The conventional Newton's method has been considered inadequate to obtain the maximum loading point of power systems due to the Jacobian matrix singularity. Continuation methods are efficient tools for solving this kind of problem, and different parameterizations are used to avoid the matrix singularity. This paper presents a new geometric parameterization scheme that allows the complete tracing of the PV curves without ill-conditioning problems. The proposed technique associates the robustness to the simplicity and easy understanding. The Jacobian matrix singularity is overcome by the addition of a line equation, which passes through a point in the plane determined by the real power losses and loading factor variables, two parameters with clear physical meaning. The application of this new technique to the IEEE systems shows that the characteristics of the conventional Newton's method are improved.
Continuation Methods; Voltage Collapse; Load Flow; Multiple Solutions; Maximum Loading Point
