Estimation Of Wind Power Density Research Articles

Bayesian method for estimating Weibull parameters for wind resource assessment in a tropical region: a comparison between two-parameter and three-parameter Weibull distributions

Abstract. The two-parameter Weibull distribution has garnered much attention in the assessment of wind energy potential. The estimation of the shape and scale parameters of the distribution has brought forth a successful tool for the wind energy industry. However, it may be inappropriate to use the two-parameter Weibull distribution to assess energy at every location, especially at sites where low wind speeds are frequent, such as in tropical regions. In this work, a robust technique for wind resource assessment using a Bayesian approach for estimating Weibull parameters is first proposed. Secondly, the wind resource assessment techniques using a two-parameter Weibull distribution and a three-parameter Weibull distribution, which is a generalized form of two-parameter Weibull distribution, are compared. Simulation studies confirm that the Bayesian approach seems a more robust technique for accurate estimation of Weibull parameters. The research is conducted using data from seven sites in the tropical region from 1∘ N of the Equator to 21∘ S of the Equator. Results reveal that a three-parameter Weibull distribution with a non-zero shift parameter is a better fit for the wind data with a higher percentage of low wind speeds (0–1 m s−1) and low skewness. However, wind data with a smaller percentage of low wind speeds and high skewness showed better results with a two-parameter distribution that is a special case of the three-parameter Weibull distribution with a zero shift parameter. The proposed distribution can be incorporated into commercial software like WAsP to improve the accuracy of wind resource assessments. The results also demonstrate that the proposed Bayesian approach and application of a three-parameter Weibull distribution are extremely useful for accurate estimation of wind power density.

New estimation method of wind power density with three‐parameter Weibull distribution: A case on Central Inner Mongolia suburbs

AbstractSuburbs have the potential for future wind energy development because of their open terrain, good wind conditions, closeness to the city, wind power that can be absorbed in place, and other advantages. Therefore, accurately evaluating the wind energy resources in the suburbs is particularly important. The three‐parameter Weibull distribution can accurately describe the wind speed in the suburbs, but research on the estimation of wind power density (WPD) with it is limited. On the basis of the mathematical models of wind speed probability distribution as Rayleigh, two‐parameter Weibull, and three‐parameter Weibull, a new WPD estimation formula with three‐parameter Weibull distribution is derived using the partial integration method and by introducing incomplete gamma function to solve the transcendental integration. A field experiment platform is built, and the accuracy of the formula is verified by the measured data. The analysis of the measured data collected in recent 3 years in the suburbs of Hohhot, Inner Mongolia, concludes that the statistical characteristics of the measured wind speed and the distribution of wind energy resources are more conducive to capture the scattered and changing wind energy in the suburbs by taking the month as the time scale. Moreover, the three‐parameter Weibull distribution estimated by the least square method can be used as the local wind speed model. The new method of WPD estimation can also reduce the calculation error by approximately 21.06%. This study provides an important reference for the subsequent analysis of wind power fluctuation characteristics and wind energy development planning.

Kratkoročno predviđanje gustine snage vetra korišćenjem konvolucione LSTM mreže

Efficient extraction of renewable energy from wind depends on the reliable estimation of wind characteristics and optimization of wind farm installation and operation conditions. There exists uncertainty in the prediction of wind energy tapping potential based on the variability in wind behavior. Thus the estimation of wind power density based on empirical models demand subsequent data processing to ensure accuracy and reliability in energy computations. Present study analyses the reliability of the ANN-based machine learning approach in predicting wind power density for five stations (Chennai, Coimbatore, Madurai, Salem, and Tirunelveli) in the state of Tamil Nadu, India using five different non-linear models. The selected models such as Convolutional Neural Network (CNN), Dense Neural Network (DNN), Recurrent Neural Network (RNN), Bidirectional Long Short Term Memory (LSTM) Network, and linear regression are employed for comparing the data for a period from Jan 1980 to May 2018. Based on the results, it was found that the performance of (1->Conv1D|2->LSTM|1-dense) is better than the other models in estimating wind power density with minimum error values (based on mean absolute error and root mean squared error).

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.

The Effect of Averaging, Sampling, and Time Series Length on Wind Power Density Estimations

The Wind Power Density (WPD) is widely used for wind resource characterization. However, there is a significant level of uncertainty associated with its estimation. Here, we analyze the effect of sampling frequencies, averaging periods, and the length of time series on the WPD estimation. We perform this analysis using four approaches. First, we analytically evaluate the impact of assuming that the WPD can simply be computed from the cube of the mean wind speed. Second, the wind speed time series from two meteorological stations are used to assess the effect of sampling and averaging on the WPD. Third, we use numerical weather prediction model outputs and observational data to demonstrate that the error in the WPD estimate is also dependent on the length of the time series. Finally, artificial time series are generated to control the characteristics of the wind speed distribution, and we analyze the sensitivity of the WPD to variations of these characteristics. The WPD estimation error is expressed mathematically using a numerical-data-driven model. This numerical-data-driven model can then be used to predict the WPD estimation errors at other sites. We demonstrate that substantial errors can be introduced by choosing too short time series. Furthermore, averaging leads to an underestimation of the WPD. The error introduced by sampling is strongly site-dependent.

