Modeling Transmission Line Constraints in Two-Stage Robust Unit Commitment Problem

Integration of renewable energy sources and demand response poses new challenges to system operators as they increase the uncertainty of the power supply and demand. Recently, robust optimization techniques are applied to the unit commitment problem with uncertainty as an alternative to the stochastic programming approaches. However, it remains challenging to solve the robust unit commitment model with full transmission line constraints. In this paper, we propose novel acceleration techniques for solving two-stage robust unit commitment problem with consideration of full transmission line constraints. We use 1) the cutting-plane algorithm for the master problem, which dynamically includes critical transmission line constraints, and 2) column-generation methods, including the branch-and-price-and-cut algorithm and heuristic approaches, for the subproblems, which add only necessary transmission line dual variables on the fly. Computational results for the modified IEEE 118-bus system show that the combination of the cutting-plane algorithm and the heuristic column-generation approach greatly reduces the total solution time of the two-stage robust unit commitment problem.