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.