Evaluation of Probability Distribution Models for Renewable Energy Forecasting Under Uncertain Conditions

Thai An Nguyen; Mi Sa Nguyen Thi; Huy Anh Quyen; Tu Duc Nguyen

doi:10.48084/etasr.17452

Authors

Thai An Nguyen Faculty of Electrical and Electronics Engineering, HCMC University of Technology and Engineering, Ho Chi Minh City, Vietnam
Mi Sa Nguyen Thi Faculty of Electrical and Electronics Engineering, HCMC University of Technology and Engineering, Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-4123-8918
Huy Anh Quyen Faculty of Electrical and Electronics Engineering, HCMC University of Technology and Engineering, Ho Chi Minh City, Vietnam https://orcid.org/0000-0001-8946-1302
Tu Duc Nguyen Faculty of Electrical and Electronics Engineering, HCMC University of Technology and Engineering, Ho Chi Minh City, Vietnam https://orcid.org/0009-0008-2053-8592

Volume: 16 | Issue: 3 | Pages: 35178-35185 | June 2026 | https://doi.org/10.48084/etasr.17452

Received: 10 January 2026 | Revised: 12 February 2026, 9 March 2026, and 21 March 2026 | Accepted: 23 March 2026 | Online: 9 April 2026

Corresponding author: Thai An Nguyen

Abstract

This study explores the capability of several Probability Distribution Functions (PDFs) to effectively model and forecast power generation from renewable energy sources integrated within a Microgrid (MG). The focus is specifically on wind and solar Photovoltaic (PV) systems. The wind speed datasets are analyzed using the Weibull, Rayleigh, Lognormal, Generalized Extreme Value (GEV), and Normal distributions, while solar irradiance data are represented through the Beta, Normal, Triangular, and Lognormal distributions. Actual meteorological data are sourced from the Wind Resource Database (WRDB) and the National Solar Radiation Database (NSRDB), with a focus on the Kauai region of Hawaii. Model performance and suitability are evaluated using multiple statistical indicators, including the coefficient of determination (R²), the Log-Likelihood, the Akaike Information Criterion (AIC), and the Root Mean Square Error (RMSE). The comparative analysis reveals that the Weibull distribution provides the most precise representation of wind speed behavior, outperforming the other models. Meanwhile, for solar irradiance, the Beta distribution demonstrates superior accuracy and adaptability, while the Normal and Triangular models are less effective due to their simplified assumptions.

Keywords:

Probability Distribution Function (PDF), weibull distribution, beta distribution, renewable energy modeling, wind speed modeling, solar radiation modeling, power output estimation

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References

M. M. R. Ahmed et al., "Mitigating Uncertainty Problems of Renewable Energy Resources Through Efficient Integration of Hybrid Solar PV/Wind Systems Into Power Networks," IEEE Access, vol. 12, pp. 30311–30328, 2024.

A. R. Krishna, A. V. Kumar, A. G. Krushna, J. Shanmugapriyan, and C. Keertana, "The Study of Solar and Wind Power Systems under Different Weather Conditions," in Proceeding of the International Conference on Sustainable Green Energy Technologies (ICSGET), Hyderabad, India, June 14–15, 2024, vol. 547, 2024, Art. no. 03009.

E. Gardashov and R. Gardashov, "On the derivation of an analytical expression for wind power probability distribution function and capacity factor of turbine," International Journal of Sustainable Energy, vol. 43, no. 1, Dec. 2024, Art. no. 2390447.

S.-D. Kwon, "Uncertainty analysis of wind energy potential assessment," Applied Energy, vol. 87, no. 3, pp. 856–865, Mar. 2010.

R. Xezile and N. Mbuli, "Review of Application of Probability Distribution Functions in Assessment of Variable Load, PV Solar and Wind," in 5th International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), Zanzibar, Tanzania, Oct. 16–-19, 2025, pp. 1–6.

T. B. M. J. Ouarda et al., "Probability distributions of wind speed in the UAE," Energy Conversion and Management, vol. 93, pp. 414–434, Mar. 2015.

B. El Kihel, N. E. El Kadri Elyamani, and A. Chillali, "Wind energy potential assessment using the Weibull distribution method for future energy self-sufficiency," Scientific African, vol. 26, Dec. 2024, Art. no. e02482.

P. Lencastre, A. Yazidi, and P. G. Lind, "Modeling Wind-Speed Statistics beyond the Weibull Distribution," Energies, vol. 17, no. 11, 2024, Art. no. 2621.

