On Robust Optimization, Blackouts and the Law

Vehicle-to-grid is a concept for mitigating the growing storage demand of electricity grids by using the batteries of parked electric vehicles for providing frequency regulation. Vehicles owners offering frequency regulation promise to charge or discharge their batteries whenever the grid frequency deviates from its nominal value, and they must be able to honor their promises for all frequency deviation trajectories that satisfy certain properties prescribed by EU law. We show that the relevant EU regulations can be encoded exactly in a robust optimization model, and we use this model to demonstrate that the penalties for non-compliance with market rules are currently too low. This suggests that “crime pays” and that the stability of the electricity grid is jeopardized if many frequency providers abuse the system, which could ultimately result in blackouts. The decision problem of a vehicle owner constitutes a non-convex robust optimization problem affected by functional uncertainties. By exploiting the structure of the uncertainty set and exact linear decision rules, however, we can prove that this problem is equivalent to a tractable linear program. Through numerical experiments based on data from France, we quantify the economic value of vehicle-to-grid and elucidate the financial incentives of vehicle owners, aggregators, equipment manufacturers, and regulators. The proposed robust optimization model is relevant for a range of applications involving energy storage.