Optimal transmission switching with uncertainties from both renewable energy and N-k contingencies

This paper focuses on the N −k security-constrainedoptimal transmission switching (OTS) problem for variable renewable energy (VRE) penetrated power grids. A new three-stagestochastic and distributionally robust OTS model is proposed.The first stage has the primary purpose to schedule the powergeneration and network topology based on the forecast of VRE.The second stage controls the power generation and voltagemagnitudes of voltage-controlled buses in response to VREuncertainty, and the third stage reacts to N −k contingenciesadditionally by line switching and load shedding. The VREand N − k contingencies, considering different availability oftheir probability distributions, are tackled by stochastic anddistributionally robust optimization, respectively. By adoptingstage-wise realization of uncertainties in VRE and contingencies,the associated corrective controls with different mechanisms canbe handled separately and properly, which makes the proposedOTS model more realistic than existing two-stage ones. Forsolving the proposed OTS model, its tractable reformulationis derived, and a solution approach that combines the nestedcolumn-and-constraint generation algorithm and Dantzig–Wolfeprocedure is developed. Finally, case studies include a simpleIEEE network for illustrative purposes and then real systemnetworks to demonstrate the efficacy of the proposed approach.