Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

TL;DR

This paper develops an adaptive learning framework for distributionally robust incentive design in voltage regulation, addressing information asymmetry between the DSO and DERAs through iterative learning and robust optimization.

Contribution

It introduces a novel adaptive conservativeness mechanism using Wasserstein metric-based ambiguity sets for improved incentive design under uncertainty.

Findings

The proposed method effectively controls voltage regulation failure probability.

Adaptive conservativeness improves incentive strategies over iterations.

Numerical experiments validate the robustness and effectiveness of the approach.

Abstract

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.