# Newton–Krylov Power Flow Solver

Chapter
Part of the Atlantis Studies in Scientific Computing in Electromagnetics book series (ASSCE, volume 1)

## Abstract

Newton power flow solvers traditionally use a direct method to solve the linear systems. For large linear systems of equations with a sparse coefficient matrix, iterative linear solvers are generally more efficient than direct solvers. Using a Krylov method to solve the Jacobian systems in the Newton-Raphson method, leads to a Newton-Krylov method. In this chapter, computational aspects of Newton-Krylov power flow solvers are discussed. It is shown that direct solvers, and other methods using the LU factorisation, scale very badly in the problem size. The alternatives proposed in this chapter are faster for all tested problems and have near linear scaling, thus being much faster for large power flow problems. The largest test problem, with a million buses, takes over an hour to solve using a direct solver, while a Newton-Krylov solver can solve it in less than 30 seconds. That is 120 times faster.

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