scholarly journals Comparison of Weibull and Gaussian Mixture Models for Wind Speed Data Analysis

2020 ◽  
Vol 11 (1) ◽  
pp. 10-16
Author(s):  
Muhammad Shoaib ◽  
Saif Ur Rehman ◽  
Imran Siddiqui ◽  
Shafiqur Rehman ◽  
Shamim Khan ◽  
...  
Keyword(s):  
Wind Speed ◽  
Wind Power ◽  
Gaussian Mixture ◽  
Descriptive Statistics ◽  
Wind Data ◽  
Weibull Function ◽  
Data Sets ◽  
Data Set ◽  
Wind Speeds ◽  
Power Densities

In order to have a reliable estimate of wind energy potential of a site, high frequency wind speed and direction data recorded for an extended period of time is required. Weibull distribution function is commonly used to approximate the recorded data distribution for estimation of wind energy. In the present study a comparison of Weibull function and Gaussian mixture model (GMM) as theoretical functions are used. The data set used for the study consists of hourly wind speeds and wind directions of 54 years duration recorded at Ijmuiden wind site located in north of Holland. The entire hourly data set of 54 years is reduced to 12 sets of hourly averaged data corresponding to 12 months. Authenticity of data is assessed by computing descriptive statistics on the entire data set without average and on monthly 12 data sets. Additionally, descriptive statistics show that wind speeds are positively skewed and most of the wind data points are observed to be blowing in south-west direction. Cumulative distribution and probability density function for all data sets are determined for both Weibull function and GMM. Wind power densities on monthly as well as for the entire set are determined from both models using probability density functions of Weibull function and GMM. In order to assess the goodness-of-fit of the fitted Weibull function and GMM, coefficient of determination (R2) and Kolmogorov-Smirnov (K-S) tests are also determined. Although R2 test values for Weibull function are much closer to ‘1’ compared to its values for GMM. Nevertheless, overall performance of GMM is superior to Weibull function in terms of estimated wind power densities using GMM which are in good agreement with the power densities estimated using wind data for the same duration. It is reported that wind power densities for the entire wind data set are 307 W/m2 and 403.96 W/m2 estimated using GMM and Weibull function, respectively.

scholarly journals Comparison of Weibull and Gaussian Mixture Models for Wind Speed Data Analysis

2020 ◽  
Vol 11 (1) ◽  
pp. 10-16
Author(s):  
Muhammad Shoaib ◽  
Saif Ur Rehman ◽  
Imran Siddiqui ◽  
Shafiqur Rehman ◽  
Shamim Khan ◽  
...  
Keyword(s):  
Wind Speed ◽  
Wind Power ◽  
Gaussian Mixture ◽  
Descriptive Statistics ◽  
Wind Data ◽  
Weibull Function ◽  
Data Sets ◽  
Data Set ◽  
Wind Speeds ◽  
Power Densities

In order to have a reliable estimate of wind energy potential of a site, high frequency wind speed and direction data recorded for an extended period of time is required. Weibull distribution function is commonly used to approximate the recorded data distribution for estimation of wind energy. In the present study a comparison of Weibull function and Gaussian mixture model (GMM) as theoretical functions are used. The data set used for the study consists of hourly wind speeds and wind directions of 54 years duration recorded at Ijmuiden wind site located in north of Holland. The entire hourly data set of 54 years is reduced to 12 sets of hourly averaged data corresponding to 12 months. Authenticity of data is assessed by computing descriptive statistics on the entire data set without average and on monthly 12 data sets. Additionally, descriptive statistics show that wind speeds are positively skewed and most of the wind data points are observed to be blowing in south-west direction. Cumulative distribution and probability density function for all data sets are determined for both Weibull function and GMM. Wind power densities on monthly as well as for the entire set are determined from both models using probability density functions of Weibull function and GMM. In order to assess the goodness-of-fit of the fitted Weibull function and GMM, coefficient of determination (R2) and Kolmogorov-Smirnov (K-S) tests are also determined. Although R2 test values for Weibull function are much closer to ‘1’ compared to its values for GMM. Nevertheless, overall performance of GMM is superior to Weibull function in terms of estimated wind power densities using GMM which are in good agreement with the power densities estimated using wind data for the same duration. It is reported that wind power densities for the entire wind data set are 307 W/m2 and 403.96 W/m2 estimated using GMM and Weibull function, respectively.

scholarly journals Performance evaluation of Weibull function for wind data analysis in two selected locations in North-Western, Nigeria

2018 ◽  
Vol 6 (1) ◽  
pp. 18
Author(s):  
Boluwaji Olomiyesan
Keyword(s):  
Wind Speed ◽  
Wind Power ◽  
Predictive Ability ◽  
Maximum Energy ◽  
Wind Data ◽  
Weibull Function ◽  
Wind Speed Data ◽  
Wind Speeds ◽  
The North ◽  
North Western