Kernel density estimation model for wind speed probability distribution with applicability to wind energy assessment in China

A kernel density estimation (KDE) model for the probability distribution of wind speed (PDWS) is proposed in this paper for application to wind energy assessment (WEA) in China. Four bandwidth selectors, including normal scale (NS), plug in, biased cross-validation, and least-square cross validation, are proposed for the KDE model. Popular parametric distribution models are also introduced for comparisons with the KDE models. Based on five-year day-average wind speed data from 698 nationwide wind stations in China, the performance and robustness of both parametric and KDE models were evaluated comprehensively on the regional scale. Wind power density (WPD) and wind turbine power output (WTPO), which are the priorities in WEA, are subsequently calculated based on the estimated PDWS models. The ranking results of four individual metrics and one comprehensive metric indicate that the four KDE models outperform the parametric models in fitting the PDWS. The KDE-NS model performs the best compared to the other three KDE models. In addition to the KDE models, the generalized gamma and generalized extreme values were considered as better parametric models in fitting the PDWS. KDE models also performed well in WPD estimation, especially the KDE-NS model with a mean absolute percentage error (MAPE) value as low as 2%. Some parametric models, i.e., Johnson SB and Wakeby, which are not outstanding in PDWS fitting, however perform well in WPD estimation, and their MAPE values can be controlled to remain within 3%. This indicates that the result of the PDWS is not completely equivalent to that of WPD estimation. The WPD and WTPO in most of China's interior areas are less than 40W/m2 and 1.2 GWh, respectively. In the eastern coastal areas, middle and eastern Inner Mongolia, and some western provinces, the WPD and WTPO are relatively higher, and can reach or exceed 240W/m2 and 3.5 GWh, respectively.

Alternative Calibration of Cup Anemometers: A Way to Reduce the Uncertainty of Wind Power Density Estimation.

This study presents a procedure to reduce the uncertainty of wind power density estimations, which is useful to improve the energy production predictions of wind farms. Power density is usually determined from the wind speed measured by a cup anemometer and the air density value (conventional procedure). An alternative procedure based on wind speed and dynamic pressure estimations provided by a cup anemometer is proposed. The dynamic pressure is obtained by means of a calibration curve that relates the anemometer rotation frequency and the dynamic pressure measured by a Pitot tube. The quadratic regression, used to define the calibration curve, and its uncertainty are both detailed. A comparison between the alternative procedure and the conventional one points out the advantage of the proposed alternative since results show a high reduction of the indirect measurement uncertainty of wind power density.

Technical potential assessment of offshore wind energy over shallow continent shelf along China coast

Abstract Offshore wind resource assessment seems to be urgently needed due to the rapid development of offshore wind energy in the coming decades. Technical potential of offshore wind energy over the sea area shallower than 250 m along China coast is investigated. To avoid erroneous estimation of wind power density, a statistical model considering sea state effect is proposed. Long-term CCMP wind field data are examined using that model to reduce uncertainties. Further, influential factors including wind power density, water depth, wind turbine size, wind farm layout and various spatial constraints are analyzed on the GIS platform. Technical potential under different scenarios are presented and discussed. It shows that wind resource at Taiwan Strait is particularly abundant, where wind power density at 70 m height can be above 900 W/m2. Technical potential is quite sensitive to the size of wind turbine. Taking the layout S1 (8 × 15 turbines in each farm, 8 rotor diameters apart between wind turbines, 20 km buffer region between neighboring farms) as an example: the total technical potential of the study area is 613 GW for rotor radius 60 m, and that for rotor radius 90 m is 1264 GW; the growth rates of technical potential with rotor radius is 19.3 GW/m roughly. Spatial constraints has significant impact on the region with water depth less than 50 m, where only 48.1% of area is available for developing wind energy and the technical potential there is about 23% of that of the study area.

Comparison of several measure-correlate-predict models using support vector regression techniques to estimate wind power densities. A case study