Z. Cai and S. Zuo, "Optimal System Analysis for Hybrid Wind-Solar-Pumped Storage Systems under Renewable Output Uncertainty," International Journal of Frontiers in Engineering Technology, vol. 6, no. 4, 2024.

S. Patty and T. Malakar, "Performance analysis of machine learning based prediction models in assessing optimal operation of microgrid under uncertainty," Results in Control and Optimization, vol. 15, June 2024, Art. no. 100407.

"NSRDB: National Solar Radiation Database." National Laboratory of the Rockies (NLR). https://nsrdb.nlr.gov/.

M. Sengupta, Y. Xie, A. Lopez, A. Habte, G. Maclaurin, and J. Shelby, "The National Solar Radiation Data Base (NSRDB)," Renewable and Sustainable Energy Reviews, vol. 89, pp. 51–60, June 2018.

"WRDB: Wind Resource Database." National Laboratory of the Rockies (NLR). https://wrdb.nlr.gov/.

C. Draxl, A. Clifton, B.-M. Hodge, and J. McCaa, "The Wind Integration National Dataset (WIND) Toolkit," Applied Energy, vol. 151, pp. 355–366, Aug. 2015.

Y. Kassem, H. Camur, and A. A. S. Mosbah, "Wind Resource Evaluation in Libya: A Comparative Study of Ten Numerical Methods for the Estimation of Weibull Parameters using Multiple Datasets," Engineering, Technology & Applied Science Research, vol. 14, no. 2, pp. 13388–13397, Apr. 2024.

Z. Wang and W. Liu, "Wind energy potential assessment based on wind speed, its direction and power data," Scientific Reports, vol. 11, no. 1,Aug. 2021, Art. no. 16879.

R. B. Millar, Maximum likelihood estimation and inference : with examples in R, SAS and ADMB, 1st ed. Chichester, United Kingdom: John Wiley & Sons, Ltd, 2011.

R. H. Norden, "A Survey of Maximum Likelihood Estimation," International Statistical Review / Revue Internationale de Statistique, vol. 40, no. 3, pp. 329–354, Dec. 1972.

R. Mullen, L. Marshall, and B. McGlynn, "A Beta Regression Model for Improved Solar Radiation Predictions," Journal of Applied Meteorology and Climatology, vol. 52, no. 8, pp. 1923–1938, 2013.

K. Krishnamoorthy, Handbook of Statistical Distributions with Applications, 1st ed. Boca Raton, Florida, USA: Chapman and Hall/CRC, 2006.

B. E. Smith and F. J. Merceret, "The Lognormal Distribution," The College Mathematics Journal, vol. 31, no. 4, pp. 259–261, 2000.

W. E. Stein and M. F. Keblis, "A new method to simulate the triangular distribution," Mathematical and Computer Modelling, vol. 49, no. 5–6, pp. 1143–1147, Mar. 2009.

P. Megantoro et al., "Modeling the uncertainties and active power generation of wind-solar energy with data acquisition from telemetry weather measurement," Results in Engineering, vol. 25, Mar. 2025, Art. no. 104392.

P. Wais, "A review of Weibull functions in wind sector," Renewable and Sustainable Energy Reviews, vol. 70, pp. 1099–1107, Apr. 2017.

F. Homa, M. Khetan, Mohd. Arshad, and P. Mishra, Distribution theory: Principles and Applications, 1st ed. Boca Raton, Florida, USA: CRC Press, 2023.

J. A. R. Villaseñor, Frequency analyses of natural extreme events: A Spreadsheets Approach, 1st ed. Cham, Switzerland: Springer Nature, 2021.

M. Ebeed and Shady H. E. Abdel Aleem, "Overview of uncertainties in modern power systems: uncertainty models and methods," in Uncertainties in Modern Power Systems, Ahmed F. Zobaa and Shady H. E. Abdel Aleem, Eds., 1st ed. London, United Kingdom: Academic Press, 2021, ch. 1, pp. 1–34.

"Siemens SWT-3.0-108 - Manufacturers and turbines" The Wind Power, https://www.thewindpower.net/turbine_en_920_siemens_swt-3.0-108.php.

Canadian Solar, "TOPBiHiKu7 BIFACIAL TOPCON," CS7L-590TB-AG datasheet, Oct. 2022.