A Distributionally Robust Optimization Approach to Unit Commitment in Microgrids

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 cost 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.