Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures

Gómez-Lázaro, Emilio; Bueso, María; Kessler, Mathieu; Martín-Martínez, Sergio; Zhang, Jie; Hodge, Bri-Mathias; Molina-García, Angel

doi:10.3390/en9020091

Title: Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures

Abstract

Here, the Weibull probability distribution has been widely applied to characterize wind speeds for wind energy resources. Wind power generation modeling is different, however, due in particular to power curve limitations, wind turbine control methods, and transmission system operation requirements. These differences are even greater for aggregated wind power generation in power systems with high wind penetration. Consequently, models based on one-Weibull component can provide poor characterizations for aggregated wind power generation. With this aim, the present paper focuses on discussing Weibull mixtures to characterize the probability density function (PDF) for aggregated wind power generation. PDFs of wind power data are firstly classified attending to hourly and seasonal patterns. The selection of the number of components in the mixture is analyzed through two well-known different criteria: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Finally, the optimal number of Weibull components for maximum likelihood is explored for the defined patterns, including the estimated weight, scale, and shape parameters. Results show that multi-Weibull models are more suitable to characterize aggregated wind power data due to the impact of distributed generation, variety of wind speed values and wind power curtailment.

Authors:: Gómez-Lázaro, Emilio; Bueso, María; Kessler, Mathieu; Martín-Martínez, Sergio; Zhang, Jie; Hodge, Bri-Mathias; Molina-García, Angel

Publication Date:: Tue Feb 02 00:00:00 EST 2016

Research Org.:: National Renewable Energy Lab. (NREL), Golden, CO (United States)

Sponsoring Org.:: USDOE Office of Energy Efficiency and Renewable Energy (EERE)

OSTI Identifier:: 1419591

Alternate Identifier(s):: OSTI ID: 1238038

Report Number(s):: NREL/JA-5D00-65841
Journal ID: ISSN 1996-1073; ENERGA; PII: en9020091

Grant/Contract Number:: AC36-08-GO28308; AC36-08GO28308

Resource Type:: Published Article

Journal Name:: Energies (Basel)

Additional Journal Information:: Journal Name: Energies (Basel) Journal Volume: 9 Journal Issue: 12; Journal ID: ISSN 1996-1073

Publisher:: MDPI AG

Country of Publication:: Switzerland

Language:: English

Subject:: 17 WIND ENERGY; 24 POWER TRANSMISSION AND DISTRIBUTION; wind power generation; Weibull distributions; Weibull mixtures; Akaike information criterion; AIC; Bayesian information criterion; BIC

Citation Formats


                    Gómez-Lázaro, Emilio, Bueso, María, Kessler, Mathieu, Martín-Martínez, Sergio, Zhang, Jie, Hodge, Bri-Mathias, and Molina-García, Angel. Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures.  Switzerland: N. p., 2016. 
Web.  doi:10.3390/en9020091.

Copy to clipboard


                    Gómez-Lázaro, Emilio, Bueso, María, Kessler, Mathieu, Martín-Martínez, Sergio, Zhang, Jie, Hodge, Bri-Mathias, & Molina-García, Angel. Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures.  Switzerland.  https://doi.org/10.3390/en9020091

Copy to clipboard


                    Gómez-Lázaro, Emilio, Bueso, María, Kessler, Mathieu, Martín-Martínez, Sergio, Zhang, Jie, Hodge, Bri-Mathias, and Molina-García, Angel. Tue .  
"Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures".  Switzerland.  https://doi.org/10.3390/en9020091.

Copy to clipboard


                    
@article{osti_1419591,

  title        = {Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures},

  author       = {Gómez-Lázaro, Emilio and Bueso, María and Kessler, Mathieu and Martín-Martínez, Sergio and Zhang, Jie and Hodge, Bri-Mathias and Molina-García, Angel},

  abstractNote = {Here, the Weibull probability distribution has been widely applied to characterize wind speeds for wind energy resources. Wind power generation modeling is different, however, due in particular to power curve limitations, wind turbine control methods, and transmission system operation requirements. These differences are even greater for aggregated wind power generation in power systems with high wind penetration. Consequently, models based on one-Weibull component can provide poor characterizations for aggregated wind power generation. With this aim, the present paper focuses on discussing Weibull mixtures to characterize the probability density function (PDF) for aggregated wind power generation. PDFs of wind power data are firstly classified attending to hourly and seasonal patterns. The selection of the number of components in the mixture is analyzed through two well-known different criteria: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Finally, the optimal number of Weibull components for maximum likelihood is explored for the defined patterns, including the estimated weight, scale, and shape parameters. Results show that multi-Weibull models are more suitable to characterize aggregated wind power data due to the impact of distributed generation, variety of wind speed values and wind power curtailment.},

  doi          = {10.3390/en9020091},

  journal      = {Energies (Basel)},

  number       = 12,

  volume       = 9,

  place        = {Switzerland},

  year         = {Tue Feb 02 00:00:00 EST 2016},

  month        = {Tue Feb 02 00:00:00 EST 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.3390/en9020091

