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.

Linear Power Flow Method Improved With Numerical Analysis Techniques Applied to a Very Large Network

“…After the computation, original V 2 is calculated as V 2 = V r 2 + ıV m 2 using the computed real V r 2 and imaginary parts V m 2 in Equation (15). In this case, we double the size of the equations but can avoid the complex numbering.…”

“…In this subsection, we consider the LLPF problem with complex components Equations (9) and (15). For simplicity, let us denote the matrix…”

“…Several reviews on distribution power flow solution methods can be found in References [10][11][12].All iterative power flow solution methods use a direct solver eventually for the linearized NPF problem in every iteration. It has been shown that iterative linear solvers can result in faster performances over sparse direct solvers for very large power flow problems [13][14][15]. In other words, the computational time of NPF computations can be improved by studying the properties of the linear system solved in every iteration and applying Numerical Analysis (NA) techniques such as different reordering schemes, various direct solvers and numerous Krylov subspace methods on them.Another way to ease the calculation and to speed up the computational time is to linearize NPF equations using some approximations and assumptions in order to obtain the Linear Power Flow (LPF) equations.…”

“…All iterative power flow solution methods use a direct solver eventually for the linearized NPF problem in every iteration. It has been shown that iterative linear solvers can result in faster performances over sparse direct solvers for very large power flow problems [13][14][15]. In other words, the computational time of NPF computations can be improved by studying the properties of the linear system solved in every iteration and applying Numerical Analysis (NA) techniques such as different reordering schemes, various direct solvers and numerous Krylov subspace methods on them.…”