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Extremal-Distribution-Based Cutting Plane Algorithm for Efficiently Solving Two-Stage Distributionally Robust Unit Commitment Problems

The increasing penetration of renewable generation has introduced significant uncertainties to the power system. In order for system operators to derive a robust and efficient operation scheme, skilled decision-making methods are vital. In this paper, we present a distributionally robust unit com-mitment model, where the renewable generation is modeled as a bounded right-hand-side random vector. The model is built on a data-driven ambiguity set that exploits the expectation and probability density of random renewable generation. We first verify that a discrete extremal distribution always exists in such a model. Then, an extremal-distribution-based algorithmic framework is developed to efficiently handle the problem. The novel solution algorithm is shown to have a higher convergence rate theoretically, and perform faster practically compared with Benders-type algorithms. In the numerical experiments, we demonstrate the way of obtaining an extremal distribution, and validate the computational efficiency of our solution algorithm.