Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to the electricity grid. We formulate a robust optimization problem with functional uncertainties that maximizes the expected profit from selling primary frequency regulation to the grid and guarantees that vehicle owners can meet their market commitments for all frequency deviation trajectories in an uncertainty set that encodes applicable EU legislation. Faithfully modeling the energy conversion losses during battery charging and discharging renders this optimization problem non-convex. By exploiting a total unimodularity property of the proposed uncertainty sets and an exact linear decision rule reformulation, we prove that this non-convex robust optimization problem with functional uncertainties is equivalent to a tractable linear program. Through extensive numerical experiments based on real-world data, we faithfully quantify the value of vehicle-to-grid, which helps us to understand the economic incentives of vehicle owners, aggregators, equipment manufacturers and regulators.
Technical Report, Ecole polytechnique fédérale de Lausanne, September/2021