Fluid Approximation of Smart Grid Systems: Optimal Control of Energy Storage Unit

A model of the smart grid system with two different energy sources - the main grid and the energy storage units - is considered. The arriving power demands can be activated by either type of energy sources, with differing rates and costs. Finding an optimal policy that minimizes the expected long-run operational cost of the system is the main interest of this work. The problem is considered in a so called heavy traffic regime, and is solved using fluid approximation techniques. The formal scaling limit of the problem leads to a simple deterministic optimization problem, whose solution is shown to be an achievable lower bound on the limiting cost of the stochastic problem. Three different scenarios are considered according to whether the batteries are disposable or rechargeable and whether the arrival rates are homogeneous or nonhomogeneous. The solution method provides a good alternative to numerical methods such as Markov Decision Processes.