Iterative solvers in the Newton power flow problem: Preconditioners, inexact solutions and partial Jacobian updates

A comparative study of available iterative solvers (for linear systems of equations) applied to the solution of the nonlinear Newton power flow problem is presented. Iterative solvers are combined with Newton's method and an optimal stopping strategy is included to obtain an efficient solution for large power systems. Using the solvers and preconditioners available in Matlab, it is shown that iterative solvers are more efficient than the direct LU solution for large power systems. An easy to implement refinement is the introduction of partial Jacobian updates to avoid additional computations when an equation has reached the convergence tolerance. For large power systems (3000 buses and more), we have obtained savings (in flops) in the order of 25% compared to the direct LU solution. A convergence characterisation of the Newton power flow based on the Jacobian's spectrum and its condition number is also presented.