Application of Fixed-Point Techniques to Load-Flow Studies

A fixed-point formulation is used to show that the Gauss-Seidel procedure and the Newton method for solving load- flow problems are similar successive-approximation methods differing only slightly in the form of their iteration functions. The added insight gained by this fixed-point formulation shows that the range of the Gauss-Seidel procedure is severely limited, and why convergence takes many iterations. A modified Newton method is also presented which eliminates the repeated inversion of the Jacobian matrix, as required by the regular Newton method. A combination of the regular and modified Newton methods seems warranted. A theorem giving sufficient criteria to guarantee convergence of both the regular and modified Newton methods is included. The theorem also contains error bounds for both methods. Tests of these concepts on the Ward and Hale six-bus system are included.