Bayesian Nonparametric Two-Stage Distributionally Robust Unit Commitment Optimization: From Global Multimodality to Local Trimming-Wasserstein Ambiguity

Uncertainty brought by the deep penetration of renewable energy has imposed great challenges on the operation of power systems. Accurately characterizing the global-local features of an unknown uncertainty distribution is crucial for making operation decisions that are both distributionally robust and economically efficient. To this end, this paper proposes a novel data-driven Bayesian nonparametric two-stage distributionally robust optimization (BN-TSDRO) framework for unit commitment (UC) problems under uncertainty. We first leverage a Bayesian nonparametric mixture model to decompose the complex uncertainty distribution into local mixture components. Subsequently, a novel mixture ambiguity set is cast as the weighted Minkowski sum of several local ambiguity sets, which accurately characterize the distributional ambiguity of each mixture component. Specifically, by leveraging a novel probability trimming method and the celebrated Wasserstein metric, the local ambiguity set encodes information from both the Bayesian inference and the data, thus mitigating conservatism remarkably. To efficiently solve the resulting UC problem under the BN-TSDRO framework, we employ the duality theory and the sample average approximation to reformulate it into a mixed-integer linear program, upon which a complete solution algorithm is further developed. Numerical experiments on three representative test systems demonstrate the effectiveness and scalability of the proposed framework compared with state-of-the-art methods in both in-sample and out-of-sample performances.