Product of Spacing methodologies are employed in estimating the parameters of the IKum distribution. A Monte Carlo simulation study is conducted for comparing the efficiencies of these methods. The wind speed data sets considered in this study include wind speeds from 6 stations located around Lake Van in Turkey. Modeling performances of the Weibull and IKum distributions are evaluated with the well-known goodness-of-fit criteria and power density error values. Results show that the IKum distribution can be considered as an alternative to the well-accepted Weibull distribution.

Marshall–Olkin Power Lomax distribution for modeling of wind speed data

Accurate collection of wind speed records is significant for numerous wind power applications. The present investigation aims to highlight the use of the Marshall–Olkin Power Lomax (MOPLx) distribution for wind speed data. We examine the actual wind speed records gathered from three stations Bahawalpur, Gwadar, and Haripur. The dataset is demonstrated by using MOPLx distribution and compare its modeling performance with renowned probability distributions, for example, Weibull–Lomax, power Lomax, Weibull, power Lindley, Lindley, and Lomax. Findings indicate that MOPLx distribution gives the best fitting as per model evaluation criteria, Akaike information criterion (AIC), Bayesian information criterion (BIC), Kolmogorov Smirnov test (KS), coefficient of determination (R2) and root mean square error (RMSE). Overall, the results demonstrate the feasibility, precision, and effectiveness of the MOPLx distribution for portraying wind speed modeling. It is also observed that the MOPLx model is ideal in terms of the power density error (PDE) criterion.

Assessing wind energy potential using finite mixture distributions

Wind has become a popular renewable energy resource in the last two decades. Wind speed modeling is a crucial task for investors to estimate the energy potential of a region. The aim of this paper was to compare the popular unimodal wind speed distributions with their two-component mixture forms. Accordingly, Weibull, gamma, normal, lognormal distributions, and their two-component mixture forms; two-component mixture Weibull, two-component mixture gamma, two-component mixture normal, and two-component mixture lognormal distributions were employed to model wind speed datasets obtained from Belen Wind Power Plant and G??k?ßeada Meteorological Station. This paper also provides the comparison of gradient-based and gradient-free optimization algorithms for maximum likelihood (ML) estimators of the selected wind speed distributions. ML estimators of the distributions were obtained by using Newton--Raphson, Broyden--Fletcher--Goldfarb--Shanno, Nelder--Mead, and simulated annealing algorithms. Fit performances were compared based on Kolmogorov--Smirnov test, root mean square error, coefficient of determination ($R^2$), and power density error criteria. Results reveal that two-component mixture wind speed distributions have superiority over the unimodal wind speed distributions.

Application of the Cuckoo Search in the Adjustment of Weibull Curves for Wind Energy Using Wind Data of Petrolina City

In this work a Cuckoo Search (CS) applicability study was carried out using the methodology described by Yang and Deb (2009) in the optimization of Weibull curves, being implemented from an algorithm written in programming language R. The real velocity data were obtained from the National System for the Organization of Environmental Data (SONDA) platform for the city of Petrolina - PE, because it is located in a state with great potential for wind energy generation. The Cuckoo Search heuristic method was compared with six deterministic methods widely used in the literature from the results of the statistical tests Root Mean Square Error (RMSE), R 2 , Mean Absolute Error (MAE) and Power Density Error (EDP). With the objective function used, Cuckoo Search was satisfactory in the wind representation of the studied region, presenting RMSE of 0.006052, R 2 of 0.99348 and MAE of 0.003979, more desirable in relation to the other methods. Also, an EDP of approximately 1.12% above the actual power density was obtained, which makes it difficult to use for problems in which energy oversizing is not allowed.

Deep assessment of wind speed distribution models: A case study of four sites in Algeria

The aim of this study is to assess the accuracy of different probability functions for modeling wind speed distribution at four locations, distributed over Algeria, to minimize the uncertainty in wind resource estimates. Despite mixture models perform better results, their complexity induced us to use in this work eight distributions with a maximum of three parameters, namely Weibull, Gamma, Inverse Gaussian, Log Normal, Gumbel, GEV, Nakagami and Generalized Logistic distribution to model the wind speed, fitted with four parameter estimation methods. In addition to the methods of moments and the maximum likelihood which are commonly used, the power density method and the L-moments method are developed and utilized for the first time in wind resource assessment field, to estimate the parameters of most distributions used in this work. Moreover, two goodness-of-fit tests based on the coefficient of determination and the root mean square error, are conducted in order to select good fitting probability distribution functions. According to the coefficient of determination and the root mean square error, the GEV and Gamma are the most appropriate, compared to the others used distributions. Furthermore, the L-moments method is the most effective one, among the used parameter estimators, followed by the maximum likelihood method. On the other hand, in term of power density error, different results were found, where the Power Density Method gave the best results with the Gamma, Inverse Gaussian and Log Normal distributions. Otherwise, owing to the difference in the wind characteristics for each studied site, it can be stated that to minimize the uncertainty in wind resource estimates, it is important to determine the method that gives the best parameters for each distribution.

