A Connectivity Constrained MILP Model for Optimal Transmission Switching
Peijie Li, Xiaoqian Huang, Junjian Qi, Hua Wei, Xiaoqing Bai
Abstract
This letter formulates network connectivity as Miller-Tucker-Zemlin (MTZ) constraints and incorporates them into the mixed-integer linear programming (MILP) model for the optimal transmission switching (OTS) problem. The connectivity constraints are linear and for a power network with n buses, m branches, and d loads in pre-contingency or each post-contingency state there are approximately <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (n+5m+d) constraints, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (n) continuous and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (2 m) binary variables, which is much smaller than those in the existing formulations. The MILP OTS model with the proposed connectivity constraints can be readily solved by well-developed MILP solvers. Case studies on the PJM 5-bus system, IEEE 300-bus system, and French 1888-bus system validate the effectiveness of the proposed model.