Adversarially and Distributionally Robust Virtual Energy Storage Systems via the Scenario Approach
This addresses the challenge of reliable and efficient virtual energy storage for prosumer communities and parking lot managers, offering a tunable profit-risk trade-off, but it is incremental as it builds on existing scenario approach methods.
The paper tackles the problem of aggregating parked electric vehicle batteries into virtual energy storage systems under uncertain departures and state-of-charge caps, proposing an optimization model that provides provably robust services with tight finite-sample certificates and demonstrating out-of-sample and out-of-distribution constraint satisfaction in numerical studies.
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.