Stochastic Hybrid Automata for Power Profile Modeling in Energy Systems

RESUMO

Power profiles are widely used to describe power demand and production in energy systems. Yet, real-world usage often involves uncertainty, making it challenging to determine, e.g., whether a battery can reliably meet a given profile. Formal modeling enables the computation of probabilities that a battery will satisfy such demands. Given the combination of discrete and continuous dynamics, along with uncertain usage patterns, stochastic hybrid automata (SHA) offer a suitable framework for such modeling and analysis. In this paper, we formalize two orthogonal approaches to specify the (uncertain) power profiles that a specific battery can serve as well as a storage model. For both types of power profiles, we provide formal construction rules for SHA reflecting the behavior of the storage model given a specific power profile. We analyze how design choices, such as the power profile, storage model, and representation of uncertainty, affect the complexity of the resulting SHA. Finally, we demonstrate how these models quantify feasibility using the tools Modest and realyst, and assess how the analysis scales with profile size and the number of stochastic components.