A Study on Determining the Output Power of Wind Energy Generation Considering Uncertainty in Input Power Forecasting
Published online: 19/03/2026
Corressponding author's email:
ntan@hcmute.edu.vnDOI:
https://doi.org/10.54644/jte.2026.1975Keywords:
Wind energy, Weibull Distribution, Rayleigh Distribution, Wind uncertainty, Wind speedAbstract
This paper presents a method for determining the output power of a wind power generation system under wind speed uncertainty. Hourly wind data collected in Hawaii, USA, is statistically modeled using four probability distribution functions: Weibull, Rayleigh, Log-normal, and Gamma. The distribution parameters are estimated via the Maximum Likelihood Estimation (MLE) method and subsequently applied to a Doubly-Fed Induction Generator (DFIG) model in MATLAB/Simulink to simulate power output variations based on probabilistically modeled wind speed. The fit quality of each distribution is assessed by calculating the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the coefficient of determination (R²), in comparison to the empirical histogram. The results indicate that the two-parameter Weibull distribution best fits the measured data (MAE = 0.00708, RMSE = 0.0097, R² = 0.93), followed by the Gamma distribution. In contrast, the Rayleigh and Log-normal distributions exhibit significant deviations. When the Weibull parameters are applied to the DFIG model, the simulated weekly power output ranges from 0.96 MW to 1.37 MW, clearly illustrating the nonlinear relationship between wind speed and output power. The proposed approach thus provides a rigorous quantitative framework that links the probabilistic characteristics of wind to the actual power output range, thereby enhancing reliability in operational planning and mitigating risks in modern power systems.
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References
Y. Wang, Q. Hu, D. Srinivasan, and Z. Wang, "Wind Power Curve Modeling and Wind Power Forecasting With Inconsistent Data," in IEEE Transactions on Sustainable Energy, vol. 10, no. 1, pp. 16-25, Jan. 2019, doi: 10.1109/TSTE.2018.2820198.
J. Wang, A. AlShelahi, M. You, E. Byon, and R. Saigal, "Integrative Density Forecast and Uncertainty Quantification of Wind Power Generation," in IEEE Transactions on Sustainable Energy, vol. 12, no. 4, pp. 1864-1875, Oct. 2021, doi: 10.1109/TSTE.2021.3069111.
H. Wen, P. Pinson, J. Ma, J. Gu, and Z. Jin, "Continuous and Distribution-Free Probabilistic Wind Power Forecasting: A Conditional Normalizing Flow Approach," in IEEE Transactions on Sustainable Energy, vol. 13, no. 4, pp. 2250-2263, Oct. 2022, doi: 10.1109/TSTE.2022.3191330.
P. Guo and D. Infield, "Wind Turbine Power Curve Modeling and Monitoring With Gaussian Process and SPRT," in IEEE Transactions on Sustainable Energy, vol. 11, no. 1, pp. 107-115, Jan. 2020, doi: 10.1109/TSTE.2018.2884699.
M. You, B. Liu, E. Byon, S. Huang, and J. Jin, "Direction-Dependent Power Curve Modeling for Multiple Interacting Wind Turbines," in IEEE Transactions on Power Systems, vol. 33, no. 2, pp. 1725-1733, March 2018, doi: 10.1109/TPWRS.2017.2737529.
S. Shokrzadeh, M. J. Jozani, and E. Bibeau, "Wind Turbine Power Curve Modeling Using Advanced Parametric and Nonparametric Methods," in IEEE Transactions on Sustainable Energy, vol. 5, no. 4, pp. 1262-1269, Oct. 2014, doi: 10.1109/TSTE.2014.2345059.
E. Gómez-Lázaro et al., “Probability density function characterization for aggregated large-scale wind power based on Weibull mixtures,” Energies (Basel), vol. 9, no. 2, 2016, doi: 10.3390/en9020091.
L. S. Paraschiv, S. Paraschiv, and I. V. Ion, “Investigation of wind power density distribution using Rayleigh probability density function,” in Energy Procedia, Elsevier Ltd, 2019, pp. 1546–1552, doi: 10.1016/j.egypro.2018.11.320.
S. Baran and S. Lerch, “Log-normal distribution based EMOS models for probabilistic wind speed forecasting,” Jul. 2014, doi: 10.1002/qj.2521.
D. Castro-Camilo, R. Huser, and H. Rue, “A Spliced Gamma-Generalized Pareto Model for Short-Term Extreme Wind Speed Probabilistic Forecasting,” J Agric Biol Environ Stat, vol. 24, no. 3, pp. 517–534, Sep. 2019, doi: 10.1007/s13253-019-00369-z.