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 14 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Some Aspects of Wind Power Statistics
journal, February 1977

Hennessey, Joseph P.
Journal of Applied Meteorology, Vol. 16, Issue 2
DOI: 10.1175/1520-0450(1977)016<0119:SAOWPS>2.0.CO;2

Review of Weibull Statistics for Estimation of Wind Speed Distributions
journal, August 1984

Conradsen, K.; Nielsen, L. B.; Prahm, L. P.
Journal of Climate and Applied Meteorology, Vol. 23, Issue 8
DOI: 10.1175/1520-0450(1984)023<1173:ROWSFE>2.0.CO;2

Wind speed analysis in La Ventosa, Mexico: a bimodal probability distribution case
journal, August 2004

Jaramillo, O. A.; Borja, M. A.
Renewable Energy, Vol. 29, Issue 10
DOI: 10.1016/j.renene.2004.02.001

Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application
journal, January 2011

Chang, Tian Pau
Applied Energy, Vol. 88, Issue 1
DOI: 10.1016/j.apenergy.2010.06.018

Impacts of large amounts of wind power on design and operation of power systems, results of IEA collaboration
journal, March 2011

Holttinen, Hannele; Meibom, Peter; Orths, Antje
Wind Energy, Vol. 14, Issue 2
DOI: 10.1002/we.410

A study of Weibull parameters using long-term wind observations
journal, June 2000

Lun, Isaac Y. F.; Lam, Joseph C.
Renewable Energy, Vol. 20, Issue 2
DOI: 10.1016/S0960-1481(99)00103-2

Studying the Variability and Uncertainty Impacts of Variable Generation at Multiple Timescales
journal, August 2012

Ela, Erik; O'Malley, Mark
IEEE Transactions on Power Systems, Vol. 27, Issue 3
DOI: 10.1109/TPWRS.2012.2185816

A Production Simulation Tool for Systems With Integrated Wind Energy Resources
journal, November 2011

Maisonneuve, Nicolas; Gross, George
IEEE Transactions on Power Systems, Vol. 26, Issue 4
DOI: 10.1109/TPWRS.2011.2143437

Influence of the data sampling interval in the estimation of the parameters of the Weibull wind speed probability density distribution: a case study
journal, September 2005

Ramírez, Penélope; Carta, José Antonio
Energy Conversion and Management, Vol. 46, Issue 15-16
DOI: 10.1016/j.enconman.2004.11.004

Finite Mixture Estimation Algorithm for Arbitrary Function Approximation
journal, February 2012

Volk, Matej; Nagode, Marko; Fajdiga, Matija
Strojniški vestnik – Journal of Mechanical Engineering, Vol. 58, Issue 2
DOI: 10.5545/sv-jme.2011.085

Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions
journal, March 2007

Carta, J. A.; Ramírez, P.
Renewable Energy, Vol. 32, Issue 3
DOI: 10.1016/j.renene.2006.05.005

Estimation of wind energy potential using finite mixture distribution models
journal, April 2009

Akpinar, Sinan; Akpinar, Ebru Kavak
Energy Conversion and Management, Vol. 50, Issue 4
DOI: 10.1016/j.enconman.2009.01.007

A Hybrid Intelligent Model for Deterministic and Quantile Regression Approach for Probabilistic Wind Power Forecasting
journal, July 2014

Haque, Ashraf Ul; Nehrir, M. Hashem; Mandal, Paras
IEEE Transactions on Power Systems, Vol. 29, Issue 4
DOI: 10.1109/TPWRS.2014.2299801

The REBMIX Algorithm and the Univariate Finite Mixture Estimation
journal, February 2011

Nagode, Marko; Fajdiga, Matija
Communications in Statistics - Theory and Methods, Vol. 40, Issue 5
DOI: 10.1080/03610920903480890

Mixture probability distribution functions to model wind speed distributions
journal, January 2012

Kollu, Ravindra; Rayapudi, Srinivasa; Narasimham, Svl
International Journal of Energy and Environmental Engineering, Vol. 3, Issue 1
DOI: 10.1186/2251-6832-3-27

