Adaptive robust unit commitment considering distributional uncertainty

Abstract

To reduce the conservativeness of robust optimization-based unit commitment methods, an uncertainty set is usually prespecified with respect to the distributions of uncertain renewable resources, i.e., wind power. However, since the law of large numbers does not always work in practice, the obtained probability distribution may be unreliable. In this paper, a data-driven adaptive robust optimization method for the unit commitment of bulk power systems with high-level wind power integration is proposed. Different from the conventional robust unit commitment methods, the distributional uncertainty of wind power is well respected in the proposed approach. An imprecise-Dirichlet-model-based method is developed to construct the ambiguity set of wind power, which incorporates all possible probability distributions confirmed by historical data. The set can dynamically change with the data, i.e., the more valid data we have, the smaller the ambiguity set will become. With respect to the bounds of the ambiguity set, a polyhedron uncertainty set of wind power is constructed. By tuning the parameters of the uncertainty set, a balance between operational efficiency and risk can be achieved. An adaptive, robust unit commitment model is constructed based on the uncertainty set. By using the duality principle and big-M method, the formulations are converted into a mixed integer linear programming problem and solved using a column and constraint generation algorithm. Case studies on two benchmark systems illustrate the effectiveness and efficiency of the proposed method.