Solving Combined Optimal Transmission Switching and Optimal Power Flow sequentially as convexificated Quadratically Constrained Quadratic Program

Abstract

A novel approach to efficiently solve a combined optimal transmission switching and optimal power flow problem is derived and evaluated. The approach is based on a sequentially solved quadratically constrained quadratic program with a new way of convexification. This convexification requires adapted modeling and uses two procedural steps: First, nonlinear equality constraints are eliminated by quadratically approximating their inverse system of functions and inserting it into the objective function and into the inequality constraints. The resulting objective function and inequality constraints are approximated quadratically. Second, the remaining nonconvex parts of the objective function and the inequality constraints are identified by eigenvalue analysis of their Hessian matrices and eliminated by using piecewise linear approximations. Issues of accuracy and convergence are examined and countermeasures are presented. Additionally, the avoidance of islanding and the sequentiality of parallel circuits are considered. Case studies show fast und stable convergence of the approach.