Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

revision under review
  • This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the Convex Quadratic relaxation of the Optimal Transmission Switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the Optimal Transmission Switching problem in Power Systems. Using the proposed improvements, along with bound propagation, on 23 medium-size test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on 5 instances. The tightened model has promising computational results when compared to state-of-the-art formulations.
Author:Ksenia BestuzhevaORCiD, Hassan Hijazi, Carleton Coffrin
Document Type:Article
Parent Title (English):INFORMS Journal on Computing
Year of first publication:2019