  The rapid and massive diffusion of electric vehicles poses new challenges to
the electric system, which must be able to supply these new loads, but at the
same time opens up new opportunities thanks to the possible provision of
ancillary services. Indeed, in the so-called Vehicle-to-Grid (V2G) set-up, the
charging power can be modulated throughout the day so that a fleet of vehicles
can absorb an excess of power from the grid or provide extra power during a
shortage.To this end, many works in the literature focus on the optimization of
each vehicle daily charging profiles to offer the requested ancillary services
while guaranteeing a charged battery for each vehicle at the end of the day.
However, the size of the economic benefits related to the provision of
ancillary services varies significantly with the modeling approaches, different
assumptions, and considered scenarios. In this paper we propose a profitability
analysis with reference to a recently proposed framework for V2G optimal
operation in presence of uncertainty. We provide necessary and sufficient
conditions for profitability in a simplified case and we show via simulation
that they also hold for the general case.
