Singularities Analysis of the Jacobian Matrix Modified in the Continuation Power Flow: Performance Evaluation

Abstract

In the literature, a study to analyze stability and voltage instability is related to the P-V curve (power versus voltage magnitude) and the maximum loading point (MLP) (point on the curve that separates the stable operation of the unstable). The maximum loading point may be consequent to a saddle node bifurcation (SNB) related to transmission capacity limit in an electrical system where the Jacobian matrix is singular, or limit induced bifurcation (LIB), related the reactive power limit of the generator, where the matrix is not singular. In this sense, it is presented in this second part of the paper the trajectory of the values of the determinants of the modified Jacobian matrices (|Jm|) of these methods. A graphical analysis is also shown for a better understanding. The methods studied are: local parameterization, global parameterization (total real power losses (Pa), angular coefficient at the plane defined by sum of the magnitudes of nodal voltage (Vk) or angles (k)) as a function of loading factor and the quadratic equation in Pa plane in function of loading factor. The results are obtained for the IEEE test systems 14 and 300 buses. A study in the MLP is performed in order to verify that the point corresponds to a saddle node bifurcation (SNB) or a limit induced bifurcation (LIB).