Estimation of wind energy potential using different probability density functions
journal, May 2011

Chang, Tian Pau
Applied Energy, Vol. 88, Issue 5
DOI: 10.1016/j.apenergy.2010.11.010

Operational Adequacy Studies of Power Systems With Wind Farms and Energy Storages
journal, November 2012

Wang, Peng; Gao, Zhiyong; Bertling, Lina
IEEE Transactions on Power Systems, Vol. 27, Issue 4
DOI: 10.1109/TPWRS.2012.2201181

Influence of the level of fit of a density probability function to wind-speed data on the WECS mean power output estimation
journal, October 2008

Carta, José A.; Ramírez, Penélope; Velázquez, Sergio
Energy Conversion and Management, Vol. 49, Issue 10
DOI: 10.1016/j.enconman.2008.04.012

Methods for Estimating Wind Speed Frequency Distributions
journal, March 1978

Justus, C. G.; Hargraves, W. R.; Mikhail, Amir
Journal of Applied Meteorology, Vol. 17, Issue 3
DOI: 10.1175/1520-0450(1978)017<0350:MFEWSF>2.0.CO;2

The Effect of Large-Scale Wind Power on System Balancing in Northern Europe
journal, October 2012

Aigner, Tobias; Jaehnert, Stefan; Doorman, Gerard L.
IEEE Transactions on Sustainable Energy, Vol. 3, Issue 4
DOI: 10.1109/TSTE.2012.2203157

Use of two-component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean
journal, August 2010

Akdağ, S. A.; Bagiorgas, H. S.; Mihalakakou, G.
Applied Energy, Vol. 87, Issue 8
DOI: 10.1016/j.apenergy.2010.02.033

A review of wind speed probability distributions used in wind energy analysis
journal, June 2009

Carta, J. A.; Ramírez, P.; Velázquez, S.
Renewable and Sustainable Energy Reviews, Vol. 13, Issue 5
DOI: 10.1016/j.rser.2008.05.005

Wind Power Forecasts Using Gaussian Processes and Numerical Weather Prediction
journal, March 2014

Chen, Niya; Qian, Zheng; Nabney, Ian T.
IEEE Transactions on Power Systems, Vol. 29, Issue 2
DOI: 10.1109/TPWRS.2013.2282366

Finite Mixture Modeling via REBMIX
journal, April 2015

Nagode, Marko
Journal of Algorithms and Optimization
DOI: 10.5963/JAO0302001

Generation System Reliability Evaluation Incorporating Correlations of Wind Speeds With Different Distributions
journal, February 2013

Qin, Zhilong; Li, Wenyuan; Xiong, Xiaofu
IEEE Transactions on Power Systems, Vol. 28, Issue 1
DOI: 10.1109/TPWRS.2012.2205410

A Versatile Probability Distribution Model for Wind Power Forecast Errors and Its Application in Economic Dispatch
journal, August 2013

Zhang, Zhao-Sui; Sun, Yuan-Zhang; Gao, David Wenzhong
IEEE Transactions on Power Systems, Vol. 28, Issue 3
DOI: 10.1109/TPWRS.2013.2249596

Assessment of wind energy resources for electricity generation using WECS in North-Central region, Nigeria
journal, May 2011

Ohunakin, Olayinka S.
Renewable and Sustainable Energy Reviews, Vol. 15, Issue 4
DOI: 10.1016/j.rser.2011.01.001

Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis
journal, March 2000

Seguro, J. V.; Lambert, T. W.
Journal of Wind Engineering and Industrial Aerodynamics, Vol. 85, Issue 1
DOI: 10.1016/S0167-6105(99)00122-1

Extrapolating wind speed time series vs. Weibull distribution to assess wind resource to the turbine hub height: A case study on coastal location in Southern Italy
journal, February 2014

Gualtieri, Giovanni; Secci, Sauro
Renewable Energy, Vol. 62
DOI: 10.1016/j.renene.2013.07.003

Works referencing / citing this record:

Economic Dispatch of the Low-Carbon Green Certificate with Wind Farms Based on Fuzzy Chance Constraints
journal, April 2018

Wang, Xiuyun; Wang, Jian; Tian, Biyuan
Energies, Vol. 11, Issue 4
DOI: 10.3390/en11040943

Similar Records in DOE PAGES and OSTI.GOV collections:

Method for including wind-generated power within electric utility generation scheduling

