Probability Distribution of Solar Radiation to Determine the Output Power of the PV System Under Uncertain Conditions
Published online: 16/03/2026
Corressponding author's email:
ntan@hcmute.edu.vnDOI:
https://doi.org/10.54644/jte.2026.1980Keywords:
Solar irradiance, Solar irradiance uncertainty, Probability distribution, Beta distribution, Solar Power outputAbstract
This study introduces a probabilistic modeling framework for solar irradiance that aims to enhance the output power stability of photovoltaic (PV) systems by explicitly accounting for the stochastic nature of solar radiation. Real – world irradiance measurements are first preprocessed and smoothed to remove noise and short – term fluctuations, thereby improving the reliability of statistical estimation. Three probability distributions Weibull, Beta, and Lognormal – are modeled, with their parameters estimated through the Maximum Likelihood Estimation (MLE) method. The suitability of each distribution is assessed using multiple statistical performance indicators, including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R²). Comparative analysis reveals that the Beta distribution provides the highest degree of fit and the lowest prediction error, making it the most appropriate model for representing the temporal variability of solar irradiance in the given dataset. Synthetic irradiance samples generated from the optimal distribution are subsequently integrated into a 250 kW grid – connected PV array model implemented in MATLAB/Simulink to evaluate power output characteristics under uncertain meteorological conditions. Simulation results confirm the method’s ability to capture dynamic fluctuations in solar energy availability and support robust power prediction. The proposed approach can assist in power system analysis, operational planning, and decision-making for PV integration, thereby contributing to improved grid stability and energy management strategies in renewable-rich environments.
Downloads: 0
References
N. Md. Saad et al., “Solar irradiance uncertainty management based on Monte Carlo-beta probability density function: case in Malaysian tropical climate,” Bulletin of Electrical Engineering and Informatics, vol. 8, no. 3, pp. 1135–1143, Sep. 2019, doi: 10.11591/EEI.V8I4.1581.
S. Coppolino, “Validation of a very simple model for computing global solar radiation in the European, African, Asian and North American areas,” Solar & Wind Technology, vol. 7, no. 4, pp. 489–494, Jan. 1990, doi: 10.1016/0741-983X(90)90034-Y.
B. Y. H. Liu and R. C. Jordan, “The interrelationship and characteristic distribution of direct, diffuse and total solar radiation,” Solar Energy, vol. 4, no. 3, pp. 1–19, Jul. 1960, doi: 10.1016/0038-092x(60)90062-1.
J. A. Olseth and A. Skartveit, “A probability density model for hourly total and beam irradiance on arbitrarily orientated planes,” Solar Energy, vol. 39, no. 4, pp. 343–351, 1987, doi: 10.1016/s0038-092x(87)80020-8.
M. U. Afzaal et al., “Probabilistic Generation Model of Solar Irradiance for Grid Connected Photovoltaic Systems Using Weibull Distribution,” Sustainability, vol. 12, no. 6, p. 2241, Mar. 2020, doi: 10.3390/su12062241.
L. Garbai and Z. Kovacs, “The estimation and forecast of solar energy yield with Weibull distribution,” International Review of Applied Sciences and Engineering, vol. 13, no. 3, pp. 247–256, Oct. 2022, doi: 10.1556/1848.2021.00344.
H. F. Assuncao, J. F. Escobedo, and A. P. Oliveira, “Modelling frequency distributions of 5 minute-averaged solar radiation indexes using Beta probability functions,” Theoretical and Applied Climatology, vol. 75, no. 3–4, pp. 213–224, Sep. 2003, doi: 10.1007/s00704-003-0733-9.
F. Youcef Ettoumi, A. Mefti, A. Adane, and M. Y. Bouroubi, “Statistical analysis of solar measurements in Algeria using beta distributions,” Renewable Energy, vol. 26, no. 1, pp. 47–67, May 2002, doi: 10.1016/s0960-1481(01)00100-8.
M. S. Rawat and S. Vadhera, “Impact of Photovoltaic Penetration on Static Voltage Stability of Distribution Networks: A Probabilistic Approach,” Asian Journal of Water, Environment and Pollution, vol. 15, no. 3, pp. 51–62, Aug. 2018, doi: 10.3233/ajw-180043.
Z. M. Salameh, B. S. Borowy, and A. R. A. Amin, “Photovoltaic module-site matching based on the capacity factors,” IEEE Transactions on Energy Conversion, vol. 10, no. 2, pp. 326–332, Jun. 1995, doi: 10.1109/60.391899.
A. Soroudi, M. Aien, and M. Ehsan, “A Probabilistic Modeling of Photo Voltaic Modules and Wind Power Generation Impact on Distribution Networks,” IEEE Systems Journal, vol. 6, no. 2, pp. 254–259, Jun. 2012, doi: 10.1109/jsyst.2011.2162994.
“Forecasting of Solar Irradiance using Probability Distributions for a PV System: A Case Study,” International Journal of Renewable Energy Research, no. v9i2, 2019, doi: 10.20508/ijrer.v9i2.9216.g7643.
T. R. Ayodele, “Determination of Probability Distribution Function for Modelling Global Solar Radiation: Case Study of Ibadan, Nigeria,” International Journal of Applied Science and Engineering, vol. 13, no. 3, pp. 233–245, Sep. 2015, doi: 10.6703/IJASE.2015.13(3).233.
A. Abdulkarim, S. M. Abdelkader, and D. J. Morrow, “Statistical Analyses of Wind and Solar Energy Resources for the Development of Hybrid Microgrid,” Springer, Cham, doi: 10.1007/978-3-319-16901-9_2
A. Sedić, D. Pavković, and M. Firak, “A methodology for normal distribution-based statistical characterization of long-term insolation by means of historical data,” Solar Energy, vol. 122, pp. 440–454, Dec. 2015, doi: 10.1016/J.SOLENER.2015.09.014.
I. J. Myung, “Tutorial on maximum likelihood estimation,” Journal of Mathematical Psychology, vol. 47, no. 1, pp. 90–100, Feb. 2003, doi: 10.1016/S0022-2496(02)00028-7.
W. S. Cleveland, “Robust Locally Weighted Regression and Smoothing Scatterplots,” Journal of the American Statistical Association, vol. 74, no. 368, pp. 829–836, Dec. 1979, doi: 10.1080/01621459.1979.10481038.
P. A. Costa, B. M. L. A. Costa, G. Rozenbaum, and P. Barreto-Coelho, “Anti-Ma paraneoplastic opsoclonus–myoclonus syndrome,” BMJ Case Reports, vol. 14, no. 5, p. e243136, May 2021, doi: 10.1136/bcr-2021-243136.
P. P. Biswas, P. N. Suganthan, and G. A. J. Amaratunga, “Optimal power flow solutions incorporating stochastic wind and solar power,” Energy Conversion and Management, vol. 148, pp. 1194–1207, Sep. 2017, doi: 10.1016/j.enconman.2017.06.071.
M. Teimouri, S. M. Hoseini, and S. Nadarajah, “Comparison of estimation methods for the Weibull distribution,” Statistics, vol. 47, no. 1, pp. 93–109, Feb. 2013, doi: 10.1080/02331888.2011.559657.
A. Tatachar, “Comparative Assessment of Regression Models Based On Model Evaluation Metrics,” International Research Journal of Engineering and Technology (IRJET), vol. 8, no. 9, pp. 853-860, Sep. 2021.
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2026 Journal of Technical Education Science
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright © JTE.
