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

Abstract

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.