Load Flow Convergence in the Vicinity of a Voltage Stability Limit

Because load flow problems are expressed as sets of nonlinear simultaneous equations, they have no unique solutions. In this paper a region where a set of initial values converges to a stable load flow solution under specified conditions, is investigated theoretically when the Newton-Raphson method is applied to a set of nodal power equations expressed in either polar or rectangular coordinates. The results are tested in load flow calculations on a 28-node power system and the convergence characteristics for the two types of coordinates are compared.