Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation
<|reference_start|>Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.<|reference_end|>
@article{liang2024learning,
    title={Learning with Adaptive Conservativeness for Distributionally Robust
  Optimization: Incentive Design for Voltage Regulation},
    author={Zhirui Liang, Qi Li, Joshua Comden, Andrey Bernstein, Yury Dvorkin},
    journal={arXiv preprint arXiv:2408.02765},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.02765},
    primaryClass={eess.SY cs.SY}
}