  An important function of aggregators is to enable the participation of small
energy storage units in electricity markets. This paper studies two generally
overlooked aspects related to aggregators of energy storage: i) the
relationship between the aggregator and its constituent storage units and ii)
the aggregator's effect on system welfare. Regarding i), we show that
short-term outcomes can be Pareto-inefficient: all players could be better-off.
In practice, however, aggregators and storage units are likely to engage in
long rather than short-term relationships. Using Nash Bargaining Theory, we
show that aggregators and storage units are likely to cooperate in the
long-term. A rigorous understanding of the aggregator-storage unit relationship
is fundamental to model the aggregator's participation in the market. Regarding
ii), we first show that a profit-seeking energy storage aggregator is always
beneficial to the system when compared to a system without storage, regardless
of size or market power the aggregator may have. However, due to market power,
a monopolist aggregator may act in a socially suboptimal manner. We propose a
pricing scheme designed to mitigate market power abuse by the aggregator. This
pricing scheme has several important characteristics: its formulation requires
no private information, it incentivizes a rational aggregator to behave in a
socially optimal manner, and allows for regulation of the aggregator's profit.
