A Distributionally Robust Optimization Approach for Unit Commitment in Microgrids

TL;DR

This paper introduces a distributionally robust unit commitment method for microgrids that accounts for uncertainties in load and prices by using Kullback-Leibler divergence, historical data, and clustering techniques to improve decision-making.

Contribution

It presents a novel distributionally robust optimization framework utilizing KL divergence and clustering to better handle uncertainties in microgrid unit commitment problems.

Findings

The proposed method outperforms traditional stochastic models under various divergence levels.

Efficient two-level decomposition enables practical solution of the complex optimization problem.

Clustering-based data processing enhances the robustness of the unit commitment decisions.

Abstract

This paper proposes a distributionally robust unit commitment approach for microgrids under net load and electricity market price uncertainty. The key thrust of the proposed approach is to leverage the Kullback-Leibler divergence to construct an ambiguity set of probability distributions and formulate an optimization problem that minimizes the expected costs brought about by the worst-case distribution in the ambiguity set. The proposed approach effectively exploits historical data and capitalizes on the k-means clustering algorithm, in conjunction with the soft dynamic time warping score, to form the nominal probability distribution and its associated support. A two-level decomposition method is developed to enable the efficient solution of the devised problem. We carry out representative studies and quantify the relative merits of the proposed approach vis-\`a-vis a stochastic optimization-based model under different divergence tolerance values.