Newton-Type Methods for Solution of the Electric Network Equations

Abstract

Electric newtork equations give rise to interesting mathematical models that must be faced with efficient numerical optimization techniques. Here, the classical power flow problem represented by a nonlinear system of equations is solved by inexact Newton methods in which each step only approximately satisfies the linear Newton equation. The problem of restoring solution from the prior one comes when no real solution is possible. In this case, a constrained nonlinear least squares problem emerges and Newton and Gauss Newton methods for this formulation are employed.