Newton Power Flow Methods for Unbalanced Three-Phase Distribution Networks

Two mismatch functions (power or current) and three coordinates (polar, Cartesian andcomplex form) result in six versions of the Newton–Raphson method for the solution of powerflow problems. In this paper, five new versions of the Newton power flow method developed forsingle-phase problems in our previous paper are extended to three-phase power flow problems.Mathematical models of the load, load connection, transformer, and distributed generation (DG)are presented. A three-phase power flow formulation is described for both power and currentmismatch functions. Extended versions of the Newton power flow method are compared with thebackward-forward sweep-based algorithm. Furthermore, the convergence behavior for differentloading conditions,R/Xratios, and load models, is investigated by numerical experiments onbalanced and unbalanced distribution networks. On the basis of these experiments, we conclude thattwo versions using the current mismatch function in polar and Cartesian coordinates perform thebest for both balanced and unbalanced distribution networks.