A Probabilistic Theoric Framework for Uncertainty Cost Functions in Scheduling Optimization in Hybrid Renewable Microgrids

NONE 20260529105055868 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON MATHEMATICS 1109-2769 2224-2880 A Probabilistic Theoric Framework for Uncertainty Cost Functions in Scheduling Optimization in Hybrid Renewable Microgrids Carlos Sanchez Reinoso Grupo de Modelado, Optimización y Control (MOC), Universidad Tecnológica Nacional, Argentina Departamento de Ingeniería Electrica Y Electrónica, Universidad Nacional de Colombia COLOMBIA Sergio Raul Rivera Grupo de Modelado, Optimización y Control (MOC), Universidad Tecnológica Nacional, Argentina Departamento de Ingeniería Electrica Y Electrónica, Universidad Nacional de Colombia COLOMBIA In this paper is developed a mathematical framework for uncertainty quantification in energy systems through Uncertainty Cost Functions (UCFs), in order to schedule the operation. We establish probabilistic models for solar photovoltaic generation, wind energy generation, and plug-in electric vehicles, deriving exact expressions for expected penalty costs using measure-theoretic probability. The main results include existence theorems for UCFs, closed-form solutions under specific distributional assumptions, and optimal scheduling policy. 12 31 2025 12 31 2025 794 79 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/23206.2025.24.79 https://wseas.com/journals/mathematics/2025/b605106-039(2025).pdf A. Ferrero and D. Petri, ”Measurement Uncertainty and Information Enabled Decision Making,” in IEEE Open Journal of Instrumentation and Measurement, vol. 4, pp. 1-9, 2025, Art no. 1000409, https://doi.org/10.1109/OJIM.2025.3626105. T. Li, R. Song and X. Ye, ”Uncertainty Quantification and Calibration in Full-Wave Inverse Scattering Problems With Evidential Neural Networks,” in IEEE Transactions on Microwave Theory and Techniques, vol. 73, no. 9, pp. 6304-6316, Sept. 2025, https://doi.org/10.1109/TMTT.2025.3555256. D. Lee, D. Kim and S. -K. Joo, ”IntervalStochastic Programming for Integrated Generation, Transmission, and Energy Storage System (ESS) Planning Considering Uncertainty in Renewable Energy Sources,” in IEEE Access, vol. 13, pp. 30834-30844, 2025, https://doi.org/10.1109/ACCESS.2025.3538649. Y. Yao, Y. Xu, W. Gu, K. Liu, S. Lu and L. Mili, ”Inverse Uncertainty Quantification Assisted Forward Uncertainty Quantification in Power System Dynamic Simulations,” in IEEE Transactions on Power Systems, vol. 40, no. 5, pp. 4307-4321, Sept. 2025, https://doi.org/10.1109/TPWRS.2025.3537758. X. Yang, Y. Li, Y. Zhao, G. Hao, T. Ishizaki and Z. Zeng, ”Hierarchical Uncertainty Characterization of Monthly Net Load in Renewable Power Systems,” in IEEE Transactions on Automation Science and Engineering, vol. 22, pp. 3515-3527, 2025, https://doi.org/10.1109/TASE.2024.3395634. N. Talebpour and M. Ilbeigi, ”Modeling and Predicting Uncertainty in Tidal Turbine Power Output: A Data-Driven Time-Series Approach,” in IEEE Access, vol. 13, pp. 82986-82994, 2025, https://doi.org/10.1109/ACCESS.2025.3567884. Y. Cui, Y. Xu, Y. Wang, Y. Li and Y. Zhao, ”Multi-Microgrid Optimization Operation Strategy Considering Nonlinear Conditions and Renewable Energy Uncertainty: A Data-Driven Method,” in IEEE Transactions on Industry Applications, vol. 61, no. 1, pp. 1533-1545, Jan.-Feb. 2025, https://doi.org/10.1109/TIA.2024.3371966. W. Liu, R. -p. Liu, S. Chen, Q. Wang and Z. Yang, ”Data-Driven Energy and Reserve Management of Prosumers Under Multi-Uncertainties,” in IEEE Transactions on Industry Applications, vol. 61, no. 2, pp. 2759-2769, March-April 2025, https://doi.org/10.1109/TIA.2024.3462667. M. Yang, R. Xie, Y. Zhang and Y. Chen, ”Robust Microgrid Dispatch With Real-Time Energy Sharing and Endogenous Uncertainty,” in IEEE Transactions on Smart Grid, vol. 16, no. 4, pp. 3085-3098, July 2025, https://doi.org/10.1109/TSG.2025.3569095. T. Alharbi, A. Abdalrahman, M. H. Mostafa and L. Alkhalifa, ”Joint Optimization of EV Charging and Renewable Distributed Energy With Storage Systems Under Uncertainty,” in IEEE Access, vol. 13, pp. 76838-76856, 2025, https://doi.org/10.1109/ACCESS.2025.3562531. J. Yu, P. Yong, Z. Yang and J. Yu, ”StochasticRobust Optimal Power Flow With Small-Signal Stability Guarantee Under Renewable Uncertainties,” in IEEE Transactions on Sustainable Energy, vol. 16, no. 3, pp. 1711-1722, July 2025, https://doi.org/10.1109/TSTE.2025.3529254. R. P. B. Poubel, M. C. S. Perpétuo and W. Peres, ”Probabilistic Transmission Expansion Planning Under Renewable and Load Uncertainty,” in IEEE Access, vol. 13, pp. 151275-151288, 2025, https://doi.org/10.1109/ACCESS.2025.3600866. N. Sakib, M. A. Hosen, B. Khan, B. Gunn and M. Johnstone, ”Prediction Interval in Renewable Energy Forecasting: A Comprehensive Review of Uncertainty Quantification Methods,” in IEEE Access, vol. 13, pp. 185466-185492, 2025, https://doi.org/10.1109/ACCESS.2025.3625924.