  In future smart grids, energy storage systems (ESSs) are expected to play a
key role in reducing peak hour electricity generation cost and the associated
level of carbon emissions. Considering their high acquisition, operation, and
maintenance costs, ESSs are likely to serve a large number of users. Hence,
optimal sizing of energy ESSs plays a critical role as over-provisioning ESS
size leads to under-utilizing costly assets and under-provisioning it taxes
operation lifetime. This paper proposes a stochastic framework for analyzing
the optimal size of energy storage systems. In this framework the demand of
each customer is modeled stochastically and the aggregate demand is
accommodated by a combination of power drawn from the grid and the storage unit
when the demand exceed grid capacity. In this framework an analytical method is
developed, which provides tractable solution to the ESS sizing problem of
interest. The results indicate that significant savings in terms of ESS size
can be achieved.