The long-term annual mean wind power density (WPD) is an important indicator of wind as a power source which is usually included in regional wind resource maps as useful prior information to identify potentially attractive sites for the installation of wind projects. In this paper, a comparison is made of eight proposed Measure-Correlate-Predict (MCP) models to estimate the WPDs at a target site. Seven of these models use the Support Vector Regression (SVR) and the eighth the Multiple Linear Regression (MLR) technique, which serves as a basis to compare the performance of the other models. In addition, a wrapper technique with 10-fold cross-validation has been used to select the optimal set of input features for the SVR and MLR models. Some of the eight models were trained to directly estimate the mean hourly WPDs at a target site. Others, however, were firstly trained to estimate the parameters on which the WPD depends (i.e. wind speed and air density) and then, using these parameters, the target site mean hourly WPDs. The explanatory features considered are different combinations of the mean hourly wind speeds, wind directions and air densities recorded in 2014 at ten weather stations in the Canary Archipelago (Spain).The conclusions that can be drawn from the study undertaken include the argument that the most accurate method for the long-term estimation of WPDs requires the execution of a specially trained model which considers the variability of the wind speeds of the reference stations, as well as of the wind directions and air densities, and in addition the functional manner in which these variables participate in the proposed MCP models. It is also concluded that it is important to consider the annual variation of air density even in regions at sea level. It is further concluded that, of the eight MCP models under comparison, the one that predicts the WPDs based on two sub-models (which estimate the wind speeds and air densities in an unlinked manner) always provides the best MAE (Mean Absolute Error), MARE (Mean Absolute Relative Error) and R2 (Coefficient of determination) metrics, with the differences being statistically significant (5% significance) for most of the cases assessed. Additionally, the regulatory capacity of the SVR technique was sufficient to manage most of the overfitting problems, and hence the contribution of the wrapper method was not relevant in our study.

Estimation of Wind Power Density at a Wind Farm Site Located in Western Rajasthan Region of India

Wind power density is an important parameter for the potential estimation of a wind farm and is used to compare different sites. This paper estimates wind power density of Soda site located at Western Rajasthan in India. Modified Maximum Likelihood, Empirical, and Graphical methods are used for estimating Weibull distribution parameters, which are used for calculating wind power density. The calculated wind power density is then compared with actual measured values for validation. The results obtained using Empirical method shows better agreement with the measured data of wind power density.

Effects of different wind data sources in offshore wind power assessment

Currently, approximately 5.3% of electricity production in Europe comes from wind energy. The increase of the size and the improved efficiency of wind generators have permitted their utilization offshore, leading to exploitation of offshore wind energy. Although offshore wind farms are well established in northern European countries, in the Mediterranean Sea they are still in their infancy. It is expected that within the next few years, offshore wind farming will grow considerably in this area. The accurate estimation of the wind speed fields is of most importance for the assessment of offshore wind energy resources. In this work, the effects of alternative wind data sources on the wind climate analysis are examined along with the offshore wind power density estimation in four locations across the Aegean Sea. In order to develop correction relations for satellite and model wind data, taking as reference the buoy measurements, the data are analysed and calibrated using the Error-In-Variables approach. The effects of the different data sources on the wind climate analysis and the estimation of the mean wind power density before and after the calibration procedure are presented and discussed. The Error-In-Variables approach performed better and reduced significantly the uncertainties of the alternative data sources.

Statistical Analysis of Wind Power Density Based on the Weibull and Rayleigh Models of Selected Site in Malaysia

The demand for electricity in Malaysia is growing in tandem with its Gross Domestic Product (GDP) growth. Malaysia is going to need even more energy as it strives to grow towards a high-income economy. Malaysia has taken steps to exploring the renewable energy (RE) including wind energy as an alternative source for generating electricity. In the present study, the wind energy potential of the site is statistically analyzed based on 1-year measured hourly time-series wind speed data. Wind data were obtained from the Malaysian Meteorological Department (MMD) weather stations at nine selected sites in Malaysia. The data were calculated by using the MATLAB programming to determine and generate the Weibull and Rayleigh distribution functions. Both Weibull and Rayleigh models are fitted and compared to the Field data probability distributions of year 2011. From the analysis, it was shown that the Weibull distribution is fitting the Field data better than the Rayleigh distribution for the whole year 2011. The wind power density of every site has been studied based on the Weibull and Rayleigh functions. The Weibull distribution shows a good approximation for estimation of wind power density in Malaysia.

한반도 풍력 자원 지도의 공간 해상도가 풍력자원 예측 정확도에 미치는 영향에 관한 수치연구

In order to make sure the impact of spatial resolution of wind energy map on the estimation of wind power density in the Korean Peninsula, the comparison studies on the characteristics of wind energy map with three different spatial resolutions were carried out. Numerical model used in the establishment of wind map is MM5 (5th generation Mesoscale Model) with RBAPS (Regional Data Assimilation and Prediction System) as initial and boundary data. Analyzed Period are four months (March, August, October, and December), which are representative of four seasons. Since high spatial resolution of wind map make the undulation of topography be clear, wind pattern in high resolution wind map is correspond well with topography pattern and maximum value of wind speed is also increase. Indication of island and mountains in wind energy map depends on the its spatial resolution, so wind patterns in Heuksan island and Jiri mountains are clearly different in high and low resolutions. And area averaged power density can be changed by estimation method of wind speed for unit area in the numerical model and by treatment of air density. Therefore the studiable resolution for the topography should be evaluated and set before the estimation of wind resources in the Korean Peninsula.