In this study, the predictive ability of two-parameter Weibull distribution function in analyzing wind speed data was assessed in two selected sites with different mean wind speeds in the North-Western region of Nigeria. Twenty-two years wind speed data spanning from 1984 to 2005 was used in the analysis. The data were obtained from the Nigerian Meteorological Agency (NIMET) in Lagos. The results of the analysis show that Weibull function is suitable for analyzing measured wind speed data and in predicting the wind-power density in both locations and that Weibull function is not discriminative between locations with high and low mean wind speeds in analyzing wind data. The annual mean wind speeds for the two sites (Sokoto and Yelwa) are 7.99 ms-1 and 2.59 ms-1 respectively, while the annual values of the most probable wind speed and the maximum, energy-carrying wind speeds are respectively:3.52 and 4.34 ms-1 for Yelwa and 8.33 and 9.02 ms-1 for Sokoto. The estimated annual wind power densities for Yelwa and Sokoto are respectively 36.91 and 359.96 Wm-2. Therefore, Sokoto has a better prospect for wind power generation.

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

2017 ◽  
Vol 17 (4B) ◽  
pp. 37-43
Author(s):  
Pham Xuan Thanh ◽  
Nguyen Xuan Anh ◽  
Le Van Luu ◽  
Hiep Van Nguyen ◽  
Hoang Hai Son ◽  
...  
Keyword(s):  
Wind Speed ◽  
Shape Factor ◽  
Maximum Energy ◽  
Weibull Function ◽  
Data Set ◽  
Wind Speeds ◽  
Mean Wind Speed ◽  
Wind Characteristics ◽  
Two Parameters ◽  
Factor C

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).

scholarly journals Scatterometer hurricane wind speed retrievals using cross polarization

2013 ◽  
Vol 6 (4) ◽  
pp. 7945-7984 ◽  
Author(s):  
G.-J. van Zadelhoff ◽  
A. Stoffelen ◽  
P. W. Vachon ◽  
J. Wolfe ◽  
J. Horstmann ◽  
...  
Keyword(s):  
Wind Speed ◽  
Weather Prediction ◽  
Data Sets ◽  
Data Set ◽  
Wind Speeds ◽  
Geophysical Model ◽  
Hurricane Wind ◽  
Geophysical Model Function ◽  
Sar Imagery ◽  
Nwp Model

Abstract. Hurricane-force wind speeds can have a large societal impact and in this paper microwave C-band cross-polarized (VH) signals are investigated to assess if they can be used to derive extreme wind speed conditions. European satellite scatterometers have excellent hurricane penetration capability at C-band, but the vertically (VV) polarized signals become insensitive above 25 m s−1. VV and VH polarized backscatter signals from RADARSAT-2 SAR imagery acquired during severe hurricane events were compared to collocated SFMR wind measurements acquired by NOAA's hurricane-hunter aircraft. From this data set a Geophysical Model Function (GMF) at strong-to-extreme/severe wind speeds (i.e. 20 m s−1 < U10 < 45 m s−1) is derived. Within this wind speed regime, cross-polarized data showed no distinguishable loss of sensitivity and as such, cross-polarized data can be considered a good candidate for the retrieval of strong-to-severe wind speeds from satellite instruments. The upper limit of 45 m s−1 is defined by the currently available collocated data. The validity of the derived relationship between wind speed and VH has been evaluated by comparing the cross polarized signals to two independent wind speed datasets, i.e. short-range ECMWF Numerical Weather Prediction (NWP) model forecast winds and the NOAA best estimate one-minute maximum sustained winds. Analysis of the three comparison data sets confirm that cross-polarized signals from satellites will enable the retrieval of strong-to-severe wind speeds where VV or horizontal (HH) polarization data has saturated. The VH backscatter increases exponentially with respect to wind speed (linear against VH [dB]) and a near real time assessment of maximum sustained wind speed is possible using VH measurements. VH measurements thus would be an extremely valuable complement on next-generation scatterometers for Hurricane forecast warnings and hurricane model initialization.

scholarly journals Statistical Analysis of Wind Speed & Wind Direction in Tantan Province, Morocco

2019 ◽  
Vol 8 (4) ◽  
pp. 3955-3959
Keyword(s):  
Wind Speed ◽  
Wind Power ◽  
Wind Direction ◽  
Energy System ◽  
Average Frequency ◽  
Wind Rose ◽  
Data Set ◽  
Wind Speeds ◽  
Mean Wind Speed ◽  
The Mean

