Adversarially and Distributionally Robust Virtual Energy Storage Systems via the Scenario Approach

We propose an optimization model where a parking lot manager (PLM) can aggregate parked EV batteries to provide virtual energy storage services that are provably robust under uncertain EV departures and state-of-charge caps. Our formulation yields a data-driven convex optimization problem where a prosumer community agrees on a contract with the PLM for the provision of storage services over a finite horizon. Leveraging recent results in the scenario approach, we certify out-of-sample constraint safety. Furthermore, we enable a tunable profit-risk trade-off through scenario relaxation and extend our model to account for robustness to adversarial perturbations and distributional shifts over Wasserstein-based ambiguity sets. All the approaches are accompanied by tight finite-sample certificates. Numerical studies demonstrate the out-of-sample and out-of-distribution constraint satisfaction of our proposed model compared to the developed theoretical guarantees, showing their effectiveness and potential in robust and efficient virtual energy services.