On convergence of Newton's method for load flow problems

The Kantorovich theorem is virtually the only known sufficiency condition for convergence of Newton's method on a set of non‐linear equations. The theorem gives very conservative bounds and is difficult to apply. In this paper the power system load flow problem is solved by Newton's method, and a sufficiency condition for the convergence of the iterations on this particular problem is given. The criterion relates to a condition number defined on the Jacobian matrix associated with the non‐linear equations. Computational feasibility is considered and the merits of its use are discussed.