In this paper, a two-parameter Weibull statistical distribution is used to analyze the characteristics of the wind from the Saharan area, located in the Tantan province, Morocco, for 08 years at 10 m. During those 08 years (2009-2017) the frequency distribution of the wind speed, the wind direction, the mean wind speed, the shape and scale (k & c) Weibull parameters have been calculated for the province. The mean wind speed for the entire data set is 6.4 m/s. The parameters k & c are found as 1.9 and 2.52 m/s in relative order. The study also provides an analysis of the wind direction along with a wind rose chart for the province. The analysis suggests that the highest wind speeds that vary (vm = 5.1m/s; vmax = 18.5m/s) prevail between sectors 165-175 ° with an average frequency of 1.4% and lower wind speeds (vm = 2.5m/s; vmax = 9.7m/s) occur between sectors 245-255° with an average frequency of 0.6%. The results of this document help to understand the wind power potential of the province and serve as a source of wind power projects. From a perspective, the wind energy system is an alternative to the future of the Sahara province of Morocco.

scholarly journals Retrieving hurricane wind speeds using cross-polarization C-band measurements

2014 ◽  
Vol 7 (2) ◽  
pp. 437-449 ◽  
Author(s):  
G.-J. van Zadelhoff ◽  
A. Stoffelen ◽  
P. W. Vachon ◽  
J. Wolfe ◽  
J. Horstmann ◽  
...  
Keyword(s):  
Wind Speed ◽  
Weather Prediction ◽  
Data Sets ◽  
Data Set ◽  
Wind Speeds ◽  
Geophysical Model ◽  
Hurricane Wind ◽  
Geophysical Model Function ◽  
Sar Imagery ◽  
Nwp Model

Abstract. Hurricane-force wind speeds can have a large societal impact and in this paper microwave C-band cross-polarized (VH) signals are investigated to assess if they can be used to derive extreme wind-speed conditions. European satellite scatterometers have excellent hurricane penetration capability at C-band, but the vertically (VV) polarized signals become insensitive above 25 m s−1. VV and VH polarized backscatter signals from RADARSAT-2 SAR imagery acquired during severe hurricane events were compared to collocated SFMR wind measurements acquired by NOAA's hurricane-hunter aircraft. From this data set a geophysical model function (GMF) at strong-to-extreme/severe wind speeds (i.e., 20 m s−1 < U10 < 45 m s−1) is derived. Within this wind speed regime, cross-polarized data showed no distinguishable loss of sensitivity and as such, cross-polarized data can be considered a good candidate for the retrieval of strong-to-severe wind speeds from satellite instruments. The upper limit of 45 m s−1 is defined by the currently available collocated data. The validity of the derived relationship between wind speed and VH backscatter has been evaluated by comparing the cross-polarized signals to two independent wind-speed data sets (i.e., short-range ECMWF numerical weather prediction (NWP) model forecast winds and the NOAA best estimate 1-minute maximum sustained winds). Analysis of the three comparison data sets confirm that cross-polarized signals from satellites will enable the retrieval of strong-to-severe wind speeds where VV or horizontal (HH) polarization data has saturated. The VH backscatter increases exponentially with respect to wind speed (linear against VH [dB]) and a near-real-time assessment of maximum sustained wind speed is possible using VH measurements. VH measurements thus would be an extremely valuable complement on next-generation scatterometers for hurricane forecast warnings and hurricane model initialization.

scholarly journals The 3 km Norwegian reanalysis (NORA3) – a validation of offshore wind resources in the North Sea and the Norwegian Sea

2021 ◽  
Vol 6 (6) ◽  
pp. 1501-1519
Author(s):  
Ida Marie Solbrekke ◽  
Asgeir Sorteberg ◽  
Hilde Haakenstad
Keyword(s):  
Wind Speed ◽  
Wind Power ◽  
Offshore Wind ◽  
Data Set ◽  
Norwegian Sea ◽  
Offshore Wind Power ◽  
Wind Speeds ◽  
The North ◽  
The North Sea ◽  
Simulated Wind

Abstract. We validate a new high-resolution (3 km) numerical mesoscale weather simulation for offshore wind power purposes for the time period 2004–2016 for the North Sea and the Norwegian Sea. The 3 km Norwegian reanalysis (NORA3) is a dynamically downscaled data set, forced with state-of-the-art atmospheric reanalysis as boundary conditions. We conduct an in-depth validation of the simulated wind climatology towards the observed wind climatology to determine whether NORA3 can serve as a wind resource data set in the planning phase of future offshore wind power installations. We place special emphasis on evaluating offshore wind-power-related metrics and the impact of simulated wind speed deviations on the estimated wind power and the related variability. We conclude that the NORA3 data are well suited for wind power estimates but give slightly conservative estimates of the offshore wind metrics. In other words, wind speeds in NORA3 are typically 5 % (0.5 m s−1) lower than observed wind speeds, giving an underestimation of offshore wind power of 10 %–20 % (equivalent to an underestimation of 3 percentage points in the capacity factor) for a selected turbine type and hub height. The model is biased towards lower wind power estimates due to overestimation of the wind speed events below typical wind speed limits of rated wind power (u<11–13 m s−1) and underestimation of high-wind-speed events (u>11–13 m s−1). The hourly wind speed and wind power variability are slightly underestimated in NORA3. However, the number of hours with zero power production caused by the wind conditions (around 12 % of the time) is well captured, while the duration of each of these events is slightly overestimated, leading to 25-year return values for zero-power duration being too high for the majority of the sites. The model performs well in capturing spatial co-variability in hourly wind power production, with only small deviations in the spatial correlation coefficients among the sites. We estimate the observation-based decorrelation length to be 425.3 km, whereas the model-based length is 19 % longer.

