Robust transmission constrained unit commitment: A column merging method

With the rapid integration of power sources with uncertainty, robustness must be carefully considered in the transmission constrained unit commitment (TCUC) problem. The overall computational complexity of the robust TCUC methods is closely related to the vertex number of the uncertainty set. The vertex number is further associated with: (i) the period number in the scheduling horizon, (ii) the number of nodes with uncertain power injections. In this study, a column merging method (CMM) is proposed to reduce the computational burden by merging the uncertain nodes, while still guaranteeing the robustness of the solution. By the CMM, the transmission constraints are modified, with the parameters obtained based on an analytical solution of a uniform approximation problem, so that the computational time for obtaining the modified constraints is negligible. The CMM is applied under a greedy-algorithm-based framework, where the number of merged nodes and the approximation error can be well balanced. The CMM is designed as a preprocessing tool to improve the solution efficiency for robust TCUC problems and is compatible with many solution methods (like two-stage and multi-stage robust optimisation methods). Numerical tests show the method is effective.