Globalized Newton–Krylov–Schwarz AC Load Flow Methods for Future Power Systems

Abstract

The load flow equations express the balance of power in an electrical power system. The power generated must equal the power consumed. In the AC time-harmonic case, the load flow equations are non-linear in the voltage phasors associated with the nodes in the network. The development of future power systems urgently requires new, highly efficient and robust load flow solvers. In this contribution we aim at making the following three scientific contributions. We first show that the use of a globalization procedure is required to ensure the convergence of a Newton load flow simulation of a stressed network. Such operational conditions are more likely to occur in the future. We subsequently show that the use of an inexact Newton–Krylov method results in faster computations. We employ Quotient Minimal Degree (QMD) as a matrix reordering method, incomplete LU factorization (ILU) as a preconditioner, Generalized Minimal Residual (GMRES) as a Krylov acceleration, and the Dembo-Steihaus strategy to defined the accuracy of the linear solver at each Newton iteration. We finally show the results of iterative solution algorithms that allow to exploit the decomposition of a network into subnetworks. Decompositions with and without overlapping nodes are tested.