Thesis/Dissertation Davarya, F

The time series analyses of hourly wind speeds from two stations (Boise, Idaho, and Spokane, Washington), and hourly load demands from Washington Water Power Company, based on Box-Jenkins technique, were conducted for the purpose of forecasting and scheduling. Correlation techniques were used to identify the candidate models and the parameters for the resultant models were estimated. After preliminary diagnostic checks for the goodness of fit of the models (using Chi-square test and R-test), the candidate models were selected. Finally, Akaike's Information Criteria (AIC and BIC tests), in conjunction with Kashyap's Posterior Probability Criterion (PP test), were applied to select themore »« less
On Model Selection Criteria in Multimodel Analysis

Journal Article Ye, Ming ; Meyer, Philip D ; Neuman, Shlomo P - Water Resources Research, 44(3):Art. no. W03428

Hydrologic systems are open and complex, rendering them prone to multiple conceptualizations and mathematical descriptions. There has been a growing tendency to postulate several alternative hydrologic models for a site and use model selection criteria to (a) rank these models, (b) eliminate some of them and/or (c) weigh and average predictions and statistics generated by multiple models. This has led to some debate among hydrogeologists about the merits and demerits of common model selection (also known as model discrimination or information) criteria such as AIC [Akaike, 1974], AICc [Hurvich and Tsai, 1989], BIC [Schwartz, 1978] and KIC [Kashyap, 1982] andmore »« less
https://doi.org/10.1029/2008WR006803
{sup 18}F-FLT uptake kinetics in head and neck squamous cell carcinoma: A PET imaging study

Journal Article Liu, Dan ; Fenwick, John D. ; Chalkidou, Anastasia ; ... - Medical Physics

Purpose: To analyze the kinetics of 3{sup ′}-deoxy-3{sup ′}-[F-18]-fluorothymidine (18F-FLT) uptake by head and neck squamous cell carcinomas and involved nodes imaged using positron emission tomography (PET). Methods: Two- and three-tissue compartment models were fitted to 12 tumor time-activity-curves (TACs) obtained for 6 structures (tumors or involved nodes) imaged in ten dynamic PET studies of 1 h duration, carried out for five patients. The ability of the models to describe the data was assessed using a runs test, the Akaike information criterion (AIC) and leave-one-out cross-validation. To generate parametric maps the models were also fitted to TACs of individual voxels.more »« less
https://doi.org/10.1118/1.4868462
MMA, A Computer Code for Multi-Model Analysis

Technical Report Eileen P. Poeter and Mary C. Hill

This report documents the Multi-Model Analysis (MMA) computer code. MMA can be used to evaluate results from alternative models of a single system using the same set of observations for all models. As long as the observations, the observation weighting, and system being represented are the same, the models can differ in nearly any way imaginable. For example, they may include different processes, different simulation software, different temporal definitions (for example, steady-state and transient models could be considered), and so on. The multiple models need to be calibrated by nonlinear regression. Calibration of the individual models needs to be completedmore »« less
https://doi.org/10.2172/920086

Full Text Available
Joint Planck and WMAP assessment of low CMB multipoles

Journal Article Iqbal, Asif ; Malik, Manzoor A. ; Prasad, Jayanti ; ... - Journal of Cosmology and Astroparticle Physics

The remarkable progress in cosmic microwave background (CMB) studies over past decade has led to the era of precision cosmology in striking agreement with the ΛCDM model. However, the lack of power in the CMB temperature anisotropies at large angular scales (low-ℓ), as has been confirmed by the recent Planck data also (up to 0ℓ=4), although statistically not very strong (less than 3σ), is still an open problem. One can avoid to seek an explanation for this problem by attributing the lack of power to cosmic variance or can look for explanations i.e., different inflationary potentials or initial conditions formore »« less
https://doi.org/10.1088/1475-7516/2015/06/014

Similar Records

Title: Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures

Abstract

Citation Formats

Some Aspects of Wind Power Statistics journal, February 1977

Review of Weibull Statistics for Estimation of Wind Speed Distributions journal, August 1984

Wind speed analysis in La Ventosa, Mexico: a bimodal probability distribution case journal, August 2004

Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application journal, January 2011

Impacts of large amounts of wind power on design and operation of power systems, results of IEA collaboration journal, March 2011

A study of Weibull parameters using long-term wind observations journal, June 2000

Studying the Variability and Uncertainty Impacts of Variable Generation at Multiple Timescales journal, August 2012

A Production Simulation Tool for Systems With Integrated Wind Energy Resources journal, November 2011

Influence of the data sampling interval in the estimation of the parameters of the Weibull wind speed probability density distribution: a case study journal, September 2005

