A Domain Decomposition Approach for Solving Dynamic Optimal Power Flow Problems in Parallel with Application to the German Transmission Grid

Abstract

We propose a parallel solver for linear systems of equations arising from the application of Primal Dual Interior Point methods to Dynamic Optimal Power Flow problems. Our solver is based on the Generalized Minimal Residual method in combination with an additive Schwarz domain decomposition method as preconditioner. This preconditioner exploits the structure of Dynamic Optimal Power Flow problems which, after linearization, is given as block-tridiagonal matrix with large diagonal blocks and only few off-diagonal entries. These entries correspond to intertemporal couplings due to ramping and energy storage constraints and are partially neglected in order to induce parallelism. We test our method on a large-scale optimization problem based on data of the German transmission grid and show that a significant parallel speedup can be obtained.