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.

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