Solving the nonlinear power flow equations with an inexact Newton method using GMRES

Abstract

This paper presents a detailed investigation into the effectiveness of iterative methods in solving the linear system subproblem of a Newton power flow solution process. An exact Newton method employing an LU factorization has been one of the most widely used power flow solution algorithms, due to the efficient minimum degree ordering techniques that attempt to minimize fill-in. However, the LU factorization remains a computationally expensive task that can be avoided by the use of an iterative method in solving the linear subproblem. An inexact Newton method with a preconditioned Generalized Minimal Residual (GMRES) linear solver is presented as a promising alternative for solving the power flow equations. When combined with a good quality preconditioner, the Newton-GMRES method achieves a better than 50% reduction in computation, compared to Newton-LU, for two large-scale power systems: one with 3493 buses and 6689 branches, another with 8027 buses and 13765 branches.