Modeling and Analysis of Energy Micro-Grids Using Hybrid Petri Nets

Hybrid Petri nets (HPN) are frequently used to model and study hybrid systems, i.e. those with both discrete (events, state changes) and continuous (flows, changing physical variables) dynamics. In recent years, their field of application has been extended to energy systems, and in particular to the modeling of electrical microgrids. These microgrids are often powered by renewable energy sources, whose operation is variable and subject to environmental constraints. With this in mind, the present study suggests an HPN-based modeling technique to illustrate the operation of an electrical microgrid that integrates a photovoltaic installation associated with a battery storage system. The idea is to capture the complex interaction between various energy sources, storage units, energy demand and possible complementary sources. The associated mathematical model is based on a linear algebraic representation of type Ax ≤ b, which formalizes the system's constraints, tracks the evolution of its state over time, and anticipates its future behavior. Simultaneously, a state observer is developed with the intention of evaluating the current Petri net marking exclusively from observable results, in order to deduce an accurate estimate of the internal state. By comparing the simulation results with the estimation results, we are able to assess the robustness and accuracy of the suggested model. This research is part of an approach aimed at optimizing and intelligently supervising sustainable energy systems.