Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Georgios Pantazis, Nicola Mignoni, Raffaele Carli, Mariagrazia Dotoli, Sergio Grammatico

TL;DR

This work addresses robust provision of virtual energy storage by aggregating parked EV batteries through a data-driven, convex optimization framework. It leverages the scenario approach to obtain finite-sample, out-of-sample guarantees on constraint satisfaction and extends to adversarial perturbations and Wasserstein-based distributional shifts, with a tunable risk parameter to balance profit and reliability. The key contributions include convex formulation for VESS under uncertainty, a priori and a posteriori safety certificates, and a distributionally robust extension that accounts for both data poisoning and distributional drift, all supported by finite-sample bounds. Numerical studies validate the theoretical guarantees, showing robust performance against unseen departures and capacity variations and illustrating practical profit–risk trade-offs for parking lot operators, prosumers, and retailers.

Abstract

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.

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

TL;DR

This work addresses robust provision of virtual energy storage by aggregating parked EV batteries through a data-driven, convex optimization framework. It leverages the scenario approach to obtain finite-sample, out-of-sample guarantees on constraint satisfaction and extends to adversarial perturbations and Wasserstein-based distributional shifts, with a tunable risk parameter to balance profit and reliability. The key contributions include convex formulation for VESS under uncertainty, a priori and a posteriori safety certificates, and a distributionally robust extension that accounts for both data poisoning and distributional drift, all supported by finite-sample bounds. Numerical studies validate the theoretical guarantees, showing robust performance against unseen departures and capacity variations and illustrating practical profit–risk trade-offs for parking lot operators, prosumers, and retailers.

Abstract

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.

Paper Structure

This paper contains 9 sections, 4 theorems, 32 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Challenges and Main Contributions
  3. Problem Formulation
  4. Robust Virtual Energy Storage Services
  5. Profit vs Risk in EV Parking Lot Management
  6. Distributionally Robust Virtual Storage Services
  7. EV Departures and Capacity Distributional Shifts
  8. Numerical Study
  9. Conclusion

Key Result

Lemma 1

Consider the data-driven program eq:PLM-N with $N > 2K$. Then, the following holds: with $\varepsilon \in [0,1]$ being a violation level upper bound set by the PLM.

Figures (5)

  • Figure 1: The parking lot manager (PLM) leverages the available storage of the parked EVs, as agreed with the EV users, to provide virtual energy storage services to a community of prosumers. Furthermore, the PLM is allowed to trade energy with retailers.
  • Figure 2: Trade-off stydy between adversarially robust empirical probability of violation vs the profit of the PLM for varying values of $R$.
  • Figure 3: Optimal virtual state of charge $b_k$ of the PLM's energy buffer at each time step $k$.
  • Figure 4: Optimal energy $r_k$ sold to the retailer at each time step $k$.
  • Figure 5: Empirical distributional violations among $N'=40$ different distribution perturbations from the ambiguity set.

Theorems & Definitions (11)

  • Remark 1
  • Remark 2
  • Definition 1: Support constraints/ samples
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Definition 2
  • ...and 1 more