Generalized Lindley and Power Lindley distributions for modeling the wind speed data

In this study, we propose to use Generalized Lindley (GL) and Power Lindley (PL) distributions as an alternative to the Weibull distribution for modeling the wind speed data. In the application part of the study, we consider the actual wind speed data collected in hourly basis from the Bilecik, Bursa, Eskisehir and Sakarya sites, Turkey in 2009. These data sets are modeled by using GL and PL distributions. To compare their modeling performance with well known and widely used Weibull distribution, Weibull distribution is also included into the study. The results show that GL distribution provides the best fitting according to root mean square error (RMSE), coefficient of determination (R2), maximum value of the likelihood function corresponding to the ML estimates of the parameters (lnL) and Akaike information criterion (AIC). It is also seen that PL distribution is preferable in terms of power density error (PDE) criterion.

Comparison of Some Estimation Methods of the two parameter Weibull Distribution for Unusual Wind Speed Data Cases

Since the Weibull distribution has been accepted reference distribution in wind energy field, topics on its parameter estimation methods have been attracted issue. In this context, the literature have generally focused on non-robust methods which may yield questionable results in the cases of unusual and contaminated wind speed data. This paper discusses some robust estimation methods of the Weibull distribution for unusual wind speed data cases. The considered robust methods are evaluated by using artificially generated unusual wind speed data cases. It was found that some of the considered robust methods provide reliable results compared classical ones. Also, the same results are observed for the estimation of mean power density error. As a result, analyzes performed shows that robust and efficient classical methods can be used together to check results.

Spatial and temporal patterns of global onshore wind speed distribution

Wind power, a renewable energy source, can play an important role in electrical energy generation. Information regarding wind energy potential is important both for energy related modeling and for decision-making in the policy community. While wind speed datasets with high spatial and temporal resolution are often ultimately used for detailed planning, simpler assumptions are often used in analysis work. An accurate representation of the wind speed frequency distribution is needed in order to properly characterize wind energy potential. Using a power density method, this study estimated global variation in wind parameters as fitted to a Weibull density function using NCEP/climate forecast system reanalysis (CFSR) data over land areas. The Weibull distribution performs well in fitting the time series wind speed data at most locations according to R2, root mean square error, and power density error. The wind speed frequency distribution, as represented by the Weibull k parameter, exhibits a large amount of spatial variation, a regionally varying amount of seasonal variation, and relatively low decadal variation. We also analyzed the potential error in wind power estimation when a commonly assumed Rayleigh distribution (Weibull k = 2) is used. We find that the assumption of the same Weibull parameter across large regions can result in non-negligible errors. While large-scale wind speed data are often presented in the form of mean wind speeds, these results highlight the need to also provide information on the wind speed frequency distribution.

Mixture probability distribution functions to model wind speed distributions

Accurate wind speed modeling is critical in estimating wind energy potential for harnessing wind power effectively. The quality of wind speed assessment depends on the capability of chosen probability density function (PDF) to describe the measured wind speed frequency distribution. The objective of this study is to describe (model) wind speed characteristics using three mixture probability density functions Weibull-extreme value distribution (GEV), Weibull-lognormal, and GEV-lognormal which were not tried before. Statistical parameters such as maximum error in the Kolmogorov-Smirnov test, root mean square error, Chi-square error, coefficient of determination, and power density error are considered as judgment criteria to assess the fitness of the probability density functions. Results indicate that Weibull-GEV PDF is able to describe unimodal as well as bimodal wind distributions accurately whereas GEV-lognormal PDF is able to describe familiar bell-shaped unimodal distribution well. Results show that mixture probability functions are better alternatives to conventional Weibull, two-component mixture Weibull, gamma, and lognormal PDFs to describe wind speed characteristics.