A Multilevel Domain Decomposition approach for solving time constrained Optimal Power Flow problems

Abstract

Solving Time Constrained Optimal Power Flow problems (TCOPF) is a major task for determining optimal extensions of a given power grid. When employing any gradient based optimization algorithm such as Interior Point Method or Sequential Quadratic Programming for TCOPF, the main computational effort lies in the solution of large and coupled linear systems. Even for medium-sized electrical networks and time periods in the range of a few days, these systems can contain several millions of equations. The corresponding matrix is block tri-diagonal with non-diagonal blocks corresponding to intertemporal couplings. In our work, we exploit this fact by using Schwarz preconditioning techniques in combination with iterative Krylov subspace methods such as GMRES for solving linear systems in parallel. We propose a way of applying these domain decomposition methods in context of TCOPF problems and present numerical experiments that illustrate their behaviour on two benchmark problems.