A Connectivity Constrained MILP Model for Optimal Transmission Switching

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 <inline-formula><tex-math notation= LaTeX >$n$</tex-math></inline-formula> buses, <inline-formula><tex-math notation= LaTeX >$m$</tex-math></inline-formula> branches, and <inline-formula><tex-math notation= LaTeX >$d$</tex-math></inline-formula> loads in pre-contingency or each post-contingency state there are approximately <inline-formula><tex-math notation= LaTeX >$\\mathcal {O}(n+5m+d)$</tex-math></inline-formula> constraints, and <inline-formula><tex-math notation= LaTeX >$\\mathcal {O}(n)$</tex-math></inline-formula> continuous and <inline-formula><tex-math notation= LaTeX >$\\mathcal {O}(\\text{2 m})$</tex-math></inline-formula> 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.