TY - JOUR

T1 - Solving Combined Optimal Transmission Switching and Optimal Power Flow sequentially as convexificated Quadratically Constrained Quadratic Program

AU - Leveringhaus, Thomas

AU - Kluß, Leonard

AU - Bekker, Iwo

AU - Hofmann, Lutz

N1 - Funding Information: Although there has been substantial progress in advanced methods for optimizing power systems in the last years [1] , the optimal power flow (OPF) [ 2,3 ] as well as its extensions is still challenging to solve today [4–6] . Basically, the associated power equations, interrelating the active and reactive powers with the nodal voltages, lead to nonlinearity and nonconvexity of the optimization problem. Extensions of the equations and the optimization exacerbate the challenges of solving. Although the aforementioned cited references are several years old, they still reflect the general state of the art and the persisting challenges, according to the best knowledge of the authors. Recent progress in research, worth mentioning according to the author's conviction, is discussed hereinafter: Convex relaxations of the power equations have attracted a lot of attention and revealed interesting insights and noticeable progress in the last years [7–12] . For radial networks even an exact convex relaxation has been found [13] . Reference [14] is seen as an up-to-date survey of the state of the art of relaxations of the Power Flow Equations. However, for meshed networks latest research has shown that the relaxation approaches developed so far lack of accuracy and feasibility [15] . Strengthening the relaxations and quickly and reliably tightening the lower and upper bounds during presolve and solve are still subject of research. The continuing necessity for research becomes apparent by the Grid Optimization Competition (GOC) most recently announced by the Advanced Research Projects Agency-Energy (ARPA-E) of the U.S. Department of Energy (DOE) [16] . The aim of the still running GOC is to accelerate the development of methods for solving the most pressing power system problems.

PY - 2022/11

Y1 - 2022/11

N2 - 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.

AB - 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.

KW - Convexification

KW - Network configurations

KW - Optimal power flow

KW - Optimized transmission switching

KW - Quadratically constrained quadratic program

UR - http://www.scopus.com/inward/record.url?scp=85134608011&partnerID=8YFLogxK

U2 - 10.1016/j.epsr.2022.108534

DO - 10.1016/j.epsr.2022.108534

M3 - Article

VL - 212

JO - Electric Power Systems Research

JF - Electric Power Systems Research

SN - 0378-7796

M1 - 108534

ER -