Finite Mixture Estimation Algorithm for Arbitrary Function Approximation journal, February 2012

Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions journal, March 2007

Estimation of wind energy potential using finite mixture distribution models journal, April 2009

A Hybrid Intelligent Model for Deterministic and Quantile Regression Approach for Probabilistic Wind Power Forecasting journal, July 2014

The REBMIX Algorithm and the Univariate Finite Mixture Estimation journal, February 2011

Mixture probability distribution functions to model wind speed distributions journal, January 2012

Estimation of wind energy potential using different probability density functions journal, May 2011

Operational Adequacy Studies of Power Systems With Wind Farms and Energy Storages journal, November 2012

Influence of the level of fit of a density probability function to wind-speed data on the WECS mean power output estimation journal, October 2008

Methods for Estimating Wind Speed Frequency Distributions journal, March 1978

The Effect of Large-Scale Wind Power on System Balancing in Northern Europe journal, October 2012

Use of two-component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean journal, August 2010

A review of wind speed probability distributions used in wind energy analysis journal, June 2009

Wind Power Forecasts Using Gaussian Processes and Numerical Weather Prediction journal, March 2014

Finite Mixture Modeling via REBMIX journal, April 2015

Generation System Reliability Evaluation Incorporating Correlations of Wind Speeds With Different Distributions journal, February 2013

A Versatile Probability Distribution Model for Wind Power Forecast Errors and Its Application in Economic Dispatch journal, August 2013

Assessment of wind energy resources for electricity generation using WECS in North-Central region, Nigeria journal, May 2011

Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis journal, March 2000

Extrapolating wind speed time series vs. Weibull distribution to assess wind resource to the turbine hub height: A case study on coastal location in Southern Italy journal, February 2014

Economic Dispatch of the Low-Carbon Green Certificate with Wind Farms Based on Fuzzy Chance Constraints journal, April 2018

Some Aspects of Wind Power Statistics
journal, February 1977

Review of Weibull Statistics for Estimation of Wind Speed Distributions
journal, August 1984

Wind speed analysis in La Ventosa, Mexico: a bimodal probability distribution case
journal, August 2004

Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application
journal, January 2011

Impacts of large amounts of wind power on design and operation of power systems, results of IEA collaboration
journal, March 2011

A study of Weibull parameters using long-term wind observations
journal, June 2000

Studying the Variability and Uncertainty Impacts of Variable Generation at Multiple Timescales
journal, August 2012

A Production Simulation Tool for Systems With Integrated Wind Energy Resources
journal, November 2011

Influence of the data sampling interval in the estimation of the parameters of the Weibull wind speed probability density distribution: a case study
journal, September 2005

Finite Mixture Estimation Algorithm for Arbitrary Function Approximation
journal, February 2012

Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions
journal, March 2007

Estimation of wind energy potential using finite mixture distribution models
journal, April 2009

A Hybrid Intelligent Model for Deterministic and Quantile Regression Approach for Probabilistic Wind Power Forecasting
journal, July 2014

The REBMIX Algorithm and the Univariate Finite Mixture Estimation
journal, February 2011

Mixture probability distribution functions to model wind speed distributions
journal, January 2012

Estimation of wind energy potential using different probability density functions
journal, May 2011

Operational Adequacy Studies of Power Systems With Wind Farms and Energy Storages
journal, November 2012

Influence of the level of fit of a density probability function to wind-speed data on the WECS mean power output estimation
journal, October 2008

Methods for Estimating Wind Speed Frequency Distributions
journal, March 1978

The Effect of Large-Scale Wind Power on System Balancing in Northern Europe
journal, October 2012

Use of two-component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean
journal, August 2010

A review of wind speed probability distributions used in wind energy analysis
journal, June 2009

Wind Power Forecasts Using Gaussian Processes and Numerical Weather Prediction
journal, March 2014

Finite Mixture Modeling via REBMIX
journal, April 2015

Generation System Reliability Evaluation Incorporating Correlations of Wind Speeds With Different Distributions
journal, February 2013

A Versatile Probability Distribution Model for Wind Power Forecast Errors and Its Application in Economic Dispatch
journal, August 2013

Assessment of wind energy resources for electricity generation using WECS in North-Central region, Nigeria
journal, May 2011

Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis
journal, March 2000

Extrapolating wind speed time series vs. Weibull distribution to assess wind resource to the turbine hub height: A case study on coastal location in Southern Italy
journal, February 2014

Economic Dispatch of the Low-Carbon Green Certificate with Wind Farms Based on Fuzzy Chance Constraints
journal, April 2018