An Electrical Grid with Discrete Energy Levels

Minimizing both power fluctuations and energy waste in an electrical grid is a central challenge to energy policy. Any discrepancy between power production and loads may lead to inefficiencies and instability in the system. While sensors and predictive models, which are based on historical data, have been implemented to make the grid more responsive to instabilities, they have difficulty addressing fluctuations in real time. Here we explore a model of an electrical grid which delivers discrete energy to the nodes and is supported by short-term energy storage units (STESU). The model is analyzed within the framework of randomly perturbed Markovian chain. We show that under reasonable assumptions the averaged energy in the grid maintains stability under randomly fluctuating energy conditions.