Day-ahead Network-constrained Unit Commitment Considering Distributional Robustness and Intraday Discreteness: A Sparse Solution Approach

Quick-start generation units are critical devices and flexible resources to ensure a high penetration level of renewable energy in power systems. By considering the wind uncertainty and both binary and continuous decisions of quick-start generation units within the intraday dispatch, we develop a Wasserstein-metric-based distributionally robust optimization model for the day-ahead network-constrained unit commitment (NCUC) problem with mixed-integer recourse. We propose two feasible frameworks for solving the optimization problem. One approximates the continuous support of random wind power with a finite number of events, and the other leverages the extremal distributions instead. Both solution frameworks rely on the classic nested column-and-constraint generation (C&CG) method. It is shown that due to the sparsity of $L_{1}$-norm Wasserstein metric, the continuous support of wind power generation could be represented by a discrete one with a small number of events, and the rendered extremal distributions are sparse as well. With this reduction, the distributionally robust NCUC model with complicated mixed-integer recourse problems can be efficiently handled by both solution frameworks. Numerical studies are carried out, demonstrating that the model considering quick-start generation units ensures unit commitment (UC) schedules to be more robust and cost-effective, and the distributionally robust optimization method captures the wind uncertainty well in terms of out-of-sample tests.