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

2019 ◽  
Vol 30 (4) ◽  
pp. 13-25
Author(s):  
F. Lubbe ◽  
T. Harms ◽  
J. Maritz
Keyword(s):  
Wind Speed ◽  
Wind Power ◽  
Cost Reduction ◽  
Data Sets ◽  
Data Set ◽  
Shape Factors ◽  
Weibull Parameters ◽  
Wind Speed Data ◽  
Relative Errors

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.

scholarly journals Optimization of a Small Wind Power Plant for Annual Wind Speed Distribution

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1587
Author(s):  
Krzysztof Wrobel ◽  
Krzysztof Tomczewski ◽  
Artur Sliwinski ◽  
Andrzej Tomczewski
Keyword(s):  
Wind Speed ◽  
Power Plant ◽  
Wind Power ◽  
Power Plants ◽  
Control Method ◽  
Wind Power Plant ◽  
Switched Reluctance ◽  
Wind Speeds ◽  
Wind Speed Distribution ◽  
And Control

This article presents a method to adjust the elements of a small wind power plant to the wind speed characterized by the highest annual level of energy. Tests were carried out on the basis of annual wind distributions at three locations. The standard range of wind speeds was reduced to that resulting from the annual wind speed distributions in these locations. The construction of the generators and the method of their excitation were adapted to the characteristics of the turbines. The results obtained for the designed power plants were compared with those obtained for a power plant with a commercial turbine adapted to a wind speed of 10 mps. The generator structure and control method were optimized using a genetic algorithm in the MATLAB program (Mathworks, Natick, MA, USA); magnetostatic calculations were carried out using the FEMM program; the simulations were conducted using a proprietary simulation program. The simulation results were verified by measurement for a switched reluctance machine of the same voltage, power, and design. Finally, the yields of the designed generators in various locations were determined.

scholarly journals Wind Speed Retrieval from Simulated RADARSAT Constellation Mission Compact Polarimetry SAR Data for Marine Application

2019 ◽  
Vol 11 (14) ◽  
pp. 1682 ◽  
Author(s):  
Torsten Geldsetzer ◽  
Shahid K. Khurshid ◽  
Kerri Warner ◽  
Filipe Botelho ◽  
Dean Flett
Keyword(s):  
Wind Speed ◽  
Low Noise ◽  
Quality Data ◽  
Band Model ◽  
Data Set ◽  
Wind Retrieval ◽  
Wind Speeds ◽  
Geophysical Model ◽  
The Right ◽  
Quality Threshold

RADARSAT Constellation Mission (RCM) compact polarimetry (CP) data were simulated using 504 RADARSAT-2 quad-pol SAR images. These images were used to samples CP data in three RCM modes to build a data set with co-located ocean wind vector observations from in situ buoys on the West and East coasts of Canada. Wind speeds up to 18 m/s were included. CP and linear polarization parameters were related to the C-band model (CMOD) geophysical model functions CMOD-IFR2 and CMOD5n. These were evaluated for their wind retrieval potential in each RCM mode. The CP parameter Conformity was investigated to establish a data-quality threshold (>0.2), to ensure high-quality data for model validation. An accuracy analysis shows that the first Stokes vector (SV0) and the right-transmit vertical-receive backscatter (RV) parameters were as good as the VV backscatter with CMOD inversion. SV0 produced wind speed retrieval accuracies between 2.13 m/s and 2.22 m/s, depending on the RCM mode. The RCM Medium Resolution 50 m mode produced the best results. The Low Resolution 100 m and Low Noise modes provided similar results. The efficacy of SV0 and RV imparts confidence in the continuity of robust wind speed retrieval with RCM CP data. Three image-based case studies illustrate the potential for the application of CP parameters and RCM modes in operational wind retrieval systems. The results of this study provide guidance to direct research objectives once RCM is launched. The results also provide guidance for operational RCM data implementation in Canada’s National SAR winds system, which provides near-real-time wind speed estimates to operational marine forecasters and meteorologists within Environment and Climate Change Canada.

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