M. Sun, C. Feng, and J. Zhang, “Multi-Distribution Ensemble Probabilistic Wind Power Forecasting,” Renewable Energy, vol. 148, pp. 135-149, 2020, doi: 10.1016/j.renene.2019.11.145.
T. P. Chang, “Estimation of wind energy potential using different probability density functions,” Appl. Energy, vol. 88, no. 5, pp. 1848–1856, 2011, doi: 10.1016/j.apenergy.2010.11.010.
G. J. Bowden, P. R. Barker, V. O. Shestopal, and J. W. Twidell, “The Weibull distribution function and wind power statistics,” Wind Engineering, pp. 85–98, 1983.
H. Shi, Z. Dong, N. Xiao, and Q. Huang, “Wind Speed Distributions Used in Wind Energy Assessment: A Review,” Front. Energy Res., Nov. 22, 2021, doi: 10.3389/fenrg.2021.769920.
V. Sohoni, S. Gupta, and R. Nema, “A comparative analysis of wind speed probability distributions for wind power assessment of four sites,” Turkish Journal of Electrical Engineering and Computer Sciences, vol. 24, no. 6, pp. 4724–4735, 2016, doi: 10.3906/elk-1412-207.
C. Ozay and M. S. Celiktas, “Statistical analysis of wind speed using two-parameter Weibull distribution in AlaçatI region,” Energy Convers. Manag., vol. 121, pp. 49–54, Aug. 2016, doi: 10.1016/j.enconman.2016.05.026.
F. G. Akgül, B. Şenoʇlu, and T. Arslan, “An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution,” Energy Convers. Manag., vol. 114, pp. 234–240, Apr. 2016, doi: 10.1016/j.enconman.2016.02.026.
A. Serban, L. S. Paraschiv, and S. Paraschiv, “Assessment of wind energy potential based on Weibull and Rayleigh distribution models,” Energy Reports, vol. 6, pp. 250–267, Nov. 2020, doi: 10.1016/j.egyr.2020.08.048.
J. Wang, J. Hu, and K. Ma, “Wind speed probability distribution estimation and wind energy assessment,” Jul. 01, 2016, Elsevier Ltd., doi: 10.1016/j.rser.2016.01.057.
P. Wais, “A review of Weibull functions in wind sector,” 2017, Elsevier Ltd., doi: 10.1016/j.rser.2016.12.014.
F. G. Akgül, B. Şenoʇlu, and T. Arslan, “An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution,” Energy Convers. Manag., vol. 114, pp. 234–240, Apr. 2016, doi: 10.1016/j.enconman.2016.02.026.
F. N. Nwobi and C. A. Ugomma, “A Comparison of Methods for the Estimation of Weibull Distribution Parameters,” 2014.
J. V. Seguro and T. W. Lambert, “Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 85, no. 1, pp. 75–84, 2000.
I. Pobočíková, Z. Sedliačková, and M. Michalková, “Application of Four Probability Distributions for Wind Speed Modeling,” in Procedia Engineering, Elsevier Ltd, 2017, pp. 713–718, doi: 10.1016/j.proeng.2017.06.123.
T. Chai and R. R. Draxler, “Root mean square error (RMSE) or mean absolute error (MAE),” Feb. 28, 2014, doi: 10.5194/gmdd-7-1525-2014.
H. Bidaoui, I. E. Abbassi, A. E. Bouardi, and A. Darcherif, “Wind Speed Data Analysis Using Weibull and Rayleigh Distribution Functions, Case Study: Five Cities Northern Morocco,” in Procedia Manufacturing, Elsevier B. V., 2019, pp. 786–793, doi: 10.1016/j.promfg.2019.02.286.
M. H. Ouahabi, F. Benabdelouahab, and A. Khamlichi, “Analyzing wind speed data and wind power density of Tetouan city in Morocco by adjustment to Weibull and Rayleigh distribution functions,” Wind Engineering, vol. 41, no. 3, pp. 174–184, 2017.
National Renewable Energy Laboratory, “Wind Resource Database (WRDB) – Data Viewer.” [Online]. Available: https://wrdb.nrel.gov/data-viewer
D. Ochoa and S. Martinez, “Fast-Frequency Response Provided by DFIG-Wind Turbines and its Impact on the Grid,” IEEE Transactions on Power Systems, vol. 32, no. 5, pp. 4002–4011, Sep. 2017, doi: 10.1109/TPWRS.2016.2636374.
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